有限翼数の羽根車に生じるキャビテーションの定常流れ解析と安定解析

In order to study the effect of different numbers of impeller blades on the performance of mixed-flow pump “saddle zone”, the external characteristic test and numerical simulation of mixed-flow pumps with three different impeller blade numbers were carried out. Based on high-precision numerical prediction, the internal flow field and tip leakage flow field of mixed flow pump under design conditions and stall conditions are investigated. By studying the vorticity transport in the stall flow field, the specific location of the high loss area inside the mixed flow pump impeller with different numbers of blades is located. The research results show that the increase in the number of impeller blades improve the pump head and efficiency under design conditions. Compared to the 4-blade impeller, the head and efficiency of the 5-blade impeller are increased by 5.4% and 21.9% respectively. However, the increase in the number of blades also leads to the widening of the “saddle area” of the mixed-flow pump, which leads to the early occurrence of stall and increases the instability of the mixed-flow pump. As the mixed-flow pump enters the stall condition, the inlet of the mixed-flow pump has a spiral swirl structure near the end wall for different blade numbers, but the depth and range of the swirling flow are different due to the change in the number of blades. At the same time, the change in the number of blades also makes the flow angle at 75% span change significantly, but the flow angle at 95% span is not much different because the tip leakage flow recirculates at the leading edge. Through the analysis of the vorticity transport results in the impeller with different numbers of blades, it is found that the reasons for the increase in the values of the vorticity transport in the stall condition are mainly impacted by the swirl flow at the impeller inlet, the tip leakage flow at the leading edge and the increased unsteady flow structures.

An analysis of steady cavitation on flat plate cascade is performed by a singularity method based on closed cavity model. As a result, it is found that two kinds of the steady cavitation patterns exist. One is equal length cavitation in which the cavity lengths of all blades are the same. The other is alternate blade cavitation in which the cavity length changes alternately from blade to blade. Although the present model fails to predict the range of cavitation number where alternate blade cavitation occurs, it predicts alternate blade cavitation in terms of cavity length fairly well. The static pressure losses in both the equal length cavitation and the alternate blade cavitation are estimated. A parameter study is carried out to educe the general characteristics of alternate blade cavitation.

This paper describes an experimental investigation of rotor–stator interaction in a centrifugal pump with several vaned diffusers. Steady and unsteady diffuser vane pressure measurements were made for a two–dimensional test impeller. Unsteady impeller blade pressure measurements were made for a second two–dimensional impeller with blade number and blade geometry identical to the two–dimensional impeller used for the diffuser vane pressure measurements. The experiments were conducted for different flow coefficients and different radial gaps between the impeller blade trailing edge and the diffuser vane leading edge (5% and 8% of the impeller discharge radius). The largest pressure fluctuations on the diffuser vanes and the impeller blades were found to be of the same order of magnitude as the total pressure rise across the pump. The largest pressure fluctuations on the diffuser vanes were observed to occur on the suction side of the vane near the vane leading edge, whereas on the impeller blades the largest fluctuations were observed to occur at the blade trailing edge. However, the dependence of the fluctuations on the flow coefficient was found to be different for the diffuser vanes and the impeller blades; on the vane suction side, the fluctuations were largest for the maximum flow coefficient and decreased with decreasing flow coefficient, whereas at the blade trailing edge, the fluctuations were smallest for the maximum flow coefficient and increased with decreasing flow coefficient. Increasing the number of the diffuser vanes resulted in a significant decrease of the impeller blade pressure fluctuations. The resulting lift on the diffuser vanes was computed from the vane pressure measurements; the magnitude of the fluctuating lift was found to be larger than the steady lift.

The effect of diffuser on compressor performance and noise emission is studied in this paper. Firstly, on the basis of the mature compressor model, the airflow geometry from impeller inlet to volute exit has been simulated numerically. Then, the number of diffuser blade is changed and the impeller blade number remains unchanged. The effects of different diffuser blade number on compressor performance at three different compressor operating lines were analyzed and noise emission has been investigated at selected compressor operating point. It is found that flow range narrows down with blade number increase but there are pressure and efficiency enhancement at maximum efficiency working range with specific blade number. The noise simulation results show that there has the best stator blade number when the impeller blade unchanged. Moreover, a special kind of technique that called pinched diffuser is investigated in this paper. The results of four different pinch constructions indicate that the pinched diffuser can shift the surge line to low flow rates but the pressure passing through centrifugal compressor has decreased at the same time, small pinch is conducive to noise reduction which means there is also an optional structure that can obtain minimum noise, which means a more reasonable pinched construction design should be studied to improve the compressor performance and control the radiated noise.

