0
Research Papers: Flows in Complex Systems

Modification of Energy Equation for Homogeneous Cavitation Simulation With Thermodynamic Effect

[+] Author and Article Information
Anh Dinh Le

Graduate School of Engineering,
Tohoku University,
2-1-1 Katahira, Aoba Ward,
Sendai 980-8577, Miyagi, Japan
e-mail: le@cfs.ifs.tohoku.ac.jp

Junosuke Okajima

Institute of Fluid Science,
Tohoku University,
2-1-1 Katahira, Aoba Ward,
Sendai 980-8577, Miyagi, Japan
e-mail: j.okajima@tohoku.ac.jp

Yuka Iga

Institute of Fluid Science,
Tohoku University,
2-1-1 Katahira, Aoba Ward,
Sendai 980-8577, Miyagi, Japan
e-mail: iga@cfs.ifs.tohoku.ac.jp

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 27, 2018; final manuscript received December 3, 2018; published online January 30, 2019. Assoc. Editor: Matevz Dular.

J. Fluids Eng 141(8), 081102 (Jan 30, 2019) (12 pages) Paper No: FE-18-1437; doi: 10.1115/1.4042257 History: Received June 27, 2018; Revised December 03, 2018

In industrial applications, cryogenic liquids are sometimes used as the working fluid of fluid machineries. In those fluids, the thermodynamic suppression effect of cavitation, which is normally ignored in water at room temperature, becomes obvious. When evaporation occurs in the cavitation region, the heat is supplied from the surrounding liquid. Hence, the liquid temperature is decreased, and cavitation is suppressed due to the decrease in saturated vapor pressure. Therefore, the performance of the fluid machinery can be improved. Computational fluid dynamics, which involves the use of a homogeneous model coupled with a thermal transport equation, is a powerful tool for the prediction of cavitation under thermodynamic effects. In this study, a thermodynamic model for a homogeneous model is introduced. In this model, the source term related to the latent heat of phase change appears explicitly, and the degree of heat transfer rate for evaporation and condensation can be adjusted separately to suit the homogeneous model. Our simplified thermodynamic model coupled with the Merkle cavitation model was validated for cryogenic cavitation on a two-dimensional (2D) quarter hydrofoil. The results obtained during the validation showed good agreement (in both pressure and temperature profiles) with the experimental data and were better than existing numerical results obtained by other researchers.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Hord, J. , 1972, “ Cavitation in Liquid Cryogens I—Venturi,” National Aeronautics and Space Administration, Washington, DC, Report No. NASA CR-2054. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720016713.pdf
Hord, J. , 1973, “ Cavitation in Liquid Cryogens II—Hydrofoil,” National Aeronautics and Space Administration, Washington, DC, Report No. NASA CR-2156. https://ntrs.nasa.gov/search.jsp?R=19730007528
Hord, J. , 1973, “ Cavitation in Liquid Cryogens III—Ogive,” National Aeronautics and Space Administration, Washington, DC, Report No. NASA CR-2242. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19730019421.pdf
Franc, J.-P. , Rebattlet, C. , and Coulon, A. , 2004, “ An Experimental Investigation of Thermal Effects in a Cavitating Inducer,” ASME J. Fluids Eng., 126(5), pp. 716–723. [CrossRef]
Cervone, A. , Bramanti, C. , Rapposelli, E. , and Agostino, L. , 2006, “ Thermal Cavitation Experiments on a NACA0015 Hydrofoil,” ASME J. Fluids Eng., 128(2), pp. 326–331. [CrossRef]
Petkovsek, M. , and Dulaz, M. , 2013, “ IR Measurements of the Thermodynamic Effects in Cavitating Flow,” Int. J. Heat Fluid Flow, 44, pp. 756–763. [CrossRef]
Petkovsek, M. , and Dulaz, M. , 2017, “ Observing the Thermodynamic Effects in Cavitating Flow by IR Thermography,” Exp. Therm. Fluid Sci., 88, pp. 450–460. [CrossRef]
Yamaguchi, Y. , and Iga, Y. , 2014, “ Thermodynamics Effects on Cavitation in High Temperature Water,” ASME Paper No. FEDSM2014-21433.
Iga, Y. , Ochiai, N. , Yoshida, Y. , and Ikohagi, T. , 2009, “ Numerical Investigation of Thermodynamic Effect on Unsteady Cavitation in Cascade,” Seventh International Symposium on Cavitation, Ann Arbor, MI, Aug. 17–22, Paper No. CAV2009-78. https://deepblue.lib.umich.edu/handle/2027.42/84272
