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.

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]

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.

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.

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.

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.

Transition of streamwise streaks in zero-pressure-gradient boundary layers

2002 ◽  
Vol 472 ◽  
pp. 229-261 ◽  
Author(s):  
LUCA BRANDT ◽  
DAN S. HENNINGSON
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
High Speed ◽  
Plate Boundary ◽  
Transition Process ◽  
Free Stream Turbulence ◽  
Tollmien Schlichting ◽  
Streamwise Streaks ◽  
The Stability ◽  
Optimal Disturbances

A transition scenario initiated by streamwise low- and high-speed streaks in a flat-plate boundary layer is studied. In many shear flows, the perturbations that show the highest potential for transient energy amplification consist of streamwise-aligned vortices. Due to the lift-up mechanism these optimal disturbances lead to elongated streamwise streaks downstream, with significant spanwise modulation. In a previous investigation (Andersson et al. 2001), the stability of these streaks in a zero-pressure-gradient boundary layer was studied by means of Floquet theory and numerical simulations. The sinuous instability mode was found to be the most dangerous disturbance. We present here the first simulation of the breakdown to turbulence originating from the sinuous instability of streamwise streaks. The main structures observed during the transition process consist of elongated quasi-streamwise vortices located on the flanks of the low-speed streak. Vortices of alternating sign are overlapping in the streamwise direction in a staggered pattern. The present scenario is compared with transition initiated by Tollmien–Schlichting waves and their secondary instability and by-pass transition initiated by a pair of oblique waves. The relevance of this scenario to transition induced by free-stream turbulence is also discussed.

Modeling of External Pressure Gradient Influence on the Stability of Disturbances in the Boundary Layers of Compressed Gas

2013 ◽  
Vol 8 (4) ◽  
pp. 64-75
Author(s):  
Sergey Gaponov ◽  
Natalya Terekhova
Keyword(s):  
Mach Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Leading Edge ◽  
External Pressure ◽  
Transition To Turbulence ◽  
Compressed Gas ◽  
High Mach ◽  
The Stability ◽  
Very High

This work continues the research on modeling of passive methods of management of flow regimes in the boundary layers of compressed gas. Authors consider the influence of pressure gradient on the evolution of perturbations of different nature. For low Mach number M = 2 increase in pressure contributes to an earlier transition of laminar to turbulent flow, and, on the contrary, drop in the pressure leads to a prolongation of the transition to turbulence. For high Mach number M = 5.35 found that the acoustic disturbances exhibit a very high dependence on the sign and magnitude of the external gradient, with a favorable gradient of the critical Reynolds number becomes smaller than the vortex disturbances, and at worst – boundary layer is destabilized directly on the leading edge

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