Research Papers: Nuclear Power

Analysis of Thermal Effects in a Cavitating Orifice Using Rayleigh Equation and Experiments

[+] Author and Article Information
Maria Grazia De Giorgi

Department of Engineering for Innovation, University of Salento, Via per Monteroni, Lecce I-73100, Italymariagrazia.degiorgi@unisalento.it

Daniela Bello

Department of Engineering for Innovation, University of Salento, Via per Monteroni, Lecce I-73100, Italydaniela.bello@unisalento.it

Antonio Ficarella

Department of Engineering for Innovation, University of Salento, Via per Monteroni, Lecce I-73100, Italyantonio.ficarella@unisalento.it

J. Eng. Gas Turbines Power 132(9), 092901 (Jun 17, 2010) (10 pages) doi:10.1115/1.4000367 History: Received July 22, 2009; Revised August 10, 2009; Published June 17, 2010; Online June 17, 2010

The cavitation phenomenon interests a wide range of machines, from internal combustion engines to turbines and pumps of all sizes. It affects negatively the hydraulic machines’ performance and may cause materials’ erosion. The cavitation, in most cases, is a phenomenon that develops at a constant temperature, and only a relatively small amount of heat is required for the formation of a significant volume of vapor, and the flow is assumed isothermal. However, in some cases, such as thermosensible fluids and cryogenic liquid, the heat transfer needed for the vaporization is such that phase change occurs at a temperature lower than the ambient liquid temperature. The focus of this research is the experimental and analytical studies of the cavitation phenomena in internal flows in the presence of thermal effects. Experiments have been done on water and nitrogen cavitating flows in orifices at different operating conditions. Transient growth process of the cloud cavitation induced by flow through the throat is observed using high-speed video images and analyzed by pressure signals. The experiments show different cavitating behaviors at different temperatures and different fluids; this is related to the bubble dynamics inside the flow. So to investigate possible explanations for the influence of fluid temperature and of heat transfer during the phase change, initially, a steady, quasi-one-dimensional model has been implemented to study an internal cavitating flow. The nonlinear dynamics of the bubbles has been modeled by Rayleigh–Plesset equation. In the case of nitrogen, thermal effects in the Rayleigh equation are taken into account by considering the vapor pressure at the actual bubble temperature, which is different from the liquid temperature far from the bubble. A convective approach has been used to estimate the bubble temperature. The quasisteady one-dimensional model can be extensively used to conduct parametric studies useful for fast estimation of the overall performance of any geometric design. For complex geometry, three-dimensional computational fluid dynamic (CFD) codes are necessary. In the present work good agreements have been found between numerical predictions by the CFD FLUENT code, in which a simplified form of the Rayleigh equation taking into account thermal effects has been implemented by external user routines and some experimental observations.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Distribution of the normalized area A¯ along the axis of the nozzle used by Wang and Brennen (12)

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Figure 2

Normalized radius Rb¯=Rb/Rb0 along the axis of the nozzle used by Wang and Brennen (12), at different water temperatures (Re=988, R0=1×10−4 m, σ=0.8, and α=0.00003)

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Figure 3

Void fraction profile, along the axis of the nozzle used by Wang and Brennen (12), at water temperature equal to 293 K for different initial void fractions

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Figure 4

Cavitation number σ, as a function of critical initial void fraction α0. The regions over and to the left of the plotted data represent stable (unshocked) solutions, while below and to the right represent unstable (shocked) solutions.

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Figure 5

Distribution of the normalized radius along the axis of the nozzle, used by Wang and Brennen (12) in the case of nitrogen fluid at T=77 K and water at T=343 K, under the flow conditions: u0=20 m/s, R0=1×10−6 m, σ=0.9, and α=0.000003

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Figure 6

Particular of the sharp-edged orifice for water experiments

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Figure 7

On the top: cavitation in the restricted area for different water temperatures and for different cavitation numbers σ. On the bottom: enlarged view of the entire orifice at different temperatures, (flow inlet on the left).

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Figure 8

Critical cavitation number σexp, at which cavitation starts, at different flow temperatures

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Figure 9

Amplitude spectrum of the downstream pressure oscillations measured at constant temperature T=308.15 K and at T=343.15 K

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Figure 10

Standard deviation of the downstream pressure signals (T=308.15 K and at T=343.15 K)

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Figure 11

Axial vapor fraction profiles at T=343.15 K; axial coordinate starts at the restricted area inlet

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Figure 12

Experimental maximum and minimum measured length and predicted cavitation structures length for different σ at T=323.15 K

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Figure 13

Cavitation structures in the restricted area of the sharp-edged orifice for nitrogen at 77 K at different cavitation numbers σ (flow inlet on the right)

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Figure 14

FFT of the downstream pressure signal in the case of nitrogen flow

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Figure 15

Computational grid of the Laval nozzle (20)

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Figure 16

Predicted pressure profile for the cryogenic flow in the Laval nozzle (20)

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Figure 17

Predicted temperature and vapor fraction profiles at the straight wall for the cryogenic flow in the Laval nozzle (20)



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