design & manufacturing with modeling of multi … · design & manufacturing with modeling...

16.1

ASME Early Career Technical Journal 2009 ASME Early Career Technical Conference, ASME ECTC

October 2-3, 2009, Tuscaloosa, Alabama, USA

DESIGN & MANUFACTURING WITH MODELING OF MULTI COMPONENT – SINGLE HYDRAULIC FIXTURE WITH 10 CYLINDERS & EXPANDABLE UNIFORCE CLAMP

FOR MACHINING EARTHING TERMINAL BLOCK ON CNC - VMC 430

Chetan M. Patel R. K. College of Engineering & Technology,

Mechanical Engineering Department, Rajkot, Gujarat, India

Nirav P. Maniar V. V. P. Engineering College,

Mechanical Engineering Department, Rajkot, Gujarat, India

D. P. Vakharia

S. V. National Institute of Technology, Mechanical Engineering Department,

Surat, Gujarat, India

ABSTRACT The fixtures are generally used on conventional

machines. This paper covers unique design of a multi

component – single hydraulic fixture for CNC - VMC

430. Fixture is generally used for single job; this paper

provides locating and clamping arrangement for drilling

and tapping as large as 80 components from 10 different

strips in a single fixture set up. The component is

earthing terminal block and made up of brass. The real

time application of the research reflects from the fact that

a real industrial component is taken for fixture designing.

The paper uses newer and really innovative design

of present day manufacturing industries for clamping,

which is expandable uniforce clamp with hydraulic

clamping. Time estimation proves the mass production

feature of fixture from the fact that it just takes 7 second

to clamp and 5 second to unclamp the strips. By

operating a single lever, all components are clamped and

unclamped at the same time. The salient feature of the

paper is the design of fixture to accommodate 5 various

types of strips of same shape but of different size.

While designing this paper, a good number of

literature and titles written on the subject by renowned

authors are referred. The paper includes finished part

drawing, fixture drawing, 3D assembled view of fixture

using Pro/Engineer Wildfire 4.0. Scope of additional

fixture for performing operations on another face of the

components is also included. The present volume of the

paper also couples the research work and manufacturing.

The highlight of the paper is that a fixture is not only

designed but manufactured also. The photographs of the

fixture and uniforce clamp are also included.

Keywords: multi component, single hydraulic fixture, 10

cylinders, expandable uniforce clamp, earthing terminal

block, CNC (Computerized Numerical Control), VMC

(Vertical machining centre)

INTRODUCTION The design of machining fixtures is a highly

complex process that relies on designer experience and

his/her implicit knowledge to achieve a good design [1].

When considering the methodologies developed for the

design of fixtures, it can be stated that in general they are

rational and propose a series of steps to follow.

From the literature review [2-4] and from the

interview with designers of machining fixtures, it can be

concluded that basic functional requirements that any

fixture solution must satisfy are related to: centring,

locating, orientating, clamping, and supporting. A

methodology based on this function concept and aiming

to formalize such design process is proposed in this paper

by taking a real industrial component for fixture

designing. The fixture designing and manufacturing is

considered as complex process that demands the

knowledge of different areas, such as geometry,

tolerances, dimensions, procedures and manufacturing

processes. Due to the complexity of the fixture design

process, the fixture design cannot be considered as an

independent process with respect to the manufacturing

process. In this sense, the information of the

manufacturing process is directly present in the fixture

design process. In a similar way, the resources involved

in the manufacturing process have a narrow relationship

ASME 2009 Early Career Technical Journal, Vol. 8 XXX 118

16.2

with the fixture resources, in terms of machine tools and

commercial elements of fixture [5].

While designing this work, careful consideration is

given to manufacturing and machining aspects; hydraulic

fixture for machining 80 components in single set up is

designed and manufactured also. Considering

commercial elements of fixture, innovative design of

expandable uniforce clamps are used to hold 10 strips.

Various areas related to design of fixture are already

been very well described by various renowned authors,

this paper integrates all these research works and

transforms the theoretical knowledge of fixture design to

practical application by designing a fixture for a real

industrial component – earthing terminal block.

STATEMENT OF PROBLEM “Design & manufacturing of fixture for machining

earthing terminal block on CNC - VMC 430. The

operations to be performed are drilling and tapping. The

fixture should be able to accommodate components of

different size.”

DESIGN OF FIXTURE – LOCATION AND CLAMPING CONSIDERATIONS In machining, work holding is a key aspect, and

fixtures are the elements responsible to satisfy this

general goal. Usually, a fixture solution is made of one or

several physical elements, as a whole the designed fixture

solution must satisfy the entire Functional Requirements

and the associated Constraints. Centering, locating,

orientating, clamping, and supporting, can be considered

the functional requirements of fixtures [1].

In terms of constraints, there are many factors to be

considered, mainly dealing with: shape and dimensions

of the part to be machined, tolerances, sequence of

operations, machining strategies, cutting forces, number

of set-ups, set-up times, volume of material to be

removed, batch size, production rate, machine

morphology, machine capacity, cost, etc. At the end, the

solution can be characterized by its: simplicity, rigidity,

accuracy, reliability, and economy.

CNC - VMC 430 is computerized numerical control

vertical machining centre having stroke length of 400

mm in x - direction, 300 mm in y – direction and 300

mm in z – direction.

The raw material is earthing terminal block [Figure

1] in the form of 10 different strips; total 80 finished

components of different size from these 10 strips can be

machined with the use of designed fixture [Figure 2-4];

subsequently finished components are cut from these

strips. The fixture uses 6 locators as rest blocks and dowel

pin as stopper to locate 10 strips.

The paper uses newer and really innovative design

of present day manufacturing industries for clamping,

which is expandable uniforce clamp with hydraulic

clamping [Figure 5-10]. The specially designed steel

wedge spreads the clamping force uniformly on both

sides of the aluminium channel. The clamping is

accomplished by hydraulic pulling of bottom cylindrical

part of clamp which expands upper part of clamp and

thus tightly presses the strip against rest block [Figure

6,8,9]. The compact, economical uniforce clamp enables

to fixture more parts on the machine table. The

advantages of uniforce clamp are- increases production,

minimizes tool changes, holds two parts with equilateral

clamping action, ideal for clamping flat or round

workpieces and reduces wasted space.

A mechanical link is used to accommodate two

clamps [Figure 5,11]. Each clamp presses two strips on

opposite sides [Figure 8,9] and 4 clamps are used to hold

two strips. Thus fixture uses 20 clamps to hold 10 strips.

All clamps are connected by single hydraulic pipe line.

Enough care is taken that clamps must not loosen by

vibration caused by interrupted cutting of the cutter.

Roemheld type manifold mounting hydraulic

cylinders are used, with one cylinder to operate two

clamps and thus 10 cylinders are used for 20 clamps. By

operating a single lever, all components are clamped and

unclamped at the same time.

The cylinder type used in the designed fixture can be

categorized as solid piston threaded body cylinder, single

acting (spring cylinder), and push type [Figure 13,14].

The cylinder is most simple in construction and very easy

for maintenance. The piston force can be directly used for

clamping and can be increased by using clamping strap

leverage.

Figure 1. Finished component drawing


16.3

Figure 2. 3D view of fixture assembly

Figure 3. 2D drawing of fixture assembly

Figure 4. 3D view of fixture showing links and

clamps

Unexploded

Exploded

Figure 5. 3D view of expandable uniforce clamp

Figure 6. 2D view showing Uniforce clamp with

expanding action

Figure 7. Dimensional notations of Uniforce clamp


16.4

(b)

Figure 8. Uniforce clamp clearance

Table 1. Dimensions of Uniforce clamp

Notation Dimension

A 18.6 mm

B 19.0 mm

B1 19.05 mm

C 23.8 mm

D* 16.1 mm

E 9.5 mm

F* 19.0 mm

Thread size M6

Maximum spread 20.3 mm

Torque 14.30 N.m

Max. holding force 6675 N

Key size 5

D* - A milled slot wider than D dimension will insure

clamp remains in line with workpiece. Clamp sides

should not come in contact with slot walls during

expansion.

F* - The distance needed between workpieces for clamp

clearance. Drill and tap mounting hole on the center of F

dimension.

Figure 9. 3D view of Uniforce clamp with clamping

action

Figure 10. Photograph of Uniforce clamp

Figure 11. Photograph of fixture showing links

Figure 12. Photograph of assembled fixture

Figure 13. Threaded Body Cylinder


16.5

Table 2. Dimensions of Cylinder

Notation Dimension

Force 3 kN

ØBORE 16 mm

D 21.8 mm

d 9.52 mm

D1 30 mm

E 9 mm

F M24 x 2 mm

G 1/8˝

H 12 mm

J 7 mm

K M6

SW 8

STROKE 15 mm

L 78 mm

L1 58 mm

Min. Spring Force 79.8 N

OIL VOL 3 cc

Weight 0.25 kg

Figure 14. Photograph of threaded body cylinder

CONCLUSION In the recent past there has been a significant

increase in the use of hydraulics in our industries.

Application of hydraulic systems till now was limited to

machine tools, material handling devices, transport &

other mobile equipment, in aviations systems, etc. but

very few applications and research work is carried out on

hydraulic fixture. The present volume of this paper

includes the unique aspect of designing and

manufacturing a hydraulic fixture for machining earthing

terminal block on CNC – VMC 430.

An integrated approach of manufacturing to the

design process of hydraulic fixture has been adopted in

this work. This approach is of crucial importance in real

manufacturing environment. While designing this paper,

a good number of literature and titles written on the

subject by renowned authors are referred. The application

of hydraulic for fixture is dealt in concise and self

contained with maximum possible pictorial illustration

for easy understanding and clear conception. Time

estimation proves the mass production feature of fixture

from the fact that it just takes 7 second to clamp and 5

second to unclamp the strips. By operating a single lever,

all components are clamped and unclamped at the same

time. The salient feature of the paper is the design of

fixture to accommodate 5 various types of strips of same

shape but of different size. The same fixture can be used

for all various strips with just a change of rest block; the

clamps being the same. The same methodology of

location and clamping are used for all 5 strips.

Traditionally, the component under consideration

was machined on drilling and tapping machine using

drill template, one component at a time. The entire

machining sequence was manual and accuracy of

operations was completely dependent on experience of

operator. Against one component at a time in traditional

manufacturing environment, now 80 components can be

machined with drilling and tapping operations in a single

set up using designed fixture.

Use of CNC - VMC 430 assures close dimensional

accuracy. The rejection rate is reduced to less than 1 % in

a new set up in comparison to 15 % in an old traditional

set up and productivity is increased by 25 %. Threaded

body cylinder requires an oil volume of 3 cc and hence

total volume required is 30 cc for 10 cylinders. The

hydraulic power unit provides a flow rate of 6000 cc/min

and hence it takes only 0.33 sec to fill 10 cylinders for

clamping and unclamping. However, 7 sec for clamping

and 5 sec for unclamping are claimed to be on higher side

considering pipe friction, solid friction, pivot friction and

inertia. With less than 1 % rejection rate and 25 %

increase in productivity, cost to build and maintain this

design can be recovered and break even point can be

achieved in less than a year.


16.6

FUTURE SCOPE

This paper covers the first set up of fixture; second

set up of fixture will perform drilling and tapping

operations on another face of the components. This

second set up is also hydraulic in nature with 20 cylinders

to machine 80 components in a single set up.

ACKNOWLEDGEMENT

The authors wish to thank to Mr. Sudhirbhai Thakar

and Mr. Pradipbhai Thanki. This work was supported by

Trend Incorporation, Rajkot, Gujarat, India.

REFERENCES [1] Hunter R., Rios J., Perez J. M., and Vizan A., 2006,

“A functional approach for the formalization of the

fixture design process,” International Journal of Machine

Tools and Manufacture, 46(6), pp. 683-697.

[2] Boyes W., 2000, Handbook of jig and fixture design,

Society of manufacturing Engineers.

[3] Nee A. Y. C., Whybrew K., Senthil Kumar A.,1995,

Advanced Fixture Design for FMS, Springer, London.

[4] Rong Y., Zhu Y., 1999, Computer Aided Fixture

Design, Marcel Dekker Inc., New York.

[5] Hunter R., Rios J., Perez J. M., and Vizan A., 2005,

“Knowledge model as an integral way to reuse the

knowledge for fixture design process,” Journal of

Materials Processing Technology, 164-165, pp. 1510-

1518.

[6] www.miteebite.com

[7] www.hypowerclamps.com


http://www.sciencedirect.com/science/journal/08906955


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http://www.miteebite.com/

17.1



DESIGN OF LABORATORY SCALE AXIAL FLOW TURBINE

Asnaf Qadar Pakistan Institute of Engineering and Applied

Sciences, PIEAS P.O Nilore, Islamabad, Pakistan

ABSTRACT Due to wide areas of application of the gas turbine, high efficiency and high speed gas turbine design is an important area of research to the designers. More than one design parameters are to be addressed simultaneously for an efficient design under the given conditions.

This paper is the output of the project to design an axial flow gas turbine for laboratory use. The work in the paper include optimization of all parameters which are imperative for turbine design and ultimately to draw the drawings of turbine stator and rotor blades. In the design calculations, for a 50% reaction turbine, the design is optimized for an inlet temperature of 900 K, rotational speed of 15000 rpm, and pressure ratio of 2. Blade loading coefficient ' ' of 3.02 and flow coefficient ' ' of 0.7 are selected for the design calculations as a result of optimization. The calculations are then carried out for constant root radius so that the same size mold can be used to manufacture rotor disks. The inlet and outlet blade angles are calculated to be β2=α3=20˚ and β3=α2=60.84˚ respectively. All these values determine a turbine which has the design parameters within the design range. Blade profiles calculations for stator and rotor blades are carried out. Two and three dimensional drawings of axial flow turbine have been generated using Pro-E software.

1 INTRODUCTION Gas turbines are used in diversified services from jet engines and simple mechanical drives (on land, sea and air) to sophisticated gas lasers and supersonic wind tunnels. The growth of the gas turbine in recent years has been brought about most significantly by metallurgical advances to employ high temperatures in the combustor and turbine components, the cumulative background of aerodynamic and thermodynamic knowledge, and the utilization of computer technology in the design and simulation of turbine blade[4].

1.1 RANGE OF DESIGN PARAMETERS AND TURBINE SIZING

Figure 1 shows the result of plotting nozzle outlet angle α2 and stage outlet swirl angle α3 temperature drop coefficient versus flow coefficient for a 50% reaction gas turbine [2].

Figure 1 50% Reaction Turbine

The ranges of parameters to be used in the designing are given below in Table 1:


17.2

Table 1 Range of different parameters for designing of axial flow turbine [2] Parameter Value range

Blade Loading Coefficient ' '

3-5

Swirl Angle 3' ' 0°-20°

Flow Coefficient ' ' 0.8-1 Degree of Reaction ' ' 50% Nozzle Exit Angle 2' ' >60°

Height to chord ratio hc

3-4

Space to blade width ratio 0.25-0.5 Lift Coefficient LC 0.9-1.2

Number of blades ' 'n 11-110

opening to pitch ratio os

0-1(depend on Mach number)

Surface curvature

downstream of throat se

0.25-0.625

Leading edge radius 0.05s-0.1s Trailing edge thickness ' 'tes 0.015c-0.05c

Stagger angle ' ' In range of 30°, 45°, 60°

Hub to tip ratios r

t

rr

0.5-0.75

Angle of divergence 25°

2 INTRODUCTION TO AXIAL FLOW GAS TURBINE

Theoretical cycle on which gas turbine power plants work is the Brayton cycle as shown in Figure 2.

Figure 2 Reversible and Irreversible Brayton cycles on Ts diagram There are three state points within a turbine that are important when analyzing the flow. They are located at the nozzle inlet, the rotor entrance, and at the rotor exit as shown in Figure 3.

Figure 3 Axial flow turbine annulus

The subscript 1 and 01 with T and p will represent static and stagnation temperatures and pressures respectively for any state of fluid through the turbine.

2.1 VELOCITY DIAGRAMS

Figure 4 Combined velocity diagram

From combined velocity diagram of Figure 4 for gas turbine, work output per unit mass flow rate is

2 3( )w wW C C u (2.1) from the steady flow energy equation, For a perfect gas Δh= p osC T and this relation is usually sufficiently accurate for real gases under conditions encountered in gas turbines if a mean Cp over the relevant range of temperature is used.

p osW C T (2.2)

The stagnation pressure ratio of the stage pOl/pO3 can be found from [2]


17.3

1

0 0101

03

11s sT T pp

(2.3)

3 TEMPERATURE DROP COEFFICIENT (Ψ) It expresses the work capacity of a stage, and is the ratio of the stage work output to the half of the square of the blade speed is called the Blade Loading Coefficient or Temperature drop coefficient ‘ ’ [2].

2

2 p sC TU

(2.4)

3.1 DEGREE OF REACTION (Λ)

Degree of reaction is defined as the ratio of static enthalpy drop in rotor to the static enthalpy drop in the whole stage [2]. It is given by

2 3

1 3

T TT T

(2.5)

Where T1, T2 and T3 are the static temperatures at the three sections of turbine from.

3.2 FLOW COEFFICIENT (Φ)

Flow coefficient is the ratio between the axial velocity of fluid and the blade velocity U [2].

CaU

(2.6)

For a reaction turbine in which axial velocity is kept constant and stage is repetitive Ca2=Ca3=Ca and C3=C1, there is still an infinite choice facing the designer (flow coefficient, blade loading coefficient etc). The following equality between the gas and blade angles is obtained for a 50% reaction turbine, which is used in the designing

2 3 3 2, (2.7) and the velocity diagram becomes symmetrical.

3.3 LIMITING FACTORS IN TURBINE DESIGN

Centrifugal stresses in the blades are proportional to the square of the rotational speed N and the annulus area. Gas bending stresses are inversely proportional to the number of blades and blade section moduli, while directly proportional to the blade height and specific work output. The number of blades cannot be increased beyond a point set by blade fixing considerations.

The blade height might be reduced by reducing the annulus area (with the added benefit of reducing the centrifugal blade stresses) but, for a given mass flow, only increasing the axial velocity. An aerodynamic limit on Ca will be set by the need to keep it below the levels which cause high friction losses in the blading and jet pipe respectively. Optimizing the design, so that it just falls within the limits set by all these conflicting mechanical and aerodynamic requirements, will lead to an efficient turbine of minimum weight. If it proves to be impossible to meet one or more of the limiting conditions, the required work output must be split between two stages. The second design attempt is based on the assumption that the efficiency is likely to be a maximum the wok is divided equally between the stages to get a 50% reaction turbine of repetitive stage and ultimately to get a of turbine proper hub to tip ratio and angle of divergence. The velocity triangles, upon which the rotor blade section depends, are partially determined by the desire to work with an average degree of reaction of 50 percent to obtain low blade loss coefficients and zero swirl for minimum loss in the jet pipe.

4 OPTIMIZATION OF PARAMETERS Turbine designing parameters are to be kept within the range to obtain an optimum design. All these parameters are strongly dependent upon each other. Variation in blade heights, hub to tip ratios and overall turbine sizing all varies with the basic conditions like rotational speed, pressure ratio and mass flow rate and the important parameters mentioned above. These variations and their effects on the design of gas turbine also need to be addressed. Interdependencies and selection of main parameters for designing is shown below.

4.1 VARIATION OF TEMPERATURE DROP COEFFICIENT WITH FLOW COEFFICIENT AT VARIOUS SWIRL ANGLES

Figure 5 Variation of temperature drop coefficient against Flow coefficient at various swirl angles

1.5

2

2.5

3

3.5

4

4.5

0.5 0.6 0.7 0.8 0.9 1Temperature drop coefficient

Flow coefficent

Swirl angle=0 degreesSwirl angle=5 degreesSwirl angle=10 degreesSwirl angle=15 degreesSwirl angle=20 degreesSwirl angle=25 degrees


17.4

From trends of Figure 5, a value of 0.7 for flow coefficient and 20° swirl angle yields blade loading coefficient of 3.02. A value of flow coefficient greater than 0.7 will yield higher value of blade loading coefficient (range is 3-5) but rotor blade angle at exit β3 will be decreased to a value less than 60° which should be kept above 60° as explained in the Figure 6.

4.2 VARIATION OF ROTOR EXIT ANGLE AGAINST FLOW COEFFICIENT AT VARIOUS SWIRL ANGLES

Figure 6 Rotor exit angle against Flow coefficient at various swirl angles

As shown in Figure 6, rotor exit angle can be selected against a flow coefficient and swirl angle. A suitable value of rotor exit angle of 60.84° is given by a swirl angle of 20° and flow coefficient of 0.7.

4.3 HUB TO TIP RATIO AGAINST REVOLUTION PER MINUTE (RPM)

The pressure ratio is 2 and the temperature at the turbine inlet is 900K which are to be used for the final design calculations. High rpm and mass flow rate will give lower hub to tip ratios. The value of hub to tip ratios comes out to be in the range of 0.55 to 0.67 from inlet to outlet sections which are reasonable. However at low pressure ratios, lower rotational speeds (13000 rpm) can be suggested and the hub to tip ratio value would be still in range but the rotational speed is also fixed by the compressor design as shown in Figure 7.

Figure 7 Hub to tip ratio against Revolution per minute (RPM)

4.4 ROTOR HEIGHT AGAINST REVOLUTION PER MINUTE (RPM)

Figure 8 shows the rotor blade height variation with the rotational speed for different values of mass flow rate for constant mean radius. The flow coefficient is 0.7, pressure ratio is 4, swirl angle is 20° and the turbine inlet temperature is 950K.

Figure 8 Rotor height against Revolution per minute (RPM)

Rotor height increases with rotational speed and mass flow rate. Similar trends of rotor heights are observed for constant root radius based calculations however blade heights will be more compared to constant root radius design. The rotor blade mean heights comes out to be 8.93 cm and 11.08 cm in first and second stages of a constant root radius based design for pressure ratio of 2 and inlet temperature of 900K while rest of the parameters are same.

35

40

45

50

55

60

65

70

0.5 0.6 0.7 0.8 0.9 1

Rotor exit an

gle(β

3)

Flow Coefficient

Swile angle=0 degrees

Swirl angle=5 degrees


Swil angle=15 degrees




0.5

0.6

0.7

0.8

0.9

1

1000 4000 7000 1000013000

Hub to tip ratio

RPM

m= 2 kg/sec

m= 4 kg/sec

m= 6 kg/sec

m= 8 kg/sec

m= 10 kg/sec

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 5000 10000 15000

Rotor height(cm

)

RPM

m= 2kg/sec

m=4 kg/sec

m= 6kg/sec

m= 8 kg/sec

m= 10kg/sec


17.5

4.5 HUB TO TIP RATIO AGAINST REVOLUTION PER MINUTE (RPM) AT DIFFERENT PRESSURE RATIOS

Figure 9 indicates the variation of hub to tip ratios with the rotational speed at different values of pressure ratios. Flow coefficient is 0.7, mass flow rate is 10 kg/sec, swirl angle is 20° and the turbine inlet temperature is 900K and the root radius is kept constant. It is concluded that low pressure ratios yield low hub to tip ratios compared to high pressure ratios for the same rotational speeds. The value of hub to tip ratio for stage 1 is 0.61.

