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.

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 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.

The Clogging Behavior of a Vortex Pump: An Experimental Study on the Influence of Impeller Designs

2017 ◽  
Author(s):  
Angela Gerlach ◽  
Dorian Perlitz ◽  
Flemming Lykholt-Ustrup ◽  
Christian Brix Jacobsen ◽  
Paul Uwe Thamsen
Keyword(s):  
Experimental Study ◽  
Power Consumption ◽  
Clear Water ◽  
Blade Angle ◽  
Flow Rates ◽  
Blade Number ◽  
Outlet Angle ◽  
Vortex Pump ◽  
Efficiency Losses ◽  
Angle Blade

This paper analyzes the clogging behavior of a vortex pump with different impeller designs. The influence of blade outlet angle, blade number, and impeller diameter were tested. Non-woven textiles in different concentrations served as the clogging material. The results suggest that a smaller outlet blade angle, a higher blade number, and a larger impeller diameter allow pumping more textiles. Impellers that were capable of pumping more textiles, however, were less efficient. Overall, pumping textiles causes efficiency losses. However, this could not be only related to increased power consumption. Flow rates under clogging operation were close to the flow rates under clear water operation irrespective of the amount of clogging material and the impellers design. Further, in all tests clogging material accumulated at the suction mouth in the casing.

On the factorization of rotations with examples in diffractometry

1990 ◽  
Vol 428 (1875) ◽  
pp. 451-472 ◽  
Keyword(s):  
Rotation Angle ◽  
Rotation Axis ◽  
Axial Direction ◽  
The Other ◽  
Rotation Vector ◽  
Coordinate Transformations ◽  
Rotation Axes ◽  
Analytic Expressions ◽  
Direction Cosines

An analysis of compound rotations, such as occur in eulerian cradles, is presented in terms of a calculus of rotation axes, without reference to the associated coordinate transformations. The general case of three rotation shafts mounted on one another, with any relation between them at datum zero, is presented. The problem and its solution may be represented entirely in terms of a plane octagon in which four sides have directions that are instrumental constants and the other four sides have lengths that are instrumental constants. When the first four sides are given lengths that express both the rotation angle and the axial direction of the required rotation, then the remaining four sides have directions that directly express the rotations in the drive shafts, that will generate the required rotation. Analytic expressions are given for the shaft setting angles in the general case. If the first and third axes are parallel and the intermediate one perpendicular to these at datum zero (as in the four-circle diffractometer) then these reduce to θ 1 = arctan ( μ, σ ) + [arctan ( λ , v ) - ψ -½8π], θ 2 = 2 s arcsin ( λ 2 + v 2 )½, θ 3 = ( μ, σ ) - [arctan ( λ , v ) - ψ - ½8π], s = ± 1, 0 ≤ arcsin ( λ 2 + v 2)½ ≤ ½π, in which λ, μ, v and σ are the four components of a rotation vector constructed such that λ, μ and v are the direction cosines of the rotation axis multiplied by sin½ θ for a rotation angle θ and σ is cos½ θ . ψ is a constant determined by the choice of directions to which λ and v are measured. The results for the general case are also expressed in terms of more conventional variables.

Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

1995 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Axial Direction ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

A Numerical Investigation of the Effect of Inlet Preswirl Ratio on Rotordynamic Characteristics of Labyrinth Seal

2017 ◽  
Author(s):  
Tomohiko Tsukuda ◽  
Toshio Hirano ◽  
Cori Watson ◽  
Neal R. Morgan ◽  
Brian K. Weaver ◽  
...  
Keyword(s):  
Flow Model ◽  
Three Dimensional ◽  
Axial Direction ◽  
Labyrinth Seal ◽  
Flow Fields ◽  
Bulk Flow ◽  
The Other ◽  
Circumferential Velocity ◽  
Stiffness Coefficients ◽  
Inlet Swirl

Full three-dimensional CFD simulations are carried out using ANSYS CFX to obtain the detailed flow field and to estimate the rotordynamic coefficients of a labyrinth seal for various inlet swirl ratios. Flow fields in the labyrinth seal with the eccentricity of the rotor are observed in detail and the detailed mechanisms that increase the destabilizing forces at high inlet swirl ratios are discussed based on the fluid governing equations associated with the flow fields. By evaluating the contributions from each term of the governing equation to cross coupled force, it is found that circumferential velocity and circumferential distribution of axial mass flow rate play key roles in generating cross coupled forces. In the case that circumferential velocity is high and decreases along the axial direction, all contributions from each term are positive cross coupled force. On the other hand, in the case that circumferential velocity is low and increases along the axial direction, one contribution is positive but the other is negative. Therefore, cross coupled force can be negative in the local chamber depending on the balance even if circumferential velocity is positive. CFD predictions of cross coupled stiffness coefficients and direct damping coefficients show better agreement with experimental results than a bulk flow model does by considering the force on the rotor in the inlet region. Cross coupled stiffness coefficients derived from the force on the rotor in the seal section agree well with those of the bulk flow model.

