1,341 research outputs found
Supersonic quasi-axisymmetric vortex breakdown
An extensive computational study of supersonic quasi-axisymmetric vortex breakdown in a configured circular duct is presented. The unsteady, compressible, full Navier-Stokes (NS) equations are used. The NS equations are solved for the quasi-axisymmetric flows using an implicit, upwind, flux difference splitting, finite volume scheme. The quasi-axisymmetric solutions are time accurate and are obtained by forcing the components of the flowfield vector to be equal on two axial planes, which are in close proximity of each other. The effect of Reynolds number, for laminar flows, on the evolution and persistence of vortex breakdown, is studied. Finally, the effect of swirl ration at the duct inlet is investigated
On the plane wave Riemann Problem in Fluid Dynamics
The paper contains a stability analysis of the plane-wave Riemann problem for
the two-dimensional hyperbolic conservation laws for an ideal compressible gas.
It is proved that the contact discontinuity in the plane-wave Riemann problem
is unstable under perturbations. The implications for Godunovs method are
discussed and it is shown that numerical post shock noise can set of a contact
instability. A relation to carbuncle instabilities is established.Comment: 27 pages, 1 figur
Stability of Transonic Characteristic Discontinuities in Two-Dimensional Steady Compressible Euler Flows
For a two-dimensional steady supersonic Euler flow past a convex cornered
wall with right angle, a characteristic discontinuity (vortex sheet and/or
entropy wave) is generated, which separates the supersonic flow from the gas at
rest (hence subsonic). We proved that such a transonic characteristic
discontinuity is structurally stable under small perturbations of the upstream
supersonic flow in . The existence of a weak entropy solution and Lipschitz
continuous free boundary (i.e. characteristic discontinuity) is established. To
achieve this, the problem is formulated as a free boundary problem for a
nonstrictly hyperbolic system of conservation laws; and the free boundary
problem is then solved by analyzing nonlinear wave interactions and employing
the front tracking method.Comment: 26 pages, 3 figure
Fast Euler solver for steady, 1-dimensional flows
A numerical technique to solve the Euler equations for steady, one dimensional flows is presented. The technique is essentially implicit, but is structured as a sequence of explicit solutions for each Riemann variable separately. Each solution is obtained by integrating in the direction prescribed by the propagation of the Riemann variables. The technique is second-order accurate. It requires very few steps for convergence, and each step requires a minimal number of operations. Therefore, it is three orders of magnitude more efficient than a standard time-dependent technique. The technique works very well for transonic flows and provides shock fitting with errors as small as 0.001. Results are presented for subsonic problems. Errors are evaluated by comparison with exact solutions
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