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The multiphase rotodynamic pump is crucial for the multiphase blending transportation process. However, desigining such pump with high hydraulic performance and good blending transportation ability is quite challenging because of its unique structure. This study constructed a multi-objective optimization design system, which combines the 3D inverse design theory, response surface methodology, genetic algorithm, computational fluid dynamics simulation, and multi-objective optimization strategy, to improve the multiphase pump performance. Five optimization variables, namely the impeller loading parameters ( m1,S, m1,H, kS, kH) and the high-pressure edge angle ( θ), were selected in this study. Furthermore, two optimization objectives were considered at inlet gas void fraction ( IGVF) = 10%, namely the pump efficiency and the gas uniformity at the impeller outlet. The optimization results demonstrated that the pump efficiency and blending transportation ability would improve if the impeller blades had for-loaded loading distribution and the negative high-pressure edge angle. After optimization, the pump efficiency and the gas uniformity for the optimized impeller Opt1 improved by 2.6% and 18.2% at IGVF = 10%, respectively. Moreover, the internal flow pattern in the impeller was improved significantly, resulting in the maximum amplitude of pressure fluctuation in impeller Opt1 being 0.42 times that in the original test impeller.

Hydropower is one environmentally friendly option for meeting these energy demands. Because such technologies do not require a weir or a dam, they may be used with minimal environmental effect. The drag-based Savonius turbine is characterized by working at low-flow speeds which fits well the natural water streams. In spite of its simple and robust design, the Savonius turbine suffers from low efficiency and high static torque fluctuations. In view of this, CFD-based optimization is applied to a Savonius-type hydrokinetic turbine inspired by a couple of swimming Koi fish. The two main design parameters; overlap ratio and gap ratio are used in this paper to define the gap between the blades. The maximum power coefficient can be obtained by employing an evolution strategy optimization technique over the constructed metamodel. The results revealed that the optimal design for the bio-inspired Savonius hydrokinetic turbine corresponds to overlap and gap ratios of 0.2085 and 0.0057, respectively. The optimal configuration generates a maximum power coefficient of 0.2521, which is 17.6% higher than that for a conventional shape at the same tip speed ratio. The new bio-inspired design performs better than the conventional Savonius hydrokinetic turbine for the considered operating range.

A centrifugal impeller with splitters was designed by three-dimensional (3D) inverse design method, and its efficiency, velocity non-uniformity at impeller exit and maximum equivalent stress of blades were optimized by providing the suitable blade stacking angle, work ratio and circumferential location of the splitter. First, 80 samples were generated by optimal Latin hypercube technique and the corresponding impellers were designed by 3D inverse design. Using computational fluid dynamics (CFD) and fluid structure interaction (FSI), the optimization objectives were obtained. Then, the group method of data handling (GMDH) artificial neural networks was established to link the design parameters and objectives by the specific formulas. The reference-point-based non-dominated sorting genetic algorithm (NSGA- III) was applied to search the Pareto front. Finally, the preferred impeller was selected by adopting entropy weight and the method of technique for order preference by similarity to an ideal solution (TOPSIS). The results showed that the splitter of the preferred impeller had a circumferential location of 0.58, blade stacking angle of 28° and work ratio of 0.48. The nonuniformity at impeller exit and maximum equivalent stress of blades of preferred impeller obtained by NSGA-III were decreased, while the efficiency was improved.

