Blade Stagger Angle Research Articles

Improving near-stall performance of axial flow compressors using variable rotor tandem stage. A steady analysis

This paper investigates the idea of substituting the first stage of a conventional axial-flow compressor and its inlet guide vane (IGV) row with a variable rotor tandem (VRT) stage to reduce the size and weight of axial-flow compressors. It is expected that a tandem stage gains higher pressure ratio than a conventional stage, and simultaneously, its variable stagger rotor provides more flexibility in handling unsteady phenomena at low mass flow rates. A three-dimensional numerical model based on Reynolds-Averaged Navier–Stokes equations is developed to conduct this investigation. To validate the numerical model, experimental tests are conducted on a tandem single-stage axial-flow compressor test bench in the Dana laboratory of Amirkabir University of Technology, to compare the performance map with numerical results. The validated numerical model is then employed to simulate the performance of both front and aft variable rotor blades. The proposed tandem stage effectively performs the IGV duty, suppresses instabilities at low mass flow rates, and eventually extends the compressor's stable operational range. This proves that a VRT stage is an efficient active surge-control system tool. The detailed survey of the three-dimensional flow field reveals that the aft tandem rotor blade stagger angle is more effective in increasing the stall margin and decreasing the minimum operational mass flow rate than the front row of blades. It is observed that when the aft blades rotate in the direction of decreasing the tandem blades' gap area, the flow momentum increases and causes the compressor stability at lower mass flow rates.

Design method for a bidirectional ducted tidal turbine based on conventional turbomachinery methods

Renewable energy sources include solar, wind, hydro, geothermal and biomass. Furthermore, ocean energy is being rapidly harnessed worldwide. In this study, to establish a suitable design method for various bidirectional ducted tidal turbines, instead of using blade element momentum theory and CFD, which have been used previously, the method used for turbomachinery was used for designing the turbines. A bidirectional turbine optimises the equipment design and reduces manufacturing and maintenance costs. Using the turbine power as the design condition, the difference in the tangential velocity between the front and rear of the turbine was calculated using Euler’s equation, and the blade stagger angle was determined based on the potential flow theory. To incorporate the effect of duct geometry into this design method in the future, the effect on the internal flow of the duct was experimentally investigated using three ducts with different maximum cross-sectional areas. Performance tests showed that the duct geometry had a negligible effect on the flow rate through the turbine. Therefore, the larger the maximum diameter of the duct, the greater the flow rate into the outside of the duct. The pressure difference between front and rear of the turbine and the inflow energy into the duct were different due to the energy conversion as the flow turned outside of the duct. To improve the accuracy of the design method, the effect of flow at the duct inlet and the energy conversion should be incorporated, and a review of the estimation method for the axial velocity ratio and the selection method for the design representative value should be conducted.

Numerical investigation of the effect of blade distortion laws on the corner flow separation of the axial-flow fan

To study the effect on performance of different blade distortion laws of axial flow fans, the radial distributions of blade stagger angle were fit as Bézier curves, and five distribution laws were established. Three-dimensional numerical simulations were carried out for the fan schemes. The results show that distortion near the blade root can effectively restrain the corner separation vortex from climbing along the blade suction surface, so that the low-energy fluid accumulates in the corner region. Tip distortion rises the pressure difference between the pressure and the suction surface, and the turbulence intensity of the tip leakage is increased. Root distortion inhibits the CV diffusion, resulting the decay of tip leakage vortex, thereby improving the stall margin. Relative to a uniform distortion blade, the blade-root distortion scheme increases the radial load of the blade, while the tip distortion scheme results in a decrease of the blade load coefficient. The maximum load position of the end-zone distorted blade moves to the root area, while the maximum load position of the middle distorted blade shifts to the tip area. The end-zone distortion improves the efficiency and total pressure of the fan without changing the efficient working range, and is considered to be the optimal scheme. The maximum pressure coefficient of the end-zone distortion scheme is increased by 4.97% and the maximum efficiency is increased by 1.28%.

