Numerical Simulation of Flow around a Podded Propeller

Wei Li1 and Chi Yang2 1School of Naval Architecture, Civil and Ocean Engineering, Shanghai Jiao Tong University

Shanghai, China

2Dept. of Computational and Data Sciences, George Mason University Fairfax, Virginia, USA

ABSTRACT In this paper the viscous steady flow around a podded propeller is simulated using two CFD tools. Specifically, an open source CFD toolbox, called OpenFOAM, is further developed to study the open water hydrodynamic performance of the podded propeller and the hydrodynamic interactions between the pod and the propeller. The standard k-ε turbulence model is used in the viscous flow simulation. In addition, the same simulation studies are also performed using commercial CFD software FLUENT. Numerical results obtained using two CFD tools are compares with experimental measurements. Fairly good agreement is obtained. The interaction between the strut and the propeller and the effect of the strut on the hydrodynamic performance are analyzed by comparing the flows around the podded propeller and the single propeller. KEY WORDS: Podded-propeller; OpenFOAM; viscous flow. INTRODUCTION Podded propellers have recently been widely used in modern commercial ships due to their relatively high efficiency and good sea-keeping ability. As a new type of propulsion, podded propellers usually have large hubs and good maneuverability. Podded propellers can reduce noise, vibration and the fuel consumption of a vessel with the proper design of the pod and the strut. The overall efficiency of a podded propulsion system can have a gain in the order of 2% to 4% over a conventional propeller. In addition, podded propellers can be used in dynamic positioning systems of floating structures to provide thrust in all horizontal directions by being mounted on the bottom of the hull. The performance of the podded propeller has been studied numerically and experimentally. For example, Mewis (1998) investigated the open water performance of podded propellers with different configurations. The test was performed to study the total propeller thrust and the total unit thrust, including scale effects leading to an accurate power prediction. The effective wake fraction and the blade thrust were also provided in this study. Poustoshniy et al. (1998) investigated the scaling problems of the pushing-mode podded propeller.

The numerical methods based on potential flow theory have been used widely and successfully to predict the performance of conventional propellers. The modified wake model must be assumed in order to predict the performance of podded propellers using potential-flow based numerical method. The potential-flow method was used to calculate the flow around podded propellers by Ghassemi and Allievi (1999), Yang and Ma (2003) and Ma et al. (2006) with a modified wake model. However, different wake models will affect the accuracy of the prediction directly. With the development of computer hardware and the numerical methods based on Euler/RANS solvers, many difficult and complex flow phenomenons can be modeled directly, including the detailed flow information in the wake of the flow around a propeller. Kinnas et al. (2004) applied the coupled Euler solver with a potential flow method to analyze the performance of podded propellers. Sanchez-Caja et al. (1999) and Li et al (2007) applied viscous flow methods to study the flow around a podded propeller. OpenFOAM (Open Field Operation and Manipulation) is an object oriented C++ toolbox for solving various systems of partial differential equations using the finite volume method on arbitrary control volume shapes and configurations. It includes preprocessing (grid generator, converters, manipulators, case setup), postprocessing (using OpenSource Paraview), and many specialized CFD solvers (http://www.openfoam.org). The features in OpenFOAM are comparable to what is available in the major commercial CFD codes. Some of the more specialized features that are included in OpenFOAM are: sliding grid, moving meshes, two-phase flow and fluid-structure interaction. Since OpenFOAM is an open-source code, it is possible to gain control over the exact implementations of different features and it is reasonably straightforward to implement new models and fit them into the whole code structure. Many researchers are using OpenFOAM, which allows international exchange of development. Based on the successful application of OpenFOAM in the simulation of the flow around a conventional propeller, the OpenFOAM is further developed in this study to investigate the open water hydrodynamic performance of the podded propeller. The open water performance results are compared to those measured in experiments and obtained by other software. The effect of strut on the performance of the podded propeller is analyzed and the hydrodynamic interactions between the pod and the propeller are studied in the present paper.

