Heat Release

Heat release analysis of in-cylinder pressure of an internal combustion engine has been solved previously by many researchers . The goal in calculating heat release is to determine on a crank-angle resolved (or time) basis the energy released by fuel during the combustion stroke of the engine cycle. Since the pressure rise due to combustion inside the cylinder is linked to the fuel energy release (or fuel heat release), one can calculate this energy release by analyzing the cylinder pressure. Cylinder pressure measurement is now a standard diagnostic in any research engine. Note that the heat release calculation is only computed during the closed part of an engine cycle from Intake Valve Closing (IVC) to Exhaust Valve Opening (EVO).

Complete Equation

To calculate heat release from cylinder pressure, one must begin with the First Law of Thermodynamics. The First Law fundamentally states that energy can neither be created nor destroyed. For an engine cycle this means that the energy entering the cylinder, mostly in the form of fuel potential, must equal the energy exiting the cylinder in the forms of work output, change in internal energy, heat transfer and lost fuel mass. In mathematical terms, calculation of heat release decomposes into the following equation:

(1)

where is the apparent heat release from the fuel, represents the internal energy of the cylinder components, represents the work done by the piston motion, represents the heat transfer to/from the walls of the cylinder and the last term describes blow-by or crevice flow losses.

To satisfy the First Law of Thermodynamics, the solution to Equation (1) should exactly equal the heat provided by the fuel. To solve this equation, one must accurately determine each of the four terms listed on the right-hand side. Since engine cycles are complex physical processes, it is not possible to assign a closed form equation to all of these terms. Therefore, each of the terms are approximated through numerical methods and models of physical processes. This immediately indicates that the heat release calculation can only be approximated and never solved exactly.

Notice that Equation (1) is written on a per degree basis, or a crank-angle (q) basis. This results from the pressure data experimentally measured on a crank-angle basis. The pressure data can be converted to a time scale by considering the engine speed and the number of crankshaft revolutions per cycle (two for a four-stroke engine).

Internal Energy

The first term shown on the right-hand side of Equation (1) relates to the change in internal energy of the cylinder mixture. As a mixture’s temperature and pressure change, so too does its “stored energy”, or internal energy. Internal energy in a fundamental sense relates to the various forms of energy that molecules and atoms posses. For example, inter-molecular forces that hold compounds together contribute to the molecule’s state of energy. As a molecule’s temperature increases, these forces gain magnitude (i.e. increased linear vibration, atomic rotation, and/or molecule rotation to suggest a few) thus increasing the amount of energy within the molecule. The total internal energy can be split into two components:

(2)

where m represents the total trapped mass of the control volume and the specific internal energy in the cylinder. To model the physical change in the mixture’s internal energy, one usually relies on the change of internal energy for an ideal gas ( ). This change in internal energy is given mathematically as Equation (3).

(3)

where

(4)

with representing the constant volume specific heat of the mixture and T the temperature of the trapped mass. The mean temperature determined from the ideal gas law is close to the mass-averaged cylinder temperature during combustion, because the molecular weights of the burned and unburned gases have been found to be nearly the same [, ].

Work

The second term on the right-hand side of Equation (1) is the work term. This is the term engine researchers are most interested in since it directly relates to the purpose of the engine. The work produced by the engine is given mathematically as Equation (5):

(5)

where P is the measured cylinder pressure and V is the cylinder volume.

The work computation is perhaps the least contested term of heat release analysis, since pressure is accurately measured and volume is accurately calculated. Equation (5) in essence provides a numerical approximation to the true work term, which is the integral of PdV. Since the volume of the cylinder can be calculated exactly on a per degree basis, the first derivative of the volume can be determined analytically .

Heat Transfer

While work is perhaps the least contested term, heat transfer is perhaps the most debated term in heat release analysis. In mathematical form, the heat transfer term is calculated by:

(6)

where is the convective heat transfer coefficient, is the radiative heat transfer coefficient, is the surface area of the cylinder and is the temperature of the cylinder wall. Spark ignition engines have very low luminous flames, whereas compression ignition engines have very luminous, radiating flames. Therefore, the spark-ignition heat transfer correlation involves only convective heat transfer, while the compression-ignition heat transfer correlation involves both convective and radiative effects. Similarly, air motions within the cylinder such as swirl, tumble, and squish all impact heat transfer. As a result of the complexity of the various heat transfer mechanisms, heat transfer coefficients are largely empirical and very specific to individual engine applications.

Blowby and Crevice Flow Effects

The fourth term in Equation (1) relates to the blowby and/or crevice flow effect in the engine. Due to imperfect sealing of the piston rings, gases flow into the ring region (crevice flow) and possibly past the rings (blowby). For homogenous charge engines this results in a loss of fuel mass. Therefore without accurate modeling of these flow effects, one might under-predict the heat release (since they assume more fuel mass than really exists). For heterogeneous charge engines air mass is usually the only lost mass. Although fuel mass may remain nearly constant, the loss of air mass reduces the total trapped mass, which has implications on the heat release calculations.

References

[1] Brunt, M.F.J. and A.L. Emtage, “Evaluation of Burn Rate Routines and Analysis Errors.” , 1997.
[2] Brunt, M.F.J., H. Rai, and A.L. Emtage, “The Calculation of Heat Release Energy from Engine Cylinder Pressure Data.” , 1998.
[3] Brunt, M.F.J. and K.C. Platts, “Calculation of Heat Release in Direct Injection Diesel Engines.” , 1999.
[4] Chmela, F.G. and G.C. Orthaber, “Rate of Heat Release Prediction for Direct Injection Diesel Engines Based on Purely Mixing Controlled Combustion.” , 1999.
[5] Gatowski, J.A., et al., “Heat Release Analysis of Engine Pressure Data.” , 1984.
[6] Grimm, B.M. and R.T. Johnson, “Review of Simple Heat Release Computations.” , 1990.
[7] Heywood, J.B., Internal Combustion Engine Fundamentals. 1988, New York:
[8] Homsy, S.C. and A. Atreya, “An Experimental Heat Release Rate Analysis of a Diesel Engine Operating Under Steady State Conditions.” , 1997.
[9] Jensen, T.K. and J. Schramm, “A Three-Zone Heat Release Model for Combustion Analysis in a Natural Gas SI Engine - Effects of Crevices and Cyclic Variations on UHC Emissions.” , 2000.
[10] Krieger, R.B. and G.L. Borman, “Computation of Apparent Heat Release for Internal Combustion Engines.” - Papers, 66-Winter Anual Meeting/DGP-4, 1966.
[11] Rakopoulos, C.D. and D.T. Hountalas, “Net and Gross Heat Release Rate Calculations in a DI Diesel Engine Using Various Heat Transfer Models.” , Advanced Energy Systems Division (Publication) AES, 1994. 33: p. 251-262.
[12] Shayler, P.J., M.W. Wiseman, and T. Ma, “Improving the Determination of Mass Fraction Burnt.”, 1990.

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Date Created: 05/28/2003
Date Revised: 10/11/2005