Effect of Non-Uniformity of Rotor Stagger Angle on the Stability of a Low-Speed Axial Compressor

It is well known that variations in stagger angle between rotor blades affect compressor performance. In this paper, the stagger angle of blade No. 8 is increased or decreased by six degrees for non-uniformity, and the influence of rotor non-uniformity caused by the change in only one blade stagger angle on the performance and stability of the compressor is investigated. The experimental results show that whether the local rotor stagger angle increases or decreases, the compressor stability will deteriorate. If the stagger angle of blade No. 8 is reduced by six degrees, the flow coefficient at the stall point increases by 8.5%. If the stagger angle of blade No. 8 is increased by six degrees, the flow coefficient at the stall point increases by 1.5%. The reason for the deterioration of compressor stability caused by the local non-uniform rotor stagger angle is explored. When the stagger angle of rotor blade No. 8 deviates from the designed state, the load of blade No. 8 and the surrounding blades will change. The load on rotor blade No. 8 increases when the stagger angle decreases. In the near-stall condition, blade No. 8 becomes the “dangerous blade” that triggers the stall. As the stagger angle of rotor blade No. 8 increases, the load on blade No. 8 decreases. However, the load on blade No. 9 increases due to flow redistribution and blade No. 9 becomes a “dangerous blade” that triggers stall. The “dangerous blade” caused by the non-uniformity of stagger angle is the direct reason for the advance of the compressor rotating stall.

Evaluation of the Skewing Effect on the Electromagnetic and Fluid Mechanics Performance of an Integrated Motor-Compressor

An integrated motor-compressor synergistically combines a flux-switching permanent magnet machine with an axial-flow compressor by shaping the rotor poles of the motor into airfoils. The airfoil-shaped rotor functions as the rotor of a motor as well as the rotor of an axial-flow compressor. The airfoil-shaped rotor poles need to be skewed by the proper blade stagger angle to obtain optimal fluid mechanics performance. The objective of this article is to investigate the effects of the stagger angle (skew) of the airfoil-shaped rotor on the thermodynamic and fluid mechanics performance of the integrated motor-compressor by mean line calculations and computational fluid dynamics (CFD). The skewing effects on the electromagnetic performance of the integrated motor-compressor with aligned and unaligned stator-rotor configurations are also investigated by analytical equations and three-dimensional finite-element analysis. A prototype is built for the integrated motor-compressor. Experimental results are also included to validate the simulations.

Experimental Investigation of Rotating Instability in an Axial Compressor with a Steady Swirl Distortion Inlet

In this paper, an experimental study was carried out on the rotating instability in an axial compressor subjected to inlet steady paired swirl distortion. In order to deepen the understanding of the rotating stall mechanism under inlet steady paired swirl distortion, the dynamic-wall static pressure near the rotor tip was monitored to characterize the flow in the rotor tip region at different circumferential stations. In the experiment, the dynamic characteristics of the rotor tip flow field at a stable operating point and during the process from the stable point to complete stall were measured. The results indicated that for the compressor with a 2 mm rotor tip clearance, the inlet paired swirl distortion induced rotating instability (RI) near the stall point, causing the compressor to enter stall in advance. Compared with the RI intensity of the clean inlet, the distortion with a swirling blade stagger angle (αst) of ±20° increased the RI intensity up to 69.8%, while for αst equal to ±40°, the RI intensity increased at most by 135.8%. As the rotor tip clearance increased to 3 mm, the co-rotating swirl in the paired swirl distortion inhibited the appearance of RI, while the counter-rotating part aggravated the development of RI. At the beginning, the process of the compressor rotating stall involved the alternation of short-scale disturbance and long-scale disturbance. The co-rotating swirl weakened the perturbation propagated from the counter-rotating swirl sector. Once the inhibition was no longer present, the short-scale disturbance rapidly developed into a long-scale disturbance and then entered the rotating stall.

A low-loss vector exhaust guide vanes and its application

The exhaust device of gas-driven fan propulsion system (for a VTOL aircraft) adopts vector exhaust guide vane (VEGV) to achieve vector thrust in the range of 0-90°, which requires that the deflection angle of the VEGV reach about ±45∘ and the total pressure recovery coefficient above 0.985. Therefore, the exhaust device needs a wide-range and low-loss VEGV to ensure efficient operation of the propulsion system. And the key of this VEGV is to eliminate the separation of the suction side under large deflection angle. So, this paper designed a new type of VEGV that can meet the demands by reducing the inverse pressure gradient of the suction surface (one of the necessary conditions for two-dimensional separation). In order to realize this design process, the spectral method of small disturbance equation (SMSDE) for two-dimensional subsonic flow was developed. Then, two VEGVs were designed by the SMSDE and verified by numerical simulation with Reynolds number 106 and blade solidity 1.18. The results show that the two VEGVs eliminate the separation of suction side at inlet Mach number of 0.25 and blade stagger angle of 45°. And the VEGV with lateral blade guarantees this characteristic up to Mach 0.3. Besides, when the inlet Mach number is below 0.3, the VEGV with lateral blade can ensure that the total pressure recovery coefficient is greater than 0.985, the outlet area ratio is greater than 0.95 and the exhaust angle error is less than 3.5°. Finally, Experimental verification of the vector exhaust device using the VEGV with lateral blade was carried out. The results show that the new VEGV has a higher total pressure recovery coefficient and outlet area ratio than the traditional VIGV at large deflection angles.