Proceedings of the Nineteenth (2009) International Offshore and Polar Engineering ConferenceOsaka, Japan, June 21-26, 2009Copyright © 2009 by The International Society of Offshore and Polar Engineers (ISOPE)ISBN 978-1-880653-53-1 (Set); ISSN 1098-618

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SOLUTION METHOD OpenFOAM is primarily designed to solve problems in continuum mechanics, i.e. the branch of mechanics concerned with the stresses in solids, liquids and gases and the deformation or flow of these materials. OpenFOAM is therefore based in three dimensional space and time and deals with physical entities described by tensors (http://www.openfoam.org). Finite volume methods are used in OpenFOAM CFD toolbox to solve systems of partial differential equations described on any 3D unstructured mesh of polyhedral cells. The incompressible flow solvers are developed within a robust, implicit, pressure-velocity, iterative solution framework. Discretization Schemes The finite volume method is used to solve the Reynolds-averaged Navier-Stokes (RANS) equations described on three dimensional unstructured polyhedral cells. The spatial discretization is defined in the solution domain by a set of points that fill and bound a region of space. The space domain is discretized into computational mesh on which the PDEs are subsequently discretized. Dependent variable and other properties are stored at the cell centre point P, and the cell is bounded by a set of flat faces, as shown in Fig. 1. In OpenFOAM there is no limitation on the number of faces bounding each cell, nor restriction on the alignment of each face. This kind of mesh is referred to as “arbitrarily unstructured”. Codes with arbitrarily unstructured meshes offer greater freedom in mesh generation and manipulation in particular when the geometry of the domain is complex. Most properties are defined at the cell centre points; some are defined at cell faces.

Fig. 1: Parameters in finite volume discretization A system of algebraic equations is generated in terms of discrete quantities defined at specific location in the flow domain (http://www.openfoam.org). For example, the convection term in RANS equations is integrated over a control volume and linearized as follows:

( ) ( ) ( ) ∑∑∫∫ =⋅=⋅=⋅∇f

ff

fffSV

FUUdSdVU φφρφρφρ S (1)

Where V is cell volume, Sf is surface area vector, and fφ represents

face field. The face field fφ can be evaluated using a variety of schemes. The Gamma scheme is a smooth and bounded blend between the second-order central differencing (CD) scheme and the first order

upwind differencing (UD) scheme. CD is used wherever it satisfies the boundedness requirements, and UD is used wherever CD is unbounded. In an attempt to preserve boundedness with reasonable accuracy, blended differencing (BD) scheme is used to combine UD and CD.

( )( ) ( )CDfUDff φγφγφ +−= 1 (2)

OpenFOAM has several implementations of the Gamma differencing scheme to select the blending coefficient γ . The smooth transition between the CD and UD schemes is controlled by a blending coefficient γ . The smaller value the sharper switch and the larger value the smoother switch between the schemes. For good resolution, this value should be kept as low as possible, while higher values are more numerically stable. To the steady flow problem the dissipation terms of RANS Equations are evaluated by taking the gradient of the resulting gradient field. And the gradient term is performed using the standard method of applying Gauss’s theorem to the volume integral. The explicit source terms are incorporated into an equation simply as a field of values. The multi-reference frame solver (MRFSimpleFoam) is developed to simulate the rotational parts and is available as part of OpenFOAM. The standard k-ε model with wall functions is used. In this case one frame attributed to different parts of geometry is defined. And there are two parts of fluid: one is surrounding the rotating propeller blades and the remaining is stationary. Structure of OpenFOAM OpenFOAM is a C++ library primarily to create executables, known as applications. Based on the standard applications provided in OpenFOAM, the user applications can be created and organized as Fig. 2. In the working directory the source code is called podpropeller.C and the header file with .H file extension are included. Each class used in the source code requires a class declaration contained in this .H header file. The Make subdirectory must contain two files, called files and options. The file options defines the full directory path to locate header files and library files used in the source code. The file files defines the full list of .C source files. The wmake command is executed to compile the source code.

