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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.

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.

To study the effect of tip clearance on unsteady flow in a tubular turbine, a full-channel numerical calculation was carried out based on the SST k–ω turbulence model using a power-plant prototype as the research object. Tip leakage flow characteristics of three clearance δ schemes were compared. The results show that the clearance value is directly proportional to the axial velocity, momentum, and flow sum of the leakage flow but inversely proportional to turbulent kinetic energy. At approximately 35–50% of the flow direction, velocity and turbulent kinetic energy of the leakage flow show the trough and peak variation law, respectively. The leakage vortex includes a primary tip leakage vortex (PTLV) and a secondary tip leakage vortex (STLV). Increasing clearance increases the vortex strength of both parts, as the STLV vortex core overlaps Core A of PTLV, and Core B of PTLV becomes the main part of the tip leakage vortex. A “right angle effect” causes flow separation on the pressure side of the tip, and a local low-pressure area subsequently generates a separation vortex. Increasing the gap strengthens the separation vortex, intensifying the flow instability. Tip clearance should therefore be maximally reduced in tubular turbines, barring other considerations.

Leading-edge tubercles on the humpback whale pectoral fin are known to have aerodynamic benefits, particularly in the post-stall regime. In this research, a horizontal-axis wind turbine blade was modelled with tubercles distributed on its leading edge to mimic the humpback whale pectoral fin. A parametric study of the effect of tubercles on the reference NREL Phase VI wind turbine was conducted via computational fluid dynamics. Three parameters—amplitude, wavelength, and tubercle location along the blade span—were varied. The results showed that tubercles have negative effects on the turbine performance at wind speeds (V∞) ≤ 7 m/s. However, when tubercles are placed over 60% of the blade span, the backflow area can be eliminated at V∞ = 10 m/s. It is found that the vortices in the stable-flow zone over the suction surface can be reduced when tubercles of a relatively small amplitude-wavelength ratio are employed, thereby maintaining turbine performance. Compared with the reference blade, tubercles provided benefits at higher wind speeds. The generated vortices due to the presence of tubercles, leading to both blockage effects and stall delay. The results revealed that the pressure on the suction surface of the tubercled blade decreases, thereby increasing lift and enhancing the turbine performance.

The pressure fluctuations and flow pattern in a mixed-flow pump are numerically investigated under design and off-design conditions. The accuracy and reliability are validated by good agreement of numerical results and experimental data of pump energy performance. At design flow rate, the dominant frequencies of pressure fluctuations are impeller rotation frequency or integer multiples of it, which are mainly induced by the rotor–stator interaction. At overload condition, the dominant frequencies of pressure fluctuations are similar as those of design flow rate, but the maximum amplitudes increase to about 2.5 times of those of design flow rate. At partial load condition, the pressure fluctuations and flow pattern are complicated. The low dominant frequencies below the impeller rotation frequency are related to the process of vortex emergency, movement and disappearance.

In order to investigate the mechanism and the characteristics of the noise induced by unstable flow in a centrifugal pump, the internal flow characteristics in the pump were numerically researched, and the acoustic pressure fluctuations at the pump inlet and outlet were experimentally investigated. Obvious corresponding relationships between the flow instabilities, the cavitation and the noise were established. It was found that the rotating stall, the backflow, the hump, the occurrence of unstable flow and the cavitation in such a centrifugal pump were effectively detected through the noise, which could help to provide fundamental information on flow instabilities and guarantee safe and steady operating conditions for the system. The recirculation and prewhirl regions in the pump upstream pipe, which were caused by the backflow and the rotation of the impeller, presented the circumferential movement with a spiral shape, causing apparent broadband fluctuations at low frequency band of the acoustic pressure. The backflow and rotating stall could also result in broadband fluctuations of the pump outlet noise, which was distributed from 100 Hz to 150 Hz. Meanwhile, the broadband fluctuations of the pump outlet acoustic pressure distributed in the low frequency range, which was produced by the occurrence of cavitation, moved to the lower frequency band as the flow rate increased. The enhanced broadband fluctuations of the pump inlet and outlet noise distributed from 1 kHz to 6 kHz were caused by the coupling between the cavitation-induced noise and the system-produced noise. The broadband fluctuations of the pump inlet noise distributed between 6 kHz and 9 kHz were regarded as the typical frequency band of cavitation in the centrifugal pump.

