An Elliptic Blending Turbulence Model-Based Scale-Adaptive Simulation Model Applied to Fluid Flows Separated from Curved Surfaces

Xianglong Yang,Lei Yang

doi:10.3390/app12042058

Abstract

On the basis of a previously developed elliptic blending turbulence model (SST–k–ω–φ–α model), a scale-adaptive simulation (SAS) model is developed by following Menter and Egorov’s SAS concept. An SAS source term, which is related to the ratio of the modeled turbulence scale to the von Kármán length scale, is introduced into the corresponding length-scale determining equation. The major motivation of this study is that the conventional unsteady Reynolds-averaged Navier–Stokes (URANS) models provide only large-scale unsteadiness. The introduction of the SAS term allows the proposed SAS model to dynamically adjust to resolved structures in a URANS framework because this term is sensitive to resolved fluctuations. The predictive capabilities of the proposed SAS model are demonstrated by computing the complex flow configurations in three cases with flow separation from curved surfaces, namely, three-dimensional (3D) diffuser flow, two-dimensional (2D) periodic hills flow, and 2D U-turn duct flow. For comparison, the results predicted by the SST–k–ω–φ–α model and the Menter and Egorov’s SAS model (SST–SAS) are provided. The results are also compared with the relevant experimental, direct numerical simulation, and large eddy simulation data. The results show that the SST–k–ω–φ–α model cannot capture the critical features for all three flows, and that the SST–SAS model is able to predict the results reasonably well. The proposed SAS model is capable of resolving more portions of the turbulence structures, and it yields the best results in all the cases.

Highlights

Turbulence is a three-dimensional (3D), time-dependent, nonlinear, and ubiquitous phenomenon in nature
The performance of the proposed scale-adaptive simulation (SAS) model was illustrated by computing the complex flow configurations in three cases with boundary layer separation from curved surfaces, namely, the 3D asymmetric diffuser flow, 2D periodic hills flow, and 2D U-turn duct flow
An SAS model was developed on the basis of a previously developed elliptic blendingbased Reynoldsaveraged Navier–Stokes (RANS) model

Summary

Introduction

Turbulence is a three-dimensional (3D), time-dependent, nonlinear, and ubiquitous phenomenon in nature. LES is based on the approach of resolving large turbulent structures in space down to the grid limit everywhere in the flow. If the grid resolution is not sufficiently fine, the SAS model provides the URANS performance, which is reasonably capable of handling the flow This feature seems attractive and can be regarded as a safeguard in the simulation of complex industrial flows [3]. The present authors [14] developed an elliptic blending turbulence model by transforming the k–ε-based BL − v2/k model of Billard and Laurence [8] into a k–ω system. The only one found in the literature was developed by Krumbein et al [15] They proposed an SAS model based on the elliptic relaxation model of Hanjalicet al.

Model Formulation and Implementation

Results and Discussion

H H x Inlet

Conclusions

Methods