Fig. 2: Directory structure of application

In OpenFOAM the format for input/output file is flexible. In the present study, the software GAMBIT is used to generate mesh and define boundary conditions. The mesh file is then exported and converted by OpenFOAM converter to generate the mesh file and other input data

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files which define initial condition, boundary condition, moving frame condition, differential schemes etc. required by OpenFOAM. These files are saved in pod-propeller directories. The software Fluent is used as postprocessing software in this study to obtain the performance results and display the detail flow information around the podded propeller. Geometrical Model The podded propeller considered in this study was designed at Shanghai Jiao Tong University (SJTU). The experiments were conducted at the cavitation tunnel of SJTU. This podded propeller is a puller-type podded propeller, which means that the propeller is fixed in front of the strut. The geometry parameters of the podded propeller shown in Fig. 3 are defined as follows, Number of Blades: 4 Diameter of Propeller: D = 0.24m

Pitch Ratio: (P/D)r = 0.7 = 1.270 Height of Strut 0.19m

Fig. 3: Podded propeller model

The geometric model is set up by software GAMBIT. The sketch of the flow domain is shown in Fig. 4. The whole podded propeller is laid inside one big cylindrical domain. The upstream inlet is located at 2D ahead of the propeller. The downstream outlet is located at the 5D behind the propeller. The length of the computational domain is 7D, and the diameter of the cylindrical computational domain is 5D.

Fig. 4: Sketch of computational domain

In order to define all boundary conditions correctly for OpenFOAM, there are two fluid parts defined in GAMBIT for the computational domain. The propeller part is surrounded by a small cylinder as shown in Fig. 5. The close look of the local domain near the podded propeller

is shown in Fig. 6. The fluid inside the small cylinder is defined as a rotating zone in GAMBIT so that the boundary conditions on the propeller blades can be correctly captured and converted to OpenFOAM. The rest of the fluid is stationary.

Fig. 5: Different fluid parts and boundary conditions

Fig. 6: The close look of the local domain near propeller

Grid The grid used in the open-water podded propeller case is generated by the GAMBIT software, and so are the boundary conditions. The mesh data are then exported as a file with .msh extension. There is a converter in OpenFOAM toolbox to convert the GAMBIT mesh data to the required grid data and boundary conditions. The surface grids are shown in Fig. 7. The grid dependence in simulating the podded propeller case was studied in author’s previous work (Li et al., 2009). Based on the grid density from the previous study, the grid points in the present study consist of 5,000 on the blade surface, 8,000 on the strut surface, and 1,335,726 in the entire computational domain. Specifically, the grid size near the leading edge and trailing edge of the propeller are controlled by the size function in GAMBIT in order to correctly capture the flow information.

Fig. 7: Surface grids

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Boundary Conditions In order to capture the rotating boundary condition by OpenFOAM converter, the following boundary conditions are specified in GAMBIT:

Inlet: Velocity_inlet Outlet: Pressure_outlet Farfield: Velocity_inlet Propeller: Wall Strut & Pod: Wall Slideface: Interior

which are corresponding to the boundary conditions shown in Fig. 5. It is noted that the “Slideface” is the surface of the small cylinder surrounding the propeller and its type is defined as “interior”. This is a virtual interface used to capture the moving boundary of the propeller blades. The podded propeller rotates along z-axis. After the GAMBIT mesh file is converted by OpenFOAM converter, the boundary conditions are specified on each boundary of the domain for OpenFOAM, which can be described as follows: • Inflow boundary condition

