Predicting plume-induced separation on bluff-base bodies

Fox, J.

doi:10.2514/6.1984-315

Cited by 7 publications

(2 citation statements)

References 2 publications

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“…2). Depending on the downstream position, different properties should be observed corresponding to the characteristic paths emanating from point E. Following the idea proposed by Fox,14 the boundary values at point E are expanded to the line BCD for high-pressure jets (when p j > Sp^). A Prandtl-Meyer expansion, corresponding to the pressure at point B, is used to define properties about the point E that are then extrapolated isentropically, but with changing area, to a distribution along CD.…”

Section: Boundary Conditionsmentioning

confidence: 99%

Theoretical analysis of aircraft afterbody flow

Deiwert

Andrews

Nakahashi³

1987

Journal of Spacecraft and Rockets

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The strongly interactive flow field about aircraft afterbodies is investigated using computational techniques by which the thin-shear-layer formulation of the compressible, Reynolds-averaged Navier-Stokes equations is solved. A time-dependent implicit numerical algorithm is used to obtain solutions for a variety of afterbody and nozzle geometries, within the class of bodies of revolution for both subsonic and supersonic external flows and for sonic and supersonic underexpanded jets. Only centered nozzles with either a sharp lip or a blunt base are considered. In all cases, computed results are compared with experimental data. Turbulence closure is realized using algebraic eddy-viscosity concepts. A new and unique adaptive grid technique is used to resolve flow regimes with large gradients and to improve the accuracy and efficiency of the computational scheme. Special singular-point boundary conditions are used for similar purposes and are especially effective for highly underexpanded jets. For the cases considered, the agreement with experimental measurements is very good in invisciddominated regimes and qualitatively good, but less accurate, in regions where there is recirculation. Nomenclaturecalibers D -forebody diameter / = afterbody length, calibers M =Mach number p = pressure r = radial coordinate Re = Reynolds number based on diameter T = temperature U, V = contravariant velocity components X E = end of afterbody %,y = curvilinear coordinates H T = turbulent viscosity coefficient co = vorticity Subscripts J =jet / = local value £,77 = differentiation with respect to £ and 77 oo = freestream condition

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Section: Boundary Conditionsmentioning

confidence: 99%

Theoretical analysis of aircraft afterbody flow

Deiwert

Andrews

Nakahashi³

1987

Journal of Spacecraft and Rockets

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“…Many methods predict an "undershoot" in the pressure which can produce negative pressures at moderate 'NPR and terminate the calculation. Fox 13 and Deiwert et al 5 circumvented this problem by imposing nozzle exit boundary conditions a short distance downstream of the actual exit, where the scale of the flow gradients was large enough to resolve without excessive grid clustering. Venkatapathy and Lombard 14 used a grid-imbedding technique to cluster many points in these regions; however, the undershoot in pressure still existed.…”

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confidence: 99%

Assessment of modeling and discretization accuracy for high-speed afterbody flows

Childs

Caruso

1991

Journal of Propulsion and Power

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The accuracy of Reynolds-averaged Navier-Stokes calculations of axisymmetric high-speed afterbody flows is investigated. An approximate truncation error analysis is used to identify specific regions where discretization errors are large, and grid refinement is used to evaluate global solution accuracy. Good alignment of grid lines with streamlines in the shear layer at the nozzle exit is found to be important for obtaining solutions at high nozzle pressure ratios. Solution-adapted grids are used, and solutions that are essentially grid-independent are obtained. Modifications to the k-model for Mach number and streamline curvature effects are presented and validated in flows unrelated to base flows. In base flow calculations, these model modifications produce changes hi base drag in excess of 20%. Computed solutions agree well with experiment for base pressure and flow structure. Nomenclature a = sound speed C = turbulence modeling coefficient h = distance between grid nodes k = turbulence kinetic energy per unit mass L = symbolic representation of governing equation M = Mach number, U/d NPR = nozzle pressure ratio, PJ/POO p = pressure P k -rate of production of pk in Eqs. (6) and (7) q = flow variables Re = Reynolds number U,V = mean velocities x,r = spatial coordinates, normalized by body radius d = shear layer thickness 3^ = Kronecker delta e = rate of dissipation of k per unit mass /A = viscosity p = density a = model coefficients Tfj = stress tensor Subscripts h = associated with grid spacing h j = nozzle exit conditions t = turbulent oo = freestream conditions Model Designations STD = standard k-e model, Eqs. (5-7) M = with Mach number modification, Eq. (8) C = with curvature modification, Eqs. (9-11) MC = with both M and C modifications

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