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Research Papers: Multiphase Flows

# 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,
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

## Abstract

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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## Figures

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)

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

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.

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.

Fig. 5

Baseline validation for BES and TES of the hemispherical headform case

Fig. 6

Hemispherical headform normalized pressure distributions—turbulence model influence

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.

Fig. 8

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

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

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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