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NUMERICAL STUDY OF UNSTEADY HEAT TRANSFER

AROUND AN ENGINE CYLINDER:

EFFECT OF COMBUSTION HEAT FLUX FREQUENCY FOR

KNOCK DETECTION

P. Lamarche1, F. Daumas-Bataille and J. Bellettre

3

1GEPEA, UMR 6144 CNRS / University of Nantes / Ecole des Mines de Nantes / ENITIAA, DSEE

4 rue Alfred Kastler, B.P. 20722, 44307 Nantes Cedex 3, France

2Laboratoire PROMES, UPR 8521 CNRS / University of Perpignan

Rambla de la thermodynamique Tecnosud, 66100 Perpignan, France

3Laboratoire de Thermocintique, UMR 6607 CNRS / University of Nantes

Rue Christian Pauc, BP 50609, 44306 Nantes Cedex 3, France

tel.: +33 2 40 68 31 33, fax: +33 2 40 68 31 41, e-mail: [email protected]

Abstract

This paper focuses on the improvement of a new and non-intrusive method of knock detection for

spark ignition engine. This method shows that a knocking combustion can be detected by the

analysis of the transient component of the flow temperature acquired in the coolant channel. But,although turbulent promoters are used to enhance the signal level, this remains too small

(about 1 K) to use an industrial temperature probe. The present paper studies the possibility toimprove detection by studying signal level at different frequencies. So, numerical simulations of

unsteady heat transfer through the cylinder and inside the coolant flow are performed to observehow the signal temperature changes when combustion peak heat flux signal frequency increases.

The results show that the frequency changes significantly the signal amplitude. For a combustion

heat flux intensity of 8 MW.m-2

, while at 12.5 Hz the amplitude value works in an 8 K range (peakto peak amplitude), this range at 75 Hz, reaches only 6 mK on a plate wall (without promoter).

Effects with rib are similar and more significant: the variation at 75 Hz is limited to 1 mK while at12.5 Hz variations reach almost 29 K.

Nomenclature

CT cycle time, sg gravity, m.s

-2

H enthalpy (mean value), J.kg-1

h' enthalpy fluctuation, J.kg

-1

k turbulent kinetic energy, m.s- ( = 2'

2

1iuk

)

n harmonic rank

q heat flux, W.m-2

T* variation of temperature, KU velocity (mean value), m.s

-1

u' velocity fluctuation, m.s-1

y+ wall unit (

w

y =* )

5th European Thermal-Sciences Conference, The Netherlands, 2008

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Greek letters

distance from the wallij Kronecker symbol turbulent kinetic energy dissipation rate, m.s

-3

thermal conductivity, W.m-1.K-1

heartbeat, rad.s-1

Subscript

av averagei, j, k i, j and k directionsext external

p closed to the wall (i.e. at the first

cell center)t turbulent

1 Introduction

Knock is due to an unexpected combustion in Spark Ignition (SI) engines. It is a result of

spontaneous ignition of a portion of end charge in the engine chamber, ahead of the propagatingflame. The very rapid heat release implied by this abnormal combustion generates shock waves that

can lead to decrease of the output work, increase in pollutants and the destruction of the enginecomponents. Nowadays, the growth of downsizing (turbocharged systems) and development of

alternative fuels with variable knock-resistance give to engines a higher sensivity to knock. Hence,

a reliable method for the detection of knock in SI engine is of high interest.Brecq et al. (2001, 2003) precise that knock detection is currently based on data generated by

accelerometers or cylinder pressure sensors. Due to its simplicity, accelerometry (vibrationmeasurement) is largely employed in industry. Nevertheless, parasitic noises relative to engine

operation often affect the quality of knock detection in this method. On the other hand, cylinderpressure data provides a direct and reliable way to analyze knock. The major disadvantage is that a

suitable probe has to be provided on the engine cylinder that may reduce the engines life time asexplained by Brecq (2002).

Syrimis (1996) and Enomoto et al. (1994) revealed that knock occurrence is accompanied by animportant increase (up to 4 times higher) of the wall heat transfer inside the combustion chamber.

Thus, an alternative to the current methods could be the detection by analysis of the thermal signalmeasured near the outer side of the cylinder. However, the damping effect of the cylinder wall

makes such a detection difficult. Previous works from Bellettre et al. (2003) and Loubar et al.

(2005) have shown that acquiring a representative temperature signal from the knocking

combustion is possible. Although turbulent promoters are used to enhance the signal level, this

remains too small (about 1 K) to use an industrial temperature probe.

