Wrap Angle Research Articles

Multiobjective and multicondition optimization for a gas–liquid mixed-flow pump based on a three-dimensional inverse design

The mixed-flow pump performs well in transporting gas–liquid mixtures with large flow rates and high inlet gas volume fractions. However, its extensive development is still limited by the operating range and poor overall performance. In this study, a multiobjective and multicondition optimization methodology for improving the gas–liquid flow performance of a mixed-flow pump based on the inverse design is proposed. The impeller blade load is taken as the optimization variable. Moreover, the Euclidean distances of the pressure increment, efficiency, and gas volume fraction in the diffuser are adopted as optimization objectives. Results show that the numerical methodology is verified by the pressure increment and gas distribution obtained in the tests of the original pump. Optimized results demonstrate that the slope of the straight line, the stacking angle at the hub, and the intersection point of the rear parabola and the straight line significantly affect the objectives. The increased load of the first half of the impeller and the reduced load of the second half may improve the comprehensive performance of mixed-flow pumps. The blade length and wrap angle are reduced after optimization, which changes the inlet and outlet angles and deflection of the blade, thereby helping to enhance the cognition of mixed-flow pump performance optimization.

Case Calculation and Analysis of Insufficient Traction Force in Elevator

For the traction driven elevator, the satisfaction of traction conditions is the basic guarantee for the normal operation of the elevator. If the traction force is insufficient, there will be skid, slip and other phenomena, which not only cannot meet the design requirements of the elevator manufacturers, but also easy to cause safety accidents. The equivalent friction coefficient f (depending on groove shape, groove material and groove lubrication) and the wrap angle of the wire rope on the traction wheel play a decisive role in the traction force. Based on a case of insufficient traction force caused by too small Angle, the cause of its failure is calculated and analyzed, and corresponding corrective measures are put forward to avoid the occurrence of such problems.

Optimization Design and Pressure Fluctuation Suppression Based on Orthogonal Method for a Centrifugal Compressor

An air compressor is the core component of the air supply system of a hydrogen fuel cell, which demands high efficiency and reliable stability in a wide operation region. In this work, a centrifugal air compressor for a hydrogen fuel cell is first designed and then measured experimentally. Furthermore, a test rig for assessing the aerodynamic performance of the centrifugal air compressor is established, which includes a pipeline, gas flowmeter, flow regulating valve, pressure transmitter, centrifugal compressor, controller, DC power supply and computer. Then, the orthogonal method is employed to conduct the aerodynamic performance optimization. Four optimization parameters—including blade number, blade angle at the inlet, blade angle at the outlet and wrap angle—are set with three levels. Nine compressor individuals are designed according to the orthogonal method, and then numerical simulation is implemented to confirm the aerodynamic performance and flow pattern. Results show that the blade number has the greatest influence on the compressor’s performance, and the blade angle at inlet is also very important. The optimal performance of the compressor improves compared to that of the baseline compressor; the efficiencies of the baseline compressor and optimal compressor are 81.3% and 83.8%, respectively, improving by 2.5%. The frequency domain of pressure fluctuation in the centrifugal compressor is related to the stator-rotor interaction. The peak value of pressure fluctuation amplitude occurs at the rotation frequency of 833 Hz and its harmonic frequency. In comparison with the baseline compressor, the pressure fluctuation amplitude of the optimal compressor is obviously reduced, especially near the volute tongue.

Numerical Investigation of Compression and Expansion Process of Twin-Screw Machine Using R-134a

Increasing the efficiency of twin-screw machines is beneficial for gas compression and expansion applications. We used a computation fluid dynamic approach to obtain the flow field and efficiency of a twin-screw machine that used R-134a as the working fluid. The leakage flow and sealing lines were obtained to study their geometrical effects during the compression and expansion process. The effects of the wrap angle (280°, 290°, and 300°) and pressure ratios on the compression efficiency were studied. During the compression process, the volumetric efficiency was more than 70% regardless of the wrap angle. We found that the volumetric efficiency slightly decreased when the wrap angle increased. However, the effect of the wrap angle on the isentropic efficiency was not substantial. An increase in the pressure ratio decreased the mass flow rate and increased the leakage flow. This screw machine can also be operated in an expansion process, and the simulated expansion ratio was 3:1. However, this expansion ratio contributed to an underexpanded condition, which led to a lower volumetric and isentropic efficiencies compared with the original built-in expansion ratio scenario.

