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).

Figure 10 shows the turbulent structures for this flow using the Q-criterion, (Q =S2 ? ?2 = 5 × 104, where S is the strain rate and ? is the vorticity). The dynamics of the downstream flow behind the bluff-body was largely driven by the shear layer and wake processes alone. For this Reynolds number range (sub-critical flow regime, 1000<Re<200000), both absolute and convective instabilities are present – asymmetric vortex shedding (the Bénard/von Kármán instability) and Kelvin-Helmholtz instability of the separated shear layer [5]. Investigation of the shear-layer instability was out of scope of the present work. The vortex shedding instability was periodic and had a characteristic frequency of fvs = StU?/H, where St is the Strouhal number. As a general observation for circular cylinders, the Strouhal number is independent of Reynolds number (St = 0.21) in the post-shear-layer region. The Strouhal numbers determined from the Fast Fourier transform of the sampled velocity (about 1.8×105 samples during 40 vortex-shedding periods) were St = 0.28, 0.27 and 0.30 for the SASI1, SASI2 and SASI3 runs, respectively. Results obtained by URANS (with the low-Reynolds k-? turbulence model of Launder and Sharma) and reported previously [11] were St = 0.28. This value was in reasonable agreement with the experimental data by Sjunnesson et al. [2] and Sanquer et al. [10], who measured St = 0.25 and St = 0.26, respectively. This corresponded with the LES data reported by Manickam et al. [17] (St = 0.28) and the Detached-Eddy Simulation by Hasse et al. [16] (St = 0.28) for the same Volvo configuration and identical conditions.

Figure 11 compares one-dimensional frequency spectra extracted from the present solutions at the downstream location x/H = 1.75 on the centerline of the wake. About 1.8×105 samples of the cross-flow velocities were collected (or Nvp ? 35). The spectra calculated from these time series were then averaged in the span-wise direction to increase the statistical meaning. To obtain the spectra, the Welch periodogram technique was used. The frequency was non-dimensionalized by the Strouhal shedding frequency (fvs). The spectra obtained by LES of Manickam et al. [17] and measured by Sanquer et al. [10] were added to compare the present SAS results with other numerical solutions. A ?5/3 slope is shown as well. All numerical data sets yielded very similar power spectra. However, it is clearly seen that the numerical solutions provided over-dissipative spectra in respect to the ?5/3 slope. It is worth noting that the present results were less dissipative than the LES data by Manickam et al. [17] and reproduced the same trend as the measured spectrum by Sanquer et al. [10]. It is well-known that the effect of an excessive dissipation of a numerical method leads to a rapid decay of the spectrum so that no inertial subrange can be satisfactorily captured. The over-dissipation of the present method could probably be explained by using the TVD scheme to approximate convective terms in the momentum equation, which is more dissipative compared to CDS-2. Additionally, the unstructured hexahedral/tetrahedral mesh designed for the present calculations might have added extra dissipation to the method as well. And, of course, the implemented procedure for the high frequency damping of the turbulent viscosity using the WALE sub-grid scale model may also contribute.

Figure 10: Flow structures for the Volvo test rig, case C0. Iso-surface of the Q-criterion, Q = 5×10⁴ (SAS2)

Figure 11: One-dimensional spectra of the transverse velocity in the wake for the Volvo test rig: non reactive SAS results, case C0

Inert calculations (LES)

Three non-reacting LES runs have been carried out to investigate the effects of the SGS models. For this purpose the k-equation and the Smagorinsky model with two different constants (Cs = 0.1 and Cs = 0.053, respectively ) were applied. For a quantitative validation of the present LES simulations, the averages have been computed by sampling over 50 vortex shedding periods (Nvs ).

Figure 12 shows the measured and predicted mean stream-wise velocity and its fluctuation as well as the normalized turbulence kinetic energy along the center-line behind the obstacle. In general, all three LES runs match the experimental data by Sjunnesson et al. [2] reasonably well. The discrepancies between all SGS models are negligible. The differences between the LES and the SASI3 results are small as well. The recirculation zone length was predicted as <Lr> /H = 1.28 for all LES runs (the same as for SASI3), which is in fairly good agreement with experimental data of Sjunnesson et al. [2],<Lr> /H = 1.35.

Figure 13 compares one-dimensional frequency spectra extracted from the present solutions at the downstream location x/H = 1.75 on the centerline of the wake. About 6 × 105 samples of the cross-flow velocities were collected (or Nvp ? 50). For sake of completeness, the spectrum obtained by SASI3 was added to assess the dissipative properties of the SAS and LES results. It can be seen clearly that the spectra obtained by LES collapsed well and had a similar distribution, while the SAS spectrum became more dissipative after f/fvs = 2.5. The Strouhal numbers are St = 0.27, 0.29 and 0.28 for the LESI1, LESI2 and LESI3 runs, respectively. These values were in reasonable agreement with the experimental data by Sjunnesson et al. [2] and Sanquer et al. [10], who measured St = 0.25 and St = 0.26, and corresponded also well with the SAS runs.

Figure 12: Normalized mean stream-wise velocity (a), its fluctuations (b) and normalized turbulence kinetic energy (c) in the wake centerline for the Volvo test rig, case C0