### Tech Briefs

Simulating Cavitation

Cavitation occurs in many industrial applications such as in pumps, injectors, and around propellers and underwater vehicles. This phenomenon has been receiving attention because it can cause significant damage to solid structures and generate much noise. Cavitating flows are characterized by the phase change between liquid and vapor that occurs when the local pressure drops below the vapor pressure of the liquid [1]. In industrial applications, cavitation often occurs in turbulent flows accompanied by rapid phase changes. Over the cavitation interfaces, the density and viscosity of the fluids can have very strong changes. These strong variations, together with turbulent flows which have a wide range of length and time scales, make the simulation of cavitating flows very challenging.

In this Brief, we demonstrate the simulation of cavitating flows using ADINA in three examples. The cavitation models are built using the Volume-of-Fluid (VOF) method.

The first example is a 2D axisymmetric hemispherical cavitation problem, shown schematically in Figure 1.

**Figure 1** Schematic of the 2D axisymmetric hemispherical cavitation problem

The material properties are listed in Table 1 below.

**Table 1** Material properties of the 2D axisymmetric hemispherical cavitation problem

Vapor density |
0.017 kg/m^{3} |

Vapor viscosity | 10^{-5} kg/(ms) |

Liquid density | 998 kg/m^{3} |

Liquid viscosity | 10^{-3} kg/(ms) |

Vapor pressure of liquid | 2339 Pa |

The Reynolds number for this 2D axisymmetric cavitation problem is

where and are the liquid density and liquid dynamic viscosity respectively, is the diameter of the hemispherical cylinder, and is the velocity at the inlet. The density and viscosity ratios for this problem are 58706 and 100, respectively. A pressure boundary condition is specified at the outlet. Its value () is obtained from the cavitation number

where is the vapor pressure of the liquid. Simulations have been carried out with three different cavitation numbers ( = 0.2, 0.3 and 0.4).

Figures 2 to 4 show the simulation results near the cavitation region computed by using the ZGB model [2]: the VOF contours, the velocity profile, and the pressure contours, respectively, for = 0.2. The cavitation region is shown in blue in the VOF contour plot of Figure 2. The re-entry jet at the trailing edge of the cavitation region can be seen in Figure 3. This re-entry jet is caused by the large pressure increase at the trailing edge of the cavitation region, see Figure 4.

**Figure 2** VOF contours (blue represents vapor and red represents liquid)

**Figure 3** Velocity profile

**Figure 4** Pressure contours

The computed and experimental [4] pressure coefficient distributions (the experiment of course performed in 3D) for different cavitation numbers are compared in Figure 5. There is excellent agreement between the computational and experimental results.

**Figure 5** Pressure coefficient distributions for the first example with different cavitation numbers: (a) = 0.2, (b) = 0.3 and (c) = 0.4. The pressure coefficient is defined as . s/D is the dimensionless distance, where s is the distance along the surface line starting from the leading point of the hemispherical cylinder in the axis direction, and D is the hemispherical cylinder diameter, see Figure 1.

We next solve the problem considered above in 3D using two different cavitation models (the ZGB model [2] and the Kunz model [3]). The 3D geometry is generated by revolving the 2D geometry about the axis of symmetry, as shown in Figure 6a. The material properties are the same as those of the 2D case, and the boundary conditions are also the same as the 2D setup but adapted to the 3D configuration. The computational results are plotted in Figure 6b and 6c (VOF contours) and Figure 7 (pressure coefficient distributions), for = 0.3. Again, we see that ADINA also works well for the simulation of 3D cavitating flows.

(a)

(b)

(c)

**Figure 6** 3D hemispherical cylinder cavitating flow: (a) schematic, and VOF contours on a cutting plane,

**Figure 7** Pressure coefficient of the 3D hemispherical cylinder cavitating flow, *σ* = 0.3

The third example is a 2D cavitating flow around an NACA0015 hydrofoil, shown schematically in Figure 8, with the material properties listed in Table 2. The Reynolds number based on the chord length is 1.09 x 10^{6}. The density and viscosity ratios for this case are 43391 and 110.6, respectively. The ZGB model [2] is used for this simulation and the cavitation number is 1.0.

**Figure 8** The schematic of the 2D NACA0015 hydrofoil cavitating flow problem (not to scale). The hydrofoil chord length is *C* = 0.2m, and the angle of attack is 6°. The cavitation number for this problem is 1.0.

**Table 2** Material properties of the 2D NACA0015 hydrofoil cavitating flow problem

Vapor density |
0.023 kg/m^{3 } |

Vapor viscosity | 9.95 x 10^{-6} kg/(ms) |

Liquid density | 998 kg/m^{3} |

Liquid viscosity | 1.10 x 10^{-3} kg/(ms) |

Vapor pressure of liquid | 2339 Pa |

In the movie above, the transient dynamics of this cavitating flow can be clearly observed on the suction side of the hydrofoil. The typical feature of this dynamic process is that the cavitation occurs near the leading edge of the hydrofoil, and the vapor bubble travels a short distance along the hydrofoil surface before breaking into small bubbles that later collapse.

ADINA can be used to accurately simulate cavitating flows with very large density and viscosity ratios, making it useful in many industrial applications where cavitation control and reduction are important.

**References**

- C. E. Brennen.
*Cavitation and Bubble Dynamics*, Oxford University Press, 1995. - P. J. Zwart, A. G. Gerber, and T. Belamri. "A Two-Phase Flow Model for Predicting Cavitation Dynamics",
*Proceedings of ICMF 2004 International Conference on Multiphase Flow*, Yokohama, Japan, 2004. -
R. F. Kunz, D. A. Boger, D. R. Stinebring, T. S. Chyczewski, J. W. Lindau, H. J. Gibeling, S. Venkateswaran, and T. R. Govindan. "A Preconditioned Navier-Stokes Method for Two-Phase Flows with Application to Cavitation Prediction",
*Computers & Fluids*, 29 (2000) 849-875. -
H. Rouse and J. S. McNown. "Cavitation and Pressure Distribution, Head Forms at Zero Angle of Yaw",
*Studies in Engineering, Bulletin 32*, State University of Iowa, Iowa, 1948.

*Keywords:*

CFD, cavitation, ZGB model, Kunz model, NACA0015 hydrofoil