BLEED SYSTEM DESIGN OF A SUPERSONIC RECTANGULAR-DUCT WIND TUNNEL

By

ZHANGMING ZENG

A THESIS PRESENTED TO THE GRADUATE SCHOOL

OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

UNIVERSITY OF FLORIDA

2018

© 2018 Zhangming Zeng

To my parents and Mengfei Liu

4

ACKNOWLEDGMENTS

Firstly, I would like to thank Prof. Corin Segal for granting me the opportunity to perform

research in his facilities. His guidance and mentorship through this process has had a great

impact on my growth in professional knowledge and engineering skills.

Secondly, I would also like to thank the passionate and highly gifted individuals in the

Combustion and Propulsion Laboratory for continuously pushing my knowledge and curiosity.

Finally, this process could not have been possible without the love and support from my

family.

5

TABLE OF CONTENTS

page

ACKNOWLEDGMENTS ...............................................................................................................4

LIST OF TABLES ...........................................................................................................................7

LIST OF FIGURES .........................................................................................................................8

NOMENCLATURE ......................................................................................................................10

ABSTRACT ...................................................................................................................................13

CHAPTER

1 INTRODUCTION ..................................................................................................................15

1.1 Boundary Layer in Supersonic Duct Flow ......................................................................15

1.2 Bleed System Design .......................................................................................................16 1.3 Scope of Study .................................................................................................................18

2 FACILITY SETUP .................................................................................................................22

3 DESIGN AND ANALYSIS ...................................................................................................26

3.1 Preliminary Design and Analysis ....................................................................................26

3.2 Design Generation ...........................................................................................................28 3.3 Final Result ......................................................................................................................28

4 DISCUSSION .........................................................................................................................40

4.1 Limitation ........................................................................................................................40 4.2 Future Work .....................................................................................................................41

APPENDIX

A VELOCITY PROFILE IN THE TURBULENT BOUNDARY LAYER ..............................43

B ESTIMATION OF THE BOUNDARY LAYER MASS FLOW RATE AT THE EXIT

OF THE ISOLATOR ..............................................................................................................48

B.1 Description ......................................................................................................................48 B.2 Assumptions ....................................................................................................................48 B.3 Data Source .....................................................................................................................49

B.4 Calculation Method .........................................................................................................49 B.4.1 Free Stream Parameters Calculation .....................................................................49 B.4.2 Boundary Layer Mass Flow Rate Calculation ......................................................49

B.4.3 Estimation of Total Area of the Holes on the Porous Wall ..................................50

6

B.5 Results .............................................................................................................................51

C EVALUATION OF THE BLEEDING SYSTEM OPERATING TIME ...............................54

C.1 Description ......................................................................................................................54 C.2 Assumptions ....................................................................................................................54 C.3 Data source ......................................................................................................................54 C.4 Calculation Methods .......................................................................................................55

C.4.1 Calculation of the Choked Condition ...................................................................55

C.4.2 Calculation of the Tube-Unchoked Condition ......................................................55 C.5 Results .............................................................................................................................57 C.6 Matlab Code ....................................................................................................................58

C.6.1 Matlab Code for Choked Condition ......................................................................58

C.6.2 Matlab Code for Unchoked Condition ..................................................................59

D CALCULATION OF THE FINAL DESIGN .........................................................................61

D.1 Description ......................................................................................................................61

D.2 Assumptions....................................................................................................................61 D.3 Data Source .....................................................................................................................61

D.4 Calculation Methods .......................................................................................................62 D.5 Results .............................................................................................................................63 D.6 Matlab Code ....................................................................................................................63

E THE DESIGN DRAWING OF THE BLEEDING DEVICE .................................................65

REFERENCES ..............................................................................................................................72

BIOGRAPHICAL SKETCH .........................................................................................................73

7

LIST OF TABLES

Table page

3-1 Result along 4-inch wall ....................................................................................................38

3-2 Result along 1-inch wall ....................................................................................................39

8

LIST OF FIGURES

Figure page

1-1 Mean Axial Velocity Contours of Square Duct [2] ...........................................................19

1-2 Bleed system design procedure[4] .....................................................................................20

1-3 Bleed holes geometry[4] ....................................................................................................21

2-1 UFHRF scramjet wind tunnel system ................................................................................24

2-2 Cross-sectional view of the UFHRF scramjet wind tunnel. ..............................................24

2-3 Cross-sectional view of the modified wind tunnel ............................................................25

3-1 Mass flux contour of the exit plane[7] ...............................................................................30

3-2 Pressure-time plot of choked condition, when extracting all the boundary layer at the

exit of the isolator ..............................................................................................................30

3-3 Pressure-time plot in unchoked condition,when extracting all the boundary layer at

the exit of the isolator ........................................................................................................31

3-4 Inflow & Outflow-time plot in unchoked condition,when extracting all the boundary

layer at the exit of the isolator ............................................................................................32

3-5 Pressure-time plot of choked condition, when extracting the boundary layer along

one 4-inch wall at the entrance of the isolator ...................................................................33

3-6 Entire Assembly of the Devices .........................................................................................33

3-7 Part1_1inwall .....................................................................................................................34

3-8 Part2_4inwallA ..................................................................................................................34

3-9 Part3_4inwallB ..................................................................................................................35

3-10 Part4_Pipeplate ..................................................................................................................35

3-11 O-ring groove .....................................................................................................................36

3-12 Plenum-like Cavity ............................................................................................................36

3-13 The slot for perforated plate ...............................................................................................37

B-1 Mass Flow Rate Profile of Boundary Layer Along 4-inch Wall .......................................53

B-2 Mass Flow Rate Profile of Boundary Layer Along 1-inch Wall .......................................53

9

E-1 Assembly............................................................................................................................66

E-2 Part 1 of 4_1in Wall ...........................................................................................................67

E-3 Part 2 of 4_4in Wall A .......................................................................................................68

E-4 Part 3(a) of 4_4in Wall B ...................................................................................................69

E-5 Part 3(b) of 4_ 4in Wall B..................................................................................................70

E-6 Part 4 of 4_Pipe Plate .........................................................................................................71

10

NOMENCLATURE

A constant of Crocco Energy Theorem

Ah total area of bleed holes

B constant of Crocco Energy Theorem

C constant in Law of the Wall

Cf skin friction coefficient

D diameter of bleed hole

i measure point number

κ von Karman constant

L length of bleed hole

m0 initial mass of air in the vacuum tank

B.L.,wallm general boundary layer mass flux rate along the wall

B.L.,im mass flux rate per unit spanwise length at measure point i

em mass flow rate of free stream

inm inflow rate of the vacuum tank

outm outflow rate of the vacuum tank

mtank mass of air in the vacuum tank

M local Mach number

Me free stream Mach number

Mh Mach number of holes

Pe free stream static pressure

Pt free stream stagnation pressure

Pt,h stagnation pressure of flow through bleed holes

11

Ptank pressure in the vacuum tank

R specific gas constant of air

Reδ Reynold’s number based on δ

Te free stream static temperature

Th static temperature of flow through bleed holes

Tt free stream stagnation temperature

Tt,h stagnation temperature of flow through bleed holes

Ttank temperature in the vacuum tank

Tw wall static temperature

u local velocity in streamwise direction

ue free stream velocity

uτ shear or friction velocity

u* Van Driest’s general velocity

ue* Van Driest’s general velocity at boundary layer edge

Vtank vacuum tank volume

outV volumetric outflow rate of the vacuum tank

x directional coordinate in streamwise direction

X row spacing

y directional coordinate normal from wall

Y bleed hole spacing

z1 directional coordinate of isolator exit plane

z2 directional coordinate of isolator exit plane

α bleed hole angle

12

γ specific heat ratio

δ boundary layer thickness

δ* displacement thickness

θ momentum thickness

μe dynamic viscosity at boundary layer edge

μw dynamic viscosity at wall

ν kinematic viscosity

νe kinematic viscosity at boundary layer edge

νw kinematic viscosity at wall

Π coefficient of wake function

ρ local density

ρe density of free stream

ρtank density of the air in the vacuum tank

ρh density of the flow through the bleed holes

τ shear stress

τw wall shear stress

13

Abstract of Thesis Presented to the Graduate School

of the University of Florida in Partial Fulfillment of the

Requirements for the Degree Mater of Science

BLEED SYSTEM DESIGN OF A SUPERSONIC RECTANGULAR-DUCT WIND TUNNEL

By

Zhangming Zeng

August 2018

Chair: Corin Segal

Major: Aerospace Engineering

Presented in this paper is the design process of a boundary layer bleed system for a

rectangular-duct supersonic wind tunnel. Calculations were conducted to evaluate the mass flow

rate of the boundary layer at the exit plane and the entrance plane of the isolator of the wind

tunnel. Based on the mass flow rate calculation result, a detailed design was generated.

