Quasi-Three-Dimensional Analysis of Cavitation in an Inducer

2004 ◽  
Vol 126 (5) ◽  
pp. 709-715 ◽  
Author(s):  
Hironori Horiguchi ◽  
Souhei Arai ◽  
Junichiro Fukutomi ◽  
Yoshiyuki Nakase ◽  
Yoshinobu Tsujimoto
Keyword(s):  
Present Method ◽  
Radial Direction ◽  
Three Dimensional ◽  
Meridian Plane ◽  
Cavity Model ◽  
Closed Cavity ◽  
Stream Surface ◽  
Meridional Velocity ◽  
Singularity Method ◽  
Rotationally Symmetric

A method for the prediction of steady cavitation in turbopumps is proposed on the assumption that the fluid is inviscid and the stream surface is rotationally symmetric. The analysis in the meridian plane is combined with that in a blade-to-blade stream surface where a singularity method based on a closed cavity model is used. The present method is applied to a helical inducer and it is found that the influence of the three-dimensionality of the flow on cavitation mainly appears as the change of angle of attack associated with the change of meridional velocity caused by the movement of meridian streamline in radial direction.

Quasi Three-Dimensional Analysis of Cavitation in an Inducer

2003 ◽  
Author(s):  
Hironori Horiguchi ◽  
Souhei Arai ◽  
Junichiro Fukutomi ◽  
Yoshiyuki Nakase ◽  
Yoshinobu Tsujimoto
Keyword(s):  
Dimensional Analysis ◽  
Radial Direction ◽  
Angle Of Attack ◽  
Three Dimensional ◽  
Meridian Plane ◽  
Cavity Model ◽  
Closed Cavity ◽  
Stream Surface ◽  
Singularity Method ◽  
Rotationally Symmetric

A quasi three-dimensional analysis of steady cavitation in a herical inducer is carried out by a method based on the assumption that the fluid is inviscid and the stream surface is rotationally symmetric. The analysis in the meridian plane are combined with that in blade-to-blade stream surface where a singularity method is used based on a closed cavity model. It was found that the influence of the three-dimensionality of the flow on cavitation mainly appears as the change of angle of attack associated with the change of meridian velocity caused by the movement of meridian streamline in radial direction.

Analysis of Rotating Cavitation in a Finite Pitch Cascade Using a Closed Cavity Model and a Singularity Method

1999 ◽  
Vol 121 (4) ◽  
pp. 834-840 ◽  
Author(s):  
Satoshi Watanabe ◽  
Kotaro Sato ◽  
Yoshinobu Tsujimoto ◽  
Kenjiro Kamijo
Keyword(s):  
Cavity Length ◽  
Gain Factor ◽  
Cavitation Number ◽  
Cavity Model ◽  
Closed Cavity ◽  
Cavity Shape ◽  
Actuator Disk ◽  
Singularity Method ◽  
Eigen Value ◽  
The Stability

A new method is proposed for the stability analysis of cavitating flow. In combination with the singularity method, a closed cavity model is employed allowing the cavity length freely to oscillate. An eigen-value problem is constituted from the boundary and supplementary conditions. This method is applied for the analysis of rotating cavitation in a cascade with a finite pitch and a finite chordlength. Unlike previous semi-actuator disk analyses (Tsujimoto et al., 1993 and Watanabe et al., 1997a), it is not required to input any information about the unsteady cavitation characteristics such as mass flow gain factor and cavitation compliance. Various kinds of instability are predicted. One of them corresponds to the forward rotating cavitation, which is often observed in experiments. The propagation velocity ration of this mode agrees with that of experiments, while the onset range in terms of cavitation number is larger than that of experiments. The second solution corresponds to the backward mode, which is also found in semi-actuator disk analyses and identified in an experiments. Other solutions are found to be associated with higher order cavity shape fluctuations, which have not yet been identified in experiments.

scholarly journals Linear Stability Analysis of the Effects of Camber and Blade Thickness on Cavitation Instabilities in Inducers

