Topological evolution in compressible turbulent boundary layers

2013 ◽  
Vol 733 ◽  
pp. 414-438 ◽  
Author(s):  
You-Biao Chu ◽  
Xi-Yun Lu
Keyword(s):  
Boundary Layers ◽  
Evolution Equations ◽  
Turbulent Boundary Layers ◽  
Rate Of Change ◽  
Power Law Distribution ◽  
Flow Topology ◽  
Local Flow ◽  
Compressibility Effect ◽  
Topological Evolution ◽  
The Mean

AbstractTopological evolution of compressible turbulent boundary layers at Mach 2 is investigated by means of statistical analysis of the invariants of the velocity gradient tensor based on the direct numerical simulation database. The probability density functions of the rate of change of the invariants exhibit the $- 3$ power-law distribution in the region of large Lagrangian derivative of the invariants in the inner and outer layers. The topological evolution is studied by conditional mean trajectories for the evolution of the invariants. The trajectories illustrate inward-spiralling orbits around and converging to the origin of the space of invariants in the outer layer, while they are repelled by the vicinity of the origin and converge towards a limit cycle in the inner layer. The compressibility effect on the mean topological evolution is studied in terms of the ‘incompressible’, compressed and expanding regions. It is found that the mean evolution of flow topologies is altered by the compressibility. The evolution equations of the invariants are derived and the relevant dynamics of the mean topological evolution are analysed. The compressibility effect is mainly related to the pressure effect. The mutual-interaction terms among the invariants are the root of the clockwise spiral behaviour of the local flow topology in the space of invariants.

Turbulent Boundary Layers Subjected to Multiple Strains

1999 ◽  
Vol 121 (3) ◽  
pp. 526-532 ◽  
Author(s):  
Andreas C. Schwarz ◽  
Michael W. Plesniak ◽  
S. N. B. Murthy
Keyword(s):  
Shear Stress ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Turbulent Boundary Layers ◽  
Laser Doppler Velocimeter ◽  
Strain Rates ◽  
The Mean ◽  
Convex Curvature ◽  
Multiple Strain Rates

Turbomachinery flows can be extremely difficult to predict, due to a multitude of effects, including interacting strain rates, compressibility, and rotation. The primary objective of this investigation was to study the influence of multiple strain rates (favorable streamwise pressure gradient combined with radial pressure gradient due to convex curvature) on the structure of the turbulent boundary layer. The emphasis was on the initial region of curvature, which is relevant to the leading edge of a stator vane, for example. In order to gain better insight into the dynamics of complex turbulent boundary layers, detailed velocity measurements were made in a low-speed water tunnel using a two-component laser Doppler velocimeter. The mean and fluctuating velocity profiles showed that the influence of the strong favorable pressure augmented the stabilizing effects of convex curvature. The trends exhibited by the primary Reynolds shear stress followed those of the mean turbulent bursting frequency, i.e., a decrease in the bursting frequency coincided with a reduction of the peak Reynolds shear stress. It was found that the effects of these two strain rates were not superposable, or additive in any simple manner. Thus, the dynamics of the large energy-containing eddies and their interaction with the turbulence production mechanisms must be considered for modeling turbulent flows with multiple strain rates.

scholarly journals On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients

2002 ◽  
Vol 461 ◽  
pp. 61-91 ◽  
Author(s):  
A. E. PERRY ◽  
IVAN MARUSIC ◽  
M. B. JONES
Keyword(s):  
Boundary Layers ◽  
Scaling Laws ◽  
Power Spectra ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Stream Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
The Mean

A new approach to the classic closure problem for turbulent boundary layers is presented. This involves, first, using the well-known mean-flow scaling laws such as the log law of the wall and the law of the wake of Coles (1956) together with the mean continuity and the mean momentum differential and integral equations. The important parameters governing the flow in the general non-equilibrium case are identified and are used for establishing a framework for closure. Initially closure is achieved here empirically and the potential for achieving closure in the future using the wall-wake attached eddy model of Perry & Marusic (1995) is outlined. Comparisons are made with experiments covering adverse-pressure-gradient flows in relaxing and developing states and flows approaching equilibrium sink flow. Mean velocity profiles, total shear stress and Reynolds stress profiles can be computed for different streamwise stations, given an initial upstream mean velocity profile and the streamwise variation of free-stream velocity. The attached eddy model of Perry & Marusic (1995) can then be utilized, with some refinement, to compute the remaining unknown quantities such as Reynolds normal stresses and associated spectra and cross-power spectra in the fully turbulent part of the flow.

