Theoretical analysis of aircraft afterbody flow

Abstract

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

Three-dimensional adaptive grid method

“…These features make this adaptive grid method practical and robust, and the scheme has been successfully applied to the problems of two-dimensional, transonic and supersonic airfoil flowfields and axisymmetric, supersonic afterbody flowfields with propulsive jets. 9 These results show that shock waves and free shear layers are clearly described by clustering the grid points near those regions. The significant improvements of the accuracy of the solutions and the efficiency of computation confirm the usefulness of the adaptive grid scheme.…”

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

“…T tJ = iitfUi/toj + dUj/toi) -8jj(pk +;M«//ta,)2/3 (5) in which ^ = c^k^e. The ^-equation is obtained from the trace of the Reynolds-stress transport equations with an approximation for diffusive transport and the assumption that pressure-strain correlations do not alter the turbulence energy in compressible flow.…”

“…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.…”

“…Computational methods based on the Navier-Stokes equations were first applied to afterbody flows during the 1970's (e.g., Hoist, 3 Mikhail 4 ). During the early 1980s, Deiwert et al 5 employed the Beam-Warming algorithm 6 to compute a variety of afterbody flows, including ones with propulsive jets. Solution-adapted grids were used to obtain good resolution of shocks and shear layers, and the Baldwin-Lomax model was used to predict turbulent stresses.…”