Débit critique d'apparition de la recirculation à l'entrée des roues de pompes centrifuges : phénomènes déterminants, méthodes de détection, critères de prévision

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When a centrifugal-, mixed - or axial-flow pump operates at partial capacity, a highly unsteady flow suddently appears, at a certain capacity, at the impeller entrance in the suction pipe. As soon as the capacity slightly decreases, a steady annular swirling reverse flow arises at the pipe wall. The flow becomes tridimensional with a velocity pattern showing axial (reversed at the wall : reverse flow), tangential (prerotation) and radial components. At the same time a sudden remarkable increase of the static pressure can be observed. The capacity at which the swirling reverse flow appears at the leading edge of the impeller blade tip section is defined as the "critical capacity" ; it dictates the reliable operating range of the pump. At smaller capacities, the reverse flow develops more and more and changes the level of noise, of vibrations and pressure, torque and thrusts' pulsations. According to flow visualizations in the impeller and to the more significant experimental data published in literature it can be supposed that the suction reverse flow is strictly related to a boundary layer separation near the leading edge on the suction side of the blade at tip. A clear typical liaison exists in all impeller types : centrifugal-, mixed- and axial-flow between the peak of the incipient cavitation at part capacities, the leading edge flow separation and the reverse flow onset. Such liaison is an evident proof of the fact that the aerodynamic pressure field represents the critical phenomenon for the start of recirculation. A physical analysis, simple and qualitative, of the phenomenon of the boundary layer separation on the blade suction side in the centrifugal pump impeller shows that there is : a) no direct influence of the centrifugal forces b) a limited direct influence of the Coriolis forces c) a critical influence of the aerodynamic forces d) an important influence of the tridimensional and viscous phenomena. The impeller design appeared more crucial than the volute design. Several variants of a reference impeller have been designed and tested in the same volute. The design criteria of the variants and the critical parameters have been radically and sistematically changed. The research program covered two reference values of the specific speed : NQ = 37.2 (4 impellers) and NQ = 48.2 (2 impellers). Moreover the influence of the impeller-volute matching conditions (2 impellers) was investigated. Particularly, with the variants A2 and C1 new design criteria were introduced, which concern the hub-to-tip distribution of the aerodynamic loading on the blade (tridimensional effects). The detection of the critical capacity is important in order to determine the reliable operating range of the pump. Several detection methods can be tested, both direct and indirect. The direct methods consist in detecting the sudden change of the flow in each section of the suction pipe. The one dimensional velocity and pressure field suddenly changes into a fully tridimensional flow. The directs methods are the following ; A) flow visualization, B) axial and tangential velocity traverses, C) oscillating small vanes, D) variation of the wall pressure. The indirect methods are based on the liaison between the reverse flow onset and the peak of the incipient cavitation curve. They are essentially incipient cavitation detection methods. The development and collapse of the cavitation bubbles cause the variation of : A) the energy (head) level, B) the sound pressure level (noise), C) the suction pressure fluctuations, D) volute pressure fluctuations, E) the axial vibrations of the pump casing, F) the shaft torque fluctuations. The direct methods for test and detection are more suitable for research on models because they are accurate and complete but also rather time consuming. The indirect methods show a more or less acceptable scattering. The noise method and the torque fluctuations method require additional refinements. The adoption of several indirect methods reduces the uncertainty degree and seems to be a reliable procedure for field detection of the critical capacity of fully scale pumps. The elaborated set of experimental data concerns velocity traverses and wall pressure measurements at the impeller inlet and exit sections for several capacities. The critical capacity referred to the design capacity, Qcr/Qdes, reached considerably different values for the tested impeller variants. Tests clearly point out that : 1) the impeller design is very crucial, whereas the direct influence of the volute is negligible ; 2) there is no univocal link between the critical capacity and the specific speed, simply the general trend showing that Qcr/Qdes is an increasing function of the Ns for impellers of conventional design can be indicated. Several criteria have been applied in order to establish a global simple correlation between the critical capacity and the design parameters. The general approach was to examine the several physical causes, which are susceptible from the theoretical point of view of generating the boundary layer separation near the leading edge on the suction side of the blade at tip. The onset of the suction recirculation is not related to the pressure peak at the impeller exit forced by the volute. The pressure average overall increase (centrifugal and aerodynamic) through the impeller does not directly produce the reverse flow. But, if the pressure gradient given by the centrifugal forces is excluded, a relationship between the aerodynamic pressure increase and the reverse flow onset is evident and can be fully explained from the physical point of view. Therefore, it is experimentally demonstrated that the centrifugal pressure field doesn't influence the boundary layer separation and the onset of the suction reverse flow in the centrifugal impellers, while the effects of the aerodynamic pressure field are very crucial. According to Figure 12 it can be seen that, at the critical capacity, a well-defined liaison between the aerodynamic pressure coefficient, the aerodynamic loading and the effects of losses and of the secondary flows for the impeller tip blades cascade is present. All these effects are typical of the impeller relative flow. The accurate prediction of the velocities and of the angles in the relative flow appears as a necessary and at the same time very delicate step for establishing a global accurate criterium for predicting the critical capacity.The relative flow in the centrifugal impellers is given by the superimposition of : 1) "displacement flow" (vortex flow without capacity), 2) "relative through flow" (with positive capacity). The ideal slip factor caused by the "displacement flow" has been determined by using the Busemann's theory, which applies to very thin, uncambered blades' cascades, both radial and rotating. An additional deviation, which is introduced by the "relative through flow" because of the blades camber and the tridimensional and viscous effects, has also been considered. In order to estimate the additional deviation according to rel. (8) the correlations commonly used for the axial blades cascades were taken into account. These correlations have been transformed and extended by the author to the radial blades cascade by means of some (classified) purely theoretical criteria, which establish a physical relation between the phenomena responsible for the additional deviation in both the axial and radial flow fields. A global slip factor has been defined and calculated and then compared to the real slip factor derived from the velocity traverses at the impeller exit. The comparison results quite acceptable (~ 5 %), exceptions made for variants C and C1 requiring further refïnements, which are already defined from the theoretical point of view. The approach to the problem of predicting the critical capacity has followed various criteria. However these criteria are based on the common theoretical hypotesis rel. (10), that the "displacement flow" is invariable with the capacity. The analysis of the different global criteria of predicting Qc/Qdes shows that the criteria elaborated on the basis of the diffusion factor are the most significative and complete from the point of view of the physical description of the phenomenon. According to relations (13) - (17) and to Figure 13, it seems that the onset of centrifugal pumps suction recirculation is linked to a critical value of the diffusion factor in the relative flow at the impeller tip blade section. This critical value can be derived from the limit value in the axial cascade two dimensional flow modified by : a) the tridimensional (aerodynamic blade distribution from the hub to the blade tip), b) viscous (friction and secondary flow losses) and c) meridional streamlines curvature (tip shroud curvature) effects. Similar elaborations, still based on the diffusion factor concepts, are presented within relations (18) and (22). They confirm that these concepts are the most effective, although their formulation and application are not completely correct from either the theoretical or the experimental points of view. The other theoretical approaches (diffusion ratio ; lift coefficient ; incidence angle) or the empiriral correlations published in literature do not show an accurate prediction for the tested configurations.