Research Papers: Techniques and Procedures

Turbulence Modeling of Cavitating Flows in Liquid Rocket Turbopumps

[+] Author and Article Information
Karthik V. Mani

Spacecraft Department,
German Aerospace Center (DLR),
Bunsenstr. 10,
Göttingen 37073, Germany;
Space Systems Engineering,
Delft University of Technology,
Kluyverweg 1,
Delft 2629, The Netherlands
e-mail: karthikvenkateshmani@gmail.com

Angelo Cervone

Space Systems Engineering,
Delft University of Technology,
Kluyverweg 1,
Delft 2629, The Netherlands
e-mail: a.cervone@tudelft.nl

Jean-Pierre Hickey

Spacecraft Department,
German Aerospace Center (DLR),
Bunsenstr. 10,
Göttingen 37073, Germany;
Department of Mechanical and
Mechatronics Engineering,
University of Waterloo,
200 University Avenue West,
Waterloo, ON N2L 3G1, Canada
e-mail: jean-pierre.hickey@uwaterloo.ca

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 3, 2016; final manuscript received June 28, 2016; published online September 14, 2016. Assoc. Editor: Matevz Dular.

J. Fluids Eng 139(1), 011301 (Sep 14, 2016) (10 pages) Paper No: FE-16-1135; doi: 10.1115/1.4034096 History: Received March 03, 2016; Revised June 28, 2016

An accurate prediction of the performance characteristics of cavitating cryogenic turbopump inducers is essential for an increased reliance on numerical simulations in the early turbopump design stages of liquid rocket engines (LRE). This work focuses on the sensitivities related to the choice of turbulence models on the cavitation prediction in flow setups relevant to cryogenic turbopump inducers. To isolate the influence of the turbulence closure models for Reynolds-Averaged Navier–Stokes (RANS) equations, four canonical problems are abstracted and studied individually to separately consider cavitation occurring in flows with a bluff body pressure drop, adverse pressure gradient, blade passage contraction, and rotation. The choice of turbulence model plays a significant role in the prediction of the phase distribution in the flow. It was found that the sensitivity to the closure model depends on the choice of cavitation model itself; the barotropic equation of state (BES) cavitation models are far more sensitive to the turbulence closure than the transport-based models. The sensitivity of the turbulence model is also strongly dependent on the type of flow. For bounded cavitation flows (blade passage), stark variations in the cavitation topology are observed based on the selection of the turbulence model. For unbounded problems, the spread in the results due to the choice of turbulence models is similar to noncavitating, single-phase flow cases.

