Numerical Investigations of Rotating Liquids with the DLR THETA code

Abstract

Spin-up from rest (Rossby number Ro=1) for a completely fluid-filled cylinder (R = 0.707m, H = 2m) has been analysed analytically and numerically. As grounds for the analytical analysis the Wedemeyer model [38] along with its weaknesses has been investigated. It was found that contradictions exist in literature how to implement a non-linear Ekman compatibility condition. The governing partial differential equation (PDE) describing the circumferential velocity over the radius and time has been solved numerically applying MATLAB’s pdepe solver. Numerical studies applying the DLR THETA solver have been conducted for two liquids, water (1bar, 300K) and liquid hydrogen (LH2; 1bar, 22.91K). Furthermore, it has been investigated whether THETA is capable of holding an initialized rotating solution stable (initialization, Ro=0). Generally, one can conclude that a second order upwind scheme (QUDS) is more precise than a central differencing scheme (CDS), that the errors become smaller for larger dynamic viscosities ν (water always shows smaller errors than LH2) and lower rotational velocities Ω. Overall, the THETA results on the structured grids show what the analytical analysis predicts and mirror the expected physical behavior for the transients and the steady state solution good and very good, respectively. It is not clear why the computations on unstructured grids do not mirror the expected physical behavior. DLR DLR – Numerical Investigations of Rotating Liquids with