Head Curve Research Articles

Quantitative analysis of energy loss and vibration performance in a circulating axial pump

The influence of vortex on steady flow and pressure fluctuation of circulating axial pump under pump condition is illustrated by numerical method validated by experiment measurement, a method for analyzing vibration by using Euler head density function (EHDF) is established. Based on the matching equation of the flowing angle of impeller and guide vane, two groups of guide vanes are designed to relate the same impeller as comparison. When the stagnation point at the guide vane inlet is offset, the low-speed vortex (LSV) is generated in the area from the mid flow surface to the hub surface, where the local Euler head (LEH) curves’ distribution is disarranged and the EHDF of this part is larger and closes to the EHDF value of the whole spanwise region, furthermore, the pressure fluctuation levels of low frequency band here deteriorate seriously. The larger EHDF value means the flow state and pressure fluctuation are worse, and the mainly developing of LSV is in this problematical area where the EHDF value has deteriorated the most. With quantizing image analysis of vorticity and LEH of the circulating pump by the EHDF, the structure position of LSV can be analyzed and the vibration level can be predicted.

An insight into the flow field characteristics of the high temperature liquid Sodium (Na) with cavitation effects in the 600 MW fast reactor system

The paper explores the flow field characteristics of liquid Sodium pump, the flow field calculation model is established. The head and efficiency curves of sodium pump obtained by simulation are compared with the test data to verify the accuracy of the model. Flow characteristics inside the impeller, guide vane and the volute are investigated and summarized. The pressure distribution and velocity distribution characteristics of the steady flow field and the pressure fluctuation and fluid force characteristics of the unsteady flow field are further analyzed, which provides the basis for the calculation of flow induced vibration and sound field. The dynamic processes of Sodium cavitation effects are stimulated and studied systematically. The causes of fluid excited vibrations in Sodium pump are preliminarily revealed. Researches have remarkable guiding significances for the analysis of flow characteristics of Sodium pump system of the new generation 600 MW nuclear main pump system.

Investigation of the flow energy dissipation law in a centrifugal impeller in pump mode

Centrifugal impeller is usually designed for water pumping. Fluid get energy from impeller but also lose energy when passing through it. To improve the efficiency and have a better operation stability, it is necessary to understand the flow energy dissipation in centrifugal impeller in pump mode. In this case, a thermodynamic analysis is conducted on a model centrifugal pump unit based on computational fluid dynamics (CFD) simulation. Typical performance curve is found with a positive-slope efficiency curve and a negative-slope head curve. With the decreasing of flow rate, both the impeller head and the flow energy dissipation (FED) will rise up. The FED is found related to the flow regime. The complex undesirable flow pattern induces high FED under off-design conditions especially at very small partial-load. Based on the visualization, FED is found with two main sources including the wall friction and the flow interaction. At over-load and design-load, the wall friction induced FED is dominant. With the decreasing of flow rate, flow interaction induced FED becomes dominant. The typical strong FED sites are found related to the striking, separation, merging and interaction of both smooth flow and vortical flow. The FED analysis will correlate the pump performance estimation and guide the design.

Kinematic gait characteristics of straight line walk in clinically sound dairy cows.

The aim of this study is to describe the kinematic gait characteristics of straight line walk in clinically sound dairy cows using body mounted Inertial Measurement Units (IMUs) at multiple anatomical locations. The temporal parameters used are speed and non-speed normalized stance duration, bipedal and tripedal support durations, maximal protraction and retraction angles of the distal limbs and vertical displacement curves of the upper body. Gait analysis was performed by letting 17 dairy cows walk in a straight line at their own chosen pace while equipped with IMU sensors on tubera sacrale, left and right tuber coxae (LTC and RTC), back, withers, head, neck and all four lower limbs. Data intervals with stride by stride regularity were selected based on video data. For temporal parameters, the median was calculated and 95% confidence intervals (CI) were estimated based on linear mixed model (LMM) analysis, while for limb and vertical displacement curves, the median and most typical curves were calculated. The temporal parameters and distal limb angles showed consistent results with low variance and LMM analysis showed non-overlapping CI for all temporal parameters. The distal limb angle curves showed a larger and steeper retraction angle range for the distal front limbs compared with the hind limbs. The vertical displacement curves of the sacrum, withers, LTC and RTC showed a consistent sinusoidal pattern while the head, back and collar curves were less consistent and showed more variation between and within cows. This kinematic description might allow to objectively differentiate between normal and lame gait in the future and determine the best anatomical location for sensor attachment for lameness detection purposes.

