The American Petroleum Institute (API) level 2 rotordynamic stability analysis requires determination of possible destabilization forces on a compressor or pump impeller. Dynamic forces in transient regimes are often excluded although a turbomachine impeller may experience transient operation intentionally or accidentally. The centrifugal pump head, flow direction, rotation and torque can be both positive and negative in transient regimes. For example, in a renewable energy application, pump flow direction and rotation are reversed to generate power from the imposed fluid head. The complete characteristics of a centrifugal pump correspond to all four quadrants (4Q) of operation, to encompass all possible operating conditions. It is required to understand centrifugal pump impeller dynamic forces and rotordynamic responses for all 4Q for design, fault diagnostic, instability analysis, upset conditions (such as water hammer, surge etc.) and for reliable operation of high energy density machines. In the open literature, whirling impeller rotordynamic analyses appears only for normal pump operation. Centrifugal pump dynamic forces, rotordynamic impedances and flow instabilities of an open impeller are reported for 4Q operating regimes in this paper. A transient Computational Fluid Dynamics (CFD)-based model is implemented which is applicable to nonaxisymmetric turbomachinery components, such as with a volute and/or vaned diffuser. Whirling motion of the impeller is modeled by imposing mesh deformation at the impeller walls. A phase modulated multi-frequency mesh deformation method is imposed for better numerical efficiency. Reynolds Averaged Navier-Stokes (RANS) equations with the Shear Stress Transport (SST) turbulence model along with a transitional bypass turbulence model are employed for the CFD solution. The results show the underlying flow field instability and stall cells responsible for the impedance shapes. Furthermore, the model is employed for determining the dependence of the outputs on specific speed to extract rotordynamic forces more efficiently. Impeller dynamic forces are found to scale with the size of the impeller for the same eccentricity ratio and the same flow coefficient. Strength of impeller rotating stalls has dependence on whirl frequency ratio.

With the increasing demand of the oil & gas industry, many pump companies are developing multiphase pumps, which can handle liquid-gas flow directly without separating the liquid from a mixed flow. The see-through labyrinth seal is one of the popular types of non-contact annular seals that act as a balancing piston seal to reduce the axial thrust of a high-performance centrifugal pump. The see-through labyrinth seal also generates reaction forces that can significantly impact the rotordynamic performance of the pump. Multiphase pumps are expected to operate from pure-liquid to pure-gas conditions. Zhang et al. (2019) conducted a comprehensive experimental study on the performance (leakage and rotordynamic coefficients) of a see-through labyrinth seal under mainly-gas conditions. This paper continues Zhang et al.’s (2019) research and studies the performance of the see-through TOS (tooth-on-stator) labyrinth seal under mainly-liquid conditions. The test seal’s inner diameter, length, and radial clearance are 89.256 mm, 66.68 mm, and 0.178 mm, respectively. The test fluid is a mixture of air and silicone oil (PSF-5cSt), and the inlet GVF (gas volume fraction) varies from zero to 12%. Tests are conducted at an exit pressure of 6.9 bars, an inlet temperature of 39.1 °C, three pressure drops PDs (27.6 bars, 34.5 bars, and 48.3 bars), and three rotating speeds ω (5 krpm, 10 krpm, and 15 krpm). The seal is always concentric with the rotor, and there is no intentional fluid pre-rotation at the seal inlet. The air presence in the oil flow significantly impacts the leakage as well as the dynamic forces of the test seal. The first air increment (increasing inlet GVF from 0% to 3%) slightly increases the leakage mass flow rate, while further air increments steadily decrease the leakage mass flow rate. For all test conditions, the leakage mass flow rate does not change as ω increases from 5 krpm to 10 krpm but decreases as ω is further increased to 15 krpm. The reduction in the leakage mass flow rate indicates that there is an increase in the friction factor, and there could be a highly possible flow regime change as ω increases from 10 krpm to 15 krpm. For ω ≤ 10 krpm, effective stiffness K eff increases as inlet GVF increases. K eff represents the test seal’s total centering force on the pump rotor. The increase of K eff increases the seal’s centering force and would increase the pump rotor’s critical speeds. C eff indicates the test seal’s total damping force on the pump rotor. For ω ≤ 10 krpm, C eff first decreases as inlet GVF increases from zero to 3%, and then remains unchanged as inlet GVF is further increased to 12%. For ω = 15 krpm, K eff first increases as inlet GVF increases from zero to 3% and then decreases as inlet GVF is further increased. As inlet GVF increases, C eff steadily decreases for ω = 15 krpm.