Dynamic response analysis of shrouded blades under impact-friction considering the influence of passive blade vibration

A new dynamic model of shrouded blades with elastic support and variable cross-section is derived based on the Timoshenko beam theory, in which factors to be considered include centrifugal stiffening, spin softening, Coriolis force, blade stagger angle, and twist angle. The proposed model (PM) is verified by comparing the dynamic frequency results of the finite element model (FEM) and the PM. An impact-friction model of shrouded blades is established which can take into account the inertia effects of two passive blades. By comparing the vibration response of the two models (PM and FEM), the established impact-friction model is verified. Finally, the influences of normal contact stiffness, blade root support stiffness, and shroud position on the vibration response of the system are analyzed. Meanwhile, bifurcation diagrams, time-domain waveforms, phase diagrams, Poincaré maps, and frequency spectrum are utilized to analyze the nonlinear vibration characteristics of shrouded blades. The results show that the impact and friction between adjacent shrouds will cause the complex nonlinear vibration of the blades. Under small initial gaps, hard nonlinear phenomena can be observed in the vibration response of the shrouded blade. While under small initial preloads, it shows an obvious soft nonlinear phenomenon. Furthermore, with the increase of normal contact stiffness and blade root support stiffness, the resonance peak of the blade-tip flexural displacement decreases. When the shroud is closer to the blade-tip of the blade, the vibration reduction effect of the shrouded blade is better. The active blade experiences the chaos, period-one motion due to the nonlinear behavior of the impact-friction coupling at the adjacent shroud contact interfaces.

A numerical investigation of the rotor blockage effect on cascade noise using a sliding mesh method

The accurate evaluation of the broadband noise generated by fan wakes interacting with the outlet guide vanes (OGVs) in the aero-engines remains challenging due to the stochastic nature of sound and the complex flow conditions. A systematic study of the design parameters from full-scale and three-dimensional turbulence simulations is still expensive from a computational perspective. A simplified approach is to unwrap the fan blades and OGVs at a constant radial location to reproduce two-dimensional cascades. This approach assumes periodic boundary conditions at the upper and lower boundaries. For realistic cascades, there are relative motions between the rotating fan blades and stationary OGVs. The fan wakes are convected downstream towards the OGVs, and the turbulent wakes are distorted in the vicinity of the OGVs leading edge, which produce broadband noise. This paper aims at studying the upstream-travelling sound waves that is scattered by the solid surfaces of the fan blades, which alter the sound distribution. This scattering process is called the blockage or shielding effect, and it is influenced by the fan speed, blade geometry and spectral content of the sound. In this work, a synthetic turbulence method is employed to reproduce the fan wakes, and the Euler equations are solved to model the sound generation and propagation. An efficient sliding mesh method is developed to capture the physics due to the relative motions between the fan blades and OGVs. The numerical implementation is validated for various turbulence-cascade interaction configurations and the blockage effect due to the fan blades is studied in detail. A significant blockage effect due to a moving blade row on fan-OGV noise can be noticed on the acoustic power radiation. A decrease in sound power level (PWL) in the upstream direction is seen at low frequencies while an increase can be observed at high frequencies, which can be attributed to the sound power transfer between frequencies and modes. Both the effect of fan rotating speed and the rotor blade stagger angle are further tested and compared with the benchmark cases on the variation of PWL spectra and changes of acoustic modal distributions to study the impact of operation conditions and geometric parameters.