Hosangadi, A. , and Ahuja, V. , 2005, “ Numerical Study of Cavitation in Cryogenic Fluids,” ASME J. Fluids Eng., 127(2), pp. 267–281. [CrossRef]
Utturkar, Y. , Wu, Y. J. , and Wang, Y. G. , 2005, “ Recent Progress in Modeling of Cryogenic Cavitation for Liquid Rocket Propulsion,” Prog. Aerosp. Sci., 41(7), pp. 558–608. [CrossRef]
Tseng, C.-C. , and Shyy, W. , 2009, “ Turbulence Modeling for Isothermal and Cryogenic Cavitation,” AIAA Paper No. 2009-1215.
Long, X. , Liu, Q. , Ji, B. , and Lu, Y. , 2017, “ Numerical Investigation of Two Typical Cavitation Shedding Dynamics Flow in Liquid Hydrogen With Thermodynamics Effects,” Int. J. Heat Mass Transfer, 109, pp. 879–893. [CrossRef]
Xue, L. , Ruan, Y. , Liu, X. , Cao, F. , and Hou, Y. , 2017, “ The Influence of Cavitation on the Flow Characteristic of Liquid Nitrogen Through Spary Nozzle: A CFD Study,” Cryogenics, 86, pp. 24–56. [CrossRef]
Chen, T. , Huang, B. , Wang, G. , and Zhao, X. , 2016, “ Numerical Study of Cavitating Flows in a Wide Range of Water Temperature With Special Emphasis on Two Typical Cavitation Dynamics,” Int. J. Heat Mass Transfer, 101, pp. 886–900. [CrossRef]
Zhang, S. , Li, X. , and Zhu, Z. , 2018, “ Numerical Simulation of Cryogenic Cavitating Flow by an Extended Transport Based Cavitation Model With Thermal Effects,” Cryogenics, 92, pp. 98–104. [CrossRef]
Tsuda, S. , Tani, N. , and Yamanishi, N. , 2012, “ Development and Validation of a Reduced Critical Radius Model for Cryogenic Cavitation,” ASME J. Fluids Eng., 134(5), p. 051301. [CrossRef]
Stepanoff, A. J. , 1964, “ Cavitation Properties of Liquids,” ASME J. Eng. Power, 86(2), pp. 195–200. [CrossRef]
Iga, Y. , Nohmi, M. , Goto, A. , Shin, B. R. , and Ikohagi, T. , 2003, “ Numerical Study of Sheet Cavitation Breakoff Phenomenon on a Cascade Hydrofoil,” ASME J. Fluids Eng., 125(4), pp. 643–651. [CrossRef]
Iga, Y. , Nohmi, M. , Goto, A. , and Ikohagi, T. , 2004, “ Numerical Analysis of Cavitation Instabilities Arising in the Three-Blade Cascade,” ASME J. Fluids Eng., 126(3), pp. 419–429. [CrossRef]
Chen, H. T. , and Collins, R. , 1971, “ Shock Wave Propagation Past on Ocean Surface,” J. Comput. Phys., 7(1), pp. 89–101. [CrossRef]
Sugawara, S. , 1993, “ New Steam Table,” J. Jpn. Soc. Mech. Eng., 35(186), pp. 999–1004.
Van Itterbeek, A. , Verbeke, O. , Theewes, F. , Staes, K. , and de Boelpaep, J. , 1964, “ The Difference in Vapour Pressure Between Normal and Equilibrium Hydrogen. Vapour Pressure of Normal Hydrogen Between 200K and 320K,” Physica, 30(6), pp. 1238–1244. [CrossRef]
Wilcox, D. C. , 1994, Turbulence Modeling for CFD, DCW Industries, La Cañada Flintridge, CA.
Beattie, D. R. H. , and Whally, P. B. , “ A Simple Two-Phase Frictional Pressure Drop Calculation Method,” Int. J. Multiphase Flow, 8(1), pp. 83–87. [CrossRef]
Karplus, H. B. , 1957, “ The Velocity of Sound in a Liquid Containing Gas Bubbles,” J. Acoust. Soc. Am., 29(11), p. 1261.
Maccormack, R. W. , 1969, “ The Effect of Viscosity in Hyper-Velocity Impact Cratering,” Fourth Aerodynamic Testing Conference, Cincinnati, OH, April 30–May 2, pp. 69–354.
Yee, H. C. , 1987, “ Upwind and Symmetric Shock—Capturing Schemes,” National Aeronautics and Space Administration, Ames Research Center Moffett Field, CA, Report No. NASA-TM-89464. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19870014712.pdf
Menter, F. R. , and Esch, T. , 2001, “ Elements of Industrial Heat Transfer Predictions,” 16th Brazilian Congress of Mechanical Engineering (COBEM), Uberlandia, Brazil, Nov. 26–30, pp. 118–127.
Rouse, H. , and McNown, J. S. , 1948, Cavitation and Pressure Distribution Head Forms at Zero Angle of Yaw, State University of Iowa, Iowa City, IA.
Hosangadi, A. , and Ahuja, V. , “ A New Unsteady Model for Dense Cloud Cavitation in Cryogenic Fluids,” AIAA Paper No. 2005-5347.
Watanabe, S. , Hidaka, T. , Horiguchi, H. , Furukawa, A. , and Tsujimoto, Y. , 2006, “ Steady Analysis of the Thermodynamics Effect of Partial Cavitation Using the Singularity Method,” ASME J. Fluids Eng., 129(2), pp. 121–127. [CrossRef]
Anh, D. L. , and Iga, Y. , 2017, “ Simplified Modeling of Cavitating Flow With Thermodynamic Effects for Homogeneous Model,” International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Maui, HI, Dec. 16–21, p. 404.

