Analysis of Heat Transfer in the Combustion Chamber of an InternalCombustion Engine using Thermal Networks

KRISZTINA UZUNEANU, TANASE PANAITDepartment of Thermal Systems and Environmental Engineering

University “Dunarea de Jos” of GalatiStr. Domneasca no. 47, 800008 Galati

ROMANIAkristina.uzuneanu@ugal.ro http://www.ugal.ro/

Abstract: - The heat transfer processes in an internal combustion engine can be modeled with a variety ofmethods. These methods range from simple thermal networks to multidimensional differential equationmodeling. Thermal network models, using resistors and capacitors, are very useful for rapid and efficientestimation of conduction, convection and radiation heat transfer processes in engines. Using a thermal network,the significant resistances to heat flow, and the effects of changing material thermal conductivity, thickness,and coolant properties can be easily determined.

Key-Words: - cylinder wall, piston, cylinder head, heat transfer, thermal stresses

1 IntroductionThermal stresses analysis in combustion chamber ofspark ignition engine is an important field whichautomobile engineers study in order to increase lifeof mechanical parts.Some of studies have been presented about thermalstresses and analysis for various engines. Localconvective heat transfer in a four-stroke singlecylinder engine using a computational fluiddynamics code was analyzed by Mohammadi andYaghoubi [11]. The results were compared withexperimental measurement in the literature. Besides,new correlations were proposed to predict maximumand minimum convective heat transfer coefficient ina SI engine’s combustion chamber. Lee and Assanis[8] analyzed thermo-mechanical of opticallyaccessible quartz cylinder under fired engineoperation. Using FEM analysis, temperature andstress distributions were estimated. Three types ofoutside cooling for reducing thermal stress level(natural, moderate forced and intensive forcedconvection), were considered. Thermal analysis ofcylinder head carbon deposits from single cylinderdiesel engine was researched by Husnawan et al.[7].The thermal stresses in the cylinder head and in thepiston head of an internal combustion engine aredetermined as a function of the level oftemperatures, the temperature difference betweendifferent parts and the heat transfer between parts.These further depend on the speed and the way the

heat is transferred to the parts, on the part shape,their thermal conductivity and cooling.The temperature of the parts has an effect onoperating temperature of the lubricating oil andhence, on its viscosity, oil – film thickness whichseparates of the rubbing pair and the nature offriction [4].The latter together with wear characteristics ofmaterials, which also depend on the temperature ofparts, determine the wear rate.Temperature stresses appear because of unevendistribution of temperature in the parts and alsobecause the majority of parts do not enable the mostheated portions to expand freely.By the thermal load it is meant the value of specificheat flux transferred from the working fluid to thesurface of a part. Transfer of heat from the workingfluid to the surface of parts is affected in two ways:by convection and by radiation. Convection has amajor importance for engines because combustion isaccompanied by formation of soot which burns outsubsequently.The soot content in the flame is the cause of itsdegree of blackness, and therefore, of high emissivepower of flame. High flame – temperatures anddegrees of blackness of flame are the cause of highfraction of heat transferred by radiation.The thermal stress level of separate portions of partsdepends mainly on the disposition of the portionrelative to the flame and is therefore not the same.

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In the piston – bowl combustion chamber engines,some zones of the parts like cylinder head, cylinderliner and piston head are shielded by the piston bodyfrom the flame in the period of the most intenseradiation [6].It follows that the thermal stress level depends onthe distribution of temperature in the parts. It is afunction of the heat load, design of the parts andcooling conditions. The distribution of localresistances depends on the design of parts. Thecylinder head and the piston head are the mostthermally stressed parts. The thermal state of thecylinder liner is also of importance, because it hasan appreciable effect on the thermal state of thepiston.From engines operating experience the maximumpermissible temperatures of different parts areknown. They should not exceed 3500C. Theminimum temperature (about 160 - 1800C) of thecylinder liner is restricted because of its effect onthe water vapour condensation conditions,depending also of the materials of the parts.The given values may also be regarded as tentative,because the design and definite working conditionsof a part affect the limiting possible temperature.Measuring the temperatures in different parts of thecylinder head and the piston head, the cooling canbe adjusted or the materials can be improved, oreven the properties of the fuels can be improved.We can take into consideration the mixture of asmall quantity of alcohol with gasoline in order toreduce the level of temperature [15].

