UFR 3-36 Best Practice Advice

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Best Practice Advice

Key Physics

The key flow physics to be accurately captured in this UFR are turbulent boundary layers subjected to an adverse pressure gradient over a curved surface with and without separation and reattachment.

Numerical Modelling

With the FV-Code TAU a second order discretization for convective fluxes was used including the turbulence model. For grid details please refer to the previous section ("CFD Methods"). Otherwise, standard rules of grid generation apply. To ensure the upper boundary will not influence the flow over the curved wall, a study was performed to find the optimal position for the far-field boundary condition. It was found that a distance to the curved wall less than ${179H}$ shows an influence on the computed pressure distributions. With a distance larger than ${179H}$ the influence vanishes. These results were generated during the initial design stage of the testcase applying a cheaper negative Spalart-Allmaras turbulence model (SA-neg). Results of this study are given in Fig. 7.

Figure 7: Pressure distributions for varying distances of the far-field boundary condition

Physical Modelling

The test case for this numerical experiment needs to be well-defined and all boundary conditions as well as the flow conditions at suitable reference positions need to be specified. The reason behind this is to produce a reliable basis for subsequent DNS computations of the test case. Therefore, a study of the grid space was conducted. Three key features were investigated: the far-field position and the inlet position and laminar-turbulent transition. Each of these features was varied to ensure they do not affect the flow behavior.

Furthermore, five RANS turbulence models already released in TAU and one additional model modification were used for the simulations:

• Four variations of the one-equation Spalart-Allmaras RANS turbulence model:
  • SA-neg [‌9]
  • Non-linear SA-neg model version with rotation and curvature correction (RC) and quadratic constitutive relation (QCR) [‌10][‌11]: SA-RC-QCR
  • SA model version with Low-Re-modifications [‌12][‌13]: SA-LRe
  • Non-linear SA-neg model version with rotation and curvature correction (RC) and quadratic constitutive relation (QCR) as well as Low-Re-modifications: SA-RC-QCR-LRe
• Two variations of the two-equation Menter SST RANS turbulence model:
  • SST2003 [‌14]
  • Non-linear model version SST2003-RC-QCR [‌15][‌11]
• The seven-equation omega-based Differential Reynolds stress turbulence model SSG/LRR-$\omega$ [‌16] including the length scale correction [‌17]

Figure 8: Skin friction and pressure coefficient distributions with different RANS turbulence models

Application Uncertainties

The Reynolds numbers used for the test case were determined, on the one hand, low enough to be affordable for DNS computations and on the other hand, high enough to avoid re-laminarization in the accelerated region of the boundary layer upstream the APG region. The latter was ensured by applying two different criteria for possible re-laminarization, the acceleration parameter

$K_{acc}=-{\frac {\nu }{\rho U_{\infty }^{3}}}{\frac {\partial p}{\partial s}}$

as well as the pressure-gradient parameter

$\Delta _{p}=-{\frac {\nu }{\rho U_{\tau }^{3}}}{\frac {\partial p}{\partial s}}$

and compared to limiting values for re-laminarization according to the literature [‌24], [‌25] and [‌26]. Here, $U_{\tau }$ is the friction velocity. Fig. 8 shows the distribution of $K_{acc}$ and $\Delta _{p}$ for the Reynolds number $Re_{H}=78,490$ together with the threshold values for both parameters, which this Reynolds number does not exceed.

Figure 8: Applied criteria for re-laminarization

Recommendations for Future Work

This test case was designed to be part of a family of test cases with varying pressure gradient and Reynolds number to provide a comprehensive data base for data-driven turbulence modeling. As soon as DNS data for the other configurations are available, these cases should be added to the test case description and evaluation.

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Contributed by: Erij Alaya and Cornelia Grabe — Deutsches Luft-und Raumfahrt Zentrum (DLR)

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Description

Test Case Studies

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Best Practice Advice

References

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