Several improvements to the mathematical model for the indicator process in a diesel engine cylinder are proposed. The thermodynamic behavior of working media is described by the equation of state valid for real gases. Analytical mathematical dependencies between thermal parameters (pressure, temperature, volume) and caloric parameters (internal energy, enthalpy, specific heat capacities) have been obtained. These equations have been applied to the various products encountered during the burning of fuel and the gas mixture as a whole in the engine cylinder under conditions of high pressures. An improved mathematical model, based on the first law of thermodynamics, has been developed by taking into account imperfections in the working media that appear under high pressures. The numerical solution of the simultaneous differential equations is obtained by Runge–Kutta-type method. The mathematical model is then used to solve the desired practical problems in two different two-stroke turbo-charged engines: 8DKRN 74/160 and Sulzer-RLB66. Significant differences between the values calculated using ideal gas behavior and the real gas at high-pressure conditions have been found. The numerical experiments show that if the pressure is above 8 to 9 MPa, the imperfections in working medium must be taken into consideration. The results obtained from the mathematical dependencies of the caloric parameters can also be used to model energy conversion and combustion processes in other thermal machines such as advanced gas turbine engines with high-pressure ratios.

Issue Section:
Internal Combustion Engines: Fuels and Combustion Technology
Keywords:
internal combustion engines, gas mixtures, fuel, combustion, high-pressure effects, gas turbines, modelling
Topics:
Combustion, Cylinders, Diesel engines, Differential equations, Engine cylinders, Fuels, Gases, Pressure, Specific heat, Temperature, Engines, Enthalpy, Internal energy (Physics), High pressure (Physics), Gas turbines, Equations of state
1.
Glagolev, N. M., 1950, Working Processes in Internal Combustion Engines (Mashgiz, Moscow) (in Russian).
2.
Woschni
,
G.
,
1965
, “
Electronische Berechnung von Verbrenung Motor-krei-Prozessen
,”
MTZ
,
26
, No.
11
, pp.
439
–
446
.
3.
McAulay, et al., 1965, “Development Evaluation of the Simulation of the Compression Ignition Engine,” SAE paper 650452, p. 30.
4.
Samsonov
,
L. A.
,
1980
, “
Modeling the Indicator Process of Marine Diesel Engines by using the Monte-Carlo Method
,”
Dvigatelestroenie
,
1980
, No. (
4
), pp.
23
–
25
(in Russian).
5.
Klaus
,
H.
,
1984
, “
Bettbag zur Berechnung des Betriebsverhaltens Gleichstromgespulter zweitakt-Schiffs-dieselmotoren
,”
MTZ
,
45
, No.
9
, pp.
345
–
352
.
6.
Wark, K., 1995, Advanced Thermodynamics for Engineers, McGraw-Hill, New York.
7.
Shpillrain
,
E.
, and
Kessellman
,
P.
,
1977
, “
Bases of the Theory of Thermo-Physical Properties of Materials
,”
Energy (Moscow)
,
1977
, p.
248
248
(in Russian).
8.
Bird, G. A., 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford University Press, Oxford, p. 480.
9.
Turns, S., 1996, An Introduction to Combustion Concepts and Applications, McGraw-Hill, New York.
10.
Dorn, W. S., and McCracken, D. D., 1972, Numerical Methods With “FORTRAN 4” Case Studies, John Wiley and Sons, Inc., New York.
11.
Danov
,
S.
, and
Gupta
,
K.
,
2000
, “
Effect of Sauter Mean Diameter on the Combustion Related Parameters in Heavy-Duty Diesel Engines
,”
AIAA J. Propulsion and Power
,
16
, No.
6
, Nov.–Dec., pp.
980
–
987
.
12.
Woschni
,
G.
, and
Fleger
,
J.
,
1979
, “
Auswertung gemessener Temperatur felder zur Bestimmang ortlicher warmeulergangs koeffizienten am kollben eingines schnellaufenden Dieselmotors
,”
MTZ
,
1979
, pp.
153
–
158
.
13.
Danov, S., 1988, “Mathematical Modeling of Energy Conversion Characteristics of Ship Diesel Power Plants,” Ph.D. thesis, Varna Technological University.
14.
Danov, S., 1989, “Modeling the Combustion Process of a Diesel Engine for Partial Operating Conditions,” Fourth International Symposium “PRADS’89,” Varna, Vol. 3, pp. 156.1–156.5.
15.
Fox, L., 1962, Numerical Solution of Ordinary and Partial Differential Equations, Pergamon Press, Oxford.
16.
Ralston
,
A.
,
1962
, “
Runge-Kutta Methods With Minimum Error Bounds
,”
Math. Comput.
,
16
, pp.
431
–
437
.
17.
Rabiner, L., and Gold, B., 1985, Theory and Application of Digital Signal Processing, Prentice-Hall, Englewood Cliffs, NJ.
Copyright © 2001
 by ASME
You do not currently have access to this content.