A Numerical Study of the Unsteady Flow Field and Tonal Hydrodynamic Sound of a Centrifugal Pump

Abstract

In this paper, the 3-D unsteady turbulent flow inside a centrifugal pump is investigated by computational fluid dynamics (CFD) in ANSYS CFX, using Detached Eddy Simulation (DES) as the turbulence approach. The pump has a single end-suction and a single volute discharge. The impeller is semi-open (unshrouded with baseplate) and has five backswept blades and pump-out back blades. The CFD model of the pump consists of the inlet, the impeller, and the volute. A sliding mesh technique has been applied to the interfaces in order to allow unsteady interactions between the rotating impeller and the stationary parts. These unsteady interactions generate pressure fluctuations over the volute casing and blade surfaces that are hydroacoustic dipoles according to Lighthill’s acoustic analogy theory. The pressure fluctuation spectra at the volute tongue show that pressure fluctuations are generated mainly by the discrete components related to the impeller rotation at low frequencies, especially the blade-passing frequency (BPF) component. This component is approximately 1% of the reference dynamic pressure 0.5ρν22 where ν2 is the circumferential velocity at the impeller outlet. The discrete components with frequency larger than 4 times BPF are no longer obvious in the spectra. Compared to the experimental results, the CFD simulation predicts much lower amplitudes for the broad band pressure fluctuations. This is reasonable, because DES combines a classical Reynolds averaged Navier Stokes (RANS) simulation with elements of Large Eddy Simulation (LES), and both RANS and LES use average methods which filter out the high frequency fluctuations. Nevertheless, CFD is capable of accurately predict the BPF component. The pressure fluctuations on the casing and blade surfaces are extracted and modelled as the stationary and rotary dipoles, respectively, according to the Ffowcs Williams and Hawkings (FW-H) equation of the acoustic analogy theory. After Fast Fourier Transform, the spectra of the pressure fluctuations are obtained, and are used to predict the tonal hydrodynamic sound radiation at BPF and its low order harmonics. The sound radiation of casing surface dipoles is calculated by extracting the tonal components, and performing a surface integration with the fundamental solution to Helmholtz equation as the kernel. A frequency domain formulation of the FW-H equation with the moving surface dipole is employed to predict the tonal blade noise. The results from these acoustical simulations show that the sound power generated by the casing surface dipole is three orders of magnitude higher than that of the blade surface dipole, and the main hydroacoustic sources are located at the volute tongue.