Rotating stall characteristics in the vaned diffuser of a centrifugal pump

Rotating stall in centrifugal pumps takes place frequently under part-load conditions, along with high pressure pulsation. The major focus for studies is rotating stall inside the impeller, rarely paying attention to that in the vaned diffuser. In this study, rotating stall behavior in a vaned diffuser centrifugal pump has been numerically investigated, and the cross-power spectrum method is adopted to identify low-frequency pressure signals. The applied numerical method has been validated by experimental results including flow structures provided by PIV measurements. For the vaned diffuser pump, a hump region in head curve is observed between 0.25Qd and 0.5Qd conditions. Under 0.41Qd condition, rotating stall occurs in the vaned diffuser of the pump, with three stall cells rotating opposite to the direction of impeller rotation and the rotating frequency being 0.083 Hz equal to 1/600 of the impeller rotating frequency. Rotating stall takes place under 0.5Qd condition as well, whereas only a periodic process of stall cell from inception to disappearance appears in the diffuser channel under 0.35Qd condition. Furthermore, the effect of number of diffuser vanes on rotating stall characteristics has been analyzed in detail.

New Expressions to Apply the Variation Operation Strategy in Engineering Tools Using Pumps Working as Turbines

The improvement in energy saving aspects in water systems is currently a topic of major interest. The utilization of pumps working as turbines is a relevant strategy in water distribution networks consisting of pressurized pipes, using these machines to recover energy, generate green energy and reduce leakages in water systems. The need to develop energy studies, prior to the installation of these facilities, requires the use of simulation tools. These tools should be able to define the operation curves of the machine as a function of the flow rate. This research proposes a new strategy to develop a mathematics model for pumps working as turbines (PATs), considering the modified affinity laws. This proposed model, which can be input into hydraulic simulation tools (e.g., Epanet, WaterGems), allows estimation of the head, efficiency, and power curves of the PATs when operating at different rotational speeds. The research used 87 different curves for 15 different machines to develop the new model. This model improves the results of the previously published models, reducing the error in the estimation of the height, efficiency, and power values. The proposed model reduced the errors by between 30 and 50% compared to the rest of the models.

Optimal Operation of Farm Turbine Pumps.(Dept.C)

One of the costiest items in agriculture is the cost of providing water. The purpose of this investigation is to operate the turbine pumps to cope with the irrigation water and pressure requirements for the existing system of irrigation. It is also desired to maintain a constant pump discharge for different static water levels by varying the pump speed to adjust an increase or decrease in water discharge. The study was carried out on two turbine pumps at the College Research Station, each of which has fourteen stages; these pumps are supposed to irrigate the College Farm including two centre pivots. The system head curves were constructed, points of intersection with the pump characteristic curves at different pump speeds, are the operating points, which could be used to give the required discharge and pressure at a specified pump speed according to the given tables for the gross irrigation water requirements. Equations of system head curves and pump characteristic curves are presented, from which the operating points could be obtained.

MATHEMATICAL MODELLING OF ONE-GROUP GAS-HYDRAULIC CIRCUIT OF THERMAL POWER PLANT STEAM BOILER AUXILIARIES

The paper presents algebraic mathematical models of centrifugal mechanisms that operate in the power boiler gas-hydraulic circuit. The models have been built by means of head-flow curve approximation. The head-flow curve depends on the centrifugal mechanism blade rotating speed and guide vane angle. The least squares method has been applied for centrifugal mechanism head-curve approximation on the basis of experimental or numerical data. Different configurations for the connections of centrifugal mechanisms in the power boiler gas-hydraulic circuit have been considered, relationships for their performance assessment obtained, and efficiency factors for various methods of their capacity control introduced. The state equation for a complex gas-hydraulic network in the problem of its efficiency analysis has been obtained with application of Kirchhoff laws. Numerical algorithms have been developed to solve group control parameter optimization problems for the considered connections of centrifugal mechanisms. Features of mathematical models for groups of series-, parallel- and complex-connected centrifugal mechanisms with different head curves in the power boiler maintenance system have been specified. An optimal group control problem for a group of centrifugal mechanisms has been formulated and solved under various power boiler modes. For the feed pumps, individual frequency control proves to be the most effective method, while for the boiler draft mechanisms group frequency regulation turns out to be the most efficient. In a typical summer month, implementation of energy-efficient centrifugal mechanism capacity regulation method in a Thermal Power Plant is shown to result in auxiliary electricity consumption reduction by 10.96 % as compared with available actual data.