Figure 9 Hub to tip ratio against Revolution per minute (RPM) at different pressure ratios

4.6 ROTOR HEIGHT AGAINST REVOLUTION PER MINUTE (RPM) AT DIFFERENT PRESSURE RATIOS

Figure 10 is for flow coefficient of 0.7, pressure ratio is 2, swirl angle is 20° and the turbine inlet temperature is 900K and mass flow rate is 10 kg/sec when the root radius is kept constant.

Figure 10 Rotor height against Revolution per minute (RPM) at different pressure ratios

High pressure ratios give low blade heights at same rotational speed. For a pressure ratio of 2 the rotor blade mean height of the second stage is 11.08 as shown in Figure 10. Similar trend is observed for first stage.

5 DESIGN CALCULATIONS

Two dimensional flow is assumed the blade angle remains constant throughout its height for simplicity. The degree of reaction is 50% and a repetition stage is assumed (C1=C3 and α1=α3 ), as for such design, the blade angles at inlet and exit remain the same in successive stages.

5.1 CALCULATIONS BASED ON ROOT RADIUS

The input data for the turbine design is given in the Table 2. Table 2 Data for designing of axial flow turbine

Turbine inlet temperature, T01

900K

Atmospheric temperature, T03

288K

Pressure ratio 2 Mass flow rate, m 10 kg/sec Degree of reaction, Λ 0.5

Rotational speed, N 15000rpm

Flow coefficient , Φ 0.7

Swirl angle, α3 20˚

For gas turbine cycle, the temperature at the exit of the turbine is determined by using isentropic relation between the inlet and exit of turbine, for the overall pressure ratio of 2 and inlet temperature being 900K.Since expansion process is isentropiche change in kinetic energy of the working fluid between the inlet and outlet of each turbine is negligible.The working fluid has the same composition through the turbine and is perfect gas with constant specific heats. Mass flow rate is constant though the turbine.

1

03

0101

03

T p

T p

(5.1)

0.6

0.7

0.8

0.9

1

1000 4000 7000 1000013000

Hub to tip ratio

RPM

Pressure ratio=2

Pressure ratio=4

Pressure ratio=6

0

2

4

6

8

10

1000 4000 7000 10000 13000

Rotor height(cm

)

RPM

Pressure ratio=2

Pressure ratio=4

Pressure ratio=6


17.6

03 756.91T K

this is the total temperature of gases at the exit of the

turbine.

For 50% reaction turbine and repetition stage using

3 2

1tan tan

(5.2) Using flow coefficient of 0.7 and swirl angle of 20˚, (5.2) gives

3 60.84 0.906isen

01 03sT T T (5.3)

129.63sT K

The calculations for a single stage turbine for the given conditions yields a large angle of divergence of the casing of the gas turbine (55º), which should be or nearer to 25º and a larger hub to tip ratios (0.7-0.8). Both these values will cause the actual efficiency of the gas turbine to drop due to losses, therefore a two stage design is finally decided for an efficient gas turbine in which all the parameters are with in the range. For higher efficiency, equal temperature drop is considered in each stage [2]. Static temperature drop in each stage is thus

64.82sT K

blade loading coefficient will now be determined. =3.019

Table 3 Thermodynamic gas constants for combustion gases [2]

Cp (kj/kg.K) γ R (kj/kg.K)

1.148 1.33 0.287 Rotor velocity at mean and tip section is now determined to be

β3=60.84˚ ηisen= 0.906 Ut)rotor= 282.78 m/sec

Ut)rotor= 348.7m/sec

Gross Power= 1488 Kwatt

Compressor input power=743.67 Kwatt

Net power output=744.57 Kwatt

The results of analytical calculations for all sections of

two stage gas turbine are shown in Table 4.

Table 4 Results of calculations based on constant root radius

Section-1

Section-2 Section-3 Section-4 Section-5

Stagnation temperature, T0, (K)

900 900 835.18 835.18 770.36

Stagnation pressure, p0, (bar)

2 1.98 1.436 1.422 1.01

Axial velocity, Ca, (m/sec)

155.41 155.41 155.41 155.41 155.41

Absolute velocity, C, (m/sec)

165.36 319 165.36 319 165.36

Density, ρ, (kg/m3) 0.744 0.658 0.58 0.508 0.436

Area, A, (m2) 0.0812 0.097 0.111 0.126 0.147

Root radius, rr, (m) 0.1413 0.1413 0.1413 0.1413 0.1413

Tip radius, rt, (m) 0.214 0.226 0.235 0.245 0.258

Hub to tip ratio, rr/rt 0.66 0.62 0.6 0.57 0.54

Height, h, (m) 0.0728 0.0847 0.0939 0.104 0.1108


17.7

6 BLADE PROFILE The cascade notation for a turbine blade is shown in Figure 11. Lift coefficient is given by

22 cos (tan tan )L ex in exx

sCb

(6.1)

If the optimum lift coefficient is CL,op, then the optimum “axial solidity” defined by, (bx/s) is,

2

,

2 cos (tan tan )xex in ex

L opop

bs C

(6.2)

Figure 11 Cascade notation for turbine blade rows [4]

10 0.5

7 cos 10 46ex Mt

o ss e

(6.3)

where o = diameter of throat opening (Figure 11) s = blade pitch e= radius of curvature of blade convex surface downstream of throat, Mt= Mach number at throat

6.1 ACTUAL BLADE PROFILE For minimum loss assume a tangential lift coefficient of,

1.0LC The gas angles are

3

2

2060.82

in

ex

To obtain a reduction of area at the throat setting or stagger angle is now determined, the stagger angle is chosen to be 36˚ [4].

36

6.2 BLADE PROFILE OF ROTOR-1

Mach number at exit of blade passage is calculated to be M3=0.294. The blade profiles of stator and rotor blades of both stages are shown in Table 5 are generated in using Pro-E wildfire 2 software. One blade profile is shown in Figure 12.

Table 5 Parameters for profiles of stator and rotor blades

Blade

Blade Height

h (cm)

Chord c (cm) Axial chord bx

(cm)

BladePitch

s (cm)

e (cm)

o (cm)

e+o (cm)

tes

(cm)

d (cm)

Stator-1 7.87 2.62 2.12 3.13 12.52 1.5 14.02 0.109 0.313

Rotor-1 8.93 2.97 2.40 3.55 14.19 1.7 15.9 0.123 0.355

Stator-2 9.9 3.3 2.67 3.93 15.75 1.89 17.64 0.137 0.393

Rotor-2 11.08 3.69 2.98 4.4 17.62 2.11 19.74 0.153 0.44


17.8

Figure 12 Blade profile generated in Pro-E

After generating two dimensional profiles, three dimensional profiles are generated according to the blade heights; assembly is performed according to the calculated size and blade spacing. The blade passages of assembled blades are shown in Figure 13. Angle of divergence of turbine is calculated to be 32˚.

Figure 13 Axial blade passages through two stage turbine (Front View)

7 CONCLUSIONS To manufacture a gas turbine, it must be properly designed i.e. all the parameters like blade speed, blade angles, temperature drop coefficient, and flow coefficient are to be kept within the limits to get a required power output. It is concluded that for an inlet temperature of 900K and pressure ratio of 2, the blade heights are 8.93cm and 11.08cm in the first and second stage respectively at fixed root radius of 14.14cm for manufacturing of a constant diameter disk. Hub to tip ratio varies from 0.55 to 0.67 which are quite satisfactory. The net power output is 744 kWatt and a starting motor of 37 kWatt is required for the initial starting of the power plant.

Calculations show that temperature drop coefficient increases with flow coefficient and it also increases with swirl, however swirl cannot be increased from a certain value due to losses. The rotor exit angle decreases with flow coefficient. Hence a limiting range of these three design parameters is available. The angle of divergence of turbine is about 32⁰ which is a bit larger. The shaft length for turbine section is 15.5cm. The blade and flow angles calculated are α2=β3=60.84⁰ and α3=β2=20⁰, and the blade loading and flow coefficients are 3.02 and 0.7. All these parameters are within the acceptable range except the flow coefficient whose lower range is 0.8 but some compromise is to be there to place other values in range. Axial, tangential and radial loads on the blades and turbine shaft have been calculated which can be used in shaft design and bearing selection etc and drawings of all components have been generated using Pro-E wildfire 2.0. Further it is concluded that larger blade heights are obtained when mean radius is kept constant but low (suitable) hub to tip ratios are obtained with this design compared to the one in which root radius is kept constant. Other parameters like flow angles, flow and blade loading coefficients do not alter in both designs. Hub to tip ratios decrease with rotational speed and mass flow rate in both designs. Similarly hub to tip ratios also decreases with the pressure ratios. Hence for high pressure ratios, high speeds and mass flow rate will give a better design (with respect to hub to tip ratios and blade heights) while relatively low speeds can be suggested for low pressure ratios. The blade profile may be modified after analyzing it with the considerations of flow and stresses.

8 REFERENCES [1] Tony Giampaolo, 2006, Gas Turbine Handbook:

Principles and Practices, 3rd edition CRC Press. [2] HIH Saraavanamuttoo, GFC Rogers, H Cohen, 2001, Gas

Turbine Theory, 5th edition, Pearson Education. [3] Meherwan P.Boyce,., P.E, ,2002, Gas Turbine Engineering

Handbook, 2nd edition, GPP,Heinemann. [4] David Gordon Wilson, Theodosios Korakianitis, 1998, The

Design of High Efficiency Turbomachinery and Gas Turbines, second 2nd Edition, Pearson Education, Prentice Hall.

[5] NASA Case LEW-11815, A computer program for Preliminary Design Analysis of axial flow turbines.

[6] Ronald H. Aungier, 2006, Turbine Aerodynamics. [7] Jack Swiderski, Ottawa, Axial flow turbine development

for ultra low head hydro projects. [8] K.V. Alexander, E.P. Giddens, A.M. Fuller, A paper on

“Radial and mixed flow turbinefor low head microhydro systems”.

Stator Rotor Stator Rotor


17.9

List of symbols

C1 Absolute velocity of fluid at inlet to stator

C2 Absolute velocity of fluid at exit from stator

C3 Absolute velocity of fluid at exit from rotor

Ca Axial velocity of fluid

U Blade velocity

v2 Relative velocity of fluid at rotor inlet

v3 Relative velocity of fluid at rotor exit

α1 Angle of C1 with axial direction

α2 Angle of C2 with axial direction

β2 Angle of v2 with axial direction (blade inlet angle)

β3 Angle of v3 with axial direction (blade exit angle)

ΔTos Stagnation temperature drop per stage

p01/p03 Stagnation pressure ratio per stage

λN or YN Nozzle loss coefficient

λR Rotor loss coefficient

ηs Isentropic efficiency of stage

Λ Degree of reaction

LC Lift Coefficient n Number of blades os

Opening to pith ratio

se

Surface curvature downstream of throat

tes Trailing edge thickness Stagger angle

r

t

rr

Hub to tip ratios


18.1



MECHANICAL TRACHEOBRONCHIAL MODEL FOR HUMAN LUNG INHALATION STUDY

Mohammed Ali Department of Technology Jackson State University

Jackson, Mississippi, USA

ABSTRACT

A two-stage mechanical tracheobronchial model

(MTBM) of human lung’s tracheobronchial airways was

designed, developed, and validated with the respiratory

deposition data predicted by the International

Commission on Radiological Protection. The MTBM

assembly was based on widely used human lung’s

morphological dimensions specified in the Ewald R.

Weibel’s dichotomous lung morphometry. It could

physically simulate the surface area and the Reynolds

number of the trachea, main, lobar and segmental bronchi

of the human lung. The experimental data agreed with the

reported aerosol particle deposition measurements using

the United State Pharmacopeia approved Andersen

Cascade Impactor, which is often used for inhaled aerosol

deposition studies.

INTRODUCTION

A surrogate lung model is the one which closely approximates the flow characteristics, surface area, and aerosol deposition patterns of the human lung. The advantages of such model are enormous. (A) It serves as a basic tool for determining the performance of pulmonary medicine delivery into the lung. (B) It can be employed as a surrogate lung for in vitro studies on inhalation of workplace atmospheric pollutant dust; determination of diesel and gasoline exhaust particles regional lung deposition and toxicity. (C) It will eliminate safety issues and variability that are inherent with the use of human subjects.

According to the United States Environmental Protection Agency’s ‘Guidelines on Speciated Particulate Monitoring’ human respiratory tract is an aerodynamic classifying system for inhaled particles [1]. A sampling device can be used as a substitute for the respiratory tract as a particle collector, and it can effectively simulate the mechanisms of electromechanical deposition of the inhaled particles including inertial impaction, gravitational settling, interception, diffusion, and electrostatic force as depicted in Figure 1. Investigators in this area of study often times use Andersen Cascade Impactor (ACI), an

aerodynamic classifying system. However, the chief limitation of the ACI is that it is unable to simulate other deposition mechanisms besides inertial impaction [2]

Others have shown that a physical lung model

simulated by a multi-layer granular bead filter provides a good approximation of the deposition detected in the in

vivo experimental data [2]. Gebhart and Heyder (1985) developed the first granular bead filter to use as a surrogate for human subjects in their study of aerosol deposition [3]. The filter consisted of a 30-cm long by 15.24-cm diameter acrylic cylinder, sealed by a cone at each end. The cone and cylinder were packed with 2.5-mm glass beads, resulting in airspace of approximately 2 L. Their model had several limitations. (A) It possessed a single passageway to simulate all respiratory airways though parameters of successive branching airways differ widely. (B) It was geometrically dissimilar with in vivo anatomy, and (C) it was unable to test site-specific

Aerosol Inhalation

Electrostatic Force Inertial

Impaction

Aerosol Flow

Aerosol Flow

Gravitational Settling

Brownian Diffusion

Interception

Figure 1. Electromechanical deposition mechanisms of aerosol particles in the human

lung [5].


18.2

3

2

1

0

3

2

1

0

3

2

1

0

3

2

1

0

United States Pharmacopeia Induction Throat

Trachea ≅ MTBM Stage 1

Main and ≅ MTBM Stage 2 Lobar Bronchus

(a) Ewald R. Weibel’s symmetric and dichotomous lung morphology

(b) Mechanical Tracheobronchial Model (MTBM) Stages 1 and 2

Figure 2. Two Stage mechanical tracheobronchial model simulates trachea, main and lobar bronchial regions of the human respiratory system [5,6].

deposition for corresponding regions of the respiratory tract [4].

In order to study the regional deposition of aerosol particles, it was necessary to design a multi-stage model to simulate various regions of the lung anatomy. With this concept in mind, present work designed and developed a physical tracheobronchial model using a United States Pharmacopeia (USP) induction throat, and 2 packed beds (Stages) of glass beads in the shape of a wedding cake (Figure 2b), hereafter referred to as the Mechanical Tracheobronchial Model (MTBM). Since the MTBM was constructed to mimic flow parameters and dimensions of the lung airways, it could simulate all 5 mechanisms of deposition of inhaled aerosol particles as illustrated in Figure 1.

The objectives of the current work were to (a) design and develop 2 layers of glass-bead filters to serve as a surrogate for tracheobronchial regions of respiratory airways, (b) investigate the aerosols particle deposition generated by a commercially available aerosol generator (nebulizer), and (c) validate the deposition results with empirical lung deposition model proposed by the International Commission on Radiological Protection (ICRP) deposition model [7], and Andersen Cascade Impactor (ACI) [8].

MATERIALS AND METHODS

A mathematical analysis was required to understand the fundamental morphometry of human lung’ various regions, which established the basis for the design and construction of the MTBM. Motion of a spherical particle in a given geometry is affected by the Stokes number, Stk, particle size, Reynolds number, Re, and non-dimensional settling velocity [9-12]. It is notable that Stokes number was originated from Stokes’s law by solving the unsolvable Navier-Stokes equation based upon several assumptions [13]. One of them was that the fluid should be incompressible, which is unlikely in case of atmospheric or medicinal aerosols. Additionally, in practice, Stokes law is restricted to situations in which Reynolds number is less than 1.0 [13]. For an inhalation rate of 28.3 l/min, the Reynolds number in the tracheobronchial region is very

high (Re>>1.0). Therefore, the simulation of Stokes number in this study was not considered. Besides, air inhalation rate of a normal adult was used in the MTBM experiments, which conforms that both particle size and non-dimensional settling velocity were also simulated as well. It is well accepted fact that the Reynolds number in principle determines the nature of the flow, it can simulate the characteristics of 2 different fluid flows and the flow profiles irrespective of the actual dimensions of the aerosol flows. Therefore, various regions of the lung can be classified according to the Reynolds numbers of the air flows in the respiratory airways for a given inhalation flow rate.


18.3

Calculations, beginning from the Reynolds numbers can be used to determine the diameter and the number of glass beads for each Stage. Mathematically, the Reynolds number of a fluid flow can be determined from Equation 1.

where Re = Reynolds number, Db = packed bed diameter, vs = superficial velocity through the pipe, ρ = aerosol particle density, µ = aerosol viscosity, and ε = bed porosity.

Table 1. Summary of the design parameters of the mechanical tracheobronchial model.

Design parameter Stage 1: Trachea

Stage 2: Main and Lobar Bronchus

Flow rate through Stage, Q, l/min

28.3 28.3

Bed Porosity, ε 0.38 0.36

Mean velocity on packed bed, v

m, cm/s

383.5 234.53

Superficial velocity through Stage, v

s, cm/s

145.73 84.43

Stage diameter, D, cm 2.03 2.67

Stage Length, L, cm 18.875 18.733

Volume of the inside Stage, Vp, cm3

61.09 104.65

Total volume of beads needed, V

g, cm3

37.88 66.98

Bead diameter, dg, cm 1.37 1.10

Number of glass beads, n 28 50

Surface area of packed bed, cm2

165.88 293.33

Reynolds number of packed bed, Re

2135 1198

Reynolds number in Weibel’s model, Re

2213 1241

The other parameters of the MTBM were calculated from Equations 2 – 6. (2) Superficial velocity due to the packed bed, vs = vm ε

(3) Volumetric flow rate through the Stage, qv= (π/4)D2 vm

(4) Volume of glass beads, Vg = (π/4)D2 L(1 – ε)

(5) Number of beads, n = Vg / (π/6)dg3

(6) Total surface area of the beads = nπdg2

where vm is the average velocity of aerosol flow through the packed bed an approximation based on the range of air velocity from Weibel’s model, dg = glass bead

diameter, D = bed (Stage) diameter, and L = Stage length. Table 1 shows the design parameters of the MTBM Stages 1 and 2.

Figure 2 shows the MTBM and the corresponding simulated regions of the human lung. The dimensions of the lung airway regions were based upon widely used and adopted symmetric and dichotomous lung morphological data in Ewald R. Weibel lung model with some modifications due to the more recently published data of Horsfield et al. [6,14].

Weibel’s model portrays the common and standard understanding of human lung anatomy. It divides the human respiratory tract into 24 generations (from G0 to G23). Since inception, it has been regarded as a detailed anatomical approach to lung morphology, the model was tested and validated with experimental results. Weibel’s morphometric data provide specific length, diameter, area, and volume for each generation. For the MTBM, Stage 1 simulated the trachea, the first generation (G0) of the lung (Figure 2). Stage 2 simulated the main and lobar bronchi, the second, third, and fourth generations (G1–G3) of the lung as well. Each of these Stages was stacked one on top of the other with wire-mesh support to maintain the flow of aerosol for uniform distribution over each Stage. Each lung region was represented by a glass-bead-packed bed with a diameter that simulated the surface area of the region and the Reynolds number at an inspiratory flow rate of 28.3 l/min.

Ideally, each generation of the respiratory system should be simulated by a single bed of glass beads of relevant size and thickness. However, for expediency in constructing the physical model, three generations of bronchi was represented by Stage 2 in such a way that particle deposition should not have changed significantly. In order to obtain a Reynolds number as close as possible to that of the tracheal region (2235), this study made the surface area of packed bed in Stage 1 166 cm2. The surface area of packed bed in Stage 2 was made 293 cm2 to achieve a Reynolds number (1241) as close as possible to that of the bronchial region. The circular cylinders of the Stages 1 and 2 were made from 2.03-cm and 2.67-cm

PVC pipes, respectively (American Valve, 3/4” and 1” Fix-It Coupling PVC, Model: P232, Lowe's Companies, Inc. North Wilkesboro, NC). The sizes of the glass beads were based upon the required bed porosity in order to achieve the closest possible Reynolds numbers for a fixed inhalation flow rate (Glen Mills Inc., Clifton, NJ). The copper wire mesh supported the glass beads and maintained a uniform flow (TWP Inc., Berkeley, CA).

Figure 3 depicts the experimental setup, which consisted of several components addressed below.

1. To generate test aerosols, a nebulizer (PARI LC

Plus, Midlothian, VA) was used with sodium chloride solution (7 g/ml). The generated aerosol particles’ mass

)1( ε)(1µ3

ρvD2Re sb

−=


18.4

Figure 3. Schematic of the experimental setup indicating the placement of functional components to measure the aerosol particle counts and aerodynamic size (diameter)

distributions with and without passing through the mechanical tracheobronchial model.

Vacuum Pump

Electronic Single Particle Aerodynamic

Relaxation Time (ESPART) Analyzer

Filter

Isokinetic Sampling Probe

Isokinetic Sampling Chamber

Vacuum Pump

Filter

Mechanical Tracheobronchial Model (MTBM)

Stage 2

Stage 1

Aerosol Generator

Filtered Dry Air

Aerosol Holding Chamber United States

Pharmacopeia Induction Throat

median aerodynamic diameters (MMAD) ranged from 4.0 µm to 5.5 µm.

2. An Aerosol Holding Chamber (AHC) with

dimensions of 21 cm x 18 cm x 21 cm (LxWx H) was used to hold generated aerosols before inhalation. The aerosols were mixed with the filtered dry air to raise the volume into the required quantity for inhalation through the MTBM at the rate of 28.3 l/min.

3. The USP induction throat was used for introducing aerosols into the MTBM. It is an L shaped tubular standard stainless steel pipe with silicon rubber adapter at one end, which simulates human throat for in vitro studies. Manufacturers also specify the use of such a USP throat for introducing aerosols into the Andersen Cascade Impactor (e.g., 8 Stage Non-Viable Cascade Impactor of New Star Environmental LLC, Roswell, GA).

