Heat Transfer Modeling of a Diesel Engine

8/10/2019 Heat Transfer Modeling of a Diesel Engine

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HEAT TRANSFER MODELING OF A DIESEL ENGINE

The solution of heat transfer phenomena in Internal Combustion Engines is a very

challenging task considering the number of systems (intake and exhaust ports, coolantsubsystem, lubricant oil subsystem), the different heat transfer mechanisms (convection,conduction and radiation) and the quick and unsteady changes inside the cylinder that take

place at the same time These difficulties had led to a lot of experimental and theoretical!ork over the last years " revie! of these !orks can be found in #orman and $ishi!aki%&', and obinson % '

*everal authors %+ -' have documented the relevance of the understanding of heat transfer phenomena at the earlier stages of engine design, !hen the thermal endurance and stabilityof the composing combustion chamber parts have to be assured *ince engine efficiencyand emissions are affected by the magnitude of engine heat transfer, !hich is directly

related to the magnitude of combustion chamber !all temperatures %. &+', it is also duringthe design stage, that the strategies to control these temperatures, as !ell as heat and masstransfer involved in the engine cooling system, especially during cold start and transientregimes, must be envisaged "mong others, coolant temperature control is being consideredas part of various technology solutions to control material temperatures, given the linear dependency bet!een them %/, &0'

The definition of the requirements for the coolant temperature control and the enginecontrol strategies require detailed kno!ledge about the thermal engine behaviour *o, anaccurate prediction of the metal temperatures and heat flo!s through the cylinder head,

piston and the cylinder liner boundaries is important to engine design, performance prediction and engine diagnosis

"forementioned explains the continuous !ork on engine heat transfer and thermalmanagement carried out by many research groups In the frame!ork of a research programconcerning heat transfer in 1iesel engines, the authors %/, -' already discussed theconvenience of using a reduced thermal model for calculating the cylinder head, piston andliner temperature, !hile conducting combustion analysis The aim of the present work is toimprove the thermal resolution of the mentioned model, and also to extend its capabilitiesin order to incorporate it into a more comprehensive engine thermal management model.The developed tool can be used in the modelling of different cooling system architectures toassess their impact on oil, coolant and metal temperature, thus saving on extensive and time consuming test work. With this aim the following procedure has been chosen:

& " more detailed partitioning of the engine geometry into nodes, !ithout loosing thefunctionality and readiness of the program that characteri2e the concise !all temperature

predictive model reported in %&+'

The assessment of engine energy balances, as !ell as the rate of heat re3ection to thecoolant system


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"s a result, in addition to the calculation of metal temperatures, the thermal model allo!sthe calculation of the heat fluxes through combustion chamber elements (in !hich theengine enclosure has been divided) and engine boundaries and, in particular, !ith thecalibrated engine predictive thermal model it can be estimated the engine heat re3ection tothe coolant

The presentation of the !ork is organi2ed as follo!s4 first, a brief description of theelectrical equivalent model of the engine is explained, including a brief explanation of thecombustion chamber nodes "fter that, the modelling of the boundary conditions is treated,that is4 the model of heat transfer bet!een the in cylinder gases and combustion chamber !alls5 bet!een the gas and the intake6exhaust runners5 bet!een the coolant and the liner and cylinder head5 bet!een the oil and the piston5 bet!een the oil and the liner5 bet!een the

piston and the liner Then, a short explanation of the model code is described, follo!ed by acomparison bet!een experimental and model results 7inally, the main conclusions of this!ork are given

2. THE THERMAL MODEL.The thermal model developed has been ad3usted by means of a thorough experimental !ork on a specific four cylinder 1iesel engine, in !hich its first cylinder !as isolated from theother three and instrumented !ith + thermocouples in the cylinder liner, &- thermocouplesin the cylinder head, and thermocouples in the piston (a detailed description of the set upcan be found in %&-' The main characteristics of this engine are given on table &

Table &4 Engine main characteristics*troke 89 mm#ore ./ mm:aximum #:E; &,


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The models of the cylinder head, liner and piston !ere created by using a commercial +1soft!are This allo!ed splitting these complex components into small parts and getting themechanical characteristics such as connecting areas, distances bet!een centres of mass, andmasses of elements =alves and in3ector !ere also decomposed into smaller parts Thecylinder liner !as divided in the axial, circumferential and radial direction as sho!n in

figure & The fact that only three quarters of the piston stroke !as cooled !as also takeninto account In total the cylinder liner is made up of /& cylinder nodes The nodes at theinside are connected !ith the piston through the segments

