Study of Turbulent Boundary Layers Over Rough Surfaces, with Emphasis on the Effects of Roughness Character and Mach Number

1982 ◽  
Author(s):  
M. L. Finson
Keyword(s):  
Mach Number ◽  
Boundary Layers ◽  
Rough Surfaces ◽  
Turbulent Boundary Layers

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

2019 ◽  
Vol 880 ◽  
pp. 239-283 ◽  
Author(s):  
Christoph Wenzel ◽  
Tobias Gibis ◽  
Markus Kloker ◽  
Ulrich Rist
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Mach Number ◽  
Direct Numerical Simulation ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Shear Stresses ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Self Similar

A direct numerical simulation study of self-similar compressible flat-plate turbulent boundary layers (TBLs) with pressure gradients (PGs) has been performed for inflow Mach numbers of 0.5 and 2.0. All cases are computed with smooth PGs for both favourable and adverse PG distributions (FPG, APG) and thus are akin to experiments using a reflected-wave set-up. The equilibrium character allows for a systematic comparison between sub- and supersonic cases, enabling the isolation of pure PG effects from Mach-number effects and thus an investigation of the validity of common compressibility transformations for compressible PG TBLs. It turned out that the kinematic Rotta–Clauser parameter $\unicode[STIX]{x1D6FD}_{K}$ calculated using the incompressible form of the boundary-layer displacement thickness as length scale is the appropriate similarity parameter to compare both sub- and supersonic cases. Whereas the subsonic APG cases show trends known from incompressible flow, the interpretation of the supersonic PG cases is intricate. Both sub- and supersonic regions exist in the boundary layer, which counteract in their spatial evolution. The boundary-layer thickness $\unicode[STIX]{x1D6FF}_{99}$ and the skin-friction coefficient $c_{f}$, for instance, are therefore in a comparable range for all compressible APG cases. The evaluation of local non-dimensionalized total and turbulent shear stresses shows an almost identical behaviour for both sub- and supersonic cases characterized by similar $\unicode[STIX]{x1D6FD}_{K}$, which indicates the (approximate) validity of Morkovin’s scaling/hypothesis also for compressible PG TBLs. Likewise, the local non-dimensionalized distributions of the mean-flow pressure and the pressure fluctuations are virtually invariant to the local Mach number for same $\unicode[STIX]{x1D6FD}_{K}$-cases. In the inner layer, the van Driest transformation collapses compressible mean-flow data of the streamwise velocity component well into their nearly incompressible counterparts with the same $\unicode[STIX]{x1D6FD}_{K}$. However, noticeable differences can be observed in the wake region of the velocity profiles, depending on the strength of the PG. For both sub- and supersonic cases the recovery factor was found to be significantly decreased by APGs and increased by FPGs, but also to remain virtually constant in regions of approximated equilibrium.

Compressibility and Variable Density Effects in Turbulent Boundary layers

2006 ◽  
Vol 129 (4) ◽  
pp. 441-448 ◽  
Author(s):  
Kunlun Liu ◽  
Richard H. Pletcher
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Stokes Equations ◽  
Variable Density ◽  
Turbulent Boundary Layers ◽  
Reynolds Analogy ◽  
Density Effects

Two compressible turbulent boundary layers have been calculated by using direct numerical simulation. One case is a subsonic turbulent boundary layer with constant wall temperature for which the wall temperature is 1.58 times the freestream temperature and the other is a supersonic adiabatic turbulent boundary layer subjected to a supersonic freestream with a Mach number 1.8. The purpose of this study is to test the strong Reynolds analogy (SRA), the Van Driest transformation, and the applicability of Morkovin’s hypothesis. For the first case, the influence of the variable density effects will be addressed. For the second case, the role of the density fluctuations, the turbulent Mach number, and dilatation on the compressibility will be investigated. The results show that the Van Driest transformation and the SRA are satisfied for both of the flows. Use of local properties enable the statistical curves to collapse toward the corresponding incompressible curves. These facts reveal that both the compressibility and variable density effects satisfy the similarity laws. A study about the differences between the compressibility effects and the variable density effects associated with heat transfer is performed. In addition, the difference between the Favre average and Reynolds average is measured, and the SGS terms of the Favre-filtered Navier-Stokes equations are calculated and analyzed.

