Surrogate-based modeling for emulation of supercritical injector flow and combustion

High-fidelity simulations play an increasingly important role in understanding fundamental turbulence-chemistry interactions and combustion dynamics in practical propulsion and power-generation systems. These simulations are, however, too computationally expensive and unwieldy for the purposes of design and optimization, given the large group of design parameters and wide design space. In this paper, we present an efficient surrogate-based modeling strategy to emulate spatiotemporal flows and combustion at supercritical pressures with accuracy similar to that of large-eddy simulations (LES). A common kernel-smoothed proper orthogonal decomposition (CKSPOD)-based surrogate model is developed, incorporating computer experiments, projection-based model reduction, kriging, and uncertainty quantification. The surrogate model (emulator) is carefully trained using a database drawn from a set of LES-based simulations that are conducted at designated sampling points in a given design space. A common Gram matrix is built using a Hadamard product to transform reduced spatial basis functions to remedy phase deviations among different design settings. Kriging is then used to obtain temporal spatial functions and associated coefficients for flowfield reconstruction at a new design setting. The framework is examined with two case studies: an emulation of flow dynamics in a simplex swirl injector, and an emulation of mixing and combustion in a gas-centered liquid-swirl coaxial injector. The surrogate model not only faithfully captures the salient features of its LES counterpart, but also shortens the computation time dramatically, by up to five orders of magnitude. The developed surrogate model can be applied to a broad range of engineering systems and will provide support for future engineering innovation and design.