4. The Mechanical Tracheobronchial Model was placed between the USP throat and the aerosol isokinetic sampling chamber (ISC). The Stages 1 and 2 could be separated or connected (together or individually) with the USP throat and the ISC.

5. The Electronic Single Particle Aerodynamic Relaxation Time (ESPART) analyzer was used to measure

aerodynamic sizes and electrostatic charges in real time [15]. Its working principle was demonstrated elsewhere [16].

6. An aerosol isokinetic sampling chamber (ISC) was used to facilitate the characterization of aerosols isokinetically (Figure 3). The suction mouth of the ESPART analyzer was placed at the center of the chamber and always pointed in the direction opposite of the aerosol flow.

External filtered dry air (18.3 l/min) and generated aerosol (10 l/min) were delivered to the AHC to simulate a light physical activity inhalation flow rate of 28.3 l/min through the MTBM. The flow rate was measured using an

Extech Heavy Duty Hot Wire Thermo-Anemometer (Extech Instruments, Waltham, Massachusetts, USA). The constant inhalation rate of 28.3 l/min served two purposes. (1) The manufacturer-specified flow rate for a Mark II Andersen Cascade Impactor (ACI) is 28.3 l/min, which enabled MTBM comparability with the ACI. (2) The


18.5

vacuum pump and the ESPART could have drawn 27.3 l/min and 1 l/min, respectively. The environmental conditions such as lab temperature (20oC) and humidity

(51.2%) were recorded using Testo625 (Testo GmbH & Co., Lenzkirch, Germany) thermo-anemometer.

In order to determine the aerosol particle deposition characteristics in the MTBM and to compare the results with the deposition data for the ACI and ICRP models, the investigation was divided into 3 experimental treatments of the aerosol:

(1) not passed through the MTBM (USP throat was directly connected to ISC)

(2) passed through the MTBM Stage 1(USP throat was connected to the MTBM Stage 1)

(3) passed through the MTBM Stages 1 and 2 (the USP throat was connected to the MTBM Stages 1 and 2).

Before starting each run of the experiment, the ISC and AHC were cleaned thoroughly. The MTBM was washed with distilled water. The generation and sampling of the aerosol particles started simultaneously. Each run continued for 5 minutes and was then stopped. The AHC, USP throat, MTBM, and the ISC were cleaned again. To ensure our assumption of equal particle losses each time in the USP induction throat, the throat was in place for the scenarios described above. The procedure was repeated for 10 consecutive runs for each treatment. The aerodynamic size distribution was measured in each case.

Raw data was acquired through LabVIEW (National Instruments, Austin, TX, USA) and mined by Aerosol Particle Data Analyzer software (developed at the Aerosol Drug Delivery Research Lab of the University of Arkansas at Little Rock, Little Rock, AR, USA). It is necessary to mention that this study focused on particles in the aerodynamic size range of 0.5 µm - 10 µm with a geometric standard deviation greater than 1.5 purposely, because, medicinal or workplace atmospheric aerosols known at present or anticipated to be of primary practical importance for predicting lung deposition have aerodynamic diameters in the range of 0.5 µm - 10 µm [17].

RESULTS

The present study assumed that the both Stages of the MTBM would operate on one basic principle, which is, a particle whose inertia exceeds a certain value (cutoff size) would be unable to follow the streamlines and will impact upon the packed bed. In addition, particles would deposit on the bead surfaces due to diffusion, gravitational settling, interception, and electrostatic force. Thus, each Stage of the MTBM would separate aerosol particles into two size ranges; particles larger than the cutoff size will be removed from the aerosol stream, and particles smaller than that size will remain airborne and pass through the

Stage. As a result, each Stage of the MTBM will be characterized by a cutoff diameter.

The ESPART analyzer operates on the principle of Laser Doppler Velocimetry [18]. In this study it acquired the counts and aerodynamic diameters of the particles contained in the inhaled aerosols before and after passing through the MTBM stages. Figure 4 shows the cutoff curves, or collection-efficiency curves of the MTBM Stages 1 and 2. Cutoff or collection efficiency curves are characterized by a single number Stk50, the Stokes number that gives 50% collection efficiency [13].

Figure 5. Illustration shows the comparison of the deposition fractions of the mechanical tracheobronchial model (MTBM) and the International Commission on Radiological

Protection tracheobronchial (ICRP TB) model for the respirable range aerosol particles.

0.00

0.02

0.04

0.06

0.08

0.10

0.1 1 10

ICRP TB Model

GBTB Model

0.00

0.02

0.04

0.06

0.08

0.10

0.1 1 10

ICRP TB Model

GBTB ModelMTBM

0.00

0.02

0.04

0.06

0.08

0.10

0.1 1 10

ICRP TB Model

GBTB Model

0.00

0.02

0.04

0.06

0.08

0.10

0.1 1 10

ICRP TB Model

GBTB ModelMTBM

Dep

osi

tio

n F

ract

ion

Aerodynamic Diameter, µm

Figure 4. Aerosol-particle-collection-efficiency curves (lognormal) comparison among the

mechanical tracheobronchial model (MTBM) Stages 1 and 2, and without the MTBM.

0

10

20

30

40

50

60

70

80

90

100

0.1 1 10

Without MTBM

MTBM Stage 1

MTBM Stage 2

32

Stage 2 cutoff point 2.9 µm


Cutoff point

3.5 µm

0

10

20

30

40

50

60

70

80

90

100

0.1 1 10

Without MTBM

MTBM Stage 1

MTBM Stage 2

Without MTBM

MTBM Stage 1

MTBM Stage 2

32



Cutoff point

3.5 µm

Par

ticl

e C

oll

ecti

on

Eff

icie

ncy

, %

Aerodynamic Diameter, µm


18.6

(a) Mechanical Tracheobronchial Model (MTBM)

(b) Human Lung’s Branching Airways

(c) Andersen Cascade Impactor (ACI)

Figure 6. Illustration shows the comparison of the cut-off diameters (collection efficiencies) of MTBM and ACI stages with human lung’s branching airways.

MTBM Stage 1 with cut-off

diameter 3.25 µm

MTBM Stage 2 with

cut-off diameter 2.9 µm

ACI Stage 3 with cut-off diameter

3.3-4.7 µm

ACI Stage 4 with cut-off diameter

3.3-4.7 µm

The deposition fraction will be defined as the ratio of the number of particles removed from the aerosol (i.e., deposited) while traveling through the MTBM to the number of particles originally entering it. Figure 5 shows a comparison of the respiratory deposition fraction in the MTBM airways to the respiratory deposition fraction in the ICRP model for the respirable range aerosol particles. Although the basic ICRP deposition curve was developed for particles in the size range of 0.001 µm – 100 µm, this study compared MTBM with the ICRP’s respirable size range (0.5 µm - 10 µm) portion only.

Figure 6 shows the comparison of the cut-off diameters (collection efficiencies) of MTBM and ACI stages with human lung’s branching airways. The MTBM Stage 1 has a cut-off diameter of 3.25 µm, which was designed to correspond to the trachea in the human lung. Similarly, the MTBM Stage 2 has a cut-off diameter of 2.9 µm corresponds main and lobar bronchi. Whereas, according to the ACI specifications provided by the manufacturer its stage 3 corresponds aerosol particle filtering characteristics of lung’s trachea and main bronchus. In the same fashion ACI Stage 4 corresponds lobar and segmental bronchi [NSE, 2004].

DISCUSSION

This study has reported physical simulations (2-Stage MTBM) of the tracheobronchial airways of the human lung. The model was designed and developed to simulate the human respiratory tract Generation 0 (trachea, G0) and Generations 1, 2, and 3 (main and lobar bronchi, G1-G3), respectively. The first Stage simulated Reynolds number

was 2135, which was in close approximation with the Reynolds number in the trachea of 2213 (ideal case) for an inhalation flow rate of 28.3 l/m. The second Stage simulated Reynolds number was 1198, which was also in close approximation with the average Reynolds number of 1241 for the first, second, and third bronchi for the given inhalation flow rate. However, for convenience in constructing the physical model and to achieve the closest possible flow parameters, the surface areas of the packed bead Stages were 5 and 17 times the in vivo surface areas, respectively. In spite of these differences in surface areas

between the actual tracheobronchial morphology and the MTBM, simulated depositions are in accordance with previously reported empirical lung deposition by the ICRP (ICRP66 1994). The collection efficiency or cut-off points of the MTBM Stages are in the range (Figure 6) that has been specified by the manufacturer of the ACI (NSE 2004).

Human lung’s various regional deposition model developed by the ICRP takes into account particle parameters such as aerodynamic size, shape, and density, as well as anatomical parameters such as airway dimensions and flow rates. In addition to all the considerations taken by ICRP, the present MTBM took into account other environmental parameters such as, aerosol’s temperature and humidity was monitored and controlled in the AHC. Although, the model predicted deposition for each aerodynamic size was about 5% lower, overall, results were fairly consistent with the ICRP depositions for the particle size range of 0.5 µm - 10 µm (Figure 5). The difference could be due to different


18.7

assumptions and methods used in the derivation of the formulae such as, ICRP Model is an empirical lung deposition model which considered aerodynamic and thermodynamic deposition formulas to derive respiratory deposition of radionuclide particles, whereas the MTBM is a physical model simulating integrated electromechanical deposition mechanisms as stated in Figure 1. The present MTBM can be employed as an experimental tool for in-vitro studies of pulmonary medicinal aerosol drug delivery to the lung.

Compared to the commonly used ACI aerodynamic classifying system, which provides a quick estimation for aerosol depositions, the MTBM described in this paper offers more detailed description of aerodynamic size distribution of the deposited particles (Figures 4, and 5). However, the ACI Stages are made of electrically conductive materials but the MTBM Stages are not. This is a limitation that can be overcome in the production of future MTBMs by constructing Stage cylinders with conductive materials.

CONCLUSIONS

A two-Stage mechanical tracheobronchial model of the upper airways of the human lung has been designed, developed, and realized. It is comparable to the Mark II ACI. In addition, the MTBM simulated by packed bed media is simple, inexpensive, and a prospective model for the in vitro investigation of atmospheric pollutant particles or pulmonary aerosolized medicine delivery to the lung. The respirable size range aerosol particle deposition in the MTBM is comparable with the mathematical and theoretical results reported in the ICRP model. It is believed that present study is an important step in finding an alternative to the ACI, which is unable to simulate the interactive behaviors of aerosol particles’ electromechanical deposition mechanisms in pulmonary airways.

REFERENCES [1] US Environmental Protection Agency, 1998, “Guidelines on speciated particulate monitoring,” Draft 3, USEPA, Research Triangle Park, NC, pp. 3-1, Available from: http://www.epa.gov. [2] Altshuler, B., Yarmus, L, Palmes, E. D., and N Nelson, 1957, “Aerosol Deposition in the Human Respiratory Tract I: Experimental Procedures and Total Deposition,” Am. Med. Assoc. Arch. Ind. Health, 15, pp. 293-303. [3] Gebhart, J., and Heyder, J., 1985, “Removal of Aerosol Particles from Stationary Air within Porous Media,” J. Aerosol Sci., 16(2), pp. 175-187. [4] Gao, S., 1994, “Development of Two-component Packed Granular Filters with Triboelectric Enhancement,” Ph.D. thesis, University of Arkansas at Little Rock, Little

Rock, AR. [5] Ali, M., 2008, “Physical and Computational Models of Human Lung for Optimizing Respiratory Drug Delivery,” Ph.D. thesis, University of Arkansas at Little Rock, AR. [6] Weibel, E. R., 1963. Morphometry of the Human Lung, Springer-Verlag, Berlin, p. 340. [7] International Commission on Radiological Protection, 1994, “Human Respiratory Tract Model for Radiological Protection,” ICRP Publication 66, Elsevier Sci. Inc., New York, NY. [8] New Star Environmental LLC., 2004, “Instruction Manual for 8 Stage Non-Viable Cascade Impactor,” Roswell, GA, p. 7. [9] Chan, T. L., and Schreck, R. M., 1980, “Effect of the Laryngeal Jet on Particle Deposition in the Human Trachea and Upper Bronchial Airways,” J. Aerosol Sci., 11, pp. 447-459. [10] Kim, C. S., Fisher, D. M., Lutz, D. J., and Gerrityet, T. R. 1994, “Deposition of Inhaled Particles in Bifurcating Airway Models with Varying Airway Geometry,” J. Aerosol Sci., 25, pp. 567-581. [11] Schlesinger, R. B., Bohning, D. E., Chan, T. L., and Lippmann, M., 1977, “Particle Deposition in a Hollow Cast of the Human Tracheobronchial Tree,” J. Aerosol Sci., 8, pp. 429-445. [12] Zhang, Y., and Finlay, W. H., 2005, “Experimental Measurements of Particle Deposition in Three Proximal Lung Bifurcation Models with an Idealized Mouth-throat,” J. Aerosol Med., 18(4), pp. 460-473. [13] Hinds, W. C., 1998, “Aerosol Technology: Properties, Behavior and Measurement of Airborne Particles,” Wiley, New York, NY, Chap. 3. [14] Horsfield, K., Dart, G., Olson, D. E., Filley, G. F., and Cumming, G., 1971, “Models of the Human Bronchial Tree,” J. Applied Physio. 31(2), pp. 207-217. [15] Mazumder, M. K., and Ware, R. W., 1987, “Aerosol Particles Charge and Size Analyzer,” US Patent number 4633714. [16] Mazumder, M. K., Wilson, J. D., Wankum, D. L., Cole, R., Northrop, G. M., Neidhardt, L. T., and Martonen, T. B., 1989, “Dual Laser Doppler System for Real-time Simultaneous Characterization of Aerosols by Size and Concentration,” In: Lung Dosimetry, Crapo, J. D., (editor), Academic Press, San Diego, CA, pp. 211- 234. [17] Swift, D. L., 1996, “Use of Mathematical Aerosol Deposition Models in Predicting the Distribution of Inhaled Therapeutic Aerosols,” In: Inhalation Aerosols, Hickey, A. J., (editor), Marcel Dekker, New York, NY, pp 51-81. [18] Czarske, J. W., 2006, “Laser Doppler Velocimetry Using Powerful Solid-state Light Sources,” Measurement Sci. Technol., 17, pp. R71-R91.


19.1



CUTTING EDGE PROFILE CHARACTERIZATIONS BY WHITE-LIGHT INTERFEROMETRY

Andrew Ogilvie and Kevin Chou Mechanical Engineering Department

The University of Alabama Tuscaloosa, Alabama, USA

ABSTRACT Diamond coated cutting tools provide several advantages

over traditional cutting tools, specifically in the machining of advanced materials such as composites. One of the main disadvantages of diamond coated cutting tools is the residual stresses induced from the diamond deposition, which lead to tool failure. Moreover, the cutting edge geometry can be critical to the deposition residual stresses of diamond coated tools.

In this study, a white-light interferometer was used to acquire tool edge surface data, and a MATLAB-based algorithm was developed to accurately characterize the tool edge radius and the wedge angle. Commercial carbide inserts with five different edge radii were evaluated. In addition, carbide inserts before and after diamond deposition were evaluated to estimate the coating thickness. The insert edge geometry and coating thickness will allow for a quantitative relationship that predicts the residual stress level at the tool edge.

The results demonstrate the ability of the MATLAB algorithm, both in its accuracy and efficiency. It is also found that large edge radius cases tend to have a greater deviation from the manufactured specification. Moreover, tools with a larger edge radius have a less perfect round profile at the flank face transition. BACKGROUND

In an effort to replace costly polycrystalline diamond (PCD) cutting tools in the machining of advanced materials, technologies such as chemical vapor deposition (CVD) have been developed to apply diamond coatings to cutting tools [1-3]. Diamond coatings have been the subject of several previous studies [4] due to their unique properties and wide applications for the machining of advanced materials. Diamond coated tools have also been studied with regard to deposition residual stresses with various results reported [5]. Despite their economic advantages, the performance of CVD diamond tools is sorely outmatched by the PCD counterparts.

The less ideal performance of CVD diamond tools is due to their main failure mode, coating delamination [6]. These failures can be catastrophic and are responsible for limiting the

tool life of CVD diamond tooling [7]. The major cause for delamination (which occurs most often at the tool flank) is high stresses and degraded adhesion during machining. High stresses are induced during the diamond deposition processes of the tool’s manufacture.

During the deposition process, the tool substrate (typically cobalt-cemented tungsten carbide, WC-Co) is heated to a high temperature, 800 to 1000 oC, and after diamond deposition, the coated tool is cooled down to room temperature. Due to the differences in the properties of each material, specifically the thermal expansion coefficient, high stresses are imposed upon each material during cooling. The substrate experiences tensile stresses while the diamond coating, which possesses a smaller thermal expansion coefficient, experiences compressive stresses on the order of giga-pascals.

Moreover, the change of geometry around the cutting tip area will generate stress concentrations and yet additional stress components. Information about the cutting edge geometry of a cutting insert is essential to predict the deposition residual stresses. In order to determine the maximum allowable stress endurable by the machining process, the deposition residual stresses must be taken into account. A larger cutting radius will alleviate the stress concentration and may increase the allowable machining stresses for the tool insert, also dependent upon cutting conditions [8].

Cutting edge radius is known as a significant factor to the chip formation and the thermo-mechanical states of the cutting tool, etc., in machining processes. Accurate measurements of cutting edge radius are desired for tool quality control as well as performance evaluation [9], especially for high precision machining such as diamond turning [10]. This is particularly important to diamond coated tools for the reason discussed above, deposition stresses [11]. Cutting edge geometry measurements have long been practiced and investigated. In general, there are contact and non-contact measurement methods, e.g., stylus profilometry and optical projection, respectively. Advanced techniques such as atomic force microscopy have also been developed to measure ultra-sharp edges (order of 10 nm) [12]. Recently, white-light interferometry (WLI) has been applied to surface/profile


19.2

measurements of small parts, e.g., MEMS devices. The powerful surface-profile data capability makes WLI ideal for tool geometry measurements, though less frequently reported. In addition, data processing methods to quantify the edge profiles deserve a closer look to examine the error and uncertainty associated with such methods.

The objective of this research is to apply WLI to investigate carbide tool edge geometry, of different radius specifications, for diamond coated tool practices. A data processing algorithm was developed to objectively evaluate the edge radius and the wedge angle. Moreover, measurements of both uncoated and coated tools were employed attempting to estimate the coating thickness. The results of this research will enable CVD diamond tool manufacturers to improve the performance of diamond coating tool inserts and lead to their emergence as the optimal tooling for the machining of advanced materials. MEASUREMENT EXPERIMENTATION Instrumentation and Samples

A white light interferometer, NT1100 from Veeco Metrology, was used to collect surface height data around a cutting edge. An objective lens of 50X and a 0.5X field of view lens were used. A low scanning speed and a 0.8% threshold were employed. Commercial WC-Co cutting inserts of square shape were used (SPG422): 12.7 mm width and 3.1 mm thickness. The nominal corner radius was 0.8 mm and the wedge angle was 79o. Five levels of edge radii, nominally 5 µm, 25 µm, 51 µm, 102 µm, and 152 µm were examined. For each level, 10 samples were tested. Both straight cutting edges and the insert corner areas were measured. For straight cutting edges, the single scan mode was used, but the corner area was measured using the stitching function in order to include most corner areas. Figure 1 shows the instrument and measuring setup.

Figure 1. Experimental Setup.

In order to interpret the data from the white light

interferometer, a computer workstation running WYKO Vision software, packaged with the interferometer from the

manufacturer, was used. The Vision software provides over 200 built-in features to quantify and visualize the surface profile data collected by the interferometer [13] for analyses such as roughness. The various displays allow the user to visually confirm that the data captured is representative of the actual tool insert that was measured. Though the software offers profile analysis, it can be complicated by operator’s subjective evaluation. Moreover, accuracy issues inevitably arise for the insert corner area when using Vision analysis. The main features in Vision used in this study were the visualization tools and initial processing. Therefore, more rigorous engineering analysis is required to accurately characterize the tool edge geometry. Once finished with any Vision operations, the raw or processed data can be saved in WYKO’s opd format.

The Vision software was used for initial processing of the data. A low pass filter was used to identify erroneous data and the built-in data restoration was used to interpolate and replace the identified missing data. The low pass filter function utilized in this study used a three pixel by three pixel window to scan the data and remove data whose value was not in agreement with the value predicted by Vision. The data restoration uses the height information of a five pixel by five pixel window centered on any missing data to interpolate a value to replace any data that was filtered out. An example of the raw tool height data from the white light interferometer is shown in Figure 2 and the same data after processing is shown in Figure 3.

Figure 2. An Edge Image from Measurement.

Figure 3. An Edge Image after Vision Processing

Rake face

Flank face


19.3

ALGORITHM METHODOLOGY

Due to its computing advantages, MATLAB was used to further analyze the tool geometry using the data cloud obtained from the WLI. In MATLAB, a Savitzky-Golay filtering function was first used with an eighth order polynomial fit and a frame length of sixty-one. The polynomial order and frame length were experimentally determined to be the optimal values by comparing an overlay of the raw data to the filtered data. By visually inspecting the filtered data for numerous combinations of sampling size and frame length, the values above were found to give the best representation of the raw data. After identifying the erroneous data, an inpainting method was used to determine interpolated values to replace the original missing data. Inpainting is a technique used in digital photography to improve the quality of a digital photograph where data may be missing or irresolute. Inpainting uses a system of partial derivatives to interpolate within a three-dimensional matrix and thus predicts the value of any missing/irresolute points more accurately than general linear techniques. The data set previously shown in Figures 2 and 3 is now shown in Figure 4 prior to processing, and again in Figure 5 after MATLAB processing.

Figure 4. An Edge Profile Using Imported Data in MATLAB

Figure 5. An Edge Profile after MATLAB Processing

The area of interest for the tool insert is the edge radius and

the wedge angle (the included angle between the rake and flank faces). When measured by the white light interferometer, the

tool insert was placed at approximately a 50o angle to the horizontal allowing the area of interest to be the peak of the data taken, as in Figure 1. After processing by MATLAB, a two-dimensional profile of the tool edge is clearly seen, as in Figure 6.

Figure 6. Example Column of Data from MATLAB.

From this MATLAB plot, the areas that correspond to the

rounded curves and the insert flat faces are visually distinguishable. However, there could be subjective determination, with uncertainty, of the curve area for radius estimates. In addition, some edge profiles are not as ideal as a simple circular arc connected with two tangent lines.

To calculate the edge radius and the wedge angle, a circle is fitted to the area corresponding to the rounded curve portion and two lines are fitted to the portion corresponding to the insert faces. The slopes of the fit lines are then used to calculate the angle between the faces. Using the same data set as the previous figures, Figure 7 shows the concept of these measurements.

Figure 7. Methodology Illustration.

