Transition correlations for hypersonic wakes

Zeiberg, Seymour L.

doi:10.2514/3.2364

Cited by 23 publications

(6 citation statements)

References 7 publications

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“…Inserting Eq. (15) into (13) we get for the nondimensional transition distance (17) This equation not only supports qualitatively the experimental findings listed in the Introduction, but for the first time presents quantitatively the dependence of X T on M ef Q, Re w , etc. It is seen that the transition zone moves downstream very fast as the Mach number increases.…”

Section: Extension To Compressible Wakesupporting

confidence: 79%

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Transition to turbulence in two-dimensional wakes

Demetriades

1978

AIAA Journal

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A new technique is advanced for predicting the location of the laminar turbiiient transition zone in twodimensional wake flows. The technique is based on postulating a minimum turbulence Reynolds number required for sustaining the turbulence once it occurs. Using existing wake turbulence data and compressible laminar wake theory, the turbulence Reynolds number is then algebraically expressed in terms of freestream or wake edge conditions and integral properties. An example is calculated using laminar wake similarity, and a simple formula is found by which the transition distance is linked to the stream Mach number, the heat transfer rate, ratio of specific heats, and other parameters. Some of the existing transition data are utilized to find that the minimum or threshold turbulence Reynolds number is about 15, whereas other available data are compared and found in good agreement with the resulting formula. NomenclatureB = a constant, see Eq. (20) C } -3. constant in the fluctuation formula, Eq. (5) C 2 = a constant in the scale formula, Eq. (6) £3 -C}C2 C D h -momentum defect of wake d = diameter of wake-shedding body k = exponent in the viscosity-temperature relation, Eq. (11) M = Mach number Q = dimensionless thermal power exchanged, Eq. (16) Q = dimensional thermal power exchanged between body and flow Re = Reynolds number Re 0 = minimum Reynolds number for transition Re w = wake Reynolds number (based on edge properties and C^/2) •Re do = defined by Eq. (9) Re A = turbulence Reynolds number Re^0 = minimum possible turbulence Reynolds number Re xT = Reynolds number based on edge properties and X T t = temperature defect, = [T(Q)-T e ]/T e T = static temperature u = velocity x = distance from the wake-shedding body x = nondimensional distance -xiC D h y = ratio of specific heats A = integral scale of turbulence v -kinematic viscosity p = density a = Prandtl number ( )' • = rms wideband fluctuation (• )"' = freestream properties ( ) e = wake edge properties ( )(0) = axis properties ( ) T = properties at the transition point (zone)

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Section: Extension To Compressible Wakesupporting

confidence: 79%

“…Using an exponent of k=0.15 for the temperature-viscosity relation, the transition formula (17) has been plotted on Fig. 3.…”

Section: Numerical Evaluation Of the Transition Criterionmentioning

confidence: 99%

Transition to turbulence in two-dimensional wakes

Demetriades

1978

AIAA Journal

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“…The theory that the reattachment region is where transition occurs is based on studies by Lees 28 , Demetriades 29 , and Zeiberg 30 . In these studies, it was observed that at low Reynolds numbers, transition first occurs far downstream from the reattachment point (or from the neck of the wake in the case of an actual vehicle, which would not have a sting and reattachment point).…”

Section: Comparison Of Experiments and Computationsmentioning

confidence: 99%

Transition effects on heating in the wake of a blunt body

Hollis

Perkins

1997

32nd Thermophysics Conference

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A series of aerodynamic heating tests was conducted on a 70-deg sphere-cone planetary entry vehicle model in a Mach 10 perfect-gas wind tunnel at freestream Reynolds numbers based on diameter of 8.23x10 4 to 3.15x10 5 . Surface heating distributions were determined from temperature time-histories measured on the model and on its support sting using thin-film resistance gages. The experimental heating data were compared to computations made using an axisymmetric/2D, laminar, perfect-gas Navier-Stokes solver. Agreement between computational and experimental heating distributions to within, or slightly greater than, the experimental uncertainty was obtained on the forebody and afterbody of the entry vehicle as well as on the sting upstream of the free-shear-layer reattachment point. However, the distributions began to diverge near the reattachment point, with the experimental heating becoming increasingly greater than the computed heating with distance downstream from the reattachment point. It was concluded that this divergence was due to transition of the wake free shear layer just upstream of the reattachment point on the sting. Nomenclature B C,Hheating bias error

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“…This virtual diameter is the logical normalizing factor of the proper axial coordinate which, when combined with the results of Sec. 3.1, becomes x=(x - (7) Figure 4 designates by WEB (Wake Experiment B) the results obtained by traversing the probes in the z direction (Sec. 2.4) at each axial position, designated by XSTATION on Fig.…”

Section: Wake Dragmentioning

confidence: 99%

Mean-flow measurements in an axisymmetric compressible turbulent wake.

Demetriades

1968

AIAA Journal

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The mean flowfield of the axisymmetric turbulent wake shed by a very slender body at Mach 3 has been mapped with the aid of the pilot and static pressure probes and the hot-wire anemometer. The experimental geometry was chosen so that no inviscid wake existed, and the measurements were carried out to about 100 diam downstream of the base. The axial variation of the velocity and temperature defects appears to obey classical decay laws following a relaxation distance of at least 40 diam from the transition region. By contrast, the radial profiles of these properties relax quickly to a self-preserving form; both the temperature and the velocity radial variations fit single-parameter Gaussian distributions quite well. The proper radial similarity variable is the radius divided by the transverse wake scale; equally good agreement obtains for a Howarth-Dorodnitzyn-transformed radius, although this issue is still unsettled because of the low Mach number used. The turbulent Reynolds and Prandtl numbers computed indirectly from the data agree well with similar results from low-speed turbulent flows. Nomenclature 6* = wake half-diameter c p = specific heat at constant pressure (Cz>A) 1/2 = virtual wake diameter D = model diameter / = nondimensional radial distribution of velocity g = nondimensional radial distribution of density h = static enthalpy I = pure number [see Eq. (16)] L = transverse wake scale L' = defined by Eq. (18) p = static pressure r = radial coordinate f = Howarth-Dorodnitzyn radial coordinate r* = wake half-radius RT = turbulent Reynolds number REO( 1) = indirectly measured wire Reynolds number RERD = directly measured wire Reynolds number 5 = function of the turbulent Prandtl number T = static temperature T = nondimensional static temperature To = stagnation temperature u = axial velocity u = nondimensional axial velocity U -local velocity scale w == velocity defect [Eq. (1)] x = axial coordinate x = nondimensional axial coordinate #o = axial location of virtual origin y = radial direction z = radial direction (normal to y) T} = nondimensional radial coordinate [Eq. (17)] YI' = defined by Eq. (13) 6 = temperature defect [Eq. (2)] 9= temperature scale T(Q) -T m

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Transition correlations for hypersonic wakes

Cited by 23 publications

References 7 publications

Transition to turbulence in two-dimensional wakes

Transition to turbulence in two-dimensional wakes

Transition effects on heating in the wake of a blunt body

Mean-flow measurements in an axisymmetric compressible turbulent wake.

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