Abstract.Simulations are performed using a multiple temperature gas model to investigate translational non-equilibrium effects in a rapid expansion of a high temperature argon gas cloud into a rarefied atmosphere. A set of continuum conservation equations based on kinetic theory, which includes anisotropic forms for the temperature, pressure and speed ratio, are solved numerically using a flux splitting scheme for the inviscid fluxes and a central difference scheme for the viscous fluxes in a time accurate manner. Results obtained for the initial expansion of the spherical gas cloud from a high density source condition show that translational non-equilibrium exists in the shock front region which propagates into the ambient atmosphere. For a lower density source condition, translational non-equilibrium not only exists in the shock front but also in the inner gas cloud region where the temperature normal to the radial direction freezes at a value just below the initial source temperature.
A study of transition and turbulence in hypersonic blunt-body wake flows is presented. The current approach combines the A>£ turbulence closure model with a newly developed transition prediction method. This method utilizes results from linear stability theory and treats transitional flows in a turbulence-like manner. As a result, the onset and extent of transition are determined as part of the solution. The model is used to study flows past two spherically blunted 70-deg cone geometries at Mach 6 and 10. Two mechanisms of instability are examined. Comparison between computation and experiment suggests that for the cases considered, transition is a result of the instability of the free shear layer emanating from the shoulder region.Nomenclature k = turbulent kinetic energy M = Mach number p_ = pressure Q = Reynolds-or time-averaged value of Q Q = Favre-averaged value of Q q = heat transfer rate Re = Reynolds number R n = nose radius s = linear surface distance T = temperature U = Velocity magnitude Ui -velocity vector f = distance measured along sting support F = intermittency 8 = boundary-or shear-layer thickness; k-£ model constant Sfj -Kronecker delta 5* = boundary-layer displacement thickness £ = enstrophy A = transition-extent parameter /i = dynamic viscosity v = kinematic viscosity p = density T = characteristic time scale TU -Reynolds stress tensor a> = transitional frequency
The capability of accurately estimating pitch damping values for missile-like geometries over a range of Mach numbers and at high angles of attack using state-of-the-art CFD techniques has been investigated. Toward this effort three geometries were examined: the Army-Navy Finner model, the extended Army-Navy Finner model, and the M823 research store. Pitch damping values are predicted using forced oscillation calculations performed with the RavenCFD Navier-Stokes flow solver. Additionally, pitch decay calculations and aerodynamic build-up methods are also employed using the RavenCFD solver. These methods are compared to both experimental results and AP09, a fast-running engineering tool. Pitch damping variations due to geometric changes, Mach number changes, and angle of attack changes are explored with each method. Overall, each CFD method exhibits an outstanding agreement with experiment and range data at the lower angles of attack. Both pitch decay and forced oscillation approaches provide good agreement for low-to-moderate angles. At angles of attack greater than 30 degrees, the forced oscillation approach provides the best agreement. Pitch damping variations at angles higher than 60-70 degrees for the Army-Navy Finner have been shown to be a peripheral effect of the extreme unsteadiness of the wake flow at these conditions.
NomenclatureA = amplitude of oscillation k = reduced frequency c = chord C m = pitching moment coefficient ̇ = pitch damping sum = normal force coefficient = normal force curve slope d ref = reference length (typically missile diameter) FOA = Forced Oscillation Approach yy I = moment of inertia about the pitch axis k = reduced frequency, M = Mach number ncyc = number of points per cycle PD = Pitch Decay Approach 2 q = dynamic pressure, = reference area tp = time for given peak (used in pitch decay) t = time U ∞ = freestream velocity w = aerodynamic load = x-location of the i th missile panel (used in build-up approaches) xcg = x-location of the center of gravity xcp = x-location of the model center of pressure α = angle of attack α m = mean angle of attack α o = angle of attack amplitude α p = peak pitch angle (used in pitch decay) t = time step = width of the i th missile panel (used in build-up approaches) = ratio of specific heats = density = angular frequency
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