lowwvuwvu inf),,(),,( = , 0=∂∂

zp

• Outflow boundary condition

0),,(=

∂∂

zwvu

• Far field boundary condition

lowwvuwvu inf),,(),,( = , 0=∂∂np

• Propeller blade boundary condition 0=×Ω− rq

rvr

• Solid boundary condition except propeller blades

0=⋅nqrr

, 0=∂∂np

where ),,( wvuq =

r, and Ω

vis angular velocity vector and r

ris position

vector. COMPUTATIONAL RESULTS Validations The present OpenFOAM code and the numerical algorithms are validated by comparing the results with those measured at SJTU and obtained using Fluent. More detailed results, including experimental data, Fluent results and grid dependence studies can be found in authors’ previous work (Li et al., 2007; 2009). The following parameter and coefficients are defined to describe the numerical results discussed

hereafter:

Advance ratio: nDVJ 0=

Thrust coefficient: 42DnTKt

ρ=

Torque coefficient: 52Dn

QKqρ

=

Efficiency: π

η2J

KqKt

=

where T is the thrust, Q is the torque, ρ is the fluid density, n is the propeller rotating speed, D is the diameter of the propeller, and V0 is the uniform inflow speed. A puller-type podded propeller at zero degree angle of attack subject to the uniform inflow is first considered. It is noted that the results obtained using OpenFOAM is based on the quasi-steady approach, and the results obtained by Fluent is based on mixing plane approach. The hydrodynamic performance results of the propeller including the thrust and torque coefficients Ktp, Kq predicted by OpenFOAM and Fluent are shown in Fig. 8, respectively. The corresponding experimental measurement is also plotted in Fig. 8. One can observe from Fig. 8 that OpenFOAM is sufficient accurate and can be used in practice.

J

Ktp

,10K

q

0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6OpenFOAMFluentexp.

10Kq

Ktp

Fig. 8: Hydrodynamics performance curve of propeller

Fig. 9 shows the pressure contours on the blade surfaces at advance ratio J = 0.6. Fig. 10 shows the pressure contours on all solid surfaces of the podded propeller at J = 0.8. For the lower advance ratio, the attack angle of inflow increases, so the propeller load increases. By comparing the pressure contours on the back face of the propeller blades at J = 0.8 with these at J = 0.6, one can observe that the pressure near the leading edge of the back blade face is higher at J = 0.8 than that at J = 0.6, which further demonstrates that the load decreases with the increase of the advance ratio. The velocity and pressure contours in the center plane are shown in Fig. 11 and Fig. 12, respectively, for J=0.8. It can be observed from Fig. 11 that the flow is accelerated after it passes the propeller plane. Due to the block of the strut, the increase of the flow velocity on the top of the propeller is not as larger as that on the bottom. After the strut the flow is accelerated further. The wake is observed clearly after the pod. It can be observed from Fig. 12 that the strut produces a force that is opposite to the thrust of the propeller. The reason is that the inflow approaches to the strut with an angle of attack due to the existence of the propeller in front of the strut.

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Front blade face

Back blade face

Fig. 9: Pressure contours of podded propeller at J=0.6

Fig. 10: Pressure contours of podded propeller at J=0.8

Fig. 11: Velocity contours in the center plane of podded propeller at J=0.8

Fig. 12: Pressure contours in the center plane of podded propeller at J=0.8

Interaction between Propeller and Strut The total force and force components are shown in Table 1, where Kt is the total thrust coefficient, Ktp is the thrust coefficient of the propeller, and Kts is the thrust coefficient of the strut. It can be seen from Table 1 that the influences of the strut on the total force become more obvious with the increase of the advance ratio J. The force ratio of the strut force over the total force is about 8.3% at J=1.0. This result shows that it is very important to study the influence of the strut to the propeller at the high advance ratio case in the design of the podded propeller.

Table 1: Comparison of force components

J 0.6 0.8 1.0 Ktp 0.319 0.213 0.118 Kts -0.014 -0.011 -0.009 Kt 0.305 0.202 0.109 Kts/Kt 4.5% 5.1％ 8.3%

In order to study the influences of the strut on the performance of the podded propeller, the open-water performance of a single propeller is simulated. According to the recommendation of the 23rd ITTC committee, the hub influence can be ignored if it is taken as the one shown in Fig. 13. The same numerical model and grid generation technique as these described above for the podded propeller case are used for this single propeller case.

