Review of vortex methods for simulation of vortex breakdown

1987

A numerical sim ulation of vortex breakdown using the time-dependent Navier-Stokes equations was performed. Unlike previous stu d ie s, the numerical algorithm, formulated in terms of the v e lo c ity and v o r tic ity , was not r e str ic ted to axisymmetric flows. Prototype v o rtice s were parameterized in terms of their Reynolds number and Rossby number. Two cases were studied e x te n s iv e ly. In one case, a vortex was imbedded in a uniform free stream. In the other case, the axial v e lo c ity of the free stream was decelerated in the streamwise d ir e c tio n. For both cases breakdown occurred when the Rossby number was below a c r it ic a l value. Vortex lin e s , p a rticle traces and velocity vector projections of the resu ltin g solutions have been developed. Contour p lo ts of v o r tic ity , v e lo c ity and pressure are presented, and the streamwise variation of the rates of change of energy and enstrophy were examined. The computational resu lts have been compared with ob servation s, in terms of flow structures and vortex breakdown. Previous numerical in vestigation s have a lso been discussed. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGEMENTS I would lik e to give my sincere thanks to Dr. Thomas Gatski of NASA Langley Research Center for fundamental contributions and guidance in performing th is research. I would lik e to thank Dr. Robert Ash for his support and for his assistan ce in developing th is d isser ta tio n. I am also grateful to Professors Grosch, von Lavante and Tiwari for their in t e r e s t in reviewing th is d isse r ta tio n. Mrs. Rowena Pierce is thanked for her p r o fic ie n t typing of the manuscript. I would also lik e to acknowledge the support and helpful comments contributed by Dennis Bushnell, and Dr. Milton Rose. This work was supported in part by the ODU/ICAM program. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Journal of Fluid Mechanics, 2010

13th Applied Aerodynamics Conference, 1995

Vortex flows on a 74' delta wing and two modular transonic vortex interaction (MTVI) models, one twin tail and the other single tail, are computationally s i m u l a t e d u s i n g t h e T h r e e d i m e n s i o n a l EulerINavier-Stokes Aerodynamic Method (TEAM). The primary objective is to assess viscous effects for benign and burst vortex flow solutions. Viscous effects are assessed by comparing the computed forces, moments and surface pressures from inviscid and viscous solutions with each other and with experimental data. The results show that proper accounting of viscous effects is necessary for detailed design and optimization but Euler solutions can provide meaningful guidelines for preliminary aerodynamic design of flight vehicles which exhibit vortex flows in parts of their flight envelope. LIST OF SYMBOLS C~ coefficient of pressure CD, CL, Cm drag, lift, and pitching moment coefficient L local semi-span M free stream Mach Number Re Reynolds number XJJ body fixed Cartesian coordinate system: x positive along model axis, y positive from symmetry plane to wing tip (starboard), and z positive UP CI

Fluid Dynamics of High Angle of Attack, 1993

Computational simulation and study of shock/vortex interaction and vortex-breakdown modes are considered for bound (internal) and unbound (external) flow domains. The problem is formulated using the unsteady, compressible, full Navier-Stokes (NS) equations which are solved using an implicit, flux-difference splitting, finite-volume scheme. For the bound flow domain, a supersonic swirling flow is considered in a configured circular duct and the problem is solved for quasi-axisymmetric and three-dimensional flows. For the unbound domain, a supersonic swirling flow issued from a nozzle into a uniform supersonic flow of lower Mach number is considered for quasi-axisymmetric and three-dimensionai flows. The results show several modes of breakdown; e.g., no-breakdown, transient single-bubble breakdown, transient multi-bubble breakdown, periodic multi-bubble multi-frequency breakdown and helical breakdown. Highlights of Formulation and Computational Scheme Formulation: The conservative,unsteady, compressible, fullNavier-Stokes equations in terms of time-independent,body-conformed coordinates_I, _2 and _3 are used to solve the problem. The equations arc given in Ref. [II] and hence they are not presented hem. Along with these equations, boundary conditions arc specifiedat the computational-domain inlet, side wall and downstream exit.The downstream exit boundary conditions will be presented and discussed in the next sectionof the computational results. The initial conditionsarc also presented in the next section. Computational Scheme: The computational scheme used to solve the unsteady, compressible full NS equations is an implicit, upwind, flux-difference splitting, finite-volume scheme. It employs the flux-difference splitting scheme of Roe which is based on the solution of the approximate one-dimensional Riemann problem in each of the three directions. In the Roe scheme, the inviscid flux difference at the interface of a computational cell is split into left and right flux differences. The splitting is accomplished according to the signs of the eigenvalues of the Roe averaged-Jacobian roan'ix of the inviscid flux at the cell interface. The smooth limiter is used to eliminate oscillations in the shock region. The viscous and heat-flux terms am differenced using second-order spatially accurate central differencing. The resulting contours for this case. These snapshots show a vortex breakdown mechanism of evolution, Concluding Remarks Computational simulation and study of shock/vortex interaction and vortex breakdown have been considered for internal and external supersonic swirling flow. The time-accurate computation for full Navier-Stokes equations is used to produce all the present cases.

