## 3 Rotor-Fuselage Computations  
Rotor-fuselage flow simulations are also considered in this paper. For the simulation of the rotor over the fuselage, a sliding surface is constructed that divides the computational domain into two parts (Figure 4). The movable upper part corresponds to the rotor, that includes four-blades made of NACA 23012 airfoils with the root cut-off \(r=0.2R\), where \(R\) is the radius of the rotor. A simplified elliptical hub is used. The geometry of the upper part is inclined to allow forward tilting of the rotor. The CFD grids are constructed using the ICAM-hexa software of ANSYSTM. The topology of the blocks and the parameters of the computational grids correspond to what was used for the isolated fuselage of the helicopter. The fixed part of the mesh contains 688 blocks and \(9\times 10^{6}\) cells. The computational grid of the rotor was assembled in several stages. At the first stage, the computational grid for a quarter of the computational domain (for one blade) was generated, as shown in Figure 5. The computational grid for each blade comprises 144 blocks and \(6\times 10^{6}\) cells. Figure 4: Far and near view of the computation domain. Figure 3: Pressure coefficients along the rotor section: (a) \(\overline{r}=0.68\), (b) \(\overline{r}=0.96\). The boundary conditions are shown in Figure 5. Only a single blade was meshed, but using periodic conditions between blades allows for the full rotor to be considered by copying and rotating the mesh of a single blade around the azimuth (Figure 6). This method simplifies the process of constructing the computational grid for the main rotor and keeps constant the characteristics of the computational grid for each blade. After assembling of all elements, the computational grid had 1144 blocks and 33 \(\times\) 10\({}^{6}\) cells. The simulation concerns forward flight for a 1:6 scaled helicopter model, and all geometric and flight parameters are presented in Table 1. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Geometry Parameters**} \\ \hline Number of blades, \(N\) & 4 \\ Rotor diameter, \(2R\) (m) & 1.92 \\ Root cut-out, (m) & 0.19 \\ Blade twist, \(\Phi\) (deg) & \(-5.3\) \\ Blade chord, \(c\) (mm) & 52 \\ Blade thickness, \(f\) (\%c) & 12 \\ \hline \multicolumn{2}{c}{**Operation Parameters**} \\ \hline Collective pitch angle, \(\theta_{0}\) (deg) & 8 \\ Cyclic pitch angle, \(\theta_{1s}\) (deg) & \(-2\) \\ Cyclic pitch angle, \(\theta_{1c}\) (deg) & 2 \\ Coning angle, \(\beta\) (deg) & 0 \\ Angle of attack, \(\alpha\) (deg) & \(-4\) \\ Tip Mach number & \(M_{\text{tip}}=0.64\) \\ Advance ratio, \(\mu\) & 0.15 \\ Direction of rotation & Counter clockwise \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main rotor parameters. Figure 5: Sliding plane arrangement near the main rotor hub. Figure 6: Multi-block topology (**a**) and mesh section (**b**). The following assumptions were made:  
* Rigid blades;
* No flapping motion of the blades, only pitch input is considered;
* No lead-lag. Changing the cyclic pitch of the rotor is achieved by deforming the computational grid. The employed method is described in [13]. The simulation was unsteady, and with a time step corresponding to 1 degree in rotor azimuth. An example of the surface pressure distribution at the azimuth of \(\psi=80^{\circ}\) is shown in Figure 7.  
Analysis of the results was carried out using Tecplot \(360^{\mathrm{TM}}\), and normal vectors to the surface of the body oriented towards the outside were computed. Variation of the pressure distribution over the surface of the fuselage and the rotor blades leads to variable fuselage drag (\(C_{D}\)) and rotor thrust (\(C_{T}\)) coefficients, which are computed by:  
\[C_{D}=\frac{D}{q_{\infty}S_{F}},C_{T}=\frac{T}{q_{tip}\pi R^{2}},\]  
where \(q_{\infty}\) is the free stream dynamic pressure, \(q_{tip}\) is the dynamic pressure at the blade tip, \(S_{F}\) is the reference fuselage area, \(D\) is the drag force, and \(T\) the rotor thrust.