The first data sets used when creating the algorithm were

the straight edge regions of studied cutting inserts. Since these data represented a straight edge, they did not involve the complexity of the nose regions and thus provided simpler data sets to develop the algorithm from its conception.

The data set was first imported from Vision using a MATLAB file. This m-file converts the matrix of discrete data,


19.4

of a specified sampling distance (~350 to 400 nm), from the Vision format into a matrix that is used by the algorithm for the duration of that particular data set’s fitting; the imported matrix represents the z axis values of the three-dimensional tool insert. After importing the matrix, corresponding vectors are created for the x and y axes, with the x axis parallel to the insert edge. The previously discussed MATLAB processing is now executed with the imported matrix to smooth the data while preserving the shape of the tool edge.

Once a smoothed matrix is produced, the algorithm runs a loop through the columns of data (in a direction parallel with the insert edge) and determines the slope of the linear regions (that correspond to the tool faces) using a robust linear fitting technique built into MATLAB. For this step, the entire face region is assumed to have the same linear properties of the furthest twenty-five percent of the face region from the insert edge. After numerous trial runs, this criterion was deemed accurate; example results for this process are shown later. The algorithm then determines the very tip of the insert edge by finding the maximum value for the current column and begins iterating outward one x-interval at a time until the slope between two consecutive points is within 99.9% of the slope for the face region on that particular side of the insert edge. When the iteration for the left-hand side ends, the process is repeated for the right-hand side. The locations on the x axis where the iterations end define the curved region of the insert edge. Using this data, a least sum of squared radial deviations method is used to fit the curved edge region with a circle whose radius of is the edge radius of the insert. The slope calculated by the robust fit for the insert faces is used to calculate the angle of the tool edge. These steps are preformed for every column of data in the imported matrix before the loop ends.

After the loop has calculated a radius and angle for every column of data, an average and standard deviation are calculated for the entire matrix. In order to eliminate any outliers, any columns with a radius, x or y-center location outside of three standard deviations from their respective averages are removed from the original matrix and the radius and angle loop is performed again with the modified matrix until no data is removed.

The algorithm then returns the final average radius and wedge angle values as well as the standard deviations for each. In addition to the numerical results, plots can be generated to display the input data, the circle fit overlaid on the input data and the linear fit and iteratively defined curved region overlaid on the input data. These plots allow the user to visually confirm that the fit created is appropriate for the input data; result examples are shown in Figures 8, 9 and 10, respectively.

Figure 8. 2D Projection of Raw Data.

Figure 9. Fitted Circle overlaid on Raw Data.

Figure 10. Raw Data with Overlaid Linear and Circle Fit.

RESULTS AND DISCUSSION

The tool height data, obtained via the white light interferometer, for the straight edge regions of the cutting tools with 5 different edge radii used are shown, in Vision display, in


19.5

Figure 11. Different sharpness levels can be visually noted. These Figures show scans of the uncoated inserts and for these inserts, the nominal radii, in micrometers, are approximately 25, 51, 102, 5 and 152, for cutting insert A, B, C, D, and E, respectively.

(a) Insert A

(b) Insert B

(c) Insert C

(d) Insert D

(e) Insert E

Figure 11. Interferometer Images of Uncoated Inserts. Several samples of the above inserts were processed and

analyzed by the algorithm and sample plots of the example data given above are shown in Figure 12. It can be noted that the obtained curves (with radius and lines) from the algorithm represent the raw data well despite the noisy data. This demonstrates the capability of the developed data processing/evaluation algorithm. Another observation is that for the tools with larger radii, i.e., nominally 30 µm, the transition between the flank face and round edge is not tangent, possibly a fabrication defect.

(a) Insert A

Rake face profile

Flank face profile


19.6

(b) Insert B

(c) Insert C

(d) Insert D

(e) Insert E

Figure 12. Example Results for Uncoated Inserts,

Table 1 below summarizes the measured results, edge radius and wedge angle, of different tools. The measured radii are in general smaller than the target values. In addition, the variation of the edge radius within a batch is reasonable. The wedge angle is fairly aligned with the manufacturer specification.

Table 1. Uncoated Inserts Result Summary TOOL A B C D E Nom. Rad. (µm)

25 51 102 5.0 152

Avg. Rad. (µm)

17.87 39.06 80.09 4.025 105.7

Std. Dev. Rad. (µm)

1.350 2.696 6.913 0.672 6.994

Avg. Angle (°)

77.89 78.43 79.06 78.25 80.44

Std. Dev. Angle (°)

0.328 0.318 0.670 0.446 0.596

For the coated inserts, only samples of the 102 µm and 5

µm cases were available, for one target coating thickness, at the time of preparation of this paper. Interferometer profile scans of these samples are shown in Figure 13.

(a) Insert C


19.7

(b) Insert D

Figure 13. Interferometer Data of Coated Inserts.

Again, examples of the above coated insert data were processed and analyzed by the algorithm and sample 2D profile plots of the example data given above are shown in Figure 14. The plots also indicated much more noisy data on the flank faces. Table 2 below further compares the measured results of coated tool inserts to their uncoated counterparts with the estimated coating thickness.

(a) Insert C

(b) Insert D

Figure 14. Example Results for Coated Inserts.

Table 2. Comparison of Coated and Uncoated Inserts INSERT C INSERT D

Coated Uncoated Coated Uncoated Avg. Rad.

(µm) 96.28 80.09 17.29 4.025

Avg. Angle (°)

78.48 79.06 76.98 78.25

Coating Thick. (µm)

16.19 13.27

Although the straight edge results exemplify the precision

of the algorithm and offer some insight into the geometrical differences between the tool insert before and after coating, the area of greatest interest for the inserts is the nose region as this is the region engaged during machining. Thus, the developed algorithm is extended, work in progress, for the measurement of the tool insert nose region. Figure 15 shows an example of the interferometric height data image and MATLAB-processed image.

(a) Interferometer Data Image

(b) MATLAB Data Image

Figure 15. Surface Data Image of the Tool Nose Region.

After MATLAB processing, sample slices can be taken with a given orientation in reference to the nose center. The slices are then analyzed with a similar methodology, longer computational time though, as the straight edge regions. The result plot is shown in Figure 16 as an example, insert A case.

Rake face

Corner radius

Flank face


19.8

The evaluated radius and wedge angle are around 25 µm and 78°.

Figure 16. 2D Profile for the Middle Slice of Corner Region of

an Uncoated Insert, A.

CONCLUSIONS It has been known that the cutting edge radius is critical to

deposition residual stresses of CVD diamond tools. Thus, accurate measurements are needed to better quantify the deposition stresses which affect the tool wear and performance. In this study, an algorithm was developed to objectively analyze the edge radius and wedge angle using data collected by white-light interferometry. The results of this analysis show that the edge radius deviates noticeably from the manufacturer’s specifications, especially for large radius cases. Despite the large deviation from the specifications, the variations of edge radii among different tool samples in a single batch are reasonably small.

This study shows that the use of white light interferometry, combined with a MATLAB-based data/geometry algorithm, is a powerful tool for high precision measurements of the surface profiles on the scale of micrometers, with a potential applicability to sub-micron sized edges.

The analysis of the coated tool insert samples show that the coating thickness can be estimated and that the coating is possibly thicker at the edge of the insert as evidenced by the decrease in the wedge angle between the coated and uncoated trials.

In the future, the tool corner region algorithm will be completed and will achieve a highly accurate and precise method of determining the edge radius and wedge angle of diamond coated cutting tools, before and after coating, leading to a quantitative relationship for the prediction of residual stresses due to the diamond deposition process. The results will enable the optimization of these tools and their emergence as the ideal cutting tool for advanced machining processes. ACKNOWLEDGEMENTS

This material is based upon work supported by the National Science Foundation under Grant No. CMMI 0728228. Kimerlee Fraser (University of South Florida) conducted some analysis,

REFERENCES [1] Kustas, F.M., Fehrehnbacher, L.L., and Komanduri, R., (1997), “Nanocoatings on Cutting Tools for Dry Machining,” Annals of CIRP, 46(1), pp.39-42. [2] Grzesik, W., Zulisz, Z., and Nieslony, P., (2002), “Friction and Wear Testing of Multilayer Coatings on Carbide Substrates for Dry Machining Applications,” Surface and Coatings Technology, 155(1), pp.37-45. [3] Bouzakis, K.-D., Hadjiyiannis, S., Skordaris, G., Minisidias, I., Michailidis, N., Efstathiou, K., Pavlidov, E., Erkens, G., Crener, R., Rambadt, S., and I. Wirth, (2004), “The Effect of Coating Thickness, Mechanical Strength and Hardness Properties on the Milling Performance of PVD Coated Cemented Carbides Inserts,” Surface and Coatings Technology, 177-178, pp. 657-664. [4] Hu, J., Chou, Y.K., and Thompson, R.G., (2008), “Nanocrystalline Diamond Coating Tools for Machining of High-strength Al Alloys,” International Journal of Refractory Metals and Hard Materials, Vol. 26, pp. 135-144, 2008. [5] Hu, J., Qin, F., Chou, Y.K., and Renaud, A., (2008), “Numerical Simulations of 3D Tool Geometry Effects on Deposition Stresses in Diamond Coated Cutting Tools,” MSEC 2008. [6] Amirhaghi, S., Reehal, H.S., Wood, R.J.K., and Wheeler, D.W., (2001), “Diamond Coatings on Tungsten Carbide and Their Erosive Wear Properties,” Surface and Coatings Technology, 135(2-3), pp. 126-138. [7] Chou, Y.K., and Liu, J., (2005), “CVD Diamond Tool Performance in Composite Machining,” Surface and Coatings Technology, 200, pp. 1872-1878. [8] Hu, J., Y. K. Chou, R. G. Thompson, (2007), "Cutting Edge Radius Effects on Diamond Coated Cutting Tools: From Deposition to Machining,” Proceedings of the 2007 International Manufacturing Science and Engineering Conference, October 15-17, 2007, Atlanta, Georgia, 2007, MSEC2007-31043. [9] Schimmel, R.J., Manjunathaiah, J., and Endres, W.J., 2000, “Edge Radius Variability and Force Measurement Considerations,” Transactions of the ASME, Journal of Manufacturing Science and Engineering, 122, pp. 590-593. [10] Drescher, J., (1993), “Scanning Electron Microscopic Technique for Imaging a Diamond Tool Edge,” Precision Engineering, Vol. 15(2), pp. 112-112. [11] Qin, F., Chou, K., Nolen, D., Thompson, R.G., Ni, W., (2009), “Cutting Edge Radius Effects on Diamond Coated Tools,” Transactions of NAMRI/SME, Vol. 37, pp. 653-660. [12] Gao, W., Asai, T., Arai, Y., (2009), “Precision and fast Measurement of 3D Cutting Edge Profiles of Single Point Diamond Micro-Tools,” Annals of CIRP, Vol. 58, pp. 451-454. [13] Veeco, (2006), “WYKO NT1100 Optical Profiling System,” http://www.veeco.com/pdfs/datasheets/nt1100%20reva5%20final_394.pdf


20.1



A CRITICAL REVIEW ON SINGLE COMPONENT WORKING FLUIDS FOR ORGANIC

RANKINE CYCLES (ORCs)

Rambod Rayegan, Yong X. Tao

Florida International University Miami, Florida, USA

ABSTARCT

An Organic Rankine Cycle (ORC) is a substitutive

technology that employs an organic fluid as working

fluid to recover low grade heat sources, such as from

solar or waste heat. The selection of working fluid and

their operation conditions has a great effect on the

system operation, and its energy efficiency and impact

on the environment.

This paper presents a critical review on single

component working fluids in Organic Rankine Cycles

(ORCs). The study focuses on practical considerations

for providing guidelines for the categorization of

working fluids based on their capabilities and

shortcomings for power generation in a Rankine cycle.

INTRODUCTION

High-temperature thermal power plants that work

based on the conventional Rankine cycle are not

economic in small scale applications. The Organic

Rankine Cycle (ORC) is a substitutive technology

which is applicable for small scale power generation for

use in residential and commercial buildings or in

desalination plants. ORC employs low grade heat from

different sources such as biomass, geothermal, solar and

waste heat of industrial processes. The main difference

between the ORC and the conventional Rankine cycle is

the working fluid. The boiling point of working fluid in

the ORC is much lower than steam, hence there is no

need to achieve high temperatures to generate vapor for

running a micro-turbine or expander. As a result ORCs

can be driven at lower temperatures than the Rankine

cycles that use water.

The selection of working fluid and operation

conditions has a great effect on the system operation,

and its energy efficiency and impact on the

environment.

The main advantage of using multicomponent

organic fluids in the Rankine cycle is non-isothermal

phase change processes in the evaporator and

condenser. Siloxanes have the same advantage among

single component working fluids. In addition,

muticomponent organic fluids cover an unlimited

number of fluids and studies on them are more

fundamental than practical. For these reasons this

literature review has been narrowed to single

component working fluids to reach to more practical

conclusions.

Single component organic fluids have different

categories which have desirable and undesirable

properties for use in ORC.

The main purpose of this study is to present a

practical view to help readers categorize working fluids

based on their capabilities and shortcomings for power

generation in a Rankine cycle.

GENERALCRITERIA FOR SELECTING WORKING FLUIDS IN ORC

There are some general desirable properties of the working fluids in a thermodynamic cycle regardless of its application that help reduce equipment size and decrease different types of fluid loss (i.e. heat and pressure loss) while passing through a component or fluid interaction with its environment. Some of these desirable properties of working fluids in ORCs can be listed as follows [1]:

• Small specific volume

• Low viscosity and surface tension

• High thermal conductivity

• Suitable thermal stability

• Non-corrosive, non toxic and compatible with engine materials and lubricating oils

• Moderate vapor pressure in the range (0.1-2.5 Mpa) in the heat exchange units

• High availability and low costs

• Low safety, health and environmental hazards

Low Ozone Depletion Potential (ODP) is one of

the most important environmental characteristic of the fluid used as the working fluid in the ORC system. Chlorine containing fluids are not Ozone-safe and have been banned by Montreal protocol [2] and thus should be avoided in new systems.

We can also recognize properties of working fluids that are generally beneficial for ORCs and help us for preliminary selection of fluids before computing calculations.

Depending on the slope of the temperature-entropy curve to be infinity, positive, or negative, working fluids can be classified into isentropic, dry, or wet respectively [3]. Dry or isentropic working fluids are more appropriate for ORC systems. This is because dry or isentropic fluids are superheated after isentropic expansion. Therefore there is no concern for existing liquid droplets at the turbine outlet.


20.2

When the heat source is waste heat, organic fluids with lower specific vaporization heat are preferred. Lower vaporization heat of the working fluid causes the heat transfer process in the evaporator to occur mostly at variable temperature. Therefore the temperature profile of the working fluid in the evaporator better follows the temperature profile of heating fluid in the heat source [4]. This means that the temperature difference between fluids in the heat exchanger is reduced as illustrated in Fig. 1. Hence the irreversibility in the heat transfer process is decreased.

Fig. 1 Organic fluids with lower specific vaporization heat produce less irreversibility [4]

A few parameters which have the main effects on the cycle’s thermodynamic performance are introduced as follows [5]:

• Critical Temperature: At the fixed evaporating temperature (Teva) and condensing temperature (Tcon) the higher critical temperature (Tcr) results

in higher pressure ratio but lower condensing pressure which could conflict with cycle components design.

• Molecular complexity: More complex fluids usually are dry fluids. Majority of organic fluids are fluids with high complexity molecules. This means most organic fluids can satisfy the dry condition to be employed in a Rankine cycle.

• Molecular mass: In general for heavy fluids a lower vapor expansion ratio occurs across the turbine. Then the turbine tends to have a low peripheral speed and a small number of stages.

From the structural point of view and type of atoms

in the fluid molecule, the ORC working fluids can be categorized under four main classes [5]:

1. Hydrocarbons including linear (n-Butane, n-Pentane), branched (Isobutane, Isopentane), and aromatic hydrocarbons (Toluene, Benzene) have:

• Desirable thermodynamic properties

• Flammability issues 2. Perfluorocarbons (Fully fluorinated

hydrocarbons) (Hexaflourobenzene) are/have:

• Extremely inert and stable

• Extreme molecular complexity

• Thermodynamically undesirable 3. Partially flouro-substituted straight chain

hydrocarbons

• There are several zero ODP fluids among them which are of considerable potential interest

4. Siloxanes (MM, MM/MDM/MD2M)

• Attractive for a mix of physical and thermal properties (low toxicity and flammability level; high molecular mass; prolonged use as a high temperature heat carrier)

• They are often available as mixtures rather than as pure fluids

• Isobaric condensation and evaporation are not isothermal and exhibit a certain glide

As we can see there is no single category of fluids

that satisfies all desirable properties for use in an ORC system. Hence after preliminary selection of fluids by discarding chlorine containing and wet fluids, we seek an optimization process that may lead to the final choice for better cycle performance.

In [6-7] comprehensive studies have been done for a large number of fluids but in most of papers that have been reviewed so far ORC optimization has been done for a limited number of fluids [8-16] or the optimization procedure has been applied on an ORC system using one specific working fluid [17-18].

Because of the wide variety of fluid parameters and the cycle conditions that have been considered in the literature there have been very limited attempts at systematically categorizing the selection of working fluids for an ORC. In the following sections we will fill this gap by categorizing the results in the literature based on our selection criteria.

STUDIES BASED ON CRITICAL TEMPERATURE

Bruno et al. have accomplished a wide-ranging study on the working fluids in an ORC system that produces energy for running a reverse osmosis desalination system [6]. The authors considered the Aspen plus software library as their reference. At the first step they discarded chlorine included, wet and isentropic fluids.

During the second step for the preliminary selected working fluids the optimum high and low pressure of the saturated cycle maintaining the maximum first law efficiency of the cycle were found.

In general, employing a fluid with higher critical temperature results in higher efficiency but lower condensing pressure. Three groups of fluids can be recognized in the results: (A) fluids with a high efficiency close to 30% with low condensing pressures under atmospheric pressure, such as the siloxane fluids, (B) fluids with atmospheric pressure at the condensing section and with medium efficiency of around 20%, such as n-Pentane and Isopentane. Isopentane has the best performance according to the efficiency (27.2 %) and the minimum pressure in the cycle (1 bar). Therefore Isopentane is the best choice for the ORC cycle if the heat source can provide the proper evaporating temperature (about 180 ºC) (C) there is another group of fluids such as Isobutane working at high condensing pressures showing an efficiency lower than 15%.

For a practical comparison between fluids at this stage, a complementary study is necessary to increase the group A condensing pressure to atmospheric pressure and repeat the simulation process to find the cycle efficiency at new working conditions.


20.3

In the last step for four different types of solar collectors the optimization to find the best high temperature in a superheated ORC cycle has been done. Generally, superheating in an ORC increases the first law efficiency of the cycle with a very low slope but decreases the second law efficiency of the cycle. Then superheated cycles are never recommended unless in order to gain more power at the expense of losing efficiency. In addition, in solar cycles increasing the maximum temperature of the collector increases the heat loss of it.

Except for the general trend of increasing the efficiency of the cycle with the critical temperature of the working fluid no discussion about the relation between fluid properties and the ORC efficiency can be found in the said paper.

Drescher and Bruggemann fulfilled an inclusive research to identify the most suitable fluids for ORC in biomass power and heat plants [7]. In this study the Design Institute for Physical Properties (DIPPR) database has been considered as the reference. For preliminary selection, the authors extracted cycle pressure and temperature requirements for an ORC with a biomass heat source from literature.

About 700 substances of the DIPPR database pass the pre-selection criteria and are included in the subsequent comparison.

The efficiency of the 100 best-suited fluids ranges from 24.3% to 25.4% for the regenerative ORC. According to the results, the efficiency rises to approximately 25% at 1 MPa with a slight decrease for higher pressures. The slight decrease can be explained by the needed work of the feed pump. This means that there is an optimal maximum process pressure. In this study, a detailed analysis for typical fluids has been carried out to demonstrate critical temperature effect on the cycle efficiency. Results and typical fluid properties can be taken from Table 1.

To illustrate the influence of vaporization enthalpy (h5 - h4), its ratio to input enthalpy (h6 - h3) has been considered as an index that we call the vaporization enthalpy ratio. Fig. 2 shows the different states of the fluid in the plan layout and typical T-S diagram for a regenerative ORC.

Toluene has the highest vaporization enthalpy ratio, but at a low temperature level. Thus, toluene shows the worst efficiency of the alkylbenzenes. On the other hand OMTS has a high vaporization temperature but the lowest vaporization enthalpy ratio. It has the lowest efficiency of the selected fluids. Therefore both high vaporization temperature and enthalpy result in high ORC efficiency. This means that fluids with a higher critical temperature and wider saturation dome are most efficient fluids for an ORC.

Mago et al. determined the influence of the boiling point temperature (Tbp) on the system thermal efficiency for both basic and regenerative ORCs by comparing simulation results for R113, R123, R245ca and Isobutane [8]. Since fluids with higher boiling temperature have higher critical temperature, this study can be considered as a critical temperature based study. The results demonstrate that the fluid which shows the best thermal efficiency is the one that has the highest boiling point among the selected fluids (R113, Tbp = 47.59 ºC), while the fluid with the worst thermal

efficiency has the lowest boiling point temperature (Isobutane, Tbp = -11.61ºC). Therefore, it can be concluded that the higher the boiling point temperature of the organic fluid the better the thermal efficiency that will be achieved by the ORC.

Fig. 2 (a) Plant layout (b) Typical T-S diagram for a regenerative ORC [7]

STUDIES BASED ON MOLECULAR COMPLEXITY

Invernizzi et al. presented a relation between molecular complexity (σ) and thermodynamic properties of the fluid [9]. They also introduced the acentric factor (ω) as a new effective factor on the cycle performance. Molecular complexity and acentric factor are defined as:

7.0,))((=

∂

∂= TrSV

cr

T

S

R

Tσ

7.0)log(Pr1=

−−= Tr

Satω

where Pr and Tr are reduced pressure and temperature respectively.

For simple molecules the slope of the saturated vapor line in the T–S plan is negative. The slope of the saturated line increases by increasing the molecular complexity of the fluid as illustrated in Fig. 3. Thus simple molecule fluids are wet and complex molecule fluids are dry.

In this paper the authors believe that as a rule, the critical temperature of a fluid increases with the molecular complexity, but as we will see later this rule is only correct for fluids in the same category (i.e. hydrocarbons or siloxanes). For homologous fluids, σ increases with the number of atoms in the molecule.

The analysis has been done for an ORC that employs exhaust gas of a micro –gas turbine as a heat source. The working fluids have been selected from fluids with critical temperatures between 180 ºC and


20.4

320 ºC with positive molecular complexity. At the authors selection there are some linear hydrocarbons, two branched hydrocarbons, some linear CFCs, two aromatic fluoro-carbons, some linear and cyclic siloxanes.

