Transformation of the Compressible Turbulent Boundary Layer

Mager, Artur

doi:10.2514/8.7647

Cited by 32 publications

(7 citation statements)

References 5 publications

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“…No significant difference was found. Mager's (1958) compressibility transformation, as used here, (with y = 1.4) is defined bv the relations…”

Section: Head's Methods For Incompressible Flowsmentioning

confidence: 99%

“…In his original paper, Mager (1958) presented more general relations than those above, claiming to improve the transformation by allowing a more accurate description of the variation of viscosity with temperature. However, following publication by Squire (1962) of an unfavourable comparison between skinfriction measurements in helium and the predictions of this more general form of the transformation, Mager (1962) reimposed Stewartson's restriction on viscosity variation.…”

Section: Mager's Transformationmentioning

confidence: 99%

“…The extension of this method to deal with compressible flow is approached in two contrasting ways. The first of these employs Mager's (1958) transformation, which is an adaptation to turbulent flow of Stewartson's (1949) compressibility transformation for the laminar boundary layer. The second extends the underlying assumptions of Head's method to embrace compressible flows by direct physical argument.…”

Section: Introductionmentioning

confidence: 99%

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The prediction of turbulent boundary layer development in compressible flow

Green

1968

J. Fluid Mech.

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Starting from Head's semi-empirical method for incompressible flow, two approaches to the prediction of turbulent boundary-layer development in compressible flow are explored. The first uses Head's incompressible method in conjunction with a compressibility transformation similar to Stewartson's transformation for laminar flow; the second carries over Head's physical arguments to treat the compressible flow directly. Measurements in supersonic flow, both on flat plates and downstream of an abrupt pressure rise, show broad agreement with the predictions of the second method but do not support the compressibility transformation. In particular, measurements on flat plates reveal that as Mach number increases the entrainment rate decreases to a lesser extent than the skin-friction coefficient. Whilst this result is consistent with the second treatment in this paper, it is difficult to reconcile with any of the compressibility transformations discussed, and the validity of these transformations in turbulent flow is therefore questioned.

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“…No significant difference was found. Mager's (1958) compressibility transformation, as used here, (with y = 1.4) is defined bv the relations…”

Section: Head's Methods For Incompressible Flowsmentioning

confidence: 99%

Section: Mager's Transformationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The prediction of turbulent boundary layer development in compressible flow

Green

1968

J. Fluid Mech.

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“…The momentum equation, however, is not similarly simplified, unless an extra conservation law is postulated between the two systems. This was introduced first by Mager (1958) in planar turbulent boundary layers and conserves the turbulent inertia forces (terms proportional to u v ) between the two systems. A similar law (and the one that will be used here) was later used by Libby (1962) and Ting & Libby (1960) in the treatment of axisymmetric turbulent flames.…”

Section: Theoretical Premisesmentioning

confidence: 99%

Self-similarity, momentum scaling and Reynolds stress in non-premixed turbulent spray flames

Karpetis

Gomez

1999

J. Fluid Mech.

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An experimental study was conducted in a turbulent spray flame in which droplets were produced ultrasonically at low velocity relative to the host gas. In this fashion, injector-specific effects on the two-phase flow were minimized and a scenario generally characteristic of the far field of practical spray systems could be simulated. Close to the burner exit, the spray flame appeared as a dense column of drops burning with an envelope flame. Further downstream, it opened up slowly in the radial direction and developed a turbulent ‘brush’ appearance. Measurements of the size, velocity and concentration of the droplets, and of gas-phase velocity and temperature were made by combining a Phase-Doppler interferometric technique with Stokes/anti-Stokes Raman thermometry. The experimental data were used to derive scaling and self-similarity for the Reynolds-averaged continuity and momentum equations using suitable transformations.Results showed three distinct regions, on the basis of the behaviour of the gas axial velocity in the spray flame. In the lower part of the flame, the gas momentum increased because of vaporization. In the intermediate region of the spray flame, the axial velocity decayed along the centreline as an inverse power of the distance from the virtual origin, with exponents smaller than unity. In the upper part of the spray flame, the flow field recovered the axial velocity decay that is typical of incompressible jets, namely as an inverse of the axial distance. Self-similar behaviour held for the axial velocity throughout the intermediate region. The vapour source term in the gas continuity equation scaled approximately as an inverse power of axial distance, and exhibited self-similarity throughout the spray flame. As a result, a simple model of the Reynolds stress term could be formulated, in which two competing contributions appear: one, that is due to turbulent transport, tends to increase the value of the velocity correlation; another, that is due to the vaporization term, tends to reduce the value of the velocity correlation and can be construed as a vaporization-induced tendency towards relaminarization. The first term is modelled by a classic gradient-transport approach yielding an empirical mixing length relating the velocity correlation to the average velocity gradient. Model and experiments are found to be in good agreement, especially sufficiently far from the injector, where one-way coupling between the two phases holds.

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“…The first of these attempts was made by Mager. 5 The only systematic attempt to find a suitable transformation was made by Coles 6 for the turbulent boundary-layer problem. Incidentally, in almost all cases examined by these authors, attention was focused on an incomplete form of the equations of the mean motion.…”

mentioning

confidence: 99%

Turbulent shear flows of variable density

Laufer¹

1968

6th Aerospace Sciences Meeting

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Th ris ruwaoh i., wprZ d 1) 0,I All jl (., Rm' .-arch P rtojtuI-A pecyi iT Cont~ramNo. RAHI-I1S 67 C 01 11. HA NI %1lmraida ar ri ujiri-v 14) crig if al ru-x i,-i proc-Mdurv, al thv rvv~arch 'Imrartm~ut and (iirpoirati ImL 4.1. Vi,%% aml t-mnclu-jon, v.~pri.-cII hervin art, nm'l rthtI'". 1h prima ry re-Ilonsiililt of ii iihtr. and ~Ioumld nol liw inti-rpretd ari-pri4-nIimg ihe oil-al ojinii or uoic of AIIPA or of Timv RAND) Corporation. DISTRIBUTION STATEMENTThis document had wen approxi-d frpitiuldic rc~va-cand jim; it' di~trihtution i-mninmilvd. PREFACEThe purpose of this paper is to show that the turbulent field in a variable-density shear layer is equivalent to one of a constantdensity layer i, which the lateral dimension becomes a random func-

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Transformation of the Compressible Turbulent Boundary Layer

Cited by 32 publications

References 5 publications

The prediction of turbulent boundary layer development in compressible flow

The prediction of turbulent boundary layer development in compressible flow

Self-similarity, momentum scaling and Reynolds stress in non-premixed turbulent spray flames

Turbulent shear flows of variable density

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