Comparison of algebraic turbulence models for afterbody flows with jet exhaust

Abstract

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.

Global Artificial Boundary Conditions for Computation of External Flows with Jets

“…Besides, these particular computed pro les have also been chosen by Compton for presenting in Ref. 27; and the results of our computations display a goodcorrelation with the results by Compton that have been obtained on a v ery large computational domain.…”

“…The particular geometry of the body shown in Figure 2 is the following: rectangular cross section yz = 6 :26:8 with rounded edges; sharp nose and boat-tail afterbody; total length in the x direction is 63; rectangular nozzle outlet y z = 2 :62 5:12; full description can be found in the work by Compton. 27 The geometry and the ow are symmetric with respect to the plane z = 0 zero angle of attack. For our computations we have used three di erent domains with successively reduced dimensions, see Figure 4; domain I or large domain with the diameter of about 30 calibers of the body was used for calculating the reference solutions, domain II is 0:36 or about 1=3 of the size of domain I in each direction and domain IIIis 0:22 or about 1=5 of the size of domain I in each direction.…”

“…The speci c shape of the body see Figure 2 as well as parameters of the ow h a ve been previously proposed for numerical study and analyzed in work by Compton. 27 In this original work, 27 Compton had calculated external ow with the propulsive jet and also considered the interior portion of the ow, namely the ow in the actual nozzle located inside the afterbody this nozzle ow obviously produces the jet. For our study, we have generated new grids and also simpli ed the overall formulation by eliminating the nozzle and specifying instead the uniform supersonic ow conditions at the nozzle outlet i.e., at the place where the jet starts.…”

“…For our study, we have generated new grids and also simpli ed the overall formulation by eliminating the nozzle and specifying instead the uniform supersonic ow conditions at the nozzle outlet i.e., at the place where the jet starts. Compton's goal 27 was to assess the performance of di erent turbulence models including their prediction capabilities for the ow inside the nozzle; our goal is to assess the performance of di erent external boundary conditions for the ows with jet exhaust. We, therefore, think that the aforementioned simpli cation is justi ed.…”

A turbulence model study of separated 3D jet/afterbody flow

“…The majority of computational studies reported prior to 1995 were undertaken with linear eddy-viscosity models, some as simple as the Baldwin-Lomax model (11) and its combination with the Goldberg backflow model (12) . Studies by Peace (13) , Newbold (14) , Carlson et al (15) and Compton (16) with the k − ε model applied to the AGARD and ONERA jet/afterbody flows represent the state of the art, in terms of modelling sophistication, around 1995/6. Later studies by Carlson (17) , Loyau et al (18) , Batten et al (19,20) , Barakos and Drikakis (21) and Hasan and McGuirk (5) investigated the performance of more elaborate non-linear eddy-viscosity and Reynolds-stresstransport models, in comparison to simpler linear eddy-viscosity formulations, using in part test cases reviewed by Berrier (22) .…”