A parametric, hybrid reduced order model approach based on the Proper Orthogonal Decomposition with both Galerkin projection and interpolation based on Radial Basis Functions method is presented. This method is tested against a case of turbulent non-isothermal mixing in a T-junction pipe, a common ow arrangement found in nuclear reactor cooling systems. The reduced order model is derived from the 3D unsteady, incompressible Navier-Stokes equations weakly coupled with the energy equation. For high Reynolds numbers, the eddy viscosity and eddy diffusivity are incorporated into the reduced order model with a Proper Orthogonal Decomposition (nested and standard) with Interpolation (PODI), where the interpolation is performed using Radial Basis Functions. The reduced order solver, obtained using a k-ω SST URANS full order model, is tested against the full order solver in a 3D T-junction pipe with parametric velocity inlet boundary conditions.

VL - 208 UR - https://arxiv.org/abs/1906.08725 ER - TY - UNPB T1 - A POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step Y1 - 2020 A1 - Kelbij Star A1 - Giovanni Stabile A1 - Gianluigi Rozza A1 - Joris Degroote AB -A Finite-Volume based POD-Galerkin reduced order modeling strategy for steady-state Reynolds averaged Navier–Stokes (RANS) simulation is extended for low-Prandtl number flow. The reduced order model is based on a full order model for which the effects of buoyancy on the flow and heat transfer are characterized by varying the Richardson number. The Reynolds stresses are computed with a linear eddy viscosity model. A single gradient diffusion hypothesis, together with a local correlation for the evaluation of the turbulent Prandtl number, is used to model the turbulent heat fluxes. The contribution of the eddy viscosity and turbulent thermal diffusivity fields are considered in the reduced order model with an interpolation based data-driven method. The reduced order model is tested for buoyancy-aided turbulent liquid sodium flow over a vertical backward-facing step with a uniform heat flux applied on the wall downstream of the step. The wall heat flux is incorporated with a Neumann boundary condition in both the full order model and the reduced order model. The velocity and temperature profiles predicted with the reduced order model for the same and new Richardson numbers inside the range of parameter values are in good agreement with the RANS simulations. Also, the local Stanton number and skin friction distribution at the heated wall are qualitatively well captured. Finally, the reduced order simulations, performed on a single core, are about $10^5$ times faster than the RANS simulations that are performed on eight cores.

UR - https://arxiv.org/abs/2003.01114 ER - TY - CONF T1 - Pod-Galerkin reduced order model of the Boussinesq approximation for buoyancy-driven enclosed flows T2 - International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019 Y1 - 2019 A1 - Kelbij Star A1 - Giovanni Stabile A1 - Sokratia Georgaka A1 - F. Belloni A1 - Gianluigi Rozza A1 - Joris Degroote AB -A parametric Reduced Order Model (ROM) for buoyancy-driven flow is developed for which the Full Order Model (FOM) is based on the finite volume approximation and the Boussinesq approximation is used for modeling the buoyancy. Therefore, there exists a two-way coupling between the incompressible Boussinesq equations and the energy equation. The reduced basis is constructed with a Proper Orthogonal Decomposition (POD) approach and to obtain the Reduced Order Model, a Galerkin projection of the governing equations onto the reduced basis is performed. The ROM is tested on a 2D differentially heated cavity of which the side wall temperatures are parametrized. The parametrization is done using a control function method. The aim of the method is to obtain homogeneous POD basis functions. The control functions are obtained solving a Laplacian function for temperature. Only one full order solution was required for the reduced basis creation. The obtained ROM is stable for different parameter sets for which the temperature difference between the walls is smaller than for the set in the FOM used for the POD basis creation. Then, the relative error between the FOM and the ROM for temperature is below 10−4 and for velocity below 10−1 for the vast part of the simulation time. Finally, the ROM is about 20 times faster than the FOM run on a single processor.

JF - International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019 ER -