This paper deals with numerical predictions of the leakage flow rates, drag power and rotordynamic force coefficients for three types of helically-grooved liquid annular seals, which include a liquid annular seal with helically-grooved stator (GS/SR seal), one with helically-grooved rotor (SS/GR seal), and one with helical grooves on stator and rotor (GS/GR seal). These seals are frequently used for multiple-stage centrifugal pumps as they have the advantage of low leakage (even to zero) due to the “pumping effect” of the helical grooves. However, the static and rotordynamic characteristics of helically-grooved liquid annular seals still are not fully understood, and even more pronounced is the lack of effective numerical models in the literature. A novel transient CFD-based perturbation method was proposed for the predictions of the leakage flow rates, drag power and rotordynamic force coefficients of helically-grooved liquid annular seals. This method is based on the unsteady Reynolds-Averaged Navier–Stokes (RANS) solution with the mesh deformation technique and the multiple reference frame theory. The time-varying fluid-induced forces acting on the rotor/stator surface were obtained as a response to the time-dependent perturbation of the seal stator surface with the periodic motion, based on the multiple-frequency elliptical-orbit stator whirling model. The frequency-independent rotordynamic force coefficients were determined using curve fit and Fast Fourier Transform (FFT) in the frequency domain. The CFD-based method was adequately validated by comparisons to the published experiment data of leakage flow rates and fluid response forces for three types of helically-grooved liquid annular seals. Based on the transient CFD-based perturbation method, numerical results of the leakage flow rates, drag powers and rotordynamic force coefficients were presented and compared for three types of helically-grooved liquid annular seals at five rotational speeds (n = 0.5 krpm, 1.0 krpm, 2.0 krpm, 3.0 krpm and 4.0 krpm), paying special attention to the effective stiffness coefficient and effective damping coefficient. Results show that the GS/GR seal has the best sealing capability, followed by the GS/SR seal and then the SS/GR seal. The leakage flow rate of all three helically-grooved seals monotonically decreases with the increasing rotational speed. The GS/SR seal possesses the best stiffness and damping capability, followed by the SS/GR seal and then the GS/GR seal. Rotordynamic instability problems are more likely caused by the GS/GR seal in multi-stage centrifugal pumps. From a rotordynamic viewpoint, the GS/SR helically-grooved liquid annular seal is a better seal concept for multi-stage centrifugal pumps.

Liquid annular seals with parallelly-grooved stator or rotor are used as replacements for smooth plain seals in centrifugal pumps to reduce leakage and break up contaminants within the working fluid. Parallelly-grooved liquid annular seals have advantages of less leakage and smaller possibility of abrasion when the seal rotor-stator rubs in comparison to smooth plain seals. This paper deals with the static and rotordynamic characteristics of parallelly-grooved liquid annular seals, which are limited in the literature. Numerical results of leakage flow rates, drag powers and rotordynamic force coefficients were presented and compared for a grooved-stator/smooth-rotor (GS-SR) liquid annular seal and a smooth-stator/grooved-rotor (SS-GR) liquid annular seal, utilizing a modified transient CFD-based perturbation approach based on the multiple-frequency elliptical-orbit rotor whirling model. Both liquid annular seals have identical seal axial length, rotor diameter, sealing clearance, groove number and geometry. The present transient CFD-based perturbation method was adequately validated based on the published experiment data of leakage flow rates and frequency-independent rotordynamic force coefficients for the GS-SR and SS-GR liquid annular seals at various pressure drops with differential inlet preswirl ratios. Simulations were performed at three pressure drops (4.14 bar, 6.21 bar, 8.27 bar), three rotational speeds (2 krpm, 4 krpm, 6 krpm) and three inlet preswirl ratios (0, 0.5, 1.0), applying a wide rotor whirling frequency range up to 200 Hz, to analyze and compare the influences of operation conditions on the static and rotordynamic characteristics for both the GS-SR and SS-GR liquid annular seals. Results show that the present two liquid annular seals possess similar sealing capability, and the SS-GR seal produces a slightly larger (∼ 2–10%) drag power loss than the GS-SR seal. For small rotor whirling motion around a centered position, both seals have the identical direct force coefficients and the equal-magnitude opposite-sign cross-coupling force coefficients in the orthogonal directions x and y . For all operation conditions, both the GS-SR and SS-GR liquid annular seals possess negative direct stiffness K and positive direct damping C . The GS-SR seal produces purely positive C eff throughout the whirling frequency range for all operation conditions, while C eff for the SS-GR seal shows a significant decrease and transitions to negative value at the crossover frequency f co with increasing rotational speed and inlet preswirl. From a rotordynamic viewpoint, the GS-SR liquid annular seal is a better seal concept for pumps.

