  High-fidelity simulations of mixing and combustion processes are generally
computationally demanding and time-consuming, hindering their wide application
in industrial design and optimization. The present study proposes parametric
reduced order models (ROMs) to emulate spatial distributions of physical fields
for multi-species mixing and combustion problems in a fast and accurate manner.
The model integrates recent advances in experimental design, high-dimensional
data assimilation, proper-orthogonal-decomposition (POD)-based model reduction,
and machine learning (ML). The ML methods of concern include Gaussian process
kriging, second-order polynomial regression, k-nearest neighbors, deep neural
network (DNN), and support vector regression. Parametric ROMs with different ML
methods are carefully examined through the emulation of mixing and combustion
of steam-diluted fuel blend and oxygen issuing from a triple-coaxial nozzle.
Two design parameters, fuel blending ratio (hydrogen/methane) and steam
dilution ratio, are considered. Numerical simulations are performed and
training data is assimilated at sampling points determined by the
Latin-hypercube design method. The results show that ROM with kriging presents
a superior performance in predicting almost all physical fields, such as
temperature, velocity magnitude, and combustion products, at different
validation points. The accuracy of ROM with DNN is not encouraging owing to the
stringent requirement on the size of training database, which cannot be
guaranteed as many engineering problems are specific and associated data
availability is limited. For the emulation of spatial field, the parametric
ROMs achieve a turnaround time of up to eight orders of magnitude faster than
conventional numerical simulation, facilitating an efficient framework for
design and optimization.