Left Ventricular Assist Device Flow Pattern Analysis Using a Novel Model Incorporating Left Ventricular Pulsatility.

Our current understanding of flow through the circuit of left ventricular assist device (LVAD), left ventricle and ascending aorta remains incompletely understood. Computational fluid dynamics, which allow for analysis of flow in the cardiovascular system, have been used for this purpose, although current simulation models have failed to fully incorporate the interplay between the pulsatile left ventricle and continuous-flow generated by the LVAD. Flow-through the LVAD is dependent on the interaction between device and patient-specific factors with suboptimal flow patterns evoking increased risk of LVAD-related complications. Computational fluid dynamics can be used to analyze how different pump and patient factors affect flow patterns in the left ventricle and the aorta. Computational fluid dynamics simulations were carried out on a patient with a HeartMate II. Simulations were also conducted for theoretical scenarios substituting HeartWare HVAD, HeartMate 3 (HM3) in continuous mode and HM3 with Artificial Pulse. An anatomical model of the patient was reconstructed from computed tomography (CT) images, and the LVAD outflow was used as the inflow boundary condition. The LVAD outflow was calculated separately using a lumped-parameter-model of the systemic circulation, which was calibrated to the patient based on the patient-specific ventricular volume change reconstructed from 4 dimensional computed tomography and pulmonary capillary wedge pressure tracings. The LVADs were implemented in the lumped-parameter-model via published pressure head versus flow (H-Q) curves. To quantify the flushing effect, virtual contrast agent was released in the ascending aorta and its flushing over the cycles was quantified. Shear stress acting on the aortic endothelium and shear rate in the bloodstream were also quantified as indicators of normal/abnormal blood flow, especially the latter being a biomarker of platelet activation and hemolysis. LVAD speeds for the HVAD and HM3 were selected to match flow rates for the patient's HMII (9,000 RPM for HMII, 5,500 RPM for HM3, and 2,200 RPM for HVAD), the cardiac outputs were 5.81 L/min, 5.83 L/min, and 5.92 L/min, respectively. The velocity of blood flow in the outflow cannula was higher in the HVAD than in the two HeartMate pumps with a cycle average (range) of 0.92 m/s (0.78-1.19 m/s), 0.91 m/s (0.86-1.00 m/s), and 1.74 m/s (1.40-2.24 m/s) for HMII, HM3, and HVAD, respectively. Artificial pulse increased the peak flow rate to 9.84 L/min for the HM3 but the overall cardiac output was 5.96 L/min, which was similar to the continuous mode. Artificial pulse markedly decreased blood stagnation in the ascending aorta; after six cardiac cycles, 48% of the blood was flushed out from the ascending aorta under the continuous operation mode while 60% was flushed under artificial pulse. Shear stress and shear rate in the aortic arch were higher with the HVAD compared to the HMII and HM3, respectively (shear stress: 1.76 vs. 1.33 vs. 1.33 Pa, shear rate: 136 vs. 91.5 vs. 89.4 s-1). Pump-specific factors such as LVAD type and programmed flow algorithms lead to unique flow patterns which influence blood stagnation, shear stress, and platelet activation. The pump-patient interaction can be studied using a novel computational fluid dynamics model to better understand and potentially mitigate the risk of downstream LVAD complications.

Time-dependent load transfer behavior of grouted anchors in laterite

The load transfer behavior of grouted anchors is time-dependent under long-term (creep) load. This study aims at investigating the time-dependent behavior of grouted anchors in laterite by both physical model test and theoretical simulation. A laboratory creep pullout model test of full-length-bond grouted anchor in laterite was carried out using a special developed apparatus. The creep pullout load–displacement response at anchor head and time history curves of axial strain were tested and presented. The creep behavior on the grout - soil interface was simulated using Merchant rheological model in theoretical simulation. By comparing the experimental data with predictions, the applicability of the proposed theoretical method was validated, and the time-dependent load transfer behavior of grouted anchors was discussed. The impacts of five model parameters on the time-dependent pullout response were further analyzed by parametric studies. It revealed that the tensile force distribution tends to be linear, and the shear stress distribution towards uniformity as time elapsed. Additionally, the time-dependent load transfer behavior for grouted anchors is influenced by the above parameters in various levels. This work provides insights into understandings of time-dependent behavior, and facilitates the service life design practice for grouted anchors embedded in laterite.