Sediments flowing along with water through guide vanes induces abrasive and erosive wear in the GV surface. The effect of these wears differs with the shape of GV profiles. This study presents an alternative clearance gap method to compare the effects of clearance gap (CG) in the GV of Francis turbine with different hydrofoils. Numerical prediction of the performance of Francis turbine with symmetrical and asymmetrical hydrofoils is studied with the CG of 0 mm, 2 mm, and 4 mm thickness. Increase in the size of the gap deteriorates the performance of the runner. In case of asymmetrical GV profile, the effects in the runner is found to be less than the symmetrical profile. It is due to lesser pressure difference between the adjacent sides of the GV profile. With the alternative clearance gap approach, it distinguishes the effect of CG and the pressure pulsation due to rotor-stator interaction for a single numerical model.

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.

Clearance gap in guide vanes of Francis turbine induces the leakage vortex. This vortex flow interacts with the main flow and leads to the instability in the fluid flow pattern and eventually deteriorates the performance of the turbine. In this study, the detailed numerical examination of the unsteady flow due to leakage vortex and influence of this in the performance of turbine is carried out using time dependent numerical analysis. The numerical simulation is carried out using SST turbulence model with numerical validation. The development of leakage vortex is studied within the clearance gap region. Time dependent numerical simulation is carried out to investigate the growth and vortex propagation considering five revolutions of the runner. Results shows that the leakage vortex travelling form the guide vane clearance gaps influence the performance of the runner. On analysing the leakage vortex path, it is seen that the vortex travels from the pressure side of runner blade to the suction side of adjacent blade opposite to the runner rotation. Furthermore, this leakage vortex is carried down to the draft tube where the vortex rope seems to grow up to 50% geometric progression of draft tube cone and gradually decreases before reaching the elbow. Upon investigation of resulting torque and head during runner rotation, the periodic variation of torque and head can be seen, however with different phase. This is inferred to be the influence of leakage vortex that travels along with the main flow.

The working environment for Helium Circulator in HTR (high temperature gas-cooled reactor) is high temperature about 523 K and high pressure about 7 MPa. So the efficiency of Helium Circulator’s impeller is extremely important. At present, the blade loading parameters and meridional geometry parameters are obtained through the 3D inverse design methods and the widely used Bessel curves. The optimization design strategy was built by combining the 3D inverse design method, CFD analyses, Design of Experiment (DOE), Response Surface Methodology (RSM), Multi-Island Genetic Algorithm (MIGA). The optimization objective is the impeller efficiency at the design point. The input parameters are related to the blade loading, blade lean angle and the meridional channel shape. The results show that the SLOPEH, NCH, Ɵ1, and YH and Ɵ2 are the main influencing factors. The best blade loading distribution is the positive SLOPEH of high value combined with the negative SLOPES. The positive DRVT on the hub and shroud will improve the blade loading at the blade leading edge. The curve with the relative reduced curvature is beneficial to the performance of the impeller. The efficiency of the optimized impeller is 0.77% at Qd and 2.80% at 0.75Qd higher than the original impeller.

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.

A numerical method of large eddy simulation (LES) combined with a characteristic-based split scheme (CBS) is proposed. The CBS scheme is introduced to discretize the motion equation in the time domain along the characteristic line, and the space domain is discretized by the split algorithm, which calculates the velocity and pressure separately. Turbulent flow simulations in a lid-driven cubical cavity and two circular section 90° pipes are conducted, and the results are validated by comparison with experimental data and other direct numerical simulation results. For a circular section 90° pipe, an additional pair of vortexes that is near the curved section inner side has been observed, and their rotational direction is the same as that of the main vortex. To the author’s knowledge, this type of four-vortex structure has not been previously reported.

