Numerical simulation of backward step and jet exhaust flows

Lombard, C. K.; Luh, Raymond Ching-Chung; Nagaraj, N.; Bardina, J.; Venkatapathy, Ethiraj

doi:10.2514/6.1986-432

Cited by 12 publications

(10 citation statements)

References 12 publications

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“…Arai et al [5] applied the total variation diminishing (TVD) finite-difference scheme, in which eddy viscosity was determined using the Baldwin-Lomax turbulence model. On patched mesh systems, Lombard et al [10] used the implicit upwind scheme, which was based on a characteristic eigenvector decomposition of the spatially averaged flux difference Jacobian matrix. Tucker and Shyy [12] introduced the FDNS code [14], in which the k-e turbulence model was corrected to treat compressible flows.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, nonintrusive optical methods such as laser Doppler velocimetry (LDV) [3][4][5] and planar laserinduced fluorescence (PLIF) [6] have been applied to measure the flow properties directly. A number of computational fluid dynamics (CFD) researchers solved Euler [7,8] and Navier-Stokes [5,[9][10][11][12][13] equations to investigate the supersonic flows over a backward-facing step. Loth et al [7] utilized the finite-element method-flux corrected transport algorithm and adaptive unstructured gridding to solve the unsteady Euler equations.…”

Section: Introductionmentioning

confidence: 99%

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Remeshing Strategy of the Supersonic Turbulent Flow Over a Backward-Facing Step

Yang¹

2004

Numerical Heat Transfer, Part B: Fundamentals

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A modified error indicator and a locally implicit scheme with anisotropic dissipation model on quadrilateral-triangular mesh are developed to study the supersonic turbulent flow over a backward-facing step. In the Cartesian coordinate system, the unsteady Favre-averaged Navier-Stokes equations with a low-Reynolds-number k-« turbulence model are solved. The modified error indicator, in which the unified magnitude of substantial derivative of pressure and unified magnitude of substantial derivative of vorticity magnitude are incorporated, is applied to treat the new node spacing of mesh remeshing. To assess the present approach, the transsonic turbulent flow around an NACA 0012 airfoil is performed. According to the high-resolution result on the adaptive mesh, the structure of the back-step corner vortex, expansion wave, and oblique shock wave are distinctly captured.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Remeshing Strategy of the Supersonic Turbulent Flow Over a Backward-Facing Step

Yang¹

2004

Numerical Heat Transfer, Part B: Fundamentals

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“…Sahu and Nietubicz 7 used a similar computational method to investigate a variety of projectile flows and reported reasonably good accuracy. Lombard et al 8 and Hoffman et al 9 employed different numerical algorithms and grid procedures for afterbody flows. Thomas et al 10 used the Beam-Warming algorithm and the fc-W 11 and k-e 12 turbulence models to predict an axisymmetric base flow with a propulsive jet; significant differences were noted in the results given by the two models.…”

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confidence: 99%

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

Childs

Caruso

1991

Journal of Propulsion and Power

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The accuracy of Reynolds-averaged Navier-Stokes calculations of axisymmetric high-speed afterbody flows is investigated. An approximate truncation error analysis is used to identify specific regions where discretization errors are large, and grid refinement is used to evaluate global solution accuracy. Good alignment of grid lines with streamlines in the shear layer at the nozzle exit is found to be important for obtaining solutions at high nozzle pressure ratios. Solution-adapted grids are used, and solutions that are essentially grid-independent are obtained. Modifications to the k-model for Mach number and streamline curvature effects are presented and validated in flows unrelated to base flows. In base flow calculations, these model modifications produce changes hi base drag in excess of 20%. Computed solutions agree well with experiment for base pressure and flow structure. Nomenclature a = sound speed C = turbulence modeling coefficient h = distance between grid nodes k = turbulence kinetic energy per unit mass L = symbolic representation of governing equation M = Mach number, U/d NPR = nozzle pressure ratio, PJ/POO p = pressure P k -rate of production of pk in Eqs. (6) and (7) q = flow variables Re = Reynolds number U,V = mean velocities x,r = spatial coordinates, normalized by body radius d = shear layer thickness 3^ = Kronecker delta e = rate of dissipation of k per unit mass /A = viscosity p = density a = model coefficients Tfj = stress tensor Subscripts h = associated with grid spacing h j = nozzle exit conditions t = turbulent oo = freestream conditions Model Designations STD = standard k-e model, Eqs. (5-7) M = with Mach number modification, Eq. (8) C = with curvature modification, Eqs. (9-11) MC = with both M and C modifications

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“…Recently, non-intrusive optical methods such as the laser Doppler velocimetry (LDV) [3][4][5] and planar laser-induced uorescence (PLIF) [6] have been applied to measure the ow properties directly. A number of CFD researchers solved Euler [7,8] and Navier-Stokes [5,[9][10][11][12][13] equations to investigate the supersonic ows over a backward-facing step. Loth et al [7] utilized the ÿnite element method-ux corrected transport algorithm and adaptive unstructured gridding to solve the unsteady Euler equations.…”

Section: Introductionmentioning

confidence: 99%

“…They concluded that the numerical dissipation had virtually no e ect on the results for an adiabatic wall case. On patched mesh systems, Lombard et al [10] used the implicit upwind scheme, which was based on a characteristic eigenvector decomposition of the spatially averaged ux di erence Jacobian matrix. Yang et al [11] employed a ux-vector splitting lower-upper symmetric successive overrelaxation scheme, and deduced that reduction of the base pressure and recirculation zone could cause di culties in ignition and ameholding in Scramjet combustors.…”

Section: Introductionmentioning

confidence: 99%

Adaptive strategy of the supersonic turbulent flow over a backward‐facing step

Yang

2004

Numerical Methods in Fluids

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SUMMARYAn adaptive strategy incorporating mesh remeshing and reÿning is developed to study the supersonic turbulent ow over a backward-facing step on a mixed quadrilateral-triangular mesh. In the Cartesian co-ordinate system, the unsteady Favre-averaged Navier-Stokes equations with a low-Reynolds-number k-turbulence model are solved using a locally implicit scheme with an anisotropic dissipation model. In the present adaptive strategy, two error indicators for both mesh remeshing and reÿning, respectively, are presented. The remeshing error indicator incorporates uniÿed magnitude of substantial derivative of pressure and that of vorticity magnitude, whereas the reÿning error indicator incorporates uniÿed magnitude of substantial derivative of pressure and that of weighted vorticity magnitude. To assess the present approach, the transonic turbulent ow around an NACA 0012 airfoil is performed. Based on the comparison with the experimental data, the accuracy of the present approach is conÿrmed. According to the high-resolutional result on the adaptive mesh, the structure of backstep corner vortex, expansion wave and oblique shock wave is distinctly captured.

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Numerical simulation of backward step and jet exhaust flows

Cited by 12 publications

References 12 publications

Remeshing Strategy of the Supersonic Turbulent Flow Over a Backward-Facing Step

Remeshing Strategy of the Supersonic Turbulent Flow Over a Backward-Facing Step

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

Adaptive strategy of the supersonic turbulent flow over a backward‐facing step

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