The present paper studies the possibility to improve detection of knock by studying signal level atdifferent frequencies as explained by Chen and Chiou (1996), who have studied interaction between

turbulent flow and variable heat flux with more lower frequency. As a matter of fact, everyperiodical signal is composed of sum of elementary harmonics: T(t) = q.sin(nt) where q is the

amplitude of the signal, the heartbeat in origin, and n, the harmonics rank. The aim is to observehow the temperature signal amplification of each harmonics changes when frequency increases. In

order to achieve this goal, numerical simulations of the unsteady heat transfer across the cylinder

wall and inside the coolant flow are performed at different combustion heat flux signal frequencies.The studied configuration is firstly described, before the presentation of the governing equations

and the boundary conditions. Mesh validation and time step choice are then given. Finally, mainresults regarding the effect of frequency heat flux on the coolant flow are exposed in order to

conclude about the feasibility of the proposed approach.


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2 Studied configuration and governing equations

The present paper treats the case of a water cooled engine cylinder. The geometrical characteristicsof this cylinder are representative of those of a Combined Heat and Power gas engine (bore: 152

mm, displacement volume: 3 l). The engine speed is set constant at 1500 rpm, as in an actual CHP

operation. The computational domain is two-dimensional and is constituted by the single coolantflow channel, see figure 1. The water flows is vertically introduced from the bottom to the top along

the external side of the cylinder.

outlet

Figure 1: Global configuration (a) and computational domain (b).

The governing equations regarding the coolant flow (continuity, momentum and energy) are solved

by the finite volume technique. In each equation, the diffusion terms are discretized according to acentral difference method and the convective terms using a power law scheme as described by

Patankar (1980). Pressure velocity coupling is calculated with the SIMPLE cell-centered schemeand a 1st order implicit scheme is used for time integration, Patankar (1980).

The flow is unsteady and turbulent. The equations needed are the continuity, momentum and energy

ones where the Reynolds decomposition is applied:

0=

ix

iU

(1)

ig

ju

iu

ix

jU

jx

iU

jx

ix

p

jU

iU

jxi

Ut

+++=+

''

)( (2)

( ) ( )j

x

P

jUhju

jx

jx

T

jx

HjU

jx

Ht

+=+

'')( (3)

where U,HandPare the mean values of velocity, enthalpy and pressure.gis the gravity.

cylinder wall

coolant channel

combustionchamber

inlet

adiabatic

cylinder head

combustionheat flux

side

cylinder axis

(a) (b)


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Enthalpy,H, and temperature, T, are linked by the specific heat, cp : , Trefbeing 273 K.=T

T

p

ref

dTcH

u'and h'are the velocity and enthalpy fluctuations, the fluid density, the dynamic viscosity and the thermal conductivity. , cp, and are set constant because of the small variation in temperature

observed outside of the combustion chamber.

In order to close the system (1)(3), Reynolds Stress Model (RSM) is used as turbulence model.Only useful equations are recalled in this paper and more details and physical assumptions can be

found in Launder et al. (1975). The RSM involves solving the transport equations for the Reynoldsstresses, given by (4):

ijijij

k

ji

k

t

kk

jikjiP

x

uu

xx

uuU

t

uu

++=+

)(

''''''

(4)

with )( ''''

k

ikj

k

j

kiijx

Uuu

x

UuuP

+= , ))(

3

2()

3

2( 2

''

1 CPCPCkuuk

C ijijijijjiij ++=

,

k

jik

ijx

uuUC

''

= , ijij32= , and k= 0.82, iiPP

21= , iiCC

21= , C1 = 1.8, C2 = 0.60.

The turbulent viscosity,t, is a function ofk, the turbulent kinetic energy, and the dissipation rate

ofk:

2k

Ct = , with C = 0.09.

k, the turbulent kinetic energy, is obtained by summing three of Reynolds stresses ( = 2'2

1iuk ).

The turbulent kinetic energy dissipation rate, , is computed by solving the transport equation (5):

kC

k

jjP

C

kx

t

kxjx

jU

t

2

221)(

+

+=

+

(5)

with c = 1.0, C1 = 1.44 and C2 = 1.92.

The turbulent heat transfer appearing in the energy equation (3) is modeled using the turbulent

viscosity:j

p

h

tj

x

Tchu

='' (6)

with h

= 0.7(turbulent Prandtl number).

