Elsevier

Ocean Engineering

Volume 222, 15 February 2021, 108559
Ocean Engineering

Assessment of algebraic subgrid scale models for the flow over a triangular cylinder at Re = 45000

https://doi.org/10.1016/j.oceaneng.2020.108559Get rights and content

Highlights

  • LES of turbulent, separated flow over a triangular cylinder at Re=45000 is presented.

  • Several algebraic SGS models (Smagorinsky, Vreman and k-equation) are assessed.

  • Blockage effects for BR=1/2, 1/3, 1/9 and 1/20 are investigated in details.

  • Some aspects of the turbulence kinetic energy dissipation rate modeling are discussed.

  • Overall, the present LES provided 10% dispersion between different SGS models.

Abstract

The turbulent separated flow over an equilateral triangular cylinder at a Reynolds number 45000 (based on the triangle edge) is studied by means of large-eddy simulation (LES). The moderate Reynolds number is chosen in order to replicate available experimental data (Laser Doppler Anemometry measurements at the Volvo test rig). The OpenFoam CFD toolbox is used for the present numerical simulations. Several algebraic subgrid scale (SGS) closures, including the conventional Smagorinsky model (Cs=0.1 and Cs=0.053), the model by Vreman (Cs=0.1) and the dynamic version of the k-equation model are investigated. The spectral analysis of the vortex shedding and the convective instabilities as well as the turbulence kinetic energy dissipation rate is presented. Some aspects of the blockage effects are investigated and compared to experimental data available in the literature. It was shown that blockage affects significantly the mean drag and pressure coefficients of the triangular cylinder. At the same time the mean velocity field is tending to similarity. Overall, all SGS models reproduced most important aspects of the flow physics of the separated bluff-body flow, including integral flow parameters and spectral characteristics with dispersion about 10%, showing a reasonable consistency with the experimental data.

Introduction

Turbulent, separated bluff-body flows are implicated in a wide range of engineering applications. However, in spite of the fact that the flow physics has been investigated intensively by both numerical and experimental methods during the last century (the first viscous flow past a circular cylinder probably was obtained by Thom (1933) in 1933), accurate simulations are of great practical importance still.

The aim of the present work is to develop a large-eddy simulation model (LES) of the turbulent, separated bluff-body flows at high Reynolds numbers, interesting for many practical applications. The present LES is based on the core numerical method implemented in the OpenFoam toolbox (Weller et al., 1998), which became very popular in industrial engineering and academic research during the last decade. Previously, several systematic studies have been performed to validate and verify the OpenFoam capabilities for several turbulent bluff-body flows at the moderate Reynolds numbers, Re=390050000 (Lysenko et al., 2012), (Lysenko et al., 2014), (Lysenko and Ertesvåg, 2018). Here, the Reynolds number is defined as Re=ρUH/μ, where U and ρ are the free-stream velocity and mass density, respectively, H is the diameter of the obstacle and μ represents the dynamic viscosity. These works presented results both the conventional approach for solution of the unsteady, compressible Reynolds-averaged Navier-Stokes equations (URANS) (Lysenko et al., 2013) and an advanced LES technique (Lysenko et al., 2012), (Lysenko et al., 2014). Lately, both inert and reactive flows over a triangular cylinder at Re50000 using unsteady Reynolds-averaged Navier-Stokes (URANS), LES and Scale-Adaptive simulations (SAS) have been investigated (Lysenko and Ertesvåg, 2018). The global descriptions of LES, SAS and RANS/URANS indicated a clear interrelation between these three approaches to simulation of the turbulent (combustion) flows (Lysenko and Ertesvåg, 2018). In general, reasonable consistency was found for these different approaches as well as satisfactory agreement between numerical simulations and measurements. However, the most accurate results were reached using the large-eddy simulations.

Scientific and engineering background to investigate triangular cylinders is commonly driven by aerospace industry, in particular, propulsion and industrial combustion systems, where bluff-body wakes are used for the flame stabilization. Also, the simplicity of configuration is quite attractive to provide fundamental research of turbulent combustion as well as computational test cases (Shanbhogue et al., 2009). Another common applications are flow metering, where triangular cylinders are commonly used as a vortex shedder in the vortex-type flow meters (Yagmur et al., 2017).