Fig. 3 The effect of molecular complexity on the Tr-S diagram [8]

In a comparison made among different working

fluids with the same heat source (1 kg/s of 300 ºC hot gas), condensing temperature (30 ºC) and evaporating temperature (170 ºC) it can be seen:

• The ORC thermodynamic efficiency mostly increases with the molecular complexity because of its effect on critical temperature and subsequently on regeneration efficiency.

• At the fixed molecular complexity, fluids with higher Tcr have higher thermodynamic efficiency.

• The overall efficiency is influenced by both thermodynamic and heat recovery efficiencies. The thermodynamic efficiency increases and heat recovery efficiency decreases with increasing molecular complexity σ as implied in Table 2. The predominant effect is related to the heat recovery efficiency so that an increase of the molecular complexity σ results in a decrease of the power output of the recovery cycle.

• From this analysis it can be concluded that from a thermodynamic point of view it would be better to employ fluids with a rather low molecular complexity; thanks to the less specific heat duty requested by the regenerator and to their higher capacity of cooling the micro-turbine exhausts.

• Preliminary design of turbine shows us that the lower molecular complexity in single stage turbines lead to lower isentropic efficiency at the same turbine size.

As different types of molecules show different

thermal and physical behaviors, it makes more sense if we look for the relationship between cycle operation and fluid properties at least among fluids with some common characteristics.

Study of seven linear hydrocarbons from C4H10 (n-butane) to C10H22 (n-decane) shows the increase in molecular complexity has the effect of rising the fluid critical temperature while reducing its critical pressure [10]. This means the fluid with more molecular complexity has the higher normal boiling point.

For a cycle with the high and low temperatures equal to 100ºC and 40ºC respectively the following results have been obtained:

• Condensation pressure variation : From 377 to 0.49 kPa

• Evaporation pressure variation: From 1508 to 9.56 kPa

• Pressure ratio variation: From 4 to 20

• Optimized stage rotating speed variation in turbine: From 57000 rpm to 1800 rpm

• Turbine mean diameter variation: From 0.074 to 2.11 m

• Efficiency variation: increasing with molecular complexity, mainly if the cycle includes regeneration.

• Pump work variation: decreasing with molecular complexity

COMPARISON IN EFFICIENCY AMONG SELECTED FLUIDS

Hung compared ORC efficiency and irreversibility for selected refrigerants and hydrocarbons [11]. He selected R-113 and R-123 from refrigerants and p-Xylene (C8H10), Toluene (C7H8) and Benzene (C6H6) from aromatic hydrocarbons. A constant 10 MW waste heat source is employed. The cycle is saturated. Irreversibility and efficiency of the cycle have been compared between selected working fluids. Irreversibility changes are completely dependent on the heat source conditions.

At a fixed heat source temperature (TH=600 K) when turbine inlet pressure varied from 500 to 1800 kPa, the following observations have been made:

• For all fluids, irreversibility of the cycle (Irr.) is decreasing with increasing inlet turbine pressure.

• Irr. p-Xylene<Irr. Toluene< Irr. Benzene < Irr. R113 < Irr. R123

• Among aromatic hydrocarbons : The higher molecular weight, the lower irreversibility

For a fixed temperature difference between the turbine inlet and the heat source (15ºC) when turbine inlet pressure varied from 800 to 2200 kPa, the following observations have been made:

• Irr. R123 < Irr. R113<Irr. Benzene <Irr. Toluene < Irr. p-Xylene

• For all fluids, irreversibility is increasing with increasing inlet turbine pressure.

ORC efficiency calculations for the selected fluids at different turbine inlet pressures show that:

• η R123< η R113<η Benzene <η Toluene < η p-Xylene

• For all fluids, efficiency is increasing with increasing inlet turbine pressure.

• The working fluids with higher boiling temperature will have greater efficiency.

• The lower condenser exit temperature (lower ambient temp), the higher efficiency.

• System efficiency and total irreversibility have opposite trends. Using the operation conditions at the intersection point of the efficiency curve and the availability ratio


20.5

(ratio of the available energy to the total energy obtained from the heat source) curve would lead to the optimal balance between the two conflicting factors.

Hettiarachchi et al. compared a geothermal ORC

optimum performance for ammonia, R123, n-Pentane and PF5050 as the working fluid [12]. The ratio of the total heat exchanger area to net power output is considered as the objective function.

Ammonia has minimum objective function and maximum geothermal water utilization (Net work / Geothermal water mass flow rate), but not necessarily maximum cycle efficiency. PF5050 and Ammonia have the worst performance from the exergy efficiency point of view. This means not considering the objective function, Ammonia can not be a choice because of its low ORC cycle and exergy efficiency.

The fluids, n-Pentane and R123, have better cycle efficiency than PF5050, although the latter has better physical and chemical characteristics compared to other fluids considered.

Liu et al. examined the influence of various working fluids on the thermal efficiency and on the total heat-recovery efficiency of ORC for a waste heat recovery system [13]. Finding a relation between the molecular structure of the fluid and its T-S vapor saturation line slope is one of the achievements of this study. The results show that the presence of a hydrogen bond in certain molecules, such as water, ammonia, and ethanol results in wet fluids and is considered as inappropriate for ORC systems. The authors claim that although the thermal efficiency for working fluids with lower critical temperature is lower; the critical temperature of the fluid has not significant effect on the thermal efficiency of the cycle. An explanation for the contradiction between this conclusion and previous studies may lie on the use of a correlation (Watson relation) to calculate the vaporization enthalpy of the fluid by Liu and his coworkers. The heat recovery efficiency is higher for higher inlet temperatures of the waste heat and higher critical temperature fluids. The effect of the heat source temperature profile on the system performance [11] has been approved by the results of this study.

Thermal stability over the range of operating

temperatures and a minimal degradation rate over time is the only criteria in preliminary selection of the working fluids for a given ORC in Prabha’s analysis [14].

Benzene is the most thermally stable of the candidate working fluids. Next after Benzene is Toluene. Isobutane is a thermally stable fluid in Low temperature range. In this study the author concentrates on cascade solar ORCs.

A regenerative cascade cycle with toluene as the topping fluid and butane as the bottoming fluid is the optimized solar ORC plant relative to this study.

A comparison between Toluene and some selected

siloxanes for different superheating temperatures, condensation temperatures and recuperator’s efficiencies in a 100 KW power ORC in the medium range temperature has been carried out by Delgadeo-Torres and Garcia-Rodriguez [15].

Direct solar vapor generation configuration of solar ORC has been analyzed and characterized with LS3 and IND300 parabolic trough collector (PTC) models.

In the working fluid selection part D4, D5, MM and MD4M were considered from siloxanes. Then D5 and MD4M were discarded because of their low condensation pressure in the temperature range of 35-115 ºC. The ORC system with a vaporization temperature 10 to 15ºC lower than the critical temperature for each fluid has been simulated.

In a 100 kW gross mechanical output solar ORC with identical condensation temperatures toluene presents the overall efficiency followed by D4 and MM. The difference between toluene and D4 and MM is particularly important if the regeneration process is not considered.

The authors continued their work with a second ORC that is powered by the thermal power rejected by the top ORC, forming a double cascade ORC [16]. This configuration has been one of the proposed by Prabhu [14] for the system called Solar Trough Organic Rankine Electricity System (STORES).

The top temperature cycle generates 100 kW of raw power with regenerator effectiveness, εreg = 0.8 and a condensation temperature of 115ºC. The analysis has been done for the top cycle with Toluene and MM as the working fluid. The heat rejected from the top cycle is absorbed by the bottom cycle with a condensation temperature at 35ºC. The vaporization temperature of the bottom cycle is equal to 105ºC.

Butane, isobutene, pentane, isopentane and neopentane are evaluated among working fluids proposed in the literature for Organic Rankine Cycles within the temperature ranges of the bottom cycles.

From the results obtained, isopentane is selected as the most suitable working fluid for the low temperature cycle since pentane and isopentane shows superior behavior but the normal boiling point of pentane is above 35ºC.

It should be pointed out that the above discussion does not consider the difference or similarity of the thermal properties among the fluids.

ORCS AT SUPERCRITICAL REGION

Karellas and Schuster studied the effects of using working fluids at their supercritical region on the ORC performance [17]. The R-245fa was chosen as the working fluid for calculations. The authors found that in a high temperature ORC that employed exhaust gas at a temperature around 490 ºC, supercritical cycle achieved more than 9% relative efficiency gain with respect to the subcritical one.

In the low temperature ORC with a geothermal heat source at temperatures between 80 ºC and 160 ºC supercritical cycle showed a different behavior. Two working fluids have been taken into consideration because of their critical points: the working fluids R134a and R227ea. In most cases the supercritical cycle has lower thermal efficiency than the subcritical one. The expansion in the turbine ends in the two-phase area, so no recuperator can be used. That is the reason why the thermal efficiency in these cases of supercritical parameters is much lower than the subcritical ones, in which a recuperator is used.


20.6

Angelino et al. showed for a waste heat ORC that using toluene at its supercritical region increased recovered thermal power with respect to the subcritical cycle with no significant change in the cycle thermal efficiency [5]. The Maximum temperatures for subcritical and supercritical cycles were 308.6 and 342.1 respectively.

Zhang et al. analyzed a novel solar energy-powered Rankine cycle for combined power and heat generation using supercritical carbon dioxide [18]. Results show higher efficiency than conventional Rankine cycle with water at maximum temperatures between 32 ºC and 177.4 ºC but the efficiency is still low (less than 12% ) to be proper for practical power plants.

CONCLUSION

This study presents a literature review on working

fluids for organic Rankine cycles (ORCs).

In general, using supercritical cycles are only

recommended for relatively high temperature cycles

and for lower temperatures the first law efficiency of

supercritical cycles are even lower than subcritical ones.

In addition, saturation cycles have an advantage of less

expensive and simpler heat exchangers.

It can be noticed from the survey that there is no

specific category of fluids that satisfies all desirable

characteristics for an ORC system. In the majority of

papers no specific relation between thermodynamic

properties and cycle performance can be recognized.

For the better observation of the results in the

literature, a number of fluids have been chosen and the

most important characteristics of the fluids and the

cycle have been summarized in Table 3. In this

selection there are four linear hydrocarbons (Pentane,

Hexane, Heptane, and Octane), two branched

hydrocarbons (Isobutane and Isopentane), two aromatic

hydrocarbons (Benzene and Toluene) and four

refrigerants (R218, 113, R123, and R236ea).

The following conclusions can be illustrated:

• The higher critical temperature allows setting the

evaporation temperature at a higher level that

leads to the higher efficiency of the cycle.

• In the fluids of one category, at the fixed Teva and

Tcon, the higher critical temperature results in

higher pressure ratio but lower condensing

pressure.

• Fluids with higher pressure ratio in the cycle

have higher vapor expansion ratio across the

turbine as illustrated in Fig. 4. Thus the higher

vapor expansion ratio is an undesirable

subsequence of using high critical temperature

fluid in a Rankine cycle. If for a small amount of

work, a high vapor expansion ratio occurs across

the turbine, supersonic flow problems, higher

turbine size or greater number of stages are

inevitable.

• Generally, high efficiency ORCs are achievable

by using hydrocarbons rather than refrigerants. It

means hydrocarbons have a higher potential to

produce power in a Rankine cycle than

refrigerants because of their relatively high

critical temperature. But Hydrocarbons are more

flammable in comparison with refrigerants.

• The molecular complexity increases with the

number of atoms in the molecule for homologous

fluids.

• In linear hydrocarbons fluids with higher number

of atoms have higher critical and boiling

temperatures, higher molecular complexity, and

higher molecular mass and higher efficiency. As

shown in Fig. 5, the variation of above

mentioned parameters, excluding efficiency, is

very close to linear with respect to the number of

atoms in the molecule.

• Except in linear hydrocarbons no relation

between molecular mass and cycle efficiency can

be recognized.

• In hydrocarbons, acentric factor increases with

their molecular complexity. Thus acentric factor

can be used as an index to compare

hydrocarbons’ wetness.

• Molecular mass mostly is in inverse relation with

vapor expansion ratio across the turbine.

Therefore turbines in cycles using heavier fluids

are smaller or have less number of stages.

• Among refrigerants, fluids with higher critical

temperature have higher normal boiling point

and higher efficiency as demonstrated in Fig. 6.

As different fluids show different pros and cons,

fluid selection is completely dependent on the priorities

in the project design. Hence, after preliminary selection

of fluids by discarding chlorine containing and wet

fluids, the optimization process gives us the final choice

for better cycle performance.

Second law efficiency and exergetic studies on

ORCs have thus far drawn less attention by researchers

and should be subject to more extensive research in the

future studies in this area.

0

150

300

450

600

750

900

R21

8

R23

6ea

Isob

utan

e

R123

Penta

ne

R11

3

Ben

zene

Isop

enta

ne

Tolu

ene

Hep

tane

Hex

ane

Oct

ane

Pressure ratio

Vapor expansion ratio

Fig. 4 Pressure ratio and vapor expansion ratio across the turbine for selected fluids

0

50

100

150

200

250

300

350

400

Pentane Hexane Heptane Octane

Criticaltemperature(C)

Boilingtemperature(C)

10 x Molecularcomplexity

Molecular mass(kg/kmol)

1000 X Acentricfactor

10 X Efficiency (%)

Fig. 5 Variation of the fluid and cycle characteristics for linear hydrocarbons


20.7

-50

0

50

100

150

200

250

R218 R236ea R123 R113

Critical temperature(C)

Boiling temperature(C)

10 x Efficiency (%)

Fig. 6 Variation of the critical temperature, boiling temperature and efficiency for refrigerants

REFERENCES [1] Maizza, V., and Maizza, A., 1996, “Working fluids

in non-steady flows for waste energy recovery systems,” Applied Thermal Engineering, 16(7), pp. 579-590.

[2] United Nations Environmental Programme, September 2006, “Montreal protocol on substances that deplete the ozone layer,” Website: <http://ozone.unep.org/teap/Reports/TEAP_Reports/Teap-CUN-final-report-Sept-2006.pdf >.

[3] Hung, T. C., 1995, “Waste heat recovery of organic Rankine cycle using dry fluids,” Energy Conversion and Management, 42(5), pp. 539-553.

[4] Larjola, J., 1995, “Electricity from industrial waste heat using high-speed organic Rankine cycle (ORC),” International Journal of Production Economics, 41(1-3), pp. 227-235.

[5] Angelino, G., and Di Paliano, P. C., 2000, “Organic Rankine cycles (ORCs) for energy recovery from molten carbonated fuel cell,” Proceedings of the Intersociety Energy Conversion Engineering Conference, 2, pp. 1400-1409.

[6] Bruno, J. C., Lopez-Villada, J., Letelier, E., Romera, S., and Coronas, A., 2008, “Modeling and optimization of solar organic Rankine cycle engines for reverse osmosis desalination,” Applied Thermal Engineering, 28(17-18), pp. 2212-2226.

[7] Drescher, U., and Bruggemann, D., 2007, “Fluid selection for the Organic Rankine Cycle (ORC) in biomass power and heat plants,” Applied Thermal Engineering, 27, pp. 223-228.

[8] Mago, P. J., Chamra, L. M., Srinivasan, K., and Somayaji, C., 2008, “An examination of regenerative organic Rankine cycles using dry fluids,” Applied Thermal Engineering, 28, pp. 998-1007.

[9] Invernizzi, C., Iora, P., and Silva, P., 2007, “Bottoming mico-Rankine cycles for micro-gas turbines,” Applied Thermal Engineering, 27, pp. 100-110.

[10] Angelino, G., Gaia, M., and Macci, E., 1984, “A review of Italian activity in the field of organic Rankine cycles,” VDI Berichte, pp. 465-482.

[11] Hung, T. C., 2001, “Waste heat recovery of organic Rankine cycle using dry fluids” Energy Conversion & Management, 42, pp. 539-553.

[12] Hettiarachchi, H. D. M., Golubovic, M., Worek W. M., and Ikegami, Y., 2007, “Optimum design criteria for an Organic Rankine cycle using low-temperature geothermal heat sources,” Energy, 32, pp. 1698-1706.

[13] Liu, B. T., Chien, K. H., and Wang, C. C., 2004, “Effect of working fluids on organic Rankine cycle for waste heat recovery,” Energy, 29, pp. 1207-1217.

[14] Prabha, E., March 2006, “Solar Trough ORC Electricity System (STORES) Stage 1- Power plant optimization and economics,” NREL Subcontract Report, NREL/SR-550-39433

[15] Delgadeo-Torres, A. M., and Garcia-Rodriguez, L., 2007, “Preliminary assessment of solar organic Rankine cycles for driving a desalination system,” Desalination, 216, pp. 252-275.

[16] Delgadeo-Torres, A. M, and Garcia-Rodriguez, L., 2007, “Double cascade organic Rankine cycle for solar driven reverse osmosis desalination,” Desalination, 216, pp. 306-313.

[17] Karellas, s., and Schuster, A., 2008, “Supercritical fluid parameters in organic Rankine cycle applications,” International Journal of Thermodynamics, 11(3), pp. 101-108.

[18] Zhang, X. R., Yamaguchi, H., Unedo, D., Fujima, K., Enomoto, M., and Sawada, N., 2006, “Analysis of a novel solar energy-powered Rankine cycle for combined power and heat generation using supercritical carbon dioxide,” Renewable Energy, 31, pp. 1839-1854.

Table 1 Optimization results for a regenerative biomass ORC (Drescher and Bruggemann [7])

Working fluid Tcr(ºC) Pcr(MPa) Pmax(MPa) Tmax(ºC) Pmin(kPa) Tmin(ºC) [(h5-h4)/(h6-h3)](%) η (%)

OMTS 291 1.44 1.34 287 13.8 90 15 22.5 Toluene 319 4.11 2.00 263 54.1 90 42 23.2

Ethylbenzene 344 3.61 2.00 297 24.3 90 36 24.3 Propylbenzene 365 3.20 1.41 300 11.4 90 40 24.9

Butylbenzene 388 2.89 0.92 300 5.0 91 43 25.3

Table 2 Optimization results for a regenerative waste heat ORC for fluids with different molecular complexity (Invernizzi et al. [9])

Working fluid n-Pentane C6F6 MM MD2M

Molecular complexity 7 13 29 72

Exit gas temperature 74 90 106 120

Power out put 46 46 43 43


20.8

Table 3 Summary of the most important characteristics of the fluids and cycle for selected fluids Fluid Isobutane Isopentane n-Pentane n-Hexane n-Heptane n-Octane

Molecular Formula C4H10 C5H12 C5H12 C6H14 C7H16 C8H18 CAS Number 75-28-5 78-78-4 109-66-0 110-54-3 142-82-5 111-65-9

Relative Vapor Density (air=1) 2 2.2 1.8 1.3 3.46 3.94

NFPA, NPCA-HMIS Hazard Codes

Health 1 1 1 1 1 0

Flammability 4 4 4 3 3 3 Instability /Reactivity

0 0 0 0 0 0

Flash Point (ºC) Flammable

Gas < -51 - 49 -23.3 - 4 13

Autoignition Temperature (ºC) 460 420 309 225 285 220

Critical Temperature (ºC) 134.7 187.2 196.6 234.7 267.0 296.2 Boiling Temperature (ºC) -12 28 36 69 98 126

Reduced Teva 0.981 0.981 0.983 0.989 0.988 0.989

Specific Vaporization Heat at Th (kJ/kg)

116.41 111.45 109.75 85.65 80.95 75.01

Vaporization Heat Ratio At Th (%)

30.2 25.2 23.9 17.8 15.9 15.4

Vapor Expansion Ratio 13 49 52 180 650 627 Molecular Complexity 1.14 7.20 6.5 11.6 17.6 23.5

Molecular Mass (kg/kmol) 58.1 72.2 72.2 86.2 100.2 114.2 Acentric Factor 0.185 0.2296 0.251 0.299 0.349 0.393

Reported Condition

Saturated

regenerative cycle

Th=126.9ºC Ph=32 bar Tl=29.9 ºC

Pl=4 bar

Saturated

regenerative cycle


Pl=1 bar

Saturated

regenerative cycle


Pl=1 bar

Saturated

regenerative cycle

Th=229ºC Ph=28 bar Tl=34.4 ºC Pl=0.3 bar

Saturated

regenerative cycle

Th=260.3 ºC Ph=25 bar Tl=28.7 ºC

Pl=0.075 bar

Saturated

regenerative cycle

Th=289.7 ºC Ph=23 bar Tl=52.2 ºC

Pl=0.075 bar

Efficiency at Reported Condition 13.94 27.2 16.74 29.28 29.67 33.75

Fluid Benzene Toluene R218 R113 R123 R236ea

Molecular Formula C6H6 C7H8 C3F8 C2Cl3F3 C2HCl2F3 C3H2F6

CAS Number 71-43-2 108-88-3 76-19-7 76-13-1 306-83-2 431-63-0 Relative Vapor Density (air=1) 1.2 3.1 6.65 2.9 5.3 N/A

NFPA, NPCA-HMIS Hazard Codes

Health 2 2 1 1 2 N/A*

Flammability 3 3 0 0 1 N/A Instability /Reactivity

0 0 0 1 0 N/A

Flash Point (ºC) -11 4 N/A N/A N/A N/A Autoignition Temperature (ºC) 498 480 N/A 680 770 N/A

Critical Temperature (ºC) 288.9 318.6 71.9 214.1 183.7 139.3

Boiling Temperature (ºC) 80 111 -36.8 48 27.8 6.2

Reduced Teva 0.960 0.983 0.990 0.958 0.926 0.983 Specific Vaporization Heat

at Th (kJ/kg) 166.06 104.34 25.55 64.53 93.91 59.20

Vaporization Heat Ratio At Th (%)

24.8 18.3 31.1 28.5 42.9 32.12

Vapor Expansion Ratio 195.5 841.9 4.0 43.9 16.3 14.8

Molecular Complexity 4.22 8.91 4.68 6.59 1.68 3.02 Molecular Mass (kg/kmol) 78.1 92.1 188 187.4 152.9 152.0

Acentric Factor 0.2092 0.266 0.317 0.25253 0.28192 0.3794

Reported Condition

Saturated

basic cycle

Th=266.5ºC Ph=37 bar Tl=40.0 ºC Pl=0.25 bar

Saturated

regenerative cycle


Pl=0.075bar

Saturated

regenerative cycle

Th=68.6ºC Ph=25 bar Tl=29.9 ºC Pl=10 bar

Saturated basic cycle

Th=193.5ºC Ph=25 bar Tl=40.0 ºC Pl=0.78 bar

Saturated basic cycle

Th=150.0 ºC

Ph=21 bar Tl=40 ºC

Pl=1.54 bar

Saturated regenerative

cycle Th=132.2 ºC

Ph=30 bar Tl=36.4 ºC Pl=3.00 bar

Efficiency at Reported Condition 24.5 29.43 4.6 18.2 15.9 13.67

* Material is not listed under Toxic Substance Control Act (TSCA)


21. 1



PATCHING TOPOLOGICALLY SIMPLE HOLES IN UNSTRUCTURED MESH USING NON-UNIFORM RATIONAL B-SPLINES

Amitesh Kumar, Alan M. Shih University of Alabama at Birmingham

Birmingham, Alabama, USA

ABSTRACT This paper presents a hole patching algorithm for discrete

geometry using surface based hole patching approach. The algorithm uses Non-Uniform Rational B-Splines (NURBS) curves and surfaces for creating patches for holes. This algorithm is focused on recovering the missing geometric information based on the neighboring points surrounding the topologically-simple but geometrically-complex holes using concentric rings analogy. This algorithm can automatically identify the hole, obtain surrounding points, create a set of NURBS surfaces, and perform the projection of points onto the the NURBS surfaces to complete the process. It describes the algorithm step-by-step in details. Several complex geometries are used to demonstrate the success and applicability of the algorithm. Finally, a summary provides the overall assessment of this research and identify its weaknesses for future improvements.