The flow field profile at the exit plane of the isolator was measured by former researchers.

By integration of the data from the measurement results, the boundary layer mass flow rate was

obtained. At the exit plane, the cumulative mass flow rate of the boundary layer along 4-inch

wall is 0.1648 kg/s, and the cumulative mass flow rate of the boundary layer along the 1-inch

wall is 0.0401 kg/s. At the entrance plane of the isolator, the cumulative mass flow rate of the

boundary layer along 4-inch wall is about 0.0824 kg/s.

According to the data above, a calculation aiming at removing all the boundary layer mass

flow at the exit plane was conducted. The pressure-time figures were plotted for both the

bleeding holes choked and unchoked condition. It was indicated that in this case the bleeding

holes would be choked for 2.44s at the beginning, and 4 more unchoked seconds before the

device reached the final condition. Though the 2.44s working time was relatively enough, this

14

mass flow rate would be too large for the flow in the 2-inch main pipe to keep the flow speed

under Mach 0.3.

Therefore, a final design aiming at extracting only the boundary layer along one 4-inch wall

at the entrance of the isolator was raised. By referring to the design of current sections of the

supersonic wind tunnel, while introducing new technics like the TIG welding and brazing, the

final detailed design was generated.

15

CHAPTER 1

INTRODUCTION

1.1 Boundary Layer in Supersonic Duct Flow

With the development of ramjet and scramjet engines, the research interest on rectangular

cross-section duct inlet is growing these years. For flight speed over Mach 3, the compression

process can be finished solely by changing the cross section area of the inlet and the diffuser,

thus turbomachinery is not needed. This removal of turbomachinery allows the engine to have

more selections of non-circular cross section shape for the inlet, such as rectangular. Further, the

flexibility of the cross section shape makes it possible to integrate the inlet and engine with the

airframe of the aircraft, which will drastically reduce the weight and the drag force. However,

choosing non-circular shape such as rectangular inlet will lead to some problems. Due to the

non-circularity, the boundary layer distribution on the cross section is not uniform. For

rectangular duct, the interaction between boundary layers along two connected walls is a obvious

source of non-uniformity. Also, the high flight speed contributes to relative thick boundary layer,

and studies [1] show that the significant shockwave-boundary layer interaction will cause the

boundary layer separation, which triggers serious flow field distortion. Therefore, the

performance of the inlet and downstream sections like the combustor will be undermined.

Several experimental studies have been conducted to investigate the turbulent boundary

layer in rectangular duct. Meilling & Whitelaw [2] demonstrated the influence of the secondary

flow on the mean axial velocity contours. The result may be seen in Figure 1-1. The contour

indicates that there is a bulging effect towards the corners. At the center of the wall, the local

normalized velocities seems lower than those near the corner, which suggests a higher boundary

layer thickness. Also, the figure shows that although the velocity contour is non-uniform, it can

be considered as symmetry in general.

16

An effective method to suppress this shock-induced separation is to remove the low energy

part of the boundary layer by a bleed system based on porous plate. According to the research of

Wong [3], for a inlet working at M = 1.9, by removing 3% of the mass flow in the duct, the

shockwave-boundary layer interaction can be successfully suppressed. During programs like

Boeing SST, engineering methods of designing bleed system for supersonic duct flow were

developed and tested.

In University of Florida’s Hypersonic Research Facility (UFHRF), the non-uniform

boundary layers in the rectangular wind tunnel greatly influence on fuel/air mixing and flame

holding capabilities. To improve the performance of the device and investigate the shock-

induced separation, it is necessary to develop a boundary layer elimination device for the

UFHRF, which constitute the outline of this work. The analytical calculation of turbulent

boundary layer is shown in APPENDIX A.

1.2 Bleed System Design

To reduce the negative influence of the inlet boundary layer of supersonic and hypersonic

aircraft, during the research and design of supersonic and hypersonic aircraft from 1950s to

1970s, a series of engineering solutions were developed. Syberg and Koncsek [4] outlined the

basic procedure of bleed system design. In another article, Syberg and Hickox [5] provided some

recommendation of design parameters selection.

Firstly, the profile of the flow field and boundary layer development should be determined.

Secondly, based on the result of the first step, the location of the bleed system can be chosen.

Later, the target of the system, the required changes of the boundary layer properties can be set.

Then it comes to the aerodynamic calculation, data such as bleed rates and bleed geometry are

figured out. After finishing the preliminary design, detailed design are of to carry out. For bleed

17

system based on porous plate, followings are the vital characteristics to be determined: hole size,

hole spacing, wall thickness (or hole length) and hole inclination, etc.

To provide effective profile improvement, the bleed system need to be placed ahead of all

the flow separation. The bleed system itself can also increase the growth rate of the boundary

layer, because the surface roughness. There are two sources of surface roughness. The first one is

the holes themselves, and the other one is the mixing of the low and high energy air flow in the

boundary layer caused by bleeding. To minimize the surface roughness, it is necessary to keep

the bleed holes choked. Meanwhile, keeping the holes choked also prevents the flow

recirculation within the bleed system.

For the bleeding performance, hole diameter D, and the aspect ratio, L/D. An important

reference for D selection is the displacement thickness δ*. Experimental researches suggested

that the efficiency of the system improves as the hole diameter D decreases. However, when the

D is smaller than δ*, the bleed holes tend to unchoke at a lower plenum pressure as predicted,

which undermines the bleed flow rate. The suction may not able to precipitate transition when

D/δ* is lower than 0.6 according to MacManus and Eaton [6]. To reduce the inaccuracies of the

bleed flow predictions while maintain the system efficient, it is suggested that D ≈ δ*. Also, a

L/D ratio lower than 4.0 is recommended by Syberg and Koncsek. If the ratio is too large (L/D ≈

10), serious deviation from the predicted performance will take place. Meanwhile, the wall

thickness should also meet the mechanical strength requirement.

Another bleed geometry that influences the performance of the system is the hole spacing,

X/D and Y/D. Since the mixing of bled and unbled region leads to loss of total pressure, it will

not be relied on for improving the boundary layer profile. Thus a spacing (X/D and Y/D) as close

as 1.0 was recommended by Syberg and Hickox. For standardized porous plate, the hole spacing

18

can be expressed by porosity. As the porosity increases, the maximum plenum pressure that is

able to keep the hole choked also increases. Thus theoretically a higher porous ratio is preferred.

In engineering practice, the porosity or hole spacing selection also depends on the mechanical

strength of the plate material.

Also, in Syberg and Koncsek’s work, the performances of bleed system with α =

20°,40°and 90°were compared. The results indicated that the lower angle holes have better flow

coefficient, and is able to keep choked at higher plenum pressure. So an inclined bleed holes are

preferred for increasing the bleed system’s efficient. However, the 90°holes have the greatest

increase in bleed rate with the accompanying decrease in Mach number. This means they

produce normal shock stability margin than lower angle holes.

1.3 Scope of Study

As mentioned in 1.1, in the rectangular supersonic wind tunnel of UFHRF, the relatively

thick boundary layers undermined the performance of the wind tunnel. Thus a boundary layer

suction device based on porous plate powered by a vacuum pump and a vacuum tank was

designed.

In the experimental research conducted by Stuthers [7], the velocity profile contour on the

exit plane of the isolator was mapped according to the equations mentioned in APPENDIX A.

Based on the velocity contour, the mass flow rate of the boundary layer will be calculated. Then,

combined with the performance data of the vacuum system, the expected performance of the

bleed system will be estimated. After all the preliminary design process is finished, the detail

design of the bleed system will be done using SOLIDWORKS software.

19

Figure 1-1. Mean Axial Velocity Contours of Square Duct [2]

20

Figure 1-2. Bleed system design procedure[4]

21

Figure 1-3. Bleed holes geometry[4]

22

CHAPTER 2

FACILITY SETUP

The target of the design is to develop a boundary layer elimination device for the blow-

down wind tunnel of the University of Florida Hypersonic Research Facility (UFHRF). The

detail design analysis was provided by Djerekarov [8] while the facility and wind tunnel was

further characterized by Barnes [9].

The UFHRF is a unique direct-connect, supersonic combustion, blow-down wind tunnel

used primarily to study the scramjet engine configurations, fuel-air mixing, and ignitor-flame

holding capabilities. The facility is able to provide a Mach 2.2 cold inert flow up to a Mach 6

simulated flight enthalpy with the aid of a non-vitiated coiled electric heating module and a

vitiated hydrogen combustion heating module. The design of the boundary layer elimination

device is based on the working condition of the Mach 2.2 cold inert flow.