Analysis of maximum radial load capacity of hydrostatic journal bearing considering supply pressure limitation by a novel method

The aim of the present study is the numerical analysis of the operating conditions (rotary speed, supply pressure) and structure parameters’ (capillary design parameter, recess wrap angle) influence on the performance of a four-rectangle recessed hydrostatic journal bearing, taking into account the limitation of the recess pressure that is always smaller than supply pressure. A new calculation method is proposed that ensures both lower time consumption than traditional numerical method (FEM, FDM) and higher accuracy than simplified method (Liang’s method). This approach examines the effect of operating conditions and structure parameters on the maximum load capacity, attitude angle, and maximum eccentricity ratio considering the supply pressure limitation. Moreover, the pressure distribution under various operating conditions and structure parameters is also investigated to explore their contributions to the performance of the hydrostatic journal bearing. The results indicate an excellent guiding significance for the design and application of hydrostatic journal bearings.

Ordering Eyeglasses Using 3D Head Scan Technology versus Established Online and Storefront Clinic Methods.

This study investigates how a new smartphone scanning technology compares with established online and storefront vendors in providing remote measurement and adjustment of prescription eyeglasses. This study aimed to evaluate a new technology for ordering prescription eyeglasses online. Thirty participants with 2.00 to 2.75 D of presbyopia (aged 49 to 74 years) were asked to order eyeglasses with progressive addition lenses from four vendors: one online vendor using a new head scan technology (Topology, San Francisco, CA), two established Web site-based vendors (vendors A and B), and one storefront vendor: Université de Montréal's Vision Clinic (UMVC). The resulting measurements were compared with those of opticians. Participant-reported preferences on visual and physical comfort of eyeglasses were collected after 15-minute trials of eyeglasses from each vendor. Pupillary half-distance measured with Topology matched optician measurements, but online vendors A and B diverged (mean difference, - 0.80 mm [ Z = -2.79; P = .005]). Topology and vendor B segment addition heights were similar to optician measurements, but vendor A diverged (mean, -1.40 mm [ Z = -2.58; P = .01]). The personalization parameter values obtained with Topology were different from optician measurements for pantoscopic angle (-5.30° [ Z = -4.12; P < .001]) and face wrap angle (+1.25° [ Z = -2.94; P = .003]). The UMVC eyeglasses scored best for adjustment (8.71/10 [ Z = -5.53; P < .001]), with Topology coming second (7.23/10). Topology scores were equivalent to UMVC scores for all eight items of patient-reported preferences (nonparametric Friedman analysis of variance, P < .05). Basic lens centration measurements obtained with Topology compare well with those of opticians, but some aspects of the methodology for measuring personalization parameters could be improved. In comparison with two established online vendors, resulting measurements with Topology are more consistent. Initial wearer satisfaction with Topology eyeglasses was also better.

Numerical and Experimental Study on the Colliding Flow Pulp Conditioning for the Separation Intensification of Unburned Carbon from Coal Gasification Slag

As a byproduct of the coal gasification process, a large amount of coal gasification slag is generated. The failure to fully dispose of it has caused the occupation of land resources and environmental pollution. Before its comprehensive utilization, the carbon and ash constituents must be separated, for which flotation is an effective method. However, the small difference in surface hydrophobicity of them cannot result in a high-efficiency separation. Therefore, a colliding flow pulp conditioning device (CFPCD) was proposed in this work to improve the interaction between the collector droplets and fine particles, and strengthen the modification of collector on the particle surface by generating a properly constructed turbulent flow field. Computational fluid dynamics (CFD) was employed to simulate the internal flow field of CFPCD to obtain the critical flow field parameters, such as the velocity, strain rate, turbulent kinetic energy, turbulent dissipation rate, and turbulent eddy scale. Additionally, particle wrap angle measurements and flotation tests were conducted to verify the performance of pulp conditioning. The results showed that a velocity gradient was obvious in the inner cylinder colliding flow area, thereby inducing the large strain rate and the intense turbulence, which were responsible for the pulp homogenization and the enhanced particle-collector interaction. With the feeding velocity increased, the fluid shear was larger and the improved performance was more obvious. According to the flotation results, the maximum recovery of unburned carbon was obtained with the feeding velocity equal to 2.5 m/s, which was consistent with the tendency of wrap angle. Meanwhile, the loss on ignition of the tailings reached the optimal value, corresponding to 9.94%.