Conditional statistics of Reynolds stress in rough-wall and smooth-wall turbulent boundary layers

1981 ◽  
Vol 108 ◽  
pp. 363-382 ◽  
Author(s):  
M. R. Raupach
Keyword(s):  
Surface Roughness ◽  
Boundary Layers ◽  
Rough Surfaces ◽  
Reynolds Shear Stress ◽  
Roughness Element ◽  
Threshold Level ◽  
Turbulent Boundary Layers ◽  
Quadrant Analysis ◽  
Normal Velocity ◽  
The Third

Quadrant analysis has been used to investigate the events contributing to the Reynolds shear stress in zero-pressure-gradient turbulent boundary layers over regularly arrayed rough surfaces of several different densities, and over a smooth surface. By partitioning the stress into ejections, sweeps, and inward and outward interactions, it is shown that sweeps account for most of the stress close to rough surfaces, and that the relative magnitude of the sweep component increases both with surface roughness and with proximity to the surface. The sweep-dominated region delineates a ‘roughness sublayer’ with a depth of up to several roughness element heights, in which the turbulence characteristics depend explicitly on the roughness. In the remainder of the inner (or constant-stress) layer, and in the outer layer, the flow obeys familiar similarity laws with respect to surface roughness.The difference ΔS0 between the fractional contributions of sweeps and ejections to the stress is shown to be well related everywhere to the third moments of the streamwise and normal velocity fluctuations. Experimental proportionalities are established between the third moments and δS0, and are shown to agree with predictions made from cumulant-discard theory.The time scale for the passage of large coherent structures past a fixed point, T, is assumed proportional to the mean time between occurrences in a specified quadrant of an instantaneous stress u'w’ at least H times the local mean stress u'w’, where H is a threshold level. For both the ejection and sweep quadrants and for any choice of H, it is found that T scales with the friction velocity u* and the boundary-layer thickness δ, such that Tu*/δ is invariant with change of surface roughness.

scholarly journals Eddy Viscosities and Mixing Lengths for Turbulent Boundary Layers on Flat Plates, Smooth or Rough

1988 ◽  
Vol 32 (04) ◽  
pp. 229-237
Author(s):  
Paul S. Granville
Keyword(s):  
Boundary Layers ◽  
Rough Surfaces ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Turbulent Boundary Layers ◽  
Flat Plates ◽  
Low Reynolds Numbers ◽  
Low Reynolds ◽  
Similarity Laws

Algebraic formulas are derived here for the eddy viscosities and mixing lengths of turbulent boundary layers on flat plates. The effect of low Reynolds numbers, especially on rough surfaces, is included. The formulas are based on the similarity laws and the equations of motion. Both smooth and rough surfaces are considered. The agreement with Klebanoff's measurements is excellent.

Investigation of Flat-Plate Hypersonic, Turbulent Boundary Layers With Heat Transfer

1961 ◽  
Vol 28 (3) ◽  
pp. 323-329 ◽  
Author(s):  
Eva M. Winkler
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Mach Number ◽  
Flat Plate ◽  
Skin Friction ◽  
Boundary Layers ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Reynolds Analogy

Naturally turbulent boundary layers on a cooled flat plate have been investigated at several distances from the leading edge of the plate at a Mach number of 5.2 for three rates of steady-state heat transfer to the surface. Measurements of Pitot and static pressures and of total and wall temperatures made it possible to compute velocity profiles, static-temperature profiles, and boundary-layer parameters without resorting to assumptions. The data demonstrate that the Reynolds analogy between skin friction and heat transfer is valid for all conditions of the present experiments. With increasing rate of heat transfer to the surface, the skin-friction coefficient was found to decrease, a phenomenon opposite to that predicted by theories and empirical relations. On the basis of the present data and other published results of compressible and incompressible turbulent boundary-layer skin friction, a simple relation was devised which describes closely the variation of the skin-friction coefficient with Mach number, heat-transfer rate, and momentum-thickness Reynolds number.

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