Case Study of Impeller Profile With Suitable Rotative Guidevane

2006 ◽  
Author(s):  
Takuji Tsugawa
Keyword(s):  
Axial Velocity ◽  
Rotational Speed ◽  
Velocity Ratio ◽  
Diameter Ratio ◽  
Single Stage ◽  
Speed Ratio ◽  
Shape Factors ◽  
Flow Angle ◽  
Diffusion Factor ◽  
Multi Stage

In the previous paper, the optimum meridian profile of multi-stage impeller with guidevane was obtained by means of diffusion factor using twelve shape factors. The coefficient of peripheral absolute velocity at impeller inlet kCu1c means the effect of multi-stage impeller with guidevane. In this paper, the optimum meridian profile of multi-stage or single-stage impeller with rotative guidevane was obtained by means of fifteen shape factors. The fifteen shape factors mean impeller inlet relative flow angle β1, impeller turning angle Δβ, impeller axial velocity ratio kc12 = Cm2/Cm1, impeller diameter ratio kd12 = D1c/D2c, impeller outlet hub-tip ratio ν2, impeller tip solidity σt(imp), impeller mid span solidity σc(imp), impeller hub solidity σh(imp), guidevane tip solidity σt(gv), guidevane mid span solidity σc(gv), guidevane hub solidity σh(gv), guidevane axial velocity ratio kc34 = Cm4/Cm3, guidevane diameter ratio kd34 = D3c/D4c and rotational speed ratio Rn = ngv/nimp. The suitable rotational speed ratio means suitable rotational speed of guidevane. The axial velocity ratio and diameter ratio of guidevane means the optimum meridian profile of guidevane outlet. In the 15th dimensional optimum method, the hydraulic efficiency and suction specific speed are calculated by diffusion factor. This method is also used for the modification of multi-stage or single-stage present impellers and guidevanes.

Case Study of Multi-Stage Impeller with Guidevane

2005 ◽  
Author(s):  
Takuji Tsugawa
Keyword(s):  
Velocity Ratio ◽  
Optimum Shape ◽  
Hydraulic Efficiency ◽  
Mixed Flow ◽  
Shape Factors ◽  
Flow Angle ◽  
Multi Stage ◽  
Absolute Flow ◽  
Specific Speed

In the previous paper, the optimum meridian profile of impeller was obtained for various specific speed by means of eight shape factors, that is, inlet relative flow angle β1, turning angle Δβ, axial velocity ratio kc = Cm2/Cm1, impeller diameter ratio kd = D1c/D2c, outlet hub-tip ratio ν2, tip solidity σtimp, mid span solidity σcimp and hub solidity σhimp. In this paper, the optimum meridian profile of multi-stage impeller with guidevane was obtained by means of twelve shape factors. The additional four shape factors are guidevane tip solidity σtgv, mid span solidity σcgv, hub solidity σhgv and coefficient of peripheral velocity at impeller inlet or guidevane outlet kCu1c. In the optimum method, the hydraulic efficiency and suction specific speed are calculated by diffusion factor. In the optimum condition, the best hydraulic efficiency or the best suction specific speed is obtained. In the cyclic flow condition of multi-stage impeller with guidevane, the absolute flow velocity of guidevane outlet is equal to that of impeller inlet, and the diameter of guidevane outlet is equal to that of impeller inlet. In this calculation, the diameter of impeller outlet is equal to that of guidevane inlet. The total calculation number of case study is very large, so the number of each parameter is about between four and seven. The best 1000 optimum meridian profiles and the best design parameter are selected for few kinds of specific speed using twelve dimensional optimum method. As the result of this calculation, the optimum meridian profile of multi-stage impeller and guidevane. The more detailed optimum multi-stage mixed flow impeller and guidevane profile is drawn. For, example, the 1000 specific speed is selected for case study of multi-stage mixed flow impeller. At first, the approximate optimum shape factors are present shape factors. And the optimum shape factors which have better efficiency are tried to find near the present shape factors. Then the study of shape factor changes is the objective of this paper.