Prediction and Evaluation of Waterjet Pump Performance under Nonuniform Inflow Using Parallel Compressor Theory

Parallel compressor theory (PCT) is commonly used to estimate effects of inlet distortion on compressor performance. As well as compressor, the actual inflow to pump is also nonuniform and unfavorable for performances. Nowadays, insufficient understanding of nonuniform inflow effects on pump performance restricts its development. Therefore, this paper applies PCT to predict external characteristics and evaluate internal flow instability of waterjet pump under nonuniform inflow. According to features of nonuniform inflow, the traditional PCT is modified and makes waterjet pump sub-divided into two circumferential tubes owning same performances but with different inlet velocity (representing nonuniform inflow). Above all, numerical simulation has been conducted to validated the applicability and accuracy of PCT in head prediction of waterjet pump under nonuniform inflow, since area-weighted sum of each tube head (i.e., theoretical pump head) is highly consistent with simulated result. Moreover, based on identifications of when and which tube occurs stall, PCT evaluates four stall behaviors of waterjet pump: partial deep stall, partial stall, pre-stall and full stall. Furthermore, different stall behavior generates different interactions between head variation of each tube, resulting in a multi-segment head curve under nonuniform inflow. The modified PCT with associated physical interpretations are expected to provide a sufficient understanding of nonuniform inflow effects on pump performances.

Variations of Performance and Pressure Pulsation During Cavitation in Centrifugal Pumps with Entrained Air

Most of the research on the cavitation with entrained air has focused on the military direction, but it ,about centrifugal pumps, which is relevant to people's livelihood, is still relatively lacking. In order to study the basic law of the development of cavitation inside centrifugal pumps under aeration conditions, a test bench suitable for cavitation experiments with incoming flow containing gas was obtained. Furthermore, a single-stage single-suction 6-blade centrifugal pump was used as the research object to conduct pressure pulsation experiments under cavitation condition when the incoming flow was 1.0% air viod fraction at 2900r/min-50m3/h. The results showed that: After cavitation happened, the greater aeration content will deteriorate the pump's anti-cavitation performance, but the head curve is more gentle in falling down compared to natural cavitation. Hence aeration has a beneficial effect on the performance degradation of the pump under the cavitation condition. At the same time, before the cavitation number drops to the fracture cavitation number of the pump, aeration has improvement in the efficiency of the pump in different degrees , especially in the situation with the ventilated rate of 1.0%. The main frequency of pressure pulsation at the inlet and outlet of the test pump after aeration is dominated by the blade frequency. The shaft frequency signal at the outlet gradually decreases with the cavitation number lessened. Moreover the amplitude of the blade frequency grows slightly with the reduction of the cavitation number. But it tends to soar when the cavitation number is less than the fracture cavitation number.

Разработка и анализ модели процесса получения напорной характеристики центробежных насосов жидкостных ракетных двигателей

The paper describes the model of the centrifugal pump head curve obtaining process which helps in consideration of the implementation of automated systems in liquid-propellant rocket engine manufacturing. The work contains the simulation of automated and non-automated head curve obtaining. The developed model shows that the automated process exceeds the non-automated analog in terms of error values and labor intensity

Unsteady flow fluctuations in a centrifugal pump measured by laser Doppler anemometry and pressure pulsation

Turbulent flow generated by the intense rotor–stator interaction is detrimental to the safe running of the centrifugal pump. In order to gain more insight into unsteady velocity pulsation characteristics, this research applies the laser Doppler anemometry technique to capture velocity signals at various flow rates. Besides, pressure transducers are arranged on the model pump to sample transient pressure pulsation signals. The study paid particular attention to pulsation signals in the diffusion section of the volute. Results show that at low flow rates, a prominent hump phenomenon generated within the pump head curve, which indicates the development of rotating stall in the model pump. As noted from the spectra, the discrete blade passing frequency and impeller rotating frequency dominate the velocity and pressure spectra. Root mean square values of velocity signals increase rapidly at off-design flow rates, especially within the rotating stall region, and a similar trend is observed for pressure amplitude at the blade passing frequency. From the measuring point (P3) at the inlet of the discharge channel upstream of the volute tongue to the point (P10) at the volute outlet, pressure amplitude rises significantly. Meanwhile, the minimum point of pressure amplitude vs flow rate occurs around 0.4ΦN, and again, the findings show differences for comparisons between measuring points in the core flow region of the volute. This resulting phenomenon can be attributed to flow patterns in the diffusion section.

