Reference-Calibrated Thermodynamic Screening, Agreement Diagnostics, and Grid-Verified Multi-Objective Design for Hydrogen–Diesel Combustion

A transparent reduced-order framework is developed for screening hydrogen energy share, H, defined as the fraction of total lower-heating-value fuel energy supplied by hydrogen, and diesel-injection timing in a hydrogen–diesel compression-ignition engine. Slider–crank geometry is coupled according to a finite-support beta apparent-heat-release law, and the constant-γ first-law equation is integrated in closed form. The resulting pressure-response and work kernels explain the competing effects of near-top-dead-center heat release and timing retard. Three parameters are calibrated or anchored using published full-load CFD quantities, while four reported operating points are retained for quantitative agreement diagnostics. For IMEP, peak pressure, and CA10–90 duration, pooled normalized agreement gives R2 = 0.912, heuristic adjusted index = 0.879, RMSE = 1.67%, and MAPE = 1.27%. A fixed-ROM leave-one-case-out affine discrepancy check gives R2 = 0.801 and MAPE = 2.34%. A residual analysis isolates pressure-rise rate as the principal model-form discrepancy at a high hydrogen share. Conditional timing optimization is recomputed on a 0.125° CA grid, and a bi-objective formulation reveals the trade-off between IMEP and hydrogen energy substitution. The model-screened Pareto compromise occurs at H = 0.71 with u = 4.60° CA and IMEP = 22.20 bar, while an explicitly bounded 256-member epistemic ensemble retains all-scenario-feasible timing through H = 0.65. These diagnostics characterize agreement within the four-case full-load reference set and do not constitute independent experimental validation. The contribution is an auditable connection between apparent heat release, quantitative agreement, residual structure, pressure constraints, and multi-objective operating-point screening.