UFR 3-36 Best Practice Advice

HiFi-TURB-DLR rounded step

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Description

Test Case Studies

Evaluation

Best Practice Advice

References

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 and Boundary Conditions

With the DLR-TAU Code 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 when a cheaper negative Spalart-Allmaras turbulence model (SA-neg) was applied. Results of this study are given in Fig. 7. Minor deviations (not visible) only vanished for a distance larger than ${179H}$.

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

Besides studying the far-field position, three simulations were performed to study the sensitivity of the inlet position: the upstream section of the curved step was extended, a Dirichlet boundary condition was applied and laminar-turbulent transition was considered applying a RANS-based transition transport model. The results showed no significant effect and did not change the incipient character of the flow, however, an influence of the predicted skin friction coefficient distribution of the SSG/LRR-$\omega$ model in the recovery region was observed. As the RANS computations were performed to design the testcase, no DNS data were initially available to evaluate this influence.

Physical Modelling

In the early design phase of the testcase, five different RANS turbulence models already released in the DLR-TAU code and one additional model modification were used for assessment of the flow.

• 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]

For the detailed analysis of the flow only the SSG/LRR-$\omega$ model was evaluated, results for the other RANS turbulence models are not given in detail. An indication of the performance of these models is displayed in Fig. 8.

Figure 8: Skin friction (left) and pressure coefficient (right) distributions for different RANS turbulence models

Considering the skin friction coefficient distribution, the SA-neg turbulence model shows very good agreement with the DNS results, while the corrections RC + QCR outlined above moves the flow closer to separation. Adding the LowRe modifiction yields results in between the original SA-neg and the SA-neg-RC-QCR model. Predictions of the Menter-SST turbulence are close to separation, adding the corrections RC + QCR yields separated flow. The SSG/LRR-$\omega$ model shows a deviation in the recovery region downstream of the step which might be improved by extending the extent of the upstream section of the curved step.

In the ("Evaluation") section the results of the DNS are compared in detail to the results of the SSG/LRR-$\omega$ model of DLR and the Wilcox k-$\omega$ model of UniBG. From the pressure coefficient distrubution it is visible that the Wilcox k-$\omega$ model overpredicts the suction and pressure peak compared to the DNS while the SSG/LRR-$\omega$ model shows reverse behaviour. The skin friction coefficient reveals a stronger tendency of the SSG/LRR-$\omega$ model to separation compared to the DNS and the Wilcox k-$\omega$ model. Downstream of the step both models deviate in a similar manner from the DNS, however, at x/H = 5 the SSG/LRR-$\omega$ model is in better agreement with the DNS data. The streamwise velocity profiles resemble the results of the skin friction coefficient: the SSG/LRR-$\omega$ model predicts a smaller velocity in the APG region between 0 < x/H < 5 compared to the DNS and the Wilcox k-$\omega$ model and is in better agreement with the DNS data at 5 < x/H < 9. For the Reynolds stresses the SSG/LRR-$\omega$ model is not able to capture the characteristics visible in the DNS data at $0.001\leq y_{W}<0.01$ upstream of the APG region, while the Reynolds stresses are overpredicted close to the boundary-layer edge downstream the APG region. For the shear-stresses, the SSG/LRR-$\omega$ model better capture the DNS data compared to the Wilcox k-$\omega$ model.

Application uncertainties

The Reynolds numbers for the testcase 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 turbulent boundary layer upstream of 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. 9 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, not exceeded for this Reynolds number.

Figure 9: Assessment of possible re-laminarization

Recommendations for Future Work

This testcase was designed to be part of a family of testcases 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)

Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References

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