7igure & Cylinder liner decomposition 7igure ;iston decomposition

The piston !as divided in - nodes In figure the referred nodes are, from top to bottom, the bo!l centre, the bo!l rim, the piston cro!n, the piston centre, the ring!aist housing the oil cooling gallery, and the piston skirt >ith the contact area andthe distance bet!een the nodes, the conductances bet!een them could be calculated"n axisymmetric temperature distribution !as assumed for the piston and liner

The C"1 model of the cylinder head is represented in figure + It consists on fire deck,exhaust and intake runners and valves !ith their guides and the in3ector "ll these elementsare separated in t!o different parts4 lo!er and upper The cylinder head model !as dividedinto +/ nodes #ecause of the special interest the fire deck of the cylinder head, it !asmodelled in more detail The partition is sho!n in figure 0


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7igure + C"1 model of the structural part of cylinder head corresponding to one cylinder

7igure 0 Cylinder head decomposition

2.2. Interactions and o!ndar" conditions.Thermal calculations include the determination of heat fluxes from in cylinder gases tocombustion chamber !alls, the heat fluxes through the metallic parts, the convection fromthe intake and exhaust gases around the surfaces of valve stems, inner surfaces of valveseats and along the intake and exhaust port !alls, and also the convection from the metallic

parts to the cooling and lubricating oil media "lthough the heat fluxes in combustionchamber have a periodically changing nature in time, the analysis is made assuming steadystate loading using the cycle averaged values This assumption is reasonable consideringthe speed of the periodical changes as compared to thermal inertia of all the components of cylinder head, piston and liner The same assumption is valid for the exhaust and intakegases Thermal contact interactions bet!een valves and valve seats are described by heatflux AB from the solid face " to #, !hich is related to the difference of their surfacetemperatures AT and BT , according to ( ) A B AB T T k = , !here k is the contact heattransfer coefficient

#asic $rinci$les o% nodal model.7or each component, the boundary conditions are specified, either by media (coolant, oil,etc ) temperature and heat transfer coefficient from the outside !all surface to the media, or

by specified !all temperature on outside surface In the model each node is connected toother nodes and boundary conditions ?nce the structure is divided into nodes, the energyconservation equation can be !ritten for each node The sum of heat fluxes bet!een nodes,convective heat fluxes and other heat fluxes in a time span t equals the change insensible energy of the node (eq &)


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( ) ( ) ++++ ++=

! k l

it t l liliik

it t

!t t i!

it

it t

vi T T AhT T " t T T

cm (&)

>ith im the mass of node i , vc its heat capacity, i! " the conductance bet!eennode i and a node ! , lih the heat transfer coefficient bet!een node i and a

boundary l and li A the corresponding contact area "t the right side thetemperatures at the instant t t + are used (the implicit formulation) The advantageof the implicit formulation is that the solution is unconditionally stable !hensimulating transitory behaviour #ecause the model described here !as also used for transitory calculations the implicit form !as used

7or each of the n nodes of the model there is an equation like equation &, forming asystem of n equations and n unkno!n node temperatures Equation & gives rise to a setof lineari2ed, implicit equations of the form4

[ ] [ ][ ] [ ] [ ][ ] [ ] # T t

$ %T

t

$ " t t t +

+=

+ + ( )

>here, [ ] " and [ ]$ are nn conductance and capacitance matrixes, respectivelyThe i th diagonal element of the conductance matrix is the sum of all the conductiveand convective conductances to node i The element on the i th ro! and 3 th column isthe conductance bet!een nodes i and ! !ith a minus sign

!iif " "

!iif Ah " "

i!i!

l lili

!i!i!

=

=+= (+)

[ ]t T and [ ]t t T + are column vectors of n elements !ith the old and ne! temperatures

of the nodes [ ]% is a column vector !ith the sum of the heat fluxes to node i on thei th ro! This can be e g a heat flux generated by friction [ ] # is a column vector !iththe i th ro! the sum of the product terms lilil AhT for the convective boundaryconditions of node i

7or stationary conditions, nodal thermal masses are not included in the equation ,i

t i

t t T T =+ , and equation & reduces to4

[ ] [ ] [ ] [ ] # %T " += (0)

The assembly of the equations ( ) and (0) is performed automatically based on generalengine specifications and is solved implicitly for the temperature vector [ ]T ,employing a @aussian elimination procedure

Modellin& the o!ndar" conditions.The model to predict the temperatures of the metal parts, results in a thermal resistor net!ork made up of < metallic nodes and 8 convective nodes, !hich represent the

boundary conditions, characteri2ed by their instantaneous media temperatures and filmcoefficients


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The conductances bet!een the combustion chamber nodes and oil6coolant flo!s have beendetermined assuming that they depend on the boundary flo!s or the piston speed in a formlike

( )( )( )&& A & += !i &xp !iconst !i x$ " " (/)