In multiple stage centrifugal pumps, balance pistons, often comprising a grooved annular seal, equilibrate the full pressure rise across the pump. Grooves in the stator break the evolution of fluid swirl and increase mechanical energy dissipation; hence, a grooved seal offers a lesser leakage and lower cross-coupled stiffness than a similar size uniform clearance seal. To date bulk-flow models (BFMs) expediently predict leakage and rotor dynamic force coefficients of grooved seals; however, they lack accuracy for any other geometry besides rectangular. Note scalloped and triangular (serrated) groove seals are not uncommon. In these cases, computational fluid dynamics (CFD) models seals of complex shape to produce leakage and force coefficients. Alas CFD is not yet ready for routine engineer practice. Hence, an intermediate procedure presently takes an accurate two-dimensional (2D) CFD model of a smaller flow region, namely a single groove and adjacent land, to produce stator and rotor surface wall friction factors, expressed as functions of the Reynolds numbers, for integration into an existing BFM and ready prediction of seal leakage and force coefficients. The selected groove-land section is well within the seal length and far away from the effects of the inlet condition. The analysis takes three water lubricated seals with distinct groove shapes: rectangular, scalloped and triangular. Each seal, with length/diameter L/D = 0.4, has 44 grooves of shallow depth d g ∼ clearance C r , and operates at a rotor speed equal to 5,588 rpm (78 m/s surface speed) and with a pressure drop of 14.9 MPa. The method validity is asserted when 2D (single groove-land) and 3D (whole seal) predictions for pressure and velocity fields are compared against each other. The CFD predictions, 2D and 3D, show the triangular groove seal has the largest leakage, 41% greater than the rectangular groove seal does, albeit producing the smallest cross-coupled stiffnesses and whirl frequency ratio. On the other hand, the triangular groove seal has the largest direct stiffness and damping coefficients. The scalloped groove seal shows similar rotordynamic force coefficients as the rectangular groove seal but leaks 13% more. For the three seal groove types, the modified BFM predicts leakage that is less than 6% away from that delivered by CFD, whereas the seal stiffnesses (both direct and cross-coupled) differ by 13%, the direct damping coefficients by 18%, and the added mass coefficients are within 30%. The procedure introduced extends the applicability of a BFM to predict the dynamic performance of grooved seals with distinctive shapes.

In oilfield applications, an Electrical Submersible Pump (ESP) comprised of centrifugal pump, seal, and motor is placed inside a well to provide energy to lift reservoir fluids from the formation to the surface when the reservoir’s natural lift energy is insufficient. The use of an ESP as an Electrical Submersible Power Recovery Turbine (ESPRT) is the focus of this paper. As fluid is injected from the well surface to the pump discharge, through the pump stages, and out the pump intake, the ESPRT shaft rotates in reverse (counterclockwise from an uphole vantage point), compared to an ESP shaft. The moving fluid in the stages transmits energy to the impellers, which turns the motor shaft; the induction motor thereby becomes a generator. We simulated and optimized the performance of a conventional ESP stage using Computational Fluid Dynamics (CFD) and single-phase water. Before any laboratory or field testing, we simulated ESPRT performance at various speeds and flow rates to predict the performance of the turbine. The CFD prediction of the turbine follows the performance in the third quadrant of a typical four-quadrant pump curve. During the pre-field test CFD study, we did not attempt to predict the stage thrust. Later field trial results, however, showed the impellers operated in up thrust due to fluid flow through the turbine stages producing an upward reaction force on the impellers. We used the field test results to improve the CFD model and, afterwards, the stage design in order to reduce up thrust. The turbine, and pump upon which it is based, are designed to operate in down thrust. We investigated the effects of changing the diameter of the impeller balance holes and impeller-to-diffuser clearance at the impeller’s skirt and balance ring. Through several CFD iterations, we identified the optimum balance hole and clearance sizes; decreasing the size of the former feature and increasing the latter feature moved the impeller into the down thrust regime. Neither change reduced the stage head and corresponding power output.