Pressure fluctuation in the single-phase pump has been widely discussed, while less attention was paid for that in the multiphase pump. Therefore, this study investigated the pressure fluctuation in a multiphase rotodynamic pump. Unsteady simulations based on Euler two-fluid model were done with ANSYS-CFX software when the inlet gas void fractions (IGVFs) were 0.0%, 3.0%, 9.0%, and 15.0%. Under pure water (IGVF=0.0%) and gas-liquid two-phase (IGVFs=3.0%, 9.0%, 15.0%) conditions, the reliability of numerical method was verified by comparison with the experimental data. The numerical results showed that the dominant frequency in the impeller and guide vane corresponded to the blade numbers of guide vane and impeller, respectively. This illustrated that the rotor-stator interaction was the main cause for the generation of fluctuation in such pump. Meanwhile, the maximum fluctuation amplitude appeared near the impeller outlet at IGVF=0.0%, while it appeared near the guide vane inlet under two-phase conditions. Furthermore, the maximum fluctuation amplitudes at IGVF=3.0%, 9.0%, 15.0% are 1.9, 2.9, and 3.3 times as large as that at IGVF=0.0%.

A combined numerical and experimental method study was performed to detect the inner flow state for a type of centrifugal pump. It was found that the inlet attack angles of blades in an impeller have a great influence on the flow instabilities in a centrifugal pump. The mechanism of the rotating stall in the impeller channel was explained. Meanwhile, flow state identification with vibration (FSIV) was proposed to detect the flow instabilities in a centrifugal pump. The relationship between the external vibration and the inner flow state has been established by FSIV. The characteristics and mechanism of the vibration produced by the flow instabilities in a centrifugal pump were investigated. It was found that the hump, the rotating stall, the backflow, the occurrence of unstable flow, and the cavitation in the centrifugal pump can be effectively detected by applying the vibration signals, which helps to obtain safe and steady operating conditions for the system.

Leakage flow from clearance gap affects the performance of Francis turbines. This study presents the method to predict the effects of leakage flow from clearance gap of GVs. When sediments flow along with water through guide vanes it erodes the guide vane’s surface. Clearance gap of the guide vanes gradually increases due to continuous effects of abrasive wear. This phenomena of abrasion deteriorates the overall performance of the turbine. In this study, the effects of increased clearance gap of GVs of Francis turbine are studied numerically. Numerical models including the clearance gap-size of 0 mm, 2 mm and 4 mm are made to compare the effects. It uses alternative leakage flow approach, whereby current model consisting of 24 GVs contains 12 clearance gaps alternatively. This approach makes it possible to differentiate the amplitude of pressure pulsations contributed either by wakes or vortices due to leakage flow from guide vanes. Comparing the 3 different cases, it was found that increased clearance gap of the guide vanes increases the pressure pulsation at the runner inlet, reducing overall efficiency of the turbine.

Instabilities usually happen in the reversible pump-turbine in generation mode, especially in the S-shaped region. Flow separations, vortex formations and rotating stalls can exist in the runners and other components. The evolution of the instabilities in two model pump-turbine runners with large blade leans, runner A with a negative lean and runner B with a positive lean, is studied by means of numerical simulations in the present work. The guide vanes opening (GVO) is fixed as 15mm. Six operation conditions from the normal operation region to the turbine brake region are chosen to be simulated. In addition, processes with a decreasing discharge at the inlet of the volute are also calculated to trace the evolution of the instability. The pressure fluctuations in the vaneless gap are monitored in the whole annulus. Different flow structures can be detected from the power spectrum of the pressure fluctuations. As the discharge reduced, the amplitudes of the pressure fluctuations increase visibly from the normal operation region to the runaway conditions and slightly decrease if further reduce the flow rate. Rotor-stator interaction frequency and its harmonics dominate the flow field from normal operating region to turbine brake region with the frequency corresponding to 7f n, 14f n, where f n is the runner rotating frequency, and etc. Low frequency components gradually develop near the runaway points and the wavelet method detects the inception of the rotating stalls in the vaneless gap in the turbine brake region. Different blade leans give arise to an obvious distinction of the flow distributions near the inlet of the runners and in the vaneless gap. The separation generates a swirl stripe extending to opposite direction dependent on the blade lean direction. In addition, due to the different location of the swirl stripes, the pressure fluctuation distributions are opposite for the runners. Higher fluctuations locate near the hub and near the shroud for runner A and runner B respectively

