Prediction of outer layer mixing lengths in turbulent boundary layers

AIAA Journal ◽  
1977 ◽  
Vol 15 (4) ◽  
pp. 591-592 ◽  
Author(s):  
Ralph D. Watson
Keyword(s):  
Boundary Layers ◽  
Outer Layer ◽  
Turbulent Boundary Layers

Finite-difference outer-layer, analytic inner-layer method for turbulent boundary layers

AIAA Journal ◽  
1989 ◽  
Vol 27 (1) ◽  
pp. 15-22 ◽  
Author(s):  
Richard A. Wahls ◽  
Richard W. Barnwell ◽  
Fred R. DeJarnette
Keyword(s):  
Finite Difference ◽  
Boundary Layers ◽  
Outer Layer ◽  
Turbulent Boundary Layers ◽  
Layer Method

The possibility of drag reduction by outer layer manipulators in turbulent boundary layers

1988 ◽  
Vol 31 (10) ◽  
pp. 2814 ◽  
Author(s):  
Alexander Sahlin ◽  
Arne V. Johansson ◽  
P. Henrik Alfredsson
Keyword(s):  
Drag Reduction ◽  
Boundary Layers ◽  
Outer Layer ◽  
Turbulent Boundary Layers

Outer layer similarity in fully rough turbulent boundary layers

2005 ◽  
Vol 38 (3) ◽  
pp. 328-340 ◽  
Author(s):  
M. P. Schultz ◽  
K. A. Flack
Keyword(s):  
Boundary Layers ◽  
Outer Layer ◽  
Turbulent Boundary Layers

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

2019 ◽  
Vol 880 ◽  
pp. 284-325 ◽  
Author(s):  
Tobias Gibis ◽  
Christoph Wenzel ◽  
Markus Kloker ◽  
Ulrich Rist
Keyword(s):  
Shear Stress ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Outer Layer ◽  
Turbulent Boundary Layers ◽  
Similarity Analysis ◽  
Mean Flow ◽  
Self Similarity ◽  
Displacement Thickness ◽  
Characteristic Scales

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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