>ith x representing the coolant flo! or the piston speed, !i$ is a multiplicative factor and !i &xp A is an exponent to be fitted const " is a constant conductance !i " is theseries configuration of const " and the variable dependent conductance "ll conductancesof the model are discussed in detail in the follo!ing paragraph

#o!ndar" condition et'een the &as and com !stion cham er 'alls.The changing nature of intake, in cylinder and exhaust processes reflects in a changeof the boundary conditions To predict the mean !all temperatures during the engine!orking cycle, heat flo!s have to be calculated using cycle averaged boundary

conditions The mean heat flux ( ) bet!een the gas and a !all permanently incontact !ith the gas (e g piston, cylinder head) is found integrating the instantaneousflux ( ) over a cycle

( ) ( ) ( )( )[ ] d T T hd wall gas ==. 9

9

. 9

9 . 9&

. 9&

(-)

>ith ( ) h the instantaneous heat transfer coefficient as function of crank angle,( ) gasT the instantaneous gas temperature and wall T the combustion chamber !all

temperature

Introducing a mean film coefficient ( h ) and an apparent gas temperature ( gasT )4

( ) d hh =.)9

9.)9&

(.)

( ) ( )

h

d hT T

gas

gas

. 9& . 9

9

=(8)

The mean heat flux can be !ritten as4

( )wall gas T T h = (


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The conductance bet!een the in cylinder gases and the internal nodes of the cylinder has been calculated bearing in mind that they are not in contact along all the cycle *o,apparent mean gas temperature and an apparent mean heat transfer coefficient for cylinder nodes have to be found To this effect a function ( ) , ' is used in themodel 7or every node of the cylinder liner, the function is defined such that4

( ) ( )( ) ' d if

' d if '

head pist

head pist

>=

&

9,(&9)

7igure / *chematic to illustrate the notation used in the modeling of the cylinder gas B liner interaction

#eing ' the axial position along the liner measured from the fire deck, ( ) head pist d isthe distance bet!een the fire deck and the top of the piston for crank angle (asillustrated in figure /) >ith the D function, the mean gas temperature and heattransfer coefficient are defined for each position along the stroke The mean heat fluxat a distance 2 from the fire deck is

( ) ( ) ( ) ( ) ( ) ( )( )[ ] d ' T T ' hd ' ' liner gas ==. 9

9

. 9

9

,. 9

&,

. 9&

(&&)

This can be !ritten as4

( ) ( ) ( ) ( )( ) ' T ' T ' h ' liner gas = (& )>ith the mean heat transfer coefficient and gas temperature at a distance 2 from thefire deck4

( ) ( ) ( ) d h ' h. 9

& . 9

9 = (&+)


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( )( ) ( ) ( )

( ) ' h

d hT ' T

gas

gas

. 9

& . 9

9

=

(&0)

Considering a node of the cylinder liner bet!een a distance of 2 & and 2 from the firedeck, the contact area is given by4

( ) ( ) ( ) ( )[ ]{ } ( ) head pisd ' ' ' ' ' B A )))&)& ,&, = (&/)

The mean film coefficient times the area gives the conductance that has to be put on

the conductance matrix, )(, A A A 'h A " i ' gasi ' gas = , for each node of the cylinder liner in contact!ith the cylinder gases in the model The apparent gas temperature seen by the

cylinder ring band, in !hich the node is located, is used as boundary condition,)( ' T gas

The conductance bet!een the valves and the seats " valvesBhead is the product of a contact timefactor, the valve seat area ( Aseats ) and a contact conductance ( " seat )4 " valvesB head f Aseats " seat 7or the contact resistance, " seat , a value of +999 >6m F !as used% &'

Gas('all heat trans%er.The film coefficient, hgas , necessary to calculate the conductance bet!een the gas and the!alls, is obtained !ith an enhanced version of >oschni equation % '4

( )89

9&/+9899 )(&9&

++= p p( p T ( $ c$ c$ T p )h $A$A

$AT uwmw g g (&-)

Gere, ) is the bore5 T g the instantaneous gas temperature calculated !ith the measured incylinder pressure, p5 mc is the mean piston speed5 cu is the tangential velocity at thecylinder !all due to s!irl5 ( T is the displacement volume5 T ivc, p ivc and ( ivc are the gastemperature, pressure and cylinder volume at intake valve closing (I=C) and p* is the incylinder pressure under motoring conditions

In the !all temperature model the heat transfer coefficient bet!een the gas and the!alls is calculated !ith the previously described formula using the instantaneous gas

temperature, ( ) gasT , and pressure, ( ) p , from a home made combustion predictive program Then the cycle average heat transfer coefficient and gas temperature arecalculated

R!nner ) air heat trans%erThe heat transfer bet!een the runners and the gas is highly non stationary Especiallyin the exhaust !here very high gas velocities are reached during the blo! do!n#ecause the generated turbulence lasts even after valve closing, formulas based on the


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instantaneous speed cannot describe adequately the heat transfer in this pulsating flo!and in this !ork the method proposed by eyes % +' !as used The velocity iscalculated as a sum of the actual velocity and the previous velocities multiplied !iththeir respective dissipation coefficients (&.)