A method for predicting the outcome of vortex breakup in a rotating flow is introduced. The vortices dealt with here are subject to both centrifugal and barotropic instabilities. The prediction of the aftermath of the breakup relies on knowing how both centrifugal and barotropic instabilities would equilibrate separately. A theoretical model for non-linear equilibration in centrifugal instability is wedded to two-dimensional simulation of barotropic instability to predict the final vortices that emerge from the debris of the original vortex. This prediction method is tested against three-dimensional Navier-Stokes simulations. For vortices in which a rapid centrifugal instability triggers a slower barotropic instability, the method is successful both qualitatively and quantitatively. The skill of the prediction method decreases as the time scales of the two instabilities become comparable.

Journal of Fluid Mechanics, 2003

This chapter presents an application of CFD methodology based on the unsteady Reynolds-Averaged Navier-Stokes (RANS) equations with a ω − k turbulence model for the prediction of vortical flows involving vortex breakdown. A variant of the ω − k turbulence model is applied that avoids excessively high eddy viscosity in the vortex cores. Time-accurate simulations are performed for subsonic flow around the ONERA 70 degree delta wing at an angle of attack of 27 degrees. Two non-dimensional time steps of different order of magnitude, are used. Both simulations predict vortex breakdown. The smaller time step leads to a self- sustained oscillation. Computational results are compared with the experimental data, and discussed in terms of pressure coefficient, velocity and vorticity components, and turbulence kinetic energy distributions on the crossflow planes and on the longitudinal plane along the vortex core. A Fourier analysis results in a spectrum with a distinct frequency peak of the S...

Applied Mathematical Modelling, 1992

The axisymmetric vortex breakdown of a laminar, incompressible, viscous, and swirling flow in a cylindrical tube is simulated. The numerical solutions of the time-dependent axisymmetric angular momentum and the vorticity transport equations are obtained by using the jmite element method. Linear and quadratic isoparametric elements are used for the space discretization, while the leapfrog time integration scheme is employed for the time discretization. The iteration process is started with the numerical solution of the linearized equations as the Reynolds number approaches zero. As the Reynolds number is changed, the numerical solution proceeds from one steady state to another. The numerical solutions are obtainedfor different initial velocity projZes and a range of Reynolds numbers and swirl ratios. The numerical solutions are compared with experimental data and prior finite difference studies.

Fluid Dynamics Conference, 1995

A mathematical model of vortex breakdown is developed for a free cylindrical vortex of radius "a" that passes through a region of non-cylindrid flow and regains the cylindrical flow structure of radius "b" downstream. The criterion of zero axial velocity within the free vortex, dowmtmm, yields a relationship between the radius ratio bla and the

Acta Mechanica, 1994

A simple, exact, locally convergent series solution of the Navier-Stokes and continuity equations for steady, incompressible, axisymmetric fluid flow is derived which exhibits the qualitative features of vortex breakdown of the bubble or B-type. This solution, which converges in a neighborhood of the axis of symmetry of the flow, is shown to produce vortex breakdown flows which are in good qualitative agreement with both experimentally and numerically observed B-type vortex breakdown phenomena.