UFR 3-34 Evaluation

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Comparison of CFD Calculations with Experiments

In this section we first present major results of RANS computations of the considered flow performed with different turbulence models [7] and their comparison with the experimental data (sub-section 6.1). Then, in sub-section 6.2, results are presented of the scale-resolving simulations (enhanced RANS-LES methods [8], [9] and WRLES [6]). This sub-section begins with a comparison of flow visualizations from different simulations, which visually display turbulence resolving capabilities of the approaches used. Then, a comparison with the experimental data is shown for the main body of these simulations.

RANS Calculations

The 2DWMH flow has been computed and discussed in numerous RANS studies both by individual researches and in the framework of different collaborative projects and workshops. So below we present only a concise outline of major findings of these studies based on quite representative information on performance of different RANS models available at https://turbmodels.larc.nasa.gov/nasahump_val.html [7]. The models (see Table 5) include: four linear eddy viscosity models (one-equation model of Spalart & Allmaras (SA model) [31], this model with the Rotation-Curvature correction (SACC) [32], the two-equation k-. Shear Stress Transport of Menter (SST) [33]) and the two-equation k-kL model of Menter & Egorov and Abdol-Hamid (k-kL-MEAH2015 [34]) and one differential Reynolds Stress Model (RSM), namely the SSG/LLR-RSM-w2012 model [35] which “blends” the Speziale-Sarkar-Gatski (SSG) model [36] in the near wall flow region and Launder-Reece-Rodi (LRR) model [37] in the outer region.

Figures 8, 9 show plots of distributions of the pressure and friction coefficients over the hump predicted by different linear eddy viscosity models (Fig. 8) and by the RSM (Fig. 9) with the use of the two NASA codes (structured code CFL3D and unstructured code UNS3D) together with the corresponding experimental data. The figures show that in terms of agreement with the data, none of the models ensures accurate prediction of the pressure and friction distributions and that all of them considerably over-predict the reattachment location and the length of the separation bubble. Other than that, the k-kL-MEAH15 model exhibits a very poor prediction of Cf. The shortest bubble is predicted by the RSM, but it still remains roughly 25% longer than in the experiment. Moreover, as noted in [38], the SSG/LLR-RSM-w2012 predicts an unnatural back bending of the streamline near reattachment. (see Fig. 10).

Figure 8: Comparison with experiment of streamwise distributions of the pressure (a) and friction (b) coefficients predicted by linear eddy-viscosity turbulence models [7]

Figure 9: Same as in Fig. 8 for RSM model SSG/LLR-RSM-w2012 [7]

Figure 10: Streamwise velocity contours and streamlines predicted by SSG/LRR-RSM-w2012 RANS model [7]

Note that the over-prediction of the length of the separation bubble by RANS models is commonly associated with a dramatic underestimation of the peak of the Reynolds shear stress in the separated shear layer, which is typical of these models. The latter trend is clearly seen in Fig. 11.

Figure 11: Reynolds shear stress profiles predicted by linear eddy-viscosity (a) and RS (b) RANS models at x/c = 0.8 [7]

RANS-LES Hybrids and Wall Resolved LES

Sensitivity Tests

As mentioned above, the hybrid RANS-LES simulations presented and briefly analyzed in this sub-section were carried out in the framework of the collaborative EU project Go4Hybrid with the use of “mandatory” computational problem setup and grid outlined in section 5. Although both setup and grid had been carefully designed based on results of previous studies of the 2DWMH flow, no sensitivity studies aimed at evaluation of the effect of computational uncertainties had been performed. In contrast to this, within the WRLES investigation [6], such studies were carried out. They included evaluation of the following effects:

• SGS model (static SGS model of Vreman vs. no-model simulation (ILES)).
• Size of the domain in the uniform (spanwise) direction (0.2c vs. 0.4c).
• Grid-refinement (850 million vs. 420 million grid points in the wide domain simulations).
• Shape of incoming upstream boundary layer (velocity and Reynolds stress profiles from the DNS of the zero pressure gradient turbulent boundary layer at Re. = 5000, which matches the experimental skin-friction, vs. the mean velocity profile available from RANS, which matches the experimental velocity profile – see Fig. 4).
• Top wall contour (original, shown in Fig. 5 vs. the contour with 50% increased displacement).
• Mach number (0.2 vs. the experimental value of 0.1) and tunnel back pressure (pb/pref = 0.998 vs. 1.001).

