## 2 Study Object--General Dynamics F-111 \"Aardvark\"
### F-111 Aircraft Model for CFD Method  
Regarding the computational aspects of the aerodynamic characteristics of the F-111 aircraft, all calculations were conducted using the ANSYS Fluent code, a widely recognized industry standard for such analyses. The CFD simulation of the hydrodynamic tunnel demands specific settings for the model domain. Since the model is in a closed test chamber, its walls have to be present in the simulation. Moreover, the model has to have an ability to change the angle of inclination, which was treated as the angle of attack in this study. Nevertheless, the symmetry of the flow condition can be assumed along with the symmetry of the geometry. A plane of symmetry can be used, which decreases the computational effort by a half, assuming the same mesh density. The computational domain has a pressure inlet and outlet and is surrounded by walls. The upper wall is a free surface of the water in the experiment, but in this study, the wall condition was assumed. The aircraft geometry is placed in a cylinder which can be rotated to obtain the desired angle of attack, using the sliding mesh calculation ability of ANSYS Fluent. The interface zone (Figure 2) can match the flow inside and outside the cylinder, even if the meshes on both sides do not match. This zone is invisible to the flow and allows the fluid to move freely through its surface. The mesh around the model consists of tetrahedral elements with prismatic fragments around all the walls to simulate the boundary layer. The first cell height on the wall is set to obtain the Y+ parameter around 1, which is suggested in the simulations using the \(K\)-\(\omega\)\(SST\) 4-equation turbulence model (also known as \(\gamma\)-\(Re_{\theta}\)) [21]. The adequate boundary layer parameters were set for water (first layer from the wall height of 0.002 mm, height ratio of 1.2, and 20 layers). The mesh density is shown in Figure 3. A non-matching interface is shown here, and the flow through the interface does not cause errors in the flow uniformity inside the cylinder. The density of the mesh was set based on the experience and best practices of the authors, and allows reasonably accurate qualitative results to be obtained. Figure 2: Boundary conditions of hydrodynamic tunnel simulation. The default model of the water material in ANSYS Fluent was set with a constant density of 998.2 kg/m\({}^{3}\) and viscosity of 0.001003 kg/(m s). The density-based solver with an absolute velocity formulation and a steady type of time solution was set. An implicit solution formulation was used with Roe-FDS flux type and second-order flow spatial discretization. Regarding the time discretization, the Courant number was set to 5 with standard underrelaxation factors. Simulation studies were conducted under steady-state conditions to investigate quasi-static vortices shedding from the wing, as no [PERSON] vortex path or similar unsteady phenomena were observed. In all simulations the two basic coordinate systems were used: the OXYZ-CAD model coordinate system, in which the geometry was drawn; and the AX\({}_{\text{A}}\)Y\({}_{\text{A}}\)Z\({}_{\text{A}}\) flow coordinate system, with the center of the cylinder oriented with the flow direction. In this coordinate system, the results are presented in terms of aerodynamic force \(P_{x}\), \(P_{y}\), and \(P_{z}\), and moment components \(M_{x}\), \(M_{y}\), and \(M_{z}\), converted into the nondimensional, coefficient form. The aerodynamic force coefficients, \(C_{x}\), \(C_{y}\), and \(C_{z}\), are defined as:  
\[ \begin{split} C_{x}&=\frac{P_{x}}{0.5\rho V^{2}5}\\ C_{y}&=\frac{P_{y}}{0.5\rho V^{2}5}\\ C_{z}&=\frac{P_{z}}{0.5\rho V^{2}5}\\ \end{split}  \tag{1}\]  
where \(\rho\) is air density, \(S\) denotes the lifting surface, and \(V\) is the flow velocity. The symbols \(P_{x}\), \(P_{y}\), and \(P_{z}\) denote the drag force, side force, and lift force, respectively. The aerodynamic moment coefficients, \(C_{mx}\), \(C_{my}\), and \(C_{mz}\), are defined as:  
\[