Three-dimensional Navier-Stokes simulations have been done for transonic and low supersonic flow past a nonaxisymmetric nozzle typical of those advocated for advanced fighter airplanes. The jet exhaust is included in the calculations. The investigation compares the performance of the unmodified Baldwin-Lomax turbulence model with its performance when enhanced by the Degani-Schiff and the Goldberg modifications. Solutions are presented for Mach numbers of 0.80,0.94, and 1.20 at 0-deg angle of attack and a Reynolds number of 20 x 10 6 . The numerical results, which are compared to the wind-tunnel data, show that the three turbulence models predict considerably different shock locations, separated-flow regions, and flowfields.
NomenclatureA, B, Ci,C 2 = constants in the Goldberg modification for turbulence modelsfunction in the Baldwin-Lomax turbulence model [see Eq. (6)] F, G, H = flux vectors in the transformed coordinate £, T/, f directions respectively 9 =Gaussian [see Eq. (8)] K = Clauser constant L = reference length, length of model from nose to jet exit (63 in.) £ = mixing length for turbulent viscosity Moo = free-stream Mach number n = normal distance from the wall n + = law-of-the-wall coordinate, (n\lp w r w )/n w p = pressure Q = transformed vector of dependent flow variables #00 = freestream dynamic pressure, R = Reynolds number based on length of model from nose to nozzle exit / = time u s -velocity scale for separated flows [see Eq. (8)] u, v, w = velocities in the physical coordinate directions x,y 9 z, respectively x, y, z = physical (Cartesian) coordinates in the axial, horizontal, and vertical directions respectively, (origin at nose of model) a. = angle of attack, deg p = viscosity £, 77, f = generalized coordinates in transformed coordinate system (approximately the axial, circumferential, and radial directions) p = density T W = local shear stress at wall co = vorticity Subscripts i = inner max = maximum min = minimum o = outer s = separated t -turbulent w = wall oo = freestream conditionsUnless otherwise noted, all variables in this paper are nondimensionalized by appropriate combinations of the free-stream parameters and the reference length L.