Case Study of High Specific Speed Radial Impeller

2002 ◽  
Author(s):  
Takuji Tsugawa
Keyword(s):  
Radial Flow ◽  
Velocity Ratio ◽  
Axial Flow ◽  
Optimum Shape ◽  
Design Parameters ◽  
Shape Factors ◽  
Flow Angle ◽  
Diffusion Factor ◽  
Cavitation Performance ◽  
Specific Speed

The optimum shape of high specific speed impeller is usually axial flow impeller. The radial impeller is often used without axial flow guidevane. Usually, the radial impeller is the high pressure and low specific speed impeller. The design parameters of radial high specific speed impeller have not been obtained yet. In the previous papers, the optimum meridian shape of axial flow impeller with axial flow guidevane is obtained for various specific speed. The optimum meridian shapes calculated by diffusion factor agree with meridian shapes of conventional impellers. In this paper, the design parameters of radial high specific speed impellers without guidevane are calculated by diffusion factor. And the optimum meridian shapes of radial high specific speed impellers are proposed. In case of the radial impeller, the hub diameter is equal to the tip diameter in impeller outlet. So, in radial impellers, the outlet hub-tip ratio is 1.0. The optimum meridian shapes of radial impellers for various specific speed are also obtained in this paper. The relative efficiency and cavitation performance of impellers in various shape factors were calculated. The calculation of radial meridian shape needs four kinds of shape factors as the previous papers. The four shape factors are inlet relative flow angle β1, turning angle Δβ, axial velocity ratio (meridian velocity ratio) kc = Cm2/Cm1 and impeller diameter ratio kd = D1c/D2c inmid span streamsurface. In initial step of impeller design, the result of the efficiency and cavitation performance of impeller calculated in optimum principal design parameters is important. The principal design parameters are hub-tip ratio, inlet-outlet diameter ratio, axial velocity ratio, solidity, inlet flow angle, turning angle and blade number. The author proposed the optimum meridian profile design method by diffusion factor for various condition of design parameters. There is a good correlation between the optimum hub-tip ratio and the specific speed considering cavitation performance. The optimum solidity is obtained for the specific speed considering efficiency and cavitation performance. It was found that the optimum meridian profile of high specific speed impeller with appropriate efficiency and cavitation performance has large inclination on hub and tip stream lines. The calculated data base is four dimensional using four various shape parameter β1, Δβ, kc and kd. Using the four shape factor, the optimum meridian shape of radial flow impeller is able to be obtained. The best 1000 optimum design parameters are selected using four dimensional calculated data. The aspect of optimization is recognized with 1000 plotted data on 6 planes. The result of radial flow impeller optimization is different from that of axial flow impeller. In case of axial flow impellers, the shape factors are optimized for each specific speed. But, in radial flow impellers, if both the specific speed and the total head coefficient are given, the optimum shape factors are optimized. The calculation results between profiles and specifications were very useful for the development of new type high specific speed radial impellers.

Case Study of Improved High Specific Speed Radial Impeller

2003 ◽  
Author(s):  
Takuji Tsugawa
Keyword(s):  
Design Method ◽  
Velocity Ratio ◽  
Flow Analysis ◽  
Design Parameters ◽  
Mixed Flow ◽  
Shape Factors ◽  
Flow Angle ◽  
Diffusion Factor ◽  
Cavitation Performance ◽  
Specific Speed