Numerical analysis of unsteady cavitating flow in an axial inducer

This paper presents the results of an experimental investigation of the power input of pitched blade impellers and standard Rushton turbine impellers in a cylindrical vessel provided with four radial baffles at its wall under a turbulent regime of flow of an agitated liquid. The influence of the geometry of the pitched blade impellers (pitch angle, number of blades) and the off-bottom impeller clearance of both high-speed impellers tested on the impeller power input is determined in two sizes of the cylindrical vessel (0.3 m and 0.8 m diameter of vessel). A strain gauge torquemeter is used in the small vessel and a phase shift mechanical torquemeter is used in the large vessel. All results of the experiments correspond to the condition that the Reynolds number modified for the impeller exceeds ten thousand. The results of this study show that the significant influence of the separating disk thickness of the turbine impeller corresponds fairly well to the empirical equations presented in the literature. Both the influence of the number of impeller blades and the blade pitch angle of the pitched blade impeller were expressed quantitatively by means of the power dependence of the recently published correlations: the higher the pitch angle and the number of blades, the higher the values of the impeller power input. Finally, it follows from results of this study that the impeller off-bottom clearance has a weak influence on the power input of the Rushton turbine impeller, but with decreasing impeller off-bottom clearance the power input of the pitched blade impeller increases significantly.

A set of 4-bladed inducers with various amounts of cutback was tested with the aim of suppressing the rotating cavitation by applying alternate leading edge cutback. Unsteady cavitation patterns were observed by means of inlet pressure measurements and high-speed video pictures. It was found that the region with the alternate blade cavitation and asymmetric cavitation were enlarged with the increase of the amount of the cutback. As a result, the region with the rotating cavitation was diminished. At low flow rate, two types of alternate blade cavitation were found as predicted theoretically on 4-bladed inducer with smaller uneven blade length. One of them is with longer cavities on longer blades, and the other is with longer cavities on shorter blades. Switch was observed in these alternate blade cavitation patterns depending whether the cavitation number was increased or decreased. For an inducer with larger amount of cutback, the rotating cavitation and cavitation surge were almost suppressed as expected for a wide range of flow rate and cavitation number, although the cavitation performance was deteriorated. However, we should note that an asymmetric cavitation pattern occurs more easily in inducers with alternate leading edge cutback, and that the unevenness due to the cutback causes uneven blade stress.

As the centrifugal pump is running, the fluid usually flows into the impeller along pump shaft, and the fluid flows out radially by the force of the impeller. The force is mutual, so the impeller is also subjected to the reaction force of the fluid, but the distribution of this force on the blades is uneven. In addition, the front and rear shrouds of the impeller are asymmetric, which are the main causes of axial force. This paper adopts numerical calculation method studying the mechanism of axial force of impeller at all stages of multistage pump at various working conditions, and exploring the formation mechanism of shroud pressure differential force and blade twisting axial force and its variation laws of similarities and differences, analyzing the steady state and transient characteristics between axial force and hydraulic property of double-casing multistage pump. The results show that the rotational angular velocity of the fluid in the front and rear pump chamber at each stage impeller is distributed along the axial direction in three regions, the regions are pump body boundary layer, core region, and impeller boundary layer. The working surface and back surface of the blade twist have the high and low axial force area, and its distribution is staggered, at the same number of stages, the greater the flow rate, the smaller the blade twisting axial force. The shroud pressure differential force with the increase of impeller stages presents a linear increasing trend, conforms to the principle of linear superposition of cover pressure differential force. The total axial force pulsation of multi-stage pump is related to the number of secondary impeller blades, its primary frequency coincides with the secondary impeller blade frequency, increasing the flow rate can reduce the multi-stage pump axial force pulsation amplitude. The pulsation period of single-stage impeller head and efficiency are related to the number of impeller blades, the smaller the number of impeller stages, the stronger the pressure dynamic, and static interference effect of the impeller inlet and outlet. Rotation of the secondary impeller causes dynamic and static interference, which is the main reason for the pulsation of the axial force coefficient in double-casing multistage pumps, the pulsation intensity is related to the periodic generation and shedding of the blade vortex. The results of the study can be used as a reference for optimizing the axial force of double-casing multistage pumps.

Reasonable methods for determining the optimum number of blades in a low specific speed centrifugal pump with closed-type impeller with splitters, i.e. compound impeller have been rather rare in the literature so far. In the article, a new analytical method was put forward to determine such an optimum number of blades by including the effect of turbulent boundary layer over impeller blades. Three conventional impellers with different numbers of full-length blades and two compound impellers with different numbers of splitters were designed and manufactured. The corresponding performance tests were then conducted. Results showed that the optimum numbers of blades exist for two kinds of impeller in terms of head at design point, pump efficiencies at design point and best efficiency point, and slope of head-flow rate curve at shut-off point. The estimated optimum numbers of blades are in good agreement with the numbers based on the experiments. The conventional impellers with full-length blades are more prone to the hump phenomenon than the compound impellers at the optimum numbers of blades. For the compound impellers, however, the hump effect is negligible at the optimum number of blades, and their head and efficiency are higher than those for the impellers with full-length blades. The method is applicable to compound impeller design in low specific speed centrifugal pumps.

This article describes about various types of cavitation instabilities including rotating cavitation and alternate blade cavitation. In section 1, general characteristics of cavitating flow through turbopump inducers are reviewed. In section 2, rotating cavitation in 3- and 4-bladed inducers are discussed focusing on the effect of the number of blades. Section 3 is intended to show the relationship between the operating condition and various types of cavity oscillations in an inducer.

