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Understanding of complex unsteady flow behavior caused by the relative movement of the rotor with respect to stator is very important to improve current turbomachinery designs. However, in order to predict the measured temporal behavior accurately, it is necessary to consider the ratio of the rotors to stators equal to the actual case. Also, since the wake leaving the stators periodically impinging to the rotors, there occur considerable vortex stretching and change in turbulence activity in the rotor blade passages. In this study unsteady N-S equations using an improved turbulence model are solved for flow problem within axial turbine stage (the ratio of rotors to stators is equal to experimental value). The relative motion between the stator and rotor airfoils is made possible with the use of patched grids that move relative to each other. Assessment of computed results with the measured data showed a good agreement.. INTRODUCTION In order to optimizing the performance of turbomachinery, it is very useful to have an accurate numerical analysis of the flows associated with stator-rotor configurations. However, flows within the turbomachinery are generally unsteady in nature and are therefore difficult to compute. The unsteadiness is caused by (a) the interaction of the rotor airfoils with the wakes and passage vortices generated by upstream airfoils, (b) the relative motion of the rotors with respect to the stators (potential effect), and (c) the shedding of vortices by the airfoils because of blunt trailing edges. Computation of such flow is further complicated by the relative motion between the rotor and stator airfoils and the periodic transition of flow from laminar to turbulent. However, in order to improve the current design procedures a clear understanding of the unsteady process within turbomachinery is very much necessary. Over the past two decades steady progress has been made in the development of fluid flow analyses for turbomachinery blade rows. The eventual goal of these analyses is a time accurate model of the three-dimensional flow through the blade rows. In recent years, several papers on turbomachinery blade row computation are published. Several approach using two and three-dimensional Euler and Navier-Stokes equations for isolated blade rows and stator-rotor interaction are presented. Cascade flows are important to acquire a good understanding of the laminar to turbulent flow transition phenomena, interaction of shock and bondary layer, separation etc. However, information regarding the periodic transition of the flow resulted by the relative motion of the rotors with respect to the stator can not be obtained by such flow analyses. Dring et al.(1982) in his experimental work showed that the temporal pressure fluctuation near the leading edge of the rotor airfoil can be as much as 72 percent of the exit dynamic pressure, when the axial gap is reduced to 15 percent of the chord length (for the operating conditions and geometry chosen). Therefore, it is very much essential to consider the stator and rotor airfoils as a system in cases where interaction effects are predominant. It is very difficult and even impractical to treat both the stator and rotor by a single computational domain. Since it would result in considerable distortion of the stator and rotor to provide the rotor motion. Consideration of zonal grid is the obvious solution to this problem. Typically, a set of stationary grids to treat the stator airfoils and a set of moving grids (stationary with respect to the rotor) to treat the rotor airfoils can be used. Then, based on special boundary conditions, information between the several grids can be transferred.. Rai(1987a),(1987b) presented two and three dimensional rotor stator interaction results for an axial turbine. The airfoil geometry and flow conditions used in their studies were same as those in the experiments of Dring et al. The unsteady thin layer N-S equations were solved in time accurate manner to obtain the unsteady flow field associated with this configuration. The governing equations were solved on a system of patched and overlaid grids with information transfer from grid to grid taking place at the zonal boundaries. The numerically obtained results are compared with the experimental results of Dring et al.(1982). In the two-dimensional case, a good comparison between theory and experiment is obtained in the case of time averaged pressures on the rotor and stator airfoils. Pressure amplitudes corresponding to the pressure variation in time were found to compare reasonably with the experiment in their study. Later, in Rai (1987b) the approximation of two-dimensionality is removed and fully three-dimensional airfoils geometries are used. In addition, the hub, outer casing, and rotor tip clearance are all included in the calculations. As in Rai(1987a), a system of patched and overlaid grids is used to discretize the rather complex geometry of the three-dimensional configuration. An implicit, upwind third order accurate method is used in all the patches (the calculation of Rai(1987a) used hybrid upwind/central difference scheme near the surface boundaries). The equations solved are the unsteady, thin layer, Navier-Stokes equations in three dimensions. As in Rai(1987a), time-averaged airfoil surface pressure were found to compare well with experiment, but numerically obtained pressure amplitudes were only reasonably close to experimental data. One approximation that was made by Rai (1987a), (1987b) was re-scaling of the rotor geometry. The experimental turbine of Dring et al.(1982) has 22 airfoils in the stator row and 28 airfoils in the rotor row. Therefore an accurate calculation would require a minimum of 25 airfoils (11 in stator row and 14 in rotor row). In order to avoid the computational expense involved in simulating the flow associated with 25 airfoils, the rotor airfoils was enlarged by a factor of 28/22, keeping the pitch to chord ratio the same. It was then assumed that there were 22 airfoils in the rotor row. This assumption makes it possible to perform a calculation with only one rotor and one stator, thus reducing computation time by more than one order of magnitude. Whereas, this approximation has little or no effect on time averaged pressure distributions, it does affect the temporal variation of the flow variables. Far-field acoustics are significantly altered when the configuration is changed to have an equal number of rotor and stator airfoils. Later, Rai(1990) performed some computations using a solver that Copyright (c) 2003 by GTSJ Manuscript Received on July 7, 2003 Proceedings of the International Gas Turbine Congress 2003 Tokyo November 2-7, 2003 |
