Quasi-three-dimensional nonreflecting boundary conditions for Euler equations calculations

1993 ◽  
Vol 9 (2) ◽  
pp. 263-271 ◽  
Author(s):  
Andre P. Saxer ◽  
Michael B. Giles
Keyword(s):  
Boundary Conditions ◽  
Euler Equations ◽  
Three Dimensional ◽  
Nonreflecting Boundary Conditions

Advances in the Numerical Integration of the Three-Dimensional Euler Equations in Vibrating Cascades

1993 ◽  
Vol 115 (4) ◽  
pp. 781-790 ◽  
Author(s):  
G. A. Gerolymos
Keyword(s):  
Boundary Conditions ◽  
Numerical Integration ◽  
Euler Equations ◽  
Finite Volume ◽  
Three Dimensional ◽  
Computational Results ◽  
Grid Refinement ◽  
Mobile Grid ◽  
Transonic Compressor ◽  
Runge Kutta

In the present work an algorithm for the numerical integration of the three-dimensional unsteady Euler equations in vibrating transonic compressor cascades is described. The equations are discretized in finite-volume formulation in a mobile grid using isoparametric brick elements. They are integrated in time using Runge-Kutta schemes. A thorough discussion of the boundary conditions used and of their influence on results is undertaken. The influence of grid refinement on computational results is examined. Unsteady convergence of results is discussed.

scholarly journals Transonic Blade to Blade Calculations in an Axial, Radial or Mixed Flow Cascade Equipped With Splitter Blades

1985 ◽  
Author(s):  
Fernand Bertheau ◽  
Yves Ribaud ◽  
Valérie Millour
Keyword(s):  
Boundary Conditions ◽  
Numerical Method ◽  
Euler Equations ◽  
Three Dimensional ◽  
Computation Time ◽  
Leading Edge ◽  
Computer Code ◽  
Mixed Flow ◽  
Three Dimensional Flow ◽  
General Computer

A general computer code for pseudo-unsteady Euler equations integration in turbomachinery cascades has been developed. A quasi-three-dimensional flow hypothesis is assumed and only blade to blade calculation is considered here. Cascades may be axial, radial or mixed flow type. First the computerized quasi-orthogonal network is shown. This network takes into account splitters and is designed to reduce the computation time. Then, the numerical method is described and the major difficulties of this problem, which are boundary conditions, leading edge and trailing edge treatments, are presented. Finally, examples of calculations on turbines and compressors are given with emphasis on graphic representation.

Time-Accurate Euler Simulation of Interaction of Nozzle Wake and Secondary Flow With Rotor Blade in an Axial Turbine Stage Using Nonreflecting Boundary Conditions

1996 ◽  
Vol 118 (4) ◽  
pp. 663-678 ◽  
Author(s):  
S. Fan ◽  
B. Lakshminarayana
Keyword(s):  
Flow Field ◽  
Boundary Conditions ◽  
Unsteady Flow ◽  
Secondary Flow ◽  
Rotor Blade ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Turbine Stage ◽  
Unsteady Pressure ◽  
Nonreflecting Boundary Conditions

The objective of this paper is to investigate the three-dimensional unsteady flow interactions in a turbomachine stage. A three-dimensional time-accurate Euler code has been developed using an explicit four-stage Runge–Kutta scheme. Three-dimensional unsteady nonreflecting boundary conditions are formulated at the inlet and the outlet of the computational domain to remove the spurious numerical reflections. The three-dimensional code is first validated for two-dimensional and three-dimensional cascades with harmonic vortical inlet distortions. The effectiveness of the nonreflecting boundary conditions is demonstrated. The unsteady Euler solver is then used to simulate the propagation of nozzle wake and secondary flow through the rotor and the resulting unsteady pressure field in an axial turbine stage. The three-dimensional and time-dependent propagation of nozzle wakes in the rotor blade row and the effects of nozzle secondary flow on the rotor unsteady surface pressure and passage flow field are studied. It was found that the unsteady flow field in the rotor is highly three dimensional and the nozzle secondary flow has significant contribution to the unsteady pressure on the blade surfaces. Even though the steady flow at the midspan is nearly two dimensional, the unsteady flow is three dimensional and the unsteady pressure distribution cannot be predicted by a two-dimensional analysis.

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