Due to the effect of unit stages, the gas-liquid flow and the interphase forces in the multistage multiphase pump are more disordered, which will affect the energy conversion efficiency. However, the characteristics of phase interaction and gas holdup in such a pump are not clear. In this study, based on a modified Euler two-fluid model, simulations of a multiphase rotodynamic pump with two stages were carried out with medium combinations of air-water and air-crude. The characteristics of phase interaction and gas holdup were analyzed at different inlet gas void fractions (IGVFs), and inlet bubble diameters. The results show that the overall changing trend of interphase forces is the same between the first and second stages at different IGVFs, but the magnitudes of interphase forces in the second stage are slightly smaller, especially for the medium combination of air-water. Moreover, the drag is more sensitive to the IGVF, while the lift and added mass force are more sensitive to the medium viscosity. As the increase of the inlet bubble diameter, the difference of the gas holdup effect in the pump increases gradually at IGVF = 9.0%, and the maximum almost occurs in the first stage guide vane (S1). When the bubble diameter increases to 0.7 mm, the degree of gas accumulation and gas-liquid velocity difference increase significantly, resulting in a significant increase of the disordered degree of lift and added mass force.

To understand the pressure fluctuations occurring in S-shaped region of the pump-turbine and their relationships with rotor-stator interaction, rotating stall and vortex rope, the numerical and experimental studies of a reversible pump-turbine were conducted under turbine, runaway, turbine brake, small flow rate and reverse pump operating modes. The experimental results show that pressure fluctuations under turbine mode were most affected by the guide vane opening. This effect was weaker under turbine brake mode and weaker still under reverse pump mode. At a guide vane opening of 19 mm, the maximum fluctuation peak in the vaneless space is 5.7 times, 6.9 times and 2.0 times greater than that in the spiral casing inlet, draft tube cone and draft tube elbow, respectively. Unsteady simulation results for the whole flow passage of the pump-turbine show that asymmetric flow occurred in the runner under turbine, runaway and turbine brake operating modes. Meanwhile, an obvious rotating stall vortex with a frequency of 0.65fn was generated in turbine brake mode, resulting in relatively large pressure fluctuations in the vaneless space. At the small flow rate, flow separation in the vaneless space became very obvious, while that in the runner weakened, resulting in decreased pressure fluctuations in the vaneless space. Under reverse pump mode, pressure fluctuations in the vaneless space were relatively small because of obvious symmetrical flow separation in the runner. Pressure fluctuations in the draft tube were mainly attributed to the combined actions of rotating stall and vortex rope phenomena. What’s more, the fluctuation amplitudes at the rotating stall frequency of 0.65fn and the vortex rope frequencies of 0.30fn and 0.17fn were relatively large.

A pumped hydro storage energy station (PHES) is an effective and reliable station which was quickly develop. To obtain better performances, blade leans have been employed recently on pump-turbine runners. To figure out the effect of the blade leans in turbine mode, numerical simulations were performed on two blade-leaned and no-leaned runners in this work. Because blade leans were on high-pressure edges, the vaneless space was paid chiefly attention. Distinctions due to the blade leans can be found in the spanwise direction. Amplitudes of the component of blade passing frequency in pressure fluctuations show nonuniformity at different vertical locations. While in no-leaned runners, the amplitudes are almost the same. It shows close correlations between the pressure fluctuations and blade leans. In addition, this difference was more prominent in the S-shaped region. The conditions were attributed to the different separations at the inlets of runners. Separations located at the pressure side of the blades and developed vortexes located near the hub, the shroud and at the middle span for runners respectively. The vortexes generated low-pressure areas producing a higher fluctuation in the vaneless space with the same frequency of blade passing when they rotated with the runner.

Purpose The purpose of this study is to suppress secondary flows and improve aerodynamic performance of a centrifugal impeller. Design/methodology/approach A multi-objective optimisation design system was described. The optimization design system was composed of a three-dimensional (3D) inverse design, multi-objective optimisation and computational fluid dynamics (CFD) analysis. First, the control parameter ΔCp for the secondary flows was derived and selected as the optimisation objective. Then, aimed at minimising ΔCp, a 3D inverse design for impellers with different blade loading distributions and blade lean angles was completed and multi-objective optimisation was conducted. Lastly, the improvement in the distribution of secondary flows and aerodynamic performance of the optimal impeller was demonstrated by CFD analysis. Findings The study derived the control parameter ΔCp for the secondary flows. ΔCp can indicate the distribution of secondary flows both near the blade pressure and suction surfaces. As ΔCp decreased, secondary flows decreased. The blade loading distribution with fore maximum blade loading at the shroud and aft maximum blade loading at the hub, coupled with a small negative blade lean angle, could help suppress secondary flows and improve aerodynamic efficiency. Originality/value A direct control method on internal flow field characteristic-secondary flows by optimisation design was proposed for a centrifugal impeller. The impeller optimisation design process saves time by avoiding substantial CFD sample calculations.