INTRODUCTION

Computer-Aided Engineering (CAE) is increasingly playing a critical role in design, analysis, and performance predictions in mesh based computational simulations disciplines such as Computational Fluid Dynamics (CFD) and Computational Structure Mechanics (CSM). They facilitate complex design tasks and analysis processes while cutting significant amount of costs. However, before any CFD or CSM algorithms can be applied to analyze the design, a high quality mesh has to be generated. This process in turn relies on the availability of a watertight geometry. Unfortunately, such watertight geometry may not always be available due to deficiencies such as gaps and holes. This is sometimes true even for engineering configurations designed with a sophisticated Computer-Aided Design (CAD) system. Discrete geometry acquired through reverse engineering process or geometry reconstruction is even more likely to have such a deficiency. “Repairing” such defective geometry is often a tedious and labor-intensive process. Model repair is the task of removing defects or artifacts from a geometric model to produce an output model that is suitable for further processing

by downstream applications that have certain quality requirements on their input.

Many literatures proposed different approaches in an attempt to address this issue in a more automated and intelligent manner. These approaches broadly fall in two main categories: volume-based repair methods and surface-based repair methods. Volume Based Repair Methods

The key to all volume based methods lies in converting a surface model into an intermediate volumetric representation from which the output model is then extracted. Examples of volumetric representation that have been used in model repair include regular Cartesian Grids, adaptive octrees, kd-trees, BSP-trees and Delaunay triangulations. A flag at each voxel of the volumetric representation is generated representing whether the particular voxel lies inside or outside of the geometry. Due to their very nature, volumetric representations do not allow for artifacts like intersections, holes, gaps or overlaps or inconsistent normal orientation. Volumetric algorithms are typically fully automatic and produce watertight models and depending on the type of volume, they can often be implemented very robustly [1].

Volume based approaches to mesh repair also pose some potential problems. The conversion to and from a volume leads to resampling of the model. It often introduces aliasing artifacts, loss of model features and destroys any structure that might have been present in the connectivity of the input model. The number of triangles in the output of a volumetric algorithm is usually much higher than that of the input model and thus has to be decimated in a post-processing step. Also, the quality of the output triangles often degrades and has to be improved afterwards. Finally, volumetric representations are quite memory intensive so it is hard to run them at high resolutions. If the fidelity of the data is of utmost importance then we might want to consider the surface based approaches which respects the triangulation on the original mesh and hence preserves the original data in this process.

Nooruddin and Turk [2] proposed one of the first volumetric techniques to repair arbitrary models containing


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gaps, overlaps and intersections. In his method the model is converted into Cartesian voxel grid using parity-count and ray-stabbing methods. The model is projected onto an orthogonal planar grid. A voxel is classified by a ray to be inside, if it lies between two extreme depth samples, otherwise it is classified as outside. The final classification of each voxel is derived from the majority vote of all the rays passing through that voxel. A Marching Cubes algorithm [3] is then used to extract the surface between inside and outside voxels. Nooruddin and Turk [2] further took advantage of the common morphological operators, such as dilation and erosion [4], used in 3D digital image processing techniques as low pass filters to fill small gaps and tubes on the intermediate volume representation.

Bischoff et al. [5] proposed an improved volumetric technique to repair arbitrary triangle soups using user provided error tolerance value ε and a maximum diameter value ρ up to which gaps should be closed. Their algorithm first creates an adaptive octree representation of the input model where each cell stores the triangles intersecting with it. Then a sequence of morphological operations [4] is applied to the octree to determine the topology of the model. Finally, a Dual Contouring algorithm reconstructs the interface between the outside and the inside cells by connecting sample points. This produces guaranteed manifold output along with well preserved features. However, despite the adaptive octree, the resolution of the reconstruction is limited.

Shen et al. [6] proposed a volumetric repair algorithm that operates on arbitrary triangle soups. His algorithm makes use of a scattered-data interpolation method known as moving least-squares, commonly abbreviated as MLS. Their algorithm produces watertight models and automatically bridges gaps in an intuitive way however it does not cope well with the models that contain interior excess geometry and suggests removing them in preprocessing steps before using their algorithm on the models.

Davis et al. [7] and Curless et al. [8] proposed a methods to repair a mesh using volumetric approach. In their methods, the inside-outside flags are generated with the help of distance map of each point on the geometry using line-of-sight information, which is usually obtained from range-finding devices. This crucial piece of information may not be available for a purely computational geometric model. The uncertain voxels are assigned with flags based on volumetric diffusion [7]. Once all the voxels are assigned flags, the volume-based methods simply extract the contour to find a closed surface. Curless and Levoy [8] proposed a hole filling algorithm based on volumetric diffusion optimized for patching holes in models reconstructed by range-finding devices. These devices generally create very high resolution computational models which may contain holes of complex topologies due to occlusion as well as surface reflections and refractions.

Ju [9] presents a method for generating signs of voxels for repairing a polygonal mesh using an adaptive octree approach. In his paper, Ju mentions that the method, although simple in conception and design, may not be able to produce satisfactory

results for those cases which have complex holes with multiple boundaries or highly curved shapes. His algorithm produces guaranteed manifold output by the virtue of using volumetric method, however it has problem handling thin structures.

Podolak et al. [10] proposed an algorithm for 3D hole filling based on a decomposition of space into atomic volumes, which are each determined to be either completely inside or outside of the model. It is done so by computing a minimum-cost cut of a graph representation of the atomic volume structure that is guaranteed to produce non-intersecting patches. Surface Based Repair Methods

This class of repair methods operates directly on the input data and tries to explicitly identify and resolve artifacts on the surface. Surface oriented repair algorithms only minimally perturb the input model and are able to preserve the model structure in areas that are away from artifacts. In particular, structure that is encoded in the connectivity of the input or material properties that are associated with triangles or vertices are usually well preserved. These repair algorithms usually require that the input model already satisfies certain quality requirements such as error tolerances to guarantee a valid output. As these requirements cannot be guaranteed or even be checked automatically hence these algorithms are rarely fully automatic and require manual post-processing. Furthermore, due to numerical inaccuracies, certain types of artifacts like intersections or large overlaps etc. cannot be resolved robustly. Other artifacts, like gaps between two closed connected components of the input model that are geometrically close to each other, are difficult to even identify using surface based repair methods [1].

Turk et al.’s mesh zippering algorithm [11] was one of the first algorithms which tried to fuse range images using surface based approach and in this process eliminated a lot of overlaps and mesh defects. This algorithm specialized in working only with range scans.

Barequet and Sharir [12] use a dynamic programming method to find minimum area of triangulation of a three-dimensional (3D) polygon in order to fill mesh holes. Barequet and Kumar [13] describe an interactive system that closes small cracks by stitching corresponding edges and fills big holes by triangulating the hole boundary similar in approach to Barequet and Sharir [12]. Their methods, in general, are optimized for the defects generated by the CAD programs while joining the surfaces to create models, which sometime leaves narrow cracks. These algorithms also do not guarantee the quality of the output.

Borodin et al. [14] proposed a progressive gap closing algorithm which works by vertex edge contraction accompanied with insertion of vertices on the boundary edges and progressively contracting the edge. This is implemented by identification of corresponding vertex-vertex pairs and vertex-edge pairs. This method although simple in implementation, is however only suitable for narrow gaps in 3D space where such


21. 3

contraction doesn’t end up dramatically altering the surface smoothness and triangle size gradation.

Leipa [15] describes a method for filling holes by a weight-based hole triangulation, mesh refinement based on the Delaunay criterion and mesh fairing based on energy minimization as used in Kobbelt et al. [16]. The algorithm reliably closes holes in models with smooth patches with the density of the vertices in the filled area matching that of the surrounding surface. The complexity of building the initial triangulation is O(n3), which is sufficient for most holes that occur in practice. However, the algorithm does not check or avoid self intersections and does not detect or incorporate isles into the filling.

Jun [17] describes an algorithm based on stitching planar projection of complex holes and projecting back the stitched patch. This method presents significant complexity of implementation if the holes have twists shape-wise and if their intermediate projection onto a surface are self-intersecting. The resultant patch produced in this manner also may not look very elegant or smooth.

Bruno [18] attempts to fill a hole and blend surface based on global parameterization for complete geometry approximation and then energy minimization for surface blending based on the assumption that global parameterization of the complete model is available or possible.

Branch et al. [19] suggest a method for filling holes in triangular meshes using a local radial basis function. The method works quite well with skinny holes, but fails when the holes are rounder in shape.

Kumar et al. [20] presents a NURBS curves and NURBS surfaces based hole patching algorithm using concentric ring which produces smooth patches. The reliability of their method is dependent on the reliability of initial triangulation algorithm used in 3D space. The density of the vertices matches that of the average density of the surrounding vertices in the neighborhood of the holes. This algorithm only repairs the meshes with topological simple holes and doesn’t detect or incorporate isles into the filling.

Gueziec et al. [21] introduced two different strategies for stitching edges: pinching and snapping. The pinching strategy only stitches along edges that belong to the same connected component. In contrast to pinching, the snapping strategy reduces the number of connected components of the model.

The usability of most of these algorithms, with the notable exception of Leipa [15] and Kumar et al. [20], is constrained by their assumptions related with shape, size or source of the holes. CURRENT WORK

In this paper, an automatic surface based method is presented for patching holes on a triangulated surface model to achieve watertight surface. The existing points around the holes are used to obtain a set of Non-Uniform Rational B-Splines (NURBS) surfaces approximating the missing surface patches. A Delaunay triangulation method is used to generate internal

points which are then projected on to a set of NURBS surfaces to obtain the desired patch. The patches generated by this method are achieved with minimal alteration of the geometric information of the surrounding geometry. This algorithm is currently applicable to topologically simple but geometrically complex holes in the discrete geometry as a triangular mesh. Such holes are common in the geometry obtained from 3D scanners or geometry extracted from the medical image datasets using the marching cubes algorithm [3]. This method is different from other surface-based approach in many significant ways:

It makes no assumption about the orientation, shape, size or origin of the holes on the surface.

It provides a new analogy of non-intersecting rings on unstructured mesh.

The user has control over the size and density of the triangulation in the hole patching process.

The patches so produced are smooth even in highly complex areas. HOLE IDENTIFICATION

A hole is a closed set of edges with only one neighboring polygon or triangle for each of the edge in that particular set. Hole identification in a given unstructured surface mesh is the first step towards hole patching. A hole on an unstructured surface mesh is identified by looking for an edge which is shared by only one triangle. Once such an edge is found, the edges of its neighboring triangles are checked to find the presence of an edge which also shares only one triangle. This iterative process provides connecting edges which eventually form a loop. The loop thus obtained is a hole on the given unstructured surface mesh. HOLE TRIANGULATION

Hole triangulation is a multi-step process. It consists of initial triangulation of the holes identified, repeated point insertions and edge swapping based on Delaunay criteria. Point insertions and edge swapping is done to create points and good quality triangle inside the hole region. Candidate triangle for point insertion is found based on two stopping criteria which are:

Longest edge length on a given hole boundary: A candidate triangle having longest edge is chosen such that it is longer than either the longest edge on the hole or a pre-specified edge length to control resultant triangle size.

Average area of the triangles surrounding the hole on the original mesh: A candidate triangle with the largest area in the triangle database is found such that largest area is larger than the average area of triangles surrounding the hole.

A point at the centroid of the candidate triangle is inserted and is connected to its vertices resulting in the creation of three additional triangles and deletion of the original triangle from the database. Edge swapping checks based on Delaunay criteria are performed on each edge of the each newly created triangle to obtain better shaped triangles. This iterative process


21. 4

produces a fine mesh from a given initial triangulated mesh that approximately represents missing surface over the hole. Figure 1 (a) shows result of initial triangulation over a hole in 3D space while figure 1 (b) shows result of repeated point insertion and edge swapping on the initial triangulation result obtained in 1 (a).

RINGS AND RING CURVES SURROUNDING THE HOLE

A ring on an unstructured surface mesh can be defined as

an ordered set of vertices on the mesh. Its salient properties are as follows:

Each point on a ring is a vertex of a triangle on the mesh. Each edge of a ring is an edge of a triangle on the mesh. Each ring for a given hole is non-intersecting with any

other ring for that particular hole. No ring can ever intersect its parent hole. Each of the rings is incrementally numbered with the

ring closest to the hole numbered as 1st while the hole itself is numbered as 0th ring.

Two consecutively numbered rings are separated by a band of triangles.

A ring curve is the second order NURBS curve representation of the ring where the vertices on the ring are treated as the control points for the NURBS curve. The beginning and end control point are defined as one and same to get a closed loop. Ring curves are smoother representation of the original rings and are influenced by the position of neighborhood control points or vertices. This characteristic provides us with an ideal tool to create an approximation of the missing surface over the hole which would also reflect the influence of the surrounding geometry. In this research, alternate ring curves numbered 0th, 2nd, 4th and 6th have been used as a guarantee that they would never intersect each other. Ring curves have been used as a mean to incorporate geometric information surrounding the hole while designing NURBS surface. Figure 2 shows bands of triangle in different colors around a hole on an unstructured mesh forming rings around that hole. NURBS SURFACE PATCHES

The ring curves generated in the previous section are used to generate a set of smooth NURBS surfaces approximating the missing region. For describing this process we will use a simplistic representation as shown in figure 3 where hole region is shown in yellow and ring curves in red. Each of these closed curves is then divided into four segments to form a four-sided surface. The NURBS corresponding to the hole or ring curve 0 is divided in to four segments at ui

t values of 0.0, 0.25, 0.5 and 0.75 at points p1, p4, p7 and p10 where ui

t is the parametric value used in the NURBS curve formulation. These four points are projected onto 2nd, 4th and 6th ring curves using nearest point projection technique to form a four-sided surface inside. An incrementing variable t 10 t is used, as shown in equation (2), to create a set of NURBS surfaces which completely cover the region surrounding the hole in all directions and collectively show the influence from every direction.

Let the NURBS curve representation of the hole and the

2nd, 4th and 6th rings be represented by R0, R2, R4 and R6,

Figure 3. Simplistic Representation of the control net for NURBS surface

Figure 1. (a) Initial Triangulation (b) Triangulation after repeated point insertions and edge swapping

(a) (b)

Figure 2. Visual representation of rings around a hole


21. 5

respectively. Let P be the set of 12 points found on R0 by using a set of scalar values ui (i = 1, 2,…, 12) in the parametric NURBS curve. A parameter, t, increases with each incremental rotation of the rings around the hole.

1221 ,...,, pppP (1)

10 12

1 where,

110

1

ti

tu

u

u

u

uu

i

i

i

i

ii

(2)

Each of the points p2, p3, p8 and p9 is projected on the NURBS curve approximation of rings R2, R4 and R6 using nearest point projection to obtain three sets of four additional points designated as {r2p2, r2p3, r2p8, r2p9}, {r4p2, r4p3, r4p8, r4p9} and {r6p2, r6p3, r6p8, r6p9}, respectively. These points are used to obtain two ordered sets of control points S1 and S2 as shown in equation (3):

868482833234362

969492922224261

,,,,,,,,,,,,,,

prprprppprprprS

prprprppprprprS

(3)

S1 and S2 are used to create two NURBS curves, NS1 and

NS2, and they are used to obtain four additional points in the hole region designated as p1s1, p2s1, p1s2 and p2s2 by varying u values of the NURBS curves NS1 and NS2. Let u2 and u9 be the parametric positions of points p2 and p9, respectively, on NURBS curve NS1. Parametric positions of points p1s1 and p2s1

are obtained as 292 31

uuu and 292 32

uuu ,

respectively. Points p1s2 and p2s2 on NS2 are obtained in the similar fashion.

Let S3, S4, S5 and S6 be four sets of control points given as follows:

76546

8222135

9121124

10111213

,,,,,,,,,

,,,

ppppS

pspsppS

pspsppS

ppppS

(4)

These four sets of control points are used to obtain four

interpolating NURBS curves, which are collectively used to create a lofted NURBS surface.

A number of lofted NURBS surfaces are obtained by varying t value corresponding to the rotation. Each of the ring curves is divided into four segments for constructing a NURBS surface. The starting points are obtained by varying t

corresponding to a chosen increment angle (t = 0, 1/N, 2/N,…, (N-1)/N) where N is the number of desired rotations. PROJECTION OF POINTS IN THE HOLE REGION ONTO NURBS SURFACE PATCHES

All interior points on the fine mesh generated after hole triangulation are projected on to a set of lofted NURBS surfaces to find a set of coordinates for each point. A simple average of these projections is used to find the final coordinates which forms a good approximation for the hole region. In general increasing the number of approximating NURBS surface has been seen to provide a better result in general. This is done by incrementing the value of t in equation (2). In general value of t is a function of angle of rotation hence decrementing the angle of rotation of the control net would increase the number of NURBS surfaces generated. All the point not on the boundary of hole are projected onto a set of the NURBS surfaces generated in section 0. Although this approach provides an exceptionally good approximation of the missing surface in the interior of the hole region it could still cause a sudden discontinuity or bump at the interface of the patch and the original hole. SMOOTHING OF POINTS ON THE PATCH AND SURROUNDING TRIANGLES

Depending on the geometry of the hole, after projection of

points on to a set of NURBS surfaces, a slight bump could be visible at the interface of the patch and the hole. The bump in general becomes more and more pronounced when the holes becomes bigger in size or more complex in shape. As a result it becomes necessary to use smoothing technique to get rid of bump and to be able to provide a smoother transition. It was found out that the triangles enclosed between first two rings and the hole when smoothed with the patch produced a far smoother gradient. Laplacian smoothing is applied for this purpose. This approach not only creates a smoother patch but also maintain connectivity with the original mesh. Figure 4 qualitatively shows the smoothness of the patched surface. The

Figure 4. A patched surface after smoothing of the patch and surrounding triangles


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patch has been painted in a lighter shade to help distinguish it from the background mesh. RESULTS

ETLab Human Skull model: The human skull, shown in

figures 5 (a) and 5 (b), is obtained from an incomplete CT Scan dataset after image processing, segmentation and contouring using Marching Cubes algorithm at Enabling Technology Laboratory (ETLab), UAB. The data was not properly registered prior to image processing and segmentation resulting in sudden discontinuity in the data and hence crest and trough on the resultant skull surface. The incompleteness of data resulted in12 holes on the top and the bottom of the skull while contouring the image data after segmentation of skull from the CT scan dataset. One of those twelve holes is at the top of the skull in the region where parietal and frontal bone of the skull meet resulting in an incomplete dome. The skull surface is made of 778,132 triangles and 389,242 points. The hole patching algorithm was run on this human skull model and it created 12 patches corresponding to the 12 holes on its surface. The Patches are made of 23,749 triangles and 12,654 points. Figures 5 (a) and 5 (b) shows the patches in yellow placed on the skull surface in green. It needed 74.946 seconds for the computer code to complete the process.

INRIA Pagoda Lion: The Pagoda Lion model was scanned by Geometrica Group at INRIA using Minolta Vivid 910 Laser Scanner. The model is available on the Aim@Shape Project Repository [22]. The model so obtained is a dirty model with non-manifold complex edges and numerous small surface fragments and defects. The small surface fragments were removed before running the Hole Patching Algorithm although non-manifoldness of the model was not corrected. The model so obtained is made up of 481,712 triangles and 249352 points and has 325 holes of various sizes and complexities on it. The Hole patching computer program needed 429.935 seconds to generate patches made up of 129,309 triangles and 73226 points. Not all holes could be filled because non-manifold nature of many edges and mesh overlaps present in the model as well as some of the inherent inadequacies of the initial triangulation algorithm used in this method. The initial triangulation algorithm used in this work fails on few complex or extremely large sized holes which were present in this model

but we can observe however that a large number of holes have been filled as shown in Figures 6 (a) and 6 (b). Figure 6 (c) shows a ridge feature which was reconstructed using this algorithm.

ISTI Amphora: Amphora is a low resolution digital model

of an ancient Greek two handle terracotta vase originally scanned at Visual computing Lab, ISTI using Minolta Vivid 910. The model is available at Aim@Shape repository [22]. This low resolution model is made up of 17,975 triangles and 9,015 points with 33 holes on its surface. The Hole Patching algorithm needed to 1.0147 seconds to patch the terracotta vase with 462 triangles and 353 points. Figures 7 (a) and 7 (b) shows the Amphora model with patches in red placed on it. SUMMARY

A reasonably successful method of patching holes using is presented in this paper using a number of examples. The algorithm was tested against holes of various complex shapes, sizes and geometry and is applicable to topologically simple holes on unstructured mesh as commonly seen in the discrete geometries from various sources. This method can recover the missing geometry features with satisfactory results without

Figure 6. INRIA Pagoda Lion showing (a) front view, (b) back view, (c) Ridge feature restored.

(a) (b)

(c)

(a) (b)

Figure 5. ETLab Human Skull model showing (a) Bottom view, (b) Side View.


21. 7

significantly altering the surrounding geometric characteristics near the hole. The method is automatic, fast and simple to use. The usability of the method has been shown using biomedical and computational models with complex geometry and shape of holes. The quality of the patch depends on size and the geometric complexity of the hole as well as the coarseness of the surrounding mesh.

This method is particularly useful in the cases where high

curvature holes exist, eliminating the need for an intermediate plane on which those high curvature holes would have otherwise been needed to be projected before triangulation. The intermediate fine triangulation obtained using this algorithm produces a surface which lies roughly in the middle of the curvature making it easier to project on to the NURBS surface.