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Sutton, G. , and Bilbarz, O. , 2010, Rocket Propulsion Elements, 7th ed., Wiley, New York.
Wu, Y. , Li, S. , Liu, S. , Dou, H.-S. , and Qian, Z. , 2013, Vibration of Hydraulic Machinery, Springer, Heidelberg, Germany.
Brennen, C. E. , 2013, “ A Review of the Dynamics of Cavitating Pumps,” ASME J. Fluids Eng., 135(6), p. 061301. [CrossRef]
Pace, G. , Valentini, D. , Pasini, A. , Torre, L. , Fu, Y. , and d'Agostino, L. , 2015, “ Geometry Effects on Flow Instabilities of Different Three-Bladed Inducers,” ASME J. Fluids Eng., 137(4), p. 041304. [CrossRef]
Coutier-Delgosha, O. , Caignaert, G. , Bois, G. , and Leroux, J. , 2012, “ Influence of the Blade Number on Inducer Cavitating Behavior,” ASME J. Fluids Eng., 134(8), p. 081304. [CrossRef]
Stripling, L. , and Acosta, A. , 1962, “ Cavitation in Turbopumps—Part 1,” ASME J. Fluids Eng., 84(3), pp. 326–338.
Cervone, A. , Torre, L. , Pasini, A. , and d'Agostino, L. , 2009, “ Cavitation and Turbopump Hydro-Dynamics Research at Alta Spa and Pisa University,” Fluid Machinery and Fluid Mechanics, Springer, Heidelberg, Germany, pp. 80–88.
Cervone, A. , Testa, R. , Bramanti, C. , Rapposelli, E. , and D'Agostino, L. , 2005, “ Thermal Effects on Cavitation Instabilities in Helical Inducers,” J. Propul. Power, 21(5), pp. 893–899. [CrossRef]
Torre, L. , Cervone, A. , Pasini, A. , and d'Agostino, L. , 2011, “ Experimental Characterization of Thermal Cavitation Effects on Space Rocket Axial Inducers,” ASME J. Fluids Eng., 133(11), p. 111303. [CrossRef]
d'Agostino, L. , 2013, Turbomachinery Developments and Cavitation (VKI Lecture Series on Fluid Dynamics Associated to Launcher Developments), von Karman Institute of Fluid Dynamics, Rhode-Saint-Genese, Belgium, pp. 15–17.
Tsujimoto, Y. , Yoshida, Y. , Maekawa, Y. , Watanabe, S. , and Hashimoto, T. , 1997, “ Observations of Oscillating Cavitation of an Inducer,” ASME J. Fluids Eng., 119(4), pp. 775–781. [CrossRef]
Kikuta, K. , Yoshida, Y. , Watanabe, M. , Hashimoto, T. , Nagaura, K. , and Ohira, K. , 2008, “ Thermodynamic Effect on Cavitation Performances and Cavitation Instabilities in an Inducer,” ASME J. Fluids Eng., 130(11), p. 111302. [CrossRef]
Hickel, S. , 2015, “ DNS and LES of Two-Phase Flows With Cavitation,” Direct and Large-Eddy Simulation IX, Springer, Heidelberg, Germany.
Pope, S. B. , 2000, Turbulent Flows, Cambridge University Press, Cambridge, UK.
Payri, R. , Tormos, B. , Gimeno, J. , and Bracho, G. , 2010, “ The Potential of Large Eddy Simulation (LES) Code for the Modeling of Flow in Diesel Injectors,” Math. Comput. Modelling, 52(7), pp. 1151–1160. [CrossRef]
Ahuja, V. , Hosangadi, A. , and Arunajatesan, S. , 2001, “ Simulations of Cavitating Flows Using Hybrid Unstructured Meshese,” ASME J. Fluids Eng., 123(2), pp. 331–340. [CrossRef]
Wang, Y. , Huang, C. , Fang, X. , Yu, X. , Wu, X. , and Du, T. , 2015, “ On the Cloud Cavitating Flow Over a Submerged Axisymmetric Projectile and Comparison Between 2D RANS and 3D LES Methods,” ASME J. Fluids Eng., 138(6), p. 061102. [CrossRef]
Goncalves, E. , 2011, “ Numerical Study of Unsteady Turbulent Cavitating Flows,” Eur. J. Mech. B., 30(1), pp. 26–40. [CrossRef]
Decaix, J. , and Goncalvès, E. , 2012, “ Time-Dependent Simulation of Cavitating Flow With K-l Turbulence Models,” Int. J. Numer. Methods Fluids, 68(8), pp. 1053–1072. [CrossRef]
Decaix, J. , 2012, “ Modlisation et Simulation de la Turbulence Compressible en Milieu Diphasique: application aux Coulements Cavitants Instationnaire,” Ph.D thesis, University of Grenoble, Grenoble, France.
Wu, J. , Utturkar, Y. , and Shyy, W. , 2003, “ Assessmentof Modeling Strategies for Cavitating Flow Around a Hydrofoil,” Fifth International Symposium on Cavitation, Osaka, Japan, Nov. 1–4, pp. 1–4.
Wu, J. , Wang, G. , and Shyy, W. , 2005, “ Time-Dependent Turbulent Cavitating Flow Computations With Interfacial Transport and Filter-Based Models,” Int. J. Numer. Methods Fluids, 49(7), pp. 739–761. [CrossRef]
Mashayek, F. , and Pandya, R. , 2003, “ Analytical Description of Particle/Droplet-Laden Turbulent Flows,” Prog. Energy Combust. Sci., 29(4), pp. 329–378. [CrossRef]