( ) ( )

=

=

=

9

9

k

k

k

k

c

t k t ( ct ( (&.)

The average velocity ( )t ( is calculated !ith the instantaneous velocity ( )t ( and the previous average velocity ( )t t ( 4

( ) ( ) ( ) ( )t ( ct t ( ct ( += & (&8)

#eing c the dissipation constant >ith the time averaged speed, the eynolds and

$usselt numbers are calculated

)(

=e (&


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The piston is cooled in t!o !ays ;art of the heat is led a!ay through the segments tothe liner and finally to the coolant The bigger part, though, is transferred to the oil Inthe engine under study the oil is sprayed to the entrance of a gallery in the pistoncro!n from an oil cooling 3et

To find the heat transfer coefficient hoil pis, based on the boundary layer theory, anexpression of the form nm gal gal +u ;r e for the convective heat transfer in the pistongallery is used *ince no tests !ere done !ith !hich the value of exponent n could bedetermined, it !as decided to consider the factor -r n as a part of the constant Theexpression for the $usselt number then takes the follo!ing form4

m gal gal gal $ +u e= ( )

The $usselt number in the coolant gallery is defined asoil

gal gal gal k

d h +u = , the eynolds

number asoil

gal p gal

d .

e = >here d gal is the internal diameter of the oil gallery and k oil

and / oil are the conductivity and viscosity of the oil, respectively

#ased on the !ork of Fa3i!ara % /', using the piston temperature measurements, thecorrelation for the conductance bet!een the oil and the piston !as sought in the form4

( ) oil pis &xp poil pisoil pis . $ " = A ( +)

>here p is the mean piston speed The parameters $ pis oi l and &xp pis oi l determine the piston speed dependent conductance bet!een the piston and the oil The constants are

results of the optimisation routine

Liner ) oil heat trans%er.?il is continuously splashed against the cylinder !all and, in the piston some channelscoming from the cooling gallery feed the third groove *o the cylinder !all is continuously!etted !ith oil This oil is heated by the cylinder !all and scrapped of during thedo!n!ard stroke 7or this conductance ( " lin oil ), a piston speed dependence !as taken intoaccount 3ust like for the oil B piston heat transfer 1uring the optimi2ation phase of themodel this speed dependence did not appear to be very significant and only the constant

part !as included in the model "n equivalent heat transfer coefficient, h linBoil, for thismechanism can be extracted from the follo!ing expression4

oil lini!oil lin h A " = ( 0)

+iston ) c"linder liner heat trans%er#ecause measurements !ere available of both the piston and the liner temperature, anempirical model could be fitted to the data It !as supposed that the segments have a


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conductance " seg per unit of length The possible influence of the piston speed !asturned to be not significant Gence the conductance bet!een a node of the pistonH -is0i and a node of the liner H 1in0! !hich make contact through a segment is given

by the follo!ing formula4

) A A A

) "

T

t " ! 1in seg

cycle

con ! 1ini -is

= ( /)

>here, t con is the contact time bet!een the segment and the liner node, T cycle theduration of a cycle, JinA3 the angular !idth of the liner node and 1 the bore Thecontact time is calculated from the instantaneous piston position taking into accountthe position of the segment and the axial position of the liner node

*"linder head ) c"linder liner heat trans%erGeat conduction bet!een the cylinder liner and the cylinder head is possible through thegasket ( " linBhead) This conductance did not appear to be significant and !as not consideredin the model

,. THE *OM+-TATIONAL +ROGRAM."s !as mentioned in the previous paragraph the model developed is a combination of theoretical and experimental !ork 7itting the model to particular engine temperaturemeasurements, it has been taking care of representing the conductances involved in theoptimi2ation process, as functions of geometrical and operational parameters of the engine,so that the model can be readily applied to other engines !ith similar geometry and po!er as a generic template "lso a set of scale factors and relationships has been provided in the

program to ad3ust ne! engine geometries and materials

The code to model the thermal behaviour of the engine has been !ritten in CKK Itsstructure is summari2ed in figure - The inputs of the program are4 a file !ith the

names of the tests, the !all temperatures of !hich !ill be calculated5 C"J:EC ( homemade predictive computer application ) output files !ith the instantaneous temperatureand pressure in the combustion chamber for every test5 a file that contains the measuredmean variables representative of the running condiction, including prescribed coolantand oil temperatures 5 a file that describes the discreti2ation of cylinder liner, cylinder head and piston and, finally, a file !ith the parameters of the model, needed tocalculate convective conductances


