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MINISTERUL EDUCATIE NATIONALE

ANALELE UNIVERSITATII " Dunarea de Jos " DIN GALATI

Fascicula IV

FRIGOTEHNIE MOTOARE CU ARDERE INTERNA

CAZANE SI TURBINE

ANUL XXIV 2010

ISSN 1221- 4558

MINISTRY OF NATIONAL EDUCATION

THE ANNALS OF THE UNIVERSITY " Dunarea de Jos " OF GALATI

Fascicle IV

REFRIGERATING TECHNIQUE INTERNAL COMBUSTION ENGINES

BOILERS AND TURBINES

YEAR XXIV 2010

ISSN 1221 - 4558

EDITING MANAGEMENT

RESPONSIBLE EDITOR

Prof.dr.eng. Mînzu VIOREL

ASSISTANT EDITORS

Prof.dr.eng. Iulian BARSAN Prof.dr.eng. Toader MUNTEANU Prof.dr.eng.Victor CRISTEA Prof.dr. Mirela PRAISLER Prof.dr. Daniela SARPE

SECRETARY

Prof.dr.eng. Alexandru Ioan

EDITING STAFF

FASCICLE IV



EDITOR IN CHIEF Prof dr.eng. Viorel POPA

MEMBERS Prof. dr. eng. Constantin IOSIFESCU Prof. dr.eng. Michel Feidt STANCHEV Prof. dr.eng. Gianfranco RIZZO Prof. dr.eng. Sahin YILDIRIM Prof. dr.eng. Julio Maggiolly NOVAIS Prof. dr.eng. Alexandru DOBROVICESU Prof. dr.eng. Ion IONITA

Prof. dr.eng. Tanase PANAIT Prof. dr. eng. Dan SCARPETE Prof. dr. eng. Valeriu DAMIAN Prof. dr.eng. Gheorghe POPESCU Prof. dr.eng. Liviu DRUGHEAN Prof. dr.eng. Mugur BALAN Assoc.Prof.dr. Liviu COSTIUC

SECRETARY dr. eng. Ionel OPREA

MINISTERUL EDUCATIE NATIONALE

ANALELE UNIVERSITATII " Dunarea de Jos " DIN GALATI

Fascicula IV

FRIGOTEHNIE MOTOARE CU ARDERE INTERNA

CAZANE SI TURBINE

ANUL XXIV 2010

ISSN 1221- 4558

MINISTRY OF NATIONAL EDUCATION

THE ANNALS OF THE UNIVERSITY " Dunarea de Jos " OF GALATI

Fascicle IV



YEAR XXIV 2010

ISSN 1221 - 4558

THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI FASCICLE IV

REFRIGERATING TECHNIQUE, INTERNAL COMBUSTION ENGINES,


SUMMARY Graţiela Maria TÂRLEA, Ion ZABET - HEAT TRANSFER AND MASS TRANSFER IN MICRO-CHANNELS HEAT EXCHANGERS……………………………………………………..…….5 Gabriela HUMINIC, Angel HUMINIC - CFD STUDY OF A DOUBLE PIPE HELICAL HEAT EXCHANGER………………………………………………………………………………………..…….10 Gelu COMAN, Cristian IOSIFESCU, Valeriu DAMIAN - THE STUDY OF ICE FORMATION OUTSIDE A FLAT WALL…………………….…………………………………………15 Ionel OPREA - AN IMPROVED METHOD FOR HEAT PUMPS REFRIGERANT CHOICE………………………………………………………………………………………………….....19 Gelu COMAN, Critistian IOSIFESCU, Valeriu DAMIAN - THE STUDY OF ICE FORMATION OUTSIDE A CYLINDRICAL WALL………………………………………………..…25 Silviu VLASIE - HEAT CONDUCTION PROBLEMS WITH CYLINDRICAL SYMMETRY SOLVING BY INTEGRAL TRANSFORM TECHNIQUE – CYLINDRICAL HOLE………………29 Jorge MARTINS José MACHADO - SIMPLE CONTROL SYSTEM FOR SERIES-HYBRID I. C. ENGINE……………………………………………………………………………………..…………..33 Salvadore Mugurel BURCIU, Manuela BURCIU - DETERMINATION OF OPTIMUM OPERATING REGIMES OF ROAD MOTOR VEHICLES BASED ON MINIMUM FUEL CONSUMPTION…………………………………………………………………………….…………….37 Mariana LUPCHIAN - FORMULATING THERMOECONOMIC OPTIMIZATION PROBLEMS FOR THE ENERGETIC PLANT WITH INTERNAL COMBUSTION ENGINES APPLIED ON SHIP………………………………………………………………………………………..42 Alphonse DIANGO, Christelle PERILHON, Emile DANHO, Georges DESCOMBES - INFLUENCE DES TRANSFERTS THERMIQUES SUR LES PERFORMANCES DES MICRO-TURBINES A GAZ…………………………………………………………………………….…………..47 Nicuşor VATACHI - CUSTOMIZED DESIGNS AND STEAM GENERATOR PERFORMANCE…………………………………………………………………………………………..61 G.ROLEA, Ion V.ION, Florin POPESCU PREDICTION OF SYNGAS COMPOSITION PRODUCED BY BIOMASS GASIFYING………………………………………………………………65

Nicuşor VATACHI - MODIFIED CLAUS PROCESS APPLIED TO NATURAL GAS FOR SULFUR RECOVERY……………………………………………………………….…………………….69 Viorel POPA*, Ion Ion*, Alexandru SERBAN - DESIGN AND PERFORMANCE SIMULATION OF NEW SOLAR CONTINUOUS SOLID ADSORPTION REFRIGERATION AND HEATING HYBRID SYSTEM…………………………………………………………….………..75 Dan-Teodor BĂLĂNESCU, Constantin-Eusebiu HRIŢCU, Sorinel-Gicu TALIF - DIAGNOSIS OF A DOMESTIC HOT WATER PREPARATION SYSTEM CONSISTING OF A 24 KW WALL MOUNTED BOILER AND AN 80 L WATER TANK…………….……………..………..80 Gabriel IVAN, Nicolae IVAN, Dragos ISVORANU, Viorel BADESCU - HEAT EXCHANGERS FOR PASSIVE HOUSES………………………………………………………………85 Mihail VETROV, Carmen Mihaela VETROV - THE METHOD ABOUT OUTDOOR AIR INFILTRATES TO THE INDOOR SPACE……………………………………………………………..90 Elena BASOV, Ion C. IONITA - LANDFILL-GAS PRODUCTION AT THE TIRIGHINA LANDFILL………………………………………………………………………………………………….95

THE ANNALS OF "DUNAREA DE JOS” UNIVERSITY OF GALATI FASCICLE IV REFRIGERATING TECHNIQUE, INTERNAL COMBUSTION ENGINES,

BOILERS AND TURBINES, ISSN 1221-4558 2010

HEAT TRANSFER AND MASS TRANSFER IN MICRO-CHANNELS HEAT EXCHANGERS

Prof. Univ. Dr. Ing. Graţiela Maria TÂRLEA, Drd. Ing. Ion ZABET

Technical University of Civil Engineering, Faculty of Building Services, 66th Bld. Pache Protopopescu Email: [email protected], [email protected]

ABSTRACT The need for the development of efficient and effective cooling techniques for microchips has generated extensive research interest in micro-channels heat transfer. As the market induces electronic chips to undergo a size of reduction while increasing functionality, the use of convective heat transfer in micro-channels is believed to be one of the most efficient ways to provide a better understanding of liquid and gaseous flow and heat transfer at micro-scale, which is very important for micro-devices development and design. Heat transfer in micro-channel has gained more interest in the last decade due to developments for the aerospace, biomedical and electronic industries. This material shows the advantages and disadvantages of heat exchangers with micro-channels and their performances. KEYWORDS Heat exchanger, micro-channel, heat transfer, ammonia, carbon dioxide, HFC-s, convection, conduction, flow path, counter flow. 1. INTRODUCTION The need for the development of efficient and effective cooling techniques for microchips has generated extensive research interest in micro-channel heat transfer. As the market induces electronic chips to undergo a size reduction while increasing functionality, the use of convective heat transfer in micro-channels is believed to be one of the most efficient ways to provide a better understanding of liquid and gaseous flow and heat transfer at micro-scale, which is very important for micro-device development and design. Heat transfer in micro-channel has gained more interest in the last decade due to developments in the aerospace, biomedical and electronics industries. As the size decreases, more efficient ways of cooling are sought due to the reduction in the heat transfer area. Convection and conduction are the two major heat transfer mechanisms which have been investigated at micro-scale. Convective heat transfer in micro-channels has been intensively analyzed by both

experimental and analytical methods. As far as convective heat transfer is concerned, liquid and gaseous flows must be considered separately. Liquid flow has been investigated experimentally, whereas analytical, numerical and molecular simulation techniques have been applied to understand the characteristics of gaseous flow and heat transfer. The Knudsen number is used to represent the rarefaction effects. For Knudsen numbers close to zero, flow is still assumed to be continuous. As the Knudsen number takes higher values, due to a higher molecular mean free path by reduced pressure or a smaller flow dimension, rarefaction effects become more significant and play an important role in determining the heat transfer coefficient. Many definitions of micro- and mini- channel hydraulic diameter are used throughout the literature. Kandlikar and Grande (2003) proposed the following classification: • conventional channels (Dh > 3 mm); • mini-channels (200μm< Dh