Figures

Grahic Jump Location
Fig. 1

Relation between sound speed and vapor void fraction in water [26] and liquid nitrogen

Grahic Jump Location
Fig. 2

Comparison of time-averaged surface pressure distributions on the hemispherical head-form [30]

Grahic Jump Location
Fig. 3

Shape and computational grid for 2D quarter hydrofoil [2]

Grahic Jump Location
Fig. 4

The normalized pressure, density, and vapor void fraction along the cross section at x =2.4 cm (left) and the contour of vapor void fraction (right) with isothermal calculation in run 290C between coarse grid, moderate grid, and fine grid

Grahic Jump Location
Fig. 5

Time-averaged pressure profile in isothermal cal. and our model

Grahic Jump Location
Fig. 6

The contours of vapor void fraction, evaporation rate (kg m−3 s−1), condensation rate (kg m−3 s−1), and temperature (K) with isothermal cal. and our model

Grahic Jump Location
Fig. 7

Time-averaged evaporation (left) and condensation (right) rates on the hydrofoil surface in run 290C between isothermal calculation and our model

Grahic Jump Location
Fig. 8

Time-averaged surface pressure and temperature distribution in runs 290C, 293A, and 296B using our model

Grahic Jump Location
Fig. 9

Time-averaged surface pressure and temperature in run 290C with different sets of empirical constants (Ce − Cc)

Grahic Jump Location
Fig. 10

The time-averaged surface pressure and temperature distribution in run 290C with cq = 0

Grahic Jump Location
Fig. 11

Comparison of the time-averaged surface pressure and temperature distributions in runs 290C, 293A, and 296B between the full heat input case cq = 1 and the reduced heat input case cq = 0.8

Grahic Jump Location
Fig. 12

Comparison of the time-averaged surface pressure and temperature distributions in runs 247B and 248C between the full heat input case cq = 1 and the reduced heat input case cq = 0.8

Grahic Jump Location
Fig. 13

Comparison of pressure distribution between Tsuda's model and our model

Grahic Jump Location
Fig. 14

Comparison of temperature profiles obtained using Tsuda's model and our model

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In