The heat transfer during the compression process in an internal combustion engine.

Mitran, Tudor ; Pater, Sorin ; Fodor, Dinu 等

1. INTRODUCTION

The scheme of the heat transfer process is presented in figure 1.

where:--[t.sub.f] [[sup.0]C]--the temperature of the working gas

--[t.sub.iw] [[sup.0]C]--the temperature of the cylinder inner walls

--[t.sub.iw] [[sup.0]C]--the temperature of the cylinder inner walls

--[t.sub.mw1] [[sup.0]C]--the temperature of the cylinder exterior walls

--[t.sub.mw2] [[sup.0]C]--the temperature of the cylinder block inner walls

--[t.sub.c] [[sup.0]C]--the temperature of the cooling agent

The heat transfer between the working fluid and the inner walls of the combustion chamber is a convective one, than through the walls of the cylinder and the cylinder block heat transfer is conductive with an inner thermal resistance (Mollenhauer, 1997). From the walls of the cooling system to the cooling agent heat transfer is also convective (Pishinger et al., 1989).

The general equation of heat transfer is:

[??] = [DELTA]t/R x S (1)

where:--[??] [W]--the thermal flux

--[DELTA]t [[sup.0]C]--the thermal gradient

--R [m.sup.2] [sup.0]C/W]--the thermal resistance

--S [[m.sup.2]]--the heat exchange surface

[FIGURE 1 OMITTED]

The problem is to determine thermal resistances in the convective heat exchange processes between the fluids (working gas and cooling agent) and the engine walls (van Basshuysen & Schafer, 2004).

The empirical formulae used to calculate the convective coefficient (Cirkov, Sitkei, Woschni) (Grunwald, 1980) are determined in the conditions of a flow inside a manifold and can not be applied with sufficient precision for the combustion chamber which is closed during the compression process.

A more precise method to determine heat exchange in an i.c.e. is useful in order to predict fluid maximum temperature inside the combustion chamber. This is important because N[O.sub.x] emissions depend on this maximum temperature inside the combustion chamber. Formation of N[O.sub.x] increases at temperatures over 1700K.

2. THE CALCULUS OF THE THERMAL RESISTANCES

The thermal flux in heat exchange between the working gas and the cooling agent is (see fig.1) (Stefanescu et al., 1983):

[??] = ([t.sub.f] - [t.sub.c]) x [S.sub.i]/[R.sub.1] + [R.sub.2] + [R.sub.3] + [R.sub.4] + [R.sub.5] (2)

where: - [S.sub.i] [[m.sup.2]]--instantaneous heat transfer surface

[R.sub.1] = 1/[pi] x [d.sub.1] x [[alpha].sub.1] (3)

[d.sub.1] = D--the inner diameter of the cylinder

[[alpha].sub.1]--the convective coefficient in the heat transfer between working gas and cylinder walls

[[alpha].sub.1] = [Nu.sub.f] x [[lambda].sub.f]/[l.sub.f] (4)

[[lambda].sub.f]--the thermal conductivity of the working gas

[l.sub.f]--the characteristic length

[Nu.sub.f] = 0.023 * [Re.sup.0,8] * [Pr.sup.n] (5)

Nu, Re, Pr--Nusselt, Reynolds, Prandtl non-dimensional criteria applied to the working gas

[R.sub.2] = 1/2 x [pi] x [[lambda].sub.Ft] x ln [d.sub.2]/[d.sub.1] (6)

[[lambda].sub.Ft]--the thermal conductivity of cast iron

[R.sub.3] = [delta] / (0,08 x [[lambda].sub.Ft] x [[lambda].sub.Al]/[[lambda].sub.FT] + [[lambda].sub.Al] + 0,96 x [[lambda].sub.a]) (7)

[delta]=[[delta].sub.1] + [[delta].sub.2]

[[delta].sub.1], [[delta].sub.2]--the medium roughness of the two surfaces

[[lambda].sub.Al]--the thermal conductivity of aluminium alloys

[[lambda].sub.a]--the thermal conductivity of air

[R.sub.4] = 1/2 x [pi] x [[lambda].sub.Al] x ln [d.sub.3]/[d.sub.2] (8)