THE ANNALS OF ”DUNAREA DE JOS” UNIVERSITY OF GALATI FASCICLE IV __________________________________________________________________________________________

additive components: nucleate boiling and convective boiling. Nucleate boiling is due to nucleating bubbles and their subsequent growth and removal from the heated surface. Convective boiling is due to heated fluid moving from the heated surface to the flow core. These two mechanisms cannot be separated with any precision since they are closely interconnected. The aim here is to summarize recent work on heat transfer and mass transfer, to describe an experiment on the phenomenon in micro-channels and to compare the results with classical correlations. Charge minimization of HFC refrigerant systems is rapidly gaining interest as a way to reduce greenhouse gas emissions. The HEAT EXCHANGER project tries to push this minimization to the limits by answering the questions: “How can we get the maximum cooling capacity out of one kg refrigerant?” Choosing this approach a charge reduction of 95% is aimed for. By signing the international Kyoto protocol, the EU has obliged itself to reduce the emissions of greenhouse gases by 8% in 2010. Currently used refrigerants like R22 and R404A are greenhouse gases with a high global worming potential (GWP). This resulted in a phasing out of R22 starting in 2010. Several (mainly Scandinavian) countries already started a phasing out scheme for the HFC-s and also the EC has intentions in that direction (F-gas regulation).New technological solution are required to meet the demands of EU and make the profitable operation and exploitation of refrigeration possible in the future. One option to

decrease refrigerant emissions is to reduce the charge of the refrigeration installations. Until now, research and development regarding charge minimization are mainly focused on specific components of the refrigerant cycle: condenser and evaporators. For example: reducing the charge in the system will hamper the transport of lubricants through the system, thus influencing the performance of the compressor. HEAT EXCHANGER strives for an integral approach when it comes to minimizing refrigerant charges. Trying to answer the question:” How can we get the maximum cooling capacity out of one kg refrigerant?” the answer is simple: “Returning the refrigerant back to the evaporator as quickly as possible”. However, the implications faced to in achieving this task demand new developments in several fields. The heat exchanger’s design should focus on high heat transfer and less volume. Micro channels heat exchangers are considered to be a serious option. Control systems should have a higher response: decreasing the charge will also decrease the slowness of the system. Apart from the benefits for HFC refrigerants charge reduction also benefit the application for natural refrigerants. The application of natural refrigerants is limited because of safety issues and regulations: ammonia is toxic and propane is highly flammable. Reducing charge of natural refrigerants reduces safety risk, thus broadening the application range of these refrigerants.

Fig 1 Flow path in heat exchangers (type Air-Water)

6


Fig 2 Counter flow path in shell and tube heat exchangers (Type Water-Oil)

2. CONDENSATION IN MICRO CHANNELS In condensation process, an important role can also be played by: surface tension effects, surface wetting characteristics, and meta-stable phase stability. As a result of interfacial tension, the pressure inside a spherical liquid droplet of radius r must exceed that in the surrounding liquid by 2σ/r. A consequence of this and basic thermodynamics is that, at equilibrium, the surrounding vapour must actually be slightly supersaturated. The amount of super saturation required at equilibrium increases as the radius of curvature of the bubble interface decrease. For a liquid droplet on a solid surface with a specified volume, the wetting contact angle

dictates the radius of curvature of the droplet interface. Because of the linkage between the interface curvature and the required equilibrium super saturation, the wetting behaviour thus determines the level above which the vapour super saturation must be raised for the droplet to grow. Steady condensation on the droplet interface can be sustained only if the vapour is driven beyond this super saturation level by cooling or depressurization. In most refrigeration systems, the flow in the condenser is either horizontal or vertically downward. Figure 3 schematically depicts a typical condensation process in a horizontal round tube. Superheated vapour enters the tube and at the exit end the liquid is sub cooled. At some distance downstream of the entrance,

7


vapour begins to condense on the walls of the tube. The location at where this occurs is at or slightly before the bulk flow reaches the equilibrium saturation condition. In most condensers, the liquid readily wets the interior of the tube and at high vapour volume fractions the liquid forms a thin liquid film on the interior wall of the tube. The vapour velocity is generally high at the inlet end of the condenser tube, and the liquid film is driven along the tube by strong vapour shear on the film. At low vapour flow rates, some stratification may occur and the film may be thicker on the bottom of the horizontal tube. At low vapour flow rates, turbulent stresses acting on the liquid may tend to keep the thickness of the liquid film nominally uniform over the perimeter of the tube. In most condenser applications, shear-dominated annular flow persist to very low qualities and the

overwhelming majority of the heat transfer occurs in this regime. The very last stage of condensation process, corresponding to qualities less than a few percent, may occur in slug, plug, or bubbly two-phase flow. Generally these regimes represent such a small portion of the overall heat transfer in the condenser that some inaccuracy in estimating the heat transfer coefficient for them is tolerated. As a first estimate, the heat transfer coefficient may be predicted using a correlation for pure single-phase liquid flow in the tube at the same total flow rate, or a correlation for annular flow condensation may simply be extrapolated to zero quality. The form of most correlation methods for predicting local convective condensation heat transfer coefficients are optimized to match data in the annular flow regime.

Fig 3 Flow regimes during horizontal co current flow with condensation

3. ERROR ANALYSIS In measurements field all the time you have to deal with errors on reading and analysis. For avoid that errors it is necessary to take more readings for one measurement and make the average. Much more readings that you take you will have small error and a better result. Thus you are using is of limited accuracy; when you read the scale, you may have to estimate a fraction between the marks on the scale, etc. Errors may be due to such things as incorrect calibration of equipment, consistently improper use of equipment or failure to properly account for some effect. But small systematic errors will always be present. For instance, no instrument can ever be calibrated perfectly. Other sources of errors are external effects which can change the results of the experiment, but for which the corrections are not well known. Another reason for errors is fluctuation from one measurement to the next. They yield results distributed about some mean value. They can occur for a variety of reasons. They may occur due to lack of sensitivity.

For a sufficiently a small change an instrument may not be able to respond to it or to indicate it or the observer may not be able to discern it. They may occur due to noise. There may be extraneous disturbances which cannot be taken into account. They may be due to imprecise definition. The best thing that can be done to deal with random errors is to repeat the measurement many times, varying as many "irrelevant" parameters as possible and use the average as the best estimate of the true value. Doing this should give a result with less error than any of the individual measurements. 4. CONCLUSIONS The research in that domain it is still in experimental phase. A lot of science people work to improve the heat exchanger with micro-channels and have good results. Still the science men from the entire world try to obtain a better heat exchanger with micro-channels with better results and less refrigerant charge. REFERENCES

8


[1] I. COLDA, A. DAMIAN ,“Instalaţii si

echipamente de desprăfuire” , Editura

Conspres, Bucureşti, 2005

[2] I. COLDA, C. TEODOSIU, “Instalaţii de

desprăfuire si de transport

pneumatic:îndrumător de proiectare”,

Bucureşti, 1997

[3] F. CHIRIAC, A. LECA, M. POP, L.

LUCA, N. ANTONESCU, “Procese de

transfer de căldura si de masa in instalaţii

industriale” , Editura Tehnica, Bucureşti,

1982

[4] F. CHIRIAC, C. ZAMFIRESCU,

“Complemente de transfer de căldura prin

convecţie”, Editura CONSPRES,

Bucureşti, 2000

[5] GRATIELA MARIA TÂRLEA, “Sisteme

frigorifice ecologice Vol. I”, Editura

HGA, Bucureşti, 2002

[6] S. KAKAC, L.L. VASILIEV, Y.

BAYAZITOGLU AND Y. YENER,

“Micro scale Heat Transfer –

Fundamentals and Applications”, NATO

Science Series, Netherlands, 2005

[7] SATISH G. KANDLIKAR, SRINIVAS

GARIMELLA, DONGQING LI,

STEPHANE COLIN, MICHAEL R.

KING, “Heat transfer and fluid flow in

mini-channels and micro-channels”, 1st

Edition, Great Britain , 2006

[8] VDI – „Warmeatlas – 10 Auflage“,

Springer-Verlag Berlin Heidelberg New

York, 2006

[9] DONALD Q. KERN , “Process heat

transfer”, McGraw - HILL BOOK

COMPANY, Toronto; New York, London,

1950

[10] APPARATENFABRIEK HELPMAN

B.V. GRONINGEN - Data Base

Documentation

[11] H.DRAGOS, “Instalatii Frigorifice”,

Editura Matrix Rom, Bucuresti, 2004

[12] H.DRAGOS, “Criogenie Tehnica”,

Editura Matrix Rom, Bucuresti,

2002

9



CFD STUDY OF A DOUBLE PIPE HELICAL HEAT EXCHANGER

Gabriela HUMINIC, Angel HUMINIC Transilvania University of Brasov, ROMANIA

29, B-dul Eroilor, Brasov, tel.0268422921, fax0268474768 e-mail: [email protected]

ABSTRACT. Numerical studies for a double-pipe helical heat exchanger are performed with the aid of a commercial computational fluid dynamics CFD package for the fluid flow and heat transfer characteristics. The goal of this study is to evaluate a double-pipe helical heat exchanger for fluid-to-fluid flow. Simulations were performed using various flow rates (laminar regime) in the inner tube and in the annulus, as well as for parallel flow and counterflow heat exchangers.

KEYWORDS: CFD, heat exchanger, heat transfer. 1. INTRODUCTION Helical coiled tubes can be found in many

applications including compact heat exchangers, heat recovery systems, food processing, nuclear

reactors, chemical processing, low value heat exchange, and medical equipment.

Helical coils are very alluring for various processes such as heat exchangers (Fig. 1) and reactors because they can accommodate a large heat transfer area in a small space, with high heat transfer coefficients and narrow residence time distributions.