To study the influence of tip clearance on performance (external characteristics, pressure fluctuation and tip loss) of a low specific speed mixed-flow pump, unsteady simulation was performed for the whole flow passage with five tip clearance sizes ( δ0 = 0 mm, δ1 = 0.10 mm, δ2 = 0.25 mm, δ3 = 0.75 mm and δ4 = 1 mm). The reliability of the numerical methodology was verified in external characteristics (efficiency, head and power) and fluctuation. The performance of the pump was obtained under different discharges and tip clearance sizes using ANSYS CFX. The results showed that the variation of tip clearance size has greater effect on the external characteristics under large discharges. Meanwhile, along the flow direction, the fluctuation coefficients near the impeller shroud increase gradually with the smaller tip clearance sizes ( δ = 0.10 and 0.25 mm), while for the larger tip clearance sizes ( δ = 0.75 and 1.00 mm), the significant increase of fluctuation near the shroud of impeller inlet is closely associated with the clear leakage vortex and the large region of low pressure. Besides, with the increase of tip clearance size, the effect of tip clearance will become more remarkable under different discharge conditions. According to this study, for the optimization design of such pumps, the size of the tip clearance is suggested to be about 0.9% times the blade height at middle of the impeller passage.

During the process of designing the mixed-flow pump impeller, the meridional flow passage shape directly affects the obtained meridional flow field, which then has an influence on the three-dimensional impeller shape. However, the meridional flow passage shape is too complicated to be described by a simple formula for now. Therefore, reasonable parameter selection for the meridional flow passage is essential to the investigation. In order to explore the effects of the meridional flow passage shape on the impeller design and the hydraulic performance of the mixed-flow pump, the hub and shroud radius ratio (HSRR) of impeller and the outlet diffusion angle (ODA) of outlet zone are selected as the meridional flow passage parameters. 25 mixed-flow pump impellers, with specific speed of 496 under the design condition, are designed with various parameter combinations. Among these impellers, one with HSRR of 1.94 and ODA of 90° is selected to carry out the model test and the obtained experimental results are used to verify accuracies of the head and the hydraulic efficiency predicted by numerical simulation. Based on SIMPLE algorithm and standard k-ɛ two-equation turbulence model, the three-dimensional steady incompressible Reynolds averaged Navier-Stokes equations are solved and the effects of different parameters on hydraulic performance of mixed-flow pump impellers are analyzed. The analysis results demonstrate that there are optimal values of HSRR and ODA available, so the hydraulic performance and the internal flow of mixed-flow pumps can be improved by selecting appropriate values for the meridional flow passage parameters. The research on these two parameters, HSRR and ODA, has further illustrated influences of the meridional flow passage shape on the hydraulic performance of the mixed-flow pump, and is beneficial to improving the design of the mixed-flow pump impeller.

Numerical simulations were performed to investigate pressure fluctuations in the S-shaped region of a pump-turbine model. Analyses focused on pressure fluctuations in the draft tube and in the gap between the guide vanes and runner. Calculations were made under six different operating conditions with a constant guide vane opening, and the best efficiency point, runaway point, and low-discharge point in the turbine brake zone were determined. The simulated results were compared with experimental measurements. In the draft tube, a twin vortex rope was observed. In the gap between the guide vanes and runner, a low frequency component was captured at both the runaway and low-discharge points in the turbine brake zone, which rotated at 65% of the runner frequency. This low frequency component was induced by the rotating stall phenomenon. At the runaway point, a single stall cell was found in the gap between the guide vanes and runner, while at the low-discharge point, four stall cells were observed.

To explore the influence of tip clearance on pressure fluctuation in a low specific speed mixed-flow pump, tip clearances δ of 0.25 mm, 0.75 mm and 1.00 mm, along with no tip clearance, were selected. The reliability of the simulation was verified by comparison with the experimental data of external characteristics and fluctuation in the guide vane passage. Through ANSYS-CFX, MATLAB code and fast Fourier transform (FFT) algorithm, pressure fluctuation characteristics in this pump were obtained. The results show that pressure fluctuation exists in all conditions due to the rotor-stator interaction. Under the no tip clearance and tip clearance conditions, the maximum fluctuation value was located near the guide inlet and impeller outlet, respectively. Clearance leakage had less influence on pressure fluctuation at the impeller inlet and central regions within a certain range of the clearance, beyond this range, fluctuations in the whole flow passage increased significantly, while the clearance variation had less effect on fluctuation in the guide vane. When the tip clearance value was 1.00 mm, pressure fluctuation of the shroud at the impeller inlet section suddenly increases, which was closely related to the obvious leakage vortexes and a larger low pressure area.