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7igure - *tructure of the computational program used for the model %&/'

The program can be used either in predictive mode, or in an optimi2ation mode In theoptimi2ation mode, the parameters of the model affecting convective conductances(!ith the capability to be extended to other ne! parameters of interest) are ad3usted ina !ay that the error bet!een the calculated and measured temperatures of a kno!n setof tests is minimal The program uses the $elder :ead simplex algorithm % -' tooptimi2e the parameters

In the predictive mode, temperatures and heat fluxes can be calculated for any givenengine, provided its geometrical information and the instantaneous and mean variablesare kno!n

7or all the tests in the file HTests txt the program calculates the temperatures, and theresults are compared !ith the measurements 7or the cylinder liner the predictedtemperature at a thermocouple location is calculated by three dimensionalinterpolation bet!een the surrounding nodes This interpolation uses the position of the nodes and the thermocouple To compare measurements and predictions in thecylinder head and piston a !eighting procedure is performed bet!een the nodaltemperatures of close related nodes

>ith the engine used to tune the model up, the values of the optimi2ed parameters arethose referred in table

Table ?ptimi2ed values of conductance parameters used in the modelCte Alin head 9hAcool cyl 9 / 008hAcool 71 & &8-.-hAcool Exh 9


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CteApis oil . & 0 -9.ExpApis oil 9 -8.+.-Fpis lin + 8.///hAlin oil 8-0 8-8.&+

. RES-LTS AND DIS*-SSION.The experimental !ork comprises t!o stages The first stage is intended to provide enginesteady state temperature measurements to run the computational program in theoptimi2ation mode The outcome of this stage is the attainment of the optimi2ed model to

predict the thermal behaviour of 1iesel engines geometrically similar to that used in themodel development process

In the second stage, another set of tests is used to obtain measurements of the enginetemperatures over elementary transient step changes !ith the aim of assessing the

predictions of the model for heated engine transient operation Fno!n the initial and final points of transient engine operation, the model !ith the optimi2ed parameters is used to

calculate temperature evolution of the engine temperatures and heat fluxes for a giventransient time "n interpolation procedure in the time domain, allo!s a comparison of predicted and experimental transient thermal responses of the engine

7or the first stage, the program is run in the predictive mode and the predicted temperaturesare compared to the measured ones, obtaining the model temperature errors separately for

piston, liner and cylinder head, as !ell as the global model error "fter that, the program isrequested to optimi2e the initial model parameters in the optimi2ation mode, and theresulted optimi2ed parameters are re entered to the model to recalculate the enginetemperatures and obtain the global error, the final errors in the predictions of piston, liner and fire deck temperatures, the heat fluxes bet!een engine nodes and the engine heat

balance

7or the second stage, the program is run in the predictive transitory mode, after optimi2ingthe model parameters

The test matrix !ith the mean variables used during the optimi2ation process of the thermalmodel for the engine under study is presented in table + + steady state tests !ereconducted !ith variation of the speed and load The temperatures of the + tests arecompared to those obtained experimentally for all measured points

Ta le , :ean variables of the tests performed and used to tune the model upTest Speed Tq_C1 mep C_FlB M_a1 P_In1 P_Ex1 T_In1 T_Ex1 T_oil TC_B

- rpm Nm bar l/min g/s mbar mbar C C C C

1 1 !! 1 "# $"%& #'"!& "#( 1!)% 1##) $"% &)1"' %! % "%)

# 1 !! 1 "#1 $"%# #(")) "#' 1!%! 1#&! &)#"1 %! % ")%

& & !! )"1$ #"(& (#"!$ 1("'$ 1 $) 1( &)#"# %1"' %("#

$ & !! 1$"$# $"(( (1")( 1'"!( 1 ($ 1(# $&$") %$"' % "'(

# !! ("'1 #"1' $&")( 1!"%) 1#$& 1& & "# #&)"' 1!'"( % "')

( # !! #1"(' '"!1 $$"!' 1&"1% 1$%% 1'!& &%!") 1! "1 % " $

' #!!! %"' &"1 &$")( ) 1#!( 1&1# "1 #)!"( 1!("& % "%


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) #!!! & ")1 11"( &$"') 11"!& 1() 1')! $"% !%"& 1!$"( % "#'

% #!!! ##"(& '"&1 &$"%( %")& 1$%1 1($$ $1!"# 1!&"$ % "$%

1! &!!! %" & &"!) &$"'% 1 "'1 1 $' 1('# #('"( 1!(" % "(

11 &!!! &("&) 11") &$"' 1)"&% 1)1& #!%$ "1 ") 11! %$"($

1# &!!! &("&& 11"' &$"%) 1)"$1 1)1$ #1!) "# 11! %$"