Fig. 1 - Helical coil Fig. 2 –Double-pipe helical coil

Comparisons for the heat transfer

coefficients between straight tubes and helically coiled tubes immersed in a water bath were performed by Prabhanjan et al. (2002). Findings showed that the heat transfer coefficient were

greater in the helically coiled system. Inagaki et al. (1998) studied the outside heat transfer coefficient for helically coiled bundles for Reynolds numbers in the range of 6000 to 22 000 and determined that the outside Nusselt number. Takahashi and Momozaki (2000) experimented with a two-phase mixture of air and mercury along with a magnetic

10


field to determine the heat transfer characteristics of such a system. Their work studied the combined effect of the magnetic force and the centrifugal force on the flow of mercury and its effects on the heat transfer rates. Boiling heat transfer in helical coils for steam-water was studied by Zhao et al. (2003) for a range of steam quality, mass fluxes, and heat fluxes. They presented a new correlation for pressure drop and found that the Lockhart-Martinelli type of correlation did not satisfactorily represent their experimental data. They proposed a new boiling heat transfer correlation for their data. Furthermore, they found that the boiling heat transfer was dependent on both the mass and heat fluxes. Heat transfer studies of a helical coil immersed in a water bath was studied by Prabhanjan et al. (2004). A method to predicted outlet temperatures from the helical coil was proposed which took into consideration the flow rates and geometry of the coil. The heat transfer on the outside of the coils was from natural convection. In this type of system, neither constant wall temperature, nor constant wall heat flux, could be assumed.

In this study, it is proposed to evaluate a double-pipe helical heat exchanger for fluid-to-fluid flow as shown in Fig. 2, using the facilities offered by the professional CFD code ANSYS CFX. This configuration is similar to a straight double-pipe heat exchanger, except that the tubes

are both curved to take advantage of the space saving characteristics and the enhanced heat transfer coefficients of the helical geometry.

2. CFD PROCEDURE

The heat transfer between two fluids is a process very complex. In consequence, the efficiency of a thermal CFD simulation depends on many factors. Creation of the model geometry and its integration in a physical domain, grid generation and choice of a suitable numerical computing scheme are significant factors that can determine the level of success of the simulation process. The main steps of the performed studies are briefly described in the following paragraphs.

2.1. CAD Model Geometry and mesh creation, which consists

of double pipe helical, through which circulates water, and the heat carriers directions of circulation correspond to parallel flow or counter flow, was made in ANSYS Workbench (Fig. 3). The computational grid was generated using multi-blocks scheme with tetrahedral, prism and pyramids elements. The dimensions of this are:

- global number of nodes: 2308992; -global number of elements: 6280905.

Fig. 3. CAD - Model

Two different coils were created, one for the

annulus, with inner and outer diameters of and , respectively, and with a pitch

of . The other coil was created with outer diameter of , with a pitch of , and with a wall thickness that was of the respective outer diameter. Each of the coils had a length of 2π (one full turn). The radius of curvature for all the coils was .

m 1.0 m 115.0m 115.0

m 04.0 m 115.0%15

m 8.0

2.2. Computational domain and conditions The analyses were performed in steady – state,

adiabatic, multiple domains. Simulations were performed using 3 different mass flows in the inner tube: 10.00835 m kg s−= ⋅ 10.02504 m kg s, −= ⋅

s⋅

s

and . For each inner flow rate, 3 trials were performed with annulus mass flow rates that were 1/2, 1 and 2 times the inner flow

rate. Thus, the three annulus flow rates, associated with the inner flow rate of

10.04174 m kg −=

10.00835 m kg −= ⋅ were 10.00418 m kg s−= ⋅ 10.00835 m kg s, −= ⋅

s and

10.0167 m kg −= ⋅ . Coil properties were set to those of cooper, with a thermal conductivity of

1386 W m K 1− −⋅ ⋅ , density of 89 3−30 kg m⋅1 J kg K− −

and a specific heat of 386 1⋅ ⋅

.673 W m K

. The outer coil was set to be adiabatic (representing an insulated tube) and the inner coil was set to allow conductive heat flow through the tube. Thermal conductivity, the density and the heat capacity of the fluid were constant at 0 1 1− −⋅ ⋅ , 3972 kg m−⋅ and

14194 J kg K 1− −⋅ ⋅ respectively. For a simulation an inlet velocity more

accurately was defining an inlet velocity profile. The velocity distribution of a laminar flow in pipes follows a parabolic law given by expression:

11


2

maxmax

1 rV VR

⎛ ⎞⎛ ⎞⎜ ⎟= − ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

(1)

where the maximum velocity attained at the center, is exactly twice the value of the average

flow velocity

maxV

max12mean

V V= , is the pipe

radius, and

maxR

r is the distance from the pipe centerline. The variable r is defined as:

2 2r x y= + (2) The inlet velocity profiles for hot and cold

fluids are: 2

maxmax

1zhot z hothot

rV V absR

⎛ ⎞⎛ ⎞⎜ ⎟= − ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

(3)

respectively 2 2

max minmax

max min

2(1 ( ))cold coldzcold z cold

cold cold

x y R RV V abs

R R+ − −

= −−

(4)

3. RESULTS

The solution was considerate finished, when the variations of normalized rate of change for the variables of processes were insignificant for the final steps of iterations. These variables include the components of momentum and mass (velocity, pressure), heat transfer, turbulence quantities and particle source change rates (Fig. 4).

Fig. 4 – Variations of normalized rate of change for variables of processes.

Fig. 5 - The distribution of the temperature on radial direction for parallel flow.

12


The main convergence criteria, checked very carefully, were the followings:

■ decreasing of the residuals below 1e- ; 005■ variations of the temperatures which are

acting on heat exchenger smaller than for the final steps of the iterations: %5.0

( ) ( 1)( )

( 1)

100 [%]i iii

T TT

T−

−

−Δ = ⋅ (5)

■ an acceptable value of , to the first grid points above the pipe [4].

+y

The main results evaluated by the program are

fluid temperatures and wall heat transfer coefficients. The results of performed analysis are presented graphically in Fig. 5, 6 and 7.

Fig. 6 - The distribution of the temperature on radial direction for counter flow.

Fig. 7 - The distribution of the wall heat transfer coefficient, for mass flow rate ]s/kg[ 002504.0m = .

13


4. CONCLUSION A numerical study of a double-pipe helical

heat exchanger was performed. A computational fluid dynamics package (ANSYS CFX) was used to numerically study the distribution temperatures and wall heat transfer in a double-pipe helical heat exchanger. The mass flow rates in the inner tube and in the annulus were both varied.

It has been shown that steady state two-dimensional heat transfer and flow equations in the inner and annulus tubes can be simulated using this numerical model with accuracy. This model has been verified with available numerical data and has shown good agreement [1].

According as is noticed from Figures 5 and 6, the heat amount yielded of the cold fluid is maxim for a mass flow rate 0.02504 [ / ]m kg s= , in the case of the counter flow heat exchanger. Acknowledgements. The researches were conducted in the frame of the contract no 216/01.10.2007, MEdC RO – Transilvania University of Brasov,

“Optimization of the heat transfer through devices based on the change phase of magnetic liquids.”

REFERENCES

[1] RENNIE, ] T. J., Raghavan V.G.S., “Numerical studies of a double-pipe helical heat, exchanger, Applied Thermal Engineering, Volume 26, Issues 11-12, August 2006, Pages 1266-1273. [2] HUMINIC, G., HUMINIC, A., “Conjugate heat transfer in devices with nanoparticles”, International Conference on Advanced Computational Engineering and Experimenting, ISSN 0933-5137, Barcelona, 2008, pg. 188 [3] HUMINIC, G., HUMINIC, A., “Concerning the use of the devices with magnetic liquids”, Buletin of Polytehnic Institute of Iasi, LIV (LVIII), 2, ISSN 1011-2855, Iasi, 2008, pg. 265-271. [4] ***, “ANSYS CFX 10.0, Theory Book”,

ANSYS Inc., 2006.

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THE ANNALS OF ”DUNAREA DE JOS” UNIVERSITY OF GALATI FASCICLE IV REFRIGERATING TECHNIQUE, INTERNAL COMBUSTION ENGINES,


THE STUDY OF ICE FORMATION OUTSIDE A FLAT WALL

Gelu COMAN, Cristian IOSIFESCU, Valeriu DAMIAN

“DUNĂREA DE JOS” University of Galaţi

ABSTRACT

The substances solidification issue, seen by the temperature field in solid and liquid phases calculation and by the solid-liquid interface propagation, presents a special interest (from the theoretical and practical points of view), as the conductive transfer processes together with the phase transition phenomenon are present in numerous applications, such as the ingots solidification, the controlled alloys solidification in order to obtain a certain metallographic structure, food freezing, soil freezing and de-freezing, ablation phenomenon to aerodynamic heating, phase change thermal storage etc.

I. Introduction

In the present paper we approach the unidirectional solidification on the surface of a flat metallic wall. In Fig.1 we present a diagram with the analysed spatial field, as well as the temperature field in the three areas (regions): wall, solid, liquid.

In the figure, we noted by W the metallic wall thickness (subscript "W"), we noted by S the solid field thickness, variable in time: S = S(τ), (subscript "S") and by L the liquid field thickness, also variable: L = L(τ), (subscript "L"). The thickness of the field corresponding to the phase change substance (PCS) was labelled by H.