It is usually thought that the axial impeller is used for high specific speed impeller and the radial impeller is used for low specific speed impeller. In the previous paper, the optimum meridian profile of axial impeller and radial impeller were obtained for various specific speed by means of the optimization of four shape factors using diffusion factor. The four shape factors were inlet relative flow angle β1, turning angle Δβ, axial velocity ratio (meridian velocity ratio) kc = Cm2/Cm1 and impeller diameter ratio kd = D1c/D2c in mid span stream surface. In case of axial impeller, the optimum meridian profiles agreed with meridian profiles of conventional impellers. To develop the radial high specific speed impeller, the optimum four shape factors of radial high specific speed impellers were calculated by diffusion factor. And the optimum meridian profiles of radial high specific speed impellers were proposed. In case of the radial impeller, the hub diameter is equal to the tip diameter in impeller outlet (the outlet hub-tip ratio is 1.0). And in axial impeller, the outlet blade height depends on the outlet hub-tip ratio. On the other hand, in mixed flow impeller, the outlet hub-tip ratio is various and the outlet blade height is independent of the outlet hub-tip ratio. To obtain the optimum meridian profile of mixed flow impeller, the hub-tip ratio of impeller outlet ν2 is adopted new additional independent shape factor for optimization in this paper. The mixed flow angle on tip meridian stream line (= 0 degree in axial impeller, = 90 degrees in radial impeller) isn’t able to be decided by this optimization using diffusion factor. But, the mixed flow angle will be decided by the number of blade and solidity. And, it will be decided by meridian velocity distribution from hub to tip for each specific speed of impeller. So, in this paper the five shape factors are used for optimization by diffusion factor. (β1, Δβ, kc, kd, ν2) The optimum meridian profiles of mixed flow impellers for various specific speed are obtained. The relative efficiency or the cavitation performance of mixed flow impeller is better than that of radial or axial impeller. In this optimum method, the relative efficiency and the cavitation performance are calculated for all specified combinations of five shape factors. The number of five shape factors are expressed by Nβ1, NΔβ, Nkc, Nkd and Nν2. The number of calculations is expressed by Nβ1 × NΔβ × Nkc × Nkd × Nν2. The calculation time of five shape factors method is Nν2 times the calculation time of four shape factors method. Then, the best 1000 combinations of five shape factors are plotted on β1 - Δβ, kc - kd and kd - ν2 plane. The aspect of the best 1000 optimum conditions are found by these three figures. In initial step of impeller design, the result of the efficiency and cavitation performance of impeller calculated in optimum principal design parameters is important. The principal design parameters are hub-tip ratio, inlet-outlet diameter ratio, axial velocity ratio, solidity, inlet flow angle, turning angle and blade number. The author proposed the optimum meridian profile design method by diffusion factor for various condition of design parameters. There is a good correlation between the optimum hub-tip ratio and the specific speed considering cavitation performance. The optimum solidity is obtained for the specific speed considering efficiency and cavitation performance. It was found that the optimum meridian profile of high specific speed impeller with appropriate efficiency and cavitation performance had large inclination on hub and tip stream lines. The calculated data base is five dimensional using five shape factors β1, Δβ, kc, kd and ν2. Using the five shape factors in case of the best efficiency, the optimum meridian profile of improved radial flow impeller is able to be calculated. At first step of the case study, the best 1000 optimum meridian profiles and the best design parameter are selected using five dimensional optimum method. Next, the blade section shape of impeller is decided by the blade or cascade design method. Using impeller flow analysis, the cavitation performance decided by 3% head reduction is calculated. Finally, the relations between the many type of meridian profile and its impeller performance by flow analysis are obtained. These relations are very useful for new type of high specific speed impeller design. Consequently, radial impellers and axial impellers are improved by the consideration of the additional shape factor, that is, outlet hub-tip ratio ν2. This calculation shows that the improved radial high specific speed impeller considering outlet hub-tip ratio is used for high suction specific speed and high efficiency.

