CFD analysis of a round shaped air cushion vehicle with flexible skirt segments at 90° and different air clearance height

At present time, the most used flexible skirt in construction of air cushion vehicles is the segmented one. Therefore, this study focuses on performing CFD analysis specific to the area of the segments of such a skirt. The proposed construction model has the outer diameter of flexible skirt segments of 1 meter, the segment thickness of 2 mm and the feed hole of 50 mm. A particular feature of proposed model is the circular ring shape of feed hole. Considering that segments height and air clearance height directly influence the performance of the air cushion, these two parameters were varied. Values ranged between 50 to 200 mm for flexible skirt segment height and from 10 to 50 mm for air clearance height. CFD analyses were performed in ANSYS Fluent program to determine velocity contours, pressure contours and streamlines. The main purpose of simulation was to determine lift force for all analysed configurations. The lift force variation was subsequently plotted according to air clearance height values through MATLAB program. Using Curve Fitting Toolbox application, it was concluded that the power type function with two terms best characterizes the analysed curves.


Introduction
Air cushion vehicle are unique means of transport in the world that can cross different types of soils and water. These vehicles have a flexible skirt which maintains a sufficient amount of air under the hull to achieve the lift force necessary to allow the vehicle to detach from the ground. Over time, various configurations of flexible skirts were designed, at present the most used being the segmented skirt [1], also known as bag and finger skirt. An important particularity regarding this type of flexible skirt is that each segment corresponds to a feed hole, which usually has a circular shape. An internal configuration of main components of a lift system with segmented skirt is illustrated in figure 1.

Main components and fluid flow areas inside the vehicle
Taking into account both the most commonly used flexible skirt and the configuration of a lift system, the proposed 3D constructive model is presented in figure 2. This model was designed with CATIA software and is characterized by three aspects: its outer shape is circular, bag to cushion feed orifices of the segments have a circular ring shape and the skirt segments are positioned at 90°. The interior shape of this model generated within main fluid flow area 3 specific zones, as depicted in figure 3: zone 1 -area of the cavity given by the buoyancy tank, zone 2 -area between the exit from the buoyancy tank and the entry into the segments of the skirt and zone 3 -area formed by the segments cavity and the area between the ground and the lower part of the buoyancy tank.   Figure 4. The main notations that describe the flow domains.

Limitations
Due to the complexity of fluid flow throughout the cavity, this study is limited to the zone 3 analysis. To achieve this, numerical analyses were performed for two-dimensional domains that represents a section plan of a flexible skirt segment.

Aspects regarding the dimensional characteristics of the chosen flow domains
The main characteristics of the created flow domains shown in figure 4, are denoted as: Defd -outer diameter of the fluid domain, Des -outer diameter of the segments, Dis -inner diameter of the segments, Defh -outer diameter of the feed orifice, Difh -inner diameter of the feed orifice, Hgfssheight between the ground and the upper part of the flexible skirt segments, hs -segment height and ach -air clearance height. The notations were chosen to facilitate the domains characterization, as well as the calculation of the specific parameters of the inlet and outlet boundaries.
For the present study, four cases were chosen:

Main steps of the simulations performed in the ANSYS Fluent program
When conducting CFD analyses, certain steps must be performed in order to successfully complete the proposed simulations. For the studied cases, the following steps were required:

Achieving the geometries of the flow domains and defining boundaries
Considering the geometrical characteristics of the proposed model, to simplify the simulations for all domains, a median plane was chosen and symmetry axis was considered as boundary.
After performing the entire sketch and transforming it into fluid surface, boundaries defining the fluid domain were imposed. Figure 5 presents a sketch with the locations of each boundary separately.

Mesh generation
For all studied cases, the structured mesh considered a 90°-angle formed by the segments of flexible skirt. To achieve this Edge Sizing and Face Meshing methods were employed. A representative outcome of the final mesh specific to case B is presented in figure 6.
Certain quality parameters, such as skewness and orthogonal quality, fit the generated meshes in a given spectrum. Figures 7 and 8 present the spectrum of values of these two parameters. Analysing data presented in table 1 for the final meshes parameters, it can be inferred that these meshes are qualitatively excellent.

