Turbulent separated inert and reactive flows over a triangular bluff body

Application Challenge AC2-12 © copyright ERCOFTAC 2019

Evaluation

Comparison of test data and CFD

Introduction

All simulated cases are listed in Table 6, where the following abbreviations are used: Code – the computational code: Ansys Fluent (AF) or OpenFOAM (OF), M – mesh: according to Section 4.2, N – convective schemes: the second-order upwind (SOU), the normalized variable diagram (NVD) (γ ), the total variation diminishing (TVD), CF – flow conditions: according to Table 1, TR – the approach for solution of the Navier-Stokes equations, (U)RANS , SAS or LES, TM – turbulence model: k-ε (SKE), k-ω SST (SST), k-equation eddy-viscosity sub-grid scale model (TKE), Smagorinsky (SMAG), TCM – turbulence-chemistry interaction model: Eddy Dissipation Concept (EDC), Turbulent Flame Closure (TFC), CH – chemistry mechanism: according to Section 2.5.2, R – radiation sub-model: P1 or none, Sct – turbulence Schmidt number, Prt – turbulence Prandtl number, Two and Twc – temperature boundary conditions for the obstacle and channel walls, respectively: zero-gradient (zg), isothermal (Tisoth = 300 K and Tisoth = 600 K for cases C1 and C2, respectively) or conjugate fluid-solid heat transfer (CHT). For a quantitative validation of the present SAS and LES simulations, the averages have been obtained from the computational results by sampling over 40 vortex shedding periods (Nvs ) for the SAS non-reactive solution and three flow-through times for the combustion SAS and LES. The flow-through time was defined as the ratio between the axial length of the computational domain to the jet bulk velocity.

Table 6: Run matrix for the Volvo test rig.

Inert calculations (SAS,URANS)

Figure 9 shows the measured and predicted mean stream-wise velocity and its fluctuation as well as the normalized turbulence kinetic energy along the central-line behind the obstacle (for case C0). For the sake of completeness, besides the LDA data by Sjunnesson et al. [2], the LDV data by Sanquer et al. [10], who had investigated inert bluff-body wakes as well as premixed bluff-body combustion, were added to the plot. The experimental data by Sanquer et al. [10] have been obtained for the Reynolds number, Re ≈ 6×10³, based on the bluff body height (case i3). Another important parameter in this experiment, the blockage ratio (the ratio between bluff-body to channel heights) was 0.33 as in the Volvo test rig.

Apart for the present SAS calculations, the author’s previous URANS results [11] obtained with the low-Reynolds-number k-? turbulence model of Launder and Sharma were included for comparison, as well as LES and DES results published by Hasse et al. [16]. Three inert SAS calculations have been carried out. SASI1 and SASI2 cases differed only by the applied discretization schemes for the convective terms, TVD vs. NVD. The SASI3 case was calculated using the Gamma scheme as well, to check the influence of the grid resolution. In their computations, Hasse et al. [16] utilized the Ansys CFX solver and the CDS-2 scheme for LES, and a bounded second order upwind biased discretization scheme for DES.

Figure 9: Normalized mean stream-wise velocity (a), its fluctuations (b) and and normalized turbulence kinetic energy (c) in the wake centerline for the Volvo test rig , case C0

Overall, there is a reasonable match between numerical and experimental data. One can observe the same trends between all numerical runs for the axial distribution of the mean stream-wise velocity. For the stream-wise RMS velocity the SASI3 case provided the best result. The normalized turbulence kinetic energy, Kn = ?k//U?, where the turbulence kinetic energy k = 3/4(u’2 + v’2), is shown in Fig. 9c. Results from SASI1 and SASI2 predicted quite well the measured turbulence kinetic energy in the near wake (up to x/H = 2), while over-predicting it afterwards. In contrast, the SASI3 calculations matched well the kinetic turbulence energy in the far wake, while under-predicting it in the near wake. The difference between measurements and numerical calculations for the mean recirculation zone length <Lr> is significant and often subject to discussion. By definition, the recirculation length <Lr> corresponds to the distance between the base of the triangular cylinder and the sign change of the centerline mean stream-wise velocity. The quality of <Lr> predictions may be considered as the deciding factor for the agreement between the experimental and numerical results. Some discrepancies were observed between mean velocities inside the recirculation zone. These deviations can be affected by the earlier laminar-turbulent transition in the separating shear layers, but also partially due to a lack of statistical convergence. In the present SAS, the recirculation zone length was predicted as <Lr>/H = 1.4 for the SASI1 and SASI2 runs, which is in fairly good agreement with experimental data of Sjunnesson et al. [2], <Lr>/H = 1.35. It is interesting that Hasse et al. [16] predicted the recirculation lengths with the LES and DES models similar to the present SAS results (< Lr > /H = 1.18), which deviated only about 11% from the experimental measurement (< Lr > /H = 1.33).

Contributed by: D.A. Lysenko and M. Donskov — 3DMSimtek AS, Sandnes, Norway