Integrated Multi-Scale Framework for Combustion Modeling in Alternative Fuels: Coupling Bayesian Uncertainty Quantification, Sensitivity Analysis, and Empirical Validation with High-Fidelity Computations

This paper presents an advanced framework for modeling combustion in alternative fuels, integrating multi-scale approaches from quantum chemistry to macroscopic engine performance. High-fidelity density functional theory (DFT) calculations are performed using PySCF to derive activation energies and Gibbs free energies for key reactions, including biofuels. Detailed kinetic mechanisms from AramcoMech 2.0 (493 species, 2716 reactions) are reduced using DRGEP/PFA and coupled with 2D large eddy simulation (LES)-like CFD models implemented in Python with NumPy and SciPy. Bayesian uncertainty quantification employs a Metropolis-Hastings algorithm with full diagnostics such as Gelman-Rubin statistics, effective sample size (ESS), potential scale reduction factor (PSRF), and rank plots. Global sensitivity analysis uses Sobol indices computed with a SALib-inspired implementation, with N=20,000 samples for first-, total-, and second-order indices. The framework is rigorously validated against a comprehensive dataset of 80 experimental points from shock tubes, rapid compression machines, bomb calorimeters, and engine test benches for hydrogen, biodiesel, ethanol, and sustainable aviation fuel (SAF) blends, spanning sweeps of equivalence ratio (φ=0.5-2.0), temperature (T=800-2000 K), pressure (P=1-50 bar), exhaust gas recirculation (EGR=0-30%), and blend ratios (0-100%). Validation includes blind tests on external datasets, parity plots with posterior predictive error bars, and metrics showing RMSE=12 μs for ignition delay time (IDT), R²=0.96 for flame speeds, and uncertainty propagation to engine outputs (NOx ±12%, CO ±8%, soot ±15%, efficiency ±4%). Quantitative comparisons demonstrate 45-65% uncertainty reduction over deterministic models. Simulations of aircraft engines are added using Brayton cycle calculations adjusted for alternative fuels, showing up to 2.8% fuel savings. Novel insights include the 68% contribution of biodiesel activation energy to NOx uncertainty at φ=1.2, explaining 15% deviation in emissions, and a plan for digital twin application in aircraft engines using ICAO data. Broader impacts encompass life-cycle assessment (LCA) showing 65-80% GHG reductions, economic analyses, and alignment with policies like Saudi Vision 2030 and ICAO CORSIA.