Francis turbine guide vanes have pivoted support with external control mechanism, for conversion of pressure to kinetic energy and to direct them to runner vanes. This movement along the support is dependent on variation of load and flow (operating conditions). Small clearance gaps between facing plates and the upper and lower guide vane tips are available to aid this movement, through which leakage flow occurs. This secondary flow disturbs the main flow stream, resulting performance loss. Additionally, these increased horseshoe vortex, in presence of sand, when crosses through the gaps, both the surfaces are eroded. This causes further serious effect on performance and structural property by increasing gaps. This paper discusses the observation of the severity in hydropower plants and effect of clearance gaps on general performance of the Francis turbine through computational methods. It also relates the primary result with the empirical relation for leakage flow prediction. Additionally, a possible method to computationally estimate thickness depletion has also been presented. With increasing clearance gap, leakage increases, which lowers energy conversion and turbine efficiency along with larger secondary vortex.

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 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.

SUMMARY On the basis of the Helmholtz decomposition, a grid-free numerical scheme is provided for the solution of unsteady flow in hydraulic turbines. The Lagrangian vortex method is utilized to evaluate the convection and stretch of the vorticity, and the BEM is used to solve the Neumann problem to define the potential flow. The no-slip boundary condition is satisfied by generating vortex sticks at the solid surface. A semi-analytical regularization technique is applied to evaluate the singular boundary surface integrals of the potential velocity and its gradients accurately. The fast multipole method was extended to evaluate the velocity and velocity gradients induced by the discretized vortex blobs in the Lagrangian vortex method. The successful simulation for the unsteady flow through a hydraulic turbine's runner has manifested the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.

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 paper, vortex-shedding patterns and lock-in characteristics that vortex-shedding frequency synchronizes with the natural frequency of a thin cambered blade were numerically investigated. The numerical simulation was based on solving the vorticity-stream function equations with the fourth-order Runge–Kutta scheme in time and the Chakravaythy–Oscher total variation diminishing (TVD) scheme was used to discretize the convective term. The vortex-shedding patterns for different blade attack angles were simulated. In order to confirm whether the vortex shedding would induce blade self-oscillation, numerical simulation was also carried out for blade in a forced oscillation. By changing the pitching frequency and amplitude, the occurrence of lock-in at certain attack angles was determined. Inside the lock-in zone, phase differences between the blade’s pitching displacement and the torque acting on the blade were used to infer the probability of the blade self-oscillation.

Large eddy simulation (LES) approach was used to investigate jumps of primary frequency of shear layer flow over a cavity. Comparisons between computational results and experimental data show that LES is an appropriate approach to accurately capturing the critical values of velocity and cavity length of a frequency jump, as well as characteristics of the separated shear layer. The drive force of the self-sustained oscillation of impinging shear layer is fluid injection and reinjection. Flow patterns in the shear layer and cavity before and after the frequency jump demonstrate that the frequency jump is associated with vortex–corner interaction. Before frequency jump, a mature vortex structure is observed in shear layer. The vortex is clipped by impinging corner at approximately half of its size, which induces strong vortex–corner interaction. After frequency jump, successive vortices almost escape from impinging corner without the generation of a mature vortex, thereby indicating weaker vortex–corner interaction. Two wave peaks are observed in the shear layer after the frequency jump because of: (1) vortex–corner interaction and (2) centrifugal instability in cavity. Pressure fluctuations inside the cavity are well regulated with respect to time. Peak values of correlation coefficients close to zero time lags indicate the existence of standing waves inside the cavity. Transitions from a linear to a nonlinear process occurs at the same position (i.e., x/H = 0.7) for both velocity and cavity length variations. Slopes of linear region are solely the function of cavity length, thereby showing increased steepness with increased cavity length.

The velocity and pressure field of a ship’s Weis-Fogh-type propulsion mechanism are studied in this paper using an 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. The velocity is calculated on the basis of the generalized Biot-Savart law and the pressure field is calculated from an integral, based on the instantaneous velocity and vorticity distributions in the flow field. Two-dimensional unsteady viscous flow calculations of this propulsion mechanism are shown, and the calculated results agree qualitatively with the measured thrust and drag due to unmodeled large fluctuations in the measured data.