The following equations are the ones that describe the phenomenon [1]: a) the conduction equation (Fourier equation, written for the unidirectional stationary heat transfer): - wall

2

2tW∂z

at

Ww

∂⋅=

τ∂∂

(1)

- solid

2

2

zt

at S

Ss

∂

∂⋅=

τ∂∂

(2)

- liquid

2

2

zt

at L

LL

∂∂⋅=

τ∂∂

(3)

where c

a⋅ρλ

= - thermal diffusion

b) the thermal balance equations on the separation surfaces between areas (fields): - wall - liquid: in the phase where the wall temperature hasn’t reached yet the tT value and therefore the solidification cannot take place yet (t*< tT)

Wz

LL

Wz

ww z

tz

t

==

⎟⎠

⎞⎜⎝

⎛∂∂

⋅λ−=⎟⎠

⎞⎜⎝

⎛∂∂

⋅λ− (4)

- wall - solid: after t* decreased under tT

Wz

SS

Wz

WW z

tz

t

==

⎟⎠

⎞⎜⎝

⎛∂∂

⋅λ−=⎟⎠

⎞⎜⎝

⎛∂∂

⋅λ− (5)

- solid - liquid

τ⋅⋅ρ+⎟

⎠⎞

⎜⎝⎛∂∂

⋅λ=⎟⎠⎞

⎜⎝⎛∂∂

⋅λ+=+= d

dSlzt

zt

SWz

LL

SWz

SS (6)

where λ - thermal conductivity, ρ - density, l - phase change latent heat.

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THE ANNALS OF ”DUNAREA DE JOS” UNIVERSITY OF GALATI FASCICLE IV _________________________________________________________________________________________

2. Process description

In the envisaged system cooling process progress (wall-PCS) there are three phases that have to be treated separately:

2.1 Solidification phase

It’s the main phase of the process. t* temperature is smaller than the phase transition temperature and therefore, the solid thickness layer increase in time.

The equations that describe the process are the conduction equation for the three regions: (1) - wall, (2) - solid layer, (3) - liquid layer, together with the balance equations (5) at the contact wall - solid layer and (6) at solid - liquid interface. Consequently, the calculation algorithm will have as many steps as the process has phases, and the approach will be different in the case of step I with respect to the other two. To increase the used relations generality degree, it’s a practice to dimensionless temperatures. The θ dimensionless temperature is defined by the relation[2]:

R

R

tttt−−

=θ0

(7)

where tR is refrigerant temperature. Consequently, the relations (1-6) become

respectively:

2

2

za WW

W

∂

θ∂⋅=

τ∂θ∂

(8)

2

2

za

t SS

S

∂

θ∂⋅=

τ∂∂

(9)

2

2

za LL

L

∂θ∂

⋅=τ∂θ∂

(10)

Wz

LL

Wz

WW zz ==

⎟⎠

⎞⎜⎝

⎛∂θ∂

⋅λ=⎟⎠

⎞⎜⎝

⎛∂θ∂

⋅λ (11)

Wz

SS

Wz

WW zz ==

⎟⎠

⎞⎜⎝

⎛∂θ∂

⋅λ=⎟⎠

⎞⎜⎝

⎛∂θ∂

⋅λ (12)

]z

z[

ltt

ddS)(S

SWz

L

LSWz

SS

R0

+=

+=

⎟⎟⎠

⎞⎜⎜⎝

⎛∂θ∂

⋅

⋅λ−⎟⎟⎠

⎞⎜⎜⎝

⎛∂θ∂

⋅λ⋅⋅ρ−

=τ

=τ

(13)

For elaborating the finite differences approximation diagram of the limit differential problem, we introduce the network in the respective field:

Nh Δ= (14)

where: h - network step and N = NW+NS+NL - chosen number of steps

As well, the Δτ time step size is established by choosing a convenient value.

In Fig. 2. there are represented the analysed field, together with the attached network and the temperature field at τ = p Δτ moment (p represents the number of the time step). Noting by "m" the number of a node, by notation θmp we understand the temperature in the node number m, at moment p Δτ :

( ) ( )τΔ⋅⋅θ=τθ=θ phmxpm ,, (15) where 0 ≤ m ≤ N

Fig. 1. Geometrical elements of the system flat wall-PCS

t 0

z[m]

S(τ)

L(τ)

W

H

tR tT t0 tw,0 t*

t*

tT

0

Fig 2. Diagram of some flat field and the local grid

0

z [m]

θ

N N-

m+m m-

pm 1+θ

pmθ

pm 1−θ

pθ

1 2

h

Δ

mh

=z

16

THE ANNALS OF ”DUNAREA DE JOS” UNIVERSITY OF GALATI FASCICLE IV _________________________________________________________________________________________ For writing in m current point (of coordinate z = m h) of the partial derivatives under the form of finite differences, we use the relations:

( ) ( )τΔθ−θ

=τΔ

τθ−τΔ+τθ≅

τ∂θ∂ −1,, pm

pmzz (16)

( ) ( ) ( )

h2

h2,hz,hz,hz

zp

1mp

1m −+ θ−θ=

=τ+θ+τ−θ−τ+θ

≅∂θ∂

(17)

( ) ( ) ( )

2

p1m

pm

p1m

22

2

h

2h

,hz,z2,hzz

+− θ+θ⋅−θ=

=τ+θ+τθ⋅−τ−θ

≅∂

θ∂

(18)

3. Determination of the thermal gradients at the boundaries of fields and writing of the conservation equations

These relations are necessary for writing the conservation equations of the energy at the level of these boundaries, equations which connected with the conduction finite differences equations, allow the determination of temperatures on separation surfaces among fields. The three boundaries taken into consideration are the metallic wall right side, solid - liquid interface (here the temperature is known, being equal to θT, but the gradients interpose in the speed relation) and the liquid field right limit (its end).The equation where we reintroduced the time step notation, allows the calculation at the p Δτ moment of θ* temperature on the contact surface of the wall with Δ field, after the determination of the temperatures in the 4 neighbour nodes (2 for each side).

p2WN

p1WN

p1WN,W

p2WN,W

*

3zz

34

y34

3y

++

−−

θ⋅−θ⋅⋅+

+θ⋅⋅+θ⋅−=θ (19)

Where: N

NWh

hU WWW

W ⋅Δ

⋅λλ

=⋅λλ

= ,

y1U

U=

+, z

1U1

=+

4. Results and conclusions

For the considered model, a computer program was developed in order to obtain the temperature field vs. time, and other subsequent information such as: temperature gradients (wall,

solid/wall, solid/liquid, liquid), ice thickness and solid-liquid interface velocity. The program can run with a large number of input parameters (dimensions, transport properties, convection coefficients) and any type of boundary conditions (Neumann - S1, Dirichlet - S2, Fourier - S3) on both sides of the domain.

The assumptions made for this model were as follows: t0 = 5 °C, tT = 0 °C, tR = -10 °C (if CC_S= 'S1'), q0 = 1000 W/m2 (if CC_S= 'S2'), αR = 200 W/m2-C (refrigerant convection coefficient if CC_S= 'S3'), αa = 15 W/m2-C (air), W/H = 0.004/0.01 m, number of points: N_W/N_S/N_L = 4/6/6, boundary conditions type (CC_S): S1, Δτ =0.2 s.

The ending simulation condition was that the temperature of the rightmost (outmost) point decreases below phase change point. The obtained freezing duration under these conditions was τc = 13.97 min (838 s).

Figure 3 shows the temperature distribution vs. time. One can notice the three distinct areas: wall (where temperature variation is small and linear), solid (where temperature variation is steeper but also linear), and liquid. Solid thickness starts from wall boundary (W = 0.004 m) and increases in time up to the domain limit (W+H = 0.014 m). The dimensionless phase change temperature is θT = 0.6667.

Figure 4 shows the 4 temperature gradients at the interface vs. time (initial period, 10 % of total time). The 2 temperature gradients for the solid are almost equal, and much larger compared to wall and liquid gradients. Figure 5 shows the Ice thickness (left) and solid-liquid interface velocity (right) vs. time. As expected, the solid thickness increases faster at the beginning and slower afterwards, and correspondingly, solid formation speed decrease steeply in time due to increasing thermal resistance of the solid thickness.

Fig. 3. Temperature distribution vs. time

17


Fig. 4. Temperature gradients at the interface vs.

time (initial period)

Fig. 5. Ice thickness (left) and solid-liquid interface velocity (right) vs. time REFERENCES 1. Horbaniuc B., Contribuţii la stocarea energiei termice prin schimbare de fază - Teză de doctorat, 1996. 2. Murray W.D, Landis F., Numerical and Machine Solutions of Transient Heat Conduction Problems Involving Melting and Freezing, Trans. Am. Soc. Mech. Eng. Series C- J. Heat Mass Transfer , 81, 1959 3. Hale N.W., Viskanta R. - Solid Liquid Phase - Change Heat Transfer and Interface Motion in Materials Cooled or Heated From Above and Below, Int. J. Heat Mass Transfer , 23, 1980 4. Iordache F., Băltăreţu F., Modelarea şi Simularea proceselor dinamice de transfer termic, Editura Matrix Rom 2002.

18



AN IMPROVED METHOD FOR HEAT PUMPS

REFRIGERANT CHOICE

Ionel OPREA "DUNAREA DE JOS" UNIVERSITY OF GALAŢI

ABSTRACT This paper summarizes the impact of thermo-physical properties on refrigerant selection for HP: R600,

R404a, R407c,R410a, R134a, R507, R134a and R717, which have zero ODP. Impact factors are not sufficient for a complete evaluation, whereas the multicriteria approach allows for an effective initial assessment of the refrigerant. Additional parameters such as efficiency and safety issues will be included in the detailed analysis. 1. INTRODUCTION

The choice of a Refrigerant implies compromises between conflicting desirable thermophysical properties. A refrigerant must satisfy many requirements, some of which do not directly relate to its ability to transfer heat. Chemical stability under the conditions of use is an essential requirement. Safety codes may demand for a nonflammable refrigerant of low toxicity for some applications. The environmental impact of

refrigerant leaks must also be considered. Cost, availability, efficiency, and compatibility with compressor lubricants and equipment materials are other concerns.

