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http://pid.sagepub.com/ Engineering Engineers, Part D: Journal of Automobile Proceedings of the Institution of Mechanical http://pid.sagepub.com/content/215/6/747 The online version of this article can be found at: DOI: 10.1243/0954407011528329 2001 215: 747 Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering D J Oude Nijeweme, J. B. W. Kok, C. R. Stone and L Wyszynski Unsteady in-cylinder heat transfer in a spark ignition engine: Experiments and modelling Published by: http://www.sagepublications.com On behalf of: Institution of Mechanical Engineers can be found at: Engineering Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Additional services and information for http://pid.sagepub.com/cgi/alerts Email Alerts: http://pid.sagepub.com/subscriptions Subscriptions: http://www.sagepub.com/journalsReprints.nav Reprints: http://www.sagepub.com/journalsPermissions.nav Permissions: http://pid.sagepub.com/content/215/6/747.refs.html Citations: What is This? - Jun 1, 2001 Version of Record >> at National Cheng Kung University on August 20, 2014 pid.sagepub.com Downloaded from at National Cheng Kung University on August 20, 2014 pid.sagepub.com Downloaded from
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  • http://pid.sagepub.com/Engineering

    Engineers, Part D: Journal of Automobile Proceedings of the Institution of Mechanical

    http://pid.sagepub.com/content/215/6/747The online version of this article can be found at:

    DOI: 10.1243/0954407011528329 2001 215: 747Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering

    D J Oude Nijeweme, J. B. W. Kok, C. R. Stone and L WyszynskiUnsteady in-cylinder heat transfer in a spark ignition engine: Experiments and modelling

    Published by:

    http://www.sagepublications.com

    On behalf of:

    Institution of Mechanical Engineers

    can be found at:EngineeringProceedings of the Institution of Mechanical Engineers, Part D: Journal of AutomobileAdditional services and information for

    http://pid.sagepub.com/cgi/alertsEmail Alerts:

    http://pid.sagepub.com/subscriptionsSubscriptions:

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    What is This?

    - Jun 1, 2001Version of Record >>

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  • 747

    Unsteady in-cylinder heat transfer in a spark ignitionengine: experiments and modelling

    D J Oude Nijeweme1, J B W Kok1, C R Stone2* and L Wyszynski21Department of Mechanical Engineering, University of Twente, The Netherlands2Department of Engineering Science, University of Oxford, UK

    Abstract: Instantaneous heat ux measurements have shown that, in the expansion stroke, heat canow from the wall into the combustion chamber, even though the bulk gas temperature is higherthan the wall temperature. This unexpected result has been explained by modelling of the unsteadyows and heat conduction within the gas side thermal boundary layer. This modelling has shownthat these unsteady eVects change the phasing of the heat ux, compared with that which would bepredicted by a simple convective correlation based on the bulk gas properties. Twelve fast responsethermocouples have been installed throughout the combustion chamber of a pent roof, four-valve,single-cylinder spark ignition engine. Instantaneous surface temperatures and the adjacent steadyreference temperatures were measured, and the surface heat uxes were calculated for motoring andring at diVerent speeds, throttle settings and ignition timings. To make comparisons with thesemeasurements, the combustion system was modelled with computational uid dynamics (CFD). Thiswas found to give very poor agreement with the experimental measurements, so this led to a reviewof the assumptions used in boundary layer modelling. The discrepancies were attributed to assump-tions in the law of the wall and Reynolds analogy, so instead the energy equation was solved withinthe boundary layer. The one-dimensional energy conservation equation has been linearized and nor-malized and solved in the gas side boundary layer for a motored case. The results have been usedfor a parametric study, and the individual terms of the energy equation are evaluated for theircontribution to the surface heat ux. It was clearly shown that the cylinder pressure changes causea phase shift of the heat ux forward in time.

    Keywords: heat ux, spark ignition engines, computational uid dynamics (CFD)

    NOTATION Pr Prandtl numberq heat ow per unit areaR specic gas constantA

    n, B

    nFourier series coeYcients

    t timec heat capacityT

    M semi-amplitude of temperature variation,h heat transfer coeYcientequations (1) and (2)k thermal conductivity, equations (3), (6),

    T0 mean temperature, equations (1) and (2)(15) to (17), (19), (21), (22)u tangential uid velocityk turbulence kinetic energy, equations (9),v normal velocity component(10), (12)x coordinate into surfacel depth of reference temperaturey coordinate in the gas away from the wallmeasurementz Lagrangian coordinaten harmonic number

    p pressure thermal diVusivityP variable in equation (11) ratio of heat capacities viscosity

    The MS was received on 27 September 2000 and was accepted after r densityrevision for publication on 29 January 2001. time* Corresponding author: Department of Engineering Science, Universityof Oxford, Parks Road, Oxford OX1 3PJ, UK. w wall shear stress

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  • 748 D J OUDE NIJEWEME, J B W KOK, C R STONE AND L WYSZYNSKI

    Subscripts engine, with a tumbling air motion. It has a bore of80 mm, a stroke of 89 mm and a compression ratio of

    i spatial step 10:1. Full details of the instrumentation on the enginej temporal step have already been published [2 ], so comment here willl laminar be restricted to some of the less usual features.m mean The cylinder barrel was tted with a piezo-resistivep constant pressure pressure transducer, so that when the piston was closeref reference to bottom dead centre (BDC) the transducer recordedt turbulent the cylinder pressure, thereby xing the pressure datumv constant volume for the piezoelectric pressure transducers in the cylinderw wall head. When the piston was about 20 crank angle (CA)? bulk gas or further from BDC the barrel transducer recorded

    the atmospheric pressure, thus enabling the absolutepressure datum to be xed. The Kistler 4045A10 piezo-1 INTRODUCTIONresistive transducer was in a water-cooled mount (7505)and was calibrated with a dead weight tester to give