A general schematic view of the facility is shown in Figure 2-1. In this schematic, the flow

pass through from left to right. Two 800 m3 air storage tanks are compressed to about 200 psia by

a Sulliar LS-20T screw type air compressor. Before entering the storage the moisture is extracted

from the air through the use of desiccant type air dryers. The manual operational of a Fisher

Controls pneumatic pressure regulator allows an operational facility pressure of up to 85 psia,

though experiments show a stagnation pressure of 100 psia was experienced. By measuring the

temperature of the air flowing through the plenum upstream of the wind tunnel, it was seen that a

stagnation temperature around 294 K may be sustained without the use of the two stage heating

modules.

Then the compressed air is fed into a direct-connect scramjet wind tunnel, which consists of

a nozzle inlet, an isolator, a test section and a diverging duct. A cross-sectional view of the wind

tunnel of the wind tunnel is shown in Figure 2-2. The outlet of the wind tunnel is then captured

23

and directed outside via ducted channel. Thus, the exit plane of the diverging duct experience an

expansion phase in order to meet the atmospheric pressure boundary condition. The internal

dimensions of the test section are 1 × 4 inches. Three walls of each section incorporate windows

for optical analysis while the fourth ‘back’ wall was designed to incorporate ports along the

centerline for static wall pressure and temperature measurements. The design of the boundary

layer elimination device used the data from the wall static pressure port which is nearest to the

isolator exit (1 inch from the exit plane). Also, it is assumed that the static pressure throughout

the whole cross-section was constant at its location along the constant area duct.

The extraction of the boundary layer is powered by a Torrvac TV250B vacuum pump from

US Vacuum and a series of vacuum tank. For the TV250B pump, the 10 Hp motor on the vane

pump is able to move 180 acfm (actual cubic feet per minute) of air. And the pump is connected

to a series of vacuum tanks with a total volume of 1120 gallons. When fully vacuumed, the

residual pressure in the tank can be consider as 0.1 psia. This vacuum system was selected for

use independently of the boundary layer removal mechanism concept.

The design followed the research of Stuthers which measured and analyzed the flow field

on the exit plane flow field. In his research, Stuthers modified the wind tunnel by removing all

the downstream test section. The cross-sectional view of the modified wind tunnel is shown in

Figure 2-3.

24

Figure 2-1. UFHRF scramjet wind tunnel system

Figure 2-2. Cross-sectional view of the UFHRF scramjet wind tunnel.

25

Figure 2-3. Cross-sectional view of the modified wind tunnel

26

CHAPTER 3

DESIGN AND ANALYSIS

3.1 Preliminary Design and Analysis

To start the design process of the boundary layer elimination device, the mass flow rate of

the boundary layer in the duct is required. The design is based on the result of Stuthers’ hot-wire

measurement at the exit plane of the isolator. The results of the measurement and analysis along

the 4-inch wall and the 1-inch wall are shown in Table 3-1 and Table 3-2. As it is shown in the

table, the measurement covered only 1/4 of the duct, thus it is assumed that the flow field is

symmetry. The mass flux contour of the measured plane is shown in Figure 3-1. According to the

data from Table 3-1 and Table 3-2, the cumulative mass flow rate of the boundary layer along 4-

inch wall is 0.1648 kg/s, and the cumulative mass flow rate of the boundary layer along the 1-

inch wall is 0.0401 kg/s. The detailed process of the mass flow rate estimation is shown in

APPENDIX B.

By combining the mass flow rate of the boundary layer with the data of the vacuum system,

the available working time of the elimination system was estimated. The vacuum system consists

of a vacuum tank with a volume of 1120 gallons and a vacuum pump with a volumetric outflow

rate of 180 ft3 /min. Before the start, the vacuum pump can vacuum the tank to about 0.1 psia.

During the working condition, both the vacuum tank and vacuum pump are connected to the

boundary layer elimination section and to extract the mass flow of the boundary layer. Figure 3-

2, Figure 3-3 and Figure 3-4 show the result of estimation for the condition extracting all the

boundary layer mass flow at the exit plane of the isolator. The detailed methods, process and

Matlab code of working time estimation were attached in APPENDIX C.

In this condition, the mass flow rate to be removed is 0.409 kg/s. Figure 3-2 shows that the

bleeding holes are able to keep choked for 2.44 s before the pressure in the vacuum tank reaching

27

the critical pressure to maintain the bleeding holes choked. When the pressure is higher than the

critical value, the extracted mass flow rate becomes a function of the pressure in the tank. As

shown in Figure 3-3, it takes 4 additional minutes after the holes converted to unchoked to reach

the final condition that the pressure of the vacuum tank equals the static pressure of the boundary

layer, and the bleeding is powered by only the vacuum pump.

Another restriction related with the performance of the device is the diameter of the pipe

which connect the wind tunnel with the vacuum tank. The diameter of the pipe is 2-inch, thus if

the boundary layer mass flow along all four walls at the exit of the nozzle is extracted through it

to the vacuum tank, the air flow speed in the pipe will be so large that the pressure loss will be

unacceptably high. To reduce the pressure loss in the 2-inch pipe, it was recommended that the

Mach number of the air flow through the 2-in pipe should be no higher than 0.3. Also, simple

estimation revealed that the device streamwise length would be too large to ignore its negative

influence on the flow field due to the surface roughness of the porous plate.

As a result, to make sure the air flow Mach number in the 2-inch pipe is lower than 0.3, and

shrink the length of the device to relatively acceptable size, it was decided that the device was

going to only remove the boundary layer mass flow along one 4-inch wall at the entrance,

instead of the former case that extracting all the boundary layer at the exit plane of the isolator.

In this case, based on several assumptions (see APPENDIX D), the mass flow rate needed to be

subtracted was considered as 0.0824 kg/s. Introducing this new mass inflow rate to the Matlab

code for the bleeding holes choked condition, the available working time (when bleeding holes

choked) for this new case was predicted. As it is shown in Figure 3-5, there were 14 seconds

before the pressure in the vacuum tank was unable to keep holes coked, which is long enough for

typical supersonic wind tunnel experiments.

28

3.2 Design Generation

Considering several related factors, it was decided that the boundary layer would be

extracted through a perforated metal plate which was available in the market. There was a

candidate company McNICHOLES, which provided perforated plate with various materials, hole

sizes, open area ratio, and thickness. After comparison McNICOHLS Item 1627502631 cold

rolled plain steel perforated plate was selected. The thickness of the plate is 26 Gauge (0.018 in ).

The holes are in 0.027 in diameter and 0.050 center. For this plate, the open area ratio is 23%.

The plate must be integrated into a module of the test section, so the addition of the

boundary layer removal module would slightly elongate the structure. Therefore, the designs of

the flange and the bolt patterns remained the same as the current parts, in order to guarantee the

coherence of the hole experimental facility. However, there were some slight modification on the

structural design of the boundary layer elimination device, the o-ring groove was lengthened.

Since the boundary layer mass flow were designed to be extracted to a vacuum tank,

pipelines and other hoses connections to the module were necessary. To minimize the size of the

device, the spacing of the plumbs should be as close as possible. However, enough room for

operating tools must be ensured.

3.3 Final Result

Figure 3-6 shows the entire assembly of the final design. To ensure simple facility

integration, the flange,material and assembly of the component are almost identical compared

with current sections of the UFHRF. There whole device consists of 4 parts, namely

Part1_1inwall (2 needed), Part2_4inwallA, Part3_4inwallB and Part4_Pipeplate, as shown in

Figure 3-7, Figure 3-8, Figure 3-9 and Figure 3-10.

According to the requirement, the whole 4-inch duct edge should be covered by a 4-inch

wide suction area. Thus the Part3_4inwallB, on which the perforated plate mounted on, should

29

be wider than 4 inch, which is a structural difference compared with the general structural design

of the other sections like the isolator. One result of this modification is that the 13.26 inch o-ring

groove (Figure 3-11) is longer than the existing designs.

After being extracted through the perforated plate, the boundary layer mass flow will enter a

plenum like cavity (Figure 3-12), then enter 10 brass pipes. The inner diameter of these pipes are

0.625 in, and the spacing of these pipes is 1.2 inch. To provide enough space for operating tools,

the exit of these pipes are pointing at different directions.