Electroadhesion zipping with soft grippers on curved objects

Electroadhesion soft grippers generate extremely high holding forces (> 1 kg per gram of gripper) when the fingers wrap around the object. However, adding actuators on the soft fingers to close them on the object leads to increased stiffness, which reduces the roughness-scale conforming on the fingers to the object, resulting in lower adhesion forces. With the right materials and geometry, electroadhesion forces can alone drive a soft finger to zip on an object without any added actuator. By keeping the soft fingers free from any extra device, electroadhesion zipping combines macroscopic wrapping of fingers around an object with microscopic conforming of the finger’s soft membrane to the object surface. Electroadhesion zipping shares the same mechanism with recently developed soft zipping actuators. Instead of two electrodes on polymer films zipping together and displacing a liquid, in Electroadhesion grippers the soft fingers, equipped with interdigitated electrodes, zip onto a curved object to grab it with high holding forces. In this work we investigate Electroadhesion zipping by reporting a model and a set of experimental data that relate the wrapping angle α with the applied voltage V, for given materials and geometry of object and soft fingers. We discovered that the phenomenon is governed by two voltage thresholds: a first one below which no zipping occurs (V no zip) and a second one above which the soft fingers fully collapse on the object (V full zip). We present analytical equations and design tools that quantify these voltage values for given bending stiffness, mass, shape, and capacitance of the soft finger–object pair. Our model shows that Electroadhesion zipping does not scale with V2/d2 (voltage squared over dielectric gap squared), as previously reported for Electroadhesion forces, but rather with V2/d. Our experiments fit very well with the model results, especially when zipping on dielectric objects with non-tacky surfaces (e.g., paper). We demonstrate thin electroadhesive fingers that wrap around a wide set of objects made of different materials (from conductive to dielectric) and with different geometries, reaching wrapping angles up to 90°. The new design tools and experimental data will drive the design of electroadhesion soft grippers able to conform to nearly any shape and lifting objects heavier than 1000 times their own weight.

Broadening the operating range of pump-turbine to deep-part load by runner optimization

To cooperate with new energy sources such as wind and solar, pumped storage units are required to frequently change conditions and operate under part loads, leading to the problem of violent pressure fluctuation and unit vibration. To meet this challenge, the next generation of pump-turbine runners will therefore have to be designed differently. The goal of this article is to construct a framework for broadening the operating range of pump-turbine to deep-part loads. In this study, a multi-objective optimization strategy for the runner with wider output range is suggested, wherein the blade control parameters, specifically the blade loading and blade lean angle, are optimized to enhance the efficiency, anti-cavitation, and stability of the pump-turbine runner. A runner with turbine output range of 40%–100% is optimized for a specific power station. Next, the impact of runner control parameters on runner performance is evaluated, and the runner geometric characteristics for different optimizing priorities such as the pump peak efficiency, cavitation performance, turbine rated efficiency, and turbine partial load efficiency, are concluded. The mutual restriction mechanism between the pump peak efficiency and cavitation performance of pump mode, as well as the turbine-rated efficiency and partial load efficiency of turbine mode, is revealed. The main contributions of this paper include putting forward an effective optimization design process for wide output pump-turbine, and pointing out the relationship between runner geometric characteristics and performance. The results indicate that the present approach can significantly improve the efficiency and stability of runners operating in deep-part loads. The blade loading pattern with hub section aft-loaded and shroud section fore-loaded, combined with negative blade lean angle, is recommended for such runners. Blades with a smaller wrap angle and lower arch are conducive to improving the pump peak efficiency and turbine-rated efficiency, while the opposite geometrical features are advantageous for improving the runner cavitation performance and efficiency performance under part load conditions. These findings can serve as an important guide for the development of runners with a wider output range.

