Small Perturbation Analysis of Nonuniform Rotating Disturbances in a Vaneless Diffuser

Abstract

The behavior of the distorted flow discharged from a centrifugal impeller within a vaneless diffuser is examined theoretically by assuming small disturbances to a main flow. The inlet static pressure distribution is found in the calculation and allowance is made for circumferential nonuniformity in the relative flow angle. The flow is treated as incompressible and inviscid. The analysis shows that the decay of irrotational disturbances is more rapid with increasing disturbance wave number (e.g. more impeller blades) and the effect of the main flow condition on this behavior is very small. With rotational disturbances, however, the decay is slower than in the irrotational case and the effect of wave number is less. However, the phase angle between radial and tangential velocity fluctuations is found to have a strong influence on the decay processes for rotational disturbances. The present small perturbation theory is compared with the well-known Dean and Senoo theory which assumes that the relative flow angle is circum ferentially uniform. The comparison shows that the present theory predicts results very similar to the Dean and Senoo theory for impellers with large blade numbers (>20). For small numbers of blades the large circumferential nonuniformity in relative flow angle, appears at smaller radii and the inaccuracy of the Dean and Senoo theory becomes pronounced.