Compared with previous designs, there are two new manufacturing processes required，

blazing and TIG welding. As shown in Figure 3-13, the perforated plate will be blazed into its

respective slot. Since the steel plate is relative thin compared with the pressure difference it face,

a supportive structure in the middle of the slot is needed. And in order to ensure a vacuum-

capable seal, the ten brass pipes must be TIG welded to the copper plates. Due to the thermal

conductivity of copper, only a quality TIG weld will be a viable option. The assembly and

installation process after these two manufacturing processes should be very similar to the

isolator’s process.

30

Figure 3-1. Mass flux contour of the exit plane[7]

Figure 3-2. Pressure-time plot of choked condition, when extracting all the boundary layer at the

exit of the isolator

31

Figure 3-3. Pressure-time plot in unchoked condition,when extracting all the boundary layer at

the exit of the isolator

32

Figure 3-4. Inflow & Outflow-time plot in unchoked condition,when extracting all the boundary

layer at the exit of the isolator

33

Figure 3-5. Pressure-time plot of choked condition, when extracting the boundary layer along

one 4-inch wall at the entrance of the isolator

Figure 3-6. Entire Assembly of the Devices

34

Figure 3-7. Part1_1inwall

Figure 3-8. Part2_4inwallA

35

Figure 3-9. Part3_4inwallB

Figure 3-10. Part4_Pipeplate

36

Figure 3-11. O-ring groove

Figure 3-12. Plenum-like Cavity

37

Figure 3-13. The slot for perforated plate

38

Table 3-1 Result along 4-inch wall

i z1(in) δ(in) mB.L./me ue(ft/s) ue(m/s) me(kg/s*m) mB.L.(kg/s*m)

1 1.9375 0.1053 0.7311 1447.4 441.1675 1.0645181 0.77826916

2 1.875 0.1526 0.6005 1717.8 523.5854 1.8308941 1.099451919

3 1.8125 0.1762 0.5905 1789.9 545.5615 2.2027782 1.300740528

4 1.75 0.1841 0.6134 1802.3 549.341 2.3174852 1.421545421

5 1.6875 0.1841 0.6213 1798.2 548.0914 2.3122132 1.436578073

6 1.625 0.1919 0.6307 1795 547.116 2.4058887 1.517393979

7 1.5625 0.1998 0.605 1790.5 545.7444 2.4986528 1.511684923

8 1.5 0.2234 0.5662 1794.6 546.9941 2.8001863 1.585465496

9 1.4375 0.2077 0.5701 1797.6 547.9085 2.6077482 1.486677247

10 1.375 0.2077 0.5747 1784.6 543.9461 2.5888893 1.487834689

11 1.3125 0.2313 0.5695 1787.9 544.9519 2.8883842 1.64493478

12 1.25 0.2313 0.5717 1790.5 545.7444 2.8925845 1.653690564

13 1.1875 0.2077 0.5936 1780.4 542.6659 2.5827964 1.53314797

14 1.125 0.1919 0.6145 1775.2 541.081 2.3793502 1.462110679

15 1.0625 0.2077 0.5851 1778.5 542.0868 2.5800401 1.50958149

16 1 0.2313 0.5906 1782.1 543.1841 2.8790142 1.700345763

17 0.9375 0.247 0.5665 1777.7 541.843 3.0668429 1.737366478

18 0.875 0.2156 0.5824 1773.3 540.5018 2.6703431 1.555207832

19 0.8125 0.2234 0.5785 1779.7 542.4526 2.7769373 1.606458202

20 0.75 0.2392 0.5931 1781 542.8488 2.9755085 1.764774081

21 0.6875 0.247 0.5852 1779.6 542.4221 3.0701207 1.796634627

22 0.625 0.2549 0.6024 1785.3 544.1594 3.1784628 1.914706014

23 0.5625 0.2077 0.574 1743.2 531.3274 2.528831 1.45154901

24 0.5 0.2628 0.5693 1785.5 544.2204 3.2773386 1.865788866

25 0.4375 0.2628 0.5856 1789.6 545.4701 3.2848643 1.923616519

26 0.375 0.2156 0.6002 1770.5 539.6484 2.6661267 1.60020925

27 0.3125 0.2943 0.5659 1785 544.068 3.6691425 2.076367748

28 0.25 0.3022 0.5561 1789.8 545.531 3.7777661 2.100815711

29 0.1875 0.2943 0.561 1789.3 545.3786 3.6779813 2.063347533

30 0.125 0.2864 0.5734 1789.8 545.531 3.5802522 2.052916588

31 0.0625 0.2628 0.5493 1790.4 545.7139 3.2863327 1.805182551

32 0 0.2628 0.5719 1790.3 545.6834 3.2861491 1.879348696

39

Table 3-2 Result along 1-inch wall

i z2(in) δ(in) mB.L./me ue(ft/s) ue(m/s) me(kg/s*m) mB.L.(kg/s*m)

1 0.3125 0.1762 0.6307 1794 546.8112 2.207824 1.392474567

2 0.25 0.1919 0.6242 1802.9 549.5239 2.4164773 1.508365101

3 0.1875 0.2156 0.606 1801.6 549.1277 2.712959 1.644053143

4 0.125 0.247 0.6304 1794 546.8112 3.0949632 1.951064803

5 0.0625 0.2648 0.5506 1767.1 538.6121 3.2682495 1.799498183

6 0 0.2648 0.5176 1754.4 534.7411 3.2447609 1.679488231

40

CHAPTER 4

DISCUSSION

4.1 Limitation

The estimation of the boundary layer flow rate and the design and analysis of the design

were based on several assumptions and simplifications. However, this might also limit the

performance of the device, leaded to deviation from expected performance.

Firstly, as mentioned in APPENDIX B, the data source from Stuther’s research was

measured under a stagnation pressure of 85-90 psi in the wind tunnel, while the design was based

on a working stagnation pressure of 60 psi. The assumption that the velocity and mass flow rate

profile remains the same under different wind tunnel stagnation pressure was introduced.

Obviously this assumption would lead to deviation in the boundary layer mass flow rate

estimation.

Secondly, in the wind tunnel the static pressure and static temperature along each cross

section was considered as uniform and stable. Therefore, the static pressure and temperature in

the boundary layer, which was treated as the stagnation pressure and temperature of the suction

flow, was calculated directly from the stagnation pressure and temperature as well as the Mach

number of the given working condition (see APPENDIX B).

Thirdly, to reasonably simplify the process of estimation and design, the influence of the

suction and suction device on the boundary layer was neglected. Along the streamwise direction,

there is interaction between the decrease of the boundary layer thickness during flowing over the

porous plate and the suction of boundary layer mass flow. Also, the porosity of the plate increase

the surface roughness of the duct as well. The influence of either the interaction or the increase

was not taken into consideration during the design. On the other aspect, in the estimation and

design the target mass flow rate to be removed equal to the mass flow rate of boundary layer

41

along 4-inch wall, which was based on a implicit assumption that the suction on one of the four

walls would not affect the boundary layer flow field along the rest three walls. However, in the

actual case, it is possible that the boundary layer on the adjacent two 1-inch walls will “collapse”

onto the boundary layer extracted 4-inch wall, which may lead to an increase of the amount of

mass flow to be extracted.

Fourthly, during the design of the devices, there were some idealization which would also

cause the deviation from the expected performance. As it is shown in APPENDIX B, the mass

flow rate along the spanwise direction was not uniform. However, the holes on the perforated

plate were equally-spaced distributed. Thus, in some area the mass flow may be over-extracted

while in some other area the boundary layer may not be fully extracted. Meanwhile, for the inner

flow path in the boundary layer extraction device, there are some places that the flow path

change drastically, like the entrance from the perforated plate holes to the cavity, and the

entrance from the cavity to the 10 brass pipes. The drastic change of flow path may lead to loss

of stagnation pressure of the extracted flow, but these losses were ignored during the design of

the device.

4.2 Future Work

Current work mainly focused on the estimation and design of the boundary layer extraction

device. In the future, the following works can focus on three parts, manufacturing, testing and

modification.

APPENDIX E provides the detailed design drawings and the assembly drawing of the device

and all the parts. Thus the next step is to find qualified workshop to manufacture the design.

Most of the details, like the design of the flange and selection of bolts were inherited from

the design of current sections like the isolator. Nevertheless, some new technics like the TIG

42

welding and brazing were introduced into the manufacturing process and the quality of which

should be pay attention to.

After being manufactured, the device can be assembled to the supersonic wind tunnel

facility to test the performance and effectiveness of it. The device of will be mounted at the

entrance of the isolator and the flow field after boundary layer extraction can be measured using

methods described in Stuther’s paper. In addition, the flow properties of the extracted air flow,

such as the stagnation and static pressure, the actual extracted mass flow rate and the flow speed

can also be measured to figure out the efficiency of the device and the loss of extraction

capability due to the change of flow path. Beside the experimental methods, CFD simulation

methods can also be used to estimate the performance of the device. However, although the

numerical simulation is an effective way to evaluate the detail flow field of the device, for

general effect evaluation and analysis, the experimental method is more direct and concise.

