Dimension reduction in MHD power generation models: dimensional analysis and active subspaces
For engineers studying MHD power generator designs, this work provides a practical dimension reduction approach to make computationally expensive models more tractable, though the methods themselves are not new.
The paper applies dimensional analysis and active subspaces to reduce the input dimension of MHD power generation models, enabling more efficient parameter studies. The methods are demonstrated on both a simplified Hartmann problem and a large-scale computational model, yielding insights into key driving factors.
Magnetohydrodynamics (MHD)---the study of electrically conducting fluids---can be harnessed to produce efficient, low-emissions power generation. Today, computational modeling assists engineers in studying candidate designs for such generators. However, these models are computationally expensive, so studying the effects of the model's many input parameters on output predictions is typically infeasible. We study two approaches for reducing the input dimension of the models: (i) classical dimensional analysis based on the inputs' units and (ii) active subspaces, which reveal low-dimensional subspaces in the space of inputs that affect the outputs the most. We also review the mathematical connection between the two approaches that leads to consistent application. The dimension reduction yields insights into the driving factors in the MHD power generation models. We study both the simplified Hartmann problem, which admits closed form expressions for the quantities of interest, and a large-scale computational model with adjoint capabilities that enable the derivative computations needed to estimate the active subspaces.