Case Study of Tandem Impeller Rotating at Different Speeds

2012 ◽  
Author(s):  
Takuji Tsugawa
Keyword(s):  
Velocity Ratio ◽  
Diameter Ratio ◽  
Design Parameters ◽  
Shape Factors ◽  
Flow Angle ◽  
Turning Angle ◽  
Impeller Outlet ◽  
Calculation Process ◽  
Specific Speed

In previous study, the optimum meridian profile of tandem impeller rotating at the same speed was obtained by means of calculation of efficiency and suction specific speed considering two diffusion factors of tandem impeller. The effect of theoretical head ratio between the first impeller and the second impeller was obtained. In this study, the optimum meridian profile and design parameters of tandem impeller rotating at two kinds of different speed was obtained. In the process of this study, a lot of design parameters were needed. Therefore, in the optimum calculation process the predominant design parameters of two impellers were selected and re-selected. The predominant design parameters were inlet relative flow angle, turning angle, meridian velocity ratio, inlet and outlet diameter ratio and so on. The impeller meridian velocity ratios of shape factors were defined as kc12(= Cm2/Cm1) and kcp2(= Cm2/Cmp), and the impeller diameter ratios were defined as kd12(= D1c/D2c) and kdp2(= Dpc/D2c). The subscripts 1,p and 2 means the first impeller inlet, the second impeller inlet and the second impeller outlet respectively. And theoretical head ratio between first impeller and second impeller was defined as kHth(= Htha/Hthb). The rotational ratio between the first impeller and the second impeller defined as Rna(= na/nb). The Optimum Rna(= na/nb) was effected by the other design parameter. As the result, the optimum meridian profile of tandem impeller rotating at different speeds was obtained. This method can be also used for the suitable rotative guidevane.

The Relation Between Solidity and the Other Shape Factors for Complete Optimum Meridian Profile of Impeller With Guidevane

2007 ◽  
Author(s):  
Takuji Tsugawa
Keyword(s):  
Shape Factor ◽  
Large Diameter ◽  
Axial Direction ◽  
The Other ◽  
Shape Factors ◽  
Flow Angle ◽  
Diffusion Factor ◽  
Blade Number ◽  
Outlet Flow ◽  
Angle Blade

In the previous paper, the solidity is independent shape factor of the optimum meridian profile by diffusion factor. But, the solidity is often calculated by the other shape factors, for example, the inlet and outlet flow angle, blade length, blade number and the co-ordinates of impeller meridian profile. So, in this paper, the solidity is treated as dependent shape factor and is calculated by the impeller meridian co-ordinates and flow angle. In the previous paper, the impeller meridian inlet is axial direction. In this paper, the inlet mixed flow angle of impeller inlet is one of additional shape factor. As the result, the impeller with guidevane complete meridian profile is calculated for the large diameter of guidevane outlet and the detailed meridian profile of impeller inlet.

Instability of the Flow in a Mixed-Flow-Type Vaneless Diffuser System

2003 ◽  
Author(s):  
Hiromu Tsurusaki
Keyword(s):  
Rotational Speed ◽  
Velocity Ratio ◽  
Inlet Pipe ◽  
Vaneless Diffuser ◽  
Unstable Flow ◽  
Mixed Flow ◽  
Flow Angle ◽  
Fast Speed ◽  
Flow Through ◽  
Speed Mode

This study was carried out in order to investigate the unstable flow through a mixed-flow-type vaneless diffuser system. The testing equipment consists of a vaneless diffuser, an inlet pipe, and a swirl flow generator. Pressure fluctuations of the flow through the diffuser were measured. In the experiment, the velocity ratio (axial velocity/peripheral velocity) at the diffuser inlet, diffuser width, inlet pipe length, hub diameter, and mixed flow angle of the diffuser were varied. The internal flow condition existing when the unstable flow occurred is discussed in terms of turbulent flow analysis. The main findings of this study are as follows. The unstable flow is excited when the aforementioned velocity ratio is lowered under a critical value. The source of the unstable flow is the mixed flow vaneless diffuser. The rotational speed of the cell and the intensity of pressure fluctuation are influenced remarkably by diffuser width. The inlet pipe acts as an attenuator for the unstable flow of the diffuser. A prediction equation for rotational speed of the cell is proposed. Prediction of back flow in the diffuser is useful for prediction of the onset of unstable flow. Unstable flow with a fast-speed mode was measured when the diffuser had a small hub and a small mixed flow angle. The fast-speed mode is believed to arise from instability in the inlet pipe system.