    Heat transfer aVects engine performance, eYciency and1 V/bar. Two piezo-electric pressure transducers were

    emissions. For a given mass of fuel within the cylinder,mounted in the cylinder head, a Kistler 701a in a water-

    higher heat transfer to the combustion chamber wallscooled mount and an AVL QC32D water-cooled trans-

    will lower the average combustion gas temperature andducer. Both transducers were dead weight calibrated

    pressure and therefore reduce the work per cycle trans-with their Kistler 5007 charge ampliers, and dynamic

    ferred to the piston. It is generally accepted that abouttesting in the engine showed no discernible diVerence

    30 per cent of the energy initially in the combustionbetween their measurements.

    chamber is transferred to the cooling system, and aboutAir owrate is notoriously diYcult to measure in a

    half of this is due to in-cylinder heat transfer. On thesingle-cylinder engine, because of the unsteady nature of

    other hand, cooling is necessary because during combus-the ow. For this reason a positive displacement air

    tion the gas temperatures can reach 2500 K or so. Theowmeter has been used. The engine operating points

    wall temperatures should not exceed about 300 C forwere dened in terms of the air owrate; the frictional

    cast iron cylinder heads and about 200 C for aluminiumlevels were high and not entirely repeatable, so this pre-

    heads. The lubricated walls must also be kept belowcluded the use of the brake torque for dening the engine

    about 200 C to prevent the oil lm from oxidizing.operating point. The manifold absolute pressure was

    These temperature diVerences between the bulk gas andused as a check on the engine operating points.

    the walls lead to heat uxes that can reach 10 MW/m2A fuel injection system was used for liquid fuels (at

    during combustion. Because of these high heat ux rates2 bar gauge) and methane (at 6 bar gauge) using a high

    thermal stresses occur which can cause cracks in the cyl-ow rate solenoid operated injector. The ratio of airfuel

    inder head. Cooling of the spark plug and the exhaustto stoichiometric airfuel ratio, , was monitored by a

    valves is especially important because overheating ofcalibrated analyser. Over the range of airfuel ratios

    these can cause pre-ignition.tested, the airfuel ratio was known to an accuracy of

    A very important aspect of heat transfer is the strongno worse than 1.5 per cent. The ignition timing was

    inuence it has on exhaust emissions. The formation ratecontrolled digitally, and its performance veried by an

    of nitric oxide (NO) has an exponential dependence onignition strobe and ywheel timing marks.

    temperature, so a reduction in the peak combustion tem-To be able to determine the surface heat ux accu-

    perature of 2550 K can halve the NOxemissions. Wall

    rately, a fast response surface temperature transducer istemperatures are important for emissions as well.

    needed to measure the wall temperature. As the FourierAccording to Myers and Alkidas [1 ] NO

    xemissions

    equation for the surface heat ux indicates, errors canincrease signicantly with increasing surface tempera-

    be caused by an inadequate response time and by thetures. The hydrocarbon emissions, on the other hand,

    conduction properties of the probe. Also, the fastwere found to decrease considerably at a given airfuel

    response probe should not disturb the gas ow in theratio when the coolant temperature was increased from

    cylinder or the heat ow in the wall. Gatowski et al. [3 ]298 to 373 K.

    investigated four diVerent types of fast response surfacetemperature probes and concluded that eroding-typesurface thermocouples had essentially an instantaneous2 EXPERIMENTALMEASUREMENTSresponse and were durable. Figure 1 shows the construc-tion of the erodable duplex thermocouples used here.2.1 Experimental equipment

    The erodable thermocouple uses alumel and chromelribbon elements 25 m thick. These ribbon elements areThe engine was a single-cylinder version of the Rover

    K16, pent roof combustion chamber spark ignition embedded in the probe (parallel to its axis) and separ-

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  • 749UNSTEADY IN-CYLINDER HEAT TRANSFER IN A SPARK IGNITION ENGINE

    Fig. 1 Construction of the duplex fast response surface thermocouple

    ated by thin mica sheets. The end of the thermocouple 0.76 per cent of its surface amplitude at the location ofthe reference thermocouple. Twelve of these fastis abraded so that a tiny junction is formed by plasticresponse duplex thermocouples were installed arounddeformation of the ribbon elements. Any erosion of thethe combustion chamber: four in the piston, six in thesurface by the environment will form a new junction. Incylinder head and two in the liner.order to establish the heat ux through the element a

    The thermocouples provide only a small voltage ofsecond temperature measurement is needed. This refer-about 40 V/K each, and the surface temperature uc-ence thermocouple is embedded in the probe at a knowntuations are only about 1 K when motoring, or 10 Kdistance from the wall (4.76 mm) where the temperaturewhen ring. Great care is thus needed in the ampli-uctuations have decayed. To prove that the temperaturecation and calibration of the signals. The output fromat that depth is constant, a worst-case scenario for heatthe reference thermocouple was taken to a digital displaypenetration was considered. Eckert and Drake [4 ] pre-(accuracy 1 K), but the reference thermocouple was alsosent the equations for heat transfer in a semi-inniteconnected to the surface thermocouple to give an outputsolid with periodic surface temperature variations:corresponding to the temperature diVerence. This way,only the temperature diVerence was amplied, therebyT0

    =T0M cos2n0

    (1)reducing errors compared with amplifying the signalsindependently, and eliminating the need for cold junc-where n/0 is the period. tion compensation. The signals were taken by twistedEckert and Drakes solution isscreened cables to precision instrumentation ampliers.