2 Thermal Network ModelsThermal network models, using resistors andcapacitors, are very useful for rapid and efficientestimation of conduction, convection and radiationheat transfer processes in engines [4].Using a thermal network, the significant resistancesto heat flow, and the effects of changing materialthermal conductivity, thickness, and coolantproperties can be easily determined. A simple fournode series network, which includes convection andconductivity is shown in figure 1.This is an illustration of steady state heat transferfrom engine cylinder gas to the coolant. This seriespath is composed of convection through the coolantliquid boundary layer.The cylinder gas boundary layer insulates thecylinder wall from high temperature cylinder gases.Thermal networks are primarily used for convectionand conduction heat transfer, as the radiation heattransfer equation needs to be linearized to conformto resistance model [3].

Using Fourier’s equation, the conduction resistanceis:

L

AQ

TR cond (1)

Fig. 1And using Newton’s equation, the convectionresistance is:

1

AQ

TR conv (2)

Where:Q [W] - heat flow taken by the piston [W/m K] - working fluid thermal conductivityg [W/m2 K] - instantaneous heat transfer coefficientL [m] - a length scale, such as the cylinder boreT – difference of temperature

3 Cylinder wall modelWe now consider the unsteady nature of heat fluxfrom the combustion gas to the cylinder wall. Thecylinder wall has a periodic heat flux on the gas sideand a constant surface temperature on the coolantside [4], [9].The problem posed requires solution of the heatconduction equation:

2

2

xTa

tT

(3)

where: a [m2/s] is the thermal diffusivity of the wallmaterial, a = / cSubject to the following boundary conditions:

)tsin(qqxT "

1"0

at x = 0

T = TL at x = L (4)

As well as initial condition:

T = Ti(x) at t = 0 (5)

An exact solution can be written in closed form butit is quite cumbersome and as a result, no moreillustrative than a computer solution.Fortunately, an approximate solution can be derivedfor the practical case where:

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1t anda2L2

>> 1 (6)

In this case the temperature field is given by:

4x

a2tsinx

a2exp

a

q

xLq

TT

21

21

21

"1

"0

L

(7)

The inspection of this solution shows that:The surface temperature at x = 0 oscillates with thesame frequency as the imposed heat flux but with aphase difference of /4.The amplitude of the oscillations decaysexponentially with the distance x from the surface.The amplitude is reduced to 10% of that at thesurface at the distance given by:

21

21

a23,2a210,0ln

(8)

The penetration distance is a measure of how farinto the material fluctuations about the mean heatflux penetrate. For distances x greater than , thetemperature distribution is more or less steady anddriven only by the time average heat flux. Since thelength is rather compared to the dimensions (wallthickness, bore, etc) over which conduction heattransfer occurs, two simplifications can be made:- Conduction heat transfer in the various parts can

be assumed steady and driven by the average flux;- Heat transfer from the gas can be coupled to the

conduction analysis accounting for capacitance onlyin a penetration layer of thickness in series with aresistance computed or measured for steady state.A five mode thermal network for a cylinder wall isgiven in Fig. 2.The modeling of the penetration layer can becomplicated by the presence of an oil film ordeposits.Fortunately an accurate model is not required as thefluctuations about the mean T tend to be smallcompared to the gas – penetration depth temperaturedifference TTg .For an engine operated at asteady state, the penetration layer is thin because theengine frequency, which dictates the frequencycomponents of the heat flux imposed on the gas –solid interfaces, is rather high. On the other hand, inthe case of an engine being accelerated ordecelerated, the penetration layer is thicker because

lower frequency components of the heat flux arecharacteristic of the rates of change of engine speed.

Fig. 2

Where:Rt is the conduction path resistance to coolantR = /2 and C = ρc [2], [4].

