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.

A Theoretical Analysis of Alternate Blade Cavitation in Inducers

1999 ◽  
Vol 122 (1) ◽  
pp. 156-163 ◽  
Author(s):  
Hironori Horiguchi ◽  
Satoshi Watanabe ◽  
Yoshinobu Tsujimoto ◽  
Masanori Aoki
Keyword(s):  
Present Model ◽  
Cavity Length ◽  
Flow Analysis ◽  
Cavitation Number ◽  
Equal Length ◽  
Parameter Study ◽  
Closed Cavity ◽  
Singularity Method ◽  
Length Changes ◽  
The Stability

An analysis of alternate blade cavitation on flat plate cascade is made using a singularity method based on a closed cavity model. In the steady flow analysis, it was found that two kinds of steady cavitation patterns exist. One is equal length cavitation in which the cavity lengths of all blades are the same. The other is alternate blade cavitation in which the cavity length changes alternately from blade to blade. Although the present model fails to predict the range of cavitation number where alternate blade cavitation occurs, it predicts alternate blade cavitation fairly well in terms of cavity length. A parameter study shows that the development of alternate blade cavitation is quite different depending on the solidity of cascade. The stability of equal length and alternate blade cavitation is then examined allowing the cavity length freely to change. It was found that alternate blade cavitation is stable for the cascades with larger solidity and unstable for the cascades with smaller solidity. The equal length cavitation is stable in both cases only in the region of cavitation number larger than that where the alternate blade cavitation solution separates from the equal length cavitation. [S0098-2202(00)01301-8]

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.

Frequency Dependence of Mass Flow Gain Factor and Cavitation Compliance of Cavitating Inducers

1996 ◽  
Vol 118 (2) ◽  
pp. 400-408 ◽  
Author(s):  
S. Otsuka ◽  
Y. Tsujimoto ◽  
K. Kamijo ◽  
O. Furuya
Keyword(s):  
Mass Flow ◽  
Present Model ◽  
Cavity Length ◽  
Incidence Angle ◽  
Low Frequency ◽  
Gain Factor ◽  
Cavity Model ◽  
Frequency Limit ◽  
Closed Cavity ◽  
Reduced Frequency

Unsteady cavitation characteristics are analyzed based on a closed cavity model in which the length of the cavity is allowed to oscillate. It is shown that the present model blends smoothly into quasi-steady calculations at the low frequency limit, unlike fixed cavity length models. Effects of incidence angle and cavitation number on cavitation compliance and mass flow gain factor are shown as functions of reduced frequency. The cavity volume is evaluated by three methods and the results are used to confirm the accuracy and adequacy of the numerical calculations. By comparison with experimental data on inducers, it is shown that the present model can simulate the characteristics of unsteady-cavitation qualitatively.

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.

Theoretical Analysis of Transitional and Partial Cavity Instabilities

2001 ◽  
Vol 123 (3) ◽  
pp. 692-697 ◽  
Author(s):  
Satoshi Watanabe ◽  
Yoshinobu Tsujimoto ◽  
Akinori Furukawa
Keyword(s):  
Stability Analysis ◽  
Theoretical Analysis ◽  
High Frequency ◽  
Large Amplitude ◽  
Cavity Length ◽  
Present Calculation ◽  
Blade Surface ◽  
Closed Cavity ◽  
Singularity Method ◽  
Time Marching

This paper describes a new time marching calculation of blade surface cavitation based on a linearized free streamline theory using a singularity method. In this calculation, closed cavity models for partial and super cavities are combined to simulate the transitional cavity oscillation between partial and super cavities. The results for an isolated hydrofoil located in a 2-D channel are presented. Although the re-entrant jet is not taken into account, the transitional cavity oscillation with large amplitude, which is known to occur when the cavity length exceeds 75 percent of the chord length, was simulated fairly well. The partial cavity oscillation with relatively high frequency was simulated as damping oscillations. The frequency of the damping oscillation agrees with that of a stability analysis and of experiments. The present calculation can be easily extended to simulate other cavity instabilities in pumps or cascades.

A numerical nonlinear analysis of the flow around two- and three-dimensional partially cavitating hydrofoils

1993 ◽  
Vol 254 ◽  
pp. 151-181 ◽  
Author(s):  
Spyros A. Kinnas ◽  
Neal E. Fine
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Present Method ◽  
Cavity Length ◽  
Three Dimensional ◽  
Cavitation Number ◽  
Cavity Surface ◽  
Cavity Shape ◽  
Dynamic Boundary

The partially cavitating two-dimensional hydrofoil problem is treated using nonlinear theory by employing a low-order potential-based boundary-element method. The cavity shape is determined in the framework of two independent boundary-value problems; in the first, the cavity length is specified and the cavitation number is unknown, and in the second the cavitation number is known and the cavity length is to be determined. In each case, the position of the cavity surface is determined in an iterative manner until both a prescribed pressure condition and a zero normal velocity condition are satisfied on the cavity. An initial approximation to the nonlinear cavity shape, which is determined by satisfying the boundary conditions on the hydrofoil surface rather than on the exact cavity surface, is found to differ only slightly from the converged nonlinear result.The boundary element method is then extended to treat the partially cavitating three-dimensional hydrofoil problem. The three-dimensional kinematic and dynamic boundary conditions are applied on the hydrofoil surface underneath the cavity. The cavity planform at a given cavitation number is determined via an iterative process until the thickness at the end of the cavity at all spanwise locations becomes equal to a prescribed value (in our case, zero). Cavity shapes predicted by the present method for some three-dimensional hydrofoil geometries are shown to satisfy the dynamic boundary condition to within acceptable accuracy. The method is also shown to predict the expected effect of foil thickness on the cavity size. Finally, cavity planforms predicted from the present method are shown to be in good agreement to those measured in a cavitating three-dimensional hydrofoil experiment, performed in MIT's cavitation tunnel.