Cokljat, D. , Slack, M. , Vasquez, S. , and Bakker, A. , 2006, “ Reynolds-Stress Model for Eulerian Multiphase,” Progress Comput. Fluid Dyn., 6(1), pp. 168–178. [CrossRef]
Beishuizen, N. , Naud, B. , and Roekaerts, D. , 2007, “ Evaluation of a Modified Reynolds Stress Model for Turbulent Dispersed Two-Phase Flows Including Two-Way Coupling,” Flow Turbul. Combust., 79(3), pp. 321–341. [CrossRef]
Wang, J. , Wang, Y. , Liu, H. , Huang, H. , and Jiang, L. , 2015, “ An Improved Turbulence Model for Predicting Unsteady Cavitating Flows in Centrifugal Pump,” Int. J. Numer. Methods Heat Fluid Flow, 25(5), pp. 1198–1213. [CrossRef]
Weller, H. G. , Tabor, G. , Jasak, H. , and Fureby, C. , 1998, “ A Tensorial Approach to Computational Continuum Mechanics Using Object-Oriented Techniques,” Comput. Phys., 12(6), pp. 620–631.
Brennen, C. E. , 2005, Fundamentals of Multiphase Flow, Cambridge University Press, Cambridge, UK.
Goncalvès, E. , 2014, “ Modeling for Non Isothermal Cavitation Using 4-Equation Models,” Int. J. Heat Mass Transfer, 76, pp. 247–262. [CrossRef]
Kunz, R. F. , Boger, D. A. , Stinebring, D. R. , Chyczewski, T. S. , Lindau, J. W. , Gibeling, H. J. , Venkateswaran, S. , and Govindan, T. , 2000, “ A Preconditioned Navier–Stokes Method for Twophase Flows With Application to Cavitation Prediction,” Comp. Fluids, 29(8), pp. 849–875. [CrossRef]
Senocak, I. , and Shyy, W. , 2002, “ A Pressure-Based Method for Turbulent Cavitating Flow Computations,” J. Comput. Phys., 176(2), pp. 363–383. [CrossRef]
Wilcox, D. C. , 1998, Turbulence Modeling for CFD, Vol. 2, DCW Industries, La Canada, CA.
Mani, K. , 2015, “ Turbulence Modelling of Cavitating Flows in Cryogenic Turbopumps,” Master's thesis, Delft University of Technology, Delft, The Netherlands.
Rouse, H. , and McNown, J. S. , 1948, Cavitation and Pressure Distribution: Head Forms at Zero Angle of Yaw, State University of Iowa, Technical Report No. 420.
Hord, J. , 1973, “ Cavitation in Liquid Cryogens: Hydrofoil II,” National Aeronautics and Space Administration, NASA Technical Report No. NASA-CR-2156.
Kim, J. , and Song, S. J. , 2016, “ Measurement of Temperature Effects on Cavitation in a Turbopump Inducer,” ASME J. Fluids Eng., 138(1), p. 011304. [CrossRef]
Sipila, T. , Sanchez-Caja, A. , and Siikonen, T. , 2014, “ Eddy Vorticity in Cavitating Tip Vortices Modelled by Different Turbulence Models Using the RANS Approach,” 11th World Congress on Computational Mechanics (WCCM XI), pp. 4741–4752.
Launder, B. E. , and Spalding, D. , 1974, “ The Numerical Computation of Turbulent Flows,” Comput. Methods Appl. Mech. Eng., 3(2), pp. 269–289. [CrossRef]
Launder, B. , and Sharma, B. , 1974, “ Application of the Energy-Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disc,” Lett. Heat Mass Transfer, 1(2), pp. 131–137. [CrossRef]
Yakhot, V. , Orszag, S. , Thangam, S. , Gatski, T. , and Speziale, C. , 1992, “ Development of Turbulence Models for Shear Flows by a Double Expansion Technique,” Phys. Fluids, 4(7), pp. 1510–1520. [CrossRef]
Launder, B. , Reece, G. J. , and Rodi, W. , 1975, “ Progress in the Development of a Reynolds-Stress Turbulence Closure,” J. Fluid Mech., 68(3), pp. 537–566. [CrossRef]
Charriere, B. , Decaix, J. , and Goncalves, E. , 2015, “ A Comparative Study of Cavitation Models in a Venturi Flow,” Eur. J. Mech. B, 49(Part A), pp. 287–297. [CrossRef]
Reboud, J. , Coutier-Delgosha, O. , Pouffary, B. , and Fortes-Patella, R. , 2003, “ Numerical Simulation of Unsteady Cavitation Flows: Some Applications and Open Problems,” Fifth International Symposium on Cavitation, Osaka, Japan, Nov. 1–5.
Utturkar, Y. , Wu, J. , Wang, G. , and Shyy, W. , 2005, “ Recent Progress in Modeling of Cryogenic Cavitation for Liquid Rocket Propulsion,” Prog. Aerosp. Sci., 41(7), pp. 558–608. [CrossRef]
Singhal, A. K. , Athavale, M. M. , Li, H. , and Jiang, Y. , 2002, “ Mathematical Basis and Validation of the Full Cavitation Model,” ASME J. Fluids Eng., 124(3), pp. 617–624. [CrossRef]
Jakirlic, S. , Hanjalic, K. , and Tropea, C. , 2002, “ Modeling Rotating and Swirling Turbulent Flows: A Perpetual Challenge,” AIAA J., 40(10), pp. 1984–1996. [CrossRef]