Nested sparse-grid Stochastic Collocation Method for uncertainty quantification of blade stagger angle

In the present paper, the Nested Sparse-grid Stochastic Collocation Method (NSSCM) is utilized to investigate the uncertain effects of stochastic blade stagger angles on the aerodynamic performance of the turbine blade. Two typical test functions are used to validate the calculation efficiency and precision of the NSSCM in Uncertainty Quantification (UQ). Based on the validation, non-deterministic CFD (Computational Fluid Dynamics) simulations are applied to estimate the impact on the aerodynamic performance of 2D (two-dimensional) turbine blades cases, and the blade stagger angles are considered as the stochastic variables in a Gaussian distribution. Four schemes of a single blade, two adjacent blades, two separated blades, and five blades with stochastic blade stagger angle errors are studied. The calculation results show that the aerodynamic performance was significantly influenced, and the stochastic fluctuations of total pressure loss caused by uncertain stagger angles can be up to 40%. The uncertain errors of the blade stagger angle have a significant effect on the suction side, and the wake region, and the 30%–50% axial region on the blade suction side is the sensitive region. The effects on the flow field propagate from the pressure side to the suction side.

The Influences of Stagger and Pretwist Angles of Blades on Coupling Vibration in Shaft-Disk-Blade Systems

Abstract The influences of stagger angle (α) and pretwist angle (βL) of blades on the coupling vibration among shaft bending and blade bending in a shaft-disk-blade (SDB) system are investigated using a Lagrangian approach in combination with the assumed modes method (AMM). The disk is rigid, and the flexible shaft is supported with two rigid bearings. It is shown that α and βL have variable effects on the coupling vibration because their influences can be increased, reduced, or even completely eliminated for different values of disk location (λ), blade thickness ratio (δ), and blade aspect ratio (γ). To study the coupling vibration in an SDB system, consideration of λ, δ, and γ are very important because those can alter the coupling magnitude, the coupling pattern as well as the predominant modes. Nevertheless, previous researches rarely take into account these parameters. Moreover, in the present work, to investigate the natural frequencies and critical speeds versus λ, δ, and γ, new diagrams are introduced. Also, the relation between the in-plane and out-of-plane motions of the blades with the coupling vibration is precisely analyzed.

Efficiency improvement of a self-rectifying radial impulse turbine for wave energy conversion

This paper aims to improve the performances of a self-rectifying radial impulse turbine used in wave energy conversion. The turbine design involves blades of circular profiles. The Design of Experiments method has been implemented for the efficiency optimization. The objective function aims to maximize the average turbine efficiency between the inhalation and the exhalation modes. A 3D viscous flow modelling has been performed with the ANSYS Fluent code. Simulations allow the turbine efficiency computation accordingly to the changes in the turbine geometry. Influence of ten geometrical parameters has been considered in the optimization process. According to a confidence degree of 95%, it has been found that only four of them have significant influence on the turbine efficiency. The rotor geometry admits the highest influence, particularly the blade angle. Additional analysis has been conducted by considering the rotor blade stagger angle. It has been found that the efficiency can be kept high in the both modes with a stagger angle of 4°. Efficiencies more than 50% have been reached. The present turbine efficiency has been compared to that of a turbine of elliptical profiles. An increase of about 19% in the efficiency has been reached with the present turbine.

Rapid method of Predicting the Subsonic Flutter Stability of AGTE Axial-Flow Compressor Blade Cascades. Part 2. Mathematical Implementation of Method and its Potentional Application

The paper considers the implementation of the rapid method of predicting the dynamic stability of the compressor blade assemblies against subsonic flutter. The first flexural mode of blade vibrations is analyzed at the design stage for a wide range of the angle of attack based on the developed database of the critical values of the reduced vibration frequency in straight cascades of blade airfoils. The multiple regression equation is developed that depends on the relative blade spacing and stagger angle of the straight cascade of blade airfoils, coefficient of the flexural-torsional coupling of the blade, and angle of attack with the correlation factor of the studied parameters in the range of 0.92–0.98. Using the obtained equation, the numerical program has been developed for the determination of the dynamic stability limit against subsonic flutter for the first flexural mode of the blade vibrations. The program allows one to find the numerical values of critical reduced frequencies as the characteristics of its dynamic stability and determine their dependence on the angle of attack. The results of practical application of the developed program are presented using the assessment of the dynamic stability of the flexural mode of axial compressors in four modern aircraft gas-turbine engines. It is shown that at the design engine stage it is possible to select the reduced vibration frequencies of the blade assembly for the specified geometry of its peripheral sections and angle of attack of the inflow upon the condition of the occurrence of subsonic flutter.