Based on the result of performance and effectiveness measurement, modifications can be

made. Modification choices include change of the perforate plate area, introducing non-

uniformly distributed porous plate holes and optimization of the inner flow path of the device.

Also, modification focus on the versatility of the device can also be made. Currently the

perforated plate is brazed with the copper parts. The advantage of this is the simplification of

structural design, but if it is needed to change some experimental parameters, like the amount of

mass flow rate being removed, the distribution of the porous plate, the hole device will need to

be dissembled thoroughly and newly manufactured duct wall parts are required. In the future,

modification on the structural design can be made to improve the versatility of the device,

hopefully make the change of extraction parameters easier.

43

APPENDIX A

VELOCITY PROFILE IN THE TURBULENT BOUNDARY LAYER

According to an extensive survey, Coles [10] indicated that the velocity profile for the two-

dimensional incompressible turbulent boundary layer flow can be represented by a linear

combination of two universal functions. The first one is law of the wall, and the second one is

law of the wake. Both functions are considered to be established empirically. Ultimately, the

development of a turbulent boundary layer is interpreted by an equivalent profile. It is supposed

that this profile represents the large-eddy structure and is a consequence of the constraints

contributed by inertia. Also, this wake profile is modified by the presence of a wall, at which the

viscosity serves as another constraint. Under such influence, the logarithmic profile is dominant

in the sublayer near the wall.

Coles supposed that the flow exerts a shearing stress τw(x) on a smooth impermeable wall at

rest at y = 0. For an incompressible fluid, define the friction velocity uτ(x) as

wu =2

(A-1)

Thus in the region near the wall the velocity profile is described by following function, which is

named as ”law of the wall”:

)(

yuf

u

u= . (A-2)

For incompressible, steady and two-dimensional turbulent flow, the equation above takes the

form

,)ln(1

Cyu

u

u+=

(A-3)

where κ and C are constants determined by experiments. When it comes to turbulent shear flow,

equation (A-3) can be summarized as

),,()( yxhyu

fu

u+=

(A-4)

For flow field in pipe, duct and on flat plate, according to experimental results, equation (A-4)

have a specific form

),,()(

yg

yuf

u

u+= (A-5)

44

where Π is a parameter independent of x and y. Profile similarity in terms of the argument y/δ is

usually expressed by “velocity-defect law”. In the region outside the sublayer, it is an immediate

consequence of the logarithmic variation of f in equation (A-5) that

),(g

yF

u

uue =−

(A-6)

with u = ue at y = δ.

Given the law of the wall above, to establish a defect law, other assumptions about the

motion are needed. The key for searching additional assumptions is investigating the h(x,y) term

in equation (A-4). By extensive survey of experimental data at large Reynolds numbers, Coles

conclude that h(x,y) can be reduced directly to a second universal similarity law. Thus, equation

(A-4) can be written in the form

).()(

yW

yuf

u

u += (A-7)

The function W(y/δ) is referred as “law of the wake”, which is common to all two-dimensional

turbulent boundary layer flows. This wake function has been subjected to the normalized

conditions as W(0) = 0, W(1) = 2 and 1)/(2

0= dwy . The parameter Π is determined by the

local skin friction coefficient Cf, displacement thickness δ* and momentum thickness θ.

Combining equation (A-3), (A-4) and (A-4), the velocity profile for the turbulent boundary

layer can be expressed as

).()ln(1

yWC

yu

u

u ++= (A-8)

At the boundary layer edge, set the boundary condition as u = ue and w(1) = 2. Therefore, the

wall-wake mean-velocity profile for an incompressible turbulent boundary layer is derived as

.)(2)()ln()(1

1

−

−+=

y

Wu

uy

u

u

u

u

eee

(A-9)

Although this expression is based on incompressible flow, it provides a good representation to

the turbulent velocity profile with or without pressure gradient.

Based on a thin boundary layer assumption, compressibility was introduced in to the

turbulent flow governing equations by Van Direst [11], thus a law of the wall for compressible

turbulent boundary layer was obtained in the form

45

−=−

y

u

u

u

ue ln1**

. (A-10)

In equation (A-10), the term u* is known as Van Driest’s generalized velocity, which

+

−=

2/122

2

)4(

)/(2arcsin)

1(*

AB

BuuA

Auu e

e (A-11)

where

ew

e

TT

MA

/

]2/)1[(2

2 −=

(A-12)

and

1/

]2/)1[(12

−−+

=ew

e

TT

MB

.

(A-13)

For adiabatic flow, equation (A-11) can be simplified as

=

e

e

u

uuu 2/1

2/1arcsin*

(A-14)

where

2

2

]2/)1[(1

]2/)1[(

e

e

M

M

−+

−=

(A-15)

Obviously, the wake component was not taken into consideration by Van Driest. However,

Maise and McDonald [12] found that when u*/uτ was plotted vs ln(y/δ), the deviation from Van

Driest’s law of the wall in the outer portion of the boundary layer was similar to the deviation

from the law of the wall in an incompressibile condition. Thus it was supposed that for

compressible adiabatic boundary layer, a form of velocity profile which was similar to the Cole’s

incompressible velocity profile may occur,

)2()ln(1**

Wy

u

u

u

ue −

+−=− .

(A-16)

Following research indicated that equation (A-16) with 1/κ = 2.5 and Π/κ = 1.25 appropriately

represents the compressible boundary layer with zero pressure gradient.

The success of Maise and MacDonald suggested that there could be a general form wall-

wake profile using Van Direst’s general velocity which is suitable for compressible turbulent

flow with pressure gradient. This general form was addressed by Mathews et. al [13].

46

Replace u with u* in equation (A-8)

).()ln(1*

yWC

yu

u

u

w

++= (A-17)

At the edge of the boundary layer, where u* = ue* and y = δ,

).(2)ln(1*

++= C

u

u

u

w

e (A-18)

Thus, subtract equation (A-18) with (A-17),

)2()ln(1**

Wy

u

u

u

ue −

+−=−

. (A-19)

The component Π/κ can be derived using the boundary condition of the boundary layer

+

−=

C

u

u

u

w

e

ln1*

2

1. (A-20)

Next, if it is assumed that

76.0

=

e

W

e

w

T

T

(A-21)

and for adiabatic turbulent flows

76.1

1

1

−=

e

w . (A-22)

From equation (A-14) and (A-19) we may derive

+

−+=

y

u

uy

u

u

u

u

eee

cos1*

)ln(*

11arcsinsin

1 2/1

2/1 (A-23)

where for mathematical convenience (2 - W) is replaced by [1 + cos(πy/δ)]. From equation (A-

20) and (A-22) and the definition of uτ, ue* and Cf , the parameters uτ/ue* and Π/κ become

2/1

2/1

arcsin

1

12/

−

=

f

e

Cuu . (A-24)

and

( )

−

−

−=

C

C

uu

f

e

26.1

2/1

12

Reln1

*/

1

2

1

. (A-25)

47

The combination of equation (A-23), (A-24), (A-25) and (A-15) outlines the velocity profile of

compressible turbulent boundary layer with non-zero pressure gradient.

48

APPENDIX B

ESTIMATION OF THE BOUNDARY LAYER MASS FLOW RATE AT THE EXIT OF THE

ISOLATOR

B.1 Description

This appendix mainly focuses on the preliminary calculation and estimation of data required

for the design of a boundary layer suction device of the 4inch × 1in supersonic wind tunnel,

including the mass flow rate of the boundary layer at the exit plane of the isolator and the back

pressure needed to keep the porous holes choked.

B.2 Assumptions

The estimation and calculation in this appendix are based on following assumptions.

1) The air is treated as perfect gas.

2) The values of the parameters of the free flow is calculated based on given general

condition, although these values are also measured in previous experiment.

3) The static temperature and static pressure are considered as uniform throughout the whole

cross section of the wind tunnel.

4) The bleed holes are simplified as a “tube”, of which the cross section area equals to the

sum of the area of each small hole in the wall.

5) In the “tube”, the stagnation pressure equals to the static temperature of the boundary layer

in the wind tunnel, and the stagnation pressure equals to the static pressure of the boundary

layer in the wind tunnel.

6) The static pressure of the airflow in the “tube” equals to the pressure in the vacuumized

container connected to the “tube”.

7) Although there is difference of total pressure between the condition in which Stuthers

49

operated the experiment (85-90 psi) and the boundary layer suction device is supposed to work

(60 psi), the velocity profile and the mass flow rate profile remain the same.

