3.3.1 C_P profile comparisons

C_P profile comparisons between CFD and experiments^{(Reference Philipsen and Heinrich21,Reference Lebrun22)} on the fuselage, fixed and tiltable wings of the ERICA tiltrotor are given in Fig. 5. They correspond to the top fuselage centre-line and inner, middle, and outer tiltable and fixed wing sections. The CFD results were not averaged in phase and with the same resolution as for the NICETRIP data, which could lead to a source of error in the comparison. Moreover, C_P values were averaged over the last computed rotor revolution instead of time-averaging. Regarding the C_P profile at the centre-line of the fuselage (Fig. 5(a)), a large zone of recirculation is seen by both sets of experiments (Modane and DNW experiments are denoted by squares and triangles, respectively), which is represented through a pressure plateau after the wing leading edge suction peak. The HMB3 predictions overestimate the suction peak (C _PHMB3 = 1.64; C_PDNW = 1.25; C_PONERA = 1.18) and do not capture the region of recirculation. Simulations carried out internally at UofG with the Menter’s k-ω SST turbulence model^{(Reference Menter50)} did not predict the zone of recirculation. Therefore, this discrepancy can be due to the lack of the complete aircraft model in the grid and the employed symmetry condition, wind tunnel effects, and lack of exact trimmed conditions. By contrast, the CFD results at the front and rear part of the fuselage are in close agreement with the experimental data, which confirms a local separation region. Considering the inner fixed wing section (Fig. 5(b)), experiments suggest that this region is separated due to the presence of a pressure plateau. CFD predictions slightly overestimate the suction peak so that the pressure plateau is not well reproduced. This is consistent with the flowfield predicted in Fig. 5(a).

Figure 5. C_P profile comparisons between CFD and experiments^{(Reference Philipsen and Heinrich21,Reference Lebrun22)} on the fixed and tiltable wings of the ERICA tiltrotor.

In the middle and outer fixed wing sections (Figs 5(c)–(e)), wind tunnel experiments show a scatter of about 9% on the suction peak. Despite that the same model and flow conditions were simulated in both wind tunnels for this configuration, a significant scatter was found for all stations in this region. As mentioned, the NICETRIP experimental data is relatively new and not well explored by researchers. Nevertheless, CFD results show good agreement with the experiments for all stations, even if the trailing edge pressure plateau is slightly under-estimated. Regarding the zone of aerodynamic interaction located near the tiltable wing sections (Figs 5(f)–(h)), a good agreement between CFD and experimental results is also observed.

Figure 6 shows profile C_P comparisons on the nacelle component, corresponding to the top and bottom centre lines, and the central and rear sections of the nacelle (see Fig. 6(c)). Considering the top and bottom centre-line sections (Figs 6(a)–(b)), a noticeable scatter of C_P is observed for both sets of experiments. The CFD results were able to capture the averaged trend of the experimental C_P for both sections. Finally, in the middle and rear part of the nacelle (Figs 6(d)–(e)), a good agreement is shown between CFD and experiments.

Figure 6. C_P profile comparisons between CFD and experiments^{(Reference Philipsen and Heinrich21,Reference Lebrun22)} on the nacelle of the ERICA tiltrotor.

Figure 7 presents C_P comparisons on the ERICA fuselage at eight cross-sections. As can been seen, all CFD curves are close to the experimental data. Better agreement is obtained at the front of the fuselage (Figs 7(a)–(d)), where the flowfield is attached. The HMB3 solution appears to capture well all features shown by the experiments. Even for stations located behind the fixed wing (Figs 7(e)–(h)), the agreement is still fair near the spoonsons and the fin of the model. Nevertheless, the overall effect of the blades on the fuselage is well captured, which encourages the use of this approach in predicting loads on the fuselage.

Figure 7. C_P profile comparisons between CFD and experiments^{(Reference Philipsen and Heinrich21,Reference Lebrun22)} on the fuselage of the ERICA tiltrotor.