Results of all these studies are discussed in detail in [6], and so we do not present them here. Note only that, although all the effects listed above result in some subtle alterations of the obtained solutions, they do not cause any significant change of the major predicted flow characteristics. For example, the minimum and maximum values of the coordinate of the reattachment point xreattach/c, whose prediction in the considered flow is the most challenging, in all these simulations varies from . 1.059 up to . 1.091 (the experimental value is . 1.1).

Flow Visualizations

Figures 12, 13 show flow visualizations from simulations carried out with TAU and NTS codes within different hybrid RANS-LES approaches. Analysis of these figures allows drawing the following conclusions.

Figure 12: Comparison of snapshots of vorticity magnitude in XY-plane and on the hump wall from simulations performed with NTS code. (a): zonal RANS - IDDES with interface at x/c = -1.0; (b): non-zonal DDES with Δmax; (c): non-zonal DDES with ΔSLA.

Figure 13: Same, as in Fig. 12, from zonal RANS-IDDES performed with TAU code (a), (b) and NTS code (c). (a): interface at x/c = -1.0; (b) and (c): at x/c = 0.5

First, the zonal RANS-IDDES combined with both STG [13] and SEM [14], [15] ensure a rapid formation of developed 3D turbulence downstream of the RANS-IDDES interface independently of its location (in the zero pressure gradient boundary layer at x/c=-1.0 or right upstream the separation at x/c=0.5). However, turbulent structures in the close vicinity of the interface predicted in the TAU and NTS simulations look somewhat different (compare frames (a) in Figs. 12 and 13 and frames (b) and (c) in Fig.13). This is not surprising considering a significant difference of the turbulence generators used in the codes. At the same time, further downstream no tangible qualitative difference of the resolved turbulence is observed. Hence, judging by the flow visualizations, both generators ensure rather short relaxation lengths within the two codes. Second, all the zonal simulations indicate a resolution of fine turbulent structures compatible with the cells sizes in the “focus” region located downstream of the separation point, thus suggesting that the unstructured TAU code using the LD2 scheme provides low numerical dissipation comparable with that of the higher-order structured NTS code. Finally, a comparison of the flow visualizations from the zonal RANS-IDDES (Fig. 12 (a)) and global DDES with the shear layer adapted length scale .SLA (Fig. 12 (c)) shows that downstream of the separation both approaches return similar solutions and, in particular, ensure a rapid break-up of the separated shear layer and transition to developed 3D turbulence. In contrast to this, the original DDES with .max (Fig. 12 (b)) reveals a considerable delay of formation of the resolved 3D turbulent structures in the separated shear layer. This supports the high efficiency of the .SLA definition of the subgrid length scale in terms of the mitigation of the grey area.

Figure 14: Instantaneous iso-surface of Q-criterion coloured by streamwise velocity: (a) WRLES [6], Q = 150U0/c; (b): zonal RANS-IDDES with interface at x/c = -1.0 from simulation performed with the NTS code [8], [9] Q = 20U0/c

The last flow visualizations presented in Fig. 14 give an idea about the considerable difference of the size of turbulent structures resolved by the WRLES [6] and by hybrid RANS-IDDES [8], [9] in the focus region of the flow.

Comparison with Experiment

Figures 15 — 19 compare distributions of the mean pressure and friction coefficients over the hump wall predicted by all the considered simulations.

Figure 15: Streamwise distributions of the pressure (a) and friction (b) coefficients from zonal RANS-IDDES simulations performed with the use of NTS and TAU codes with interface at x/c = -1.0.

Figure 16: Same, as in Fig. 15, from zonal RANS-IDDES with interface at x/c = 0.5

Figure 17: Same, as in Fig. 15, from zonal RANS-IDDES with interface at x/c = -1.0 and from non-zonal DDES with ΔSLA computed with the use of NTS code.

