Mixing length and kinematic eddy viscosity in a compressible boundary layer.

Maise, George; McDonald, H.

doi:10.2514/3.4443

Cited by 146 publications

(33 citation statements)

References 12 publications

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“…is clearly less than one at large M and y= vw , so as to remove the slight increase of ' þ m with increasing M observed previously [9]. For a M ¼ 6, Re…”

Section: Prl 109 054502 (2012) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

“…The second is not thoroughly studied [6], however. Over the past decades, a few experiments showed that ' þ m had an observable, although not strong, M effect, particularly in the outer part of the boundary layer [5,9]. Further evidence comes from direct numerical simulation (DNS) data [10], which show that the van Driest transformed MVP does not collapse well in the wake region, invalidating the M invariance of ffiffiffiffiffiffi ffi " þ p @ " u þ =@y þ and thus the second assumption.…”

mentioning

confidence: 98%

“…Further evidence comes from direct numerical simulation (DNS) data [10], which show that the van Driest transformed MVP does not collapse well in the wake region, invalidating the M invariance of ffiffiffiffiffiffi ffi " þ p @ " u þ =@y þ and thus the second assumption. After van Driest, Maise et al [9] presented a transformation for the wake region, and Huang et al [7] proposed a composite transformation by considering the near wall variation of ' þ m . Nevertheless, no existing transformation can cope with the whole MVP.…”

mentioning

confidence: 99%

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Mach-Number-Invariant Mean-Velocity Profile of Compressible Turbulent Boundary Layers

Zhang

Hussain

et al. 2012

Phys. Rev. Lett.

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A series of Mach-number-(M) invariant scalings is derived for compressible turbulent boundary layers (CTBLs), leading to a viscosity weighted transformation for the mean-velocity profile that is superior to van Driest transformation. The theory is validated by direct numerical simulation of spatially developing CTBLs with M up to 6. A boundary layer edge is introduced to compare different M flows and is shown to better present the M-invariant multilayer structure of CTBLs. The new scalings derived from the kinetic energy balance substantiate Morkovin's hypothesis and promise accurate prediction of the mean profiles of CTBLs.

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“…is clearly less than one at large M and y= vw , so as to remove the slight increase of ' þ m with increasing M observed previously [9]. For a M ¼ 6, Re…”

Section: Prl 109 054502 (2012) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

mentioning

confidence: 98%

mentioning

confidence: 99%

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Mach-Number-Invariant Mean-Velocity Profile of Compressible Turbulent Boundary Layers

Zhang

Hussain

et al. 2012

Phys. Rev. Lett.

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“…The wellknown reference temperature methods (see, for instance, Rubesin and Johnson 16 or the Appendix to the paper by Coles 17 ) provide a very simple mapping of this type that might be useful in certain restricted applications. The second mapping has been more thoroughly evaluated and is based on a transformation originally developed by Van Driest 20 from mixing length arguments for the law of the wall region of the flow and subsequently found by Maise and McDonald,21 following an observation by Coles,22 to yield a surprisingly accurate collapse of a wide range of compressible adiabatic constant-pressure boundary-layer profiles, including the wake region of the boundary layer. Two techniques have emerged from these efforts, both of which seem to have been sufficiently successful to justify their consideration for use in calculation schemes.…”

Section: Integral Methods For Predicting the Blade Boundary Layersmentioning

confidence: 99%

“…Two techniques have emerged from these efforts, both of which seem to have been sufficiently successful to justify their consideration for use in calculation schemes. Using the usual assumption that, in a transpired boundary layer, the local shear stress T is given by r = r w + puv w (6.9) the suggested form of the velocity profile for the compressible transpired boundary layer may be readily derived as "7 21 Fernholz and Finley object to the use of the conventionally defined boundary-layer thickness scale d as a profile scaling parameter to compare the measured data to the assumed profile because of the experimental difficulty of determining 8 with precision. Winter et al 18 show this to be true in the usual logarithmic region for their measurements at Mach 2.2, when they used the kinematic viscosity and density evaluated at the wall temperature in the usual law of the wall formulation for velocity.…”