    Unfortunately, because of the nature of a thermo-T=T0M expAS n0 xB cosA2n0 S n0 xB couple junction, even thermocouples made from ident-ical materials do not have the same output voltage(2)

    response. A potential is built up at the interface betweenwhere is the thermal diVusivity of the probe material two dissimilar metals, owing to the diVerence in theirand x is the distance into the probe. In this case with work functions. The lower work function metal losesaluminium, has a typical value of 7.496105 m2/s. electrons to the higher, until a charged layer has builtThe temperature variation is of a shorter period than up a potential to prevent further transfer of electrons.the engine cycle, with many higher harmonics also pre- The work functions depend on the band structure of thesent. If the fundamental period is assumed to be of equal metals, which in turn depends on their composition.duration to one revolution, then the worst case is when When a thermocouple junction is formed there will bethe cosine term becomes 1, and the engine is operating varying amounts of interpenetration of the two materialsat its lowest speed. For a speed of 750 r/min the funda- (and possible contamination), so this aVects the band

    structure and the temperaturevoltage response of themental temperature uctuation would have decayed to

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  • 750 D J OUDE NIJEWEME, J B W KOK, C R STONE AND L WYSZYNSKI

    thermocouple. In most applications a temperature where Tref is the steady state temperature at the referencepoint at distance l from the surface (x=0). So theresponse diVerence between thermocouples of 0.1 K

    would be negligible, but, when the temperature diVer- solution of equation (4) isence uctuations can be as low as 1 K, then individualcalibration is needed. Fortunately, what matters is the T(x, t) =Tm(Tm

    Tref)x

    l+ ~

    N

    n=1expAxSn2BdiVerence in the outputs of the two thermocouples in a

    duplex probe, and not their absolute valuesthis simpli-es their calibration. Prior to installation in the engine, 6CAn cosAntxSn2Bthe duplex probes were mounted in a copper block andcalibrated with their corresponding leads and ampliersby heating them in the range 50200 C in steps of about +B

    nsinAntxSn2BD (5)25 K. The temperature diVerence signal (typically of

    order 0.5 K) was then curve tted against the calibrationThis equation, diVerentiated with respect to x and substi-temperature, for subsequent correction of the in-cylindertuted in the one-dimensional version of the Fourier equa-diVerential temperature measurements.tion, gives for the heat ux at the surface (where x=0 )The 12 diVerential temperature signals, along with

    encoder ag and pressure signals, were logged everydegree CA by a 16-channel data acquisition card with qs

    =qm+k ~

    N

    n=1Sn2 [(An+Bn) cos(nt )12-bit resolution. A nite diVerence method was applied

    to calculate the temperature distribution within the walls +(BnA

    n) sin(nt)] (6)

    by solving the Fourier equation for unsteady heatwhereconduction and from that deducing the heat transfer.

    qm=k

    TmTrefl2.2 Heat ux calculations and measurements

    with qm the steady state heat ux. So, if the referenceTo solve the unsteady heat conduction equation, it istemperature and the temperature variation at the surfacenecessary to treat the problem as one dimensional. Thisare measured, a Fourier transform gives the temperatureis acceptable for the following reasons: the temperatureeld T=T(x, t), and subsequently the surface heat ux.gradient normal to the wall is large compared with the

    In contrast the approach used here has been to adopttemperature gradients along the wall; temperaturea nite diVerence solution that has been solved explicitly,diVerences along the wall decay rapidly; the silicone seal-since this is simpler and more intuitive for programming.ant and/or cyano-acrylate adhesive used to secure theIn nite diVerence form equation (3) becomesduplex probe and the stainless steel tube around the

    probe tend to insulate the probe body; and stainless steel 1t

    [T(t+t )T(t )]has a thermal conductivity at least 10 times lower thanthe aluminium alloy used.

    The Fourier equation yields for the one-dimensional =

    x2[T(x+x)2T(x)+T(xx)] (7)

    case

    To help to visualize an iteration scheme, a suitable grid isqTqt

    =1rc

    qqx Ak qTqxB (3) shown in Fig. 2 to represent the physical situa-

    tion. The temperatures at the unknown grid pointsThe most popular method to solve equation (3) is to use [the ( j+1)th time step] are calculated from knowna Fourier transform, as performed by Alkidas [5 ]. Asinusoidal variation of heat ux with time into a semi-innite solid produces the same frequency variation insurface temperature, displaced in phase by 90. So thesurface temperature can be expressed as a Fourier series:

    Ts(t)=Tm

    + ~N

    n=1[A

    ncos(nt)+B

    nsin(nt)] (4)

    where Tm is the time-averaged value of the surface tem-perature Ts(t), An and Bn are Fourier coeYcients, n is aharmonic number and is the angular frequency. Theboundary conditions are

    T(0, t)=Ts(t )

    Fig. 2 Finite diVerence solution schemeT(l, t )=Tref (constant)

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  • 751UNSTEADY IN-CYLINDER HEAT TRANSFER IN A SPARK IGNITION ENGINE

    temperatures at other grid points (the jth time step). ignored, soot deposits on the thermocouples are avoided,Rearranging equation (7) gives gas pressure and temperature are well dened and are

    almost symmetrical with respect to top dead centre(TDC) and the signals (although small ) show little cycle-T

    i,j+ 1=T

    i,j+

    tx2

    (Ti+ 1,j

    2Ti,j

    +Ti1,j

    ) (8)by-cycle variation. In Fig. 3 the surface heat ux resultsfor various locations in the cylinder can be seen forwhere for stability the Fourier number t/x2 has tomotoring operation at 1000 r/min.be in the range from 0 to 0.5. As the sample rate is xed

    Figure 3 shows that the peak heat ux occurs close toby the encoder and engine speed, this imposes limitationsTDC. Lawton [6 ] measured the peak heat ux at abouton the spatial steps in the grid. The surface temperature8 before TDC (BTDC), and he also showed the reversaland reference temperature provide boundary conditions,of the heat ux during the expansion stroke. The bulkbut it is still necessary to make an initial guess for thegas temperature during the period of negative heat uxtemperature distribution that is subsequently corrected.is higher than the wall temperature, and the reversal ofEach cycle of data has to be taken in turn, and for thethe heat ux can be explained by compression work inrst cycle analysed a linear temperature variation wasthe boundary layer as a result of the pressure change.assumed in the solid at time step 0. In general a diVerentThese unsteady eVects will be shown to cause a phasetemperature prole will be predicted 720 later, and thisadvance in the heat ux. This phase shift will thenprole is then used as the temperature distribution atexplain the diVerence in timing of the peak heat uxtime step 0. The solution is then repeated for the samemeasured by Lawton [6 ], who used a diesel engine, com-cycle, and the iterations within a cycle of data continuepared with this work. Diesel engines have a much higheruntil the changes in the temperature distribution arepressure variation than spark ignition engines and there-negligible.fore the pressure work term eVects are more important.The numerical procedure was checked by using a