Case Study of Impeller Profile Considering Additional Parameters

Volume 3 ◽  
2004 ◽  
Author(s):  
Takuji Tsugawa
Keyword(s):  
Velocity Ratio ◽  
Stream Line ◽  
Mixed Flow ◽  
Shape Factors ◽  
Flow Angle ◽  
Turning Angle ◽  
Calculation Time ◽  
Specific Speed ◽  
Stream Lines

In the previous paper, the optimum meridian profile of impeller was obtained for various specific speed by means of five shape factors. In this paper, the optimum meridian profile of impeller is obtained by means of eight shape factors. The basic five shape factors are inlet relative flow angle β1, turning angle Δβ, axial velocity ratio kc = Cm2/Cm1 impeller diameter ratio kd = D1c/D2c and outlet hub-tip ratio ν2 (β1 and Δβ are in mid span stream surface). The additional three parameters are three stream lines solidity (tip solidity σt, mid span solidity σc, and hub solidity σh). The blade length of impeller meridian profile is able to obtain by additional three parameters. The method of optimization is the calculation of hydraulic efficiency and suction specific speed in all combinations of eight shape parameters. The number of five shape factors are expressed by Nβ1, NΔβ, Nkc, Nkd, Nν2. The number of calculations is expressed by Nβ1 × NΔβ × Nkc × Nkd × Nν2. For example, Nβ1 = NΔβ = Nkc = Nkd = Nν2 = 40, the number of calculations is about 100000000. The calculation time is about 2 hours. The best parameters are selected in 100000000 cases. In case of eight shape factors, the number of calculation is Nβ1 × NΔβ × Nkc × Nkd × Nν2 × Nσt × Nσc × Nσh. Nβ1 = NΔβ = Nkc = Nkd = Nν2 = Nσt = Nσc = Nσh = 10, the number of calculation is 100000000. In this case, the calculation time of eight shape factors is as same as that of five shape factors. By means of this method, the more detailed optimum mixed flow impeller meridian shape is obtained. In case study, the best 1000 optimum meridian profiles and the best design parameter are selected for few kinds of specific speed using eight dimensional optimum method. In the previous paper, the mixed flow angle on tip meridian stream line isn’t able to be decided by this optimization using diffusion factor. But, in this paper, the mixed flow angle is able to be decided by the number of blade and optimum solidity. As the best solidity of three stream lines is obtained, the axial coordinates of impeller inlet and outlet are obtained. The more detailed optimum mixed flow impeller meridian shape is drawn.

scholarly journals On the velocity at wind turbine and propeller actuator discs

2020 ◽  
Author(s):  
Gijs A. M. van Kuik
Keyword(s):  
Wind Turbine ◽  
Axial Velocity ◽  
Rotational Speed ◽  
Power Coefficient ◽  
Positive Energy ◽  
Speed Ratio ◽  
Meridian Plane ◽  
Turbine Disc ◽  
High Torque ◽  
Uniform Deviation