The effect of the model support on the ERICA tiltrotor results was also assessed using the average C_P distribution on the bottom part of the fuselage in Fig. 8(a). The model of the DNW-LLF was supported via a ventral sting set-up at the rear part of the fuselage, while a straight sting was set-up in the ONERA model. As can be seen in Fig. 8(b), the effect of the model support on the fuselage is stronger for the DNW-LLF, being less intrusive for the ONERA model. From a numerical point of view, HMB3 predictions compare well with the experimental data of ONERA, where the support is straight. This is consistent with the fact that the model support was not modelled.

Figure 8. C_P profile comparison between CFD and experiments^{(Reference Philipsen and Heinrich21,Reference Lebrun22)} on the bottom part of the fuselage of the ERICA tiltrotor.

3.3.2 Load distributions

In this section, the integrated loads generated on the nacelle, tiltable wing, and the rest of the fuselage with the fixed wing are analysed for the AC configuration. Lift and drag coefficients on the tiltable wing as function of the main rotor azimuth Ψ are shown in Fig. 9(a). The drag and lift coefficients are represented by squares (C_D ) and triangles (C_L ), respectively, while its averaged values are represented with solid lines. As can be seen, the 4/rev. blade passage effect on the tiltable wing is well captured, with a fluctuation values of 5.14% and 23.8% for the lift and drag, respectively. Previous work^{(Reference Decours, Beaumier, Khier, Kneisch, Valentini and Vigevano31)} reported fluctuations of lift and drag between 5%–7% and 20%-30% depending on the partner.

Figure 9. History of the lift and drag coefficients in the tiltable wing, nacelle, and fuselage and fixed wing of the ERICA tiltrotor

Likewise, the history of the loads on the nacelle is given in Fig. 9(b), which reveals the 4/rev. blade passage effect for both aerodynamic coefficients. The lift and drag fluctuations are 6.86% and 2.5%, respectively, which suggests that the nacelle has a milder unsteady behaviour than the tiltable wing. The fuselage and fixed wing lift and drag coefficients are presented in Fig. 9(c), which also reveals a 4/rev. signal behaviour due to the blade passage. The results show a small fluctuation values of drag (5.64%) and lift (2.17%) coefficients.

Finally, the lift and drag coefficients of the complete ERICA tiltrotor are compared with the experimental data. Table 4 shows a breakdown of the total averaged lift and drag coefficient for each component. A discrepancy of 15.51% and 33.9% for the lift and drag coefficients is found. Results reported in Decours et al^{(Reference Decours, Beaumier, Khier, Kneisch, Valentini and Vigevano31)} also found a discrepancy on lift about 15%, and no drag values were reported.

Table 4 Averaged lift and drag coefficient comparisons between CFD and experiments^{(Reference Philipsen and Heinrich21,Reference Lebrun22)} for the ERICA tiltrotor

3.3.3 Flowfield details

Visualisation of the flowfield of the ERICA tiltrotor using the Q-criterion^{(Reference Jeong and Hussain51)} coloured by Mach number is presented in Fig. 10(a). Instantaneous solutions are shown instead of averaged values. It is interesting to note that the wake behind the rotor disk is preserved for more than one rotor diameter downstream thanks to the refined mesh employed in this region (Fig. 10(b)). This plot has only informative character, showing the interaction of the rotor wake with the nacelle and tiltable wings. From these iso-surfaces it can be seen that the rotor wake does not directly interact with the fuselage and the fixed part of the wings.

Figure 10. Wake visualisation (top) and details of the refined mesh region (bottom) of the ERICA tiltrotor using Q-criterion shaded by contours of Mach number.

4.1.1 XV-15 rotor geometry

The three-bladed XV-15 rotor geometry was generated based on the full-scale wind tunnel model performed by Betzina in the NASA Ames 80- by 120-foot wind tunnel facility^{(Reference Betzina19)}. NACA 6-series five-digit aerofoil sections comprise the rotor blade, and its identity and radial location along the rotor blade is reported in Table 5.

Table 5 Radial location of the XV-15 rotor blade aerofoils^{(Reference Felker, Betzina and Signor16)}

The main geometric characteristics of the XV-15 rotor blades^{(Reference Betzina19)} are summarised in Table 6. It is interesting to note that unlike convectional helicopter blades, tiltrotor blades are mainly characterised by a high linear twist angle and rotor solidity, along with a small rotor radius.