Grahic Jump Location
Fig. 3

Wall normal profiles of the (a) void-fraction and (b) eddy viscosity at x = 2 mm and 10 mm. The resolved (y+<70) wall with (square) and without (circle) the wall function is compared and shows very good agreement. The baseline case (dashed lines) is compared for reference.

Grahic Jump Location
Fig. 2

Grid convergence study of the hydrofoil: (a) contour plot showing the time-averaged pressure (lines) and density and (b) quantitative comparison of normalized pressure and density at x = 5 mm

Grahic Jump Location
Fig. 1

Simplification of a three-dimentional (3D) inducer geometry into canonical flow problems: (top left) bluff body cavitation at the inducer nose—hemispherical headform [34], (top right) attached leading edge cavitation—hydrofoil [35], (bottom right) inducer blade passage cavitation—2D Venturi [29], and (bottom left) rotational flow cavitation—3D rotating ship propeller (Center image reprinted with permission from American Institute of Aeronautics and Astronautics (AIAA) Copyright 1985 Copyright Clearance Center)

Grahic Jump Location
Fig. 4

Independence of the time integration error on the baseline hydrofoil case. Top half of the figure shows the comparison of the time-averaged void fraction for the baseline case at Δt≈10−6 s (based on CFL number) and the small time step simulation at Δt≈10−7 s (fixed time step). The bottom half shows an instantaneous snapshot of the flow to illustrate the inherent unsteadiness of the flow.

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Fig. 5

Baseline validation for BES and TES of the hemispherical headform case

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Fig. 6

Hemispherical headform normalized pressure distributions—turbulence model influence

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Fig. 7

Schematic difference between the thermodynamic and turbulence coupling between the BES and TES. The computed pressure is directly used in BES to compute the density which directly couples back the cavitation prediction. On the other hand, the velocity is introduced as a convective term in the TES model. It should be noted that the schematic coupling is for illustrative purposes only, and many of the more nuanced coupling has been overlooked for the sake of simplicity.

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Fig. 8

Hydrofoil normalized pressure distributions—turbulence model influence: (a) normalized pressure distribution—BES and (b) normalized pressure distribution—TES

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Fig. 9

Two-dimensional venturi liquid volume fraction αl versus distance x distribution; wall-normal αl distributions; and αl contours for k–ω SST, k−ε, k−ω, RSM, and RNG- k−ε models: (a) α versus x, (b) station 1: x = 0.014 m, (c) station 2: x = 0.024 m, (d) station 3: x = 0.048 m, (e) k–ω SST, (f) k–ε, (g) k–ω, (h) RSM, (i) Laminar, and (j) RNG k−ε

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Fig. 10

Rotating propeller phase distribution contours at αl=0.5. The direction of rotation is clockwise. The contours are shaded according to the magnitude of velocity: (a) k–ω SST, (b) k–ε, (c) k–ω, (d) RSM, and (e) RNG k–ε.




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