1& &!!! #1"&( ("% & "1& 1'"!& 1('& 1)$# &(!"& 1!("# % "&(

1$ #!!! ##" '"#1 & "&) %"'$ 1$'1 1(1# "1 $1#"% ' ") % ")$

1 #!!! ##"$) '"#' & "(( %"'$ 1$'& 1(1! "1 $1&") ) "1 % ")1

1( #!!! ##"&& '"## & " %"'# 1$'& 1(&! $1'" %$"% % "(%

1' #!!! ##"$' '"#( & "$$ %"'# 1$'$ 1(&! $1%"$ 1! "$ % "(1

1) &!!! #!"1& (" 1 ("1) 1("$) 1 # 11'1 !"1 ())"& )!"& %("!$

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#! $!!! 11"$# &"(% '&" 1%"$ 1(11 1&$1 !"1 $%1"$ ) "1 %("#1

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## $!!! 11" ' &"'$ '&"'& 1%"$ 1(1& 1&& !"1 $%!"& 1!$"# %("1

#& 1 #! '" #"$$ #'"!& &"') 1! 1 11 ! #"1 #''"( ($"( $ "

#$ 1 #! )"!$ #"( #'"!( &"'$ 1!'% 11') ("( &11"( )%"' %'

# 1 #! )"#( #"(' #("%& &"' 1!)) 11'' )"% &!(" ))"& )&"#(

#( 1 #! '"'( #" 1 #("%( &"'' 1!$( 11(# #"$ &!1 )% '%")#

#' 1 #! '"'( #" 1 #("%( &"'( 1! $ 11 1 #"1 #%#" ')"( (#"('

#) 1$&! 1("1% "#& # "11 $"!$ 1!)( 11'& ("$ $1&"1 %! %'

#% #&)! &1")1 1!"& $1"% 1!"!$ 1&() 1$#' (!"$ '%" %! ($"&'

&! #&)! &1"( 1!"# $# 1!"!' 1& & 1&)& (!"1 )&"' %!"1 )'"&'

&1 #&)! &!"%( 1! $1"%' 1!"! 1&'& 1$1) (! )("1 %! %'

#&)! &!"(1 %")% $1"%# 1!"!' 1&$' 1&(% (!"1 )!"$ %! '%"1'

.1. Tem$erat!re o% liner nodes7igure . illustrates the predicted and measured comparison of temperature distribution inthe liner at various axial locations, at a depth of +,/ mm, for three representative operation

points4 & L, ++ L, and -/ L of #:E; (tests $M &, - and & , in table +, respectively) Ingeneral it can be observed that the model predicts !ell the liner temperatures, !ith atemperature gradient descending from the top to the bottom for the refrigerated part of theliner 7or the remaining longitudinal fourth part of the liner nodes, the temperaturesexperiment a light increment :ain discrepancies (particularly for the liner nodes placed

bet!een cylinders, figure .,a), and for the nodes located in the longitudinal center of theliner) may be due to the adoption of a global spaced averaged heat transfer coefficient for the coolant liner interaction "ctually, !ithin the coolant passages more than one regimemay exist for any given load condition and !ill vary locally around the coolant circuit Inthe model for the coolant boundary condition, the variations in coolant and surfacetemperatures around the coolant circuit are neglected This can give rise to variations in thelocal rate of heat transfer to the coolant around the circuit directly due to variations in thesurface to coolant temperature difference, and indirectly through the effects on heat transfer coefficients


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a) b)

c) d)7igure . ;redicted and measured temperature distributions in the liner at various axiallocations for & L, ++ L, and -/ L of #:E;4 a) bet!een cylinders side, b) intake side, c)exhaust side, d) clutch side

The dependence of liner !all temperature on load is exemplified in figure 8, for t!ooperation points !ith the same engine speed of +999 rpm, and mean effective pressures of +,98 bar and &&,.- bar, correspondingly (tests &9 and & , respectively) The predictionsagree !ith the measured data at a good level "s !as previously said main discrepanciesmay be attributable to the variation of heat transfer coefficient for the liner coolantinterface, less important at lo! loads

a) b)

c) d)


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7igure 8 ;redicted and measured temperature distributions in the liner at various axiallocations as the load changes at a constant speed of +999 rpm, a) bet!een cylinders side, b)intake side, c) exhaust side, d) clutch side

The sensitivity of the model to the speed changes as compared to the measured values is

represented in figure < for t!o operation points !ith the same mean effective pressure of ,- bar and engine speeds of &/ 9 and +/99 rpm, correspondingly (tests + and 0,respectively) The match of predicted and measured temperatures is good, more accurate atlo! speeds

a) b)

c) d)7igure < ;redicted and measured temperature distributions in the liner at various axiallocations as the speed changes at a constant mep of ,- bar, a) bet!een cylinders side, b)intake side, c) exhaust side, d) clutch side