    Figure 4 shows the eVect engine speed has on the heatcosinusoidal surface temperature variation and compar-ux for thermocouple 1, which is at the apex of the penting the numerical results with the exact solution derivedroof and 31 mm away from the spark plug. The peakfrom the analytical solution, equation (2). For the worstheat ux rises as expected with increasing engine speed,case (assuming an engine speed of only 120 r/min) theowing to the higher gas velocities and turbulence.error in the instantaneous surface heat ux was alwaysHowever, during the expansion stroke the negative heatless than 1 per cent.ux also becomes more important, and this is a resultWhen combustion is not present, and the engine isof the unsteady processes in the boundary layer.motored, the Reynolds and Prandtl numbers are largelyAccording to Gilaber and Pinchon [7 ] the heat uxunchanged from ring operation, and thus the Nusseltvaries almost linearly with the density and is heavilynumbers for motoring and ring will be nearly the same,inuenced by the volumetric eYciency and thus by theso motoring is a useful operation when investigating heatthrottle position. This is shown in Fig. 5.transfer. The only disadvantage of a motored engine is

    When the engine is red, the signal levels rise bythat the surface temperature variation is smaller, andabout an order of magnitude, and the signalnoisehence there is likely to be a larger relative error in the

    measurements. On the other hand, radiation can be ratio increases dramatically. Because of combustion, the

    Fig. 3 Surface heat ux dependence on location in the cylinder when motoring (WOT, wide-open throttle)

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  • 752 D J OUDE NIJEWEME, J B W KOK, C R STONE AND L WYSZYNSKI

    Fig. 4 Surface heat ux dependence on speed when motoring

    Fig. 5 Surface heat ux dependence on the throttle position for thermocouple 1, in the apex of the pentroof, 31 mm away from the spark plug

    timing, magnitude and form of the surface heat ux will exhaust valves on the pent roof but close to the squishregion; the gas velocities are likely to be high here, owingmainly be determined by the ame front. Bigger cycle-

    by-cycle variations are therefore expected, as a result of to the initial tumble motion. Because of the higher gasvelocities, there will be a thinner boundary layer in thislocally irregular ame shapes. Figure 6 (compared with

    Fig. 3) shows that the location of the thermocouples in area, resulting in a higher surface heat ux, as also foundby Alkidas [8 ].the cylinder becomes more signicant when the engine

    is red. The diVerence between thermocouples 2 and 9 The occurrence of the negative heat ux in the expan-sion stroke of Fig. 6 is signicant, and it is believed thatis especially striking. Both thermocouples are mounted

    in the cylinder liner 15 mm below the top of the cylinder this is the rst time this has been reported in a ring engine.This phenomenon has already been observed duringbut diametrically opposite. This can be explained by

    local diVerences in turbulence, gas velocity and gas tem- motoring and can also be explained by the unsteadyeVects. Because of the higher pressure variations in theperature levels. Thermocouple 12 is situated in the apex

    of the pent roof 31 mm away from the spark plug, like red case, the unsteady eVects are expected to becomemore important. With the much higher burnt gas tempera-thermocouple 1. Thermocouple 3 is situated between the

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  • 753UNSTEADY IN-CYLINDER HEAT TRANSFER IN A SPARK IGNITION ENGINE

    Fig. 6 Surface heat ux dependence on location when ring

    tures, and the strong dependence of the heat ux on the rise of the surface heat ux after the ame front arrivalat the location in the cylinder concerned. Similar obser-ignition timing (the earlier the ignition timing, the earlier

    the peak heat ux and therefore a quicker decrease of the vations are described by Alkidas [5 ]. Figure 8 shows thatthe magnitude of the heat ux increases when theheat ux in the expansion stroke and therefore a greater

    chance of negative heat ux) and the possible later occur- ignition timing is advanced and that its maximum occursearlier. The magnitude of the heat ux increases bothrence of the heat ux, the negative heat ux is typically

    observed only at some locations in the cylinder. because the combustion temperatures will be higher andbecause of the higher cylinder pressure and consequentlyFigure 7 shows the heat ux measured at two diVerent

    locations in the cylinder and their distances to the spark higher gas density. These eVects have also been shownby Gilaber and Pinchon [7 ].plug. As can be seen in this gure, the ame front has

    a signicant eVect on the heat ux. The gure clearly Apart from the heat ux reversal towards the end ofexpansion, these results are in broad agreement with pre-shows the ignition at 30 BTDC, followed by an initial

    rise in heat ux, due to compression, followed by a steep viously published work. This phenomenon will be dis-

    Fig. 7 Surface heat ux dependence on location in the cylinder when ring

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  • 754 D J OUDE NIJEWEME, J B W KOK, C R STONE AND L WYSZYNSKI

    Fig. 8 Surface heat ux dependence on ignition timing for thermocouple 12, in the apex of the pent roof,31 mm away from the spark plug

    cussed in Section 4, after a discussion of CFD-based sional unsteady-ow code PROMO. PROMO providedthe instantaneous values of mass ow, temperature andpredictions of heat transfer.pressure from which the instantaneous volume owratewas calculated. Using the area at the inlet portmanifoldboundary enabled velocity to be estimated by assuming3 COMPUTATIONAL FLUID DYNAMICSplug ow, as an input condition to the three-dimensionalMODELLINGCFD code. Figure 9 illustrates the mass ow into theinlet port at two operating conditions. The remaining3.1 Results with a commercial computational uidinitial boundary conditions to be specied at the inletdynamics codeport are the fuel mass fraction and the inlet turbulence

