Total pressure loss in vortical solutions of the conical Euler equations

Powell, Kenneth G.; Murman, Earll M.; Perez, E. S.; Baron, Judson R.

doi:10.2514/3.9630

Cited by 34 publications

(12 citation statements)

References 11 publications

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“…The standard mesh dimensions, about 60,000 cells, can support only weakens just beyond the crank, where it might have been expected that another vortex would form, or, at least, the core would curve. Losses in total pressure are mostly found in the vortex core, for reasons now understood, 4 and shock waves do not contribute to the vorticity in this case. The lift and drag coefficients are C L = 0.5503 and C D = 0.930.…”

Section: Simulated Vortex Flowfieldmentioning

confidence: 93%

Vortex-stretched flow around a cranked delta wing

Rizzi

Purcell²

1986

Journal of Aircraft

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A numerical method that solves the Euler equations for compressible flow is used to study vortex stretching. The particular case simulated is subsonic flow M& -0.3, a. = 10 deg around a twisted and cambered cranked-and-cropped delta wing. This geometry induces multiple leading-edge vortices in a straining velocity field that brings about flow instabilities, but the result is a state of statistical equilibrium. The discretization contains over 600,000 cells and offers sufficient degrees of freedom in the solution to exhibit the onset of chaotic vortex flow that could well lead to turbulence. The simulated results are compared with windtunnel measurements. The agreement at inboard sections is reasonable for the position and strength of the leading-edge vortex; but outboard, it is poor because of the complex transition to disordered vortex flow at the tip. Overall, lift and drag coefficients agree well, however. Nomenclaturee y ,e z -Cartesian unit vectors FD = total flux differences H(q) = qV+p[Q,e x ,e y ,e z ] flux M w = freestream Mach number n =unit normal vector p = static pressure p t = total pressure q = [p,pu,pv,pw] variables u,v,w = Cartesian components of V V = velocity vector x,y,z = Cartesian coordinates a. = angle of attack p = density F = artificial viscosity model a? = vorticity curl V

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Section: Simulated Vortex Flowfieldmentioning

confidence: 93%

Vortex-stretched flow around a cranked delta wing

Rizzi

Purcell²

1986

Journal of Aircraft

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“…If one chooses each 151(" ) to be a constant (in this case 1/4), for bilinear shape functions one obtains the cell-vertez finite volume approximation [19,26,56]. In two dimensions, the residual matrices are identical to the equivalent residual matrices produced by a node-based finite volume method.…”

Section: Test Functions For Cell-vertex Methodsmentioning

confidence: 99%

Adaptive Finite Element Solution Algorithm for the Euler Equations

Shapiro¹

1991

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A new finite element algorithm for solving the steady Euler equations describing the flow of an inviscid, compressible, ideal gas is presented. This algorithm uses a finite element spatial discretization coupled with a Runge-Kutta time integration to relax to steady state. It is shown that other algorithms, such as finite difference and finite volume methods, can be derived using finite element principles. A higher-order biquadratic approximation is introduced. Several test problems are computed to verify the algorithms. Adaptive gridding in two and three dimensions using quadrilateral and hexahedral elements is developed and verified. Adaptation is shown to provide CPU savings of a factor of 2-16, and biquadratic elements are shown to provide potential savings of a factor of 2-6. An analysis of the dispersive properties of various discretization methods for the Euler equations is presented, and results allowing the prediction of dispersive errors are obtained. The adaptive algorithm is applied to the solution of several flows in scramjet inlets in two and three dimensions, demonstrating some of the varied physics associated with these flows. Some issues in the design and implementation of adaptive finite element algorithms on vector and parallel computers are discussed. Trust in the LORD with all thine heart; and lean not unto thine own understanding. In all thy ways acknowledge him, and he will direct thy paths.-Proverbs 3:5,6

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“…However, for some flow conditions, even using the predictor-corrector method with As = 0.001 is not sufficient to obtain the spiral trajectory. 4 For these cases, the radial velocity into the vortex center is just too small compared to the circumferential velocity.…”

Section: Conical Streamlinesmentioning

confidence: 98%

“…The integration is carried out using the parametric equations dx=u at, ay = v at (4) Starting at a point, a line segment is drawn to ^predicted point a fraction As= UAt of the cell width, where U=max(u,v) of the four corner values. With no correction step, a forward Euler method results.…”

Section: Model Problemmentioning

confidence: 99%