Mean momentum balance in moderately favourable pressure gradient turbulent boundary layers

2008 ◽  
Vol 617 ◽  
pp. 107-140 ◽  
Author(s):  
M. METZGER ◽  
A. LYONS ◽  
P. FIFE
Keyword(s):  
Pressure Gradient ◽  
Boundary Layers ◽  
Outer Region ◽  
Present Theory ◽  
Momentum Equation ◽  
Turbulent Boundary Layers ◽  
Momentum Balance ◽  
Physical Layers ◽  
Multi Scale ◽  
The Mean

Moderately favourable pressure gradient turbulent boundary layers are investigated within a theoretical framework based on the unintegrated two-dimensional mean momentum equation. The present theory stems from an observed exchange of balance between terms in the mean momentum equation across different regions of the boundary layer. This exchange of balance leads to the identification of distinct physical layers, unambiguously defined by the predominant mean dynamics active in each layer. Scaling domains congruent with the physical layers are obtained from a multi-scale analysis of the mean momentum equation. Scaling behaviours predicted by the present theory are evaluated using direct measurements of all of the terms in the mean momentum balance for the case of a sink-flow pressure gradient generated in a wind tunnel with a long development length. Measurements also captured the evolution of the turbulent boundary layers from a non-equilibrium state near the wind tunnel entrance towards an equilibrium state further downstream. Salient features of the present multi-scale theory were reproduced in all the experimental data. Under equilibrium conditions, a universal function was found to describe the decay of the Reynolds stress profile in the outer region of the boundary layer. Non-equilibrium effects appeared to be manifest primarily in the outer region, whereas differences in the inner region were attributed solely to Reynolds number effects.

Scaling of Favorable Pressure Gradient Turbulent Boundary Layers With Eventual Relaminarization

2005 ◽  
Author(s):  
Rau´l Bayoa´n Cal ◽  
Xia Wang ◽  
Luciano Castillo
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Favorable Pressure Gradient ◽  
The Mean

Applying similarity analysis to the RANS equations of motion for a pressure gradient turbulent boundary layer, Castillo and George [1] obtained the scalings for the mean deficit velocity and the Reynolds stresses. Following this analysis, Castillo and George studied favorable pressure gradient (FPG) turbulent boundary layers. They were able to obtain a single curve for FPG flows when scaling the mean deficit velocity profiles. In this study, FPG turbulent boundary layers are analyzed as well as relaminarized boundary layers subjected to an even stronger FPG. It is found that the mean deficit velocity profiles diminish when scaled using the Castillo and George [1] scaling, U∞, and the Zagarola and Smits [2] scaling, U∞δ*/δ. In addition, Reynolds stress data has been analyzed and it is found that the relaminarized boundary layer data decreases drastically in all components of the Reynolds stresses. Furthermore, it will be shown that the shape of the profile for the wall-normal and Reynolds shear stress components change drastically given the relaminarized state. Therefore, the mean velocity deficit profiles as well as Reynolds stresses are found to be necessary in order to understand not only FPG flows, but also relaminarized boundary layers.

scholarly journals Evolution and structure of sink-flow turbulent boundary layers

2001 ◽  
Vol 428 ◽  
pp. 1-27 ◽  
Author(s):  
M. B. JONES ◽  
IVAN MARUSIC ◽  
A. E. PERRY
Keyword(s):  
Boundary Layers ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Flow Measurements ◽  
Law Of The Wall ◽  
The Mean ◽  
Logarithmic Law

An experimental and theoretical investigation of turbulent boundary layers developing in a sink-flow pressure gradient was undertaken. Three flow cases were studied, corresponding to different acceleration strengths. Mean-flow measurements were taken for all three cases, while Reynolds stresses and spectra measurements were made for two of the flow cases. In this study attention was focused on the evolution of the layers to an equilibrium turbulent state. All the layers were found to attain a state very close to precise equilibrium. This gave equilibrium sink flow data at higher Reynolds numbers than in previous experiments. The mean velocity profiles were found to collapse onto the conventional logarithmic law of the wall. However, for profiles measured with the Pitot tube, a slight ‘kick-up’ from the logarithmic law was observed near the buffer region, whereas the mean velocity profiles measured with a normal hot wire did not exhibit this deviation from the logarithmic law. As the layers approached equilibrium, the mean velocity profiles were found to approach the pure wall profile and for the highest level of acceleration Π was very close to zero, where Π is the Coles wake factor. This supports the proposition of Coles (1957), that the equilibrium sink flow corresponds to pure wall flow. Particular interest was also given to the evolutionary stages of the boundary layers, in order to test and further develop the closure hypothesis of Perry, Marusic & Li (1994). Improved quantitative agreement with the experimental results was found after slight modification of their original closure equation.