B.3 Data Source

All the data used in the calculation originate from Stuthers’ research, Measurements of

Boundary Layers In a Direct-Connect Facility For Hypersonic Propulsion.

B.4 Calculation Method

B.4.1 Free Stream Parameters Calculation

According to given condition, the boundary layer suction device will work at pt= 60 psi =

413685.4 Pa, Tt = 294 K and Me= 2.2. Thus according to the following relationships,

1

2

2

11

−

−+= e

t

e MT

T

(B-1)

12)

2

11( −

−−+=

e

t

e Mp

p

(B-2)

e

ee

RT

p=

(B-3)

for the airflow in the duct, the static pressure Pe = 38688.55 Pa, static temperature Te = 149.39K,

and the density ρ = 0.902 kg/m3.

B.4.2 Boundary Layer Mass Flow Rate Calculation

In Stuther’s paper, the mass flow rate ratio of boundary layer and free stream is given as

=

0

. dyu

u

m

m

eee

LB

(B-4)

Based on the assumption that the static temperature, static pressure are equal to those of the free

stream, the mass flow rate of the boundary layer at each measurement point can be estimated as

50

e

LB

eeLBm

mum

,,

.. =

(B-5)

Thus, the results of each measurement point are listed in the Table 3-1 and Table 3-2.

Therefore, the general mass flow rate of the 4-inch wall can be estimated as

)()2

(

)(

)2

(...)2

()2

(

1,1,11.,.1

32

1

32.,.1.,.

.,.

1,1,132.,.

1

32.,.31.,.

1

3.,.2.,.

1

2.,.1.,.

.,.

zzmzmm

m

zzm

zmm

zmm

zmm

m

wallLB

i

LBLB

iLB

wallLB

LBLBLBLBLBLB

wallLB

−++

−=

−+

+++

++

+=

=

(B-6)

And the mass flow rate of the 1-inch wall can be estimated as

)()2

(

)(

)2

(...)2

()2

(

1,2,21.,.2

6

1

6.,.1.,.

.,.

1,2,21.,.

2

6.,.5.,.

2

3.,.2.,.

2

2.,.1.,.

.,.

zzmzmm

m

zzm

zmm

zmm

zmm

m

wallLB

i

LBLB

iLB

wallLB

LBLBLBLBLBLB

wallLB

−++

−=

−+

+++

++

+=

=

(B-7)

B.4.3 Estimation of Total Area of the Holes on the Porous Wall

Because the flow direction through the holes is perpendicular to the flow direction in the

wind tube, it is reasonable to take the static pressure of the tunnel flow, Pe, as the stagnation

pressure of the flow through the hole, Pt,h. The similar relationship can be established in the

temperature aspect.

eht

eht

TT

PP

=

=

,

,

(B-8)

To guarantee that the influence from downstream of the vacuum system will not propagate

upstream to the wind tunnel, the bleeding holes must be kept choked, which means Mh = 1. Thus

51

the total area of the holes needed for eliminating all the boundary layer flow along each wall can

be estimated using following equation

hhh

wallLB

hRTM

mA

.,.

=

(B-9)

where

12

,

12

,

)2

11(

)2

11(

−−

−

−+=

−+=

=

hhth

hhth

h

hh

MPP

MTT

RT

P

(B-10)

B.5 Results

The mass flow rate of the boundary layer of the 4-inch wall is 0.1648 kg/s (0.3624 lb/s). The

mass flow rate profile is shown in Figure B-1.

According to the profile, there is no data between z1=1.9375 inch and z1=2.0000 inch. Thus,

in this region, suppose the mass flow rate per spanwise unit length is equal to the value at

z1=1.9375 inch.

The mass flow rate of the boundary layer of the 1-inch wall is 0.0401 kg/s (0.0884 lb/s).

The mass flow rate profile is shown in Figure B-2.

According to the profile, there is no data between z2=0.3125 inch and z2=0.5000 inch. In this

region, suppose the mass flow rate per unit length is equal to the value at z2=0.3125 inch.

To maintain the bleeding holes choked, the pressure in the vacuum tank should be no higher

than 2.964 psi. And when the holes are choked, the capability of mass flow rate passing through

it is 127.9 kg/s-m2. Therefore, with this bleeding rate, to remove the boundary layer on the 4-inch

52

wall, the total area of the holes needed is 2 in2，and to remove the boundary layer on the 1-inch

wall, the total area of the holes needed is 0.5 in2.

53

Figure B-1. Mass Flow Rate Profile of Boundary Layer Along 4-inch Wall

Figure B-2. Mass Flow Rate Profile of Boundary Layer Along 1-inch Wall

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2

B.L.Mass flow,4-inch wall

0

0.5

1

1.5

2

2.5

0 0.1 0.2 0.3 0.4 0.5

B.L. Mass flow, 1-inch wall

Mass flow rate, kg/(s*m)

Z1, inch

Mass flow rate, kg/(s*m)

Z2, inch

54

APPENDIX C

EVALUATION OF THE BLEEDING SYSTEM OPERATING TIME

C.1 Description

APPENDIX C mainly focuses on evaluating the available operating time of the boundary

layer eliminating device when aiming at removing boundary layer mass flow on all the four

walls at the exit plane of the isolator. Two conditions, that the tube is choked and not choked,

will be considered.

C.2 Assumptions

In this appendix, the evaluation of the working time is conducted based on the following

assumptions.

1) The air is treated as perfect gas.

2) The temperature of the air in the tank is constant at Ttank = 300K.

3) The density of outcoming flow through the pump equals to the density of air in the tank.

C.3 Data source

Following is the data of the vacuum tank.

The volume of the tank is Vtank = 1120 gallons = 4.23 m3. When the tank is fully vacuumed,

initial pressure in the tank is 0.1 psia, thus the initial mass in the tank is 0.034 kg/s. The

volumetric outflow rate is outV = 180 ft3 /min = 0.085 m3/s (based on the performance of the

pump).

The parameters of the inflow air is based on the calculation in APPENDIX B

The stagnation pressure is Pt,in = 38689 Pa;

When the tube is choked, the static pressure of inflow air is Pin = 20439 Pa, and the inflow

mass flow rate is inm = 0.409 kg/s.

55

C.4 Calculation Methods

C.4.1 Calculation of the Choked Condition

In this condition, the inflow mass flow rate is constant, inm= 0.409 kg/s. The pressure in the

tank can be obtained by

)(tank

tank

tanktankn tm

V

RTRTP kta ==

(C-1)

Here the mass in the tank can be obtained by

+=

+=

+=

dt tmV

V-tmm

dt tV-tmm

m-mmtm

tank

tank

outin0

tankoutin0

outin0tank

)(

)(

)(

(C-2)

m0 is the initial mass of the air in the tank. In this case, m0 = 0.034 kg. Therefore, take the

derivative of mtank(t) with respect to time, t.

)()(

tmV

V -m

dt

tdmtank

tank

outin

tank

=

(C-3)

This ODE can be solved numerically using Explicit Euler’s method, with the initial value

034.0)0(tank ==tm kg.

The matlab code for this calculation is attached in C.6.1.

C.4.2 Calculation of the Tube-Unchoked Condition

In this condition, the inflow mass flow rate is determined by the pressure in the tank, Ptank,

thus it is a function of time inm = )(t min

.

Similar with A1,

56

)(tank

tank

tanktankn tm

V

RTRTP kta ==

(C-4)

+=

+=

+=

dt tmV

V-dttmm

dt tV-dttmm

m-mmtm

tank

tank

outin0

tankoutin0

outin0tank

)()(

)()(

)(

(C-5)

m0 is the mass of the air in the tank when the tube converts from choked to unchoked. In this

case, m0 = 1.006kg, based on the result of the calculation of the choked condition.

Therefore, differentiate mtank with respect to time, t,

)()()(

tmV

V -tm

dt

tdmtank

tank

outin

tank

=

(C-6)

The inflow mass flow rate which is the mass flow rate in the tube, can be obtained by the mass

flow equation.

)()(,

,

h

int

hint

in MqT

APKtm =

(C-7)

with

)1(2

1

2

1

1

)]2

11(

1

2[)(

)1

2(

−

+−

−

+

−+

+=

+=

hhh MMMq

RK

(C-8)

The Mach number of the airflow in the tube can be figured out using isentropic relation

12

int,

tank )2

11( −

−−+=

hMP

P

(C-9)

Therefore,

57

]1))[(1

2(

1

tank

,tank

tank −−

=

−−

m

PV

RTM

int

h

(C-10)

1

tank

int,tank

tank2)(

2

11

−−

=−

+ mPV

RTM h

(C-11)

Substitute these into the differential equation of mtank,

)(

])(1

2[]1))[(

1

2(

)( )1(2

112

11

,

,

tmV

V -

mPV

RT m

PV

RT

T

APK

dt

tdm

tank

tank

out

tank

int,tank

tanktank

int,tank

tank

int

tubeinttank

−

+−

−−

−−

+

−−

=

(C-12)

This ODE can be solved numerically using Explicit Euler’s method, with the initial value

006.1)0( ==tmtank kg.

