Development of a Mass- and Energy-Conserving Combustion-Capacity Model for Direct-Injection Diesel Heat Release

A reduced-order, mass- and energy-conserving combustion-capacity model was developed to represent premixed and mixing-controlled heat release in a direct-injection diesel engine. Unlike conventional reduced-order formulations that prescribe heat-release shape or correlate heat release directly with fitted functions, the proposed framework first determines the fuel mass physically capable of combustion from the simultaneous availability of injected fuel and stoichiometric air. Fuel prepared during the ignition-delay period forms a finite premixed reservoir that is consumed through an analytical depletion law. After the start of combustion, the remaining fuel and entrained air define a continuously evolving mixing-controlled combustion capacity consumed through a finite-rate formulation. Explicit fuel-allocation and conservation constraints prevent double-counting between the two combustion stages and limit cumulative heat release to the available fuel chemical energy. The model was evaluated using experimentally derived apparent heat-release-rate histories at six engine speeds from 1200 to 2200 rpm and brake torques of 150 and 200 N·m. The premixed combustion-rate coefficient was determined for each operating condition from the corresponding average fuel-injection pressure difference, while the mixing-controlled coefficient was maintained constant. Across the 12 operating conditions, the root-mean-square error (RMSE) ranged from 0.0055 to 0.0224 kJ/°CA, the mean absolute error (MAE) from 0.0032 to 0.0113 kJ/°CA, and R2 from 0.446 to 0.968. The absolute peak heat-release-rate error remained below 3% for 10 of the 12 cases. The results demonstrate that the proposed framework reproduces the principal apparent heat-release characteristics while maintaining explicit separation and conservation of the premixed and mixing-controlled fuel reservoirs.