Vibration Suppression Technology of Integrated NC Machining of Lightweight Monolithic Panel

The new generation spacecraft module is formed by spinning as a whole, and then the whole module is processed by integrated numerical control. Due to the characteristics of the large diameter and thin wall of the module, it is easy to produce vibration in the processing. In this paper, aiming at the vibration problem of integrated CNC machining cabin body, a method of using reconfigurable fixture internal support to suppress the vibration of weak rigid cabin body overall processing is proposed, and the ANSYS finite element analysis software is used to simulate and analyze the internal support force. The results show that the thickness uniformity of the bottom skin is similar, the dimensional accuracy is higher, and the effect of suppressing cutting chatter is obvious. This paper also improves the design of the milling tool with an unequal helix angle, adds DLC tool coating, and increases the tool rake angle. The simulation results of cutting force based on the FORCE module show that the cutting force is reduced by 31% and chatter in machining is suppressed compared with that before the tool is improved. Through the cycloid milling strategy, the wrap angle between the tool and the workpiece is reduced. It reduces the cutting force, reduces the cutting heat, and ensures the consistency of the product wall thickness and the roughness requirements. The experimental results show that these methods can effectively suppress the vibration in the processing and control the thickness of the integrated numerical control processing panel between 1.47-1.77 mm.

Influence of Inlet Vane and Wrap Angles on Cavitation Behavior of a Centrifugal Pump

This comprehensive study focuses on the relationship between the inlet vane and wrap angles of a centrifugal pump impeller and its cavitation behavior. The objective is to propose a new design for cavitation performance enhancement of the pump by reducing the required net positive suction head (NPSHR). To render a detailed study, the variations of the mentioned angles were examined both at hub and shroud. A three-dimensional two-phase parametric computational fluid dynamics (CFD) study was conducted and variations of inlet blade and wrap angles at hub and shroud were investigated separately. After validating the experimental results with the pump model, the pump parameterization process was carried out, and pump geometry was re-defined with its geometrical properties. The characteristic curves of the parameterized pump and pump model were in agreement with each other. Numerical cavitation tests were performed and the NPSHR values of each design were calculated for four different operating conditions. Results showed that cavitation performance increase was achieved with angle variations at the best efficiency point (BEP) but, this situation led the pump to operate exposed to cavitation at high flows (HF) for some designs. Therefore, the design with the best cavitation performance increased at BEP and HF was proposed as a new design. During numerical simulations, shear stress transport (SST) turbulence model and Rayleigh–Plesset equation were used.

Simplified Calculation of Recess Pressure Considering the Hydrodynamic Effect

Abstract The hydrostatic journal bearing’s recess pressure is to be determined using a novel approach. This method treats the circumferential bearing lands on both sides of recesses as infinitely long bearings, and the axial bearing lands on both sides of recesses as infinitely short bearings. The Newton–Cotes integral formula is used to solve the definite integration. By this simplification, a new analytical expression of recess pressure considering the hydrodynamic effect on bearing land is obtained. The recess pressure versus eccentricity, supply oil pressure, recess wrap angle, and attitude angle solved by the new method is compared with that calculated by the finite difference method and Liang’s method from two kinds of four-recess hydrostatic journal bearing compensated by capillary restrictor. The results indicate that the new process has high accuracy and its precision is not almost affected by the parameters change. Moreover, the new method has low time consumption.

Theoretical performance of progressive addition lenses with poorly measured individual parameters.

The aim of this paper was to present a theoretical study of how poorly measured individual parameters affect the optical performance of progressive addition lenses (PALs). Modern progressive lenses can be prescribed based on parameters such as vertex distance, pantoscopic and wrap angles. These parameters can be measured from the lens wearer using specific devices; however, not all of them can be measured with the same precision, and the impact of measurement errors on the lens performance is still unknown. Data from 1900 patients were used to simulate the performance of four PAL designs with different degrees of complexity: perfect individual design, individual design with induced errors in the individual parameters, optimised design and conventional/basic design. For each patient and design, a quality metric was calculated to describe the optical performance of the lens. The design having the best performance was the perfect individual design, followed by the individual design with induced errors, the optimised design and finally the conventional/basic design. Individual designs with measurement errors have better optical performance than lenses with less complexity, such as the optimised or conventional designs. This knowledge is useful for the eye care professional to make informed choices when dispensing these lenses.