Jiner temperatures as !ell as all others increase !ith speed and load The gradient is moresignificant in the upper part of liner Gigher engine loads translate in an increase of temperatures but !ith a higher gradient in the upper portion of the liner5 higher enginespeeds more equally distribute !all temperatures along the stroke

The computed temperatures of the liner in the cross sectional area are in good agreement!ith experimental results, as can be inferred from the temperature plot in figure &9, !heretemperatures for four orthogonal points in the liner at a distance of 00 mm and a penetrationdepth of +,/ mm, for load cases & a& , have been represented It is observed that ma3or discrepancies in the predicted temperatures as compared to measured values appear for liner nodes bet!een cylinder nodes, especially at high loads


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7igure &9 1istribution of liner node temperatures in the cross sectional area of the cylinder & at a distance of 00 mm from the fire deck, +,/ mm penetration depth

.2. Tem$erat!res %or the %ire dec/ nodes.Through the fire deck the heat flo! is transferred from the combustion chamber to the restof the nodes of the cylinder head, including intake and exhaust pipes, and coolant

The comparison of predicted (obtained by interpolation of the nodal results) and measuredtemperatures of fire deck nodes of the cylinder head, taken at depths of +,/ mm and 8,.mm, for all the experimental test conducted, is presented in figure && In general it can besaid that the fire deck temperatures are !ell rendered, especially for lo! loads The averageerror in the prediction of the fire deck temperatures is .,/ MC, !hich is lo! for theapplicability of the model (;rocurar traer aquN las conclusions de Oaime sobre sensibilidadcon C"J:EC a las predicciones de temperature de pared) The higher errors correspond tothe node represented by the in3ector hole at the exhaust side, at 8,. mm (!ith an averagevalue of #1*& C), and bet!een intake and exhaust valves (!ith an average value of '*!#C," The error plot for all the tests conducted under steady state operation points is sho!n infigure &


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7igure && ;redicted and measured temperatures in the cylinder head nodes

7igure & ;lot of the errors in the prediction of fire deck temperatures for the measuring points

The predicted temperatures of cylinder head fire deck nodes, for three representativeoperation points4 & L, ++ L, and -/ L of #:E; (tests $M &, - and &+ in table ,respectively) is presented in figure &+ The higher temperatures correspond to the exhaustvalve To illustrate the sensitivity of the thermal response of the fire deck nodes loadchanges, it is presented in the figure &0 the variation of fire deck node temperatures as theload is changed from +,98 to &&,.- bar at a constant speed of +999 rpm (tests &9 and & ,respectively) To illustrate the sensitivity of the fire deck temperatures to the speed regimechanges, the behavior of the temperatures for the referred nodes is presented in figure &/,!here the test points correspond to a speed variation from &/ 9 rpm to +/99 rpm !ith amean effective pressure of ,- bar (tests + and 0, respectively)


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7igure &+ Temperatures for the fire deck nodes predicted by the model

7igure &0 Temperatures for the fire deck nodes predicted by the model at a constantspeed and t!o different mean effective

pressure values

7igure &/ Temperatures for the fire deck nodes predicted by the model at a constant mep and t!odifferent engine speeds

.,. Tem$erat!res %or the $iston nodes.The steady state predicted and measured temperatures in the piston nodes, !herethermocouples !ere placed, are compared in the figure &- for all the experimental tests

performed 7or the bo!l rim, the temperatures are !ell predicted, !hile for the bo!l bottom the temperatures are overpredicted This overprediction of the bo!l bottomtemperatures has an acceptable magnitude though The behaviour of temperature

predictions for these nodes are 2oomed in figure &. for three !orking operating pointscorresponding to & L, ++ L, and -/ L of #:E;


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7igure &- ;redicted and measured temperatures in the piston nodes

7igure &. ;redicted and measured temperatures in the piston nodes for & L, ++ L, and -/L of #:E;

The sensitivity of the thermal response of the piston nodes to the load is illustrated in figure&8, as the load is changed from +,98 to &&,.- bar at a constant speed of +999 rpm Toillustrate the sensitivity of the piston nodes to the speed regime changes, the behavior of thetemperatures for the referred nodes is presented in figure &


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speeds

7igures 9 and & sho! a good agreement bet!een calculated and measured piston nodetemperatures along all the test history, !ith a mayor degree of overprediction for the piston

bo!l bottom

7igure 9 Test history of predicted andmeasured temperatures of the piston bo!l rim

