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Selected Case Studies
Published in Clement Kleinstreuer, Theory and Applications, 2017
Numerical method. The solution of the time-varying velocity field has been carried out with the validated finite-volume-based algorithm discussed in Sect. 4.1.2 (i.e., CFX-4 from AEA Technology) with user- Fortran programs added to account for the blood rheology, the input pulse, and the hemodynamic parameters. A structured, multiblock, body-fitted coordinate discretization scheme was employed. All flow equations were spatially discretized to be second-order accurate using a higher-order upwind scheme. The upwind scheme used has been derived by integrating the fluxes over the control volume and is, hence, completely conservative and consistent with the control volume formulation (Shyy et al., 1992). Temporal discretization was achieved using the first-order fully implicit Euler difference procedure, and it was found that 150 nonuniform time steps sufficiently resolved the velocity and shear stress fields as well as the pathline tracks. For a constant Δt ≤ 0.005, experiments with second-order temporal methods produced no significant changes in the solution, most likely due to the mildly varying input pulse. Evaluation of the resulting coupled nonlinear equations was performed iteratively using a Picard linearization and applying an algebraic multigrid technique. The outer iteration procedure was stopped when the global mass residual had been reduced from its original value by three orders of magnitude. To ensure that a converged solution had been reached, the residual reduction condition was increased to 10−4 and results were compared. The stricter convergence criterion produced a negligible effect on both velocity and wall shear stress fields. Momentum residuals were also monitored and found to be on the order of the required accuracy at convergence.
CFD-based response surface methodology for rapid thermal simulation and optimal design of data centers
Published in Advances in Building Energy Research, 2020
A general purpose CFD code is used to construct the high-fidelity 3D HT/CFD model to generate the training data and to be compared with the RSM model. Reynolds-average Navier-Stokes (RANS) equations are solved for mass, momentum, and energy equations to obtain the full HT/CFD results. The convergence criteria are set to be less than 10−4 in residuals for all computed variables. In some cases where set criteria cannot be reached, the quantity of interests are monitored to stabilize to a constant value within less than 1% of a difference for a convergence to be reached. The gradients in spatial discretization are selected as least square cell based. The pressure-velocity coupling scheme used is the SIMPLE algorithm. Second-order upwind schemes is used for momentum and energy equations while the first-order upwind scheme is used for turbulent kinetic energy and turbulent dissipation rate equations. The standard k-ε turbulence model with the standard wall function is utilized for all of the HT/CFD models.
Code-to-Code Comparison for a PbLi Mixed-Convection MHD Flow
Published in Fusion Science and Technology, 2020
S. Smolentsev, T. Rhodes, Y. Yan, A. Tassone, C. Mistrangelo, L. Bühler, F. R. Urgorri
ANSYS FLUENT uses a finite-volume method.27 A pressure-based solver was employed that includes second-order approximations for the pressure gradient and a second-order upwind scheme for the convective terms in the energy and momentum equations. The upwind scheme requires cell-centered values for each cell and cell-centered gradients in the upstream cell. In FLUENT, a Green-Gauss node-based scheme is used for gradient evaluation. Time marching is based on the second-order time-discretization scheme with a constant time increment of 0.01 s. The mesh size was similar to the medium mesh in the computations by HIMAG, i.e., 236 × 80 × 80. The convective outlet boundary condition is used at the exit of the duct at x = 1 m. A hyperbolic function–based coordinate transformation was applied to cluster the nodes inside the boundary layers. There were at least ten nodes inside each boundary layer. Mesh sensitivity studies were not performed. The time interval is 747 s of which a 600-s subinterval was used for averaging results in time. The entire computation took 20 days using a single CPU 16-core workstation.
Modeling of Transport Processes in Liquid-Metal Fusion Blankets: Past, Present, and Future
Published in Fusion Science and Technology, 2023
The customized ANSYS FLUENT used by a fusion group at the Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, Spain, also utilizes the electric potential. In this finite-volume code, a pressure-based solver was employed that includes second-order approximations for the pressure gradient and a second-order upwind scheme for the convective terms in the energy and momentum equations. The upwind scheme requires cell-centered values for each cell and cell-centered gradients in the upstream cell. The Green-Gauss node-based scheme is used for gradient evaluation. Time marching is based on the second-order time discretization scheme. The code was applied to the analysis of MHD flows and heat transfer in the EU’s DCLL blanket,78 and more recently to the EU’s WCLL blanket79 and tritium transport.80 ANSYS FLUENT was also used at the Bhabha Atomic Research Center, India, in MHD computations for the Indian LLCB test blanket module for ITER (see, for example, Refs. 81 and 82). The MHD module of FLUENT is a finite-volume and pressure-based segregated solver. The electric potential formulation in FLUENT has been used. The SIMPLE algorithm for pressure velocity coupling and the first-order upwind scheme were used along with a least-squares cell-based algorithm for spatial discretization. Solutions at high Ha numbers were obtained by gradually increasing the magnetic field from a lower value and adjusting the relaxation parameter. The converged solution was verified by checking the residuals of velocity, pressure, and current distribution and by monitoring the residuals for a sufficient number of iterations until there were no significant changes between successive iterations.