3 Boundary conditions

Computational domain is constituted by liquid water which physico-chemical proprieties are kept

constant for all simulations. As shown in figure 1, water is introduced according to vertical axis atthe channels bottom with a uniform velocity inlet value of 0.6 m.s-1. This means a Reynolds

number of 12000. Turbulent intensity is set to 5 % and temperature is kept constant to 363 K. A low

Reynolds number model approach is retained to account for the wall effects. The near-wallcalculation regarding the turbulent viscosity is described in details by Bellettre and Tazerout (2003)and the modifications regarding the RSM by Launder and Shima (1989).


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The approach, used by Mathelin et al. (2001), also allows simulating instabilities in turbulent flows

if we later disturb the flow of water. External right side channels is considered perfectly adiabatic.

Unsteady heat transfer from the hot burnt gases to the chamber wall is simulated by a self

developed C language program. This program allows fixing instantaneous local heat flux valuesdeduced from the literature, maximum amplitude is 8 MW.m- as exposed by Lu et al. (2002).

As explained earlier in the introduction, real combustion wall heat flux is a periodical signal which

could be decomposed - by Fast Fourier Transformation analysis - in a sum of elementary sinusessignals. So, heat flux is studied by different single sinusoidal signal where frequency is fixed by

harmonic rank order. Simulation were performed for four frequencies such as 1

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cool

recording p

ant flow

oint

cylinder wall

Figure 3: Stream wises observed behind the rib.

The results show that the frequency impacts significantly the signal amplitude in the two cases. Atfirst, for each design, effect of frequency is investigated. Perfect full plate study shown an important

reduction of signal temperature when frequency increases. Figure 4 presents variation of signaltemperature at recording point. While at f=12.5 Hz (n=1), signal level amplitude (peak to peak)

reaches almost 8 K, this value is even not equal to 1 K when frequency doubles, at f=50 Hz (n=2).This signal attenuation hardly continues: when f=50 Hz (n=4), it is a very lower signal which is

available, around 60 mK. Finally, signal temperature for f=75 Hz (n=6) is very poor since only4 mK is recorded. To sum up, when the pulsation increases, the variations of the temperature tend to

smooth T* variations. Note that a 10 ratio can be observed between two successive studiedfrequencies. Understanding could be obtained by investigating velocity, turbulence and temperature

field.

-0,6

-0,4

-0,2

00,2

0,4

0,6

0 20 40 60 80 100 120t (ms)

T*(K)

25 Hz 12.5 Hz x0.1

-0,04

-0,02

0

0,02

0,04

0 20 40 60 80 100 120t (ms)

T*(K)

75 Hz 50 Hz

Figure 4: Variation temperature at recording point perfect full plate channel. T*=T(t)-Tav

Effects with rib are similar and even more significant: the rib is placed 200 mm after the coolant

inlet. It is 2 mm high and 2 mm long. The flow obtained behind this rib is much more turbulent thanwithout (the turbulent kinetic energy is multiplied by more than 10 times).

Temperature signal values are presented in figure 5.

-2

-1,5

-1

-0,5

0

0,5

1

1,5

0 20 40 60 80 100 120 t (ms)T*(K)

25 Hz 12.5 Hz x0.1

-0,025

-0,015

-0,005

0,005

0,015

0,025

0 20 40 60 80 100 120t (ms)

T*(K)

75 Hz 50 Hz

Figure 5: Temperature signal at recording point ribbed duct. T*=T(t)-Tav


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Identical behaviour as full plate case is observed. Increasing frequency leads to an important

reduction of the heat transfer signal. Signal amplitude is divided by a ratio of 13 when frequencychanges from 12.5 Hz to 25 Hz. Same phenomenon reproduces between 25 Hz and 50 Hz, and

between 50 Hz and 75 Hz, variation range is respectively divided by a 52 and 10 ratio. These results

show that when frequency increases, turbulent promoter tend to be useless. Moreover, the figure 6presents a comparative diagram of dimensionless amplitude signal for full plate and ribbed

channels, effect of frequency and geometry could be clearly observed: signal amplification withpromoter is not constant. As a matter of fact, if promoter at low frequencies leads to an important

amplification, until 4 ratio at 12.5 Hz, effect forf=50 Hz andf=75 Hz is strongly inversed.