A Hydraulic Performance Comparison of Centrifugal Pump Operating in Pump and Turbine Modes

The modifications of impeller may show diverse impact on centrifugal pump operating in pump and turbine modes. To clarify this problem, the hydraulic performance of a low specific speed centrifugal pump operating in both modes was firstly obtained by CFD method and verified by experiment. Then, based on the single-factor design method, a series of calculations have been conducted to identify the effects of impeller geometry parameters on the hydraulic performance in different modes. The variations of head, shaft power and hydraulic efficiency curves with different impeller parameters were explored. It is found that compared with turbine, the pump shows a more obvious variation of head. The outlet angle has positive impact both on the head consumed by pump or generated by turbine. The change of turbine shaft power is apparently smaller than that of pump for different impeller geometry parameters. Only the outlet width somewhat changes the turbine shaft power. The hydraulic efficiency in both modes shows different variation under different impeller geometric parameters, while the hydraulic efficiency of both modes is reduced with the outlet angle increasing. Meanwhile, the response amount of hydraulic efficiency caused by certain change of impeller parameters was estimated by sensitivity analysis method. It is found that only the appropriate blade number and outlet width can improve the hydraulic performance both in pump and turbine modes. Eventually, the hydraulic loss, skin friction loss and theoretical analysis were performed to explore the reason of hydraulic performance variation due to different impeller parameters. The change of slip factor, impeller inlet area, impeller outlet area or hydraulic loss results in the change of hydraulic performance in both modes. The results can be useful for hydraulic performance improvement for both pump and turbine modes through impeller geometry modification.

Rotational speed variation assessment of centrifugal pump-as-turbine as an energy utilization device under water distribution network condition

Nowadays, to extend the application of clean energy sources, the utility of small power plants has been expanded and one of them is the potential utilization of water distribution networks (WDNs). By replacing pressure reducing valve (PRV) with a soft pressure regulating system (SPRS) the available hydraulic energy could be employed for generating electricity. A pump as turbine (PAT), considering its economic advantages and proper mechanical function, is a valuable option to be used in WDN. Since the use of PAT requires a precise understanding of how it operates under various hydraulic conditions, the lack of sufficient information in this area can be an obstacle to the expansion of PAT plants. In this paper, the results of a variable speed centrifugal pump installed in a WDN that has the task of regulating pressure and producing power were analyzed with the focus on the effects of speed variation on characteristic parameters. The findings showed that by incorporating a speed parameter in PAT descriptive relations, the prediction’s accuracy of the head, power and efficiency curves, respectively can be improved by 3.7%, 12.2% and 34.4%, compared to the nearest model. Provided correction relations help to improve estimations of PAT’s energy performance in the network.

P-y Curves of 2x2 pile group in liquefiable soil under dynamic loadings

The seismic analysis of pile groups subjected to lateral and axial loads is often implemented separately. As a result, the calculated bending moment and deflection are found to be nonrealistic in nature, as compared with conditions where a combined analysis is carried out. In reality combined loadings are encountered in almost all situations and the occurrence of pure loadings (either lateral or vertical) is either nonexistent or scarce. In the present study, the numerical analysis of a 2 × 2 pile group under the action of combined loadings (lateral load, vertical load, and seismic ground motions) and embedded in a layered soil is carried out using the FLAC3D computer program. The liquefiable soil layer is modeled using the Mohr-Coulomb with Byrne constitutive model, while the non-liquefiable soil layers are modeled with the conventional Mohr-Coulomb constitutive model. The pile group is considered an elastic model. The proposed numerical model is validated with the existing dynamic centrifuge test results and good agreement between the results is observed. Finally the dynamic P-y (P denotes the lateral load applied at the pile cap and y is the lateral pile group deflection at the pile head) curves are generated for different combinations of vertical load, lateral load, and input seismic ground motions in liquefiable and non-liquefiable soil. It is observed that for a constant vertical load (V) having a magnitude equal to 0.50 times the ultimate pile load capacity (0.50Vult), the pile group deflection increases by 36% when the lateral load increases from 300 to 900 kN, while the increase is by 48.5% for V = Vult and for the same increase in the lateral load. Similarly 2001 Bhuj and 2011 Sikkim motions caused an amplification of deflection by 8.4 and 9 times, respectively. The influence of vertical loads increases the pile head displacement and should be considered for determining the dynamic P-y curves. The proposed dynamic P-y curves will be beneficial to geotechnical engineers for understanding the qualitative response of pile groups under combined loading conditions.