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.

scholarly journals Influence of Thermodynamic Effect on Blade Load in a Cavitating Inducer

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Kengo Kikuta ◽  
Noriyuki Shimiya ◽  
Tomoyuki Hashimoto ◽  
Mitsuru Shimagaki ◽  
Hideaki Nanri ◽  
...  
Keyword(s):  
Pressure Distribution ◽  
Liquid Nitrogen ◽  
Cavity Length ◽  
Cold Water ◽  
Pressure Rise ◽  
Cavitation Number ◽  
Design Parameters ◽  
Trailing Edge ◽  
Thermodynamic Effect ◽  
Blade Tip

Distribution of the blade load is one of the design parameters for a cavitating inducer. For experimental investigation of the thermodynamic effect on the blade load, we conducted experiments in both cold water and liquid nitrogen. The thermodynamic effect on cavitation notably appears in this cryogenic fluid although it can be disregarded in cold water. In these experiments, the pressure rise along the blade tip was measured. In water, the pressure increased almost linearly from the leading edge to the trailing edge at higher cavitation number. After that, with a decrease of cavitation number, pressure rise occurred only near the trailing edge. On the other hand, in liquid nitrogen, the pressure distribution was similar to that in water at a higher cavitation number, even if the cavitation number as a cavitation parameter decreased. Because the cavitation growth is suppressed by the thermodynamic effect, the distribution of the blade load does not change even at lower cavitation number. By contrast, the pressure distribution in liquid nitrogen has the same tendency as that in water if the cavity length at the blade tip is taken as a cavitation indication. From these results, it was found that the shift of the blade load to the trailing edge depended on the increase of cavity length, and that the distribution of blade load was indicated only by the cavity length independent of the thermodynamic effect.

A Numerical Optimization Technique Applied to the Design of Two-Dimensional Cavitating Hydrofoil Sections

1996 ◽  
Vol 40 (01) ◽  
pp. 28-38
Author(s):  
Shigenori Mishima ◽  
Spyros A. Kinnas
Keyword(s):  
Numerical Optimization ◽  
Cavity Length ◽  
Optimization Technique ◽  
Cavitation Number ◽  
Quadratic Functions ◽  
Two Dimensional ◽  
Systematic Design ◽  
Hydrodynamic Analysis ◽  
Total Drag ◽  
Cavitating Hydrofoil

A numerical nonlinear optimization technique is applied to the systematic design of two-dimensional partially or supercavitating hydrofoil sections. The design objective is to minimize the hydrofoil drag for given lift and cavitation number. The hydrodynamic analysis of the cavitating hydrofoil is performed in nonlinear theory, via a low-order potential-based panel method. The effects of viscosity are taken into account via a uniform friction coefficient applied on the wetted foil surface. The total drag, lift, cavitation number, and other quantities involved in the imposed constraints, are expressed in terms of quadratic functions of the main parameters of the hydrofoil geometry, angle of attack, and the cavity length. The optimization is based on the method of multipliers by coupling the Lagrange multiplier terms and the penalty function terms. The robustness and convergence of the method are extensively investigated, and the results are compared with those from applying other design methods.

Steady Performance of a Flexible Hydrofoil Near a Free Surface

1990 ◽  
Vol 34 (04) ◽  
pp. 302-310
Author(s):  
Salwa M. Rashad ◽  
Theodore Green
Keyword(s):  
Mathematical Model ◽  
Free Surface ◽  
Cavity Length ◽  
Leading Edge ◽  
Cavity Flow ◽  
Cavitation Number ◽  
Deformation Characteristics ◽  
Flow Depth ◽  
Lift And Drag ◽  
The Galerkin Method

A linearized cavity-flow theory is used to develop a mathematical model to study the steady characteristics of a flexible hydrofoil near a free surface. The Galerkin method is employed to account for the mutual interaction between the fluid and structure forces. Cheng and Rott's method [1]2 is used to derive general expressions for the deformation characteristics in steady flow of an arbitrarily shaped hydrofoil, with a clamped trailing edge and free leading edge. From the analysis it is possible to determine the lift and drag coefficients, cavity length, and the foil steady deformation for any given specific foil shape, cavitation number, angle of attack, flow depth/chord ratio and rigidity. Sample numerical results are given, and the effects of flexibility and the proximity of the free surface are discussed. Chordwise flexibility tends to increase drag and decrease lift coefficients. This effect is more serious near the free surface. A slight increase of the thickness near the leading edge diminishes the flexibility effects.

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