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Numerical Hydrodynamic Results of the Two Stepped Planing Hull

Hadi Nourghassemi, Hassan Ghassemi*, Hamidreza Taghva

Department of Maritime Engineering Amirkabir University of Technology, Tehran, Iran

Abstract: This paper presents the hydrodynamic results of the two stepped planing hull by numerical software solver. Time-averaged Navier-Stokes equations are coupled with the standard k-ε turbulence model, and volume of fluid equations are solved to simulate transient turbulent free surface flow surrounding the hull by ANSYS-CFX. In order to predict the motion of the vessel, equations of two degrees of freedom for rigid body are coupled with governing equations of fluid flow. In order to validate the numerical model, the obtained numerical results are compared with the available experimental data. The numerical results obtained for drag, dynamic trim, rising of centre of gravity (CG) and the pressure distribution on the body at different speeds and different heights of the applied steps are presented and discussed.

Keywords: pressure, drag, stepped planing hull

Received August 28, 2018; Revised October 18, 2018; Accepted November 02, 2018

Citation: Hadi Nourghassemi, Hassan Ghassemi, Hamidreza Taghva, Numerical Hydrodynamic Results of the Two Stepped Planing Hull. American Journal of Mechanical Engineering, 6 (3). 93-97. January 2018. doi:10.12691/ajme-6-3-2

1. Introduction

In recent decades, much effort is made by researchers to reduce drag and increase speed of planing hulls by changing the geometrical parameters of the hull. Various forms have been used so far, such as Chine, Strake, Pad, Spray rail, Tunnel and Step. Among these methods, applying transverse step on the hull is known as the most effective. It is common to create holes on the outer walls of the step for air suction. Generally, it is expected to increase the speed of vessel by 10 to 15 per cent by applying stepping method [1]. The main idea of applying transverse step on the hull is to reduce the level of contact of the hull with water on two or more small planing surfaces instead of one large surface. Since the force is distributed on several surfaces throughout the hull, the longitudinal stability increases. However, despite the benefits of the transverse steps, there is also the risk of vessel capsizing if the airway is closed by the coming waves. If aeration is stopped, reverse flow occurs behind the transverse step, which leads to an excessive increase in drag. As a result, the speed suddenly decreases and the vessel may capsize. To avoid this problem, air is often sucked through the duct above the water or is supplied through pipes on deck surface. So far, most hydrodynamic studies using a variety of methods on planing hulls have been focused on the bodies without transverse steps. The process of some of these studies is provided in Table 1. Recently, according to the demands as well as the achievement of higher efficiencies, researchers have been more motivated by the use of transverse stepped hulls, and more effort is being made both numerically and experimentally to study and investigate this topic. A negligible number of studies can be found on transverse stepped hulls during the last 15 years. In Table 2, some of these studies are presented. In this paper, the effects of transverse step height on hydrodynamic performance of the planing hull in investigated by FVM. For doing this, ANSYS-CFX is used. Transient and turbulent free surface flow around the solid hull is modelled by the RANS equations along with the turbulence model standard k-ε coupled with VOF equations. To predict motion of the vessel, the equations of the two degrees of freedom of the rigid body are coupled with the equations governing the fluid flow. In this paper, the planing hull has two transversal steps. In six different modes, with variable height of transverse steps, and in three different displacements, the results of the numerical investigation obtained for drag, dynamical trim and pressure distribution on the surface of the hull are compared with the experimental data.