Section: Integral Methods For Predicting the Blade Boundary Layersmentioning

confidence: 99%

Computation of Turbomachinery Boundary Layers

1985

Aerothermodynamics of Aircraft Engine Components

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In this chapter, the term "boundary layer" is applied very loosely in the generic sense of a shear layer that is not necessarily thin, rather than the quite precise terminology usually implied in classical external aerodynamics. Excluded from this very broad category of flows are shear layers whose behavior can be adequately described by assuming that the transport of momentum or energy across the streamlines of the mean flow is quite negligible. The present chapter is devoted to describing the concepts and procedures available to allow the prediction of the behavior of these "boundary layers" in the diverse and special circumstances found in turbomachinery.In view of the crucial role of boundary layers in setting loss levels, heat-transfer rates, and operating limits, there can be no doubting the desire of the turbomachinery designer to understand and predict the behavior of these boundary layers as they are influenced by flow and geometric changes. Despite this desire, boundary-layer prediction schemes are not, with minor exceptions, at present in extensive use in practical design systems. Real engines have been found to introduce complexities that cannot be allowed for in the prediction schemes and that subsequently dominate the flow behavior. Fortunately, it appears that in the near future this rather sad state of affairs will be changed, due to the combined development of efficient methods for solving multidimensional nonlinear systems of partial differential equations, together with recent advances in the modeling of turbulent transport processes. In the subsequent sections, a hierarchy of techniques will be evolved, all based on using modern computers to effect the solution. The particular turbomachinery application of the various techniques will be introduced, together with their current status and shortcomings and, since many of the techniques are still being evolved, a prognosis for their eventual success will be given.In developing the solution hierarchy, it is first convenient to divide the problem into its two major constituents: (1) the problem of developing and then solving the set of equations purporting to describe the problem at hand, and (2) the problem of describing the turbulent transport of momentum and energy to some reasonable degree of accuracy for that problem. The first part of the problem can be broken down further on the basis that certain physical approximations greatly simplify the numerical process of 331 Purchased from American Institute of Aeronautics and Astronautics Downloaded by PURDUE UNIVERSITY on June 20, 2016 | http://arc.aiaa.org | 332 AIRCRAFT ENGINE COMPONENTSsolving the set of equations. In particular, the neglect of streamwise diffusion in the equations is usually a very good approximation. When this is followed by the assumption that the pressure forces can be approximated either locally by mass conservation (i.e., a blockage correction) and/or without an a priori knowledge of the boundary-layer behavior, the governing equations for time-averaged steady flow are grea...

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Numerical simulation of the turbulent boundary layer equations via a Runge‐Kutta algorithm

Campo

Schuler

1991

Numerical Methods Partial

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This paper addresses a hybrid computational procedure for the step-by-step calculation of momentum transfer in turbulent boundary layer flows along flat plates. The proposed procedure relies on a modified method of lines wherein transversal discretizations are carried out by a "control volume" being infinitesimal in the streamwise direction and finite in the transversal direction of the fluid flow. Using mixing length theory and coarse intervals in the transversal direction, the resulting system of ordinary differential equations of first order may be readily integrated on a personal computer utilizing a fourth-order Runge-Kutta algorithm. In general, a maximum number of sixteen lines is necessary at the trailing edge of the flat plate for a typical calculation. As a consequence, computing time and storage for each run were very small when compared to other finite-difference methods. Furthermore, to validate the hybrid procedure involving the method of lines and control volumes (MOLCV), comparisons with experimental data have been done in terms of both velocity distributions and local skin friction coefficients. For all cases tested, the proposed methodology predicts the growth of the boundary layer of gases correctly.

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Mixing length and kinematic eddy viscosity in a compressible boundary layer.

Cited by 146 publications

References 12 publications

Mach-Number-Invariant Mean-Velocity Profile of Compressible Turbulent Boundary Layers

Mach-Number-Invariant Mean-Velocity Profile of Compressible Turbulent Boundary Layers

Computation of Turbomachinery Boundary Layers

Numerical simulation of the turbulent boundary layer equations via a Runge‐Kutta algorithm

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