By Shin Hyung Rhee, Fluent Inc.; Takafumi Kawamura, Department Environmental and Ocean Engineering, University of Tokyo, Tokyo, Japan; and Huiying Li, Fluent Inc.

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The propeller geometry with hub and boss; an open-water test configuration was used, so the flow direction is from the lower-left to the upper-right

Marine propeller researchers and designers have made numerous efforts to reduce the effects of cavitation, which degrades propeller performance, erodes blade surfaces, produces noise, and causes vibration on the ship hull. However, with increasing demand for heavily loaded propellers, the occurrence of cavitation is unavoidable. Therefore, the accurate prediction of cavitation is becoming more important than ever to ensure better propulsor designs. Model tests provide valuable insights into the cavitation physics in various predetermined conditions, but they cost a significant amount of money and are vulnerable to slight flow condition changes inside cavitation tunnels.

The surface grid used for the one-quarter, rotationally periodic model

Computational methods for cavitation have been studied for over two decades. The methods can be largely categorized into two groups: singlephase modeling with cavitation interface tracking, and multiphase modeling with an embedded cavitation interface. The former approach has been widely adopted for inviscid flow solution methods. These methods have evolved significantly and many successful application results have been presented. In many cases, however, they require cumbersome iterative procedures and a considerable amount of preliminary knowledge, such as cavity closure conditions. The latter approach can be adopted for more general viscous flow solution methods, such as the Reynolds-averaged Navier-Stokes (RANS) equation solvers. This approach is more general for three-dimensional and unsteady flows. It can include the effects of compressible vapor and gas, turbulence fluctuations, and a bubbly phase within the mixture, although a closure equation is required to connect the density to the other variables. Many favorable results have been reported and various improvement efforts are underway; however, applications and validations of the methods for realistic marine propeller geometries are rare.

Table 1: Comparison of thrust coefficient, K_T, and torque coefficient, K_Q, for a cavitating propeller

The cavitation model in FLUENT was employed in the present study. It is based on the so-called "full cavitation model" by Singhal et al. (1). This model accounts for all first-order effects, such as phase change, bubble dynamics, turbulent pressure fluctuations, and non-condensable gases. However, unlike the original approach, which assumes single-phase and variable fluid density flows, the present model is under the framework of multiphase flows and has the capability of accounting for the effects of the slip velocities between liquid and gaseous phases. A single-fluid mixture model is employed, in which the continuity and momentum (and energy, if necessary) equations for the mixture are solved, along with the volume fraction equation for the secondary phases, and algebraic expressions for the slip velocities. The mass transfer through cavitation is handled by a transport equation for the vapor mass fraction.

For the validation of non-cavitating and cavitating marine propeller flows, a four-bladed marine propeller, MP 017, was selected. The propeller geometry was designed at the University of Tokyo. The flow can be characterized by a flat pressure distribution on the backside and better cavitation characteristics than the conventional MAU type propeller on which it is based. The computational domain was created as one passage surrounding a blade: the inlet is 1.5D upstream, where D is the propeller diameter; the exit is 3.5D downstream; solid surfaces on the blade and hub are centered at the coordinate system origin and aligned with uniform inflow; the outer boundary is 1.4D from the hub axis; and two rotationally periodic boundaries, subtending a 90° angle, form the boundaries in between.

Thrust (KT) and torque (K_Q) coefficients vs. cavitation number, s

A hybrid grid of about 187,000 cells was generated using GAMBIT and TGrid. First, the blade surface was meshed with triangles. The region around the root, tip, and blade edges was meshed with smaller triangles (with sides of approximately 0.001D) while the inner region was filled with triangles of appropriately increased size. Once the blade surface was meshed, the other surfaces were meshed with larger triangles, (with sides of up to 0.1D). In order to resolve the turbulent boundary layer, four layers of prismatic cells were grown from the blade and hub surfaces. The first cell height off the solid surface was approximately 10^-5D, which corresponds to a y+ value in the range of 3 to 50. Using a stretching ratio of about 1.1, the remaining region in the domain was filled with tetrahedral cells.

For the cavitating marine propeller cases, the cavitation model was activated. Boundary conditions were set to simulate the flow around a rotating propeller in open water: on the inlet boundary, velocity components for a uniform stream were imposed with a turbulence intensity of 1%; on the blade and hub surfaces, a no-slip condition was imposed; on the outer boundary, a slip boundary condition was used; on the periodic boundaries, rotational periodicity was ensured; and on the exit boundary, the pressure was set to correspond to the given cavitation number, while all other variables were extrapolated.

The simulations were used to predict the thrust (K_T) and torque (K_Q) coefficients as a function of cavitation number:

σ = (p - p_v) / (1/2 ρv²)

(where p and p_v are the freestream and vapor pressures, respectively) at an advance ratio ( J = freestream speed/tip speed) of 0.2, and the results were compared with measured values. (See Table 1.) The thrust breakdown is one of the major issues in cavitating propellers. Both K_T and K_Q start decreasing upon the onset of cavitation at σ = 2.0. This behavior is quantitatively well reproduced in the present simulation.

Cavity shape comparison

A computed iso-surface of vapor volume fraction of 0.1 and observed cavity shape were compared for the case of J = 0.2 and σ = 2.0, and good agreement was noted. It was observed, however, that the computed cavity shape showed an abrupt termination right behind the tip, and furthermore, that the vortex cavity was missing. These were attributed to the insufficient grid resolution in the region, which is entailed from the transition from the prismatic boundary layer cells to the tetrahedral outer cells. Note, however, that the resolution of the tip vortex cavity is not of primary concern in the present study, since it has little or no impact on the overall propeller performance.

The results suggest that the present approach is practicable for actual cavitating propeller design procedures without lengthy preprocessing or significant preliminary knowledge of the flow field.

References:

1. A.K. Singhal, M.M. Athavale, H.Y. Li, Y. Jiang, J Fluids Eng Trans ASME, 2002, 124, 617-624.

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