Navier-Stokes computations of prolate spheroids at angle of attack

Vatsa, Veer N.; Thomas, James L.; Wedan, Bruce W.

doi:10.2514/6.1987-2627

Cited by 69 publications

(20 citation statements)

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“…At the substantial speed of U = 100m/s (corresponding to M ~ 0.3 for a perfect gas flow) this is only 7 K, a relative small fraction of the absolute temperature (273K)[ sl (In some cases the flow will accelerate to a velocity v greater than U, but v/U is limited and the estimate is also correct, see [8]). In fact, if the kinetic energy U2/2 is fully converted into the internal energy, the upper limit of change can be estimated as 6T < U2/2cv _ 7(7 -1)M2 = 0.28M2 (17) T -a2/TR 2 which is almost the same result as Eq. (13).…”

Section: Oivi P Dtsupporting

confidence: 75%

“…Figure 8 shows the convergent history. Vatsa and Thomas [ 17] also calculated this flow by solving compressible Navier-Stokes equations. They used Roe's flux difference scheme and implicit method.…”

Section: Laminar Flows Over a Circular Cylindermentioning

confidence: 99%

“…The upper limit 1.56 is evaluated by the upper limit of temperature change (17). a = 1 is recommended for practical calculations.…”

Section: ~P ~ M 2 (18) Pmentioning

confidence: 99%

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A novel slightly compressible model for low Mach number perfect gas flow calculation

Deng

Zhuang

2002

Acta Mech Sinica

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ABSTRACT:By analyzing the characteristics of low Mach number perfect gas flows, a novel Slightly Compressible Model (SCM) for low Mach number perfect gas flows is derived. In view of numerical calculations, this model is proved very efficient~ for it is kept within the p-v frame but does not have to satisfy the time consuming divergence-free condition in order to get the incompressible Navier-Stokes equation solutions. Writing the equations in the form of conservation laws, we have derived the characteristic systems which are necessary for numerical calculations. A cellcentered finite-volume method with flux difference upwind-biased schemes is used for the equation solutions and a new Exact Newton Relaxation (ENR) implicit method is developed. Various computed results are presented to validate the present model. Laminar flow solutions over a circular cylinder with wake developing and vortex shedding are presented. Results for inviscid flow over a sphere axe compared in excellent agreement with the exact analytic incompressible solution. Three-dimensional viscous flow solutions over sphere and prolate spheroid are also calculated and compared well with experiments and other incompressible solutions. Finally, good convergent performaces are shown for sphere viscous flows.

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Section: Oivi P Dtsupporting

confidence: 75%

Section: Laminar Flows Over a Circular Cylindermentioning

confidence: 99%

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A novel slightly compressible model for low Mach number perfect gas flow calculation

Deng

Zhuang

2002

Acta Mech Sinica

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“…To further assess the shock capturing capability of the present central-difference scheme, results calculated with the code developed by J. L. Thomas, which is based on the Riemann solver of Roe and described in [18], are also included in these figures. The computed distributions exhibit excellent agreement with the data in nearly all cases.…”

Section: Compression Ramp Flowmentioning

confidence: 99%

An effective multigrid method for high‐speed flows

Swanson

Turkel

White

1992

Commun. appl. numer. methods

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We consider the use of a multigrid method with central differencing to solve the Navier-Stokes equations for high-speed flows. The time-dependent form of the equations is integrated with a Runge-Kutta scheme accelerated by local time stepping and variable coefficient implicit residual smoothing. Of particular importance are the details of the numerical dissipation formulation, especially the switch between the second and fourth difference terms. Solutions are given for two-dimensional lamipar flow over a circular cylinder and a 15 degree compression ramp. iI IntroductionDuring the 1980's a wide variety of numerical schemes were investigated for solving the Euler and Navier-Stokes equations. Multistage time-stepping schemes with central differencing and multigrid acceleration [1,2,3] were demonstrated to be quite effective in computing subsonic and transonic flows 'ver aerodynamic components and configurations. With the recent resurgence of interest in high-speed flight vehicles, we now need to construct versatile algorithms for hypersonic flow. One must keep in mind that hypersonic flows represent a formidable challenge for any flow solver. I1 particular, strong shock and expansion waves can occur in the flow field, and the3 can interact with each other and with shear layers (i.e., boundary layers, jets, wakes). Such strong nonlinear behavior and interactions can easily cause divergence of any numerical integration procedure. This is especially true during the initial phase of a calculation with a time-dependent method. So even the most successful algorithms of the last decade may require significant modifications to be effective for hypersonic flows.An initial effort [4] to apply a central-difference multigrid algorithm to high-speed flows resulted in numerical difficulties that prevented the calculation of two-dimensional flows (i.e., blunt body and wedge type) with a Mach number higher than about 7. In order to compute such flows a low Courant-Friedrichs-Lewy (CFL) number was required. Thus four and five stage schemes were not practical, since there is substantial deterioration in the high frequency damping of the scheme due to the large reduction in the CFL number. The CFL restriction reduced the potential of the scheme as a viscous flow solver. More recently an algorithm utilizing a semicoarsening technique, a symmetric TVD formulation, and a three stage Runge-Kutta scheme [5] was proposed and used to compute high Reynolds number (laminar) Mach 10 flow over an airfoil at 10 degrees angle of attack. A good resolution of the bow shock wave and a reasonable convergence rate were obtained. The method of semicoarsening considered required a much more complicated cycle strategy than that employed with standard multigrid methods. In addition, it appears to be somewhat cumbersome to implement in three dimensions.It is our contention that standard multigrid techniques can be u:.,d in conjunction with central differencing to compute hypersonic flows effectively. To achieve such success with these techniques ...

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“…In this, the evaluation of the inviscid fluxes is based on an upwind-biased fluxdifference scheme originally suggested by Roe 2 " and later extended to three-dimensional flows by Vatsa et al 20 The chief advantage of using upwinding is that it eliminates the addition of explicit numerical dissipation and has been demonstrated to produce less dissipative numerical solutions 20 . This feature, coupled with a fine grid description in the tip region, increases the accuracy of the wake simulation.…”

Section: (A2)mentioning

confidence: 99%

A Free-Wake Euler and Navier-Stokes CFD Method and its Application to Helicopter Rotors Including Dynamic Stall

Srinivasan¹

1993

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Navier-Stokes computations of prolate spheroids at angle of attack

Cited by 69 publications

References 0 publications

A novel slightly compressible model for low Mach number perfect gas flow calculation

A novel slightly compressible model for low Mach number perfect gas flow calculation

An effective multigrid method for high‐speed flows

A Free-Wake Euler and Navier-Stokes CFD Method and its Application to Helicopter Rotors Including Dynamic Stall

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