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.

The possibility of self-oscillation of a thin cambered blade, when the attack angle was near its stall angle, was experimentally investigated in a circuit-water tunnel. The vortex-shedding patterns for different attack angles of the blade were visualized by two methods: a twinkle laser sheet and high-speed-camera photography. And the torque acting on the blade was measured using strain gauges. To confirm whether the vortex shedding would induce the self-oscillation of the blade, the blade was subjected to pitching motions, and by changing the pitching frequency and amplitude, lock-in boundaries for certain attack angles were determined. Phase differences between the blade's pitching displacement and the torque to oscillate it were also investigated, and the probability of self-oscillation of the blade was inferred from these phase differences.

To explore the effect of virtual mass force, the unsteady two-phase flow in a multiphase rotodynamic pump impeller was numerically simulated, where the inlet gas void fraction was 4.9%, 14.9%, and 25.2%, respectively. The drag force and the virtual mass force were accounted for and the cases with and without the latter one were both analyzed for comparison. The results show that the trajectories of the gas bubbles are influenced by the virtual mass force evidently in the inlet extended region. Due to the effect of virtual mass force, some gas will firstly move to the shroud before accumulating in the hub region of the impeller. The characteristic of the pump head was discussed and the results demonstrate that the virtual mass force can decrease the pump head and lead to its fluctuation. In addition, the comparison between the steady and unsteady simulation shows that the virtual mass effect can be found only by unsteady simulation.

In this study, an advanced Lagrangian vortex-boundary element method is applied to simulate the unsteady impeller-diffuser interaction in a diffuser pump. Velocity calculations based on the Biot-Savart law reduce the need 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 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-deffuser interaction phenomena in a diffuser pump.

An accurate numerical analysis of the flows associated with impeller-volute configurations in turbomachinery can be extremely helpful in optimizing the performance of centrifugal turbomachinery. In the present study, without introducing the periodicity of the blade-to-blade stream, the two dimensional unsteady features of the flows through a centrifugal impeller rotating in a volute casing of a pump are directly simulated by using an advanced vortex method. Results are presented in the form of the flow pattern of discrete vortices, volocity vector, theoretical head coefficient of impeller and the unsteady hydraulic radial force on impeller. Some of the results are compared with experimental data and the agreement is found to be good.

In this study, a reciprocating-type water turbine model that applies the principle of the Weis-Fogh mechanism was proposed, and the model's unsteady flow field was calculated by an advanced vortex method. The primary conditions were as follows: wing chord C=1, wing shaft stroke length hs=2.5C, and the maximum opening angle of the wing α=36 deg. The dynamic characteristics and unsteady flow fields of a Weis-Fogh type water turbine were investigated with velocity ratios U/V = 1.0 ∼ 3.0. Force coefficients Cu and Cv acting on the wing in the U and V directions, respectively, were found to have a strong correlation each other. The size of a separated region on the back face of the wing increased as the velocity ratio increased and as the wing approached the opposite wall. The rapid drop in Cv during a stroke increased as the velocity ratio increased, and the average Cu and Cv increased as the velocity ratio increased. The maximum efficiency of this water turbine was 14.1% at U/V = 2.0 for one wing.

The energy performance and radial force of a mixed flow pump with symmetrical and unsymmetrical tip clearance are investigated in this paper. As the tip clearance increases, the pump head and efficiency both decrease. The center of the radial force on the principal axis is located at the coordinate origin when the tip clearance is symmetrical, and moves to the third quadrant when the tip clearance is unsymmetrical. Analysis results show that the total radial force on the principal axis is closely related to the fluctuation of mass flow rate in each single flow channel. Unsteady simulations show that the dominant frequencies of radial force on the hub and blade correspond to the blade number, vane number, or double blade number because of the rotor stator interaction. The radial force on the blade pressure side decreases with the tip clearance increase because of leakage flow. The unsymmetrical tip clearances in an impeller induce uneven leakage flow rate and then result in unsymmetrical work ability of each blade and flow pattern in each channel. Thus, the energy performance decreases and the total radial force increases for a mixed flow pump with unsymmetrical tip clearance.

