Gust Response Decomposition in a Stator/Rotor Axial Compressor with Varying Axial Gap

Abstract

The objective of this paper is to decompose the unsteady force on the rotor of a stator/rotor axial compressor into vortical and potential contributions, for axial gaps of 10, 20, and 30% chord between blade rows. Three methods of decomposition are proposed. The nal method adopted requires two steps. First, the potential contributed gust within the gap region is found using a panel code for stator/rotor con guration and the vortical contributed gust from the difference between that calculated by a Navier -Stokes code and the potential gust. Second, the rotor gust response is decomposed using the NavierStokes code in the rotor cascade con guration, with the vortical and potential disturbances as separate inlet boundary conditions. Results show that the rotor gust response caused by vortical contribution is dominant when the upstream wake impinges upon the rotor leading edge. The rotor gust response caused by potential contribution reaches an extremum when the stator trailing edge is closest to the rotor leading edge. Both vortical and potential contributions are important to determine the total blade response when the axial gap is less than about 30% of the chord. Nomenclatureclosure coef cients of turbulence model D = additional dissipation term of turbulence kinetic energy E, F = production and dissipation term of turbulence dissipation rate, respectively f m , , f f m m 1 2 = closure coef cients of turbulence model G k = production term of turbulence kinetic energy h = circumferential spacing of line vortices in panel method i, i = unit vector in axial direction, 21 Ï j = unit vector in tangential direction k = turbulence kinetic energy p = static pressure Re = Reynolds number based on inlet ow velocity and blade chord R t = turbulence Reynolds number S = total length of a blade surface s = coordinate along blade surface T = blade-to-blade period or spanwise moment t = time U t = wall shear velocity U`= inlet uniform velocity u = streamwise component of instantaneous velocity u = absolute ow velocity vector, ui 1 vj ub = rotor blade wheel velocity vector V = magnitude of instantaneous absolute velocity v = transverse component of instantaneous velocity W = periodic unsteady relative velocity from NS code Research Scientist, CFD and Environmental Engineering Section; currently Associate Research Scientist, National Center for High-Performance Computing, Hsinchu 300, Taiwan, ROC. ‡Doctoral Student. w = complex velocity potential x, x = position vector, axial direction y = tangential direction y 1 = wall variable used in f m Z g = axial gap z = complex number or radial direction G = circulation l = normalized turbulence length scale « = dissipation rate of turbulence kinetic energy m t = eddy viscosity coef cient, rC m f u k 2 /« s«, sk = Prandtl number of turbulence dissipation rate and kinetic energy, respectively tw = wall shear stress Subscripts B = bound circulation b = blade NS = Navier -Stokes calculation p = potential disturbance or panel code calculation v = vortical disturbance W = shedding or wake vorti...

Wake Vorticity Decay and Blade Response in an Axial Compressor With Varying Axial Gap

“…12 (Hsu and Wo, 1998). Also shown (solid line without symbol) is the stand-alone contribution by the potential disturbance of the rotor towards the total unsteady force on the stator for 10% chord gap, which is decomposed using the procedure described in Wo et al (1997). (The contribution from 30% chord gap is essentially zero, thus omitted in Fig.…”

“…Manwaring and Wisler (1993) provided extensive comparison between the state-of-the-an analysis methods and data on forced response. Chung and Wo (1997) used both Navier-Stokes and panel codes to split the disturbances between blade rows into vortical and potential contributions and Wo et al (1997) provided details on decomposition of forced response. Hsu and Wo (1998) recently showed that if the blades are clocked properly the potential disturbance from the second rotor row can substantially reduced the upstream stator response caused by wakes from the first rotor blades.…”

Reduction of Unsteady Blade Loading by Beneficial Use of Vortical and Potential Disturbances in an Axial Compressor With Rotor Clocking

“…The work by Manwaring and Wisler (1993) provided extensive comparison between the state-of-the-art analysis methods and data. Chung and Wo (1997) used both Navier-Stokes and panel codes to split the gust between blade rows into vortical and potential contributions, and Wo et al (1997) provided details on decomposition of gust response. Although the researchers aforementioned differ somewhat in their approach to decomposing disturbances into vortical and potential contributions, all agree that both need to be considered for loaded compressors and turbines, especially at small axial gap.…”

Reduction of Unsteady Blade Loading by Beneficial Use of Vortical and Potential Disturbances in an Axial Compressor With Rotor Clocking

“…The work by Manwaring and Wisler (1993) provided extensive comparison between the state-of-the-art analysis methods and data. Chung and Wo (1995) used both Navier-Stokes and panel codes to split the gust between blade rows into vortical and potential contributions, and Wo et al (1997) provided details on decomposition of gust response. Although the researchers aforementioned differ somewhat in their approach to decompose disturbances into vortical and potential contributions all agree that both need to be considered for loaded compressors and turbines, especially at small axial gap.…”