Abstract. The first version of the actuator disc momentum theory is more than 100 years old. The extension towards very low rotational speeds with high torque for discs with a constant circulation, became available only recently. This theory gives the performance data like the power coefficient and average velocity at the disc. Potential flow calculations have added flow properties like the distribution of this velocity. The present paper addresses the comparison of actuator discs representing propellers and wind turbines, with emphasis on the velocity at the disc. At a low rotational speed, propeller discs have an expanding wake while still energy is put into the wake. The high angular momentum of the wake, due to the high torque, creates a pressure deficit which is supplemented by the pressure added by the disc thrust. This results in a positive energy balance while the wake axial velocity has lowered. In the propeller and wind turbine flow regime the velocity at the disc is 0 for a certain minimum but non-zero rotational speed. At the disc, the distribution of the axial velocity component is non-uniform in all flow states. However, the distribution of the velocity in the plane containing the axis, the meridian plane, is practically uniform (deviation approximately 0.2 %) for wind turbine disc flows with tip speed ratio λ > 5, almost uniform (deviation 2 %) for wind turbine disc flows with λ = 1 and propeller flows with advance ratio J = Π, and non-uniform (deviation 5 %) for the propeller disc flow with wake expansion at J = 2 Π. These differences in uniformity are caused by the different strengths of the singularity in the wake boundary vorticity strength at its leading edge.

The Effect of Reynolds Number and Turbulence Intensity on the Performance of a Compressor Cascade with Prescribed Velocity Distribution

1977 ◽  
Vol 19 (3) ◽  
pp. 93-100 ◽  
Author(s):  
J. Citavy ◽  
J. F. Norbury
Keyword(s):  
Reynolds Number ◽  
Turbulence Intensity ◽  
Axial Velocity ◽  
Separation Bubble ◽  
Velocity Ratio ◽  
Aerodynamic Performance ◽  
Substantial Effect ◽  
Compressor Cascade ◽  
Flow Angle ◽  
Outlet Flow

Experimental results are presented on the effect of Reynolds number ( Re) and turbulence intensity ( Tu) on the aerodynamic performance of a PVD compressor cascade at design incidence. The pressure distribution, outlet flow angle and losses were measured within the ranges Re = 0.6 times 105 to 2 times 105 and Tu = 0.35 to 4.4 per cent. In some experiments, the effect of axial velocity ratio ( AVR) was investigated. A substantial effect of the Reynolds number and turbulence intensity on the growth and bursting of the separation bubble was observed, with consequent effects on the aerodynamic performance of the cascade. The bursting of the bubble also gave rise to a hysteresis effect with Reynolds number.

scholarly journals On the velocity at wind turbine and propeller actuator discs

2020 ◽  
Vol 5 (3) ◽  
pp. 855-865
Author(s):  
Gijs A. M. van Kuik
Keyword(s):  
Wind Turbine ◽  
Axial Velocity ◽  
Rotational Speed ◽  
Positive Energy ◽  
Speed Ratio ◽  
Meridian Plane ◽  
Turbine Disc ◽  
Actuator Disc ◽  
High Torque ◽  
Uniform Deviation

Abstract. The first version of the actuator disc momentum theory is more than 100 years old. The extension towards very low rotational speeds with high torque for discs with a constant circulation became available only recently. This theory gives the performance data like the power coefficient and average velocity at the disc. Potential flow calculations have added flow properties like the distribution of this velocity. The present paper addresses the comparison of actuator discs representing propellers and wind turbines, with emphasis on the velocity at the disc. At a low rotational speed, propeller discs have an expanding wake while still energy is put into the wake. The high angular momentum of the wake, due to the high torque, creates a pressure deficit which is supplemented by the pressure added by the disc thrust. This results in a positive energy balance while the wake axial velocity has lowered. In the propeller and wind turbine flow regime the velocity at the disc is 0 for a certain minimum but non-zero rotational speed. At the disc, the distribution of the axial velocity component is non-uniform in all actuator disc flows. However, the distribution of the velocity in the plane containing the axis, the meridian plane, is practically uniform (deviation <0.2 %) for wind turbine disc flows with tip speed ratio λ>5, almost uniform (deviation ≈2 %) for wind turbine disc flows with λ=1 and propeller flows with advance ratio J=π, and non-uniform (deviation 5 %) for the propeller disc flow with wake expansion at J=2π. These differences in uniformity are caused by the different strengths of the singularity in the wake boundary vorticity strength at its leading edge.

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