Supercritical CO 2 power cycles incorporate a unique combination of high fluid pressure, temperature, and density as well as limited component availability (e.g., high-temperature trip valves) that can result in operational challenges, particularly during off-design and transient operation. These conditions and various failure scenarios must be considered and addressed during the facility, component, and control system design phase in order to ensure machinery health and safety during operation. This paper discusses significant findings and resulting design/control requirements from a detailed failure modes and effects analysis that was performed for the 1 MW e -scale supercritical CO 2 test loop at Southwest Research Institute, providing insight into design and control requirements for future test facilities and applications. The test loop incorporates a centrifugal pump, axial turboexpander, gas-fired primary heat exchanger, and micro-channel recuperator for testing in a simple recuperated cycle configuration at pressures and temperatures up to 255 bara and 715°C, respectively. The analysis considered offdesign operation as well as high-impact failures of turbomachinery and loop components that may require fast shutdowns and blowdowns. The balance between fast shutdowns/blowdowns and the need to manage thermal stresses in the turbomachinery resulted in staged shutdown sequences and impacted the design/control strategies for major loop components and ancillary systems including the fill, vent, and seal supply systems.

The characteristics of a transparent centrifugal pump of radial type were investigated for different conditions when conveying two-phase (air/water) flows. A closed impeller and a geometrically similar semi-open impeller, both made out of acrylic glass, were employed for comparison purposes when increasing air loading. The performance of the pump was measured for either a constant gas volume fraction or a constant air flow rate at the pump inlet. Hysteresis effects were studied by considering three different experimental approaches to reach the desired operating conditions. A constant rotational speed of 650 rpm was set for all experiments. The whole system was made of transparent acrylic glass to allow high-quality flow visualization. A systematic experimental database was produced based on shadowgraphy imaging, so that the resulting two-phase regimes could be properly identified. The results show that for gas volume fractions between 1 and 3%, the deterioration of pump performance parameters is much lower in the semi-open impeller compared to that of the closed impeller. Nevertheless, in the gas volume fraction range between 4 and 6%, the trend is reversed; the semi-open impeller performance is reduced compared to the closed impeller, particularly in overload conditions. At even higher gas loading, the semi-open impeller shows again superior performance. Flow instabilities and pump surging were much stronger in the closed impeller. The main reason for that was the occurrence of alternating gas pockets on the blades of the closed impeller. Additionally, pump surging was observed only in a very limited range of flow conditions in the semi-open impeller. Comparing the different experimental procedures to set the desired flow conditions, no significant hysteresis effects could be observed in the closed impeller. However, in the semi-open impeller obvious hysteresis in the performance could be seen for gas volume fractions between 4 and 6%. All the obtained experimental results will be useful to check and validate computational models used for CFD in a comparison study.

Dual-pressure Organic Rankine Cycles (ORCs) driven by the low temperature heat source usually work under part-load conditions, and it is therefore essential to predict the off-design performance of such ORCs. This paper presents the off-design performance prediction of the dual-pressure ORC on the basis of the model including plate heat exchangers, axial turbines and a centrifugal pump. Pure working fluid R600a and the mixture R245fa/R600a are compared. The sliding pressure operation strategy is considered under off-design conditions. The results indicate that under the design hot water parameters (hot water 140 °C, 64.87 kg/s), compared with the single-pressure ORC using R600a, the dual-pressure ORC using R600a shows a 9.57% higher net power and a 17.32% higher heat transfer area. Furthermore, the dual-pressure ORC with the mixture R245fa/R600a (0.42/0.58 mass fraction) shows a 1.04% higher net power and a 3.87% higher heat transfer area than the dual-pressure ORC using R600a under the design hot water parameters. In the dual-pressure ORC, the rotational speed of the high-pressure pump is more strongly influenced by the inlet temperature of hot water than that of the low-pressure pump. In addition, when the mass flow rate ratio of hot water or the inlet temperature of hot water increases, the difference of the net power between the dual-pressure ORC using the proposed mixture R245fa/R600a (0.42/0.58 mass fraction) and that using pure R600a increases.