2005 ◽  
Vol 128 (3) ◽  
pp. 430-438 ◽  
Author(s):  
Hironori Horiguchi ◽  
Yury Semenov ◽  
Masataka Nakano ◽  
Yoshinobu Tsujimoto
Keyword(s):  
Pressure Gradient ◽  
Cavity Length ◽  
Angle Of Attack ◽  
Rocket Engines ◽  
Cavity Model ◽  
Closed Cavity ◽  
Singularity Method ◽  
Numerical Studies ◽  
Blade Thickness ◽  
The Stability

It has been shown by experimental and numerical studies that various cavitation instabilities occur in inducers for rocket engines when the cavity length exceeds about 65% of the blade spacing. On the other hand, it has been pointed out by an experimental study that the cavitation instabilities occur when the pressure gradient near the throat becomes small to some degree. The present study is motivated to examine the latter criterion based on pressure gradient for cavitation instabilities from the viewpoint of theoretical analysis. For this purpose, analyses of steady flow and its stability were carried out for cavitating flow in cascades with circular arc and plano-convex blades by a singularity method based on closed cavity model. It was found that the criterion based on the cavity length for the occurrence of cavitation instabilities is more adequate than the criterion based on the pressure gradient. It was also found that the steady cavity length and the stability of the flow in both cascades can be practically correlated with a parameter σ∕[2(α−α0)], where σ is a cavitation number, α is an angle of attack, and α0 is a shockless angle of attack.

A Boundary Element Method for the Analysis of the Flow Around 3-D Cavitating Hydrofoils

1993 ◽  
Vol 37 (03) ◽  
pp. 213-224
Author(s):  
Neal E. Fine ◽  
Spyros A. Kinnas
Keyword(s):  
Boundary Condition ◽  
Boundary Element Method ◽  
Pressure Distribution ◽  
Boundary Element ◽  
Present Method ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Closed Cavity ◽  
Dynamic Boundary ◽  
Element Method

The three-dimensional steady cavitating hydrofoil problem is treated in nonlinear theory by employing a low-order potential-based boundary element method. The cavity extent and shape are determined for given cavitation number by satisfying the three-dimensional kinematic and dynamic boundary conditions on the hydrofoil surface beneath the cavity and on the portion of the wake sheet overlapped by the cavity. A unified discretization and algorithm is developed to predict the occurrence of general cavity planforms, including partial cavitation, supercavitation, and mixed partial/supercavitation. The cavity planform is determined iteratively by searching for the planform which corresponds to a closed cavity at all spanwise locations. Cavity shapes predicted by the present method, applied in two dimensions, are compared to the converged nonlinear cavity shapes and are found to differ only slightly for a range of foil thicknesses and angles of attack. The accuracy of the 3-D method is gaged by satisfying Green's formula, subject to a kinematic boundary condition, on a modified foil consisting of the union of the original foil and the cavity predicted by the present method. Comparing the resulting pressure distribution to the pressure distribution from the present method shows that the dynamic boundary condition is satisfied to within acceptable accuracy.

Tool Path Optimization of 2D Contour Considering Stock Boundary

2012 ◽  
Vol 251 ◽  
pp. 169-172
Author(s):  
Fu Zhong Wu
Keyword(s):  
Present Method ◽  
Tool Path ◽  
Three Dimensional ◽  
Boundary Curve ◽  
Tool Path Generation ◽  
Path Optimization ◽  
Path Generation ◽  
Offset Curves ◽  
Measuring Machine ◽  
Tool Diameter

Based on analyzing the existing algorithms, a novel tool path generation of 2D contour considering stock boundary is presented. Firstly the boundary points of stock are obtained by three-dimensional measuring machine. And the boundary curve is constructed by method of features identifying. The stock boundary is offset toward outside with tool diameter. An enclosed region is formed between the contour curves and the offset curves of stock boundary. The tool path is generated by form of parallel spiral by offsetting the stock boundary in the enclosed region. Finally the validity of present method is demonstrated by an example.