Figure 18: Same, as in Fig.15, from non-zonal DDES with ΔSLA and Δmax computed with the use of NTS code.

Figure 19: Same, as in Fig.15, from WRLES [6] and from zonal RANS-IDDES at x/c = -1.0 computed with the use of NTS code.

In line with the expectations based on the flow visualizations, predictions of all the hybrid simulations (see Figs. 15-18) turn out to be close to each other and, in contrast to the RANS predictions (Figs. 8, 9), they all agree well with the experiment. Other than that, Fig. 18 demonstrates that the non-zonal DDES approach combined with the length scale .SLA performs considerably better than the standard DDES (with .max) and is quite competitive with the zonal RANS-IDDES. Its skin-friction distribution is naturally free from local disturbances due to injection of synthetic-turbulence at the RANS-IDDES interface in the zonal simulations but, on the other hand, it yields a slightly over-predicted separation zone, which is a “remainder” of the grey area issue.

Figure 19 compares pressure and friction distributions computed with the use of the zonal RANS-IDDES with the interface located at x/c = -1.0 and with the use of WRLES [6]. A remarkable feature of the latter is its capability of capturing a plateau of the friction coefficient curve observed in the experiment at 0.3 . x/c . 0.1, i.e., in the region of the flow accelearation driven by a strong favorable pressure gradient which, as argued in [6], results in a tendency to relaminarization of the boundary layer [6]. All the hybrid models almost completely miss this effect and predict only a minor “dent” in the friction distribution (see Figs. 15-18). On the other hand, the WRLES predicts the reattachment point a bit earlier than in the experiment and in this respect is slightly inferior to the zonal RANS-IDDES with the interface located at x/c = -1.0 (see Table 6).

Figures 20, 21 present comparisons of the profiles of the mean streamwise velocity (Fig.20) and shear Reynolds stress (Fig. 21) at different flow cross-sections predicted by all the considered simulations and measured in the experiment¹.

(a): Zonal RANS – IDDES with interface located at x/c = -1.0

(b): Zonal RANS – IDDES with interface located at x/c = 0.5

(c): Non-zonal DDES with .SLA subgrid scale and zonal RANS – IDDES with interface located at x/c = -1.0

(d): zonal RANS – IDDES with interface located at x/c = -1.0 and Wall Resolved ILES.

Figure 20: Comparison of predicted and measured streamwise velocity profiles at different flow cross-sections

General observations based on analysis of Fig. 20 are similar to those based on the comparison of the computed and measured pressure and friction distributions. However the velocity profiles predicted by the zonal RANS-IDDES methods at 0.65 = x/c = 0.9 turn out to be somewhat more sensitive to the location of the RANS-IDDES interface than the Cf and, especially CP distributions. Other than that, in the simulations with the interface located at x/c = 0.5 the difference between the TAU and NTS codes predictions becomes a bit larger than with the interface at x/c = -1.0, which is best seen by comparing the profiles at 1.0 = x/c == 1.2 in Fig. 20 (a) and 20 (b). In general, placing the RANS-IDDES interface farther upstream of the hump (at x/c = -1.0) ensures somewhat better agreement with the experiment than placing it at x/c = 0.5. In particular, the two profiles just around the separation point (x/c = 0.65 and 0.66) are best predicted with the far-upstream interface (Fig. 20(a)), whereas the downstream interface (Fig. 20(b)) and the non-zonal DDES (Fig. 20(c)) yield a slightly too large momentum loss in this critical region. Moreover, all the simulations tend to over-predict the near-wall momentum loss around reattachment and recovery, although to a different degree. In line with the mean surface data in Fig. 17, the non-zonal DDES with .SLA (Fig. 20(c)) predicts slightly larger deviations from the experiment than the zonal computations at all considered cross-sections.

Finally, as seen in Fig.20 (d), a deviation from the experiment of the velocity profiles predicted by the WRLES is opposite and somewhat larger compared to that of the profiles predicted by the RANS-IDDES methods, which is consistent with the corresponding predictions of the skin- friction distributions.

(a):

(b):

(c):

(d):

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Contributed by: E. Guseva, M. Strelets — Peter the Great St. Petersburg Polytechnic University (SPbPU)

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