7igure & Test history of predicted andmeasured temperatures of the piston bo!l

bottom

7igure sho!s the variation of temperature errors for piston bo!l rim and piston bo!l bottom for a history of tests *ince the program uses only t!o experimental pistontemperatures of a total of 0& ones in the entire engine (it !as not possible to connectenough sensors to match all the elements of the meshed model), to collectively calibrate theglobal thermal model and give !ell conditioned predictions of the engine thermal behavior,it is not likely to approximate all the measures !ith the same degree of accuracy "lthougha reevaluation of the !eighting factors for the temperatures could improve the predictions,it is true that a more detailed calibration of the engine model could be made introducingfriction model data from an engine of kno!n dimensions and masses, or obtainingexperimental friction data

7igure Error history in the temperature predictions of the piston bo!l rim and piston bo!l bottom nodes


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The behavior of the temperatures predicted by the model for all the nodes in !hich demodel has been descreti2ed is presented in figure + " larger number of temperaturemeasurements !ith good distribution uniformity in the piston could improve the predictionsif the ob3ectives of the research !ere to have a refined piston model

7igure + ;redicted temperatures of the piston nodes for a test history

" summary of the errors in the predictions of cylinder head (not only the fire deck), the piston and liner temperatures as !ell as the total error of the model is plotted in figure 0:ean errors in the evaluation of combustion chamber !all temperatures are summari2ed intable 0, being the error in the prediction of piston temperatures the larger one follo!ed bythe error in the prediction of cylinder head temperatures Jiner temperatures give the best

predictions The global mean error is lo!er than &9 MC, and is representative for theoperation points encountered by 1iesel engines during the city driving cycles esults arevery satisfactory In fact, this error is lo! enough to allo! the model to be used for research

purposes in 1iesel engine combustion predictive and diagnosing programs "lso, theinformation of the model permits to !rite the energy balance and the heat fluxes bet!eenthe components

7igure 0 Errors in the temperature predictions of combustion chamber !alls

Table 0 :ean errors in the predicted temperatures of engine metallic parts


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Error_ iner Error_.ead Error_Pis Error_totalC, C, C, C,

&")'1)' '"&) &1# 1!")$&' '"&('

In figure / the surface averaged temperatures of the cylinder liner, piston and fire deck are presented for an extended set of tests The model allo!s calculating the heat fluxes throughthe combustion chamber !alls In the follo!ing paragraph it !ill be presented the heat flux

balance for all the nodes used in the model

7igure / :ean temperatures of the cylinder liner, piston and cylinder head for anextended set of tests

. . Heat %l!0es thro!&h node o!ndariesFno!ledge about geometry, thermal properties of material, conductances, and nodetemperatures is utili2ed in the model to find the partitioning of the heat re3ected to thecombustion chamber !alls *o, the model can be easily interfaced !ith engine combustion

predictive and diagnostics programs Geat crossing any node interface of the discreti2edmodel can also be found To give an example of this model feature, based on a particular operational condition of the engine, mep +,), derived directly from themodel7rom cylinder gases to liner 0&< &9


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engine coolant This is currently one of the most important outcomes of the program to beutili2ed, since it is a primary input to the design and analysis of engine cooling systems

In the model presented, the cylinder liner model is decomposed into five longitudinalsections or cylinder ring bands The heat to the cylinder liner transferred according to this

geometrical partitioning is presented in table - for t!o running conditions (tests $M & and&+) It can be seen that almost /9 L of the heat through the cylinder liner is transferred bythe upper &9 L of the liner surface in contact !ith the gases " more refined partitioning of the liner along its length can be set in the program

Table - Geat fluxes from cylinder !orking gas through liner surfacesTest &/99 rpm, 0,) L Geat flux (>) LI 9&


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Gead flux (>) LGeat flux from cylinder gases to the liner 0&< &9+ ."FI, F " revie! of internal combustion engine heat transfer -rog. &nergy $ombust. ci., Transfer , &E, # : " Geat transfer model of a 1iesel Engine ;h 1 ThesisPniversidad ;olitWcnica de =alencia, 99-%&.' 1E*C?:#E*, @ , :" ?TE"P , 7 , and 7EI1T, : *tudy of the interaction

bet!een mechanical energy and heat exchanges applied to IC engines "pplied ThermalEngineering volume +, issue &-, $ovember 99+, pages 9-& 9.8


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%&8' #?G"C, * = , #aker, 1 : and "ssanis, 1 $ " @lobal :odel for *teady *tate andTransient * I Engine Geat Transfer *tudies *"E ;aper ?*CG$I, @ " universally applicable equation for the instantaneous heattransfer coefficient in the internal combustion engine, *"E ;aper $o -.9 G , 7J"$$E S, # ; , TEPF?J*FS, * " and =ETTE JI$@, > T

$umerical recipes in C4 the art of scientific computing, Cambridge Pniversity ;ress, $e!Sork, $S, &

Documents

Heat Transfer Modeling of a Diesel Engine