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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.