    In Section 2 the instantaneous wall heat ux in a single- characteristics. The latter are determined in the k tur-cylinder version of a Rover K16 engine was measured. bulence model, by a turbulence length scale and the tur-For engine design variation and optimization it is interes- bulence intensity as a fraction of the inlet velocity. Theseting if the heat ux can be predicted with the use of a two parameters were estimated here to be 0.50 mm andCFD code. This can save time and costs in engine test 10 per cent respectively. Kang et al. [9 ] claim that theseprogrammes. In order to investigate the accuracy of the initial conditions have little eVect on the heat ux. Thisheat ux predicted the Rover K16 engine was simulated statement can only be correct of course if the employedwith a CFD code set up specically for a reciprocating k turbulence model is suYciently accurate to predictengine. Engine geometry les provided by Rover were the heat ux. Satisfactory comparisons of the ows wereused to dene the computational domain, determined by made with data for the same engine in Jones and Jundaythe cylinder, piston, engine head, inlet and exhaust ports [10 ] [in which there are CFD predictions and laserand valves. The CFD package was selected for its ability Doppler anemometry and hot wire anemometryto adapt the mesh according to piston and valve motion. (HWA) data].In order to avoid large mesh distortions, a new mesh is Figure 10 shows a comparison between the experimen-automatically generated during the motion of the valves tal data and the instantaneous heat ux averaged overand piston when a predened mesh shape limit is the cylinder head predicted by the CFD code for aexceeded. For the simulation of 490 crank shaft rotation motored case. The data concern motored conditions atbetween inlet valve opening and exhaust valve opening 2000 r/min. It can be observed that CFD code underpre-the computational domain was remeshed 160 times. The dicts the positive heat ux at TDC by a factor of aboutmesh had about 220000 cells at BDC. 10. The smaller (but interesting) negative heat ux

    At a given engine geometry, the intake ow determines between TDC and exhaust valve open (EVO) is missedthe ow eld in the engine during the compression and completely by the CFD. Predictions (not shown here)expansion strokes [8 ]. For that reason the inlet port was from the Woschni correlation [11], which is known toincluded in the computational domain and the ow at underpredict the heat transfer in this type of combustion

    system, are similar to the CFD results. Similar resultsentry to that port was calculated with the one-dimen-

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  • 755UNSTEADY IN-CYLINDER HEAT TRANSFER IN A SPARK IGNITION ENGINE

    Fig. 9 Inlet mass ow (0 is TDC during combustion)

    Fig. 10 Comparison between the measured and CFD-calculated surface heat ux for the cylinder head

    with CFD are also shown by Han and Reitz [12] and in regions where the ow is fully turbulent. In the near-wall region, as the distinction between the large andDiana et al. [13]. The reason for the CFD underpredic-small scales of turbulent motion begins to diminish, thetion is the simplied representation of the boundaryabove assumption breaks down. The simplest and stilllayer processes in the models used in proprietary CFDthe most popular approach to near-wall modelling hascodes. It is expected that the underprediction will be evenbeen to employ the logarithmic law of the wall, alsolarger in the red case owing to uncertainties in the CFDknown as the wall function approach [14]. CFD pack-combustion modelling. In the next section these simpli-ages use the wall function method to interpolate betweened wall models used in the CFD code are analysedthe fully turbulent region and the wall.

    The hydrodynamic boundary layer is split into a lami-nar viscous sublayer and a buVer layer to adapt the lami-3.2 Boundary layer modelling in computational uidnar part of the boundary layer to the turbulent core.dynamicsThis way of representing the hydrodynamic boundary

    In the turbulence model the direct eVects of molecular layer, together with an extensive experimental investi-viscosity on the energy containing ( large) scales of the gation by Nikuradse, led to the law of the wall.uctuating motion and those of the mean strain eld on Although this law was set up just for steady, incom-the corresponding dissipative (small ) scales are assumed pressible ow through smooth pipes at moderate

    Reynolds numbers, it seems to hold for a wider rangeto be negligible. These assumptions are, in general, valid

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  • 756 D J OUDE NIJEWEME, J B W KOK, C R STONE AND L WYSZYNSKI

    of applications and is often used outside pipes as well. ary layer ow, there are also assumptions in the determi-nation of the heat ux. As the equations for heat transferThe use of wall functions removes the need to employ a

    ne mesh to resolve explicitly the ow prole in the and momentum transfer in the boundary layer are ana-logous, and their boundary and initial conditions areboundary layer, and it is therefore computationally

    eYcient. However, the modelling of the boundary layer similar, the solutions must be analogous. This is onlystrictly valid under some conditions, of which no press-using wall functions is based on a set of assumptions

    about the ow, and the accuracy of the solution obtained ure gradient is the most important one. In the viscoussublayer, the uid ow is laminar and heat transfer isis therefore dependent on how well these assumptions

    are met in any particular case. The main assumptions mainly dominated by heat conduction. In the turbulentcore the turbulence is the driving force behind theimplicit in the wall-function treatment are as follows:heat transfer. The buVer layer provides a transition,

    (a) steady ow;by accommodating both of these mechanisms. The

    (b) incompressible (i.e. no change in density);Reynolds analogy formulation is the simplest way to link

    (c) the ow is essentially one dimensional, such thatthe momentumheat transfer and is used to obtain

    gradients of velocity and scalar quantities are onlythe temperature variation in the boundary layer. The

    normal to the wall;Reynolds analogy introduces assumptions that will

    (d) the eVects of pressure gradients are small;impose some more conditions on the boundary layer,

    (e) the turbulence is in local equilibrium;including:

    (f ) the turbulence length scale varies linearly with(a) isothermal boundary layer ow;distance from the wall.(b) no chemical heat release in the boundary layer;

    In addition to these restrictions, it has been found by (c) no pressure work in the boundary layer;Gibson [15] that even slightly curved surfaces cause (d) no temperature gradient along the wall;inaccurate heat ux predictions. (e) the turbulent Prandtl number Prt is assumed to beThe wall function formulation is constant.