Transport properties (e.g., thermal conductivity and viscosity) affect the performance of heat exchangers and piping system. High thermal conductivity and low viscosity are desirable. No single fluid satisfies all the attributes desired of a refrigerant; consequently, various refrigerants are used.

Refrigerant Atmospheric Lifetime,

yearsa

ODPb GWPc100

R-600 0,018d 0 ~20d R-717 0,01d 0


2. HEAT PUMP SYSTEM

There are various technical models of heat pumps. The most advanced technical and commercial designs are the compression and absorption heat pumps. The compression heat pumps have a COP many times higher than that of the absorption versions. A simplified heat pump system consists of four major components, namely compressor, condenser, expansion valve and evaporator.

Assuming a heat pump cycle starts at the compressor outlet, it goes through a condenser, an expansion valve, an evaporator and comes back to the compressor inlet to complete a cycle. This cycle can be represented by a pressure-enthalpy diagram (p-h diagram) as shown in Figure 1, below. All values correspond to the refrigerant’s temperature under operating conditions (e.g., 70°C, 60°C, 52°C, 45°C condensing temperature and 0°C evaporating temperature).

Fig. 1 Representation of refrigerant cycle for a zeotropic refrigerant

3. COMPARATIVE ANALYSIS

This paper has investigated the properties of hydrocarbon butane R600, R404a, R407c,R410a, R507, R134a and ammonia. It is shown that the properties of hydrocarbon make them suitable as refrigerants and that the system’s efficiencies should be expected to be equal to, or higher than, those of R404a, R717, and R134a systems. The risks represented by the flammability of the hydrocarbons must be seriously taken into account. The risks can be reduced by designing the systems for a minimum charge of refrigerant, careful leak detection during production, hermetic design with a minimum number of connections, the use of spark-proof electric components and ventilation of confined spaces.

The following matters are taken into account in this multicriteria analysis: 1. COP - coefficient of performance: refrigerants with a high critical temperature give the best COP; the natural refrigerants are superior in this respect. 2. qk: in HP cycles involving condensation, a refrigerant must be chosen so that this change of

state will occur at a temperature somewhat below the critical temperature; 3. q0: since the evaporation of the liquid is the only step in the HP cycle which produces heating, the latent heat of a refrigerant should be as high as possible. Considering condensation and evaporation, ammonia (R717) is a better heat conductor, compared with the synthetic refrigerants. 4. V - swept volume flow: compressors are often some of the most critical and expensive systems at a production facility, and deserve special attention. 5. W - compressor work: for the efficiency of the process the compressor work is also of interest. The compressor work of isentropic compression from the temperature of 0°C to 70°C, 60°C, 52°C, 45°C to the condensing temperature, is given for the different fluids.

20


R407c

R407c

R407c

R134a

R134a

R134a

0

1

2

3

4

5

6

Regim I Regim II Regim II

CO

P PT

R404a R407c R410a R507 R600 R717 R134a Fig. 2 Variation of heating COP

R404a R404a R404a

R600 R600 R600

R717 R717 R717

R134a R134a R134a

0

200

400

600

800

1000

1200

1400

Regim I Regim II Regim II

Pute

rea

spec

ifica

a c

onde

nsat

orul

ui [

kJ/k

g]

R404a R407c R410a R507 R600 R717 R134a

Fig. 3 Heat transfer ability

21


Agent Cycle COP qk [kJ/kg] q0

[kJ/kg] V

[m3/kg] W

[kW] H [/] ODP GWP

Price per unit [$]

0/15/45 5.132 135.605 109.1857 144.1377 3.012 3.392=20.446/6.028

0/15/52 4.188 124.703 94.93 144.137 3.691 3.984=24.018/6.028 R404a

0/15/60 3.288 109.812 76.4137 144.1364 4.702 4.754=28.66/6.028

0 3900 234

0/15/45 5.57 198.252 162.717 226.4271 2.774 3.822=17.275/4.52

0/15/52 4.697 189.393 149.0768 226.427 3.291 4.55=20.59/4.52 R407c

0/15/60 3.905 177.753 132.245 226.4268 3.959 5.522=24.959/4.52

0 1800 299

0/15/45 5.24 193.921 156.9683 145.4327 2.946 3.382=27.014/7.986

0/15/52 4.347 182.679 140.66 145.4696 3.556 3.975=31.745/7.986 R410a

0/15/60 3.499 166.665 119.0368 145.4696 4.418 4.747=37.908/7.986

0 2100 219

0/15/45 5.38 142.541 116.05216 136.0246 2.873 3.373=21.186/6.282

0/15/52 4.463 133.971 103.961 136.0238 3.463 3.97=24.94/6.282 R507

0/15/60 3.56 120.683 86.835 136.0238 4.336 3.97=29.884/6.282

0 4000 255

0/15/52 5.22 347.6 254.1757 1540.189 3.028 4.606=7.267/1.578

0/15/60 4.473 335.574 232.783 1540.1874 3.561 5.572=8.792/1.578 R600

0/15/70 3.758 319.233 213.47 1540.1842 4.062 6.534=10.309/1.578

0 20 172

0/15/52 5.11 1311.437 1054.9183 1239.0119 3.024 4.985=21.407/4.294

0/15/60 4.44 1310.118 1015.13 1239.0116 3.481 6.088=26.143/4.294 R717

0/15/70 3.813 1306.421 979.4127 1239.011 3.882 7.712=30.894/4.294

0 1 86

0/15/52 4.916 171.256 136.417 296.9971 3.145 4.73=13.851/2.928

0/15/60 4.154 162.769 123.5823 296.9986 3.722 5.74=216.813/2.928 R134a 0/15/70 3.4 150.937 111.8546 296.9971 4.278 6.754=19.777/2.928

0 1430 129

Table 2. Numerical results for comparative analysis

6. H - compression ratio: when operating between two specific temperatures, fluids with low vapour pressures (high normal boiling point) will have larger compression ratios than fluids with high vapour pressures. However, there are exceptions to this general rule and this can be clearly seen in the comparison 7. ODP ozone depleting potential: the fact that these ‘‘harmless’’ substances were found to have a very unexpected and harmful impact on the global environment, raised doubts also about the use of other manmade substances, not present in the natural environment. Later, these doubts have been confirmed by the fact that the emissions of these

refrigerants contributed by more than 20% to the global release of CO2 - equivalents during some years before the ban of the CFCs (IPCC/TEAP, 2005) 8. GWP - global warming potential: the refrigerant selection based on a simple approach of ‘zero ODP’ will have to pay high costs to both global warming and energy efficiency. Using this single criterion is no longer environmentally acceptable today. 9. Price per Unit of refrigerant.[$]

22


3900

1800

2100

4000

20

1

1430

0 500 1000 1500 2000 2500 3000 3500 4000 4500

R404a

R407c

R410a

R507

R600

R717

R134a

Age

nt

GWP

Fig. 4 Refrigerant Global-Warming Potential (GWP)

Fig. 5 Comparative analysis (70°C, 60°C, 52°C, 45°C condensing temperature and 0°C evaporating temperature)

23


4. Conclusion

The evaporation heat content of R404a is significantly lower (90% less) than the baseline R717 value, while that of R410a is slightly higher. The COP cycle of R134a is about 17% lower than the baseline value, indicating that this refrigerant does not match the baseline R407c cycle performance. These characteristics imply that both R404a and R410a refrigerants have weaker heat transfer ability and lower cooling capacity on equal heat pump load base, as compared to R717. Increased vapor density for R507, R410a and R404a may also lead to the use of a smaller compressor and coil tubing that could result in less system power consumption and more efficient component design. Overall, however, a comparable COP system is possible for R404a, and even a moderate system efficiency improvement might be expected for R410a for a certain heat pump load. The COP system is also influenced by compressor volumetric efficiency, which is a function of compression ratio H (pcond/pevap) and compressor isentropic efficiency, which could be affected by other transport properties, as well as system design. Nomenclature COP - coefficient of performance qo - heat of vaporization (kJ/kg) qk - heat of condensation (kJ/kg) pk - condensing pressure (bar) po - evaporation pressure (bar) W - compressor work (W) V - volume flow (m3/s)

REFERENCES [1]. UNEP. 1998. 1998 Report of the Refrigeration, Air Conditioning and Heat Pumps Technical Options Committee, Nairobi, [2]. AFF. 2001. Conseil National du Froid – Livre blanc sur les fluides frigorigènes, Paris, AFF, 51 pages. [3]. UNEP. 2000. Report of the Technology and Economic Assessment Panel April 2000, Nairobi, UNEP, 193 pages [4]. Harnisch J, Hendriks C. 2001. Economic Evaluation of Emission Reductions of HFCs, PFCs and SF in Europe, Ecofys Energy and Environment. [5]. Chang,Y.S., Kim, M.S., Ro, S.T., 2000.Performance and heat transfer characteristics of hydrocarbon refrigerants in a heat pump system. International Journal of Refrigeration 23 (3), 232–242. [6]. Pelletier, O., 1998. Propaneas Refrigerant in Residential Heat Pumps. Licentiate thesis. Royal Institute of Technology, Stockholm, Sweden, ISSN 1102-0245, ISRN KTH/REFR/R-98/24-SE. Rezumat

Lucrarea sintetizeaza impactul proprietăţilor termo-fizice asupra alegerii agentilor frigorifici pentru pompele termice - R600, R404a, R407c, R410a, R134a, R507, R134a şi R717, care au ODP zero. Factorii de impact nu sunt suficienti pentru o evaluare completă, iar o abordare multicriteriala permite o apreciere iniţială eficientă a agentilor frigorifici. Parametrii suplimentari, cum ar fi eficienţa sistemului şi aspectele legate de siguranţă, vor fi incluşi în analiza detaliată.