The triangular cylinder was extensively investigated experimentally and numerically in the literature (Calvert, 1967), (Okamoto et al., 1977), (Fujii et al., 1978), (Tatsuno et al., 1990), (Sjunnesson et al., 1991), (Sanquer et al., 1998), (Obara and Matsudaira, 1998), (Zheng et al., 2016), (Yagmur et al., 2017). Among them, two experimental works can be highlighted, which provided the local flow characteristics, suitable for the detail validation of large-eddy simulations. Calvert (1967) presented Hot-Wire Anemometry (HWA) measurements of the bluff-body wake at the blockage ratio, BR=1/10. Sjunnesson et al. (1991) provided Laser Doppler Anemometry (LDV) measurements of the wake at BR=1/3. However, both studies missed the key flow parameters like forces coefficients. Yagmur et al. (2017) investigated the triangular cylinder both by means of Particle Image Velocimetry (PIV) and LES for the highest Reynolds number, Re=11600. Dynamics of the wake (in terms of Strouhal number) was investigated extensively as well by many researchers, however, experimental results for the local dynamics of the separated shear layers are not available yet. It is worth to notice, that important information related to the key integral flow features like the lift, drag and pressure forces is limited. Okamoto et al. (1977) and Tatsuno et al. (1990) presented the drag coefficient for the Reynolds number, Re=22000 and Re=90000, respectively. Yagmur et al. (2017) reported the drag using LES for (Yagmur et al., 2017). The alternative measured data of the drag force can be found in NACA TN3038.

The present study we investigated the turbulent flow over triangular cylinder at different configurations (BR=1/3 and BR=1/9,1/20) to replicate the experimental data by Calvert (1967) and Sjunnesson et al. (1991) and investigate the blockage effects. The lift, drag and pressure coefficients are reported and compared with the available data as well. An assessment of the several subgrid scale (SGS) models for the turbulent flow over an equilateral triangular cylinder is provided. The conventional Smagorinsky model (Smagorinsky, 1963) with two constants (Cs=0.1 and Cs=0.053), the Vreman model (Cs=0.1) (Vreman, 2004) and the dynamic version of the k-equation eddy-viscosity model (Yoshizawa, 1986) are investigated. Some numerical aspects, like the spectral analysis of the convective instability of the separated shear layers and the turbulence energy dissipation, missed in our previous study (Lysenko and Ertesvåg, 2018), are reported. The Volvo test rig has been chosen due to the available LDV measurements of the velocity (Sjunnesson et al., 1991).

In the present work we utilized the standard numerical platform (the second-order finite-volume method) implemented in the OpenFoam code. This numerical approach has been validated in details for the bluff-body flows during the last decade (e.g., (Lysenko et al., 2012), (Lysenko et al., 2014), (Cao and Tamura, 2015), (Robertson et al., 2015), (Cao and Tamura, 2016), (Lysenko and Ertesvåg, 2018), (Zahiri and Roohi, 2019)) and can be recommended to simulate the turbulent separated flows.

The paper is divided into five main sections. The first section of the paper describes the mathematical modeling and numerical aspects. Then, a general description of the test case is given. Finally, computational results are presented, results are analyzed and discussed, and on the top of that conclusions are drawn.

Section snippets

Brief description of mathematical modeling numerical aspects

In order to be consistent with authors’ previous results (Lysenko et al., 2012), (Lysenko et al., 2014), (Lysenko and Ertesvåg, 2018), the compressible flow and related numerical setup were considered despite of the fact that the actual Mach number was close to the incompressible limit.

Experimental set up

The description of the Volvo test rig and relevant experimental data was provided in (Sjunnesson et al., 1991). Fig. 1 shows a schematic drawing of the test section. The set-up consisted of a straight channel with a rectangular cross-section, divided into an inlet section length 0.5 m and a channel passage section length L=1 m and 0.12 m ×0.24m cross-section. The inlet section was used for flow straightening and turbulence control. The air entering the inlet section was distributed over the

Results

This section presents the obtained results in terms of the first order statistics and one-dimensional spectral data. The hat, the tilde and the bar marks denoting Favre-averaging and filtering Favre-averaging were omitted for simplicity.

Overview

High fidelity LES on relatively coarse grids is important for practical engineering applications. Several modeling aspects may be considered. On one hand, when coarse grids are used in LES, the effect of the numerical modeling on the flow resolution is increased (Lloyd and James, 2016). On the other hand, effects of the subgrid modeling become more pronounced as well. The unstructured grid strategy, which is attractive for any practical applications due to ability to focus the refinement more

Conclusions

A large eddy simulation of the turbulent flow over an equilateral triangular cylinder at Reynolds number, Re=45000 (based on the triangle edge) has been performed to replicate the well-known experimental of the Volvo test rig. A fully-conservative finite-volume method of the second-order accuracy in space and time, based on the OpenFoam technology, was used. The family of the algebraic, eddy-viscosity SGS models, including the conventional Smagorinsky, Vreman and dynamic version of k-equation,

CRediT authorship contribution statement

D.A. Lysenko: Conceptualization, Methodology, Formal analysis, Writing - original draft. I.S. Ertesvåg: Supervision, Writing - review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

We are grateful to the Norwegian e-infrastructure for Research and Education (Uninett Sigma 2) for providing the HPC computational resources and useful technical support (project No. NN9400K).

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