Flow-Induced Vibration of a Large-Diameter Elbow Piping Based on Random Force Measurement Caused by Conveying Fluid: Visualization Test Results

2005 ◽  
Author(s):  
Tomomichi Nakamura ◽  
Tadashi Shiraishi ◽  
Yoshihide Ishitani ◽  
Hisato Watakabe ◽  
Hiromi Sago ◽  
...  
Keyword(s):  
Force Measurement ◽  
Large Diameter ◽  
Pressure Fluctuations ◽  
Pressure Sensors ◽  
Maximum Flow ◽  
Axial Direction ◽  
Random Force ◽  
Test Facility ◽  
Flow Induced Vibration ◽  
Correlation Lengths

A 1/3 scale flow-induced vibration test facility that simulates the hot-leg piping of the JNC sodium-cooled fast reactor (JSFR) is used to investigate the pressure fluctuations of the pipe, where the high velocity fluid flows inside the piping. By the measurement of the pressure drop in the elbow piping while changing the Reynolds number, the similarity law of this model is confirmed. To evaluate the flow-induced vibrations for the hot-leg and cold-leg pipes, the random force distributions along the pipe and their correlations are measured with pressure sensors in a water loop. It is found that a flow velocity-dependent periodic phenomenon in the rear region of the elbow, and the maximum flow-induced random vibration force in the pipe are observed in the region of flow separation downstream the elbow. Finally, a design method is proposed with power spectral densities of the pressure fluctuations classified into four sections, correlation lengths in the axial direction divided into three sections, and with correlation lengths in the tangential direction into four sections.

Aerodynamic Data for Two Variants of Root Turbine Blade Sections for a 54″ Turbine Rotor Blade

2014 ◽  
Author(s):  
David Šimurda ◽  
Martin Luxa ◽  
Pavel Šafařík ◽  
Jaroslav Synáč ◽  
Bartoloměj Rudas
Keyword(s):  
Limit Load ◽  
Axial Direction ◽  
Turbine Rotor ◽  
Rotor Blades ◽  
Angle Of Incidence ◽  
Flow Angle ◽  
Turbine Rotor Blade ◽  
Blade Cascade ◽  
The Difference ◽  
Kinetic Energy Loss

Aerodynamic investigations were performed on planar blade cascades representing two alternative root sections of rotor blades 54″ in length with straight fir-tree root. Each of the variants was designed for different number of blades in the rotor. This paper presents the results of measurements showing the dependency of the kinetic energy loss coefficient and the exit flow angle on the exit isoentropic Mach number and the angle of incidence. Images of the flow fields are also presented. The experimental data is analyzed to assess and document the difference between the two root section designs. Results show that requirement of straight fir tree root leading to high design incidence angles significantly limit operation range. Also in case of root sections with high exit Mach numbers a limit load conditions are an issue. In order to utilize available pressure drop blade cascade throat/pitch ratios should be kept as high as possible which favorites variant with lower number of blades and higher outlet metal angle (relative to axial direction).

Longitudinal Blade-Frequency Force Induced by a Propeller on a Prolate Spheroid

1965 ◽  
Vol 9 (01) ◽  
pp. 13-22
Author(s):  
S. Tsakonas ◽  
J. P. Breslin
Keyword(s):  
Slenderness Ratio ◽  
Prolate Spheroid ◽  
Longitudinal Component ◽  
The Other ◽  
Marine Propeller ◽  
Propeller Blade ◽  
Blade Number ◽  
Analytic Expression ◽  
Blade Frequency ◽  
Source Sink

An expression has been developed for the longitudinal component of the vibratory force exerted on a prolate spheroid by the operation of a marine propeller in a space-varying field (wake). Two evaluation schemes have been considered: One by integration of the pressure signal over the surface of the ellipsoid and the other by means of Lagally's theorem with the ellipsoid represented by a known source-sink distribution. The former, considered exact, leads to a complicated analytic expression, whereas the latter, less accurate, yields simple and physically meaningful results. Numerical calculations indicate the important role played by propeller clearance and slenderness ratio in the magnitude of the vibratory force. Also considered is the vibratory force exerted on a fin tail under the same condition of propeller action in a wake. Conclusions are drawn as to the optimum propeller blade number for a given fin-tail configuration.

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