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.

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 Backflow effects on mass flow gain factor in a centrifugal pump

2021 ◽  
Vol 104 (2) ◽  
pp. 003685042199886
Author(s):  
Wenzhe Kang ◽  
Lingjiu Zhou ◽  
Dianhai Liu ◽  
Zhengwei Wang
Keyword(s):  
Centrifugal Pump ◽  
Mass Flow ◽  
Flow Rate ◽  
Low Frequency ◽  
Gain Factor ◽  
Low Flow ◽  
Cavity Volume ◽  
Cavitating Flows ◽  
Inlet Tube ◽  
Low Flow Rate

Previous researches has shown that inlet backflow may occur in a centrifugal pump when running at low-flow-rate conditions and have nonnegligible effects on cavitation behaviors (e.g. mass flow gain factor) and cavitation stability (e.g. cavitation surge). To analyze the influences of backflow in impeller inlet, comparative studies of cavitating flows are carried out for two typical centrifugal pumps. A series of computational fluid dynamics (CFD) simulations were carried out for the cavitating flows in two pumps, based on the RANS (Reynolds-Averaged Naiver-Stokes) solver with the turbulence model of k- ω shear stress transport and homogeneous multiphase model. The cavity volume in Pump A (with less reversed flow in impeller inlet) decreases with the decreasing of flow rate, while the cavity volume in Pump B (with obvious inlet backflow) reach the minimum values at δ = 0.1285 and then increase as the flow rate decreases. For Pump A, the mass flow gain factors are negative and the absolute values increase with the decrease of cavitation number for all calculation conditions. For Pump B, the mass flow gain factors are negative for most conditions but positive for some conditions with low flow rate coefficients and low cavitation numbers, reaching the minimum value at condition of σ = 0.151 for most cases. The development of backflow in impeller inlet is found to be the essential reason for the great differences. For Pump B, the strong shearing between backflow and main flow lead to the cavitation in inlet tube. The cavity volume in the impeller decreases while that in the inlet tube increases with the decreasing of flow rate, which make the total cavity volume reaches the minimum value at δ = 0.1285 and then the mass flow gain factor become positive. Through the transient calculations for cavitating flows in two pumps, low-frequency fluctuations of pressure and flow rate are found in Pump B at some off-designed conditions (e.g. δ = 0.107, σ = 0.195). The relations among inlet pressure, inlet flow rate, cavity volume, and backflow are analyzed in detail to understand the periodic evolution of low-frequency fluctuations. Backflow is found to be the main reason which cause the positive value of mass flow gain factor at low-flow-rate conditions. Through the transient simulations of cavitating flow, backflow is considered as an important aspect closely related to the hydraulic stability of cavitating pumping system.

scholarly journals Dynamics of a Cavitating Propeller in a Water Tunnel

2003 ◽  
Vol 125 (2) ◽  
pp. 283-292 ◽  
Author(s):  
Satoshi Watanabe ◽  
Christopher E. Brennen
Keyword(s):  
Present Model ◽  
Gain Factor ◽  
Operating Conditions ◽  
Water Tunnel ◽  
Tube Model ◽  
Cavity Model ◽  
Flow Tube ◽  
Stream Tube ◽  
Thrust Coefficient ◽  
One Dimensional

This study investigates the unsteady dynamics and inherent instabilities of a cavitating propeller operating in a water tunnel. First, the steady characteristics of the cavitating propeller such as the thrust coefficient are obtained by applying continuity and momentum equations to a simple one-dimensional flow tube model. The effects of the tunnel walls as well as those of the propeller operating conditions (advance ratio and cavitation number) are explored. Then the transfer matrix of the cavitating propeller (considered to be the most appropriate way to describe the dynamics of propeller) is obtained by combining the simple stream tube model with the conventional cavity model using the quasi-static cavitation compliance and mass flow gain factor representation. Finally, the surge instability of a cavitating propeller observed by Duttweiler and Brennen (2001) is examined by coupling the present model of the cavitation with a dynamic model for the water tunnel. This analysis shows that the effect of tunnel walls is to promote the surge instability.

Dynamic Responses of Partially Cavitated Hydrofoil Cascade to Axial Gust in Bubbly Water

1984 ◽  
Vol 106 (3) ◽  
pp. 312-318
Author(s):  
Tetsuo Nishiyama ◽  
Hideya Nishiyama
Keyword(s):  
Water Conservation ◽  
Pressure Rise ◽  
Volume Ratio ◽  
Gain Factor ◽  
Dynamic Responses ◽  
Cavity Model ◽  
Cavity Pressure ◽  
Reduced Frequency ◽  
The Mean ◽  
Unsteady Discharge

A method for analysis by singularity representations is presented for dynamic responses of partially cavitated hydrofoil cascade to axial gust in bubbly water. Conservation laws of mass and momentum are applied to take account of the unsteady parts of cavity area, cavity termination thickness, and cavity pressure for unsteady partial cavity model. Also, the cavitation compliance and mass flow gain factor obtained from the cavity model determined are considered in relations to cavity length, reduced frequency, and air volume ratio. Comparisons of the mean unsteady pressure rise and unsteady discharge difference are also made with the available former results.