[R.sub.5] = 1/[pi] x [d.sub.3] x [[alpha].sub.2] (9)

[[alpha].sub.2] = [Nu.sub.c] x [[lambda].sub.c]/[l.sub.c] (10)

[[lambda].sub.f]--the thermal conductivity of the cooling agent

[l.sub.f]--the characteristic length

[Nu.sub.c] = (0,35 + 0,56 * [Re.sup.0,52]) * [Pr.sup.0,3] (11)

Nu, Re, Pr--Nusselt, Reynolds, Prandtl non-dimensional criteria applied to the cooling agent

It is possible, by applying rel. (1), to determine all the temperatures presented in fig. 1.

3. THE COMPARISON BETWEEN CALCULATED AND EXPERIMENTAL DATA

To compare the calculated with experimental data it is necessary to calculate the instantaneous pressure inside the combustion chamber:

[p.sub.i] = m x R x [T.sub.f]/[V.sub.i] (12)

m [kg]--the mass of the working gas (is constant)

R [J/kgK]--the ideal gas constant

[T.sub.f] [K]--the working gas temperature

[V.sub.i] [[m.sub.3]]--the instantaneous volume of the combustion chamber

The measurements were taken on one cylinder water cooled diesel engine.

The comparison between measured and calculated pressure inside the combustion chamber during the compression process is presented in figure 2.

[FIGURE 2 OMITTED]

The differences between the two sets of data are less than 20%, that's a sufficient precision in the terms of heat exchange processes.

The general problem of heat exchange in i.c.e. is difficult to solve also because of the variable volume (surface) of the combustion chamber. One of the assumptions made in calculus was that the surface of heat exchange don't include piston head surface.

In order to calculate thermal flux, temperature of cooling agent and the rate of flow were measured at the entrance and the exit from the engine. This means that the heat exchanged with the piston is not taken in consideration.

The instantaneously heat exchange surface is:

[S.sub.i] = [pi] x D x {[.sub.c] + r x [1 - cos [alpha] + ([LAMBDA]/4)(1 - cos2[alpha])]} (13)

where:--D [m]--the cylinder bore

--[l.sub.c] [m]--the dead volume length

--r [m]--the crankshaft radius

--[LAMBDA]=r/b--the conrod ratio

--b [m]--conrod length (the distance between the centres of the small-end and the big end eyes)

--[alpha]--the rotational angle of the crankshaft

In the proximity of TDC this assumption leads to relative great differences between measured and calculated data.

4. CONCLUSION

The model presented in this paper is good enough to describe heat transfer in the compression process for this particular engine.

It would be interesting to determine a general relation for the convective coefficient of the heat transfer between the working gas and the inner walls of the combustion chamber. This general relation should be applied for a particular engine by using a correction coefficient.

The correction coefficient can be determined for each specific engine only on test benches.

For the heat transfer during burning, detention, exhaust and intake processes other general relations must be taken in consideration.

5. REFERENCES

van Basshuysen, R. & Schafer, F. (2004). Internal combustion engine, SAE International, ISBN 0-7680-1139-6, Warrendale PA

Grunwald, B. (1980). Teoria, calculul si constructia motoarelor pentru autovehicule rutiere, The Theory, the calculus and the construction of the engines for automotives, Ed. Didactica si pedagogica, Bucuresti

Mollenhauer, K. (1997). Handbuch Dieselmotoren, Diesel Engines Handbook, Springer, Berlin

Pishinger, R.; Krassnig, G.; Taucar, G. & Sams, Th. (1989). Thermodynamic der Verbrennungskraftmaschine. Die Verbrennungskraftmaschine. The Thermodynamic of the Internal Combustion Engine. The Internal Combustion Engine, Reeissue Volume5, Springer, Vienna

Stefanescu, D.; Leca, A,; Luca, L.; Badea, A. & Marinescu, M. (1983). Transfer de caldura si masa, Heat and Mass Transfer, Ed. Didactica si pedagogica, Bucuresti