Analysis of Thermal Effects in a Cavitating Inducer Using Rayleigh Equation

[+] Author and Article Information
Jean-Pierre Franc

 LEGI, BP 53, 38041 Grenoble Cedex 9, Francejean-pierre.franc@hmg.inpg.fr

Christian Pellone

 LEGI, BP 53, 38041 Grenoble Cedex 9, Francechristian.pellone@hmg.inpg.fr

J. Fluids Eng 129(8), 974-983 (Jan 31, 2007) (10 pages) doi:10.1115/1.2746919 History: Received October 31, 2006; Revised January 31, 2007

A simple model based on the resolution of Rayleigh equation is used to analyze thermal effects in cavitation. Two different assumptions are considered for the modeling of heat transfer toward the liquid∕vapor interface. One is based upon a convective type approach using a convection heat transfer coefficient or the equivalent Nusselt number. The other one is based upon the resolution of the heat diffusion equation in the liquid surrounding the bubble. This conductive-type approach requires one to specify the eddy thermal diffusivity or the equivalent Peclet number. Both models are applied to a cavitating inducer. The basic pressure distribution on the blades is determined from a potential flow computation in a two-dimensional cascade of flat plates. The sheet cavity, which develops from the leading edge, is approximated by the envelope of a hemispherical bubble traveling on the suction side of the blade. Cavity shape and temperature distribution predicted by both models are compared. The evolutions of cavity length with the cavitation number for cold water (without thermal effects) and for Refrigerant 114 at two different temperatures is compared to experimental data. Such a simple model is easy to apply and appears to be quite pertinent for the analysis of thermal effects in a cavitating inducer.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 8

Cavity length versus cavitation number. Comparison between computation and experiments (Ref. 22) for cold water and R114 at two different temperatures (20 and 40°C). Cavity length is made nondimensional using blade spacing H (convective model, Nu=2.085×106; conductive model, ε=5000).

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Figure 9

Influence of thermodynamic effect on the shape of the cavity. Results for water and R114 at two different temperatures (20 and 40°C) are compared. For the three cases, the cavity length is kept constant λH≡0.5 (conductive model, ε=5000).

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Figure 10

B factor versus cavity length for ε=5000. Comparison between computation by the conductive model and experiments (Ref. 22) for R114 at two different temperatures (20 and 40°C). Cavity length is made nondimensional using blade spacing H. The plotted value of B corresponds to maximum temperature depression.

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Figure 1

Scheme of the 2D cascade (vertical scale has been expanded)

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Figure 2

Close view of the blade leading edge

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Figure 3

Close view of the blade trailing edge

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Figure 4

Pressure distribution on the blades. Comparison between the present results and that of Watanabe (Ref. 7).

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Figure 5

Comparison between the convective (Nu=7.31×106) and the conductive (ε=5×104) models for the same cavity length. (a) cavity shape. (b) Temperature distribution (R114 40°C−σv=0).

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Figure 6

Effect of Nu (convective model) or ε (conductive model) on (a) cavity length, (b) cavity shape, and (c) maximum B factor (R114 40°C−σv=0).

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Figure 7

Effect of increasing thermal effects on the distribution of the cavitation number σc based on the vapor pressure at the local cavity temperature pv(Tc). Comparison with the pressure coefficient distribution (R114 40°C−σv=0).




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