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CASCADE OF PROFILES

Description of the problem

Experimental results

Numerical results

Bibliography


Description of the problem

This problem was investigated in Institute of Thermomechanic of the Czech Academy of Science in Prague (see [1] ). There was experimental measurement as well as some numerical calculation carried out. The cascade of profiles is viewed at Fig.1. There is a set of profiles (1), where the impermeable walls are considered. The inlet part of the boundary is denoted by (2) and the outlet by (3). As a computational domain only one (blue) period is chosen and the periodical boundary condition is prescribed on artificial cuts (4) and (5). The geometry of profile can be found here.

Fig.1: Cascade of profiles.

The experimental measurement as well as our numerical calculation was performed for the following data: angle of attack =19 degrees 34', inlet Mach number M_{int} = 0.32, outlet Mach number M_{out} = 1.18, Reynolds number = 1.5E+06 and Prandtl number 0.72.


Experimental results

Fig.2 shows the interferogram with lines of constant density, which was carried out in Institute of Thermomechanic of the Czech Academy of Science in Prague. There several shock waves, boundary layers, wake and characteristic expand region are observed. (The figure presents the frame around trailing edges of cascade of profiles.)

Fig.2: Interferogram of lines of constant density.


Numerical results

We have tried to achieve the steady state solution of the Navier-Stokes equations by the time marching method. To solve the system of the Navier-Stokes equations the operator splitting method was used. The system is split into two subsystems (inviscid and purely viscous) and each of them is discretized separately. To discretize the inviscid subsystem the finite volume method is applied while for the purely viscous subsystem the finite element method is used. Then the complete system is discretized by the combine triangular finite volumes and conforming finite elements method. More detail can be viewed in [2], [3]

Here are available our numerical results:

Mesh of computation

Detail of mesh

Lines of constant density

Distribution of the pressure along profile


Bibliography

[1] M. Stastny and P. Safarik: Experimental Analysis Data on the Transonic Flow Past a Plane Turbine, ASME Paper 90-GT-313, New York, 1990

[2] M.Feistauer, J.Felcman and V.Dolejsi : Numerical Simulation of Compressible Viscous Flow through Cascades of Profiles. ZAMM, 76:301-304, 1996.

[3] M.Feistauer and J.Felcman: Theory and applications of numerical schemes for nonlinear convection-diffusion problems and compressible viscous flow. In Proc. of the MAFELAP96 Conf., Willey 1996.