The matlab code for this calculation is attached in C.6.2.

C.5 Results

After starting, the tube will keep choked for 2.44s. When the pressure in the tank, ptank,

reaches 20439Pa, the mass of air in the tank mtank = 1.006 kg. The Ptank- t plot of this condition is

shown in Figure 3-2.

After the pressure in the tank reaches 20439 Pa, the tube will not be choked, thus the influx

mass flow rate will be a function of Ptank, which means it will vary with time. In this condition,

the Ptank-t plot is shown in Figure 3-3.

According to the plot, the pressure in the tank will finally reach about 3.86×104 Pa ( 5.60

psia )， and this process will take about 4 seconds after the inflow converting from choked to

unchoked. The inflow and outflow mass flow rate during unchoked condition is shown in Figure

3-4.

58

C.6 Matlab Code

C.6.1 Matlab Code for Choked Condition

%Calculation of working time, bleeding holes choked

%@ exit plane of the isolator, all four walls

%Numerically solving ODE, based on Explicit Euler's method

%----Settings----

delta_t = 0.0001; %step length(second)

a = 0.409; %mass influx rate 0.409 kg/s

b = 0.085/4.24; %outflow volume rate / volume of the tank, cubic meter &second

y = [];

y(1) = 0.034; %initial mass in the tank, kg

Ptank = [];

Ptank(1) = ((287.06 * 300 )/4.24) * y(1); %P = ((RT)/Vtank)* m

Pcr = 20439; %Critical tank pressure to keep the tube choked, Pa

%----Initialize----

t = [];

t(1) = 0;

f = [];

f(1) = a - b*y(1);

n = 1;

while (Ptank(n) < Pcr) % tube choke when pressure lower than 20439 Pa

y(n+1) = y(n) + delta_t * f(n);

f(n+1) = a - b*y(n);

t(n+1) = t(n) + delta_t;

Ptank(n+1) = ((287.06 * 300 )/4.24) * y(n+1);

n = n+1;

end

fprintf('Working time is %.2f s\n End Pressure is %f Pa, mass in the tank %f kg',t(n), Ptank(n),

y(n));

fprintf('Working time is %.2f s\n End Pressure is %f Pa, mass in the tank %f kg',t(n), Ptank(n),

y(n));

figure

plot(t, Ptank,'linewidth',2);

xlabel('Time, s','Fontsize',12);

ylabel('Pressure, Pa', 'Fontsize',12 );

title('Pressure in the tank','Fontsize',14);

figure

plot(t, Ptank*0.000145,'linewidth',2);

xlabel('Time, s','Fontsize',12);

59

ylabel('Pressure, psi', 'Fontsize',12 );

title('Pressure in the tank','Fontsize',14);

C.6.2 Matlab Code for Unchoked Condition

%Calculation of working time, bleeding holes not choked

%Numerically solving ODE, based on Explicit Euler's method

%----Settings----

R = 287.06; % R = 287.06 J/kg-K

r = 1.4;

Ptin = 38689; % Total pressure of flow in the tube, Pa

Ttin = 149.39; % Total temperature of flow in the tube, K

Ain = 2 * (1.285*10^(-3) + 3.135*10^(-4)); % Tube intersection area, m^2

Vtank = 4.24; % Tank Volume, m^3

Vout = 0.085; % Volumetic outflow rate, m^3/s

m0 = 1.006; % Initial mass set as 1.006kg

T = 300; % Temperature in the tank, K

delta_t = 0.0001; % step length, s

Pcr = 38689 ; % Critical tank pressure to end the calculation, Pa

%----Initialize----

K = sqrt((r/R)*(2/(r+1))^((r+1)/(r-1)));

y = [];

y(1) = m0; %initial mass in the tank, kg

Ptank = [];

Ptank(1) = ((R * T )/Vtank) * y(1); %P = ((RT)/Vtank)* m

t = [];

t(1) = 0;

%Mass changing rate in the tank

f = [];

f(1) = K*(Ptin*Ain/sqrt(Ttin))*(((2/(r-1))*((R*T*y(1)/(Vtank*Ptin))^((1-r)/r)-1))^0.5)* ...,

(((2/(r+1))*(R*T*y(1)/(Vtank*Ptin))^((1-r)/r))^((r+1)/(2-2*r))) - (Vout/Vtank)*y(1);

%Air inflow rate (mass)

f1 = [];

f1(1) = K*(Ptin*Ain/sqrt(Ttin))*(((2/(r-1))*((R*T*y(1)/(Vtank*Ptin))^((1-r)/r)-1))^0.5)* ...,

(((2/(r+1))*(R*T*y(1)/(Vtank*Ptin))^((1-r)/r))^((r+1)/(2-2*r)));

%Air outflow rate (mass)

f2 = [];

f2(1) = (Vout/Vtank)*y(1);

n = 1;

while (Ptank < 38689 & t(n) < 6) % Ending condition

y(n+1) = y(n) + delta_t * f(n);

f(n+1) = K*(Ptin*Ain/sqrt(Ttin))*(((2/(r-1))*((R*T*y(n+1)/(Vtank*Ptin))^((1-r)/r)-1))^0.5)*

...,

60

(((2/(r+1))*(R*T*y(n+1)/(Vtank*Ptin))^((1-r)/r))^((r+1)/(2-2*r))) - (Vout/Vtank)*y(n+1);

f1(n+1) = K*(Ptin*Ain/sqrt(Ttin))*(((2/(r-1))*((R*T*y(n+1)/(Vtank*Ptin))^((1-r)/r)-1))^0.5)*

...,

(((2/(r+1))*(R*T*y(n+1)/(Vtank*Ptin))^((1-r)/r))^((r+1)/(2-2*r)));

f2(n+1) = (Vout/Vtank)*y(n+1);

t(n+1) = t(n) + delta_t;

Ptank(n+1) = ((R * T )/Vtank) * y(n+1);

n = n+1;

end

fprintf('Working time is %.2f s\n End Pressure is %f Pa, mass in the tank %f kg',t(n), Ptank(n),

y(n));

figure

plot(t, Ptank,'linewidth',2);

xlabel('Time, s','Fontsize',12);

ylabel('Pressure, Pa', 'Fontsize',12 );

title('Pressure in the tank','Fontsize',14);

axis([0 6 0 4e+04])

figure

plot(t, Ptank*0.000145,'linewidth',2);

xlabel('Time, s','Fontsize',12);

ylabel('Pressure, psi', 'Fontsize',12 );

title('Pressure in the tank','Fontsize',14);

axis([0 6 0 6])

figure

plot(t, f1,'linewidth',2);

hold on ;

plot(t, f2,'-.','linewidth',1);

xlabel('Time, s','Fontsize',12);

ylabel('Mass flow rate, kg/s', 'Fontsize',12 );

title('Inflow and outflow mass flow rate','Fontsize',14);

legend('Inflow mass flow rate','Outflow mass flow rate');

61

APPENDIX D

CALCULATION OF THE FINAL DESIGN

D.1 Description

APPENDIX D mainly focuses on the calculation of the performance of the final design case.

As it is mentioned in APPENDIX C and CHAPTER 3, the case removing all the boundary layer

mass flow at the exit plane of the isolator, although with acceptable working time (2.44s), has

disadvantages such as unacceptable high flow speed in the 2-inch pipe and relatively large size

of the device. Therefore, the final design case is modified to only remove the boundary layer

alone with one 4-inch wall at the entrance, rather than the exit of the the isolator. In this

appendix, sing the same Matlab code for choked condition calculation in APPENDIX C, the

working time (bleeding holes choked time duration) of the final design is predicted.

D.2 Assumptions

In this appendix, the evaluation of the working time is conducted based on the following

assumptions.

1) The air is treated as perfect gas.

2) The temperature of the air in the tank is constant at Ttank = 300K.

3) The density of outcoming flow through the pump equals to the density of air in the tank.

4) The boundary layer thickness at the entrance plane of the isolator is half the boundary

layer thickness at the exit plane of the isolator.

5) The general parameters of the flow do not change along the isolator.

D.3 Data Source

Following is the data of the vacuum tank.