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.

Evaluation of Special Hearing Aids for Deaf Children

1971 ◽  
Vol 36 (4) ◽  
pp. 527-537 ◽  
Author(s):  
Norman P. Erber
Keyword(s):  
Hearing Aids ◽  
High Frequency ◽  
Hearing Aid ◽  
Low Frequency ◽  
Acoustic Stimulation ◽  
Deaf Children ◽  
Frequency Range ◽  
Frequency Limit ◽  
Unpublished Studies ◽  
Published Research

Two types of special hearing aid have been developed recently to improve the reception of speech by profoundly deaf children. In a different way, each special system provides greater low-frequency acoustic stimulation to deaf ears than does a conventional hearing aid. One of the devices extends the low-frequency limit of amplification; the other shifts high-frequency energy to a lower frequency range. In general, previous evaluations of these special hearing aids have obtained inconsistent or inconclusive results. This paper reviews most of the published research on the use of special hearing aids by deaf children, summarizes several unpublished studies, and suggests a set of guidelines for future evaluations of special and conventional amplification systems.

Rotor Wake Generated Unsteady Aerodynamic Response of a Compressor Stator

1978 ◽  
Vol 100 (4) ◽  
pp. 664-675 ◽  
Author(s):  
S. Fleeter ◽  
R. L. Jay ◽  
W. A. Bennett
Keyword(s):  
Pressure Difference ◽  
Second Harmonic ◽  
Incidence Angle ◽  
Dynamic Pressure ◽  
Pressure Differential ◽  
Phase Lag ◽  
Trailing Edge ◽  
Unsteady Pressure ◽  
Forcing Function ◽  
Reduced Frequency

An experimental investigation was conducted to determine the fluctuating pressure distribution on a stationary vane row, with the primary source of excitation being the wakes from the upstream rotor blades. This was accomplished in a large scale, low speed, single stage research compressor. The forcing function, the velocity defect created by the rotor wakes, was measured with a crossed hot-wire probe. The aerodynamic response on the vanes was measured by means of flush mounted high response dynamic pressure transducers. The dynamic data were analyzed to determine the chordwise distribution of the dynamic pressure coefficient and aerodynamic phase lag as referenced to a transverse gust at the vane leading edge. Vane suction and pressure surface data as well as the pressure difference across the vane were obtained for reduced frequency values ranging from 3.65 to 16.80 and for an incidence angle range of 35.5 deg. The pressure difference data were correlated with a state-of-the-art aerodynamic cascade transverse gust analysis. The correlation was quite good for all reduced frequency values for small values of incidence. For the more negative incidence angle data points, it was shown that a convected wake phenomena not modeled in the analysis existed. Both the first and second harmonic unsteady pressure differential magnitude data decrease in the chordwise direction. The second harmonic magnitude data attains a value very nearly zero at the vane trailing edge transducer location, while the first harmonic data is still finite, albeit small, at this location. That the magnitude of the unsteady pressure differential data approaches zero near to the trailing edge, particularly the second harmonic data which has reduced frequency values to 16.8, is significant in that it reflects upon the validity of the Kutta condition for unsteady flows.

Onset of size effects in lattice thermal conductivity and lifetime of low-frequency thermal phonons

2012 ◽  
Vol 1404 ◽  
Author(s):  
A.A. Maznev
Keyword(s):  
Thin Film ◽  
Thermal Conductivity ◽  
Size Effects ◽  
Lattice Thermal Conductivity ◽  
Low Frequency ◽  
Square Root ◽  
Relaxation Rates ◽  
Frequency Limit ◽  
Conductivity Of Thin Films ◽  
Closed Form Formula

ABSTRACTThe onset of size effects in phonon-mediated thermal transport along a thin film at temperatures comparable or greater than the Debye temperature is analyzed theoretically. Assuming a quadratic frequency dependence of phonon relaxation rates in the low-frequency limit, a simple closed-form formula for the reduction of the in-plane thermal conductivity of thin films is derived. The effect scales as the square root of the film thickness, which leads to the prediction of measurable size-effects even at “macroscopic” distances ~100 μm. However, this prediction needs to be corrected to account for the deviation from the ω−2 dependence of phonon lifetimes at sub-THz frequencies due to the transition from Landau-Rumer to Akhiezer mechanism of phonon dissipation.

scholarly journals Nonlinear interaction between acoustic gravity waves

1996 ◽  
Vol 14 (3) ◽  
pp. 304-308 ◽  
Author(s):  
P. Axelsson ◽  
J. Larsson ◽  
L. Stenflo
Keyword(s):  
Gravity Waves ◽  
Nonlinear Interaction ◽  
Low Frequency ◽  
Resonant Interaction ◽  
Coupling Coefficients ◽  
Symmetric Form ◽  
Frequency Limit ◽  
Acoustic Gravity Waves

Abstract. The resonant interaction between three acoustic gravity waves is considered. We improve on the results of previous authors and write the new coupling coefficients in a symmetric form. Particular attention is paid to the low-frequency limit.

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