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Multiphase Flows

Development and Validation of a Reduced Critical Radius Model for Cryogenic Cavitation

[+] Author and Article Information
Shin-ichi Tsuda1

Department of Mechanical Systems Engineering,  Shinshu University, 4-17-1 Wakasato, Nagano, Nagano 380-8553, Japantsudashin@shinshu-u.ac.jp

Naoki Tani

 Tsukuba Space Center,  Japan Aerospace Exploration Agency, 2-1-1 Sengen, Tsukuba, Ibaraki 305-8505, Japantani.naoki@jaxa.jp

Nobuhiro Yamanishi

 Tsukuba Space Center,  Japan Aerospace Exploration Agency, 2-1-1 Sengen, Tsukuba, Ibaraki 305-8505, Japanyamanishi.nobuhiro@jaxa.jp

1

Corresponding author.

J. Fluids Eng 134(5), 051301 (May 22, 2012) (10 pages) doi:10.1115/1.4006469 History: Received August 28, 2011; Revised March 24, 2012; Published May 18, 2012; Online May 22, 2012

Cryogenic fluids such as liquid hydrogen, liquid oxygen, and liquid methane have often been used as liquid rocket propellants, and it is well known that the suction performance of turbopump inducers is better in cryogenic fluids than it is in cold water due to the so-called “thermodynamic effect.” The origin of the thermodynamic effect is the temperature change inside a cavity region that arises from the latent heat transfer across the interface of a cavity. To better understand the suction performance of cavitating cryogenic inducers, we must take into account the temperature changes that take place due to the thermodynamic effect; computational fluid dynamics (CFD) analysis coupled with an energy equation is one of the most powerful tools for this purpose. The computational cost, however, becomes an obstacle for its application to the design phase, so a reduction in the number of governing equations is often preferable. In the present study, a cryogenic cavitation model that does not need to solve an energy equation is proposed as a reduced model; the model is named the “reduced critical radius model.” This model assumes that the temperature change due to the latent heat transfer can be analytically well estimated on the basis of an approximation of the local equilibrium when the pressure inside a cavity is always kept at a saturation vapor pressure at every temperature (at least on the time scale of the flow field). The proposed method was validated carefully for a variety of objects: blunt headforms, hydrofoils, a two-dimensional blunt wing, and Laval nozzles. The results obtained during the validation were in good agreement with the experimental results, except in the case of strong unsteady cavitation. This indicates that the present method, which does not involve solving an energy equation, offers good potential for application to the design phase of cryogenic cavitating inducers.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

A turbopump in a rocket engine and an inducer (inset)

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Figure 2

Computational grid with its boundary condition for an axisymmetric body. Left: spherical headform, right: square headform.

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Figure 3

Physical properties for water (at 1 atm, 20 °C)

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Figure 4

Dependency of Ce on pressure distribution around a spherical headform

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Figure 5

Comparison of pressure distribution around a spherical headform (left) and around a square headform (right)

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Figure 6

Shapes and computational grids with each boundary condition for hydrofoils. Left: Clark-Y, right: NACA0015.

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Figure 7

Lift coefficient (left) and drag coefficient (right) against cavitation number for Clark-Y 11.7%

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Figure 8

Instantaneous distribution of pressure (top) and of void fraction (bottom) for Clark-Y 11.7%

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Figure 9

Lift coefficient (left) and drag coefficient (right) against cavitation number for NACA0015

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Figure 10

Comparison of instantaneous cavity shape at σ = 1.2 on NACA0015. Left: experiment by Kubota [18], right: present computation.

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Figure 11

Strouhal number for cloud cavitation against cavitation number in the present computational results. Both Clark-Y and NACA0015 are plotted.

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Figure 12

Shape and computational grid with each boundary condition for a two-dimensional wing

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Figure 13

Physical properties of cryogenic fluids that were applied to a two-dimensional wing

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Figure 14

Comparison of pressure distributions around two-dimensional wing

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Figure 15

Contours of pressure, void fraction, and temperature for a two-dimensional wing

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Figure 16

Shape and computational grid with each boundary condition for Laval nozzles

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Figure 17

Physical properties of cryogenic fluids that were applied to a Laval nozzle

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Figure 18

Comparisons of the pressure distributions along each wall of the Laval nozzles

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