Design and structure optimization of small-scale radial inflow turbine for organic Rankine cycle system

The ORC (organic Rankine cycle) system has the advantages of simple structure, environmental friendliness, reliability and low capital cost. The expander is the key device of energy conversion in the ORC system, and its performance has a direct influence on that of the ORC. In this paper, a self-designed and manufactured radial inflow turbine is applied to low temperature waste heat power generation. The numerical model for the internal flow of the radial inflow turbine is established, and the numerical results show a better agreement with the experimental data. Firstly, the influence of blade stagger angles on nozzle performance is studied. The study finds that with the decrement of stagger angles under specific angle ranges, the velocity coefficient increases. However, the efficiency of the nozzle decreases sharply when the stagger angle exceeds 30°. Secondly, the influence of the blade profile on the efficiency of the rotor is investigated. The results indicate that with t increasing, the efficiency of the rotor firstly increases, then decreases quickly. It increases by 1% compared with that of the original rotor, when the t = 1.95. At last, the performance of the turbine is researched numerically. This paper discovers that total-to-static efficiency of the turbine increases by 1.7% compared with that of the original turbine. This research provides orientation and basis for the improvement of aerodynamic design and performance of radial inflow turbine. As for practical application, the study can provide certain reference for the structure and blade profile design of nozzles and rotors to further improve the performance, and to offer some data for the operational control and tests.

Effects of the Second-Stage of Rotor with Single Abnormal Blade Angle on Rotating Stall of a Two-Stage Variable Pitch Axial Fan

It is of great value to study the impact of abnormal blade installation angle on the inducement mechanism of rotating stall to achieve the active control of rotating stall in an axial fan. Based on throttle value function and SST k-ω turbulence model, numerical simulations of the unsteady flow process in stall condition of an axial flow fan with adjustable vanes were carried out, and the influence mechanism of abnormal stagger angle of a single blade in the second stage rotor on induced position and type of stall inception and evolution process of rotating stall were analyzed. The results show that compared with synchronous adjustment of blade angle, the blade with abnormal stagger angle will cause the increase of flow rate at the beginning of stall and make the fan fall into an unstable condition in advance. The existence of blade with abnormal angle does not cause the change of the induced position and type of stall inception and the inducement mechanism of rotating stall, which are the same as the axial fan with normal blade angle. Moreover, the single blade with abnormal deviation angle has important impacts on the 3D unsteady evolution process from stall inception to stall cell formation in two rotors.

The coupling vibration characteristics of a flexible shaft-disk-blades system with mistuned features

• The shaft-bending is firstly considered to the shaft-disk-blades coupling vibration problem . • The evolution mechanism relies on the changes of the mistuned features parameters. • The vibration localization phenomenon appear due to the mistuned features. • The mistuned features have not obviouse influencs on the Campbell results. The purpose of this paper is to investigate the coupling vibration characteristics of a flexible shaft-disk-blades system with mistuned features. There are some new phenomena due to the coupling effects of shaft-bending, shaft-torsion, disk-transverse and blade-bending. In this investigation, this paper mainly focuses on the influence of mistuned features of the blade's length and the stagger angle. It is found that there are four types of coupling modes: the coupling mode of shaft bending, disk transverse and blade bending (SDB), the coupling mode of shaft torsion disk transverse-blade bending (TDB), the coupling mode of disk transverse and blade bending (DB), the repeated mode of blade bending-blade bending (BB). With the effect of mistuned features, the natural frequencies and the coupling mode type will change correspondingly. With the mistuning value of blade length employed in this study, the TDB mode in the tuned system will disappear and shift into TSDB mode instead, and one of the repeated SDB modes will be replaced by STDB modes. Due to this mistuned features, the blades and disk experience a certain degree of vibration localization phenomenon. Different from the length feature, the influence of mistuning values of blade's stagger angle mainly take effect on the coupling modes. At last, by inspection on the Campbell diagrams, the influence of rotational speed on the transformation of natural frequencies is illustrated on the tuned/mistuned flexible shaft-disk-blades coupling structure.