Sediment erosion in guide vane of Francis turbine has been a crucial issue for turbines operating in Himalayas. Large sediment load with higher percentage of Quartz in Himalayan river causes erosion on GV faces, leaf, stem, leading and trailing edges and at clearance gaps (both facing plate and GV edges). This in turn increases profile roughness and clearance gaps height, causing higher friction losses and cross flow across the vanes, which ultimately affects inlet flow dynamics. Research attempts are limited to computational analysis and prediction of erosion losses. The effect of erosion on flow passing vanes is a crucial issue yet to be explored. This work focuses on experimental prediction of effect of erosion in 3 GV cascade system. The cascade geometry was developed with CFD based iterative method, maintaining flow similarity around GV in turbine and cascade. It has been found that the pressure on two sides of vane and at vane outlet increases with erosion for considered extent erosion.

In this study, a time-domain numerical method using dynamic stiffness matrices is proposed to obtain the characteristics of the vortex induced vibration (VIV) of a flexible riser. Due to the large ratio of length to diameter, a marine riser is approximated as a cable model. Based on the finite volume method (FVM), the cable model of the riseris dividedinto a certain number of segments. The dynamic stiffness matrix of each segment reflecting the time varying strain energy and bending stiffness are updated in calculation. The total dynamic stiffness matrix of the riser is then obtained by the superposition characteristics of the finite volume method. In the nonlinear governing equation of riser's vibration, the hydrodynamic forces are calculated by the instantaneous vorticity conserved boundary condition (IVCBC) method and the equation is solved by the step-by-step time integration method to obtain the accelerations, velocities and displacements of the riser. Validation of this numerical approach is carried out by comparing the static balance and the dynamic responses with quantities in classical experimental cases for a riser in uniform flow. The results show that:when the vibration of riser is high order mode vibration, the dynamic stiffness matrix cannot be ignored. The vortex induced vibration of the given flexible riser has a strong coupling effect between the deformation of riser and flow field. In the vibtation of the riser, there exists the multiple-frequency effect, numely, adominant frequency co-exists with some subordinate frequencies, hence the shedding frequencies can no longer be satisfied with the distributions of the Strauhal number. The wake effect onthe vortex shedding has a stronger 3-dimensional effect at the locations of smaller lateral vibrations. The numerical simulations also reveal that the vibration mode increases with the flow velocity.

In guide vane cascade of Francis turbine, highest acceleration occurs, which generates equivalent amount of force for work done and erosion due to instantaneous change in flow dynamics. Hence in addition to runner vane, suitable selection of guide vane profile has equal importance. Usually, NACA defined hydrofoils are used for guide vanes. Numerous options are available, but selection of best one for optimum energy harness is important. Primarily, guide vane torque and turbine efficiency is prioritized. For the turbines operating in sediment laden water, pressure difference between two sides of guide vane and erosion resistivity are additional factors to be considered. This work was performed in the vicinity of guide vane profile selection for Francis turbines operating in sediment laden water. Computational analysis on turbine flow passage and experimental study with Rotating Disc Apparatus were performed in order to identify suitable profile. Unsymmetrical profiles were found to be better handling erosion maintaining consistency in turbine performance.

