VERIFYING VERTEX-CFD SIMULATIONS OF HEATED LID-DRIVEN CAVITIES

Oak Ridge National Laboratory (ORNL) has demonstrated needs in modeling and simulating gas dynamics, magnetohydrodynamics (MHD), thermal hydraulics, and the plethora of other complex physics involved with fusion energy applications. To those ends, ORNL is developing a computational-fluid dynamics (CFD) code called VERTEX-CFD to model and simulate fusion blankets. In this study, VERTEX-CFD was used to simulate heated lid-driven cavities with and without obstacles at Reynolds = 100, Prandtl = 0.71, and Grashof = [10², 10³, 10⁴, 10⁵]. Grashof was varied by increasing the volumetric expansion coefficient of the enclosed fluid to test the coupling of the momentum and temperature equations and imposed boundary conditions being solved by VERTEX-CFD. Buoyancy effects were incorporated via the Boussinesq approximation which assumes density varies linearly with temperature. All other fluid properties were assumed to be constant. Within VERTEX-CFD, solvers, finite-element methods, and other relevant tools are based on the Trilinos framework. An artificial compressibility method is also employed to introduce pressure and velocity coupling when solving the incompressible Navier-Stokes equations. Numerical stability of the solution is ensured by the use of L-stable implicit temporal integrator and the use of appropriate mesh density. Boundary conditions are weakly imposed by computing numerical flux at the boundaries’ provided boundary values. For each time step, a residual vector is built and passed to the implicit solver to evaluate the numerical vector at the next time step. For simulations ran with VERTEX-CFD, linear basis functions were used, and all numerical methods employed in this analysis were second-order accurate in space. Mesh-refinement studies were conducted using a grid convergence index approach with a constant refinement factor of 2 to minimize discretization errors and verify that reported results were grid independent. Consequently, the results presented for code-to-code verification in this study come from fine-grid simulations. VERTEX-CFD results were compared against OpenFOAM and numerical results from Gürbüz and Tezer-Sezgin (2019) and were found to be in close agreement. Heated lid-driven cavity simulations in VERTEX-CFD and OpenFOAM yield results with expected second-order accuracy, matching utilized solvers. With addition of the obstacle, this expected order of accuracy was not recovered, possibly due to issues with realizing the imposed boundary conditions. ParaView was used in post-processing to produce the temperature and vorticity contours reported herein. Relative to OpenFOAM, VERTEX-CFD was shown to more closely match the temperature and vorticity contours reported by Gürbüz and Tezer-Sezgin (2019). These conclusions hold true as Gr is increased, which suggests the Bouissinesq approximation has been properly implemented, and that VERTEX-CFD is accurately capturing the underlying physics being simulated.