A hybrid sigmoid-double Wiebe correlation for reduced order modeling of hydrogen engine combustion

Lean hydrogen engine combustion exhibits delayed ignition kernel growth, slow early flame development and highly asymmetric heat release behavior that differs fundamentally from conventional hydrocarbon fuels. The CFD-derived HRR profiles show that approximately 48%–50% of the period up to 50% burn (CA50) occurs before CA10, indicating that early-stage heat release must be represented accurately in reduced-order engine combustion simulations. Conventional correlations used in one-dimensional (1D) engine cycle simulation are typically based on single or multi-Wiebe formulations. Although multi-Wiebe formulations improve fitting flexibility, they have limited capability to represent the slow early combustion phase observed in lean and stratified hydrogen direct-injection spark ignition combustion. To address this limitation, a CFD informed reduced-order combustion correlation is developed using a hybrid sigmoid-double Wiebe (SDW) formulation. The sigmoid component represents slow ignition kernel growth and transition to flame propagation before the onset of accelerated turbulent combustion, while the double Wiebe formulation represents the rapid main combustion and extended late combustion phases. The SDW model parameters are identified through nonlinear optimization using 3D-CFD derived HRR profiles across multiple operating conditions and organized into structured database indexed by ignition timing, injection timing, equivalence ratio, engine speed, and load. For the representative HRR case, the preprocessing preserved the total integrated heat release almost identically, while CA10, CA50 and CA90 remained essentially unchanged, with deviations below 0.01° CA. The calibrated reduced-order correlation is implemented in a 1D GT-Power framework, where the reconstructed HRR profiles accurately capture the in-cylinder pressure evolution observed in the corresponding 3D CFD simulations. The model enables HRR prediction at calibrated database points as well as interpolated and limited extrapolated operating points within the calibration range, providing computationally efficient pathway for transferring high-fidelity CFD informed hydrogen combustion behavior into practical system-level engine analysis and control-oriented simulations.