To explore the pressure fluctuation characteristics of a low speed specific speed mixed flow pump caused by rotor-stator interaction, the unsteady flow was simulated with CFX for the whole flow passage of a mixed flow pump with a specific speed of 148.8. The structured mesh of the computation domain was generated with ICEM CFD and TurboGrid, and mesh-independent analysis was done in the design condition. Through the comparison with the experiment data, the reliability of the simulation was verified. In different locations of the impeller passage, monitoring points were set. With Fast Fourier Transform (FFT), the characteristic analysis on the pressure fluctuation in the impeller passage was done for three flow rate conditions (0.75Qd, Qd, 1.25Qd). The results show that the pressure fluctuation amplitude increases from the inlet to the outlet. And the maximum values in different flow rates exist near the hub of the outlet; The pressure fluctuation is small in the design condition, but the largest in the small flow rate condition, accompanied by the secondary dominant frequencies with large amplitudes; In the small flow rate condition and design condition, the dominant frequency varies from the inlet to the outlet because the combine action of the impeller and guide vane; while in the large flow rate condition, the pressure fluctuation in the whole impeller passage is affected significantly by the guide vane, and the domain frequency is 8 times the rotational frequency of impeller. In addition, the change of pressure fluctuation from the pressure surface to the suction surface in the off-design conditions is investigated, and the results demonstrates that the intensity of the pressure fluctuation in the impeller passage is closely related with the impeller as well as the distribution of the vorticity and the pressure.

A grid-free numerical scheme is provided for the solution of unsteady flow in the hydraulic turbines. The Lagrangian vortex method is utilized to evaluate the convection and stretch of the vorticity, and the boundary element method is used to solve the Neumann problem to define the potential flow. The no-slip boundary condition is satisfied by generating vortex sticks at the solid surface. A semi-analytical regularization technique is applied to evaluate the singular boundary surface integrals of the potential velocity and its gradients accurately. The fast multipole method (FMM) has been extended to evaluate the velocity and velocity gradients induced by the discretized vortex blobs in the Lagrangian vortex method. The successful simulation for the unsteady flow through a hydraulic turbine’s runner has manifested the effectiveness of the proposed method.Copyright © 2011 by ASME

Based on the full cavitation model which adopts homogeneous flow supposition and considering the compressibility effect on cavitation flow to modify the re-normalization group k- turbulence model by the density function, a computational model is developed to simulate cavitation flow of a centrifugal pump at low flow rate. The Navier-Stokes equation is solved with the SIMPLEC algorithm. The calculated curves of net positive suction head available (NPSHa) HNPSHa agree well with the experimental data. The critical point of cavitation in centrifugal pump can be predicted precisely, and the NPSH critical values derived from simulation are consistent with the experimental data. Thus the veracity and reliability of this computational model are verified. Based on the result of numerical simulation, the distribution of vapor volume fraction in the impeller and pressure at the impeller inlet are analyzed. Cavities first appear on the suction side of the blade head near the front shroud. A large number of cavities block the impeller channels, which leads to the sudden drop of head at the cavitation critical point. With the reduction of NPSHa, the distribution of pressure at the impeller inlet is more uniform.

A numerical method including a macroscopic cavitation model based on the homogeneous flow theory and a microscopic cavitation model based on the bubble dynamics is proposed for the prediction of the impact force caused by cavitation bubble collapse in cavitating flows. A large eddy simulation solver, which is incorporated with a macroscopic cavitation model, is applied to simulate the unsteady cavitating flows. Based on the simulated flow field, the evolution of the cavitation bubbles is determined by a microscopic cavitation model from the resolution of a Rayleigh–Plesset equation including the effects of the surface tension, the viscosity and compressibility of fluid, the thermal conduction and radiation, the phase transition of water vapor at the interface, and the chemical reactions. The cavitation flow around a hydrofoil is simulated to validate the macroscopic cavitation model. A good quantitative agreement is obtained between the prediction and the experiment. The proposed numerical method is applied to predict the impact force at cavitation bubble collapse on a KT section in cavitating flows. It is found that the shock pressure caused by cavitation bubble collapse is very high. The impact force is predicted qualitatively compared with the experimental data.