The article describes a refining method for a fuel pump of rocket powerful turbo-pump unit by the joint usage of mathematical optimization software IOSO, meshing complex NUMECA and CFD complex ANSYS CFX. The optimization software was used for automatic change of the geometry of low-pressure impeller, transition duct and high-pressure impeller to find the optimal design. It was mandatory to keep the original variant of the remaining parts of the pump. For this reason, only geometrical parameters of the blades were varied without changing the contours of the pump meridional flow part. The investigated pump consists of five parts: inlet duct, low-pressure screw centrifugal stage, transition duct, high-pressure screw centrifugal stage and volute outlet duct. The pump main parameters with water as the working fluid (based on experiment data) were the following: high-pressure stage rotor speed was 13300 rpm; low-pressure rotor speed was 3617 rpm by gearbox; inlet total pressure was 0.4 MPa; outlet mass flow was 132.6 kg/s at the nominal mode. Creation of vane unit mesh (rotors and stator transition duct) was performed using NUMECA AutoGrid5. Sector models were used for the calculation simplification. The flow around only one blade or screw was considered. Setting up and solution of the task were carried out in the ANSYS CFX solver. Comparison of calculated characteristics of the basic pump with the experimental data was performed before the optimization. The analysis of characteristics for the obtained optimized pump geometry was carried out. It was found that pump with optimized geometry has greater efficiency in comparison with the original pump variant. The obtained reserve can be used to boost the rocket engine, and/or to reduce the loading of the main turbine, which operates in aggressive oxidizing environment.

Regenerative pumps, also referred to as “peripheral” or “side channel” pumps, are characterized by a specific speed that contextualize them between rotary positive displacement and purely radial centrifugal pumps. Although regenerative pumps are not widely distributed, they are interesting for many industrial applications. In fact, for a given flow rate they operate at lower rotational speed with respect to purely radial pumps. Furthermore, they are less affected by mechanical problems with respect to positive displacement pumps. The energy transfer mechanism is the same of centrifugal pumps, but the presence of the side channel imposes to the fluid to pass several times through the impeller, thus obtaining higher pressure rise (as for multi-stage machines) with respect to classical purely radial pumps. Unfortunately, the complexity of the flow field, the large amount of wetted surface and a disadvantageous inflow/outflow configuration contribute to limit the maximum value of hydraulic efficiency, which is also very sensitive to the design choices. Moreover, the intrinsic complexity of the helical flow path makes the theoretical performance estimation a challenging task. It is worth underlining that an accurate performance prediction using one-dimensional models would allow to accelerate greatly the design process, with a non-negligible reduction of demanding three-dimensional Computational Fluid Dynamics (CFD) campaigns. The aim of the present work is to deeply investigate the fluid dynamics of regenerative pumps and to understand how accurately the fundamental physical phenomena can be reproduced by one-dimensional theory. To comply with these aims, a systematic post-processing of the results of several steady and unsteady three-dimensional CFD simulations is exploited for the validation of the in-house one-dimensional tool DART (Design and Analysis tool for Regenerative Turbomachinery), developed at the University of Florence. The theory underlying DART is detailed, and the assumptions of the model are verified by means of comparison with the numerical results underlining the key aspects to be considered for a reliable prediction of the pump performance.