The Effect of the Steady Flow Potential on the Motions of a Moving Ship in Waves

2000 ◽  
Vol 44 (01) ◽  
pp. 14-32
Author(s):  
Ming-Chung Fang
Keyword(s):  
Steady Flow ◽  
Present Method ◽  
Three Dimensional ◽  
Source Distribution ◽  
Series Expansions ◽  
Ship Motions ◽  
Double Integral ◽  
Flow Potential ◽  
Principal Value ◽  
Good Agreement

A three-dimensional method to analyze the motions of a ship running in waves is presented, including the effects of the steady-flow potential. Basically, the general formulations are based on the source distribution technique by which the ship hull surface is regarded as the assembly of many panels. The present study includes three algorithms for treating the corresponding Green function:the Hess & Smith algorithm for the part of simple source I/r,the complex plane contour integral of the Shen & Farell algorithm for the double integral of steady flow, andthe series expansions of the Telste & Noblesse algorithm for the Cauchy principal value integral of unsteady flow. The study reveals that the effect of steady flow on ship motions is generally small, but it still cannot be neglected in some cases, especially for the ship running in oblique waves. The effect also depends on the fore-aft configuration of the ship. The results predicted by the present method are found to be in fairly good agreement with existing experiments and other theories.

Calculation of Complete Three-Dimensional Flow in a Centrifugal Rotor With Splitter Blades

1988 ◽  
Author(s):  
Liu Dian-Kui ◽  
Ji Le-Jian
Keyword(s):  
Mass Flow ◽  
Three Dimensional ◽  
Present Calculation ◽  
Flow Ratio ◽  
Three Dimensional Flow ◽  
Stream Surface ◽  
Dimensional Flow ◽  
Flow Capacity ◽  
The Given ◽  
Mass Flow Ratio

The flow within a centrifugal rotor has strong characteristics of three-dimensional effect. A procedure called “stream-surface coordinates iteration” for the calculation of complete three dimensional flow in turbo-machinery is first described. Splitter blade techniques have been used in many rotors, especially in centrifugal compressors and pumps with high flow capacity. The difficulty of the calculation of the flow field for this type of rotor lies on that the mass flow ratio between the two sub-channels is unknown for the given total flow capacity. In the second part of this paper, an assumption about how to determine this mass flow ratio and a procedure to calculate the complete three-dimensional flow are presented. Finally, some design criteria about the splitter blades are put forward. Experimental data from two centrifugal pump impellers equipped with different splitter blades are also given to demonstrate the availability of the present calculation method.

The Derivation and Application of Fundamental Solutions for Unsteady Stokes Equations

2015 ◽  
Vol 31 (6) ◽  
pp. 683-691 ◽  
Author(s):  
C-H. Hsiao ◽  
D.-L. Young
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Fundamental Solutions ◽  
Mass Source ◽  
Reynolds Number Flow ◽  
Singularity Method ◽  
Vector Calculus ◽  
Unsteady Stokes Flow ◽  
Number Flow ◽  
Unsteady Stokes Equations

AbstractIn this paper, two formulations in explicit form to derive the fundamental solutions for two and three dimensional unsteady unbounded Stokes flows due to a mass source and a point force are presented, based on the vector calculus method and also the Hörmander’s method. The mathematical derivation process for the fundamental solutions is detailed. The steady fundamental solutions of Stokes equations can be obtained from the unsteady fundamental solutions by the integral process. As an application, we adopt fundamental solutions: an unsteady Stokeslet and an unsteady potential dipole to validate a simple case that a sphere translates in Stokes or low-Reynolds-number flow by using the singularity method instead by the traditional method which in general limits to the assumption of oscillating flow. It is concluded that this study is able to extend the unsteady Stokes flow theory to more general transient motions by making use of the fundamental solutions of the linearly unsteady Stokes equations.

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