Unsteady Numerical Simulations of the Flow Related to the Unstable Energy-Discharge Characteristic of a Medium Specific Speed Double Suction Pump
Regions of positive slope in the pressure-discharge characteristics can result in a reduction or even lack of damping of system instabilities. They are therefore one of the major concerns in design and operation of centrifugal pumps as they are limiting the admissible operating range. The considered preliminary hydraulic design of an industrial double suction pump of medium specific speed n = 0.410 (0.205 per impeller side) shows a marked saddle in the energydischarge characteristic associated to a sudden drop of efficiency versus discharge at part load. Unsteady RANS type flow simulations are performed using hexahedral meshes with 2.5 million nodes to model the inlet casing, the shrouded double sided impeller with 2 x 7 blades, the diffuser with 12 blades and the volute. In unsteady solution monitoring, low frequency (below blade passing frequencies) phenomena are noticed. Therefore, simulation times of up to 10 impeller revolutions at each flow rate are requested to achieve statistically steady behavior of the flow judged on global performance numbers and circumferential flow rate distribution. The numerical simulations emphasize a drop in the characteristic, though at a lower flow rate than found on the test rig. It is shown to be associated to a one-sided separation in the diffuser, further leading to an unbalanced flow rate distribution of about 10% of flow rate between both sides of the impeller. There is a region of hysteresis, where both configurations with balanced and unbalanced flow rate distributions can be obtained for the same global flow rate. The asymmetric flow distribution leads to asymmetric velocity profiles at the impeller-diffuser interface which results in a strongly vortical flow in the diffuser channels, where an important amount of energy is dissipated in regions of increased viscous and turbulent shear.
Effect of Stall Cells on Pressure Fluctuations Characteristics in a Centrifugal Pump
Rotating stall is an unsteady flow phenomenon, which always leads to instability and efficiency degradation. In order to reveal pressure fluctuations in the impeller of centrifugal pump induced by stall cells, the flow structures in a volute-type centrifugal pump were calculated using Large Eddy Simulation (LES) method. The predicted results of the numerical model were compared with experimental flow-head curve. The simulation results were in good agreement with the experimental results. The stall phenomenon occurred when the flow rate dropped to 70% of design flow rate. Three stall cells located at the entrance of passages could be observed, which remained stationary relative to the rotating impeller. With the decrease of flow rate, the area occupied by stall cells gradually increased. The peak value of pressure fluctuation at 25% of design flow rate is obviously larger than that at 50% of design flow rate. For the unstalled or stalled passage, the impeller-volute interaction played a leading role in the pressure fluctuations of the impeller. For the stalled passage, the amplitude of the low frequency induced by stall cell is relatively insignificant.
Laminar heat or mass transfer in rectangular channels and in cylindrical tubes for fully developed flow: comparison of solutions obtained for various boundary conditions
Abstract A comparison is made of results obtained with various boundary conditions at the wall of the channels. By comparing blood Sherwood numbers for finite wall resistance with those for constant concentration boundary condition only a small variation is found for various points along the blood channel.