Semi-Confined Flows

Underlying Flow Regime 3-34

Evaluation

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).

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

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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.

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