Enhancements to Program LAURA for computation of three-dimensional hypersonic flow

Gnoffo, Peter A.; Mccandless, R. S.; Yee, H. C.

doi:10.2514/6.1987-280

Cited by 72 publications

(14 citation statements)

References 7 publications

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“…3, the integral form of the governing equations is Ifk + l /2 ' n k \fi + k + 1/2 -fk-Vi. ' n k- (2) where 6() represents a time change in the quantity (). The lower case subscripts indicate values at the cell center, unless offset by a half, in which case they indicate values at the center of a cell face.…”

Section: Governing Equationsmentioning

confidence: 99%

Viscous equilibrium computations using program LAURA

Greene

Gupta

1992

Journal of Spacecraft and Rockets

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Modifications have been made to the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) that enable it to compute viscous airflows under the assumption of thermal and chemical equilibrium. Equilibrium thermodynamic and transport property information are input to the code via curve fits. The periodic updating of this information enables the equilibrium algorithm to perform at a computational rate that is only a small percentage larger than the rate associated with the perfect-gas algorithm. Presented in this article are the results of the initial validation of the modified code. Solutions for surface pressure and heating are presented for the flow over slender and blunt cones at realistic re-entry conditions. LAURA solutions are compared with those produced by a viscous shock-layer method, and, for one case considered, with heat transfer data from a flight experiment. For both pressure and heating, the agreement is good. In general, differences in pressures of a few percent were noted, while differences in heating rates were in the 5-10% range. NomenclatureA = Jacobian matrix of g with respect to q B -Jacobian matrix of h with respect to q E = total energy per unit mass, J/kg e = internal energy per unit mass, J/kg g = inviscid flux vector H = total enthalpy per unit mass, J/kg h = enthalpy per unit mass, J/kg h = viscous flux vector 7 = identity matrix M -right eigenvector matrix of A M~l = left eigenvector matrix of A n = outward unit normal vector of a cell face Pr = total Prandtl number p = pressure, N/m 2 Re = freestream Reynolds number Rn -nose radius, m S = arc length distance along symmetry plane, m t -time, s U = contravariant velocity normal to a cell face u = velocity component in x direction, m/s V = velocity vector, m/s v = velocity component in y direction, m/s w = velocity component in z direction, m/s 7 = h/e \ = eigenvalue matrix of A IJL = viscosity, N-s/m 2 p = density, kg/m 3 a = cell face area, m 2 12= cell volume, m 3

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Section: Governing Equationsmentioning

confidence: 99%

Viscous equilibrium computations using program LAURA

Greene

Gupta

1992

Journal of Spacecraft and Rockets

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“…Perfect (nonreacting) equilibrium flow computations are available^7 and have been successfully compared with experimental data for simple geometries. 8 Nonequilibrium reactive flow computations, 9 with radiative effects, 10 have been recently made possible because of the availability of new supercomputers. These computations are very time consuming, and some attempts have been made to apply parabolized Navier Stokes codes, 11 ' 12 to nonequilibrium flows.…”

Section: Greek Lettersmentioning

confidence: 99%

Numerical simulation of unsteady flows generated by dissociating nitrogen diffusion

Marraffa

Dulikravich

Deiwert

1989

Journal of Thermophysics and Heat Transfer

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An explicit time accurate predictor-corrector scheme, similar to MacCormack's, has been used to simulate unsteady nonequilibrium laminar chemically-reacting diffusion-reaction generated flows. A zonal approach, along with nonstructured boundaries, allows computation of internal and external flow with the same computer code. Results for equilibrium flows generated by dissociating, vibrationally relaxing nitrogen in a rectangular chamber are presented. The unsteady flows were generated strictly by the chemical reactions and concentration gradients. D e h h t I k K L e m m n s P P r g R

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“…Studies indicated that employing the form R,++ such that the variation of the Q are of the same order of magnitude as for the pressure would be a good choice for hypersonic flows. The form similar to the one used by Gnoffo [16] …”

Section: Enhancement Of Convergence Rate For Hypersonic Flowsmentioning

confidence: 99%