In straight-through centrifugal pumps, a grooved seal acts as a balance piston to equilibrate the full pressure rise across the pump. As the groove pattern breaks the development of fluid swirl, this seal type offers lesser leakage and lower cross-coupled stiffnesses than a similar size and clearance annular seal. Bulk-flow models predict expediently the static and dynamic force characteristics of annular seals; however they lack accuracy for grooved seals. Computational fluid dynamics (CFD) methods give more accurate results, but are not computationally efficient. This paper presents a modified bulk-flow model to predict the rotordynamic force coefficients of shallow depth circumferentially grooved liquid seals with an accuracy comparable to a CFD solution but with a simulation time of bulk-flow analyses. The procedure utilizes the results of CFD to evaluate the bulk flow velocity field and the friction factors for a 73 grooves annular seal (depth/clearance d g / C r = 0.98 and length/diameter L/D = 0.9) operating under various sets of axial pressure drop and rotor speed. In a groove, the flow divides into a jet through the film land and a strong recirculation zone. The penetration angle ( α ), specifying the streamline separation in the groove cavity, is a function of the operating conditions; an increase in rotor speed or a lower pressure difference increases α . This angle plays a prominent role to evaluate the stator friction factor and has a marked influence on the seal direct stiffness. In the bulk-flow code the friction factor model ( f = nR e m ) is modified with the CFD extracted penetration angle ( α ) to account for the flow separation in the groove cavity. The flow rate predicted by the modified bulk-flow code shows good agreement with a measured result (6% difference). A perturbation of the flow field is performed on the bulk-flow equations to evaluate the reaction forces on the rotor surface. Compared to the rotordynamic force coefficients derived from the CFD results, the modified bulk-flow code predicts rotordynamic force coefficients within 10%, except that the cross-coupled damping coefficient is over-predicted up to 14%. An example test seal with a few grooves ( L/D = 0.5, d g /C r = 2.5) serves to further validate the predictions of the modified bulk-flow model. Compared to the original bulk-flow analysis, the current method shows a significant improvement in the predicted rotordynamic force coefficients, the direct stiffness and damping coefficients in particular.

The effect of impeller blades shape modification on the centrifugal pump performance has been investigated numerically. Impeller blades’ shape have been modified by new technique called “bladelet”. This technique has been called the “bladelet” after the name of the aeroplane winglet because of the great similarity between them in shape and function. The shapes of the blade trailing edge greatly affect the performance of the turbomachines. So, the purpose of the blade tilting (bladelet) is to decrease the recirculating flow at the pump trailing edge due to the high pressure difference and enhance the hydraulic performance of the centrifugal pump. The bladelet technique has two main geometrical parameters: radial position R BL and bladelet inclination angle θ BL . 3-D validated numerical simulation model has been carried out using commercial software, ANSYS ® CFX, to study the effect of the bladelet technique and its different parameters on the pump performance at different flow rates. In this study nine cases with different bladelet parameters have been numerically simulated in order to check its effect on the centrifugal pump performance. These nine cases have been chosen by considering the geometrical constrain of the bladelet parameters. The results of these nine cases have been compared with the basic impeller (the same impeller but without bladelet) at the same operating condition in order to discuss the effect of the bladelet parameters variation on the centrifugal pump performance. It was found that the use of the bladelet technique decrease the pressure difference between the pressure and the suction side at the blade trailing edge. This decrease in pressure difference at the blade trailing edge decreases the flow recirculation at the impeller outlet from pressure side to suction side. Also, bladelet technique improves the hydraulic efficiency at the part-load operating zone. In addition, the bladelet has a regression effect on the pump head for some cases with high inclination angle and low radial position. However, the bladelet technique increases the impeller blades’ overlap.

The complex three-dimensional turbulent flow field in a centrifugal water pump is numerically simulated considering torsional vibration of the shaft. The characteristic frequency and the frequency modulation phenomenon is investigated when the fluctuated-rotation-speed is considered. The results show that the amplitude of pressure fluctuation is bigger when the rotating-speed of shaft is unsteady, indicating that the speed fluctuations of impellers intensify the nonuniformity and instability of the whole flow field inside the pump. Besides, the Blade Passing Frequency (BPF) has obvious sidelobe frequency peaks when different frequency rate of speed appears. It can be concluded that sidelobes maybe come from the torsional vibration of the shaft. The main findings of this work can provide prediction of the pump performance and information for further optimal design of centrifugal pumps as well.