Guide vanes in Francis turbine faces frequent erosion due to its operation in sand laden water, which demands focus on design, manufacturing, operation and maintenance of turbines. These vanes are designed on high precision with standard hydrofoils for efficient conversion of pressure to kinetic energy. The erosion on surfaces, upper and lower ends and leading and trailing edges of guide vanes induces cross flow at clearance gaps, tip leakage at trailing edges and high friction on the surfaces, increasing hydraulic losses associated with flow. Review on post erosion hydraulic and mechanical effect on guide vanes and its vicinity are the main objectives of this work. It has been assisted by flow around vanes, field observation of erosion, possible operational problem and method of laboratory estimation of erosion. The vulnerable locations, erosion severity, possible post erosion problems, research gap and possible measures to comprehend them have been focused, which will be useful in further research activities.

The characteristics of bubble motion and distribution in multiphase pumps are complex and have not yet been clearly described. In this study, high-speed photography technology was used to investigate the gas-liquid flow in detail. A numerical model that considers bubble coalescence and breakup was developed based on Euler two-fluid model, and it was embedded in ANSYS-CFX software with secondary development technology. The reliability of the developed model was validated by comparison with the efficiency and head of the test pump as well as the distribution and size of bubbles. The experimental results revealed that bubbles in the impeller moved from the blade pressure surface to the blade suction surface along a similar path, and accumulated there. Then, the accumulated bubbles decreased in size as they hit the blade wall. The necessary condition for bubble accumulation at the impeller hub was obtained by numerical analysis. The force acting on the bubble, M1, which is caused by the pressure difference from the shroud to hub of the impeller, must be much greater than the sum of the centrifugal force fg and lift force Lg (M1 ≫ fg + Lg). Furthermore, the bubble diameter in the guide vane was significantly greater than that in the impeller due to the strong bubble coalescence. At IGVFs of 3.0%, 9.0%, and 15.0%, the bubble diameters in the guide vane increased by 0.03 mm, 0.21 mm, and 0.24 mm, respectively.

Frequent changes between pump and turbine operations pose significant challenges in the design of pump–turbine runners with high efficiency and stability. In this study, a multiobjective optimization design system, including a 3D inverse design, computational fluid dynamics, design of experiment, response surface methodology, and multiobjective genetic algorithm, is introduced and applied to the design of a middle-high-head pump–turbine runner. The key parameters in the design, including the blade loading, the blade lean at the high-pressure side of the runner, and the meridional channel shape, were selected as the optimized parameters. Two runners, one with a large positive blade lean and another with a large negative blade lean, were selected for further numerical investigations and measurements. Model tests show that both runners have good power performances. The runner with a negative blade lean has better stability than the runner with a positive blade lean.

Purpose – The purpose of this paper is to elucidate the detailed flow field and cavitation effect in the centrifugal pump volute at partial load condition. Design/methodology/approach – Unsteady flows in a centrifugal pump volute at non-cavitation and cavitation conditions are investigated by using a computation fluid dynamics framework combining the re-normalization group k-e turbulence model and the mass transport cavitation model. Findings – The flow field in pump volute is very complicated at part load condition with large pressure gradient and intensive vortex movement. Under cavitation conditions, the dominant frequency for most of the monitoring points in volute transit from the blade passing frequency to a lower frequency. Generally, the maximum amplitudes of pressure fluctuations in volute at serious cavitation condition is twice than that at non-cavitation condition because of the violent disturbances caused by cavitation shedding and explosion. Originality/value – The detailed flow field and cavitation effect in the centrifugal pump volute at partial load condition are revealed and analysed.

To explore the pressure fluctuation characteristics in a mixed-flow pump handling a gas-liquid two-phase flow, an unsteady simulation was carried out with ANSYS CFX for the whole flow passage when the inlet gas void fraction (IGVF) was 0%, 5%, and 10%, respectively. Under pure water conditions (IGVF = 0%), the reliability of the simulation was verified by comparing with the experiment in both aspects of external characteristics and fluctuation. Through the implementation of the fast Fourier transform (FFT) algorithm, the characteristics of the pressure fluctuation in the impeller and the guide vane were obtained at different IGVF conditions. The results demonstrate that pressure fluctuations exist under different IGVF conditions due to the rotor-stator interaction and the gas-liquid phase interaction, and the intensity of the fluctuation is firstly enhanced, and then weakened, along the streamwise direction with the maximum located near the impeller outlet. The relationship between the gas content and the pressure fluctuation was analyzed, and it is shown that the regional pressure fluctuation will be intensified only if the gas content therein reaches a certain level and the local phase interaction is strong. In addition, the pressure fluctuation in both the rotor-stator interaction region and the guide vane may be effectively inhibited under small IGVF conditions.