    Of particular signicance is the no pressure work in theboundary layer assumption, since it is this term thatu+ = Gy+ , y+ y+v1k ln(Ey+), y+ >y+v (9) leads to the reversal of the heat ux. In the CFD code,the temperature variation equation is modied to take

    where account of the Prandtl number and the so-calledsublayer resistance factor, P:u+ =u/u

    u=tangential uid velocity T+ =Prt(u+ +P) (11)

    u =(w/r)1/2

    wherew=wall shear stress

    y+ =rC1/4 k1/2y/ T+ =cpr(TTw )u

    /qy+v

    =11.6, the value of y+ at the edge of the viscous cp=isobaric specic heat capacity of the uid

    sublayer T=uid temperaturey=distance of the cell centre from the wall Tw

    =wall temperaturer=gas density q=heat ux= laminar viscosity of the uid Prt

    =turbulent Prandtl number, whose value isk=turbulence kinetic energy taken as 0.9

    P=9.0(Prl/Pr

    t1)(Prl

    /Prt)1/4and k, E and C are empirical coeYcients in the k Pr

    l= laminar Prandtl number

    model with values as follows:The heat ux can then be written as

    k=0.419

    E=9.793 q=cpy

    + (TTw)Prt [(1

    /k) ln(Ey+)+P]y(12)

    C=0.09 This expression for heat ux appears as a source termFor local equilibrium, where k=(w

    /r)C1/2 , the wall in the enthalpy equation for near-wall cells.shear stress can therefore be expressed as A local heat transfer coeYcient, h, is calculated and

    written to the post-processing le according tow=

    rC1/4 k1/2kuln(Ey+)

    (10)h=

    q

    TTw(13)

    This expression for shear stress appears as a source termin the momentum equations for near-wall cells. It is stressed that this is a local heat transfer coeYcient,

    i.e. it is based on a local uid temperature for each sur-In addition to assumptions for modelling the bound-

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  • 757UNSTEADY IN-CYLINDER HEAT TRANSFER IN A SPARK IGNITION ENGINE

    face patch. For a given heat ux, the uid temperature In prior work, Diana et al. [13] ignored the work term,in a small cell will be closer to the wall temperature than while Han and Reitz [12] and Angelberger et al.[17 ] alsothat in a large cell. As explained earlier in this section, ignored the convective term (which accounts for owthe wall function treatment is not exact and is based on normal to the wall as a result of density changes). It willa number of assumptions about the boundary layer. The be seen in the analysis to be presented here that bothformulae above are generally held to be applicable in these terms are important.the approximate range 30y+ 300, in which the cal- The heat ux term can be determined by using theculated values may be expected to be independent of y+ . concept of a turbulent conductivity (kt) to supplementHowever, in practice this is not necessarily the case, and the laminar conductivity (kl)even within the above range of y+ variations of surfacequantities may be observed. q=(kl

    +kt)qTqy

    (15)In the CFD mesh, the cell size (and hence y+) near

    the walls is subject to variations. This is a consequence Thus the energy equation (14) becomesof the mesh structure, which is in turn dictated by theautomatic mesh generation method used in the CFD rcp

    qTqt

    +rvcpqTqy

    =qqy C(k+kt) qTqyD+ dpdt (16)package. The result is that surface quantities such as

    shear stress and heat ux may display stripes or a patchi- The solution of equation (16) is facilitated by conversionness, which reects the underlying variation in near-wall to Lagrangian coordinates and normalization of the tem-cell size. This situation is compounded for heat transfer peratures. The one-dimensional energy equation for acoeYcients which, as described above, are based on local pure ideal gas can be expressed in Lagrangian coordi-cell uid temperatures; therefore the stripes in heat nates astransfer coeYcient are more pronounced than those forshear stress or heat ux.

    rcpqTqt

    =r

    r0

    qqz C rr0 k A1+ klkB qTqzD+ dpdt (17)The law of the wall and the Reynolds analogy give ina steady isobaric ow a prediction of heat transfer with

    The relation between the Lagrangian, z, and Eulerian,modest accuracy. When the pressure is changing rapidly,y, coordinates isas in a piston engine, heat transfer processes become

    important but are not taken into account by the law ofr0 dz

    =r dy or z= P y0

    r

    r0dy (18)wall and Reynolds analogy. This is clearly illustrated by

    the measurements presented in Section 2. The measuredwhich satises the continuity equation. The subscript, 0,reversal of the heat ux is evidence of the invalidationmeans the evaluation of the property at initial conditionsof the Reynolds analogy. This means that the heat trans-such as IVC. The Lagrangian coordinate is now attachedfer modelling requires more processes to be taken intoto each uid particle, which is why the second term onaccount, with greater modelling resolution in the bound-

    ary layer. Several approaches can be followed. A three- the left-hand side is made redundant.dimensional CFD method along the lines of Section 3 Since for a semi-perfect gas r=P/RT, R=cp

    cv and

    with a so-called k turbulence model can be used [16 ]. =cp/c

    v , equation (17) becomesThis is at present being implemented in a CFD code atthe University of Twente. A diVerent approach is pre-

    qTqt

    =r

    r0cp

    qqz C krk0r0 k A1+ ktkB qTqzD+ 1 Tp dpdtsented in Section 4 of this paper. This method uses a

    one-dimensional energy equation for the boundary layer. (19)This equation retains all the relevant terms and is solved

    Far away from the wall, the gas is assumed to be com-in the boundary layer by a numerical method.pressed isentropically

    4 ENERGY EQUATION MODELLING IN THE pp0=AT2T

    0B/(1) (20)BOUNDARY LAYER

    Assuming that the gas conductivity is proportional toLawton [6 ] modelled the energy equation in the thermal absolute temperature, following Isshiki and Nishiwakiboundary layer of a motored diesel engine, and des- [18 ], givespite a number of assumptions provided evidence forthe reversal of the heat ux. Using a one-dimensional kr

    k0r0=

    p

    p0(21)

    approach (since properties can be assumed to vary onlyin a direction normal to the wall ), requires solution of The relation between the thermal conductivity, k, and

    the gas viscosity, , can be described byrc

    pqTqt

    +rvcpqTqy

    convection

    =qq

    yqy

    heat flux

    +dp

    dt

    work

    (14)ktk

    =Pr

    Prt

    t

    (22)