Three nominally-identical, 4-pad flexure-pivot-pad bearings (FPBs) were manufactured, varying only in their (dimensionless) pad preloads, namely, 0.264, 0.511, and 0.695. A hybrid hydrostatic bearing (HBB) was also manufactured with the same nominal length, diameter, and clearances. Water was used as the test fluid. The FPBs were tested at the following three constant supply pressures ( P s ): 0.689, 2.76, and 5.52 bar. The HBB was tested with a supply pressure that increased linearly to these same three terminal pressures. A magnetic bearing was used to load all bearings with an applied unit-load profile that increased linearly with time to reach the following two peak values: 0.745 and 1.38 bar. The design speed ω d was the maximum planned speed for a test run, and it was varied over 3, 3.5, 4, and 4.5 krpm. The tests aimed to produce a linearly increasing speed profile, ω( t ) = At , before reaching ω d . For the HBB, bearing P s also nominally increased linearly with ω. At lift-off , the shaft leaves the bearing surface during the shaft’s angular acceleration and remains separated and supported over a finite time and speed range. In some circumstances, FPB bearings lifted off and were then forced back into contact with the shaft due to the linearly increasing applied load. Once lifted off, the HBB always remained separated from the bearing surface. The peak load capacity was the maximum load supported by a bearing once lifted off (even if it was subsequently forced back into contact). FPBs have been used successfully in commercial turbomachinery handling low viscosity fluids. The results reported here indicate that preloads of m = 0.264 and 0.695 have comparable lift-off and peak load-capacity performance, substantially better than the m = 0.511 bearing. The FPB data also show a surprising steady drop in lift-off speeds and peak-load capacity with increasing P s values, presumably because of end seals that were provided. From these results, an FPB should be used with end seals and preloads of m = 0.264 or 0.695. The HBB lift-off ω values also dropped with increasing terminal P s values. For example, at ω d = 4.5 krpm, an increase in terminal P s from 0.689 bar to 2.76 bar dropped lift-off ω from ∼3 krpm to ∼ 300 rpm. The supply pressure provided to the HBB increased linearly with time and, consequently, also increased linearly with ω. In reality, a centrifugal pump P s would be proportional to ω 2 . To the extent that HBB lift-off ω performance depends on the supply pressure at lift off, lift-off ω and load-capacity performance of the present HBB would be worse with P s ∼ ω 2 , since the same required lift-off supply pressure would occur only at a higher ω. Except at ω d = 3.5 krpm, the FPBs had better (lower) liftoff speeds than the HBB. The HBB tested maintained a consistently better peak-load capacity than the FPB. In some cases, the shaft lifted off the FPB and then returned to contact. In all cases, the HBB remained in a lifted-off condition. As a final conclusion, the present data provide no clear basis for choosing between the FPBs and the HBB.

A multi-surrogate based optimization is a technique for the optimization of a turbomachinery impeller shape, which reduces the total design time. Computational analysis and surrogate-based optimization methodology have been implemented for the shape optimization of a centrifugal impeller blade in this problem. Geometric parameters such as impeller inlet and two-point control Bezier curve blade profile were selected as design variables. The objective was to maximize the total head as well as the efficiency of the pump using surrogate based optimization methods. A sample space was created for the design variables based on the sensitivity of the variable to the objective function and literature survey give a range of sample space. A three-dimensional Reynolds-averaged Navier-Stokes equations were solved to analyze the performance of the pump and the results were validated with experimental results. The simulations were done at different design points within the sample space to train the surrogate and to find the design optimum point using genetic algorithm. The shape of the impeller was optimized, to decrease the input power and improve the total head by varying the inlet and exit angles of the impeller.

The flow characteristic inside a pump chamber is the core problem in the study of the thrust force of a centrifugal pump. A numerical study on the IS150-125-315-type centrifugal pump with four different balance hole diameters was conducted. By selecting clear water as the medium, the time-averaged continuity equation with relative coordinates and the Navier-Stokes equation are established on the basis of the FLUENT software. The RNG k – ε equation turbulence model and the SIMPLEC algorithm are used to conduct a numerical simulation. The numerical results match the accuracy of the design values on the performance of the pump. The test results match the accuracy of the numerical results on the pressure of the back chamber and clearance leakage of the back seal ring. The influence of balance hole diameters is revealed in the flow field of the back chamber of the centrifugal pump. In detail, the patterns of the axial and radial distributions of the dimensionless tangential and radial velocities and the spanwise distribution of their average values in the back chamber of the centrifugal pump with different balance hole diameters are investigated. The relationship is also obtained between fluid rotational angular velocity in the back chamber of the centrifugal pump and rotational angular velocity of the impeller. The results reveal that the turbulent boundary layer and core region of the flow always exist in the pump chamber, even if there are no balance holes. The increase in diameter of the balance holes is associated with the increase in the radial component in the core region velocity and the decrease in the value range of its tangential component. At a certain radius and angular position, the diameter of larger balance holes leads to higher normalized tangential velocity in the core region. At the same time, a higher absolute value of the normalized radial velocity near the pump cover corresponds to greater radial leakage. At the same balance hole diameters, the rotating speed of the core region fluid generally keeps constant along the axial direction, whereas a significant difference is observed along the radial and tangential directions. The dimensionless radial and tangential velocities are significantly influenced by the flow of the volute chamber in the pump and are rarely influenced by the changes in the balance hole diameters, and vice versa. The dimensionless radial velocity will exert more power on large sections, such as sections 5 and 7, than the dimensionless tangential velocity, and vice versa. For cases with balance hole diameters less than its design value, dimensionless tangential average velocity is less than 0.5 with increases and dimensionless radial average velocity is less than 0 with decreases along the radial direction in the flow core area. Otherwise, dimensionless tangential average velocity is approximately equal to 0.59 and dimensionless radial average velocity is approximately equal to 0 in the flow core area. The balance hole diameter changes from 0 mm to 12 mm, and the rotating speed of the core region fluid is 0–0.8 times, rather than half, that of the impeller.