3.1 Field of temperature in the cylinder headThe differences of the temperature between the partsof the cylinder head are important due to its shape,design and cooling. [1], [5]. According to figure 2we can assume: Heat transfer flow in the cylinder head wall:

c2

2

1

1

gw

cg

11TT

q

[W/m2] (9)

Inner temperature of cylinder head wall withcarbon soot layer:

]K[qTTgw

g1w

(10)

Inner temperature of cylinder head wall withoutcarbon soot:

1

11w2w qTT

[K] (11)

Cylinder head wall to cooling fluid:

2

22w3w qTT

[K] (12)

Where:Tg [K]- mean temperature of the gasesTc [K]- cooling fluid temperature

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gw [W/m2K] - heat transfer coefficient gas- wall1 [W/mK] - thermal conductivity of carbon soot1 [m]- thickness of carbon soot layer2 [W/mK] - thermal conductivity of cylinder headmaterial2 [m] - thickness of cylinder head wall

c [W/m2 K] - heat transfer coefficient wall –cooling fluid

4 Piston modelDetermination of the temperature profile of anengine component such as a piston requires solutionof the three – dimensional heat conduction equation.As an illustration, a case study of heat transfer in apiston will be presented. Figure 3 shows how apiston can be divided into a number of elements foranalysis. Only one quadrant of the piston in the x –y plane needs to be considered as the piston issymmetrical [12].The piston can be treated as steady and driven by anaverage heat flux since the penetration layers aresmall.

Fig. 3 Piston mesh [4]

The mean cylinder gas temperature is computingusing a cycle simulation to predict instantaneous gastemperature and then integrated according to:

dT4

1T g

4

0g

gg (13)

d4

1 4

0gg (14)

Where:g [W/m K] - average heat transfer coefficient

The average heat transfer coefficient is used inestimating the heat transfer coefficients on thecrown of the piston in contact with the cylinder gas[5].

4.1 Field of temperature in the pistonThe level of the temperatures in the pistondetermines the regular operation of the wholeengine [10].It is the most important to determine the field oftemperature in the piston head, in the center and atthe edge.If we consider the piston head a symmetrical – axialbody, the equation of conduction is:

02z

T2

rT

r1

2r

T2

(15)

Or using undimensional coordinates: = r/R = z/ andΘ = TgT the equation is written [5]:

022

2

2

2R12

2

(16)

The solution is given by integration:

KD10101

4D10

TTT

p

3

p

3

g2

6

gg

(17)

In the center of the piston head the temperature is:

]K[D1A

TT 1p

gcp

(18)

At the edge of the piston head the temperature is:

]K[Dh1A

TT 2pp

gep

(19)

Where:D [m]- piston boreh [m]– piston head heightL [m] - a length scale, such as the cylinder boreg [W/ m K] - instantaneous heat transfer coefficient

g [W/ m2 K] - average heat transfer coefficientp [W/.m K] - piston thermal conductivity1 = 1 (D,), 2 = 2 (D,) – coefficients as afunction of bore and thermal conductivity [15] [W] - heat flow taken by the piston

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5 Case StudyWe can consider a case of spark ignition enginewith the effective power Pe = 65 kW, the bore D =92 mm, capacity Vt = 2500 cm3, and speed n = 4500min-1 [15].Tg= 1365 KTc = 363 K

gw =250 W/m2K1 = 0,232 W/mK1 = 0,02 mm2 = 160 W/m K2 = 8 mm

c = 3500 W/m2 KWe can also consider the heat flow in the piston is: = 0.1 Pe. and 1 = 1,02; 2 = 2 (D,) 2 = 1,28.Using the equations (9) and (12) we obtain

51026.2q W/m2

Tw1 = 461 KTw2 = 441 KTw3 = 429 K

Using the equations (18) and (19) we obtain thetemperatures: Tcp = 523 K - piston head centertemperature and Tep= 474 K - piston head edgetemperature [15].The measured and theoretic temperatures are inputsto the ANSYS program to determine thetemperature field, thermal stresses and deformationsdue to the temperature difference in the piston head.The more recent computation finite elementprograms have implemented thermal finite elementstoo. For the purpose of this paper, use was made ofthe ANSYS program which contains 20 types ofelements for the heat transfer out of which the typesof "thermal elements" were used: for preset nodaltemperatures, axial- symmetric solid, thin plate,three- dimensional solid [13].Using these elements the piston and cylinder headwere investigated in terms of thermal steadyconditions and the temperature field, heat flowthermal stresses and displacements along differentdirections were obtained.In the thermal approach, the rigidity matrix becomesconductivity matrix, the nodal displacement vectorbecomes the nodal temperature vector and thetensions become heat flows [14].The input data in the program are:- longitudinal elasticity module, E = 0.75 1011

[N/m2]- thermal conductivity, p = 160 [W/m K]- Poisson's number, = 0.3- linear thermal expansion coefficient, =20 10-6

[K-1]

It is considered a section through piston head andcylinder head and the temperature is measured insteady conditions are input data.The engine was instaled on a testing stand. Chromel-alumel thermocouples were provided to measurethe outlet gas temperature, the cylinder - head walltemperature near the inlet and outlet ports and thepiston head temperature.The dots in figure 4 and 5 indicate the places werethermocouples are put.

