Comparison of Turbulence Models in the Flow over a Backward Facing Step

Authors: Priscila Pires Araujo; André Luiz Tenório Rezende
DIN
IJOER-NOV-2017-19
Abstract

This work presents the numerical simulation and analysis of the turbulent flow over a two-dimensional channel with a backward-facing step. The computational simulation performed in this study is based on the Reynolds equations using a technique denominated Reynolds Average Navier-Stokes (RANS). The main objective of the present work is the comparison of different models of turbulence applied to the turbulent flow over a backward-facing step. The performance of each RANS model used will be discussed and compared with the results obtained through a direct numerical simulation present in the literature. The RANS turbulence models used are k-ω, k-ε, Shear Stress Transport k-ω (SST k-ω) and the second-order closure model called Reynolds Stress Model (RSM). The Reynolds number used in all the numerical simulations constructed in this study is equal to 9000, based on the height of the step h and the inlet velocity Ub. The results are the reattachment length, the mean velocity profiles and the turbulence intensities profiles. The k-ε model obtained poor results in most of the analyzed variables in this study. Among the RANS turbulence models, the SST k-ω model presented the best results of reattachment length, mean velocity profile and contour when compared to results obtained in the literature. The RSM model found the best results of turbulence intensity profile, when compared to the models of two partial differential equations that use the Boussines hypothesis.

Keywords
backward-facing step DNS RANS turbulence models.
Introduction

The flow separation caused by an adverse pressure gradient is a common phenomenon in many practical applications in engineering. The adverse pressure gradient is the increase of the static pressure in the direction of the flow, significantly affecting the flow. In several engineering cases, the adverse pressure gradient is caused by a sudden change in geometry, leading to separation of the flow and subsequent reattachment. Such phenomenon can also be observed in devices such as electronic cooling equipment, combustion chambers, diffusers and valves. In this context, the backward-facing step is one of the most studied cases, in order to understand the effects on the flow caused by a sudden change in geometry using a simple geometry. Therefore, it has been much studied in cases of computational simulation, requiring less computational cost than other cases and presenting satisfactory results in the study of phenomena caused by the flow separation.

The present work deals with the computational simulation and analysis of the turbulent flow over a channel with a backwardfacing step by means of the construction of a relatively simple geometry with the great advantage of presenting important characteristics for the scope of the study of turbulent flows with boundary layer separation. The simulated cases in the present work are based on the study carried out by [1] using the same geometry as this one, with the objective of validating the obtained results and comparing different turbulence models, analyzing results such as the reattachment length, profiles of mean velocity, pressure coefficient and Reynolds stress components.

Conclusion

The present work carried out computational simulations of the turbulent flow over a channel with the presence of a backward-facing step with different models of turbulence that approach the methodology of Reynolds averaged equations (RANS). The model SST k-ω obtained a result for the reattachment length equal to XR = 8.50 and it was the model RANS that found the result closest to the value obtained by [1] through the direct numerical simulation, with reattachment length of XR = 8.62. The second-order RSM closure model presented the lowest value of reattachment length (XR = 5.86) and results different from that found by DNS in velocity profiles, especially in the near regions to the wall at the positions closest to the region of the collection, x/h = 4 and x/h = 8. The model k-ε obtained a value of reattachment length significantly low equal to 6.34, fact already expected since this model does not perform well in cases with pressure gradient and boundary layer separation. The RSM model obtained the best results related to the second order quantity discussed in the present study, a conclusion made when observing its profiles. This result was already expected, since it is a second-order closure model that calculates this quantity directly, unlike the other RANS models used, which use the Boussinesq Hypothesis and the turbulent viscosity modeling to calculate the quantities associated with the components of the Reynolds tensor. The k-ε model presented remarkably weak results for the analyzed second order quantity.

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