Study of Reduced Order Model for Parameterized Flow and Heat Transfer Problems

Abstract

The high-fidelity numerical simulation is the basis for constructing digital twins of reactor cores and other engineering applications. However, the traditional numerical models, such as the finite element model and/or the finite volume model, usually adopt high-resolution grids. The high computation cost makes the traditional high-fidelity models unsuitable for the application of digital twins. Model order reduction is an effective approach to accelerate the simulation whenever a trade-off between computational cost and solution accuracy is a preeminent issue. In this paper, a reduced order model (ROM) which combined both the intrusive and the non-intrusive approaches was constructed for the parameterized thermal-flow problems. The intrusive approach adopted the Galerkin projection method and the non-intrusive approach adopted the radial basis function (RBF) interpolation method. To construct the ROM, some typical numerical solutions were firstly generated by using the finite volume method (also called full-order model, FOM) and then taken as learning samples (also called the snapshots) to generate the reduced bases by the proper orthogonal decomposition (POD) method. After that, the conservation equations of mass, momentum and energy were projected onto the space spanned by the reduced bases. As a result, the number of degrees of freedom is substantially reduced. In terms of the turbulent RANS simulation, the RBF interpolation instead of the Galerkin projection was applied to predict the eddy viscosity in ROM since there exists plenty of turbulent models and projection of those various governing equations would be unfeasible. By this data-driven approach, only the eddy viscosity was treated in the ROM. The parametrization of the Dirichlet boundary conditions was treated by the lift function method, in which a special control function was firstly subtracted from the snapshots of velocity and temperature to yield homogenous field snapshots. After the reduced solution over the inner region was solved by the ROM, the boundary value was patched according to the specified boundary condition. The transient heat transfer behavior of coolant flow in a helical cruciform fuel bundle was tested of which the inlet velocity and temperature were treated as parameters. The results show that this ROM can achieve a speedup of 3-4 orders of magnitude compared to the FOM, and meanwhile the relative errors of the velocity, the pressure and the eddy viscosity field remain less than 10%. However, the prediction of the transient evolution of temperature filed from ROM shows a significant difference with FOM. This may be caused by the modal analysis of transient snapshots, and further investigation would be necessary.

Keywords

• flow and heat transfer
• reduced order model
• proper orthogonal decomposition
• radial basis function interpolation