24

THE ANNALS OF ”DUNAREA DE JOS” UNIVERSITY OF GALATI FASCICLE IV REFRIGERATING TECHNIQUE, INTERNAL COMBUSTION ENGINES,


THE STUDY OF ICE FORMATION OUTSIDE

A CYLINDRICAL WALL

Gelu COMAN, Critistian IOSIFESCU, Valeriu DAMIAN “DUNĂREA DE JOS” University of Galaţi

ABSTRACT The solidification topic, as a matter of the temperature field in solid and liquid phases calculation and by the solid-liquid interface propagation, presents a special interest (from the theoretical and practical point of view), as the conductive transfer processes together with the phase transition phenomenon are present in various applications, such as the ingots solidification, the controlled alloys solidification in order to obtain a certain metallographic structure, food freezing, soil freezing and de-freezing, ablation phenomenon to aerodynamic heating, phase change thermal storage etc.

I. Introduction The paper approaches the topic of

solidification of a substance outside a metal cylindrical wall. The analysed system is made up of the following elements, presented in Fig. 1 [1]: • the solid cylindrical wall having an internal

radius R0 and an external one RW, its thickness being equal to W (W = Rw - R0);

• the phase change substance (PCS) from outside the wall, having an internal radius Rw and an external one R (thickness H = R - Rw).

Fig. 1 - Geometrical elements of the system cylindrical wall-PCS

At time τ, the external radius of the solid layer is R

Process description

he cooling process of the envisaged system (wa

S(τ), its thickness being S(τ) = Rs(τ) - Rw. The liquid layer thickness is L(τ) = H - S(τ). II

T

ll-PCS) has three phases that have to be treated separately: • wall propagation phase (I): the phase when

the temperature perturbation produced by the sudden cooled inner side of the wall, propagate into its thickness, until reaches the outer side.

• liquid propagation phase (II): the phase in which the perturbation begins to propagate inside the liquid, and the temperature t* on the wall side in contact with PCS decreases down to value tT, corresponding to the phase transition temperature.

• solidification phase (III): it’s the main phase of the process. temperature t* is smaller than the phase transition temperature and therefore, the solid thickness layer increase in time.

Equations that describe the phenomena, written

coordi

directly in dimensionless temperatures are: Conduction equation in cylindrical

nates [2]: t [0C]

R

R [mm]

R0

Rw

S(τ)

L(τ)

RS(τ) W

H

tR tT t0 tw,0 t*

t*

tT

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂⋅+

∂

∂⋅=

∂∂θ

rrra iii

i θθτ

12

2 (1)

where subscript "i" refers to (depending on the cas

ess temperature θ is defined by:

e) to: W - wall, S - solid or L - liquid, a - thermal diffusivity

The dimensionl

25

THE ANNALS OF ”DUNAREA DE JOS” UNIVERSITY OF GALATI FASCICLE IV __________________________________________________________________________________

R0

Rtt

tt −−

(2)

Energy balance equation at interface between wall

where subscript "j" refers to (depending on phase)

Boundary conditions [4] on the internal surface of

For writing the finite-difference equations corr

the envisaged domain we define the grid with

Note:

and liquid or solid:

L - liquid (phase II) or S - solid (phase III).

the wall:

esponding to the conduction equation, we take into consideration a field having the internal Ri and the external Re radii, the thickness of which is Δ = Re - Ri.

On step h = Δ/N, where N is the total number of

nodes. The right side brackets equation, written under the form of finite differences for node m, is expressed as follows:

where id signifies normalized internal diameter.

⎟⎟⎠

⎞⎜⎜⎝

⎛+

Δ⋅⋅= m

RN2c im (14)

It results:

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

++⋅−⋅

−⋅≅

∂∂⋅+

∂

∂+− 1122

2 12111 mm

mmm

m

m

cc

cc

hrrrθθθ

θθ (15)

Equation (14) written under the form of finite differences will be expressed as follows:

⎟⎟⎠

⎞⎜⎜⎝

⎛θ⋅

++θ⋅−θ⋅

−⋅

⋅=τΔ

θ−θ

+−

−

n1m,i

m

mnm,i

n1m,i

m

m

2i

i1p

m,ip

m,i

c1c

2c

1c

h

a

(16)

The equation results under the forms [3]: • the explicit finite differences form

(EFDF):

( ) 1pm,ii

1p1m,i

m

m1p1m,i

m

mi

pm,i

21

c1c

c1c

−

−+

−−

θ⋅α⋅−+

⎟⎟⎠

⎞⎜⎜⎝

⎛θ⋅

++θ⋅

−⋅α=θ

(17)

• the implicit finite differences form (IFDF):

1p

m,ii

p1m,i

m

m

pm,i

i

p1m,i

m

m

1c

1c

12c

1c

−+

−

θ⋅α

=θ⋅+

−

−θ⋅⎟⎟⎠

⎞⎜⎜⎝

⎛α

++θ⋅−

−

(18)

The general form of the equation (17) is

obtained by multiplying it by cm / (cm -1):

m,im

mp1m,i

m

m

pm,ii

m

mp1m,i

b1c

c1c1c

1cc

⋅−

=θ⋅−+

−θ⋅σ⋅−

+θ−

+

−

(19)

where σi and bi,m results from the relations:

ii

σα

=+12 (20)

mipmi

ib ,

1,

1=⋅ −θ

α (21)

Now, introducing the notations: The general form of the finite-difference

equation within IFDF is: For the cases of boundaries between the three

fields are presented, the finite-differences equations

Rwr

jj

Rwr

ww rr

==⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

∂⋅=⎟

⎠

⎞⎜⎝

⎛∂∂θ

⋅θ

λ (3)

( )

( )]

r

r[

lttdR SR0S ⎞⎛ θ∂−

d)(R

Rsr

LL

RsrSS

τ=

τ=

⎟⎟⎠

⎞⎜⎜⎝

⎛∂θ∂

⋅λ−

−⎟⎟⎠

⎜⎜⎝ ∂⋅λ⋅

⋅ρ=

τ=τ

(4)

type I: θw,0 = 0 (6)

type II: 00

qr RRw

w =⎟⎠

⎞⎜⎝

⎛∂∂

⋅=

θλ (7)

type III: 0,0

wRr

ww kr

θθ

λ ⋅=⎟⎠

⎞⎜⎝

⎛∂∂

⋅=

(8)

])

r2h1(2

)r2h1[(

h1

rr1

r

1mm

m

1mm22

2 θ∂θ∂

+

−

θ⋅⋅

++θ⋅−

−θ⋅⋅

−⋅≅∂⋅+

∂ (9)

rm = R + m h (10)

i

Δ=

⋅= iii

dR2d

Δ

(11)

mm

m1c1c

γ=−+

(12)

m,im,imm b

1cc

β=⋅−

(13)

2426


takes special form in the nodes next to the boundaries. • m = 1 - the first node in the wall The equation general form is

• m = NW - 1 and Nw + 1 (at the wall-PCS boundary)

where: θ* - dimensionless temperature at the contact wall-PCS

R means the external radius of the liquid field in the liquid propagation phase, respectively Rs(τ) in the solidification phase. By replacing θ* in the equations Nw - 1:

1wN,w*

1wN

p1wN,w1wN,w

p2wN,w

−−

−−−

β=θ⋅γ−

−θ⋅σ+θ− (27)

and Nw + 1:

where j is a phase function of the process „L” or „S”, the results are respectively: ( )

1wN,jp

2wN,j1wN

p1wN,j1wN

p1wN,w1wN

1wN,wp

2wN,w1wN

z

z4)

y4(y1

−+−

+−−−

−−−

β=θ⋅γ⋅+

+θ⋅γ⋅⋅−θ⋅γ⋅

⋅⋅−σ+θ⋅γ⋅−−

(29)

and:

( )( ) 1wN,jp 2wN,j1wN

p1wN,j

1wN,jp

1wN,wp

2wN,w

z

z4y4y

++++

+−−

β=θ⋅−γ−θ⋅

⋅−σ+θ⋅⋅⋅θ⋅(30)

• m = Nw + NS - equation for the last but one node in the solid

The equation corresponding to this node is:

1SNwN,ST1SNwN

p1SNwN,S1SNwN,S

p2SNwN,S

−+−+

−+−+−+

β=θ⋅γ−

−θ⋅σ+θ−(31)

and becomes finally:

T1SNwN1SNwN,S

p1SNwN,S1SNwN,S

p2SNwN,S

θ⋅γ+β=

=θ⋅σ+θ−

−+−+

−+−+−+ (32)

Equation for the interface speed

The general equation is:

)]43(RR

N

)4

3(RR

N[

l2ttR

R

p2SNwN,L

p1SNwN,LTp

S

LL

p2SNwN,L

p1SNwN,L

p1SNwN,L

Tw

pS

SSR0SpS

++++

−+++−+

θ+θ⋅−θ⋅⋅−

⋅λ+

+θ+θ+θ⋅−

−θ⋅⋅−

⋅λ⋅

⋅ρ⋅−

=τΔ

Δ=

(33)

