27The Fifth International Conference on VIBRATION ENGINEERING AND TECHNOLOGY OF MACHINERY Huazhong University of Science and Technology, Wuhan, P.R. CHINA. 27-28 , August, 2009 2009 Huazhong Universiti of Science and Technology Press THE EFFECT OF CHANGE IN THE NUMBER OF STATOR BLADES IN THE STAGE ON UNSTEADY ROTOR BLADE FORCES Romuald Rzadkowski Marek Soliski Institute of Fluid-Flow Machinery Polish Academy of Sciences (Email:z3imp.gda.pl, msolimp.gda.pl) ABSTRACT Analysed here was a 100-MW steam turbine in which the unsteady forces acting on the extraction stage rotor blades were found to be large. This was in particular valid for the circumferential components unsteady forces. Results of calculations performed for the same boundary conditions but with different numbers of stator blades in the system are presented. Increasing the number of stator blades considerably affects the level of unsteady forces acting on a single blade. These changes refer to both the stationary components of these forces and their first high-frequency harmonic, which decreases when the number of stator blades is increased. KEYWORDS unsteady forces, rotor blade, stator blade. I. INTRODUCTION The number of stator blades affects the level of unsteady forces acting on rotor blades 1, 2. 1 has shown for the simplified geometry of a stator and rotor blades the minimum value of unsteady forces acting on the rotor blades occurs when the number of stator blades (zs) is equal to the number of rotor blades (zr). For each stage with a constant number of real rotor blades 2 found that when the number of stator blades increases, the levels of unsteady forces reach their maximum with zs/zr =0,25-0.3 and then decrease to minimum with zs/zr =1.2. For the 100-MW turbine extraction stage the unsteady forces acting on the blades were large (zs/zr =0,33) 3. This was in particular valid for the circumferential component, the first high-frequency harmonic of which reached even as much as 100% of the stationary component. In this stage the failure of the rotor blade was reported 3, even though the first five natural frequencies of rotor blade were beyond its resonance regions. This paper discusses the results of calculations performed for the same boundary conditions but with different numbers of stator blades in the system. For each stage, when the number of stator blades increases (zs/zr from 0,33 to 0,76) the levels of unsteady forces are considerably reduced. In order to avoid rotor blade failure we have recommended that turbine manufacturers should increase the numbers of stator blades. The other new results presenting here concern how unsteady components change along the blade length when the number of stator blades is altered. II. AERODYNAMIC MODEL Considered here is the 3D transonic flow of inviscid non-heat conductive gas through an axial turbine stage, including the nozzle cascade (NC) and the rotor wheel (RW), rotating with constant angular velocity. Usually both NC and RW have an unequal number of blades of varied configurations. Taking 28into account the flow unperiodicity from blade to blade (in a pitchwise direction) it is convenient to choose calculation domain that includes all the blades of the NC and RW assembly, the entry region, the axial clearance and the exit region (see Fig.1). The spatial transonic flow, generally including strong discontinuities in the form of shock waves and wakes behind the exit edges of blades, written in the relative Cartesian coordinate system rotating with constant angular velocity , according to full non-stationary Euler equations, is presented in the form of integral conservation laws of mass, impulse and energy 4, 5, 6. The calculated domain, including all blades on the whole annulus as well as inlet and outlet domains, consists of two subdomains (NC and RW) having a common part. Let the number of stator and rotor blades be zs and zr, respectively. The difference grid is divided into zs + zr difference segments, each of them includes a blade and expands in circumferential direction which is equal to the pitch of the stator or rotor, respectively (see Fig.1). Each of passages are dicretized using an H-type grid for the stator domain and a hybrid H-H grid for the rotor domain 6. Fig. 1 The tangential and axial section of the turbine stage. The discretized form of governed equations is obtained using the Godunov idea, but in the more universal form extended to three space coordinates 4, 6: 11 21 21 21 21 21 21 21 21 21 21 21 2tffijkijkijkijk+, ()()()()()+111knjnjnininwfwfwfwfwf ()()()()()()()+kkjjiiknFFFFFFwf 332211111+ H+ijk1 21 21 2,+ijk1 21 21 2,=0 (1) The gasodynamic parameters on the lateral sides (expressions in square brackets with integer indexes) are defined using the Riemann problem of arbitrary discontinuity on t