An interaction model of a supersonic laminar boundary layer on sharpand rounded backward facing steps.

Baum, Eric

doi:10.2514/3.4518

Cited by 32 publications

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“…Baum (28 > has calculated the effect of sharp and rounded backward-facing steps on a compressible laminar boundary layer approaching the corner. The subsonic portion of the flow is described by the boundary-layer equations, but the effect of transverse pressure gradients in the supersonic viscous region are included through the use of an inviscid transverse momentum equation.…”

Section: A Recent Corner-boundary-layer Interaction Solutionmentioning

confidence: 99%

“…A later finite difference technique for laminar equilibrium wakes, by Baum and Denison' 23 ', includes the use of an inviscid transverse momentum equation in the supersonic part of the flow, enabling the solution to be coupled to a realistic outer flow solution. The method of solution is similar to that used by Baum (28) for the flow approaching a separation corner (section 2.2.6). Profiles at the rear stagnation point are required as initial conditions; if a solution of this type were matched to a base flow solution of the type described in section 2.2.4, the result would be a complete description of the entire laminar equilibrium wake.…”

Section: Downstream Solutionsmentioning

confidence: 99%

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A Survey of Hypersonic Near Wake Studies

Crane

1969

Aeronaut. j.

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The complicated time-dependent flow in the wake of a blunt based body at low speeds is a well known phenomenon, but drastic changes in the wake structure occur as speeds increase. Somewhere in the transonic regime, the periodic vortex shedding ceases, and at supersonic Mach numbers a steady flow pattern is established. The boundary layer on the body separates to form a free shear layer, the two layers from opposite sides of the body meeting at the so-called neck of the wake. Downstream of this point, the viscous wake persists for many hundreds of body diameters, and the term “far wake” is usually taken to refer to downstream distances greater than about ten body diameters. The neck of a hypersonic wake occurs typically one or two diameters from the base, and marks the downstream end of what is often known as the base flow region; this region includes a low speed, recirculating flow bounded by the shear layers and the base wall. Between the base and somewhere a few body diameters beyond the neck, the flow field is known as the near wake, and forms the subject of this survey.

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Section: A Recent Corner-boundary-layer Interaction Solutionmentioning

confidence: 99%

Section: Downstream Solutionsmentioning

confidence: 99%

A Survey of Hypersonic Near Wake Studies

Crane

1969

Aeronaut. j.

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“…Several studies have been reported by many researchers which involve the experimental, analytical as well as numerical studies of flow over simple geometries. Also, the studies performed involve the subsonic, 16,17 supersonic, 18,19 and hypersonic flows 20,21 past the BFS, but the majority of them are in the continuum regime. Many researchers have investigated the flow past BFS at different rarefaction regimes, mostly for the low-speed microscale flows.…”

Section: Introductionmentioning

confidence: 99%

DSMC simulation of rarefied gas flow over a 2D backward-facing step in the transitional flow regime: Effect of Mach number and wall temperature

Nabapure

2020

Proceedings of the Institution of Mechanical Engineers, Part G:

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Rarefied gas flow over a backward-facing step (BFS) is often encountered in separating flows prevalent in aerodynamic flows, engine flows, condensers, space vehicles, heat transfer systems, and microflows. Direct Simulation Monte Carlo (DSMC) is a powerful tool to investigate such flows. The purpose of this research is to assess the impact of Mach number and wall temperature on the flow and surface properties in the transitional flow regime. The Mach numbers considered are 5, 10, 25, 30, and the ratio of the temperature of the wall to that of freestream considered are 1, 2, 4, 8. The Reynolds number for the cases studied is 8.6, 17.2, 43, and 51.7, respectively. Typically the flow properties near the wall are found to increase with both Mach number and wall temperature owing to compressibility and viscous dissipation effects. The variation in flow properties is more sensitive to Mach number than the wall temperature. The surface properties are found to decrease with Mach number and increase with wall temperature. Moreover, in the wake of the step, the vortex’s recirculation length is reasonably independent of both free stream Mach number and wall temperature, whereas it decreases with Knudsen number.

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“…Baum, 1 Tyson, 2 and Garvine 3 demonstrated the character of solutions along a body surface using finite-difference methods. It was found that if initial conditions are chosen to be consistent with ordinary boundary-layer development, the subsequent solution becomes extremely sensitive to small perturbations in these initial profiles.…”

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confidence: 99%

A Theoretical Model of the Near Wake of a Slender Body in Supersonic Flow

Ohrenberger¹,

Baum²

1972

AIAA Journal

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A steady-state formulation for laminar flow is employed within a region extending from the boundary layer approaching separation downstream to the axial station of the sonic point on the axis. Included are the formation of the lip shock wave, the growth of the mixing layer into the rotational inviscid wake of the boundary layer, the recirculation region, and the wake shock wave. The entire flow is treated as a viscous interaction problem. Passage of the solution through two saddle-point singularities determines uniqueness and insures that the downstream behavior is the proper one for wake flows. The flow is divided into two regions; an inner region, which includes the recirculating flow, is determined by an integral method, while an outer region employs a finite-difference technique. A rigorous matching of the flow between the two regions is included. The model is applied to a Mach 6 wedge flow corresponding to an experimental case of Batt. NomenclatureD = base diameter h = static enthalpy H = total enthalpy; also total base height h^ = cross-stream metric /z s = streamwise metric L = body length M = Mach number M = mass flow n = distance normal to streamlines P = pressure P t2 = pitot pressure Pr = Prandtl number r = radial coordinate Re = Reynolds number s = distance along streamlines 5 = streamwise orthogonal coordinate T 0 = total temperature u = axial velocity U = total velocity v = radial velocity x = axial coordinate y = lateral coordinate (a = 0) a = dimensionality factor (0 for two-dimensional flow, 1 for axisymmetric flow) 6 = radial coordinate of matching streamline { = vorticity 6 = flow angle A = 1 + a . /i = viscosity { = profile parameter p 0 ujp d u d p = density d = profile exponent T = shearing stress 0! = profile parameter hjh d 02 = profile parameter (d/h d )(dh/dr) d O = viscous dissipation term \l/ = streamfunction and orthogonal coordinate Presented as Paper 70-792 at . the authors wish to express their appreciation to M. A. Bilyk for his expert programing of the method outlined in the present paper, and to K. J. Touryan and P. J. Roache at the Sandia Corp. for their invaluable computing support. Subscripts c = cone DSL = dividing streamline inv = inviscid o = centerline s = wake stagnation point w = wedge d = matching streamline oo = freestream flow conditions

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An interaction model of a supersonic laminar boundary layer on sharpand rounded backward facing steps.

Cited by 32 publications

References 3 publications

A Survey of Hypersonic Near Wake Studies

A Survey of Hypersonic Near Wake Studies

DSMC simulation of rarefied gas flow over a 2D backward-facing step in the transitional flow regime: Effect of Mach number and wall temperature

A Theoretical Model of the Near Wake of a Slender Body in Supersonic Flow

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