Fig. 4

Fig.5

The measured temperatures are inputs to theANSYS program to determine the temperature field,thermal stresses and deformations due to thetemperature difference in the cylinder head wall [5]

Fig. 6 – Field of temperature in the piston

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Fig. 7 – Field of temperature at the bridge area ofthe cylinder head

References:[1] Asad A Salem, Heat Transfer in anaxisymmetric stagnation flow on an infinite circularcylinder - 5th WSEAS Int. Conf. on Heat and Masstransfer (HMT'0), Acapulco, Mexico, January 25-27, 2008.[2] Bhatti, S., Kumari, S., Chaitanya, V., Steadystate stress analysis and heat transfer analysis on anaxial flow gas turbine blades and disk, Proceedingsof the IASME/WSEAS International Conference onEnergy & Environmental Systems, Chalkida,Greece, May 8-10, 2006, pp. 110-116.[3] Esfahanian,V., Thermal analysis of an SI enginepiston using different combustion boundarycondition treatments, Applied Thermal Engineering26, 2006, pp. 277–287.[4] Ferguson, R.C., Kirkpatrick, T.A. InternalCombustion Engines, John Wiley &Sons, NewYork, 2001.[5] Han, S., Chung, Y., Empirical Formula forInstantaneous Heat Transfer Coefficient in SparkIgnition Engine. SAE paper 972995, 1997.[6] Heywood, J., Internal Combustion EnginesFundamentals, McGraw – Hill, New York, 1988.[7] Husnawan M., Masjuki H.H., Mahlia, T.M.I.Saifullah M.G., Thermal analysis of cylinder headcarbon deposits from single cylinder diesel enginefueled by palm oil–diesel fuel emulsions, AppliedEnergy 86, 2009, pp. 2107–2113.[8] Lee K.S., Assanis N., Thermo-mechanicalanalysis of optically accessible quartz cylinderunder fired engine operation, International Journalof Automotive Technology, 1 (2), 2000, pp. 79−87.

[9] Li, C., Piston Thermal Deformation and FrictionConsiderations, SAE paper 820086, 1982.[10] Mahdi, H., Rashidi, M., Determination ofPiston and Cylinder Head Temperature Distributionin a 4-Cylinder Gasoline Engine at Actual Process,Proceedings of the 4th WSEAS Int. Conf. on HEATTRANSFER, THERMAL ENGINEERING andENVIRONMENT, Elounda, Greece, August 21-23,2006, pp. 153-158.[11] Mohammadi, A., Yaghoubi, M., Rashidi, M.,Analysis of local convective heat transfer in a sparkignition engine, International Communications inHeat and Mass Transfer, 35, 2008, pp.215–224.[12] Riyad, M., Abdelkader, H., Analytical solutionof one-dimensional transient heat conductionproblem in thick metal slab, Proceedings of the 3rdIASME/WSEAS Int. Conf. on HEAT TRANSFER,THERMAL ENGINEERING AND ENVIRONMENT,Corfu, Greece, August 20-22, 2005, pp. 172-177[13] Riyad, M., Abdelkader H., Comparisonbetween the analytical and numerical methods ofsolving one-dimensional transient heat conductionproblems, Proceedings of the 4th WSEAS Int. Conf.on HEAT TRANSFER, THERMAL ENGINEERINGand ENVIRONMENT, Elounda, Greece, August 21-23, 2006, pp. 380-384.[14] Shojaefard, M.H., Ghaffarpour M.R., NoorpoorA.R., Alizadehnia S., Thermomechanical Analysisof an Engine Cylinder Head, Journal of AutomobileEngineering 220 (5) 2006, pp. 627-636.[15] Uzuneanu, K., Scarpete, D., Panait, T. - Studyon Thermal Stress Occuring in the BurningChamber of an Ethanol-Gasoline Fueled SparkIgnition Engine, Conference "MOTAUTO' 07" ,Varna, Bulgaria; Proceedings ISBN 954-90272-6-0,Vol.I, 2007, pp. 99 - 103.

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