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.

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 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.

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 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.

scholarly journals Performance and Exit Flow Characteristics of Mixed-Flow Turbines

1997 ◽  
Vol 3 (4) ◽  
pp. 277-293 ◽  
Author(s):  
C. Arcoumanis ◽  
R. F. Martinez-Botas ◽  
J. M. Nouri ◽  
C. C. Su
Keyword(s):  
Steady State ◽  
Velocity Ratio ◽  
Tangential Velocity ◽  
Flow Characteristics ◽  
Mixed Flow ◽  
Cross Sectional ◽  
Flow Angle ◽  
Turbine Efficiency ◽  
And Performance ◽  
Inlet Angle

The performance and exit flow characteristics of two mixed-flow turbines have been investigated under steady-state conditions. The two rotors differ mainly in their inlet angle geometry, one has a nominal constant incidence (rotor B) and the other has a constant blade angle (rotor C), but also in the number of blades. The results showed that the overall peak efficiency of rotor C is higher than that of rotor B. Two different volutes were also used for the tests, differing in their cross-sectional area, which confirm that the new larger area volute turbine has a higher efficiency than the old one, particularly at lower speeds, and a fairly uniform variation with velocity ratio.The flow exiting the blades has been quantified by laser Doppler velocimetry. A difference in the exit flow velocity for rotors B and C with the new volute was observed which is expected given their variation in geometry and performance. The tangential velocities near the shroud resemble a forced vortex flow structure, while a uniform tangential velocity component was measured near the hub. The exit flow angles for both rotor cases decreased rapidly from the shroud to a minimum value in the annular core region before increasing gradually towards the hub. In addition, the exit flow angles with both rotors were reduced with increasing rotational speeds. The magnitude of the absolute flow angle was reduced in the case of rotor C, which may explain the improved steady state performance with this rotor. The results also revealed a correlation between the exit flow angle and the performance of the turbines; a reduction in flow angle resulted in an increase in the overall turbine efficiency.

A comparative study of the performance of the mixed flow and radial flow variable geometry turbines for an automotive turbocharger

2018 ◽  
Vol 233 (8) ◽  
pp. 2696-2712 ◽  
Author(s):  
K Ramesh ◽  
BVSSS Prasad ◽  
K Sridhara
Keyword(s):  
Mass Flow ◽  
Flow Parameter ◽  
Radial Flow ◽  
Velocity Ratio ◽  
Variable Geometry ◽  
Flow Variable ◽  
Mixed Flow ◽  
Turbine Efficiency ◽  
Variable Geometry Turbine ◽  
Specific Speed

A new design of a mixed flow variable geometry turbine is developed for the turbocharger used in diesel engines having the cylinder capacity from 1.0 to 1.5 L. An equivalent size radial flow variable geometry turbine is considered as the reference for the purpose of bench-marking. For both the radial and mixed flow turbines, turbocharger components are manufactured and a test rig is developed with them to carry out performance analysis. Steady-state turbine experiments are conducted with various openings of the nozzle vanes, turbine speeds, and expansion ratios. Typical performance parameters like turbine mass flow parameter, combined turbine efficiency, velocity ratio, and specific speed are compared for both mixed flow variable geometry turbine and radial flow variable geometry turbine. The typical value of combined turbine efficiency (defined as the product of isentropic efficiency and the mechanical efficiency) of the mixed flow variable geometry turbine is found to be about 25% higher than the radial flow variable geometry turbine at the same mass flow parameter of 1425 kg/s √K/bar m2 at an expansion ratio of 1.5. The velocity ratios at which the maximum combined turbine efficiency occurs are 0.78 and 0.825 for the mixed flow variable geometry turbine and radial flow variable geometry turbine, respectively. The values of turbine specific speed for the mixed flow variable geometry turbine and radial flow variable geometry turbine respectively are 0.88 and 0.73.

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.

Search of High Efficiency Design by Another Specific Speed Design

2019 ◽  
Author(s):  
Takuji Tsugawa
Keyword(s):  
Rotational Speed ◽  
Design Parameter ◽  
Design Parameters ◽  
Initial Value ◽  
Mixed Flow ◽  
Impeller Blade ◽  
Flow Angle ◽  
3D Shape ◽  
Blade Number ◽  
Specific Speed

Abstract Quite a lot of design parameters exist when the designer designs the best performance impeller and guidevane. Finally, it is necessary to decide the detail 3D shape of impeller and guidevane. The best flow conditions of the flow velocity and the flow angle at the impeller inlet and outlet are designed as first step before impeller detailed 3D shape is designed. The detailed 3D shape is not necessary in this study. The optimum meridian shape has been found, assuming that the total loss head is addition of the blade-to-blade diffusion loss head and the hub-tip axial-symmetrical annular surface friction loss head. That is, the meridian shape is mainly decided depending on the blade-to-blade flow condition on hub surface, mean surface and tip surface. Main design parameters that decide the meridian shape is built in the loss head equation by diffusion factor and all the design parameters relate closely respectively. The value of the design parameters can be set at random for loss head calculation in a usual optimization technique. But, the loss head in the combination of the limited value design parameters can be calculated in this method. Therefore, the great change of design parameter value is not permitted in this optimum process, and the increment of all the design parameters is set respectively and the optimization of the design parameter is advanced from an initial value of the design parameters changing the value of design parameters little by little. Therefore, there is a possibility that the best solution becomes a local best solution and the influence of an initial condition value cannot be removed. In this method, it is necessary for coming out from the local best solution that the value of all the design parameters changes from an initial value to a largely different value. The specific speed influences all the other design parameters. So, the specific speed is changed gradually in restriction optimum process. In FEDSM2014-21030, the impeller blade number was assumed to be a variable real number design parameter and the specific speed that was the specification as constant value become a variable design parameter equally to other design parameters. In AJK2015-09034, the impeller outlet diameter and impeller rotational speed were assumed to be a variable optimum design parameters. As a result, all the design parameters became variable. Optimization was executed from two different initial conditions to study the initial value dependency whether the obtained two optimum solution became the same. In FEDSM2016-7518, one initial value of the specific speed was assumed to be 916 and it was confirmed to obtain the solution from the specific speed 200 to the specific speed 3000 as the variable wide range design parameter by restriction. The design parameter of mixed flow angle of impeller inlet was not change at the beginning of calculation and changed rapidly in the latter half of the calculation. The cause of the mixed flow angle of impeller inlet value jump was uncertainty. In FEDSM2017-69024, the influence of the surface roughness of the axial-symmetrical hub and tip wall was examined. The impeller blade number, the guidevane blade number and mixed flow angle of impeller inlet were able to change by restriction, and the influence of the impeller blade number and the guidevane blade number was examined. The mixed flow angle of impeller inlet was assumed 0 degrees (axial-flow) to avoid the parameter value jump. In this paper, the specific speed design parameter become the restriction design parameter. The specific speed as restriction parameter has been changed from the lower bound value to the upper bound value to come out from a local best solution. The efficiency extended to the specific speed whole area is able to be improved by the influence of the another middle specific speed with the highest efficiency. It is found that the value of the change increment at the specific speed as restriction parameter is important very much executed by the several kind of specific speed increment. In order to improve the design parameters of traditional impeller and guidevane in the future, it is convenient that total head and flow rate are new optimum design parameters instead of impeller outlet diameter and impeller rotational speed. The impeller rotational speed can be calculated by specific speed and total head.

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.

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