Hypersonic Viscous Flow on Noninsulated Flat Plate

Li, Ting-Yi; Nagamatsu, H. T.

doi:10.21236/ada278404

Cited by 7 publications

(15 citation statements)

References 5 publications

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“…the induced pressure is 10 times the free stream value ahead of the flat plate. The skin friction and heat transfer (13) for the plate will be much higher for this flow condition compared with values determined by the compressible boundary layer without pressure gradient. The results for flow Mach 15.6 lie between the induced pressure results for flow Mach 9.77 and 19.6.…”

Section: Shock Wave-boundary Layer Interaction Induced Pressure Distrmentioning

confidence: 66%

“…The other solutions (10)(11)(12) were derived on the assumption that the boundary layer and the shock wave were distinctly separated, even in the vicinity of the leading edge. A theoretical result for the hypersonic viscous flow over a noninsulated flat plate has been derived in (13). Recent experimental results (1,2) for a flat plate with a sharp leading edge have indicated that the shock wave and the boundary layer are merged for some distance back of the leading edge before separating.…”

Section: Hypersonic Shock Wave-boundary Layer Interaction and Leadingmentioning

confidence: 99%

“…Thus, the cooling effects of the plate surface upon the induced pressures caused by the shock wave boundary layer must be considered. A theoretical result for the effects of a noninsulated flat plate, for both cooling and heating of the boundary layer, is presented in (13). The real gas effects upon the induced pressure are small for this particular stagnation temperature compared to the cooling effects.…”

Section: Shock Wave-boundary Layer Interaction Induced Pressure Distrmentioning

confidence: 99%

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Hypersonic Shock Wave-Boundary Layer Interaction and Leading Edge Slip

Nagamatsu

Sheer

1960

ARS Journal

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Section: Shock Wave-boundary Layer Interaction Induced Pressure Distrmentioning

confidence: 66%

Section: Hypersonic Shock Wave-boundary Layer Interaction and Leadingmentioning

confidence: 99%

Section: Shock Wave-boundary Layer Interaction Induced Pressure Distrmentioning

confidence: 99%

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Hypersonic Shock Wave-Boundary Layer Interaction and Leading Edge Slip

Nagamatsu

Sheer

1960

ARS Journal

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“…This data resulted from Preston tube measurements and was obtained only at the two values of x at which the complete flowfield profiles were taken. Again the present analysis, as well as the analyses of Eckert 17 and Li and Nagamatsu, 18 are included for comparison. The present theory is observed to compare quite favorably at higher values of % with the strong interaction theory, and at lower x it approaches the boundary-layer predictions of Eckert.…”

Section: Presentation and Discussion Of Resultsmentioning

confidence: 99%

Hypersonic interaction along a rectangular corner

et al. 1969

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An investigation of the behavior of the three-dimensional hypersonic flow along intersecting planes has been conducted, considering both the viscous and inviscid flows and their mutual interaction. The experimental program involves measurements of surface pressures and heat-transfer rates in the vicinity of a 90° corner. The local forces and shear stresses can be obtained thereby, yielding some information on the nature of the three-dimensional boundary-layer behavior in this region. Pilot pressure contours are also obtained and utilized in the determination of the complex intersecting shock pattern in the corner. The test data was obtained at a freestream Mach number of 11.2 and a Reynolds number of 1.5 X 10 4 /in. A theoretical analysis of the corner flow was obtained by the development of a set of equations valid throughout the boundary layer, shock wave structure, and inviscid core as previously proposed by Rubin for two-dimensional and axisymmetric flows. This analysis has been shown to be valid in the continuum merged layer and in the viscous interaction regions downstream. The theory is extended here to the three-dimensional corner configuration. Where applicable, the theoretical solutions were compared to the experiments and very good agreement was found to exist over the entire spectrum of flow variables. Nomenclatureheat-transfer coefficient H = stagnation enthalpy ft = coefficient of thermal conductivity L = yM m z /Re m = reference length M = Mach number p -pressure q -surface heat transfer rate Re x = pux/p, -Reynolds number based on x Re m = POO^OO/MOO = freestream unit Reynolds number St -Qw/pu m (Haa ~ HW) = Stanton number T = temperature u = u/u^ -nondimensional velocity in the x direction u = physical velocity in the x diiection v = v/Uo>8 = nondimensional velocity in the y direction v = physical velocity in the y direction V = x/Moo 2 = rarefaction parameter w = w/u m 8 = nondimensional velocity in the z direction w = physical velocity in the z direction x = x/L = nondimensional x coordinate x = physical coordinate in the streamwise direction y = 3/8 = nondimensional y coordinate y = physical coordinate along vertical surface normal to x axis z s = two-dimensional shock displacement thickness z = z/~b = nondimensional z coordinate z = physical coordinate along horizontal surface normal to x axis 7 = ratio of specific heats 8 = (l/7 1/2 Moo) = reference number Aerospace Engineering. Associate AIAA. t NASA Trainee. § Research Fellow. 8' = physical boundary-layer thickness 8 = 8L = reference length f = z/z s = z coordinate normalized with respect to the shock layer thickness P = density M = coefficient of viscosity a-= Prandtl number T = ^(bufby) = shear stress M M *(C/Re 0 rameter _)!/2 _ viscous-inviscid interaction paSubscripts e s t w Z -> oo 2 -D = conditions external to boundary layer = stagnation conditions = Pitot conditions = conditions evaluated at the surface = flat plate conditions = freestream conditions = conditions behind a normal shock Superscript (") = physical flow variables

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“…8 They arrived at their approach after Reasonable agreement was obtained between computed results and experimental heat flux data for a favorable pressure gradient over a blunted flat plate. The Bertram and Feller method was modified by Crawford to accommodate a more general pressure profile.…”

Section: Introductionmentioning

confidence: 99%

Scaling of heat transfer augmentation due to mechanical distortions in hypervelocity boundary layers

Flaherty

Austin

2013

Physics of Fluids

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We examine the response of hypervelocity boundary layers to global mechanical distortions due to concave surface curvature. Surface heat transfer and visual boundary layer thickness data are obtained for a suite of models with different concave surface geometries. Results are compared to predictions using existing approximate methods. Near the leading edge, good agreement is observed, but at larger pressure gradients, predictions diverge significantly from the experimental data. Up to a factor of five underprediction is reported in regions with greatest distortion. Curve fits to the experimental data are compared with surface equations. We demonstrate that reasonable estimates of the laminar heat flux augmentation may be obtained as a function of the local turning angle for all model geometries, even at the conditions of greatest distortion. This scaling may be explained by the application of Lees similarity. As a means of introducing additional local distortions, vortex generators are used to impose streamwise structures into the boundary layer. The response of the large scale vortices to an adverse pressure gradient is investigated. Surface streak evolution is visualized over the different surface geometries using fast response pressure sensitive paint. For a flat plate baseline case, heat transfer augmentation at similar levels to turbulent flow is measured. For the concave geometries, increases in heat transfer by factors up to 2.6 are measured over the laminar values. The scaling of heat transfer with turning angle that is identified for the laminar boundary layer response is found to be robust even in the presence of the imposed vortex structures.

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Hypersonic Viscous Flow on Noninsulated Flat Plate

Cited by 7 publications

References 5 publications

Hypersonic Shock Wave-Boundary Layer Interaction and Leading Edge Slip

Hypersonic Shock Wave-Boundary Layer Interaction and Leading Edge Slip

Hypersonic interaction along a rectangular corner

Scaling of heat transfer augmentation due to mechanical distortions in hypervelocity boundary layers

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