Self-similar compressible turbulent boundary layers with pressure gradients. Part 1. Direct numerical simulation and assessment of Morkovin’s hypothesis

Wenzel, Christoph; Gibis, Tobias; Kloker, Markus J.; Rist, Ulrich

doi:10.1017/jfm.2019.670

Cited by 28 publications

(84 citation statements)

References 56 publications

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“…In the inner layer below roughly y/δ 99 ≈ 0.15, the plotted profiles appear to be x-dependent for both the ZPG and PG cases. As previously seen in the relations G 0 ∼ U 2 0 in figure 1(a3-d3) and the recovery factors in part 1 (see Wenzel et al 2019), all supersonic profiles are nearly identical.…”

Section: 33supporting

confidence: 81%

“…Theρ u 2 Favre stress is shown in figure 6. As discussed in Wenzel et al (2019), a second peak is forming in the outer layer of the boundary layers for increasing PG strength besides the inner peak. This peak is localized at around y/δ 99 ≈ 0.4 for the highest subsonic PG.…”

Section: Favre Stressesmentioning

confidence: 87%

“…For the Λ c distributions, the dL 0 /dx distributions have been smoothed by applying a Savitzky-Golay filter to the L 0 distributions. Note that β RC corresponds to β K in Wenzel et al (2019).…”

Section: Similarity Parametermentioning

confidence: 99%

“…All these effects render the prediction of the compressible PG TBL intricate. In fact, not much is known about the conditions of compressible turbulent self-similarity (see also Wenzel et al 2019), despite its importance for the understanding of compressible TBLs in general, and many questions are still open. To what extent can self-similarity be achieved in the compressible regime?…”

mentioning

confidence: 99%

“…1.1. Objectives of this study Using the direct numerical simulation (DNS) data presented in the first part of this series Wenzel et al (2019), where an inner scaling is mostly employed, the main goal of the present second part is to investigate both the conditions and the limits of streamwise self-similarity for the outer layer of compressible TBLs. For this purpose, a self-similarity analysis is performed for the compressible Favre-averaged two-dimensional turbulent boundary-layer equations by using the same methodical approach as for the incompressible regime.…”

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confidence: 99%

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Self-similar compressible turbulent boundary layers with pressure gradients. Part 2. Self-similarity analysis of the outer layer

et al. 2019

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A thorough self-similarity analysis is presented to investigate the properties of self-similarity for the outer layer of compressible turbulent boundary layers. The results are validated using the compressible and quasi-incompressible direct numerical simulation (DNS) data shown and discussed in the first part of this study; see Wenzel et al. (J. Fluid Mech., vol. 880, 2019, pp. 239–283). The analysis is carried out for a general set of characteristic scales, and conditions are derived which have to be fulfilled by these sets in case of self-similarity. To evaluate the main findings derived, four sets of characteristic scales are proposed and tested. These represent compressible extensions of the incompressible edge scaling, friction scaling, Zagarola–Smits scaling and a newly defined Rotta–Clauser scaling. Their scaling success is assessed by checking the collapse of flow-field profiles extracted at various streamwise positions, being normalized by the respective scales. For a good set of scales, most conditions derived in the analysis are fulfilled. As suggested by the data investigated, approximate self-similarity can be achieved for the mean-flow distributions of the velocity, mass flux and total enthalpy and the turbulent terms. Self-similarity thus can be stated to be achievable to a very high degree in the compressible regime. Revealed by the analysis and confirmed by the DNS data, this state is predicted by the compressible pressure-gradient boundary-layer growth parameter $\unicode[STIX]{x1D6EC}_{c}$, which is similar to the incompressible one found by related incompressible studies. Using appropriate adaption, $\unicode[STIX]{x1D6EC}_{c}$ values become comparable for compressible and incompressible pressure-gradient cases with similar wall-normal shear-stress distributions. The Rotta–Clauser parameter in its traditional form $\unicode[STIX]{x1D6FD}_{K}=(\unicode[STIX]{x1D6FF}_{K}^{\ast }/\bar{\unicode[STIX]{x1D70F}}_{w})(\text{d}p_{e}/\text{d}x)$ with the kinematic (incompressible) displacement thickness $\unicode[STIX]{x1D6FF}_{K}^{\ast }$ is shown to be a valid parameter of the form $\unicode[STIX]{x1D6EC}_{c}$ and hence still is a good indicator for equilibrium flow in the compressible regime at the finite Reynolds numbers considered. Furthermore, the analysis reveals that the often neglected derivative of the length scale, $\text{d}L_{0}/\text{d}x$, can be incorporated, which was found to have an important influence on the scaling success of common ‘low-Reynolds-number’ DNS data; this holds for both incompressible and compressible flow. Especially for the scaling of the $\bar{\unicode[STIX]{x1D70C}}\widetilde{u^{\prime \prime }v^{\prime \prime }}$ stress and thus also the wall shear stress $\bar{\unicode[STIX]{x1D70F}}_{w}$, the inclusion of $\text{d}L_{0}/\text{d}x$ leads to palpable improvements.

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Section: 33supporting

confidence: 81%

Section: Favre Stressesmentioning

confidence: 87%

Section: Similarity Parametermentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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