Discussion: “Experimental Measurements of Hydrodynamic Radial Forces and Stiffness Matrices for a Centrifugal Pump-Impeller” (Chamieh, Dimitri S., Acosta, Allan J., Brennen, Christopher E., and Caughey, Thomas K., 1985, ASME J. Fluids Eng., 107, pp. 307–315)

Abstract

As one who has the same interest in the hydrodynamic forces of whirling centrifugal impellers, I would like to express my respect for carrying out such delicate and complex experiments successfully. Following are a few comments on your result.1 Despite a remarkable difference in the average volute forces F Q of Volute A and B, the difference in the stiffness matrices of both volutes is surprisingly small. This may imply that stiffness matrices are insensitive to the configuration of volute casing. It is, however, still unknown how stiffness is affected by impeller geometries.The result for centrifugal impellers in vaneless diffuser obtained by our test facility [16] showed a smaller diagonal term (about one quarter of equation (4)) and cross-coupling term which was destabilizing at lower flow rate and stabilizing around design flow rate.Therefore, the stiffness matrices can be quite different from one impeller to another and the result approximately presented by equation (4) seems applicable to a specific impeller.2 Since the hydrodynamic stiffness of impeller vanes and shrouds are different in nature, the fraction of outlet width b 2 to total width vv 2 is an important parameter. Please give the value of the test Impeller X.3 At lower flow rate close to shutoff, the flow in the impeller becomes quite turbulent and the fluid force fluctuates violently. Have you experienced any measurement problems associated with this phenomena? Additional Reference16 Ohashi, H., Shoji, H., and Kato, C, "Experimental Study of Fluid Forces on Whirling Centrifugal Impeller (1st Report; Impeller in Vaneless Diffuser)," Trans. JSME, Vol. 51, No. 467, July 1985, pp. 2373-2381 or NASA CP 2338 Mechanical Engineering, University of Tokyo, Bunkyo-Ku, Tokyo 113, Japan.11 Kurokawa, J., "Theoretical Determinations of the Flow Characteristics in Volutes," IAHR/AIRH Symposium, Tokyo, Japan, 1980, pp. 623-634. Authors' ClosureThe authors wish to thank Professor Ohashi for his continuing interest in this paper in particular, and this research field in general. The work presented herein was concluded in late 1982 and has since been validated and extended at the Caltech Rotor Force Test Facility to inlcude the full dynamic effect of whirl [17,18]. Currently additional research was also initiated to study the effects of cavitation inception and net positive suction head on the magnitudes of the stiffness matrix coefficients [19]. While we agree that the similarities between the stiffness matrices of Volutes A and B are relatively striking, additional experiments by Jery, et al. [17] for 7 different volutes/diffusers and 2 different impellers of about the same specific speed seem to validate that fact. The stiffness matrices Professor Ohashi obtained in his very valuable study are much lower than those presented here probably because of the large collector case used in his experiment. An impeller discharging in an infinite medium should have no stiffness coefficients.The width of the impeller discharge including the shrouds is 26 mm. The int...