• m = Nw + Ns + 1 - equation of the first liquid node As the system for liquid is independent, for simplification reasons the numbering of liquid nodes will be made from 1 to NL. The equation corresponding to this node is:

1,Lp

2,L1p

1,L1,LT β=θ⋅γ−θ⋅σ+θ− (34)

• m = N - 1 - equation for the end of the liquid domain

1N

1N,Lp1N

1N

1N1N,Lp2N 3

33

43

−

−−

−

−−− γ−

β⋅=θ⋅

γ−

γ⋅−σ⋅+θ− (35)

The equations systems for the wall-solid connection and liquid, written under matrix form are:

wall-solid: 111 BC =θ⋅ ;liquid: (36)2122 BC =θ⋅

These systems were solved using a computer code for each time moment of the three phases of the process. III Results and conclusions

For the considered model, a computer program

was developed in order to obtain the temperature field vs. time, and other subsequent information such as: temperature gradients (wall, solid/wall, solid/liquid, liquid), ice thickness and solid-liquid interface velocity. The program can run with a large number of variable input parameters (temperatures, dimensions, transport properties, convection coefficients) and any type of boundary conditions on both sides of the domain.

mipmi

pmii

pmi b ,1,,1, =−⋅+− +− θθσθ

(22)

p

2wN,wp

1wN,w

p1wN,w

p2wN,w

*

zz4

y4y

++

−−

θ⋅−θ⋅⋅

+θ⋅⋅+θ⋅−=θ (23)

( )1U3Uy+⋅

= (24)

( )1U31z+⋅

= (25)

NN

RRRR

U w0w

ww ⋅−

−⋅

λλ

= (26)

1wN,j

p2wN,j

1wNp

1wN,j1wN,j*

++

+++

β=θ⋅

⋅γ−θ⋅σ+θ− (28)

2527


Fig. 2 - Dimensionless temperature θ distribution vs. time τ

Fig. 3 - Temperature gradients B at the interface vs. time τ

The assumptions made for this model were as follows: t0 = 5 °C, tT = 0, R0 = 10e-03 m, RW = 14e-03 m, R = 24e-03 m, tR = -10 °C (if CC_S = 'S1'), q0 = 1000 W/m2 (if CC_S = 'S2'), αR = 200 W/m2-°C (refrigerant convection coefficient if CC_S = 'S3'), αa = 15 W/m2-°C (air), W/H = 0.004/0.01 mm, number of points: N_W/NS/NL = 4/6/6, boundary conditions type (CC_S): S3 (III), Δτ =0.2 s.

Fig. 4 - Ice thickness S (left) and solid-liquid

interface velocity S_dot (right) vs. time The ending simulation condition was that

the temperature of the outmost point decreases below phase change point. The obtained freezing duration under these condition was τc = 68.45 min.

R E F E R E N C E

1. H o r b a n i u c B., Contribuţii la stocarea energiei termice prin schimbare de fază - Teza de doctorat, 1996.

2. M u r r a y W. D., L a n d i s F., Numerical and Machine Solutions of Transient Heat Conduction Problems Involving Melting and Freezing, Trans. Am. Soc. Mech. Eng. Series C- J. Heat Mass Transfer , 81, 1959

3. H a l e N. W., V i s k a n t a R. - Solid Liquid Phase - Change Heat Transfer and Interface Motion in Materials Cooled or Heated From Above and Below, Int.J. Heat Mass Transfer , 23, 1980

4. I o r d a c h e F., B ă l t ă r e ţ u F., Modelarea şi simularea proceselor dinamice de transfer termic, Editura Matrix Rom, 2002.

2628



Heat conduction problems with cylindrical symmetry solving by integral transform technique – cylindrical hole

Silviu Vlasie

”Dunărea de Jos” University of Galati ABSTRACT In solving the heat conduction problems with the integral transform technique in the cartesian system we used a polynomial approximation to represent the temperature profile. Now we investigated the application of the integral method to the solution of the heat conduction problem in regions with cylindrical symmetry using polynomial approximation multiplied by a logaritmic term. 1. Introduction Consider a region exterior to a cylindrical hole of radius r = r0 and extending to infinity. Initially the region is at zero temperature and for times τ > 0 the surface of the cylindrical hole is exposed to a constant heat flux. Assuming cylindrical symetry, the boundary value problem of heat conduction is given as

∂τ∂

∂∂ T

arTr

rr⋅=⎟

⎠⎞

⎜⎝⎛

∂∂ 11 for r0 ≤ r < ∞, τ > 0

(1a)

FrT

=⋅−∂∂λ at r = r0 , τ > 0 (1b)

T = 0 in r0 ≤ r < ∞ , τ = 0 (1c) where T = T (r, τ), [1]. Using the thermal layer which in the heat conduction problem is defined as the distance from the origin beyond which the initial temperature distribution within the region remains unaffected by the applied

r0

δ(τ)

FrT

rr=

∂∂

λ−= 0

T = 0i

Fig. 1 Region exterior to a cylindrical hole of radius r = r0 .

boundary condition, and hence there is not heat flow in the region beyond δ (τ), [3]. Multiply both sides of the differential equqtion of hwat conduction 1a by r and integrate it over the thermal layer thickness δ (τ), from r = r0 to r = r0 + δ (τ), [2], and obtain

29


( )

( )⎢⎣⎡ −⋅⋅∂∂

⋅=− ∫+

+

rrTar

TrrTr r

rrr

dτδ

τδ τ∂∂

∂∂ 0

000

1

( ) ( ) ⎥⎦⎤⋅⋅−

+ τδ

δ dd )(

0

rrTrr

(2)

which simplifies to the following heat balance integral:

τΠ

∂∂

∂∂

⋅=−ar

Trr

1

0

(3a)

where

(3b) rTrr

rd⋅⋅= ∫

+ )(0

0

τδΠ

In order to solve eq. 3 a profile should be assumed for the temperature distribution over the thermal layer. In choosing the profile we shall examine two different cases: a polynomial appoximation alone and a polynomial appoximation modified by the term lnr. 2. Polynomial approximation Assume a second degree polynomial approximation in the form

cbrarT ++= 2 in r0 ≤ r ≤ r0 + δ (τ), (4) The three unknown coefficients a, b and c are determined from the following three conditions:

FrT

r=

∂∂

λ−0

; 0)(0

=−+ τδ∂

∂λrr

T ;

0)(0 =+ τδrT (5)

Then the temperature profile becomes

2

00

20 1

2 ⎟⎟⎠

⎞⎜⎜⎝

⎛−+=

rr

rFrT δλδ

in r0 ≤ r ≤ r0 + δ(τ) (6)

Substituting the temperature profile 6 into the heat balance integral 3 and performing the operations we obtain

)4(24

1 20

30 δδτ

rdd

ar += (7)

with δ = 0 for τ = 0. The solution of this differential equation results in the following relation

2

0

3

02

0424 ⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛=⋅

rrra δδτ (8)

Equation 8 together with eq. 6 gives the temperature distribution within the solid. The temperature at the boundary surface r = r0 is obtaining from the temperature profile 6

δλ

⋅== 20

FT rr (9)

where δ is given by eq. 8. 3. Polynomial approximation

multiplied by term ln r Consider a second degree polynomial approximation multiplied by a logaritmic term in the form ( ) rcbrarT ln2 ⋅++= (10) This temperature profile satisfies the conditions considered above:

00

0

02

00

20

/1ln2

/1/ln

12

rr

rrr

rr

rFrT

δδδδ

λδ+⎟⎟

⎠

⎞⎜⎜⎝

⎛+

⎟⎟⎠

⎞⎜⎜⎝

⎛+

⎟⎟⎠

⎞⎜⎜⎝

⎛−+−=

in r0 ≤ r ≤ r0 + δ (τ) (11) The modified temperature profile given by eq. 11 involves a logarithmic term which is

30

THE ANNALS OF ”DUNAREA DE JOS” UNIVERSITY OF GALATI FASCICLE IV _________________________________________________________________________________________ multiplied the second degree polynomial profile 6. Substituting eq. 11 into the heat balance integral 3 we obtain the following relation for the thermal layer thickness δ (τ):

( )( )( ) +−+−+−ζ

−=2

1ln21144ln369672

20 ζζζ

ζζτra

( )( )1ln211449323613 24

−+−+−+

+ζζζζζζ (12)

where

0/1 rδ+=ζ Equations 11 and 12 gives the temperature distribution in the solid. The surface temperature at r = r0 is obtained from eq. 11

( )( ) 000

//1ln2/1ln

0 rrrFT rr δ+δ+

δ+⋅

λδ

==

(13)

Eq 9 Eq 13

Exact solution

a rτ / 020 1 2 3 4 5 6 7 8 9 10

2.0

1.5

1.0

0.5

0

Τ λ

/ F r 0

p

Fig. 2. Comparison of surface temperature from exact and integral solution.

4. Conclusion The figure 2 shows a comparison of the surface temperature Tp at r = r0 evaluated from the approximate eq. 9 and eq. 13 from the exact solution.

It can be seen that the approximate solution based on the second degree temperature profile modified with a

31

THE ANNALS OF ”DUNAREA DE JOS” UNIVERSITY OF GALATI FASCICLE IV _________________________________________________________________________________________ logarithmic term agrees closely with the exact solution. 5. References [1] Carslaw H. S., Jaeger J. C. Conduction of heat in solids. Oxford University Press, 2nd ed., London, 1959. [2] Necati Özişik M. Boundary value problems of heat conduction. Dover Publications Inc., New York, 1989. [3] Atthey D. R. A finite difference scheme for melting problems. Jl Inst. Math. Appl., nr. 13, pg. 353-366, 1974.

