Simulation of Flow Pulsations in Gap Geometries Using Unsteady Reynolds Averaged Navier-Stokes Modelling

Abstract

An unsteady Reynolds Averaged Navier-Stokes (URANS) based turbulence model, the Spalart-Allmaras (SA) model, was used to investigate the flow pulsation phenomenon in compound rectangular channels for isothermal flows. The computational fluid dynamics (CFD) commercial package ANSYS CFX-11.0 was used for the simulations. The studied geometry was composed of two rectangular subchannels connected by a gap, on which experiments were conducted by Meyer and Rehme [34] and were used for the validation of the numerical results. Two case studies were selected to study the effect of the advection scheme. The results using the first order upwind advection scheme had clear symmetry and periodicity. The frequency of the flow pulsations was underpredicted by almost a factor of two. Due to the inevitable numerical diffusion of the first order upwind scheme, it was more appropriate to use a second order accurate in space advection scheme for comparison with the experiments. The span-wise velocity contours and the velocity vector plots at planes parallel to the bulk flow, together with the time traces of the velocity components at selected monitor points showed the expected cross-flow mixing between the subchannels through the gap. Although the SA model does not solve directly for the turbulence kinetic energy, a kinetic energy associated with the unsteady solutions of the momentum equations was evaluated and qualitatively compared with the experimental turbulence kinetic energy. The calculated kinetic energy followed the trends of the experimental turbulence kinetic energy at the gap area, predicting two peaks at the edges of the gap. The dynamics of the gap pulsations were quantitatively described through temporal auto-correlation and auto-power spectral density functions and the numerical predictions were in agreement with the experiments. Studies on the effect of the Reynolds number and the computational length of the domain were also carried out. The numerical results reproduced the relationship between the Reynolds number and the frequency of the auto-power spectral density functions. The impact of the channel length was tested by simulating a longer channel. It was found that the channel length did not significantly affect the predictions. Simulations were also performed using the (kappa) -(epsilon) model. While flow pulsations were predicted with this model, the frequency of the pulsation was in poor agreement with the experimentally measured value.