The thermodynamic effect on a cavitating inducer is investigated from joint experiments in cold water and Refrigerant 114. The analysis is focused on leading edge cavitation and cavitation instabilities, especially on alternate blade cavitation and supersynchronous rotating cavitation. The cavity length along cylindrical cuts at different radii between the hub and casing is analyzed with respect to the local cavitation number and angle of attack. The similarity in shape of the cavity closure line between water and R114 is examined and deviation caused by thermodynamic effect is clarified. The influence of rotation speed on cavity length is investigated in both fluids and analyzed on the basis of a comparison of characteristic times, namely, the transit time and a thermal time. Thermodynamic delay in the development of leading edge cavities is determined and temperature depressions within the cavities are estimated. Thresholds for the onset of cavitation instabilities are determined for both fluids. The occurrence of cavitation instabilities is discussed with respect to the extent of leading edge cavitation. The thermodynamic delay affecting the occurrence of cavitation instabilities is estimated and compared with the delay on cavity development.

The regenerative liquid ring (RLR) pump is a type of rotodynamic pump which combines the mechanical impulses of the impeller with centrifugal force. The head is increased through recirculation, or regeneration, of the fluid in the impeller blades. The design of the regenerative machine has evolved over many decades and improvements have been made in the design, particularly in the shape and number of impeller blades. However, few publications exist on other design aspects such as the radial and axial clearances between the impeller and the casing, and more crucially most researchers tend to investigate these elements in isolation. This highlights the key driver and novelty of this current research, which applies modern Computational Fluid Dynamics (CFD) tools to systematically assess the effects on pump performance over a large range of impeller-casing clearance parameters and understand their operational behaviour. The sizes of the clearances are dictated by the manufacturer’s drawing tolerances on critical pump components. The results of the parametric clearance analysis showed that there could be a potential variation in head performance by as much as 25%. Furthermore, it highlighted the need to experimentally test a number of pumps within a representative tolerance range. Three test pumps were therefore manufactured and tested. A discrepancy between the CFD and experimental results was observed but the experimental results confirmed that variations in clearances have an impact on the performance, particularly on the developed head. This was more noticeable at higher operational speeds where the pressure differential varied by as much as 19%. A one-way Fluid-Structure Interaction analysis of the three test impellers was carried out to shed some light on the operational behaviour of the pumps and the effects on the clearances due to non-uniform loading by importing pressure profiles from the corresponding CFD simulations. Assessing the deformation against the computational and experimental pressure, the results indicate that the maximum allowable radial design clearance should be reduced by 35%. Furthermore, with this radial design tolerance the magnitudes of the drive end and non-drive end clearances have a lower impact on the performance. The RLR pump is unique and requires further comparison studies between experimental testing and computational analysis.

The present study focuses on the aerodynamic performance and structural analysis of the centrifugal compressor impeller. The performance characteristics of the impeller are analyzed with and without splitter blades by varying the total number of main and splitter blades. The operating conditions of the compressor under centrifugal force and pressure load from the aerodynamic analysis are applied to the impeller blade and hub to perform the one-way Fluid–Structure Interaction (FSI). For the stress assessment, maximum equivalent von Mises stresses in the impeller blades are compared with the maximum allowable stress of the impeller material. The effects of varying the pressure field on the deformation and stress of the impeller are also calculated. The aerodynamic and structural performance of the centrifugal compressor at 73,000 rpm are investigated in terms of the efficiency, pressure ratio, equivalent von Mises stress, and total deformation of the impeller.

Alternate blade cavitation, rotating cavitation and cavitation surge in rocket turbopump inducers were simulated by a three dimensional commercial CFD code. In order to clarify the cause of cavitation instabilities, the velocity disturbance caused by cavitation was obtained by subtracting the velocity vector under non-cavitating condition from that under cavitating condition. It was found that there exists a disturbance flow towards the trailing edge of the tip cavity. This flow has an axial flow component towards downstream which reduces the incidence angle to the next blade. It was found that all of the cavitation instabilities start to occur when this flow starts to interact with the leading edge of the next blade. The existence of the disturbance flow was validated by experiments.

A full three-dimensional inverse solution of the impeller blade shape is presented. The inverse method automatically calculates the blade shape which satisfies flow characteristics specified by a designer without trial iteration of flow analysis calculations. The flow is assumed to be inviscid and incompressible. The impeller blades are represented by superposition of vortices and sources on the blade mean surface. By expanding generalized velocity potential in a Fourier series, a set of two-dimensional quasi-Poisson equations in r and z is obtained. These equations are solved with SOR. Numerical examples are shown for the design of axial flow rotors with free vortex swirl. A blade thickness distribution and a pressure difference distribution across the blade are specified, and the blade mean-surface shape is determined by the inverse method. The results are compared with those presented in our previous report using a Fourier-Bessel expansion. The flow analysis for the designed impeller is performed by means of the two-dimensional singularity method and the three-dimensional panel method, and the calculation accuracy of the inverse method is examined.