Investigation of friction coefficient to improve traction condition in R2R transport system

In a roll-to-roll (R2R) system, the roller’s traction force for precision transportation is crucial for the commercialization of printed electronic devices. Moreover, greater traction force of the roller can prevent several issues, such as slippage, wrinkles, sagging, and air entrainment, which occur because of insufficient traction force. The wrap angle, tension, and friction coefficient between the roller and the transporting film are key factors for achieving greater traction force in an R2R transport system. However, design of the wrap angle and tension are limited by the film damage and complex arrangement of the rollers. For these reasons, this study focused on the method that increases the friction coefficient on the surface of the roller. We applied three methods—normal force, static electricity, and thin polydimethylsiloxane coating—on the surface of the roller. Then, we suggest an effective means of improving the friction coefficient to supplement the design restrictions of tension and the wrap angle in R2R transport systems.

ИССЛЕДОВАНИЕ ВЛИЯНИЯ ФОРМЫ КОЛОСНИКА НА ОТДЕЛЕНИЕ СОРА ОТ ЛЕТУЧКИ

In serial cleaners, stationary grates with a circular cross section are installed to remove foreign matter. To increase the cleaning effect, an attempt was made to activate the working surfaces of grate bars with polymer coatings. Although they increased the cleaning effect, they did not find industrial application. In recent years, imparting mobility to the grate has been used to improve performance. This is carried out in two ways: a grate which receives movement under the action of a technological load, and when a grate which is forced. To improve the cleaning effect in serrated cleaners, the cross-sectional shape of the grate has a significant influence. The article proposes profile grates from curved configurations of epicycloids. To determine the influence of the cross-sectional shape of the grate on separating impurities from raw cotton, the interaction cotton and the grate at the time of their contact is considered. The forces of separation (τy) are determined in various modules of epicycloids, which depend on the frequency of rotation and the cross-sectional shape of the grate. Given the values of the wrapping angles, the main parameters are the wrapping angle of the grate with the cotton and the relative speed of the cotton along the grate. The angle of the wrapping of the grate with cotton depends on the shape and size of the cross section of the grate.

Effect of surfactant on the attachment between coal particles and bubbles: An experimental and molecular dynamics simulation study

Surfactant plays a vital role in flotation, especially in the adsorption of particle and bubble surface. From macroscopic to atomic scales, the effects of surfactant on the attachment between coal particles and bubbles were investigated by the induction time measurements, bubble-particle wrap angle measurements, thin liquid films measurements and molecular dynamics (MD) simulation. The three surfactants are Cetyltrimethylammonium bromide (CTAB), Sodium dodecylbenzene sulfonate (SDBS), and Methyl isobutyl carbinol (MIBC). Macroscopically, the coal particles could be more easily attached to a bubble surface in three solutions, particularly in CTAB solution. This was because the speed of thinning and rupture of thin liquid film between coal-particles and bubbles was faster in CTAB solution than that in other solutions. MD simulation findings show that the adsorption of CTAB significantly improves the water molecule migration rate. In addition, the CTAB promotes the attachment efficiency in floatation.

Experimental Investigations on the Effect of Yarn Speed and Wrap Angle on Yarn-Solid and Yarn-Yarn Friction using Warp Knitting Machines

Warp knitting is appointed as a manufacturing method for high-performance and high-quality textiles due to its versatility and production speed. To ensure a continuous and error-free manufacturing process under highly dynamic production conditions, a high level of knowledge of the yarn and machine interaction is required. Mechanical stresses from the machine are transferred to the yarn via friction points, as well as during the stitching process from one yarn to another, where the yarn is subjected to high stresses.Therefore, the focus of this research is the investigation of the friction between the yarn and yarn guiding elements and the friction between the yarns themselves during the stitch formation. For this reason, all contact points between yarn and yarn guiding elements as well as between the yarns themselves are examined and classified. A test rig is set up to determine all occurring frictions as a function of various machine parameters.The knowledge gained and the derived analytical expressions between machine settings and occurring friction can thus become the basis for modeling the friction points of the warp knitting machine, which is also presented. Furthermore, based on the findings a design improvement of the machine can be achieved and the friction model can serve as part of a simulation model of the entire warp knitting machine, which will be the focus of further publications.