2. Governing Equations

In order to predict the hydrodynamic behaviour of planing hull in calm water, the craft is considered as a rigid body with two degrees of freedom, and transient simulation is carried out. Therefore, governing equations of the turbulent flow of free surface around the vessel should be coupled with equations of motion of rigid body with two degrees of freedom. The governing equations of fluid flow include the continuity and Navier-Stokes equations. By applying Reynolds averaging, RANS equations will be obtained:

[picture] | (1)

[picture] | (2)

represents Reynolds stresses. Based on turbulent viscosity theory that provides relationship between Reynolds stress terms and velocity gradients, equation (2) will be as follows:

[picture] | (3)

where is the effective viscosity defined as:

[picture] | (4)

Two-equation k-ε model is used to model turbulence flow, in which k represents turbulent kinetic energy of flow, and ε is dissipation rate of energy. In this model, eddy viscosity is related to viscous kinetic energy and dissipation rate, defined by:

[picture] | (5)

where is constant and k, ε are determined by solving the following transport equations:

[picture] | (6)

[picture] | (7)

where and are constant values, and Pk is turbulence generation due to viscous forces.

Table 1. Studies and experiments on planing hulls without step

Table 2. Studies and experiments on stepped planing hulls

2.1. Computational Domain and Boundary Conditions

The present study is conducted on a model of stepped planing hull, which is known as Lee model. This model was tested in 2014 by Lee et al., and the results are available in ref. [23]. The model has been tested in six different step heights (0.009525 and 0.00635, 0.003175) with specifications that are given in Table 3. Besides, all of the models were tested and investigated at displacements of 43.09, 55.38, and 47.62 kg. Geometrical parameters of the models are provided in Table 4. Besides, a two-dimensional view of the model is shown in Figure 1.

The flow around the vessel can be assumed to be symmetric with respect to central plane. Therefore, calculations are reduced to only half of the solution domain. The distance between boundaries of this vessel and the body are chosen in such a way that it is possible to apply boundary conditions that are consistent with reality. Solution domain and boundary conditions are shown in Figure 2.

Table 3. Transverse step heights of the models

Table 4. Characteristics of the model

Figure 1. Body plan of the hull

Figure 2. Solution domain and boundary conditions

3. Results

In this study, we used the use of k-ε turbulence model. The number of inflation layers within the boundary layer is considered equal to 22. The dimensionless thickness of the first layer on the surface is Y ⁺ = 50. In order to better approximate curves and sharp corners, the cell size is considered sufficiently small on the body surfaces. Cell sizes in the two regions in flow where high gradients are expected are considered smaller. The first region is around the free surface, where it is required to solve its shape, and the second region is a part of the first region near the body, where separation of the flow from the chine, step and water spray occurs. The computational grid generated around the body is shown in Figure 3. In order to check the grid independency, calculations are performed in several grids with different numbers of cells. For example, the variation of drag force to displacement ratio based on number of cells Froude number of 1.85 is illustrated in Figure 4. In this section, in order to validate the present numerical model, the numerical results obtained for different heights of steps are presented and compared with experimental data. The vessel model studied in this paper was tested in 2014 by Lee et al. for different heights of steps. The presented experimental results include the raise of center of mass, dynamic trim, and drag force. Comparison of the drag, trim and raise of CG is presented in Figure 5, Figure 6 and Figure 7, respectively. These results show relatively good agreement between numerical and experimental data. Figure 8 shows the pressure contour acted on the hull for different models at Fn=2.13. It can be observed that the model 1 that has the highest drag, achieves the lowest level of pressure peak. In contrast, the model 4 has the lowest drag and highest level of pressure peak.

Figure 3. View of the generated grid, a), close view b) hawse region, c) step region

Figure 4. Ratio of drag force to displacement (Fn=1.85)

Figure 5. Comparison of drag [N] against Fn

Figure 6. Comparison of dynamic trim [deg.] against Fn

Figure 7. Comparison of raise of CG against Fn

Figure 8. Pressure contour acted on the hull for different models (Fn=2.13)

4. Conclusion

In this paper, the hydrodynamic effect of planing hull is numerically calculated. The hull has two transverse stepped with different heights. The solver software is ANSYS-CFD with the standard k-ε turbulence model. The numerical results are revealed the drag, trim, rise of CG and pressure distributions. Some of the results are compared with experimental data and found relatively good agreement between them. It is found that the effect may reduce drag and pressure distribution acted on the hull makes better ride and moderate performance.

References

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