Effect of the Center Post Establishment and Its Design Variations on the Performance of a Centrifugal Rotary Blood Pump

The main purpose is to compare the characteristics and performance of a centrifugal blood pump with and without center post. Furthermore, to propose a center post design guide for the development of centrifugal blood pumps: finding the appropriate height and diameter of the center post. A centrifugal blood pump with different center post configurations is investigated using Computational Fluid Dynamics (CFD) in an extensive parametric approach. Height and diameter of the center post are varied on 4 levels each. Pressure head and hydraulic efficiency curves, pressure and velocity contours and volumetric histograms of scalar shear stress (SSS) distribution are discussed in detail. The simulation results show uniform pressure distribution around the casing in the baseline design. Although obtaining the minimum Normalized Index of Hemolysis (NIH), average scalar shear stress (ASSS), and volumetric percentage ratios (SSS > 9, 50 and 150Pa), a stagnation and recirculation zone in the impeller eye above the casing bottom is detected in center post free (H = 0mm) pump. With the establishment and further increase of the center post height, the stagnation zone disappears gradually. The results also indicate that flow recirculation and stagnation around the circumference of the center post occurs when the center post has a small diameter. As the diameter increases, a reversed flow is formed between the impeller and the center post. The center post can greatly reduce the stagnation zone occurring in the center post free pump. The diameter of center post makes a difference to the flow field in the gap between the impeller and the center post.

Total Artificial Heart Incorporating Novel Stacked Motor; First In Vivo Results

The latest version of the continuous flow total artificial heart (CFTAH), which incorporates a novel stacked motor to improve passive self-regulation of pressure difference between the left and right atria, and reduce pump rotor over-excursion, was tested in vivo in a calf model to assess operational performance. The CFTAH was implanted in a calf and run at various pump operating conditions including mean pump speeds from 2400 to 3600 RPM, sinusoidal speed modulations from 0 to 25%, and speed modulation rates from 80 to 120 B.M. It was also tested under various combinations of simulated high and low systemic vascular resistance and pulmonary vascular resistance via outlet graft clamping and administration of a Nitroprusside respectively. The CFTAH responded to all control inputs and ran as expected during the experiment. The head curves of the right and left pumps generated from measured pressures, measured right flow and calculated left flow, were consistent with in vitro data on this pump. The passive atrial pressure regulation performed well in the normal operating range, and there were no signs of excessive rotor axial displacement during extreme pressure excursions as had been seen in the previous versions of the pump. The left atrial pressure was unusually low throughout most of the experiment and we believe that this may have been due to partial blockage of the of the left inflow cuff proximal to the pressure line tap. This led to several left inlet suction conditions and extreme pressure conditions. The replacement of the standard, single stack stator motor with the new dual stator stack motor resulted in better passive regulation of the pressure difference between the left and right atria. Also, the extreme pressure conditions resulting from left inlet suction events did not cause the pump's rotor to rub against the volute housing as had been seen in previous versions of the pump. Even though the self-regulation was acceptable, shifting of the regulation characteristic to increase the nominal LAP-RAP value will improve the regulation further, and this modification will be implemented prior to the next in vivo experiment.

A Simple Analytical Model for Head Estimation of Noncavitating Inducers With Arbitrary Shape

Abstract Although the increase of suction performance is the primary objective when applying inducers to centrifugal pumps and the combined head of inducer and main impeller is finally to be judged, it is helpful for the designer to estimate the head and flow characteristics provided by the inducer alone in the early design stage. With this knowledge, the matching of inducer and pump impeller can possibly be improved and the limiting of operational range that is essentially due to the application of the inducer can be detected in the initial design phase. An already published method (Li, W.-G., 2011, “Head Curve of Noncavitating Inducer,” ASME J. Fluids Eng., 133(2), p. 024501.), which was limited to the application on inducers with cylindrical hub and shroud, is extended to work with arbitrary-shaped inducer geometries. This article discusses the method of performance estimation and its implementation in detail. Four different designs based on common guidelines available in the open literature are analyzed with the help of the method described. The predicted head curves are compared to experimental and computational results obtained as part of an earlier study by the authors. Despite the simplicity of the method, good agreement of the head estimations with the experimental and numerical data can be observed. This indicates that the loss model seems to be applicable not only to cylindrical inducers but also to arbitrary-shaped inducers. Investigations of the exit conditions show that the analytical flow model only roughly represents the simulated flow distribution at the inducer outlet.