Temperature distribution and heat flow across the combustion chamber wall.

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1 ΜΕΤΑΔΟΣΗ ΘΕΡΜΟΤΗΤΑΣ ΣΤΟΝ ΚΥΛΙΝΔΡΟ (J.B. Heywood: Internal Combustion Engine Fundamentals McGraw Hill 1988) Temperature distribution and heat flow across the combustion chamber wall. Throughout each engine operating cycle, the heat transfer takes place under conditions of varying gas pressure and temperature, and with varying local velocities depending on intake port and combustion chamber configuration. The heat flux into the containing walls changes continuously from a small negative value during the intake process to a positive value of order several megawatts per square meter early in the expansion process. The flux variation lags behind the change in gas temperature, but the precision of measurements suffice only for a rough estimate of its magnitude. Generally, the assumption of quasi steady heat transfer process is sufficiently accurate for most purposes. However, gas temperature and gas velocities vary significantly across the combustion chamber. For a steady one dimensional heat flow through a wall:

2 ΔΙΑΣΤΑΤΙΚΗ ΑΝΑΛΥΣΗ While the overall time averaged heat transfer to the coolant medium is adequate for some design purposes, the instantaneous heat flux during the engine cycle is a necessary input for realistic cycle calculations and provides the fundamental input for obtaining the heat flux distribution to various parts of an operating engine. Equations above provide the framework for calculating the heat flux q, based on the quasi steady heat transfer process assumption. Dimensional analysis can be used to develop the functional form of relationships which govern the gas side heat transfer coefficient. The engine convective heat transfer process can be characterized geometrically by a length dimension, say the bore B, and a number of length ratios y 1 y 2,y 3, (of which one will be the axial cylinder length z divided by the bore z/b), which define the cylinder and combustion chamber geometry. The flow pattern may be characterized by one chosen velocity υ and a set of velocity ratios u 1, u 2, u 3,... Important gas properties are thermal conductivity k, dynamic viscosity μ, specific heat c p and density ρ. If there is combustion, the chemical energy release rate per unit volume q ch is important. Engine speed N and crank angle θ introduce the cyclical nature of the process. Thus Applying dimensional analysis, with mass, length, time, and temperature as the independent dimensions, reduces the variables to 4 fewer dimensionsless groups: The first three groups are the familiar Nusselt, Reynolds, and Prandtl numbers, respectively. The next has the nature of a Mach number since c p T is proportional to the square of the sound speed. For Mach numbers much less than 1, the Mach number dependence is known to be small and can be omitted. It is usual to take for υ the mean piston speed S p = 2LN. Then, by introducing the bore/stroke ratio B/L, the term NB/υ is eliminated. z/b is a function of the compression ratio r c, the ratio of connecting rod to crank radius R = l/a, and θ. The dimensionless groups may be varied (not reduced in number) by combination. This equation provides a basis for evaluating proposed correlations.

3 Many formulas for calculating instantaneous heat transfer coefficients have been proposed, on the basis of the assumption that the Nu, Re and Pr number relationship follows that of turbulent flow in pipes or over flat plates: Distinctions should be made between correlations intended to predict the timeaveraged, heat flux to the combustion chamber walls, the instantaneous spatially averaged heat flux to the chamber walls (which is required for engine performance analysis), and the instantaneous local heat fluxes (which are not uniform over the combustion chamber and may be required for thermal stress calculations). In using these correlations, the critical choices to be made are the velocity to be used in the Reynolds number; the gas temperature at which the gas properties are evaluated; and the gas temperature used in the convective heat transfer equation. The most widely used correlations are summarized below. Correlations for Time Averaged Heat Flux Taylor correlated overall heat transfer data from 19 engines. It was assumed that coolant and wall temperatures varied little between designs and the effects of geometrical differences were small. Thus, at a given F/A, the convective part of the heat flux should correlate with Reynolds number. To allow for variations in F/A, they defined an average effective gas temperature T g,a such that over the engine cycle. T g,a is the temperature at which the wall would stabilize if no heat was removed from outside. T g,a was obtained by extrapolating average heat transfer data plotted versus gas side combustion chamber surface temperature back to the zero heat transfer axis. The Nusselt number, defined as plotted against Reynolds number, defined as where m is the charge mass flow rate, is shown in the following figure:

4 Taylor proposed a power law of Annand suggests 3 separate lines for the 3 different types of engines covered, with slope 0.7. The diesel line, is about 25 percent higher than the spark ignition engine line (which corresponds in part to the radiative heat flux component). The air cooled engine line is lower than the liquid cooled line, presumably because surface temperatures are higher. The average gas temperature values developed by Taylor are shown in the insert. Correlations for Instantaneous Spatial Average Coefficients Annand developed the following convective heat transfer correlation to match previously published experimental data on instantaneous heat fluxes to selected cylinder head locations:

5 The value of a varied with intensity of charge motion and engine design. With normal combustion, 0.35 < a < 0.8 with b = 0.7, and a increases with increasing intensity of charge motion. Gas properties are evaluated at the cylinder average charge temperature T g : The same temperature is used to obtain the convective heat flux. Note that in developing this correlation, the effects of differences in geometry and flow pattern between engines have been incorporated in the proportionality constant a, and the effect of chemical energy release is omitted. While only data from cylinder head thermocouple locations were used as a basis for this correlation, it has often been used to estimate instantaneous spatial average heat fluxes for the entire combustion chamber. Woschni assumed a correlation of the form With the cylinder bore B taken as the characteristic length, with w as a local average gas velocity in the cylinder, and assuming k T 0.75, p T 0.62, and p = ρrt, the above correlation can be written During intake, compression, and exhaust, Woschni argued that the average gas velocity should be proportional to the mean piston speed. During combustion and expansion, he attempted to account directly for the gas velocities induced by the change in density that results from combustion (~ 10 m/s), which are comparable to mean piston speeds. Thus a term proportional to the pressure rise due to combustion (p p m ) was added (p m is the motored cylinder pressure). The coefficients relating the local average gas velocity w to the mean piston speed and (p p m ) were determined by fitting the correlation, integrated over the engine cycle, to time averaged measurements of heat transfer to the coolant for a wide range of engine operating conditions for a direct injection four valve diesel without swirl. T is the mean cylinder gas

6 temperature; the same temperature is used to obtain the heat flux from the heat transfer coefficient h c. Thus this correlation represents spatially averaged combustion chamber heat fluxes. The average cylinder gas velocity w (meters per second) determined for a four stroke, water cooled, four valve directinjection CI engine without swirl was expressed as follows: p is the instantaneous cylinder pressure, p r, V r, T r are the working fluid pressure, volume, and temperature at some reference state (say inlet valve closing or start of combustion), and p m is the motored cylinder pressure at the same crank angle as p. Subsequent studies in higher speed engines with swirl indicated higher heat transfer than these velocities predicted. For engines with swirl, cylinder averaged gas velocities were fitted with: where υ s = Bω p /2 and ω p is the rotation speed of the paddle wheel used to measure the swirl velocity. Spark ignition engine tests showed that the above velocities gave acceptable predictions for this type of engine also. Woschni's correlation, with the exponent equal to 0.8, can be summarized as: with w defined above. Hohenberg examined Woschni's formula and made changes to give better predictions of time averaged heat fluxes measured with probes in a directinjection diesel engine with swirl. The modifications include use of a length based on instantaneous cylinder volume instead of bore, changes in the effective gas velocity, and in the exponent of the temperature term.

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