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  • 758 D J OUDE NIJEWEME, J B W KOK, C R STONE AND L WYSZYNSKI

    Finally, on following Isshiki and Nishiwaki [18], nor- greatly improving the spatial diVerences in heat ux.Temperature measurements close to the wall have beenmalizing in terms of T(?, t) withobtained by Lucht et al. [21], using a CARS (coherentanti-Stokes Raman spectroscopy) temperature measure-U(z, t )=

    T(z, t)T(?, t)

    (23)ment system. Although the engine in that study was rununder diVerent conditions from those for which theequation (19) becomestemperature eld has been calculated, a comparison(Fig. 11) none the less shows good general agreementqU

    qt=

    0p

    p0

    q2Uqz2

    laminar

    +0p

    p0

    qqz APrPrt t qUqzBturbulent

    (24)for the shape of the temperature prole at TDC in theboundary layer. It is unfortunate that the CARS tem-perature measurements were only in the region of TDC

    where 0=k0

    /r0cp. The boundary conditions and initial and did not continue far enough into the expansioncondition for equation (24) are stroke to show a reversal in the temperature gradient

    adjacent to the wall. As well as providing evidence ofU(0, t)=

    T(0, t)T(?, t)

    = f (t ) the negative heat ux, the solution of equation (14) canillustrate the relative contributions of the convective and

    U(?, t)=1 work terms, and this is shown in Fig. 12.Figure 12 clearly shows the eVects of the individual

    terms of the energy equation. The convection term is theU(z, 0 )=T(z, 0)T(?, 0)

    = f (0)g(z)most important for the magnitude of the heat transfer.

    (25) The pressure work term is very important for the phasingof the heat transfer. Even with a low pressure variationwhere g(z) is a function of z, corresponding to the initialof about 5 bar, as used here, the heat ux is advancedboundary layer existing at the beginning of the com-by 10 CA in the cycle, compared with the heat uxpression process. Equation (24) has been divided into awithout the work term.laminar and a turbulent contribution to the heat trans-

    In conclusion, it can be stated that, if the surface heatfer. The laminar part is equivalent to the conductiontransfer is modelled, both the work term and the convec-equation that has previously been solved for thetive term need to be taken into account. This is becauseunsteady heat ow in the solid, for obtaining the surfacethe convective term largely determines the magnitude ofheat ux from the measured wall temperature.the heat ux, and the work term is responsible for theAs a reminder, the following assumptions have beenphase advance of the heat ux. This phase shift enhancesmade:the peak heat ux and is also partly responsible for the

    1. Pressure is a function only of time: p=p(t). negative heat ux. To be able to model the boundary2. Radiative heat transfer and heat release in the bound-

    layer, for both modied wall functions and the directary layer are neglected.

    solution of the one-dimensional energy equation, more3. The temperature and velocity gradients in the direc-

    information is needed about the turbulent Prandtltion parallel to the wall are neglected. number and the turbulent gas viscosity in the boundary

    4. Gas transport properties are proportional to the layer, for the compressible ow eld, of an internal com-absolute gas temperature. bustion engine. If these turbulent boundary layer param-

    5. The gas is semi-perfect.eters are modelled more accurately, the energy equationcan then predict the surface heat ux more accurately.To be able to solve this equation, the turbulent thermal

    conductivity, kt , or the turbulent Prandtl number, Prt , This is especially true if modelling the energy equationin the boundary layer were to be implemented into aand the turbulent viscosity, t , need to be known across

    the boundary layer. Usually empirical expressions are CFD code, using the main ow features, such as gastemperature, turbulence intensity, gas density and press-used, obtained from measurement in incompressible

    turbulent ows, like those of Mellor [19 ] for t/ and ure data, to calculate the local instantaneous surface

    heat ux.Kays [20 ] for Pr/Prt. Because the compressibility of theboundary layer is recognized as an important parameterwhen determining the surface heat ux, this seems

    5 CONCLUSIONScontradictory.Thus a diVerent method has been adopted here. The

    turbulent thermal conductivity, kt, is tuned until equa- Instantaneous heat ux measurements from fast

    response thermocouples have shown that in the expan-tion (24) gives a temperature eld close to the wall, suchthat the heat ux matches the measured surface heat sion stroke, heat can ow from the wall into the combus-

    tion chamber, even though the bulk gas temperature isux for that location in the cylinder. Turbulence inten-sities can be calculated with CFD and so the thermal higher than the wall temperature. It is believed that this

    is the rst time such results have been reported from aconductivity expression can be tuned by location,

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  • 759UNSTEADY IN-CYLINDER HEAT TRANSFER IN A SPARK IGNITION ENGINE

    Fig. 11 Temperature prole comparison with CARS measurements by Lucht et al. [21] at TDC

    Fig. 12 The relative importance of the individual terms of the energy equation

    ring engine. This unexpected result has been explained the other (the reference junction) being 5 mm away. Thetemperature measurements were used as boundary con-by modelling the unsteady ows and heat conduction

    within the gas side thermal boundary layer. This model- ditions for solving the unsteady heat conduction equa-tions; a nite diVerence approach was used in contrastling has shown that these unsteady eVects change the

    phasing of the heat ux, compared with that which to the more usual Fourier analysis. The heat ux probeshave been installed throughout the combustion chamberwould be predicted by a simple convective correlation

    based on the bulk gas properties. In other words, it is of a pent roof, four-valve, single-cylinder spark ignitionengine. The surface heat uxes have been reported here,impossible for the widely used correlations (of the form

    Nu=ReaPrb ) to give the correct phasing when the bulk showing the eVects of location, speed and throttle settingfor both motoring and ring, and the eVect of ignitiongas temperature is being used. It has thus been shown

    that the CFD heat ux calculations need to include the timing when ring.To make comparisons with these measurements, thework term within the boundary layer and the convection

    term if accurate results are to be obtained. combustion system was modelled with CFD. Enginegeometry les were used to dene the combustionThe heat ux probes comprised a pair of thermo-

    couples inside a 5 mm diameter probe in a tapered hous- chamber, the inlet port and the piston and valve motion.Because the intake ow is highly important to the owing, one thermocouple being formed at the surface and