Direct numerical simulation of hypersonic turbulent boundary layers. Part 4. Effect of high enthalpy

2011 ◽  
Vol 684 ◽  
pp. 25-59 ◽  
Author(s):  
L. Duan ◽  
M. P. Martín
Keyword(s):  
Boundary Layers ◽  
Transport Model ◽  
Turbulent Boundary Layers ◽  
Turbulence Structure ◽  
Mean Velocity ◽  
Reynolds Analogy ◽  
High Enthalpy ◽  
Turbulent Schmidt Number ◽  
Wide Range ◽  
The Mean

AbstractIn this paper we present direct numerical simulations (DNS) of hypersonic turbulent boundary layers to study high-enthalpy effects. We study high- and low-enthalpy conditions, which are representative of those in hypersonic flight and ground-based facilities, respectively. We find that high-enthalpy boundary layers closely resemble those at low enthalpy. Many of the scaling relations for low-enthalpy flows, such as van-Driest transformation for the mean velocity, Morkovin’s scaling and the modified strong Reynolds analogy hold or can be generalized for high-enthalpy flows by removing the calorically perfect-gas assumption. We propose a generalized form of the modified Crocco relation, which relates the mean temperature and mean velocity across a wide range of conditions, including non-adiabatic cold walls and real gas effects. The DNS data predict Reynolds analogy factors in the range of those found in experimental data at low-enthalpy conditions. The gradient transport model approximately holds with turbulent Prandtl number and turbulent Schmidt number of order unity. Direct compressibility effects remain small and insignificant for all enthalpy cases. High-enthalpy effects have no sizable influence on turbulent kinetic energy (TKE) budgets or on the turbulence structure.

Transpired Turbulent Boundary Layers Subject to Forced Convection and External Pressure Gradients

2005 ◽  
Vol 127 (2) ◽  
pp. 194-198 ◽  
Author(s):  
Rau´l Bayoa´n Cal, ◽  
Xia Wang, ◽  
Luciano Castillo
Keyword(s):  
Pressure Gradient ◽  
Forced Convection ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
External Pressure ◽  
Turbulent Pipe Flow ◽  
Mean Flow ◽  
Outer Flow ◽  
The Mean ◽  
Blowing Parameter

The problem of forced convection transpired turbulent boundary layers with external pressure gradient has been studied by using different scalings proposed by various researchers. Three major results were obtained: First, for adverse pressure gradient boundary layers with suction, the mean deficit profiles collapse with the free stream velocity, U∞, but into different curves depending on the strength of the blowing parameter and the upstream conditions. Second, the dependencies on the blowing parameter, the Reynolds number, and the strength of pressure gradient are removed from the outer flow when the mean deficit profiles are normalized by the Zagarola/Smits [Zagarola, M. V., and Smits, A. J., 1998, “Mean-Flow Scaling of Turbulent Pipe Flow,” J. Fluid Mech., 373, 33–79] scaling, U∞δ*/δ. Third, the temperature profiles collapse into a single curve using the new inner and outer scalings proposed by Wang and Castillo [Wang, X., and Castillo, L., 2003, “Asymptotic Solutions in Forced Convection Turbulent Boundary Layers,” J. Turbulence, 4(006)], which produce the true asymptotic profiles even at finite Pe´clet number.

Mean force structure and its scaling in rough-wall turbulent boundary layers

2013 ◽  
Vol 731 ◽  
pp. 682-712 ◽  
Author(s):  
Faraz Mehdi ◽  
J. C. Klewicki ◽  
C. M. White
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Characteristic Length ◽  
Turbulent Boundary Layers ◽  
Rough Wall ◽  
Viscous Force ◽  
Leading Order ◽  
Smooth Wall ◽  
Wall Flows ◽  
The Mean

AbstractThe combined roughness/Reynolds number problem is explored. Existing and newly acquired data from zero pressure gradient rough-wall turbulent boundary layers are used to clarify the leading order balances of terms in the mean dynamical equation. For the variety of roughnesses examined, it is revealed that the mean viscous force retains dominant order above (and often well above) the roughness crests. Mean force balance data are shown to be usefully organized relative to the characteristic length scale, which is equal or proportional to the width of the region from the wall to where the leading order mean dynamics become described by a balance between the mean and turbulent inertia. This is equivalently the width of the region from the wall to where the mean viscous force loses leading order. For both smooth-wall and rough-wall flows, the wall-normal extent of this region consistently ends just beyond the zero-crossing of the turbulent inertia term. In smooth-wall flow this characteristic length is a known function of Reynolds number. The present analyses indicate that for rough-wall flows the wall-normal position where the mean dynamics become inertial is an irreducible function of roughness and Reynolds number, as it is an inherent function of the relative scale separations between the inner, roughness, and outer lengths. These findings indicate that, for any given roughness, new dynamical regimes will typically emerge as the Reynolds number increases. For the present range of parameters, there appear to be three identifiable regimes. These correspond to the ratio of the equivalent sand grain roughness to the characteristic length being less than, equal to, or greater than$O(1)$. The relative influences of the inner, outer, and roughness length scales on the characteristic length are explored empirically. A prediction for the decay rate of the mean vorticity is developed via extension of the smooth-wall theory. Existing data are shown to exhibit good agreement with this extension. Overall, the present results appear to expose unifying connections between the structure of smooth- and rough-wall flows. Among other findings, the present analyses show promise toward providing a self-consistent and dynamically meaningful way of identifying the domain where the wall similarity hypothesis, if operative, should hold.

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