Generating a Transient Flow Field Solver Through Computational Fluid Dynamics Using Liquid Metal*

Computational Fluid Dynamics (CFD) is an exciting approach when it comes to monitoring liquid metal flow fields inside a fusion reactor channel. This study combines 2 of 3 ways to monitor fluid dynamics using numerical and theoretical analysis, with the third being experimental. For this project a combination of theoretical derivation (steady-state/time-independent) and CFD programming (temporal/transient) were utilized to compute the Poiseuille flow field by using reduced Navier-Stokes Equations (NSEs) through MATLAB (from scratch). The NSEs are the governing equations derived from the principles of Newton’s second law ΣF = ma which is based on the conservation of momentum. For the fluid flow to be solved, the two given governing equations in NSEs that all fluid flow simulations must follow were applied. These governing equations are that mass and momentum are conserved throughout the process. By using these equations, the Finite Volume Method (FVM) was utilized to create discretized analytical equations. Based on the results of this code, the distribution of the velocity and pressure for Poiseuille flow will be obtained for the channel, and the effects of the initial/boundary conditions on the distribution of the instantaneous flow will be revealed. The numerical solution will also be verified by comparing the CFD code’s steady-state output to the analytical solution of Poiseuille flow.