The application of a cryogenic liquefied natural gas expander can reduce the production of flash steam and improve the efficiency of natural gas liquefaction. Like traditional hydraulic machinery, cavitation will occur during the operation of a liquefied natural gas expander, in particular, there is a strong vortex flow in the draft tube, and the cavitation phenomenon is serious. In this paper, the energy loss coefficient of the draft tube is used to describe the cavitation flow in the draft tube, and the goal of reducing the cavitation in the draft tube is achieved through the optimization design of the runner. Different runner models within the range of design parameters were obtained using the Latin hypercube test, and the relationship between design parameters and objective functions is constructed by a second-order response surface model. Finally, the optimized runners were obtained using a genetic algorithm. The effects of blade loading distribution and blade lean angles on the cavitation in the draft tube were studied. According to the optimization results, the blade loading distribution and blade lean angles are recommended in the end.

The existing research on improving the hydraulic performance of centrifugal pumps mainly focuses on the design method and the parameter optimization. The traditional design method for centrifugal impellers relies more on experience of engineers that typically only satisfies the continuity equation of the fluid. In this study, on the basis of the direct and inverse iteration design method which simultaneously solves the continuity and motion equations of the fluid and shapes the blade geometry by controlling the wrap angle, three centrifugal pump impellers are designed by altering blade wrap angles while keeping other parameters constant. The three-dimensional flow fields in three centrifugal pumps are numerically simulated, and the simulation results illustrate that the blade with larger wrap angle has more powerful control ability on the flow pattern in impeller. The three pumps have nearly the same pressure distributions at the small flow rate, but the pressure gradient increase in the pump with the largest wrap angle is smoother than the other two pumps at the design and large flow rates. The pump head and efficiency are also influenced by the blade wrap angle. The highest head and efficiency are also observed for the largest angle. An experiment rig is designed and built to test the performance of the pump with the largest wrap angle. The test results show that the wide space of its efficiency area and the stability of its operation ensure the excellent performance of the design method and verify the numerical analysis. The analysis on influence of the blade wrap angle for centrifugal pump performance in this paper can be beneficial to the optimization design of the centrifugal pump.

A combined direct and inverse iterative design method was developed for the hydraulic design of centrifugal pump impellers. This method is based on the fluid continuity and motion equations and solves for the meridional velocity taking into account the effects of the blade shape on the flow. The blade shape is drawn by point-by-point integration with blade thickening and smoothing using conformal mapping. Two examples designed using the direct and inverse iterative design method are compared to results using the traditional design method with significantly different meridional velocity distributions and three-dimensional blade shapes. Numerical simulations and tests show that the highest pump efficiency is 2.2% higher with this design method than with the traditional design method. The numerical results agree well with the experiments with a smoother flow pattern than with the traditional design, especially in the volute.

The valuation of the hydraulic performance of a centrifugal pump with pre-whirl regulation of the inlet guide vanes was studied experimentally by varying the pre-whirl angle from −60° to 60° with distances between the inlet guide vanes and the impeller inlet of 280 mm, 380 mm and 460 mm. The efficiency-flow curves and the characteristic curves were obtained for the pump for various operation conditions. The experiment results demonstrated that the pre-whirl regulation widened the high efficiency zone and improved the hydraulic performance for off-design conditions with the proper pre-whirl angle. The axial distance between the inlet guide vanes and the impeller inlet influenced the pre-whirl regulation effect of the inlet guide vanes with the best pre-whirl regulation effect obtained for an axial distance of 380 mm. These results showed that an appropriate axial distance between the inlet guide vanes and the impeller inlet can improve the fluid flow at the impeller entrance with pre-whirl regulation for centrifugal pumps.