62

The volume of the tank is Vtank = 1120 gallons = 4.23 m3. When the tank is fully vacuumed,

initial pressure in the tank is 0.1 psia, thus the initial mass in the tank is 0.034 kg/s. The

volumetric outflow rate is outV = 180 ft3 /min = 0.085 m3/s (based on the performance of the

pump).

The parameters of the inflow air is based on the calculation in APPENDIX B

The stagnation pressure is Pt,in = 38689 Pa;

When the tube is choked, the static pressure of inflow air is Pin = 20439 Pa, and the inflow

mass flow rate is inm = 0.0824 kg/s.

D.4 Calculation Methods

In this condition, the inflow mass flow rate is constant, inm= 0.0824 kg/s. The pressure in

the tank can be obtained by

)(tank

tank

tanktankn tm

V

RTRTP kta ==

(D-1)

Here the mass in the tank can be obtained by

+=

+=

+=

dt tmV

V-tmm

dt tV-tmm

m-mmtm

tank

tank

outin0

tankoutin0

outin0tank

)(

)(

)(

(D-2)

m0 is the initial mass of the air in the tank. In this case, m0 = 0.034 kg. Therefore, take the

derivative of mtank(t) with respect to time, t.

)()(

tmV

V -m

dt

tdmtank

tank

outin

tank

=

(D-3)

This ODE can be solved numerically using Explicit Euler’s method, with the initial value

034.0)0(tank ==tm kg.

63

The matlab code for this calculation is attached in D.6..

D.5 Results

After starting, the tube will keep choked for 13.99s. When the pressure in the tank, Ptank,

reaches 20439 Pa, the mass of air in the tank mtank = 1.006 kg. The Ptank- t plot of this condition is

shown in Figure 3-5.

D.6 Matlab Code

%Calculation of working time, bleeding holes choked

%@ Entrance of the isolator, one 4-in wall

%Numerically solving ODE, based on Explicit Euler's method

%----Settings----

delta_t = 0.0001; %step length(second)

a = 0.0824; %mass influx rate 0.0824 kg/s

b = 0.085/4.24; %outflow volume rate / volume of the tank, cubic meter &second

y = [];

y(1) = 0.034; %initial mass in the tank, kg

Ptank = [];

Ptank(1) = ((287.06 * 300 )/4.24) * y(1); %P = ((RT)/Vtank)* m

Pcr = 20439; %Critical tank pressure to keep the tube choked, Pa

%----Initialize----

t = [];

t(1) = 0;

f = [];

f(1) = a - b*y(1);

n = 1;

while (Ptank(n) < Pcr) % tube choke when pressure lower than 20439 Pa

y(n+1) = y(n) + delta_t * f(n);

f(n+1) = a - b*y(n);

t(n+1) = t(n) + delta_t;

Ptank(n+1) = ((287.06 * 300 )/4.24) * y(n+1);

n = n+1;

end

fprintf('Working time is %.2f s\n End Pressure is %f Pa, mass in the tank %f kg',t(n), Ptank(n),

y(n));

fprintf('Working time is %.2f s\n End Pressure is %f Pa, mass in the tank %f kg',t(n), Ptank(n),

y(n));

figure

plot(t, Ptank,'linewidth',2);

xlabel('Time, s','Fontsize',12);

ylabel('Pressure, Pa', 'Fontsize',12 );

64

title('Pressure in the tank','Fontsize',14);

figure

plot(t, Ptank*0.000145,'linewidth',2);

xlabel('Time, s','Fontsize',12);

ylabel('Pressure, psi', 'Fontsize',12 );

title('Pressure in the tank','Fontsize',14);

65

APPENDIX E

THE DESIGN DRAWING OF THE BLEEDING DEVICE

In this section the design drawings of the bleeding device are shown.

Figure E-1 shows the assembly of the device. The detailed drawings of the 4 designs of the

parts are shown in Figure E-2, Figure E-3, Figure E-4, Figure E-5 and Figure E-6.

Figure E-2 shows the detailed design of the 1-inch wall part. A quantity of 2 is needed for

this design. Figure E-3 shows the detailed design of one 4-inch wall. And Figure E-4 and Figure

E-5 shows the design of the other 4-inch wall. A porous plate and a pipe plate with 10 brass

pipes are mounted on this wall. And Figure E-6 shows the detailed design of the pipe plate.

66

Figure E-1. Assembly

67

Figure E-2. Part 1 of 4_1in Wall

68

Figure E-3. Part 2 of 4_4in Wall A

69

Figure E-4. Part 3(a) of 4_4in Wall B

70

Figure E-5. Part 3(b) of 4_ 4in Wall B

71

Figure E-6. Part 4 of 4_Pipe Plate

72

REFERENCES

[1] LIANG, De-wang, and QIAN, Hua-jun, ”Experimental investigation of aerodynamic

characteristics of porous plates and numerical simulation of boundary layer suction”,

Acta Aeronautica et Astronautica Sinica, Vol. 23, No. 6, 2002, pp. 512-516.

[2] Melling, A., and J.H. Whitelaw, "Turbulent Flow in a Rectangular Duct," Journal of

Fluid Mechanics, Vol. 78, Pt. 2, 1976, pp. 289-315.

[3] WONG, W., “The Application of Boundary Layer Suction to Suppress Strong Shock-

Induced Separation in Supersonic Inlet”, AIAA/SAE 10th Propulsion Conference, 1974.

[4] Syberg, Jan, and Koncsek, J. “Bleed System Design Technology for Supersonic Inlets”,

Journal of Aircraft, Vol. 10, No. 7, 1973, pp 407-413.

[5] Syberg, Jan, and Hickox, T.E., “Design of a bleed system for a Mach 3.5 Engine”, The

Boeing Company, 1973.

[6] MacManus, D.G., and Eaton, J.A.,”Flow Physics of Discrete Boundary Layer Suctions

Measurements and Predictions”, Journal of Fluid Mechanics, Vol. 417, 2000, pp. 47-75.

[7] Stuthers, Steven, “Measurements of Boundary Layers in a Direct-Connect Facility for

Hypersonic Propulsion”,M.S. thesis, 2016, University of Florida, Gainesville, Florida.

[8] Djerekarov, J., “Design of a Continuous Blowdown Facility for Hypersonic Research,”

M.S. thesis, 2012, University of Florida, Gainesville, Florida.

[9] Barnes, F., “Fuel-Air Mixing in a Directly-Fueled Supersonic Cavity Flameholder,”

Ph.D.2 thesis, 2016, University of Florida, Gainesville, Florida.

[10] Coles, D., “The Law of the Wake in the Turbulent Boundary Layer,” Journal of Fluid

Mechanics, Vol. 1, Pt. 2, 1956, pp. 191-226.

[11] Van Driest, E., “Turbulent Boundary Layer in Compressible Fluids,” Journal of the

Aeronautical Sciences, Vol. 18, No. 3, 1951, pp. 145-160, 216.

[12] Maise, G., & McDonald, H., “Mixing Length and Kinematic Eddy Viscosity in a

Compressible Boundary Layer,” AIAA, Vol. 6, No. 1, 1968, pp. 73-80.

[13] Mathews, D., Childs, M., & Paynter, G., “Use of Coles' Universal Wake Function for

Compressible Turbulent Boundary Layers,” Journal of Aircraft, Vol. 7, No. 2, 1970, pp.

137-140.

73

BIOGRAPHICAL SKETCH

Zhangming Zeng was born and finished his elementary and secondary education in

Shenzhen, China, the youngest and most innovative city in that country. He has been interested

in aircraft and spacecraft and dreamed to be an aerospace specialist since his childhood.

In 2011, he entered Beihang University (Beijing Univ. of Aero. & Astro.), majoring in

Flying Vehicle Power Engineering (aircraft propulsion). During the four years’ undergraduate

study, he studied various courses in this field. In year 2015, he served as a student researcher in

the Fluid and Acoustic Engineering Laboratory in Beihang University, conducted experimental

research on the rotor-stator interaction noise of single-stage axial fan, and finished his paper for

B.S. degree based on the result of the experiment.

He entered University of Florida as a M.S. student in aerospace engineering in 2016.

Since early 2017, he has served in the Combustion and Propulsion Laboratory in University of

Florida, under the guidance of Prof. Corin Segal, focusing on designing a boundary layer bleed

device for a supersonic rectangular-duct wind tunnel. And in spring 2018, he was employed by

Prof. William E. Lear as his teaching assistant in the Gas Turbine and Jet Engine course.

As a motivated learner and an energetic future researcher in aerospace engineering,

Zhangming decided to pursue Ph.D. degree in this field, after finishing his study as a M.S.

student.