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  • 760 D J OUDE NIJEWEME, J B W KOK, C R STONE AND L WYSZYNSKI

    5 Alkidas, A. C. Heat transfer characteristics of a spark-in an IC engine, the inlet port was modelled as well asignition engine. J. Heat Transfer, 1980, 102(2), 189193.the combustion chamber. The ow at entry to the inlet

    6 Lawton, B. EVect of compression and expansion on instan-port was modelled with a one-dimensional unsteady owtaneous heat transfer in reciprocating internal combustionpackage, and the calculated values of mass ow, tem-engines. Proc. Instn Mech. Engrs, Part A, Journal of Powerperature and pressure were then used as inlet boundaryand Energy, 1987, 201(A3).

    conditions to the three-dimensional CFD. The CFD pre- 7 Gilaber, P. and Pinchon, P. Measurements and multidimen-dictions were found to give very poor agreement with sional modelling of gaswall heat transfer in a S.I. engine.the experimental measurements, so this led to a review SAE paper 880516, 1988.of the assumptions used in boundary layer modelling 8 Alkidas, A. C. The eVects of intake-ow congurations onwithin CFD. The discrepancies were attributed to the heat-release and heat-transfer of a single cylinder four-

    valve S.I. engine. SAE paper 910296, 1991.assumptions in the law of the wall and the Reynolds9 Kang, Y. H., Chang, I.-P. and Martin, J. K. A comparisonanalogy, so instead the energy equation was solved for

    of boundary layer treatments for heat transfer in ICthe boundary layer.engines. SAE paper 90052, 1990.The one-dimensional energy conservation equation

    10 Jones, P. and Junday, J. Full cycle computational uidhas been linearized and normalized and solved in the gasdynamics calculations in a motored four valve pent roofside boundary layer for a motored case. As well as heatcombustion chamber and comparison with measurement.

    conduction, the energy equation incorporates work SAE paper 950286, 1995.being done within the boundary layer (as a result of the 11 Woschni, G. A universally applicable equation for thepressure changes) and a convective ow normal to the instantaneous heat transfer coeYcient in the internal com-surface (due to density changes arising from both press- bustion engine. SAE Trans., 1967, 76, 30653083.ure and temperature changes in the boundary layer). The 12 Han, Z. and Reitz, R. D. A temperature wall function for-

    mulation for variable-density turbulent ows with appli-results have been used for a parametric study, in whichcation to engine convective heat transfer modeling. Int. J.the individual terms of the energy equation were evalu-Heat Mass Transfer, 1997, 40, 613625.ated for their contribution to the surface heat ux. It

    13 Diana, S., Giglio, V., Police, G., Bella, G. and Cordiner, S.was clearly shown that the work term causes a phaseHeat transfer evaluation in 3D computations of premixedshift of the heat ux forward in time and that the convec-SI engines. SAE paper 972876, 1997; Diesel and SI enginetive ow term contributes signicantly to the magnitudemodelling, SP-1306, pp. 5770.

    of the heat ux. 14 Patankar, S. V. and Spalding, D. B. A calculation proced-ure for heat, mass and momentum transfer in three-dimensional parabolic ows. Int. J. Heat Mass Transfer,

    ACKNOWLEDGEMENTS 1972, 15.15 Gibson, M. M. EVects of the surface curvature on the law

    of the wall. Near-Wall Turbulence, Zoran Zaric MemorialSupport from the EPSRC, BMW/Rover Group andConference, 1988, pp. 157171 (Hemisphere, New York).Shell Global Solutions is gratefully acknowledged.

    16 Wilcox, D. C. Simulation of transition with a two-equationturbulence model. Am. Inst. Aeronaut. Astronaut. J., 1994,31(8), 14141421.

    REFERENCES 17 Angelberger, C., Poinsot, T. andDelhay, B. Improving near-wall combustion and wall heat transfer modelling in SI

    1 Myers, J. P. and Alkidas, A. C. EVects of combustion engine computations. SAE paper 972881, 1997; Diesel andchamber surface temperature on the exhaust emissions SI engine modelling, SP-1306, pp. 113130.of a single-cylinder spark-ignition engine. SAE paper 18 Isshiki, N. and Nishiwaki, N. Study on laminar heat trans-780642, 1978. fer of inside gas with cyclic pressure change on an inner

    2 Ball, J., Raine, R. and Stone, R. Combustion analysis and wall of a cylinder head. In Proceedings of the Fourthcycle-by-cycle variations in spark ignition engine combus- International Heat Transfer Conference, Versailles, Paris,tion. Part 2: a new parameter for completeness of combus- 1970, paper FC3.5, pp. 110.tion and its use in modelling cycle-by-cycle variations in 19 Mellor, G. L. In Proceedings of Symposium on Fluidicscombustion. Proc. Instn Mech. Engrs, Part D, Journal of Internal Flow, Pennsylvania State University, 1968.Automobile Engineering, 1998, 212(D6), 507524. 20 Kays, W. M. Turbulent Prandtl numberwhere are we?

    3 Gatowski, J. A., Smith, M. K. and Alkidas, A. C. An exper- Trans. ASME, J. Heat Transfer, 1994, 116, 284.imental investigation of surface thermometry and heat ux. 21 Lucht, R. P., Dunn-Rankin, D., Walter, T., Dreier, T. andExpl Thermal Fluid Sci., 1989, 2, 280292. Bopp, S. C. Heat transfer in engines: comparison of CARS

    4 Eckert, E. R. G. andDrake, R. M. Heat and Mass Transfer, thermal boundary layer measurements and heat uxmeasurements. SAE paper 910722, 1991.2nd edition, 1959 (McGraw-Hill, New York).

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