Defining the parameters characteristic of CFD analysis
The main settings made in this category are: • 2D Space: Axisymmetric.
• The required working fluid: air.
• Imposing boundary conditions: considering that all dimensions of fluid domains are known, the specific method of turbulence chosen for all studied cases is Intensity and Hydraulic Diameter. The imposed boundaries values were: fluid velocity of 15 m/s at the inlet border and gauge pressure of 0 Pa at outlet1 and outlet2. Considering the fact that in these types of simulations two outlet type boundaries are used, the turbulent intensity cannot be determined. Thus, fluid domain was imaginary divided into four major areas that help determine both the hydraulic diameter and the turbulent intensity for each of the three boundaries. A representation of these areas is shown in figure 9. In order to accurately determine the values of turbulent intensities specific to outlet1 and outlet2, a first step considered the turbulent intensities on these two boundaries to be equal to the specific turbulent intensity of the zone 2. After performing the simulation, using the option to query the mass flow rate on outlet1 and outlet2, it was possible in second step to determine the turbulent intensities on each boundary separately. A number of simulations were performed until the numerical values of the two intensities coincided and the final values of the lift forces were taken into account. • Pressure-Velocity Coupling Scheme: COUPLED.

Analysis and discussion
After performing the numerical simulations, it was found that only for all cases A, the absolute convergence value could not be fulfilled and it was necessary to impose a number of iterations. Graphical representations regarding the lift forces values obtained are shown in figure 10.
From the graphical representation, it can be inferred that the highest value of lift force is obtained for case D, where hs = 200 mm and ach = 10 mm, and the smallest values for case A where hs = 50 mm and ach = 50 mm. Another important observation from the synthesis diagram is that values of the largest lift forces meet at the values of ach = 10 mm and then decrease considerably with the increase of this parameter.  Using the Curve Fitting Toolbox application for simulation data, it turned out that the power type function with two terms best characterizes these 4 curves, figure 10 -(c). The general form of the equations as well as the values of their coefficients are presented in table 2. The main purpose of these simulations was to observe which case offers the highest value for the lift force, i.e. case D. Therefore, figures 11, 12 and 13 depict graphical representations of velocity contour, streamlines and pressure contour, respectively, obtained through the CFD-Post application for case D.   From velocity contours, pressure contours and streamlines, both a visual and a numerical analysis may be performed. Analysing streamlines and velocity contours, following aspects may be inferred: • case A: as the value of parameter ach increases, values of maximum airflow velocity decreases, the vortices extend to the axis of symmetry area and 3 main vortices increase in intensity (the one between jet and flexible skirt segment and two located on the other side of the jet); • cases B and C: as the value of parameter ach increases, values of maximum airflow velocity decreases, the number of main vortices between jet and axis of symmetry decreases and 3 main vortices increase in intensity (same as above); • case D: as the value of parameter ach increases, values of maximum airflow velocity decreases, the same number of main vortices between the jet and the axis of symmetry remains and 3 main vortices increase in intensity (same as above). With respect to the resultant pressure contours for all the studied cases, with the increase of value for ach , the following features may be observed: the value of maximum pressure inside the cavity decreases, pressure in the area between jet and the segments of flexible skirt decreases and a small area of intense pressure occurs between ground and jet. Figure 14 depicts the maximum velocities of the jet and figure 15 the maximum pressure inside the cavity, as functions of the parameter ach. Tables 3 and 4 show in tabular format the percentage decrease of lift force from its highest value, for the variables considered.

Conclusion
The computational analysis was successfully performed in the ANSYS Fluent program for a round shaped air cushion vehicle with flexible skirt segments at 90° and different air clearance height Following the simulations, it was possible to study the aerodynamics of the flow both in the inner cavity of the flexible skirt and in the immediate vicinity of the outside of the vehicle. Up to now, authors have no knowledge of prior publications with this approached for the topic. A unique feature of this study is that the feed orifice between bag and cushion has a circular ring shape, which feeds all the flexible skirt segments at once. By performing a numerical analysis in which the parameters hc and ach are taken into account, the following aspects may be inferred: • for ach = 10/20/30/40/50 mm, higher lift force is obtained for the highest hs value (hs = 200 mm); • from the highest value, lift force decreases as much as 54.1%, for hs = 50 mm and ach = 50 mm; • for hs = 50/100/150/200 mm, higher lift force is obtained for the lowest ach value (ach = 10 mm); • from the highest value, lift force decrease as much as 97.7%, for hs = 50 mm and ach = 50 mm. The most important feature of this analysis is that between 10 ÷ 20 mm range of the ach parameter, regardless of the hs value, the lift force drops drastically. Therefore, ach is the most important parameter to consider when designing such a vehicle. This study showed that both the air clearance height and the height of the flexible skirt segments play a very important role in establishing the functional characteristics of an air cushion vehicle.