Fig. 13: Single propeller model

The velocity contours in the center plane are shown in Fig. 14 for J=0.8. By comparing the velocity contours plotted in Fig. 11 and Fig. 14, one

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can find that the velocity contour patterns are quite different for the podded propeller case and the single propeller case. Without the block influence of the strut the wake flow behind the single propeller is almost symmetric about the propeller axis.

Fig. 14: Velocity contours in the center plane of single propeller at J=0.8

The comparison of the hydrodynamic performances between the podded propeller and the single propeller is plotted in Fig. 15. It can be seen from Fig. 15 that the podded propeller has larger values in both thrust coefficient and torque coefficient for all advance ratios in comparison to the single propeller due to the block effect of the strut. In addition, the increase of the thrust of the podded propeller is more dominant at higher advance ratio, where the gain in the propeller thrust is much larger than the drag induced by the strut. The comparison of the propulsion efficiencies η between the podded propeller and the single propeller is plotted in Fig. 16. It can be seen from Fig. 16 that the efficiency varies with advance ratio J. The efficiency of the single propeller is higher than that of the podded propeller at lower advance ratio, and it is opposite at the higher advance ratio.

J

Ktp

,10K

q

0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

with strutwithout strut

Ktp

10Kq

Fig. 15: Comparison of the hydrodynamic performance

with and without strut

CONCLUSIONS A new numerical model for evaluating the viscous flow around the podded propeller has been developed in the OpenFOAM CFD platform. The model has been validated against the experimental data obtained at Shanghai Jiao Tong University and the numerical results obtained by the authors using Fluent. It has been shown that the OpenFOAM CFD

toolbox can predict the hydrodynamic performance of the podded propeller with sufficient accuracy.

J

prop

ulsi

onef

ficie

ncy

0.6 0.7 0.8 0.9 10.5

0.55

0.6

0.65

0.7

0.75

with strutwithout strut

Fig. 16: Comparison of the propulsion efficiency

with and without the strut

Podded propellers have recently been widely used in modern commercial ships due to their relatively high efficiency and sea-keeping ability. It is important to study the performance of this new-type of propulsion. The interaction between the strut and the propeller and the effect of the strut on the hydrodynamic performance are analyzed in this study by comparing the performance of the podded propeller and the single propeller. Numerical results show that the podded propeller has slightly larger values in both thrust coefficient and torque coefficient for all advance ratios in comparison to the single propeller due to the block effect of the strut. The gain in the propeller thrust due to the strut is larger than the drag induced by the strut at high advance ratio. The efficiency of the single propeller is higher than that of the podded propeller at lower advance ratio, and it is opposite at the higher advance ratio. The OpenFOAM CFD toolbox is able to generate good computational results in an efficient way for the simulation of the flow around a podded propeller. Furthermore, the open-source OpenFOAM common platform can facilitate international collaborations. The future work will concentrate on further developing OpenFOAM, including implementing the mixing-plane approach and moving grid approach for true unsteady flow simulation in OpenFOAM, and compare the results with these obtained already using Fluent with these two approaches. ACKNOWLEDGEMENTS The present research was partially supported by the National 863-Plan of China (Project Contract 2008AA09Z313). All supports are greatly acknowledged. The first author would also like to acknowledge George Mason University for hosting her as a visiting scholar. The authors would also like to thank Prof. Chen-Jun Yang for his valuable discussions and suggestions. REFERENCES Ghassemi, H, Allievi, A. (1999), “A Computational Method for the

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Li, Wei, Wang, Guoqiang, Wang, Lei (2007). Numerical Simulation on viscous flow of propeller, Journal of Shanghai Jiao Tong University, Vol. 41, No 7.

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