The Weis-Fogh mechanism, found in the hovering flight of a small bee, is a unique and efficient lift generation. In this study, we proposed a rotating type propulsion model that applies the principle of the Weis-Fogh mechanism and calculated the unsteady flow field of the propulsion model with the advanced vortex method. The wing (NACA0010 airfoil) and channel are approximated by source and vortex panels, and free vortices are introduced away from the body surfaces. The viscous diffusion of fluid is represented using the core-spreading model to the discrete vortices. We investigated the thrust and drag coefficients, pressure field, vorticity field, velocity vector field, and average propulsive efficiency of the propulsion model by changing the rotating angle velocity. The force acting on the wing depended heavily on the directions of the thrust and drag and the thrust and drag coefficients largely fluctuated with the change in the rotating angles. The average thrust increased as the rotating angle velocity increased. The maximum propulsive efficiency was 27.9% at a calculated angle velocity. The flow field of this rotating type propulsion mechanism is unsteady and very complex because the wing rotates and moves unsteadily in the channel. However, using the advanced vortex method, it could be calculated accurately.

A computational method facilitating long-time and high-resolution unsteady vortical flows is developed with the advantages of the discrete vortex methods. Both the velocity and pressure distribution of the flow field are calculated by integral formulations in combination with a fast summation algorithm. The vorticity field is described by Lagrangian representation, which is well suited to the moving boundary. Viscosity diffusion of the vorticity is considered with the core spreading model corrected by an adaptive splitting and merging algorithm. The effectiveness of the present method is examined by comparing the numerical results of unsteady separated flows which pass a cylinder and a thin cambered blade undergoing rotational oscillations with available experimental results. Interesting results about vortex shedding patterns and lock-in characteristics are provided for the thin cambered blade.

In this study, an advanced Lagrangian vortex- boundary element method is applied to simulate the unsteady impeller-diffuser interactions in a diffuser pump not only for design but also for off-design considerations. In velocity calculations based on the Biot-Savart law we do not have to grid large portions of the flow field and the calculation points are concentrated in the regions where vorticity is present. Lagrangian representation of the evolving vorticity field is well suited to moving boundaries. An integral pressure equation shows that the pressure distribution can be estimated directly from the instantaneous velocity and vorticity field. The numerical results are compared with the experimental data and the comparisons show that the method used in this study can provide us insight into the complicated unsteady impeller-diffuser interaction phenomena in a diffuser pump.

For the incompressible Navier–Stokes equations, vorticity-based formulations have many attractive features over primitive-variable velocity–pressure formulations. However, some features interfere with the use of the numerical methods based on the vorticity formulations, one of them being the lack of a boundary conditions on vorticity. In this paper, a novel approach is presented to solve the velocity–vorticity integro-differential formulations. The general numerical method is based on standard finite volume scheme. The velocities needed at the vertexes of each control volume are calculated by a so-called generalized Biot–Savart formula combined with a fast summation algorithm, which makes the velocity boundary conditions implicitly satisfied by maintaining the kinematic compatibility of the velocity and vorticity fields. The well-known fractional step approaches are used to solve the vorticity transport equation. The paper describes in detail how we accurately impose no normal-flow and no tangential-flow boundary conditions. We impose a no-flux boundary condition on solid objects by the introduction of a proper amount of vorticity at wall. The diffusion term in the transport equation is treated implicitly using a conservative finite update. The diffusive fluxes of vorticity into flow domain from solid boundaries are determined by an iterative process in order to satisfy the no tangential-flow boundary condition. As application examples, the impulsively started flows through a flat plate and a circular cylinder are computed using the method. The present results are compared with the analytical solution and other numerical results and show good agreement. Copyright © 2005 John Wiley & Sons, Ltd.