The approach of using rings as a mean to define the geometrical characteristics of a surface is robust even when two holes lie in the vicinity of each other as rings would either stop on the boundary of the other hole or would simply go around it depending upon user implementation.

Although the method produces smooth and good quality patches, its success to a great degree depends on the success of initial triangulation over the hole. This algorithm is suitable only for models with topologically simple holes. Those models with topologically complex holes will require manual modification to the models in order to remove the islands before applying this algorithm.

The computer models with dirty geometry, having a number of surface artifacts such as topologically complex holes, overlaps etc., may not be very suitable for using surface based method because of its inherent limitations as discussed earlier. Additionally, in those cases where preserving original mesh is not of utmost concern, we may want to explore volume based approach for mesh repair.

ACKNOWLEDGEMENTS This research is supported in part by the NASA

Constellation University Institutes Project (CUIP) No. NCC3-994. REFERENCES [1] Botsch M., Pauly M., Kobbelt L., Alliez P., L´evy B., Bischoff S. and R¨ossl C., 2007 “Geometric Modeling Based on Polygonal Meshes,” ACM SIGGRAPH 2007 Courses - International Conference on Computer Graphics and Interactive Techniques. [2] Nooruddin F.S., Turk G., 2003, “Simplification and repair of polygonal models using volumetric techniques,” IEEE Transactions on Visualization and Computer Graphics, 9(2):191–205. [3] Lorenson E. Williams, Cline E. Harvey, 1987, “Marching Cubes: A High Resolution 3D Surface Construction Algorithm”, ACM Computer Graphics, Volume 21, Number 4. [4] Gonzalez C. Rafael, Woods E. Richard, “Digital Image Processing”, Prentice Hall; 3rd edition, ISBN-13: 978-0131687288 [5] Bischoff S., Pavic D., and Kobbelt L., 2005, “Automatic restoration of polygon models.” Transactions on Graphics, 24(4):1332–1352. [6] Shen C., O’Brien F. J. and Shewchuk R. J., 2004, “Interpolating and approximating implicit surfaces from polygon soup.” In Proc. of ACM SIGGRAPH 04, pages 896–904. [7] Davis, J., Marschner, S. R., Garr, M. and Levoy, M., 2002, “Filling Holes in Complex Surfaces using Volumetric Diffusion,” Proceedings of First International Symposium on 3D Data Processing, Visualization, Transmission, pp. 428-861. [8] Curless, B. and Levoy M., 1996, “A Volumetric Method for Building Complex Models from Range Images,” Computer Graphics, Vol. 30, pp. 303-312 [9] Ju, T., “Robust Repair of Polygonal Models,” Proceedings of ACM SIGGRAPH, 2004 ACM Transactions on Graphics, Vol. 23, pp. 888-895. [10] Podolak J. and Rusinkiewicz S., 2005, “Atomic volumes for mesh completion.” In Symposiuon Geometry Processing. [11] Turk, G. and Levoy, M., 1994, “Zippered Polygon Meshes from Range Images,” In Proceedings of ACM SIGGRAPH 94, pages 311-318. [12] Barequet, G. and Sharir M., 1995, “Filling Gaps in the Boundary of a Polyhedron,” Computer Aided Geometric Design, Vol. 12, pp. 207-229. [13] Barequet, G. and Kumar, S., 1997, “Repairing CAD Models,” Proceedings of IEEE Visualization 1997, pp. 363-370. [14] Borodin P., Novotni M. and Klein R., 2002 “Progressive Gap Closing for mesh repairing.” In J. Vince and R. Earnshaw, editors, Advances in Modelling, Animation and Rendering, pages 201-213, Springer Verlag. [15] Liepa, P., 2003, “Filling Holes in Meshes,” Proceedings of the 2003 Eurographics/ACM SIGGRAPH Symposium on

Figure 7. ISTI Amphora model showing patches in red from (a) top view and (b) bottom view.

(a) (b)


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Geometry processing, Eurographics Association, pp. 200-205. [16] Kobbelt, L. P., Vorsatz, J., Ulf, L. and Seidel, H.-P., 1999, “A Shrink Wrapping Approach to Remeshing Polygonal Surfaces,” Computer Graphics Forum (Eurographics ‘99), Vol. 18, pp. 119-130. [17] Jun Y., 2005, “A Piecewise Hole Filling Algorithm in Reverse Engineering,” Computer-Aided Design, Vol. 37, pp. 263-270. [18] Bruno, L., 2003, “Dual Domain Extrapolation,” ACM Transactions on Graphics (SIGGRAPH), Vol. 22, pp. 364-369. [19] Branch, J., Prieto, F. and Boulanger, P., 2006, “A Hole-Filling Algorithm for Triangular Meshes using Local Radial Basis Function,” Proceedings of the 15th International Meshing Roundtable, Springer, pp. 411-431. [20] Kumar, A., Shih M. A., Ito Y., Ross H. D., Soni K. B., 2007, “A Hole-Filling Algorithm Using Non-Uniform Rational B-Splines,” Proceedings of 16th International Meshing Roundtable, Springer Berlin Heidelberg, Page 169-182. ISBN: 978-3-540-75102-1. [21] Gu´eziec A., Taubin G., Lazarus F. and Horn B., 2001, “Cutting and Stitching: Converting Computer sets of Polygons to Manifold Surfaces.” IEEE Transactions on Visualization and Graphics, 7(2):136–151. [22] See Aim @ Shape Project – Shape Repository, as on August 18 2009, http://shapes.aim-at-shape.net/viewmodels.php




IN-CYLINDER FLOW VELOCITY MEASUREMENTS IN A BRIGGS-STRATTON ENGINE

Marcus Ashford, Semih Ölçmen, Tad Driver, Philip Schinetsky, Jason Davis, Mebougna Drabo The University of Alabama Tuscaloosa, Alabama, USA

ABSTRACT Unsteady velocity measurements within a motored Briggs and Stratton single-cylinder air-cooled engine are reported. Single-component of the velocity was obtained using a fiber-optic spark-plug LDV probe. Data were acquired under motored conditions at ~600 RPM. Data was analyzed to demonstrate the capability of the spark-plug LDV probe in resolving the unsteady nature of the IC velocity at a single point and to demonstrate the high velocity variations that occur in such an engine. Data was analyzed to determine the mean and the fluctuating velocity components using the wavelet decomposition technique. Both mean and fluctuating velocities indicate to the cycle-to-cycle variation in the engine. Fluctuating velocity variations indicate that the flow is highly turbulent during the intake stroke as well as at the beginning of the exhaust stroke within this motored engine. I. INTRODUCTION

Measurement of flow velocity within the cylinder of actual engines proves to be difficult due to the limited access to the engine cylinder. Flow velocity measurements are usually conducted in engines with optical access under motored conditions. Miniature fiber-optic, laser based probes that can used in such cramped environments has been developed to further increase the measurement capabilities in such flows. Esirgemez and Ölçmen [1], developed a miniature, traversable LDV probe that could be inserted into the spark-plug hole, and Ivanchenko et al [2], has developed a miniature, three-simultaneous component LDV probe. The working principle of the probes was demonstrated in free-jet flows and the two-component probe has been used to obtain brief data in a Honda engine. This paper discusses the use of a single-component LDV probe measurements in a Briggs and Stratton single cylinder engine under motored conditions. The goal of the research was to obtain high data rate velocity measurements in an off-the-shelf engine that could be

used in comparison to engine data under fired conditions. The measurements reported are the first of a kind to reveal the high fluctuating velocity values that can occur in ordinary engines.

Another focus of the current research is the use of Wavelet Decomposition (WD) in understanding the cycle-to-cycle variation of turbulence of in-cylinder flows. In a recent work [3], existing methods, including the Proper Orthogonal Decomposition, WD, and Principal Component Analysis together with WD, were compared to each other in separating the mean and the fluctuating components of a simulated unsteady in-cylinder flow signal. In that study an unsteady mean velocity signal and a turbulence signal with a predefined spectrum were used to generate a composite signal to mimic experimental data obtained in an IC engine. The signal duration, turbulence standard deviation, and the cyclic variations in the turbulence signal were varied and the methods were employed to re-obtain the defined mean and the fluctuating velocity components. Among the methods the WD technique was observed as the best technique. In the following sections first the engine used in the study is introduced. The LDV probe is briefly described. Velocity, pressure, and crank angle measurements are discussed together to describe the flow velocity variation and cycle-to-cycle variation of the flow velocity within such an engine. The data is further analyzed to discern the mean velocity from the fluctuating velocity using the wavelet-decomposition technique. Conclusions on the results are given last. II. EXPERIMANTAL SETUP

II.A. Engine The engine used in the current research was a Briggs and Stratton single-cylinder air-cooled engine designed for low emission operation. Engine data are given in Table 1. Crankshaft angular position was determined via a BEI H25 incremental encoder with 0.05° crank-angle (CA) resolution. In this paper, 0° CA corresponds to top dead center (TDC) at the beginning of the intake stroke.

ASME 2009 Early Career Technical Journal, Vol. 8 164

Cylinder pressure data were measured with a Kistler 6041A piezoelectric pressure transducer coupled to a Kistler Type 5010 charge amplifier. Engine data were recorded by a National Instruments USB-6221 data acquisition system. The DAQ also provided a time synchronization signal to the LDV system. The engine was motored at 600 RPM using its starter and a freshly charged 12 Volt battery.

Table 1 Briggs and Stratton Test Engine Relevant Data

Engine Model and Type 256427-1139-E1

Combustion Chamber

L Head

Bore [mm] 87.31

Stroke [mm] 66.68

Displacement [cc] 399.3

Advertised Power [kW]

and Torque [N.m]

8.2kW @ 3600 rpm and

20.3N.m at 2800 rpm

Figure 1a shows a picture of the Briggs-Stratton

engine and the fiber-optic LDV probe. Figure 1b shows the combustion chamber of the engine and the measurement location as shown as the crossing point of the schematic laser beams. Laser beams access into the combustion chamber through a port that was machined to accept an M-8 spark plug. LDV probe was inserted in to a connector placed in to the spark-plug port. The measurement point was chosen at a location close to both the intake valve and the spark plug locations. The measurement probe volume was placed at ~2mm away from the head surface and at ~9.3mm away from the piston when it is at the TDC. Exhaust and intake valve footprints are also shown in the picture. A black tape was placed on the combustion chamber to reduce the reflected laser beams from the surface of the engine. Figure 1c shows the piston at top-dead center together with the intake and the exhaust valves. Figure 2 shows the crank angle vs. piston lift, exhaust valve lift and the intake valve lift. Zero degree corresponds to the piston at the TDC (Figure 2a). With each successive 180° crank angle turn engine goes through the intake (360-540°), compression (540-720°), work (0-180°) and the exhaust strokes (180-360°) of a cycle. The intake valve lift profile indicates that the valve stays open well into the compression stroke (Figure 2b), in order to reduce the effective compression ratio for easier hand starting. Additionally the intake valve and the exhaust valve are both opened simultaneously close to the end of the exhaust stroke and the intake stroke to force the exhaust gases to aid heating the incoming air-fuel mixture and to improve scavenging. Initial to the experiments the engine head was removed and the measurement probe volume was placed at the desired measurement location. Next the engine head

was placed and secured. During the experiments Di-octylphatalate particles with a mean size of 0.7 microns generated using a TSI-six-jet atomizer was fed through a

Figure 1 – a) Briggs and Stratton engine used in the study, b) the combustion bowl, crossing of the schematic laser beams indicate the measurement probe volume, c) intake, exhaust valves and the piston.

A

B

C


pipe to the air intake of the engine.

II.B. LDV System In the present work, one velocity component in a plane perpendicular to the piston axis was measured using the LDV probe previously described [1]. In the previous work, a two-simultaneous velocity component, miniature LDV probe that could be placed in the spark-plug hole of a typical automobile engine was discussed. In the following sections the LDV system is briefly described. The LDV system includes the on-table equipment, the probe, and the data acquisition and reduction units. On-table optical equipment are used to generate the laser beams and to couple them to fiber-optic cables that transfer them to the probe head. The probe head is used to generate the measurement probe volume and to collect the scattered light from the particles within the flow. The scattered light is further transferred to the data-acquisition and reduction units using a fiber-optic cable.

II.B.1 On-table Optics A schematic of the on-table equipment is shown in

Figure 3. A Coherent-Innove-308 with a maximum output of 8W-all-lines, equipped with an etalon and a single-line mirror is used as the light source. The green (514.5 nm) laser beam with a diameter of 1.9mm and a polarization direction perpendicular to the optical table emerging from the laser first reflects from two mirrors to allow the use of the on-table space. The laser beam next passes through a polarization rotator and a polarizing-beam-splitter couple acting as a variable intensity beam-splitter to obtain a low power second laser beam that could be needed in system alignment. Beam passing through the BSC next the beam passes through a Bragg cell unit (Intra-Action AOM-70), to split the beam into two separate beams. While the zeroth order beams pass through without a frequency shift, the first order beam emerging from the Bragg cell experiences a +70MHz

frequency shift. Both beams are next coupled to polarization-maintaining optical fibers (Corning® PM 48-P-S) using laser-to-fiber couplers (Newport, F-91-C1) to transmit the beams to the LDV probe head. Each end of the optical fibers were terminated using an ST-PC type terminator at the on-table optics end and machinable ceramic ferrule fiber terminators at the probe end. The polarization directions of the emerging beams at the probe end were made parallel by rotating the fiber terminators, while observing the beams through a polarization direction finder.

II.B.2 LDV Probe The probe houses transmitting and receiving fiber terminators and lenses (Figure 4). Beams emerging from the terminators first pass through separate lenses for collimation. Table 2 gives the details of the lenses and the probe. Next, the collimated beams pass through a single achromatic lens, which focus them to the measurement probe volume. Probe volume is formed at the intersection of the beams. The beam waists were overlapped at the focal point by observing the overlap at a distant wall surface with a microscope objective placed at the focal point (Figure 4). The receiving optics train is also housed in the probe head. The light scattered by the particles passing through the measurement probe volume is collected by two lenses working in tandem and is focused to the receiving optical fiber. The lens couple work with a magnification ratio of 1:6, allowing collection of the light from the whole probe volume in the backscatter mode. A multi-mode, 50m core-diameter receiving fiber is used to transfer the collected light to the data acquisition unit. The outer diameter of the probe is 15mm and the length of the probe is 30mm.

The design of the probe allows measurements of velocities of up to 60mm away from the probe. The probe volume has 70µm x 70µm x 1337µm dimensions.

The probe measures the time-dependent U component of the velocity. Each validated measurement was

Figure 2 – a) Piston lift variation with the crank angle, b)

intake, and exhaust valve lift variation with the crank angle

0 100 200 300 400 500 600 700 800-80

-60

-40

-20

0

crank angle (degree)

pis

ton

lift

(mm

)

100 200 300 400 500 600 700 8000

2

4

6

8

crank angle (degree)exh

aust

- in

take

va

lve

lift

(mm

)

intakeexhaust

Figure 3- On-table optical equipment. M: mirror,

PR: polarization rotator, BSC: beam-splitter cube, BC: Bragg cell, LTFC: laser-to-fiber coupler, PM:

photo-multiplier tube.

0 shifted

40 MHz shifted

BCLTFCLTFC

LASERM

MPRBSC

PM

receiving fiber

transmitting fibers

probe

MM

M

A

B


considered as a velocity value in time. Negative U velocity values correspond to flow velocity into the engine.

Table 2. LDV probe specifications

Focal length (mm) Diameter (mm)

Transmitting lens 60 10 Receiving lens 10 5 Collimating lenses 3 3 Fringe spacing ~5µm nominal Probe volume 70X70X1337µm Probe overall size 30mm long, 15mm

diameter

II.B.3 Data Acquisition and Reduction Units

The scattered light from the in-flow particles collected by the probe is transferred to the data acquisition and reduction units using a 50 μm core diameter multi-mode fiber-optic cable. The light emerging from the fiber is directly coupled into a photo-multiplier (PM) tube (Electron Tubes, 9124SB) to convert the light information to an electrical signal. The signal is next filtered by a 25 MHz high-pass filter to eliminate the low-frequency content and the pedestal within the signal while allowing the frequency content around 70 MHz to pass. High-pass filtered signal is next amplified, and downshifted with appropriate frequency with the use of a mixer and a radio-

frequency generator (B&K 2005B RF) such that the signal frequencies are around 10 MHz. Following the down-mixing process signal is filtered using a 21.7 MHz low-pass, passive filter to further eliminate the high frequency contents within the signal. Next the signal is fed to the frequency domain processor (TSI- FSA-4000) to measure the frequency of the signal. The frequencies measured by the FSA-4000 are then used to determine the Doppler frequencies. TSI frequency-domain processor was operated in 2-20 MHz range resulting in a dynamic velocity range of ~90 m/s.

III. DATA REDUCTION METHODS

The data reduction routines were used to resample the data in equal time intervals and to separate the mean and the fluctuating components of the generated signal. Wavelet decomposition was used to generate the mean and the fluctuating velocity signals in time and these signals were next used to discuss the cycle-to-cycle variation of the velocity components. Resampling the data in equal intervals is required since the routines such as the FFT and the wavelet decomposition requires data to be in equal intervals. In this section the data reduction techniques are briefly described. The data acquired in the excess of 3000 samples/s were resampled. III.A. Sample and Hold Method The Sample and Hold method is a sampling technique used in order to transform the data obtained from the LDV system into a velocity signal with equally-spaced time intervals [4]. This is done because many data reduction methods require data that is acquired at evenly spaced time intervals. The sample and hold method is a popular method of accomplishing the goal of equidistant data points [5], although it has been shown to introduce errors, which can be broken down into a low pass filter and step noise[6][7]. In the current work the sample and hold method is implemented by an in-house code. The code works by taking the LDV data, V(t), and sampling it across equally spaced intervals. The new velocity data, SAHV(t), is generated by setting it equal to V(t) at a time when a particle velocity measured and holding that value constant until another particle velocity is measured when it is set to the corresponding value of V(t). Figure 5 shows the SAHV(t) (solid line) and the new data after re-sampling has been applied (x’s). As Figure 5 shows, with this sample and hold technique, the signal captured from the LDV system is transformed into a continuous stepwise-like data set. The SAHV(t) data is then used as the velocity data to generate velocity data in equal time intervals. III.B. Wavelet Decomposition Wavelet decomposition determines the correlations between the original signal and the prescribed wavelet

Figure 4 - Schematic of the spark-plug LDV

probe and the machined connector.

transmittingfibers

receivingfiber

traversableLDV probe

sapphire insert glass

transmitting and receiving lenses

light receiving cone

measurement probe volume

fiberterminators

collimating lens

machinedspark plug

U


function at different frequency ranges of the original signal [8]. Following the description used by Farge and Schneider [9] continuous wavelet transform is defined as the convolution of a wavelet , with the original signal to determine the wavelet coefficients,

(1)

where

(2)

“a” denotes the scale of the wavelet and related to the frequency of the signal, “b” is time value used in translating the wavelet; are the daughter wavelets generated by translating and dilating (scaling) the mother wavelet. The wavelet coefficients thus calculated can be used to approximate the original signal at different scales. Reconstruction of the original signal is obtained using linear combination of the wavelet and the wavelet coefficients

(3)

where , is a constant and depends on the wavelet used. The coefficients with small scale values correspond to the high frequency component of the signal and the ones with larger scale values correspond to low frequency values. During the reconstruction of the signal, length scales corresponding to the high frequency content can be omitted to obtain the low frequency (or mean) variation of the original signal. A history and a formal description of the wavelet transforms can be found in [10] and [11]. While the mother wavelet can be presented in a functional form for a simple wavelet such as the Haar wavelet, in general an algebraic functional form does not exist. The mother wavelet , which can be a real or complex valued function, is chosen to satisfy multiple conditions, such as the admissibility condition requiring that the energy contained within the wavelet to be a

limited value, zero mean condition requiring the wavelet to have a zero mean value, and a requirement that its higher order moments vanish [10]. In the discretized wavelet transform the scale and the position “t” are described using powers of 2. Matlab [12] gives details about the discrete wavelet transform and the reader is referred to this document for further details. For a continuous signal , the discrete wavelet transform is given as:

(4)

where and the transformation gives the wavelet coefficients, . The original signal can be recovered without any loss using the inverse transform:

(5)

where For a fixed value of j, summation on the m can be written as to give the “detail” at the jth level:

(6)

and thus,

(7)

An approximation to the signal can be made using a limited number of details. For example can be separated into two components, one using indices j J, corresponding to the scales, and one with j J.

(8)

If desired, the reconstructed signal could then be expressed only as “approximation”, , at level J. A relation exists between different approximations as:

(9) Increasing values of J indicates that lesser details are used in generating the approximate signal, thus the approximation becomes closer to signal’s mean variation. The value of J should also not be chosen large such that the details in the mean variation are also sacrificed.

Figure 5 - Sample and Hold technique [11]

A B

Figure 6 a) scaling and b) the wavelet functions for Daubechies-8 wavelet.

0 5 10 15-0.5

0

0.5

1

0 5 10 15

-1

-0.5

0

0.5

1


In the current work Daubechies 8, Symlet 8, and Coiflet 5 wavelets were tested and the results obtained did not vary with the use of different wavelets. Thus Daubechies 8 wavelet was chosen for further analysis of the data. Figure 6 shows the scaling and the wavelet functions for the Daubechies-8 wavelet. In the wavelet decomposition time dependent velocity is thus defined as an approximation plus the details:

(10)

where = , , and

J=6. Statistical quantities are calculated using:

(11)

(12)

IV. RESULTS

The results presented here are for 1 second of data obtained during the engine start. The engine was motored using its starter and a battery supplying 40 Amp to the engine. The data were acquired for periods in excess of 10 seconds with a data rate exceeding 3 kHz and the data were re-sampled at a 40Khz sample rate using the sample-and-hold technique. A high data rate for re-sampling was used in order to allow samples with close separation in time in the actual data to be present in the re-sampled data. Figure 7 shows the variation of the flow velocity together with the piston velocity, piston location, intake valve location, exhaust valve location variations for the first 4.5 engine cycles. Figure 7 and Figure 8 show that

the RPM of the engine increases with the time and the top piston speeds observed during the experiments were ~ 2 m/s. The piston velocity variation indicates that the piston speed changes during the cycle and the velocities within the 120 - 280° and the 480 – 580° crank angle values are slower compared to the rest of the cycle, as one would expect in an unbalanced single-cylinder engine. The flow velocity variation is well correlated with the piston velocity variation in the cylinder (Figure 7). A section of the Figure 7 is re-plotted in Figure 9 for a clearer discussion. In Figures 7 and 9, time=0 corresponds to the beginning of the intake stroke. Once the piston starts moving downward, air is inducted into

the cylinder. The flow velocity during the intake stroke shows high fluctuations. Turbulence during intake is essential to ensure homogenous mixing of fuel and air in the cylinder during normal fired operation. The velocity fluctuations subside during the compression stroke and flow direction reverses at the measurement location. The flow measured reflects a combination of air being pushed into the squish volume and air lost through the (barely open) intake valve. During the expansion stroke flow velocities are small relative to the other three strokes; this is the only period during the cycle that both valves are closed. Upon exhaust valve opening (~0.18 s), the velocity show very high fluctuations and flow into the cylinder. Recall that this engine has a mechanism that opens the intake valve slightly during the large portion of

Figure 8 – Piston velocity variation with the crank angle.