Energy efficiency optimization of water pump based on heuristic algorithm and computational fluid dynamics

Abstract To reduce the energy consumption of large centrifugal pumps, modified heuristic intelligent algorithms are used to directly optimize the diffuser of centrifugal pumps. Considering the hydraulic efficiency under the design condition as the optimization target, in this study, 14 geometric parameters such as the inlet diameter, outlet diameter, and leading and trailing vane angles of the diffuser are selected as design variables, and the modified particle swam optimization and gravitational search algorithm are used to directly search for optimization in the design space. The performance and loss of internal entropy production of the different models before and after optimization are compared and analyzed in detail. The results show that the global optimization ability of the modified algorithm is improved. The diffuser model changes from cylindrical to twisted, the vane wrap angle increases, and the thickness of the leading edge decreases. Under the design condition, the efficiency of modified particle swarm optimization algorithm solution is increased by 2.75% and modified gravitational search algorithm solution by 2.21%, while the power remains unchanged. Furthermore, the optimization solution has the largest lift efficiency improvement under part-load conditions. After optimization, the unstable flow in the model is improved and internal entropy production loss is reduced significantly. The interior of the diffuser is dominated by turbulent entropy production and direct entropy production under different operating conditions, and the wall entropy production accounts for the smallest proportion.

Computational fluid dynamics simulations of Taylor bubbles rising in vertical and inclined concentric annuli

Motivated by a dearth of research on the dynamics of single Taylor bubbles in annular conduits, a computational study of Taylor bubbles rising in vertical and inclined annuli is performed using a three-dimensional computational fluid dynamics (CFD) simulation with the Volume-of-Fluid (VOF) method implemented in the commercial software ANSYS Fluent (Release 19.2). The effects of Eötvös number (Eo = [10, 300]), inverse viscosity number (Nf = [40, 320]), and inclination angles (θ = {10°, 20°, 30°,…, 80°}) on the steady-state Taylor bubble shape and rise velocity are investigated. The latter is parameterized by Froude number (Fr) and simulations are carried out keeping constant liquid-gas density ratio and dynamic viscosity ratio at 1000 and 100, respectively. The simulation results provide good agreement with the existing numerical findings and experimental observations. For Taylor bubbles in a vertical annulus, the surface tension and liquid viscosity show significant impacts on bubble shape (length and trailing edge) and Fr for Eo = [10, 100] and Nf = [40, 160]. A correlation for Fr in terms of Eo and Nf is proposed and compared against 66 numerical simulations and 20 air-water experimental results available in the literature, resulting in average errors of 2.13% and 5.52%, respectively. Relatively large errors of 7.38% for characteristic dimension D* ≤ 45 mm and 11.82% for D* ≥ 344.9 mm are observed (D* = Do + Di). The correlation exhibits improved performance with an average error of 3.5% for 45 mm ≤ D* ≤ 214 mm relative to the only existing model. The shape of bubbles and Fr values in inclined annulus, where the bubble becomes more streamlined and unfolded, are observed to be dramatically different from those in vertical annulus. Interestingly, the wrap angle (θwrap) decreases linearly with the increase of inclination angle. Predictions of the dimensionless rise velocity in inclined annulus are made and successfully compared with an existing model and experimental data from the literature.

The study of the possibility of the pumping unit optimization for two operation modes, different from the optimal one

BACKGROUND: The study of factors affecting the vibroacoustic characteristics of pumps is one of the main areas of development in the current pump industry. Improvement of these characteristics allows to extend the service life of pumps by means of vibration levels reduction as well as to decrease the noise level.&#x0D; AIMS: In this study, the attempt to optimize the flow part of a multi-stage pump was made in order to obtain acceptable noise, vibration and harshness (NVH) characteristics in two operation modes that are different front the optimal one.&#x0D; METHODS: As the result of the study, it was found that changing these parameters in favour of NVH has a negative impact on the pump efficiency and vice versa. Thereby the optimal balance between these parameters should be found. The optimization was performed with the method of research of the parameter space with use of LP-tau sequences. The following elements were chosen as the optimization parameters: the area at the entrance to downstream, the angle of guide vanes at the entrance to the downstream, the width of rotor at the outlet, the angle of rotor vanes at the inlet and the outlet, the wrap angle of rotor vane. Decrease of the area of the graph of pressure pulsation spectrum was chosen as the optimization criteria. The mathematical model was verified with two designs of the flow part produced and tested earlier. The first sample has an overstated rate of the NVH spectrum in the area of high frequencies, the second sample has an overstated rate of the NVH spectrum in the area of low frequencies.&#x0D; RESULTS: The compiled mathematical model proved its good quality, showing the same results, which allows to speak about the admissibility of its use for optimization of the flow parts of pumps.&#x0D; CONCLUSIONS: This study will be useful for specialists in the field of vane hydraulic machines design.