Numerical Computation of Two-Dimensional Viscous Blunt Body Flows with an Impinging Shock

Tannehill, John C.; Holst, Terry L.; Rakich, J. V.

doi:10.2514/3.61358

Cited by 71 publications

(20 citation statements)

References 10 publications

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“…Due to the complexity of the equation set, no stability analysis for the MacCormack scheme applied to the compressible Navier-Stokes equations is available. However, Tannehill et al [38] empirically modified the CFL stability condition, and this approach is used in the present computations. The time step is calculated at each grid point and the smallest At in the computational region is used to advance the solution.…”

Section: Time Step Calculationmentioning

confidence: 99%

“…The artificial damping term used in this work was developed by Hoist [7] as a modification to the "product" fourth-order smoothing used by Tannehill et al [38]. The damping is equivalent to adding an artificial viscosity of the form to the finite-difference equations, where c, is a constant, which must be less than or equal to 0.5 to maintain stability [7].…”

Section: Artijicial Smoothingmentioning

confidence: 99%

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Supersonic, turbulent flow computation and drag optimization for axisymmetric afterbodies

Cummings

Yang

1995

Computers & Fluids

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Abstract-The compressible, turbulent flow about an axisymmetric body was numerically studied using the MacCormack unsplit explicit algorithm applied to the mass-average Navier--Stokes equations solved in conjunction with the k+ turbulence model of Jones and Launder. Numerical predictions of total body drag (pressure drag, skin friction drag, and base drag) were made for an axisymmetric body six diameters in length, with and without a boattail. Surface pressures and viscous layer profiles are compared with available wind tunnel data and are found to be in good agreement for both geometries. The Golden Section optimization method was used to optimize the body boattail angle for minimum drag. The solution method can serve as a tool for preliminary design analysis where the relative merits of utilizing boattails on axisymmetric afterbodies is being considered.

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Section: Time Step Calculationmentioning

confidence: 99%

Section: Artijicial Smoothingmentioning

confidence: 99%

Supersonic, turbulent flow computation and drag optimization for axisymmetric afterbodies

Cummings

Yang

1995

Computers & Fluids

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“…But anyway, as follows from the results in [5], the linearized (nonstationary) Navier-Stokes system behind the planar shock lacks boundary conditions: one boundary condition for the case of one space dimension (1-D) and more than one boundary condition for 2-D or 3-D. In this connection, we underline once more that, for example, in [16], [15], [17], one considers the stationary Navier-Stokes (or simplified Navier-Stokes) equations, but their solutions are calculated there by the stabilization method. Hence, it is the nonstationary linearized shock front problem that should be correctly posed according to the number of boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…At the same time, it should be noted that there are a lot of computational works in which the shock wave in a viscous gas is considered as a fictitious surface of strong discontinuity (see, e.g., [16], [15], [17] and references therein). As a rule, such works are devoted to the numerical computation of steady viscous flows near blunt bodies.…”

Section: Introductionmentioning

confidence: 99%

“…As a rule, such works are devoted to the numerical computation of steady viscous flows near blunt bodies. For example, in [16], to bound essentially the calculated domain, where solutions of the compressible Navier-Stokes equations are sought, one introduces a bow shock that is treated as a strong discontinuity on which surface corresponding jump conditions (generalized Rankine-Hugoniot conditions) hold. Moreover, steady-state solutions to the Navier-Stokes equations are computed there by the stabilization method; i.e., they are found as a limit of unsteady solutions under t -> oo.…”

Section: Introductionmentioning

confidence: 99%

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On a modified shock front problem for the compressible Navier-Stokes equations

Блохин¹,

Trakhinin²

2004

Quart. Appl. Math.

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Abstract.We discuss the possibility of considering the shock wave in a compressible viscous heat conducting gas as a strong discontinuity on which surface the generalized Rankine-Hugoniot conditions hold. The corresponding linearized stability problem for a planar shock lacks boundary conditions; i.e., the shock wave in a viscous gas viewed as a (fictitious) strong discontinuity is like undercompressive shock waves in ideal fluids and, therefore, it is unstable against small perturbations.We propose such additional jump conditions so that the stability problem becomes well-posed and its trivial solution is asymptotically stable (by Lyapunov). The choice of additional boundary conditions is motivated by a priori information about steady-state solutions of the Navier-Stokes equations which can be calculated, for example, by the stabilization method. The established asymptotic stability of the trivial solution to the modified linearized shock front problem can allow us to justify, at least on the linearized level, the stabilization method that is often used, for example, for steady-state calculations for viscous blunt body flows.

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A point implicit unstructured grid solver for the euler and Navier–Stokes equations

Thareja¹,

Stewart²,

Hassan

et al. 1989

Numerical Methods in Fluids

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An upwind finite element technique that uses cell-centred quantities and implicit and/or explicit time marching has been developed for computing hypersonic laminar viscous flows using adaptive triangular grids. The approach is an extension to unstructured grids of the LAURA algorithm due to Gnoffo. A structured grid of quadrilaterals is laid out near a solid surface. For inviscid flows the method is stable at Courant numbers of over 100000. A first-order basic scheme and a higher-order flux-corrected transport (FCT) scheme have been implemented. This technique has been applied to the problem of predicting type 111 and IV shock wave interactions on a cylinder, with a view to simulating the pressure and heating rate augmentation caused by an impinging shock on the leading edge of a cowl lip of an engine inlet. The predictions of wall pressure and heating rates compare very well with experimental data. The flow features are distinctly captured with a sequence of adaptively generated grids.

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Numerical Computation of Two-Dimensional Viscous Blunt Body Flows with an Impinging Shock

Cited by 71 publications

References 10 publications

Supersonic, turbulent flow computation and drag optimization for axisymmetric afterbodies

Supersonic, turbulent flow computation and drag optimization for axisymmetric afterbodies

On a modified shock front problem for the compressible Navier-Stokes equations

A point implicit unstructured grid solver for the euler and Navier–Stokes equations

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