Bi-Fidelity Data Ensembles of a Rocket Ignition System With Stochastic Interpolative Decomposition

Laser-induced spark is an ignition method in a rocket combustor that facilitates engine re-ignition throughout a mission. The present work generates a probability map of successful ignition that varies with laser deposition site, and also, a quantitative framework for the post-ignition pressure rise probability distribution in the combustor. Run-to-run variabilities in the system arise from uncertainty in the deposited laser energy kernel characteristics, and the stochastic nature of turbulence. Multi-fidelity Monte Carlo sampling is implemented to obtain realizations of the uncertainty space. Low fidelity is achieved by coarsening of the mesh used for simulation, and simplification of the underlying chemistry. We demonstrate the application of a novel bi-fidelity method, the stochastic interpolative decomposition, which enables the estimation of the quantity of interest for the equivalent high fidelity ensemble using a small number of runs. Bi-fidelity stochastic interpolative decomposition is a suitable uncertainty quantification tool for problems exhibiting stochastic, multi-modal outcomes in the uncertainty space, as it preserves correlations in the output space where standard interpolative decomposition fails.