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Aerodynamic Model
An ideal gas flow through the mutually moving stator and rotor blades with periodicity on the whole annulus is described by the unsteady Euler conservation equations, which are integrated using the explicit monotonous finite – volume difference scheme of Godunov-Kolgan and moving hybrid H-H grid.
The algorithm proposed allows calculate unsteady forces of the turbine stages with an arbitrary pitch ratio of stator and rotor blades.
The 3D transonic flow of inviscid non-heat conductive gas through an axial turbine stage is considered in the physical domain, including the nozzle cascade (NC) and the rotor wheel (RW), rotating with constant angular velocity. In general case both NC and RW have an unequal number of blades of the arbitrary configuration (see Figures 1). Taking into account the ft>w unperiodicity from blade to blade (in the pitchwise direction) it is convenient to choose the calculated domain including all blades of the NC and RW assembly, the entry region, the axial clearance and the exit region. Each of passages is dicretized using H-type grid for stator domain and hybrid H-H grid for rotor domain (Rzadkowski and Gnesin 2002). Here outer H-grid remains stationary during the calculation, while the inner H-grid is rebuilt in each iteration by a given algorithm, so that the external points of the inner grid remain unmoved, but the internal points (on the blade surface) move according to the blade motion.
It is assumed that the unsteady flow fluctuations are due to both the rotor wheel rotation and to prescribed blade motions, and the flows far upstream
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Figure 1. The calculated domain |
and far downstream from the blade row are at most small perturbations of uniform free streams. So, the boundary conditions formulation is based on one – dimensional theory of characteristics, where the number of physical boundary conditions depends on the number of characteristics entering the computational domain (Gnesin and Rzadkowski 2000).
In the general case, when axial velocity is subsonic, at the inlet boundary initial values for total pressure, total temperature and fbw angles are used, while at the outlet boundary only the static pressure has to be imposed. Nonrefecting boundary conditions can be used, i. e., incoming waves (three at inlet, one at the outlet) have to be suppressed, which is accomplished by setting their time derivative to zero.