Research on output performance of pneumatic turbine based on variable geometry technology

In order to solve these problems, such as excessive fluid velocity, large differences in output for all turbine level and disorder of flow field, variable geometric method was put forward as an improved method for turbine blade. The output performance of last blade and last three blades is studied by changing the stagger angle of blade for 10-stage turbine. The results show that the aerodynamic efficiency was increased by 3.72% for the variable geometry technology used in the last-stage blade. The variable geometry technology was used in last three stages blades of a 10-stage turbine, the aerodynamic efficiency increased by 4.88%, the output performance is more average than before, the fluid velocity in the flow field is reduced, and the phenomenon of dewatering is controlled.

Investigation of Energy Loss on Fractional Deposition in Last Stages of Condensing Steam Turbine Due to Blade Shape and Moisture Droplet Size

The steam consumption in a turbine within an operating pressure range determines the effectiveness of thermal energy conversion to electric power generation in a turbo-alternator. The low pressure (LP) stage of the steam turbine produces largest amount of steam to shaft-power in comparison to other stages of turbine although susceptible to various additional losses due to condensation of wet steam near penultimate and ultimate stages. The surface deposition in blade is caused by inertial impaction and turbulent-diffusion. With increasing blade stagger angle along the larger diameter of blading, the fractional deposition of wet steam is largely influenced by blade shape. From this background, the aim of this work is to predict the effect of mathematical models through computational fluid dynamics analysis on the characterization of thermodynamic and mechanical loss components based on unsaturated vapor water droplet size and pressure zones in LP stages of steam turbine and to investigate the influence of droplet size and rotor blade profile on cumulative energy losses due to condensation and provide an indication about the possible conceptual optimization of blade profile design to minimize moisture-induced energy losses.

Improving the Efficiency of Gas Turbines During Off-Design Operation by Adjusting the Turbine and Compressor Blade Stagger Angles

Gas turbines in general and aircraft engines in particular undergo frequently dynamic operations. These operations include the routine start-up, load change and shut downs to cover their operation envelope. The frequency of the dynamic operation depends on the size of the engines and the field of application. Engines for commuter aircrafts and particularly helicopter engines operate more often in an off-design mode compared to large commercial aircraft engines and power generation gas turbines. During these routine operations, the compressor mass flow, the pressure ratio, the combustion chamber fuel and air mass flow as well as turbine mass flow change. These changes affect the engine aerodynamic performance and its efficiency. To avoid the inception of rotating stall and surge, high performance gas turbines are equipped with mechanisms that adjust the stator stagger angles thus aligning the stator exit flow angle to the rotor inlet angle, which reduces an excessive incidence. The reduction of incidence angle not only preserves the stable operation of the compressor, but it also prevents the compressor efficiency from deterioration. The existence of an inherent positive pressure gradient may cause the boundary layer separation on compressor blades leading to the rotating stall and surge. Such condition, however, does not exist in a turbine, and therefore, there has been no compelling reason to apply the blade adjusting method to the turbine component. For the first time, the impact of turbine blade stagger angle adjustment on the gas turbine efficiency during the operation is shown in this paper. Given a statistically distributed load condition, the extensive dynamic simulation reported in this paper shows how the efficiency can be positively affected through proper blade adjustment. For the time dependent operation, the code GETRAN developed by the author was enhanced to include the turbine blade adjustment as a function of time. To conduct the dynamic simulation with turbine stator stagger angle adjustment during a dynamic operation, the full geometry of the Brown Boveri GT-9 gas turbine was utilized. Starting from the reference stagger angle, it is varied within an incidence range of ± 3 degree. Detailed simulation results show the substantial efficiency improvement through stator stagger blade adjustment.

Sensitivity analysis of the effective centrifugal pump parameters using the EFAST method

In the present study, the effective parameters of centrifugal pumps are investigated using the EFAST Sensitivity Analysis (SA) method. The SA is performed using GMDH type artificial neural networks (ANN) which are based on validated numerical data of flow field in centrifugal pumps. There are four design variables namely: leading edge angle of blades on hub section (β1 Hub), leading edge angle of blades on shroud section (β1 Shroud), trailing edge angle of blades (β2), and the stagger angle of blades on mid span (γ mid) and there are two objective functions namely: efficiency (h) and the required NPSH of impeller. The results show that among design variables, β2 has the highest effect on variations of h (46%) and NPSH (45%). Except β2, β1 Hub and γ mid has the highest effect on NPSH (33%) and h (28%) respectively. The effects of all of the design variables on objective functions are shown in the results.