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Shock/Vortex Interaction and Vortex-Breakdown Modes

Profile image of Hamdy KandilHamdy Kandil

1993, Fluid Dynamics of High Angle of Attack

https://doi.org/10.1007/978-3-642-52460-8_13
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Abstract

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.

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