529 research outputs found
Computational methods for internal flows with emphasis on turbomachinery
Current computational methods for analyzing flows in turbomachinery and other related internal propulsion components are presented. The methods are divided into two classes. The inviscid methods deal specifically with turbomachinery applications. Viscous methods, deal with generalized duct flows as well as flows in turbomachinery passages. Inviscid methods are categorized into the potential, stream function, and Euler aproaches. Viscous methods are treated in terms of parabolic, partially parabolic, and elliptic procedures. Various grids used in association with these procedures are also discussed
Vector potential methods
Vector potential and related methods, for the simulation of both inviscid and viscous flows over aerodynamic configurations, are briefly reviewed. The advantages and disadvantages of several formulations are discussed and alternate strategies are recommended. Scalar potential, modified potential, alternate formulations of Euler equations, least-squares formulation, variational principles, iterative techniques and related methods, and viscous flow simulation are discussed
Uniqueness of Transonic Shock Solutions in a Duct for Steady Potential Flow
We study the uniqueness of solutions with a transonic shock in a duct in a
class of transonic shock solutions, which are not necessarily small
perturbations of the background solution, for steady potential flow. We prove
that, for given uniform supersonic upstream flow in a straight duct, there
exists a unique uniform pressure at the exit of the duct such that a transonic
shock solution exists in the duct, which is unique modulo translation. For any
other given uniform pressure at the exit, there exists no transonic shock
solution in the duct. This is equivalent to establishing a uniqueness theorem
for a free boundary problem of a partial differential equation of second order
in a bounded or unbounded duct. The proof is based on the maximum/comparison
principle and a judicious choice of special transonic shock solutions as a
comparison solution.Comment: 12 page
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
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
Existence of Steady Subsonic Euler Flows through Infinitely Long Periodic Nozzles
In this paper, we study the global existence of steady subsonic Euler flows
through infinitely long nozzles which are periodic in direction with the
period . It is shown that when the variation of Bernoulli function at some
given section is small and mass flux is in a suitable regime, there exists a
unique global subsonic flow in the nozzle. Furthermore, the flow is also
periodic in direction with the period . If, in particular, the
Bernoulli function is a constant, we also get the existence of subsonic-sonic
flows when the mass flux takes the critical value
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