[4] Ingersol L. R., Zobel O. J. and Ingersol A. C. Heat conduction with engineering and geological application. McGraw-Hill Book Company, New York, 1968, pg. 16-23. [5] Stephan K., Holzknecht B. Wärmeleitung beim Erstarren geometrisch einfacher Körper. Wärme und Stoffübertragung, nr. 7, pg. 200-207, 1971.

32



SIMPLE CONTROL SYSTEM FOR SERIES-HYBRID I. C.

ENGINE

Jorge MARTINS José MACHADO

Abstract: The new bread of electric cars has a small and simple Internal Combustion Engine, that is commonly called “range extender” by General Motors. Although these vehicles are series-hybrids, General Motors and other manufacturers call them Electric Vehicles (with range extender) as the power to the wheels is purely electric. In fact, there is no direct mechanical link between the I C engine and the wheels, as in other more “usual” (parallel) hybrids, such as the Honda Insight or Toyota Prius. The I C engine of these cars in a common engine which runs at different loads and at different speeds. However, for a series-hybrid the engine is in the car with the sole purpose of charging the batteries. Therefore the engine is developed to run at only one condition, the point of maximum efficiency, which is at a nominal speed and at full load. If an engine only works at one specified condition, its control is much simplified, as there are no unsteady-state conditions, such as accelerations (speed changes) and load changes. The only unsteady condition will be the engine temperature during warm-up. The engines for these series-hybrid vehicles are small engines with the power equivalent of maintaining a steady 120-140 km/h, which is roughly 10 kW. The electric motor(s) can have more power. An engine with this kind of power is a single or twin cylinder engine with small capacity, either Spark Ignition or Diesel with capacity in the region of 100 to 200 cm3. In order to be efficient, the Diesel engine should have electronic fuel injection and turbo-charging, but, there are no such a small engine (or turbo-charger) in the market for these applications. Therefore the probable engine will be a S I with an over-expanded cycle, proven[1] to have similar efficiency characteristics as a Direct Injection Diesel engine. This engine would have a very high compression ratio (15:1 to 19:1) and a high expansion ratio[2], enabling a very high efficiency (over 35%).

Introduction The Spark Ignition Engines for road vehicles have very sophisticated control strategies, so the exhaust gases can be efficiently treated in the so called "3-way" catalyst. To achieve an efficiency over 98%, the catalyst should be hot (over 300°C) and should receive an exact (1%) stoichiometric mixture. In “normal” engines, where the driver does accelerate and desaccelerate very often, the required perfect mixture strength is very difficult to obtain, as various operations should be performed and they usually create errors and uncertainty to the mass of fuel to be burned inside the cylinder. To have the exact proportions of fuel and air, it is necessary to (1) accurately measure the amount of air drawn into the engine, (2) assess the required amount of fuel to inject, (3) inject that precise quantity, (4) measure the result by analyzing the exhaust gases and (5) “feed-back” this result in order to fine tune the amount of fuel to inject the next time. Effects such as fuel deposition, entrainment and evaporation from the walls play an important role in the mixture formation, mainly during transients. If the engine is not subjected to alterations of load and speed, its control can be greatly simplified, a the major problem in achieving perfect

33


stoichiometric mixture is unsteady operation of the engine. In a 4-stroke engine the first problem is the measurement of the airflow entering the engine. To enhance breeding and therefore torque and power, the inlet valves open before TDC (top dead centre) and closes way after BDC (bottom dead centre). This creates “back flows” from the cylinder to the inlet manifold (Fig.1), which upsets the measurement of the inlet air stream [1], usually

done by the hot wire technique. Using the hot wire a back flow is calculated as forward flow, therefore altering the measurement. Six cylinder engines are not prone to this problem, but on four-cylinder engines the back flow of the start of valve opening of one cylinder adds to the back flow of another cylinder closing its valve, creating a huge back flow (Fig.2) that moves back to the entrance of the inlet manifold, namely on the point of measurement.

air v

eloc

ity

T D C B D C Fig.1: Airflow through inlet valve [1]

mas

sflo

w

Fig.2: Air flow of a 4-cylinder engine at entrance of inlet manifold [1]

The measurement of the airflow can be made by two different methods: “massflow”, where the measurement is made by a hot wire; or “speed-density”, where the air mass flow is calculated by the value of the pressure inside the inlet manifold. The latter process is much more cheaper, but much less accurate. However, “massflow” systems have problems of accuracy during transients (throttle movements). When the engine is at light load the throttle is partially closed and the manifold is at low pressure. When the throttle is opened, the inlet

manifold eventually reaches atmospheric pressure. As this occurs, more air is entering the manifold (and being measured) than entering the cylinders (Fig.3), as the manifold is charged with a more dense (more pressure) air [2]. Also, part of the injected fuel impacts the walls around the back of the inlet valves and needs some time to fully evaporate [3]. While during steady-state operation, this effect does not create control problems, but during transients the deposition rates is not matched by the evaporation rate, therefore

34


altering the air-fuel mixture proportion entering the cylinders. One of the authors developed a model for this calculation on running engines during transients [2], [4]. Series hybrids are electric vehicles that have an internal combustion engine to produce electricity used to propel the vehicle (through the electric motors connected to the wheels) or to charge the batteries. Usually these engines are small and run always at nominal conditions, at full load and speed, producing enough power (e.g. 10 kW) to thrust the vehicle at a certain speed (e.g. 120 km/h in flat surface). Therefore, its operation is intermittent, on/off. When this engine is running, it operates always at the specified load/speed, without incurring in transients, with the exception of temperature rise during the warm-up period. As already explained, the engine for this type of vehicle is a small one, probably single or twin cylinder in the region of 100 to 200 cm3. It can be a turbo-charged direct injection electronic controlled Diesel engine, but such an engine is very expensive and there are none on the market for this type of power requirements. An over-expanded S I (spark ignition) engine can have the same efficiency [5] as a direct injection Diesel engine, at a fraction of the

price. A simple low pressure injection system and a basic electronic control system is what is required to convert a single cylinder engine commonly used for generating electricity or driving motorcycles to operate at high efficiency and low emissions. Obviously the engine also requires alterations of the camshaft and of the piston and head, enabling a high compression ratio (higher than 16:1) and a high expansion ratio [5], essential for the enhancement of efficiency. The control of such an engine is much more simplified than that of a “conventional” transient engine. Problems such as those detailed above are not a concern for this type of engine. The control should only correct the mixture based on the output of the lambda sensor, which measures the mixture strength. A basic control using a simple one dimension look-up table (fueling and ignition timing vs. engine temperature) is all it is required, together with the closed-loop control based on the lambda output. Corrections have to be made for different air temperatures. A different open-loop control is necessary for the fuelling and ignition advance during engine start. As the engine can be started at different engine temperatures, this strategy.

Air

flow

Time

t hro tt le op e nin g

th rot tle po sit ion

air p a ssin g t he v alve s

air f lo w a t th ro ttle

Fig.3: Airflow entering and leaving the inlet manifold during a throttle opening [2]

35


REFERENCES [1] Jorge MARTINS “Motores de Combustão Interna – 2nd edition”, (ISBN: 972-8953-82-X) Publindustria, Porto, 2006 (in Portuguese) [2] MARTINS,J.J.G "Heat and Mass Transfer in Intake Systems of Spark Ignition Engines", PhD thesis, University of Birmingham, UK, 1989 [3] MARTINS, J.J.G. "Fuel Preparation in Port-Injected Engines", SAE 1992 Transactions, Vol.101, Journal of Fuels & Lubricants, Section 4, 621-632, 1992 [4] BOAM, D.J., FINLAY, I.C.,, MARTINS, J.J.G

"A Model for Predicting Engine Torque Response During Rapid Throttle Transients in Port-Injected Spark-Ignition Engines", SAE Transactions, Vol.98, Journal of Engines, Section 3, 991-1010, 1989 [5] RIBEIRO, Bernardo, MARTINS, Jorge “Direct Comparison of an Engine Working under Otto, Miller and Diesel cycles: Thermodynamic Analysis and Real Engine Performance”, Technical Paper Series, nº 2007-01-0261, included in ‘New SI Engine and Component Design and Engine Lubrication and Bearing Systems’, SAE (ISBN Number:978-0-7680-1883-7), 2007

36



DETERMINATION OF OPTIMUM

OPERATING REGIMES OF ROAD MOTOR VEHICLES BASED ON MINIMUM FUEL CONSUMPTION

Assistant Professor Salvadore Mugurel BURCIU “Dunarea de Jos” University of Galaţi, Roumania

Professor Engineer Manuela BURCIU Technical College ”Traian Vuia” of Galati, Roumania

ABSTRACT

The paper deals with the mathematical calculation which permits the determination of the optimum conditions in operating the propulsion installations with internal combustion engines applied to road vehicles, in the conditions of minimum real fuel consumption, including the evaluation of the mechanical power and fuel consumption characteristics.

KEYWORDS: fuel consumption, optimum operating regimes I. Mathematical model

If we consider the working conditions quasisteady, in operating the propulsion installations applied to road motor vehicles, it is possible to determine the optimum speed of a car, Voptimum , the optimum position of accelerator pedal, ykoptimum and the optimum ratio drive, itr optimum of transmission in condition of realization of minimum real specific fuel consumption . The mathematical model contains the following equations and consists in solutions of these: -- in case of the propulsion installations with sparking plug engines [1]:

),,()_,,,,(

),(niP

roadconditionVGVPnP

tretr

autobte

vR

ηα

θ = (1)

),( obtee ncc θ=

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