Simulation of turbulent flow in a pump is carried out with the RANS equations and the RNG k-epsilon turbulence model. Numerical simulation has been compared with the experimental data. The results show that separating vortex is firstly produced at the pressure side of the impeller passage near the tongue. Then it spreads to the inlet and outlet of the impeller passages and moved to the centre region of impeller passages from the boundaries. Finally, it almost occupies all the impeller passages and multiple vortices exist in impeller passages at small flow rate. It is found that the tongue has large effect on the flow in the impeller passage approaching to it. The impeller passage near the tongue is easily tending to be unstable comparing with others passages. The energy gradient theory is used to analyze the flow stability in the impeller. The region with larger value of energy gradient function K means the bigger turbulence intensity and poor flow stability. At small flow rate the regions with large value of K are enlarged and are mainly located at both sides of blade pressure and suction surfaces where the flow is easily tending to be unstable.

Shrouded centrifugal pumps are widely used in industrial applications such as process machines, and they can suffer from rotordynamic instability. Eccentric shrouded impellers induce non-axisymmetric flow fields which, in turn, lead to rotordynamic forces. Therefore, a new analytical flow model for shrouded pump impellers (which considers non-axisymmetric flow fields in the upstream inlet duct, shrouded impeller, and downstream) has been developed using an actuator disk approach. The model can predict impeller rotordynamic stiffness values from pump geometry and operating conditions. When compared to the available pump test data [1], the new model’s predicted stiffness coefficients agree well with the measured data. The new model’s predictions show the strong influence of the non-axisymmetric shroud inlet flow on the rotordynamic stiffness forces. The shroud inlet flow non-axisymmetry, in turn, results from the non-axisymmetric flows upstream of and inside the impeller blade passage induced by impeller eccentricity.

A prototype of a new generation of centrifugal pumps has been developed, with aim to improve typical weaknesses like narrow operable range due to slip and incidence losses in off-design conditions. The peculiarity of this pump is the absence of any stator blade, which has been substituted with a counter-rotating radial impeller. According to an exhaustive literature survey, the usage of a mixed flow impeller as a front rotor, followed by a radial-flow impeller seems to be a novel approach in pump design. The combination of a high specific speed impeller with a low specific speed rotating diffuser produces a flexible adaptability against aforementioned limits. Keep on adding energy to the fluid instead of just diffusing the flow, permits to reach a downsized hydraulics and an increased entire machine power density. The characteristic of such a pump needs to be analyzed as 3D-surface, both speeds are actually independent and for a fixed discharge the head rise and efficiency become surfaces. A new definition of optimized characteristic curve, with variable speed ratio, could be identified based on those performance maps. A special test rig has been built to measure the machine performance, distinguishing the mechanical losses of both shafts separately with no-load measurements. The sensitivity of the system on speed ratio variation has been explored. The experiments show the presence of different best speed ratios which maximize alternately the head or the efficiency. Additionally, the results confirm the possibility to expand the working range acting on the rotational speeds. Head rise and efficiency curves with varying speed ratio, as functions of the flow rate are finally shown using several diagrams, highlighting the advantages of this new design.