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

12.5 Hz 25 Hz

0

0,01

0,02

0,03

0,04

0,05

0,06

0,07

0,08

0,09

0,1

25 Hz 50 Hz

0

0,001

0,002

0,003

0,004

0,005

0,006

0,007

0,008

0,009

0,01

50 Hz 75 Hz

Figure 6:Dimensionless representation of T* variations at the different frequencies. (reference

value (=1) is taken for the higher value of variation: the ribbed channel at 12.5 Hz.)

Conclusions and perspectives

The present work focused on the numerical simulations of transient heat transfer around thecombustion chamber in order to detect default in the combustion process such as knock. A knocking

combustion generates a wall heat transfer much higher than a normal one. This heat flux is the sumof singles sinuses signals. Simulations are performed for four frequencies. Heat flux is then taken

into account by a self developed program which enables fixing instantaneous heat flux on theinternal side of the cylinder. The effect of frequency increasing is first investigated. The results

shown an important reduction of the signal when frequency increases. Next, effect of ductsgeometry ribbed channel is observed. Same phenomenon is revealed, when frequency increases,

signal level decreases more strongly when promoter is used. In a common way, increasingfrequency leads to an important reduction of the heat transfer signal. This phenomenon informs us

about the use of low-pass type filter connected to the probe for signal conditioning for futureapplications. Unlike Chen and Chiou study (1996), no resonance between the turbulent flow and the

periodical heat transfer has been found but other heat flux frequencies need now to be investigated.Understanding could be obtained by looking at velocity, turbulence and temperature field. Thus,

major parameters could be identified in order to develop a mathematical model driving this specific

heat transfer.


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References

Bellettre, J. and Tazerout, M., 2003, Numerical Study of Unsteady Heat Transfer Around aCylinder. Application to Knock Detection in Gas SI Engine. Heat Transfer in Unsteady and

Transitional Flows, Eurotherm 74, pp. 99 104.

Brecq, G., 2002, Contribution la caractrisation thermodynamique du cliquetis dans les moteurs gaz : application de nouvelles mthodes de dtection. Ph.D. Thesis, University of Nantes.

Brecq, G., Bellettre, J. and Tazerout M., 2003, A new indicator for knock detection in gas SI

engines. Int. J. Therm. Sci., Vol. 42, N5 pp. 523 532, 2003.

Brecq, G., Tazerout, M. and Le Corre O., 2001, A comparison of experimental indices to determineknock limit in CHP SI engines. 5th World Conference on Experimental Heat Transfer, FluidMechanics and Thermodynamics ExHFT, Vol. 1, pp. 517-521.

Chen, C. and Chiou, J., 1996, Periodic heat transfer in a vertical plate fin cooled by a forcedconvective flow. International Journal of Heat and Mass Transfer, 39(2), pp. 429 435.

Enomoto, Y., Kitahara, N. and Takai, M., 1994, Heat losses during knocking in a four-strokegasoline engine. JSME International Journal, Serie B, Vol. 37.

Launder, B.E., Reece, G.J. and Rodi, W., 1975, Progress in the development of a Reynolds-stress

turbulence closure. J Fluid Mech., Vol. 68, pp. 537-566.

Launder, B.E. and Shima, N., 1989, Second-moment closure for the near-wall sublayer:development and application. AIAA Journal, Vol. 27, pp. 1319-1325.

Liou, T.M., Chen, S.H. and Shih, K.C., 2002, Numerical simulation of turbulent flow field and heat

transfer in a two-dimensional channel with periodic slit ribs. Int. J. Heat Mass Transfer, Vol. 45,

pp. 4493-4505.

Lopez-Matencio, J.L., Bellettre, J. and Lallemand, A., 2003, Numerical prediction of turbulent heatand mass transfer above a porous wall subjected to vaporisation cooling. I. J. Transport Phenomena,

Vol. 5, N3, pp. 185 201.

Loubar, K., Bellettre, J. and Tazerout, 2005, M., Unsteady heat transfer enhancement around anengine cylinder in order to detect knock. ASME Journal of Heat Transfer, 127(3), pp. 278 286.

Mathelin, L., Bataille, F. and Lallemand, A., 2001, Blowing models for cooling surfaces. Int. J.

Therm. Sci., Vol. 40, pp. 969-980.

Patankar, S.V., 1980, Numerical heat transfer and fluid flow. Hemisphere Publishing Corp.,Washington.

Syrimis, M., 1996, Characterization of knocking combustion and heat transfert in a spark-ignitionengine. Ph.D. Thesis, University of Illinois.


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