0 100 200 300 400 500 600 700 800-4

-2

0

2

4

angle (degree)

pist

on v

el

Figure 7 – Time variation of the flow velocity, piston velocity,

intake, exhaust and piston lift.

0 0.2 0.4 0.6 0.8 1-70

-60

-50

-40

-30

-20

-10

0

10

20

30

time (s)

velocity (m/s)piston velocity (m/s)inlet valve location (mm)exhaust valve location (mm)piston location (mm)


the compression stroke at speeds such as in this study. The effective compression ratio is reduced, but the expansion ratio remains unchanged. Thus, the in-cylinder pressure is sub-ambient during the latter stages of the expansion stroke, which is reflected in Figure 9b. The result is the high speed inflow observed upon exhaust valve opening, followed by the expected outflow once the pressure equalizes. We do not expect this phenomenon to occur in a fired engine. After time=~0.26 s the next intake stroke begins, with air again inducted in to the cylinder. Figure 10 shows the time variation of the velocity and the time variation of the mean velocity obtained once the wavelet decomposition is applied on the data. The mean velocity variation indicates that the velocity values vary from one cycle to the next, but there is a clear trend to the variation of the mean velocity. Figure 11 shows the fluctuating velocity and statistics. Figure 11a and 11b indicate that the fluctuating velocity values are larger closer to the end of the work stroke than the intake stroke. This fact is also shown in Figure 11c, where the crank angle averaged RMS fluctuating values indicate larger values between crank angles 100 to 200° than in the rest of the cycle. In the near future research the probe will be used in the engine under fired conditions. In these experiments elevated temperature, increased engine RPM and vibration are expected to affect the measurement capability and resolution. Although the probe has been previously employed on highly vibrational environments with success [1], different seeding particles (such as Al2O3) will be employed to reduce soot formation on the access window and increase the data rate in high temperature environments. V. CONCLUSIONS

Velocity measurement experiments conducted using an LDV probe in a Briggs and Stratton engine are reported. Measurements were made during the startup of the engine using the starter of the engine. The data obtained was analyzed using the wavelet decomposition technique to calculate the variation of the mean and the fluctuating velocities in time; cycle-to-cycle variations of the velocity components were observed. Results indicate to the presence of large fluctuations within the engine closer to the end of the work stroke that has twice the standard deviation that of the fluctuations during the intake stroke. ACKNOWLEDGMENTS The work presented in this paper was partially supported the National Science Foundation under award number DGE-0742504. The opinions and findings presented herein do not necessarily reflect the views of NSF or any other Federal or State agencies.

REFERENCES

[1] Esirgemez, E, and Ölçmen, M.S., 2005, “Spark-Plug LDV Probe for In-Cylinder Flow Analysis of Production IC Engines”, Meas. Sci. Technol. 16 (2005) 2038-2047. [2] Ivanchenko, O., Esirgemez, E., and Ölçmen, M.S, 2007, “A three-simultaneous velocity component miniature LDV probe”, Meas. Sci. Technol. 18 (2007) 2014–2020. [3] Ölçmen, M.S., Ashford, M.D., Schinetsky, P.A., and Drabo, M., 2009, “IC Engine Unsteady Flow Analysis”, submitted to Measurement Science and Technology. [4] Benedict, L.H., Nobach, H. and Tropea, C., 2000, “Estimation of turbulent velocity spectra from laser Doppler data”, Meas. Sci. Technol. 11 (2000) 1089–1104. [5] Simon, L., Fitzpatrick, J., 2004, “An improved sample-and-hold reconstruction procedure for estimation of power spectra from LDA data”, Experiments in Fluids 37 (2004) 272–280. [6] Boyer L, Searby G, 1986, “Random sampling: distortion and reconstruction of velocity spectra from fast Fourier-transform analysis of the analog signal of a laser Doppler processor”, J. Appl. Phys., 60(8)2699–2707. [7] Adrian RJ, Yao CS, 1987, “Power spectra of fluid velocities measured by laser Doppler velocimetry”, Experiments in Fluids, 5:17–28. [8] Torrence, C. and Compo, G.P., 1998, “A Practical Guide to Wavelet Analysis”, Bulletin of the American Meteorological Society, Vol. 79, No. 1, January 1998. [9] Farge, M., and Schneider, K., 2002, “Analyzing and Compressing Turbulent Fields with Wavelets”, Institut Pierre Simon Laplace publication, Note No:20 (http://www.ipsl.jussieu.fr/documentation/NAI/index.htm) [10] Farge, M. 1992, “Wavelet Transforms and Their Applications to Turbulence”, Annu. Rev. Fluid Mech., vol.24 , pp: 395-457. [11] Tropea, C.; Yarin, A. L.; Foss, J.F. (Eds.), 2007, Springer Handbook of Experimental Fluid Mechanics, ISBN: 978-3-540-25141-5. [12] Misiti, M., Misiti, Y., Oppenheim, G., Poggi, J-M 2008, Wavelet Toolbox™ 4, User’s Guide, Chapter 6, pp:6.12-6.18.


http://www.ipsl.jussieu.fr/documentation/NAI/index.htm�

….

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

1 atm

time (s)

pres

sure

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

-40

-30

-20

-10

0

10

20

time (s)

velocity (m/s)piston velocity (m/s)inlet valve location (mm)exhaust valve location (mm)piston location (mm)

Figure 9 – a) Time variation of in-cylinder pressure, b) time variation of flow velocity, piston velocity, intake, exhaust and piston lift.

Figure 10 – a) Time variation of the flow velocity, b) time

variation of the mean velocity after wavelet decomposition.

0 0.2 0.4 0.6 0.8 1-60

-40

-20

0

20

40

time (s)

U

0 0.2 0.4 0.6 0.8 1-40

-30

-20

-10

0

10

20

30

time (s)

Uw

d

Figure 11 - a) Fluctuating velocity, , variation in time, b) variation of the in time, c) standard deviation of the velocity calculated at 1º crank angle intervals.

0 0.2 0.4 0.6 0.8 1-50

0

50

time (s)

u wd

0 0.2 0.4 0.6 0.8 10

20

40

60

time (s)

u wd

2

0 100 200 300 400 500 600 700 8000

10

20

30

angle (degree)

σ wd

A A

B

B

C

A

B


23.1

ASME Early Career Technical Journal2009 ASME Early Career Technical Conference, ASME ECTC


SYMMETRIC-GALERKIN BOUNDARY ELEMENT TRANSIENT ANALYSIS OF THE DSIFs FOR PARTICULATE COMPOSITES

V. Guduru and A.-V. Phan

Department of Mechanical EngineeringUniversity of South AlabamaMobile, AL 36688-0002, USA

ABSTRACT Nowadays, fracture behavior of composite materials when subjected to dynamic loading has gained an importance in many industrial applications. Many numerical methods have been developed to deal with this class of problems but every method has its own advantages and disadvantages. In this work, the fracture behavior of particulate composites under impact loading conditions is studied through their dynamic stress intensity factors (DSIFs). The DSIFs at the crack tip in a composite beam is investigated by using the symmetric-Galerkin boundary element method for elastodynamics in the Fourier-space frequency domain and displacement correlation technique. Fast Fourier transform (FFT) and inverse FFT (IFFT) are subsequently employed to convert the DSIFs from the frequency domain to the time domain. A numerical example involving the DSIFs for a three point bend beam made of particulate composite is studied. The DSIF solution is compared with the experimental result produced by the measurement of transient deformations in the beam using digital image correlation method and high-speed photography [1].

1. INTRODUCTION

In general, particulate composite materials are vulnerable under impact loading conditions where loads are applied rapidly, randomly or deliberately such as those seen in aerospace, automotive, production, construction, etc. As a result, it is important to understand the fracture behavior of particulate composite materials under these loading conditions. Many numerical and experimental techniques have been developed to study the dynamic fracture behavior of particulate composite materials. On the experimental side, measuring crack deformation in particulate composite materials is quite difficult due to demand of both the spatial and temporal resolution. Many experimental studies have been made from early ages for the accurate measurement of fracture deformations. In 1964, de Graaf [2] investigated a brittle fracture in steel by using ultra high speed photography. The same photo-elastic method is applied for dynamic study of fracture by

Dally [3] in 1979. This is extended with different techniques like electronic speckle pattern interferometry [4], digital speckle photography [5], and digital image correlation (DIC) method [6-7] etc.

The invention of modern high speed camera with millions of frames per second improved the accuracy of experimental results of fracture deformation. Recently Kiugulige, Tippur and Denney [1] used a DIC and high-speed photography for the measurement of transient deformation of crack under dynamic loading. In their work, random speckle patterns on a specimen surface before and after deformation are acquired, digitized, and stored. In the undeformed image, subimage is chosen and the location of similar subimage is identified on deformed image. Once the subimage is found in deformed image the displacements can be easily quantized. The high speed camera (which can capture images up to two million frames per second at a resolution of 1KX1K pixels per image) is used for obtaining accurate results.

On the numerical modeling side, boundary element methods have been recognized as an effective technique for fracture analysis [8]. In this work, the symmetric-Galerkin boundary element method (SGBEM) for elastodynamics in the Fourier-space frequency domain is employed to evaluate the DSIFs for a three-point bend beam made of a particulate composite material. For the purpose of validation, the beam geometry, size, materials, boundary and loading conditions are adopted from Reference [1] where experimental data for the DSIFs are available.

The key feature of the boundary element method (BEM) is that only the boundary of the domain is discretized. This implies that, for fracture analysis, the singular stress field ahead of the crack is not approximated, and that remeshing a propagating crack is an easier task. Among the variants of the BEM, SGBEM [9] has several additional advantages: (a) its coefficient matrix is symmetric as the name implies; (b) the use of both displacement and traction boundary integral equations (BIEs) enable fracture problems to be solved without artificial sub-domains; and (c) unlike most variants of the BEM, standard continuous elements can be


23.2

employed. Thus, SGBEM can easily exploit the highly effective quarter-point quadratic element to accurately capture the crack tip behavior.

In addition to important developments of the SGBEM for stress and fracture analysis in elastostatics, the SGBEM for elastodynamics in the Fourier-space frequency domain has recently been extended to fracture applications [10]. Following an SGBEM fracture analysis, FFT and IFFT are subsequently employed to convert the DSIFs from the frequency domain to the time domain. This transient response, especially in the immediate aftermath of an impact loading, is of special interest as most dynamic responses usually reach their maximum value during this period.

2. FRACTURE ANALYSIS USING SGBEM

For a given angular frequency ω and a source point P interior to a domain Γ, the displacement BIE for elastodynamics in the frequency domain is known as

),(),,([),(),( QtQPUPuP jkjku

( , , ) ( , )] 0k j jT P Q u Q Q d (1)

where Ukj and Tkj are the elastodynamic kernel tensors, uj

and tj are the displacement and traction vectors respectively and Q denotes a field point [9].

For P off the boundary, the kernel functions are not singular and it is permissible to differentiate Eq. (1) with respect to P, yielding the displacement gradients. Substitution of these gradients into Hooke’s law and then Cauchy’s relation results in

),(),,([)(),(),( QtQPDPnPtP jkjllk

0dQ)],(),,( QuQPS jkjl (2)

where the elastodynamic kernel tensors Dkjl and Skjl canalso be found in [9]. The traction equation (2) is essential for treating crack geometries, and in symmetric-Galerkin approach it is this equation that is employed on the crack surface. The Galerkin boundary integral formulation is obtained by taking the shape function ψm employed in approximating the boundary tractions and displacements as weighting functions for Eqs. (1) and (2),

0PPP um

d),()( (3)

0PPPm

d),()( (4)

For symmetric-Galerkin Eq. (3) is employed on the part of the boundary where displacement is specified, while Eq. (4) is employed on the part of the boundary where traction is known. As the name implies, this results in a symmetric coefficient matrix. This remains true for fracture analysis, with the proviso that the unknowns on the crack are now the displacement jump ∆uk , and thus only one crack face is required to be discretized. Since Eqs. (1) and (2) have a similar form as those in elastostatics, the reader is referred to, for example, Ref. [9] for more details. Note that the integrals in Eqs. (1) and (2) are singular/hypersingular integrals. The main computational task in implementing Eqs. (3) and (4) is the evaluation of these singular integrals which can be decomposed into two parts as follows:

PQKKPQKPQK sdsd dd)(dddd (5)

where Kd and Ks denote an elastodynamic kernel and its elastostatic counterpart, respectively. For a numerical treatment of the singular integrals (5), the reader is referred to, for example, Reference [9]. Note that the internal damping of the materils can be considered by means of a complex shear modulus defined as

)21( ic (6)

where is the shear modulus and ζ is the damping ratio.

3. DSIFS BY SGBEM AND DCT

Among the methods available for numerically evaluating the DSIFs, the displacement correlation technique (DCT) is one of the simplest and is given by

0

1( ) 2 lim ( )I n

rK u

r

(7)

0

1( ) 2 lim ( )II t

rK u

r

(8)

where ∆un and ∆ut are the normal and tangential components of the displacement jump vector, respectively, and r is the distance to the crack tip.

In Eqs. (7) and (8),

)1(4

)1(42

22

sp

ssp

(9)


23.3

and

21 ( / )p pc c (10)

21 ( / )s sc c (11)

/)2(2 pc (12)

/2 sc (13)

where ν is Poisson’s ratio, ρ is the mass density, c is the crack growth velocity, cp and cs are the compressional and shear velocities, respectively. The dynamic fracture analysis calculations reported in this work are performed using the modified quarter point (MQP) element developed in [11]. By using the MQP shape functions in Eqs. (7) and (8), the DCT- based DSIFs are obtained as follows:

(2) (3)2( ) (8 )

3I n nK u uL

(14)

(2) (3)2( ) (8 )

3II t tK u uL

(15)

where L is the distance between the tip and ending nodes, and the superscripts (2) and (3) denote the quarter-point and ending nodes of the crack-tip element, respectively. As the DSIFs are directly given in terms of the nodal values of the displacement jump of the crack-tip element, and the MQP element enhances the accuracy of the nodal displacement jump, this enhances the accuracy of the obtained DSIFs.

3. PROCEDURE FOR OBTAINING THE TRANSIENT RESPONSES OF THE DSIFS

Figure 1: A Model for Obtaining Time-Domain Results Using FFT and IFFT.

The solution of a dynamic problem for a system can be viewed as an input/output relation where the input is the load P and the output is the dynamic response F of the system. If P and F are in the frequency domain, the relation can be written as

F (ω) = H (ω). P (ω) (16)

where H(ω) is called the frequency response. Since H(ω) = F(ω)/P(ω), the frequency response is the response of the system due to a unit harmonic load P(ω) = eiωt .

Figure 1 depicts a model for obtaining time-domain results (transient responses) from frequency response analysis. In this model, the problem under a unit harmonic load (eiωt) is analyzed first using SGBEM to obtain the frequency response H(ω). In the mean time, the time-dependent load P(t) is converted to the frequency domain (P (ω)) by means of FFT. Relation (16) is then employed to obtain the dynamic response F (ω) in the frequency domain. Finally, IFFT is used to transform F (ω) into the time domain F (t).

A procedure for obtaining the transient responses by FFT and IFFT can be summarized as follows:

(a) Determine a frequency resolution Δf (f = 2πω) which needs to be small enough to minimize the loss of frequency information.

(b) Perform SGBEM analysis for f = 0, Δf, 2Δf,…, (N/2)Δf = fNyq, where N = 2m and m is a positive integer, to obtain the frequency response H(ω) for the first (N/2+1) samples. The Nyquist frequency fNyq

needs to be chosen such that frequency responses above fNyq are not significant and can thus be discarded. Note that the very first sample (i = 1) is the static sample (f = 0).

(c) For the last (N/2-1) samples (i = N/2+2, …,N), H(ω) must be determined such that it is conjugate symmetric about the Nyquist frequency, i.e.,

H(i) = conj(H (N-i+2)) (i = N/2 + 2, ..., N) (17) (d) Perform FFT for the time-dependent load P(t) for the

first N samples (i = 1, …, N);(e) Calculate F(ω) = H(ω).P(ω);(f) Perform IFFT for F(ω) to obtain the transient

response F(t). Note that the period and time resolution (sampling interval) of this transient response are Tf = 1/ Δf and Δt = Tf /N, respectively;

(g) If the calculated Δt does not give a good indication of the shape of the transient curves, interpolation [12] can be used. This is done by increasing the value of Nyquist’s frequency while requiring no extra SGBEM analysis as extra zeros are added to the frequency response. As a result, the number of samples N is increased accordingly which improves the resolution of the transient curves.

4. NUMERICAL EXAMPLE

This problem deals with a three-point bend beam of span length L = 200 mm, with width B = 8.75 mm and depth W = 50 mm, containing edge crack of length a = 10 mm as shown in Fig. 2. The beam is subjected to an impact load P with time history as depicted in Fig. 3, and


23.4

a damping ratio ζ = 0.3% is used. The beam is made from epoxy (prepared by mixing a bisphenol-A resin and an amine based hardener in the ratio 100:38). Young’s modulus, Poisson’s ratio and the mass density of the cured material measured ultrasonically are 4.1 GPa, 0.34 and 1175 kg/m3, respectively [1].

The frequency responses of the DSIFs are obtained using SGBEM with the following data: Δf = 100 Hz, N = 210 = 1,024, fNyq = 51.2 KHz. This results in the following values for the transient analysis using FFT and IFFT: Tf

=1/Δf = 10 ms and Δt = Tf /N = 9.766 μs. In order to obtain accurate DISF results, a convergence test was carried out in which these results were plotted versus mesh refinement. This test suggests a total of 65 elements for the boundary and 5 uniform elements for the crack are sufficient to achieve convergence, thus accuracy of the SGBEM solution.

Figure 2: Three-Point Bend Beam under Impact Loading.

A comparison between the numerical (SGBEM) solution and experimental result reported in [1] is shown in Fig. 4. As it can be seen, the DSIFs obtained from the SGBEM agree well with the experimental data for the first 135 μs. It is quite interesting to note that the KI curves show similar oscillations caused by the first scattered wave at around 70 μs.

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

0 100 200 300 400 500 600 700 800

Time (microseconds)

Fo

rce (

kN

)

Figure 3: Impact Loading History

Figure 4: Numerical vs. Experimental Solutions For The Mode-I and Mode-II DSIFs.

6. CONCLUSION

A 2-D symmetric-Galerkin boundary integral

formulation for elastodynamic fracture analysis of a particulate composite beam in the frequency domain and a post-processing procedure for obtaining transient responses using FFT and IFFT were described in this paper. There are several major advantages of this dynamic fracture modeling technique: (a) Compared to a static counterpart, this formulation only requires additional integrals that are either regular or weakly singular.


23.5

However, care should be taken to avoid large round-off errors in evaluating the additional weekly singular integrals; (b) Unlike in the conventional dual BEM, standard continuous elements can be employed in the SGBEM, allowing the use of the MQP element to accurately capture the crack tip behavior; (c) The frequency domain (FD) formulation is suitable for arbitrarily time-dependent loading often seen in practical engineering as the handling of this type of loading by means of FFT is very inexpensive; and (d) The FD formulation is also known to result in stable transient responses as it is easier to select an appropriate frequency step for the FD formulation than a suitable time step for the time domain formulation. The transient responses of the DSIFs obtained for the beam problem considered in this paper suggest that the dynamic fracture modeling technique discussed herein is effective, accurate and robust. Extending this technique to dynamic crack growth analysis is currently being pursued by the authors.

ACKNOWLEDGEMENTS

This research was supported in part by the NSF Grant CMMI-0653796.

7. REFERENCES

[1] Kirugulige, M.S., Tippur, H.V., and Denney, T.S., 2007, “Measurement of Transient Deformations using Digital Image Correlation Method and High-Speed Photography: Application to Dynamic Fracture,” Appl. Opt, 46(2), pp. 5083-5096.

[2] de Graaf, J.G.A., 1964, “Investigation of Brittle Fracture in Steel by Means of Ultra High Speed Photography,” Appl. Opt, 3(11), pp. 1223-1229.

[3] Dally, J.W., 1979, “Dynamic Photo-Elastic Studies of

Fracture,” Exp. Mech, 19(10), pp. 349-361.[4] Flynn, Z.K., Bassman, L.C., Smith, T.P., Lalji, Z.,

Fullerton, L.H., Leung, T.C., Greenfield, S.R., and Koskelo, A.C., 2006, “Three-Wavelength ESPI with the Fourier Transform Method for Simulataneous Measurement of Microstructure Scale Deformations in Three Dimenstions,” Appl. Opt, 45(14), pp. 3218-3225.

[5] Feiel, R., and Wilksch, P., 2000, “High Resolution Laser Speckle Correlation for Displacement and Strain Measurement,” Appl. Opt, 38(7), pp. 1159-1162.

[6] Chao, Y.J., Luo, P.F., and Kalthoff, J.F., 1998, “An Experimental Study of the Deformation Fields around a Propagating Crack Tip,” Exp. Mech, 38(2), pp. 79-85.

[7] Zhang, D., Eggleton, C.D., and Arola, D.D., 2002, “Evaluating the Mechanical Behavior of Arterial Tissue using Digital Image Correlation,” Exp. Mech, 42(4), pp. 409-416.

[8] Bonnet, M., 1995, Boundary Integral Equation Methods for Solids and Fluids, John Wiley & Sons, England.

[9] Bonnet, M., Maier, G., and Polizzotto, C., 1998, “On Symmetric Galerkin Boundary Element Method,” ASME Applied Mechanics Reviews, 51, pp. 669-704.

[10] Phan, A.-V., Gray, L.J., and Salvadori, A., “Symmetric-Galerikin Boundary Element Analysis of Dynamic Stress Intensity Factors in the Frequency Domain,” Mechanics Research Communications, (Accepted).

[11] Gray, L.J., Phan, A.-V., Paulino, G.H., and Kaplan, T., 2003, “Improved Quarter-Point Crack Tip Element,” Engineering Fracture Mechanics, 70, pp. 269-283.

[12] Brigham, E.O., 1998, The Fast Fourier Transform and Its Applications, Prentice Hall, New Jersy.


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