Table 6 Geometric properties of the full-scale XV-15 rotor^{(Reference Betzina19)}

A detailed sketch of the XV-15 blade planform and the blade radial twist, and chord distributions is shown in Fig. 11. The rotor blade chord is held constant, and extends at almost 80% of the rotor blade. The blade root, however, was not modelled due to the lack of information on the cuff geometry in the literature.

Figure 11. Planform of the XV-15 rotor blade (above) and twist and chord distributions^{(Reference Acree52)} (below).

4.1.2 XV-15 rotor mesh

A mesh generated using the chimera technique was used for the aerodynamic study of the XV-15 rotor. It was composed by a cylindrical off-body mesh used as background, and a body-fitted mesh for the blade. The use of an overset grid method allowed for the blade pitch angle to be changed by rotating the body-fitted mesh. Because the XV-15 rotor was numerically evaluated in hover and propeller modes (axial flight), only a third of the computational domain was meshed, assuming periodic conditions for the flowfield in the azimuthal direction (not applicable to stall condition). A view of the computational domain, along with the boundary conditions employed is given in Fig. 12(a). Farfield boundaries were extended to 2R (above rotor) and 4R (below rotor and in the radial direction) from the rotor plane, which assures an independent solution with the boundary conditions employed. Furthermore, an ideal rotor hub was modelled and approximated as a cylinder, extending from inflow to outflow with a radius of 0.05R.

Figure 12. Computational domain and boundary conditions employed (left) and detailed view of the XV-15 rotor mesh (right).

A C-topology was selected for the leading edge of the blade, while an H-topology was employed at the trailing edge. This configuration permits an optimal resolution of the boundary layer due to the orthogonality of the cells around the surface blade (Fig. 12(a)). The height of the first mesh layer above the blade surface was set to 1.0 × 10⁻⁵ c _ref, which leads y ⁺ less than 1.0 all over the blade. Considering the chordwise and spanwise directions of the blade, 264 and 132 mesh points were used, while the blunt trailing-edge was modelled with 42 mesh points.

To guarantee a mesh independent solution, two computational domains were built. Table 7 lists the grids used and shows the breakdown of cells per blade. Coarse and medium meshes have 6.2 and 9.6 million cells per blade (equivalent to 18.6 and 28.8 million cells for three blades), with the same grid resolution for the body-fitted mesh (3.6 million cells). The background mesh, however, was refined at the wake and near-body regions, increasing the grid size from 2.6 to 6 million cells.

Table 7 Meshing parameters for the XV-15 rotor mesh

4.1.3 Test conditions and computations

Table 8 summarises the conditions employed and computations performed in hover and propeller mode configurations. For the hover mode, the tip Mach number was set to 0.69, and four blade collective angles were considered, corresponding to low, medium, and high disc loadings. The Reynolds number, based on the reference blade chord of 14 inches and on the tip speed, was 4.95 × 10⁶. The cruise condition was modelled at 0 ft (ISA+0°), with a tip Mach number of 0.54 and advance ratio 0.337. The Reynolds number for this case was 4.50 × 10⁶, again based on the reference blade chord and rotor tip speed (with no account for the advance velocity).

Table 8 Flow conditions for the full-scale XV-15 tiltrotor blade

All flow solutions were computed by solving the RANS equations, coupled with Menter’s k-ω SST turbulence model^{(Reference Menter50)}. The flow equations were integrated with the implicit dual-time stepping method of HMB, using a pseudo-time Courant–Friedrichs–Lewy (CFL) equal to 4 for the helicopter mode computations, and equal to 2 for the aeroplane mode. Typically, 40,000 iterations were necessary to drop the residual by 6 orders of magnitude for the flow solutions. Solutions were computed on 232 cores of the high performance computer cluster of Glasgow University, comprised of Intel Xeon E5620 processors. For the XV-15 case with the coarse chimera grid (6.2 million cells per blade), the wall-clock time needed to achieve a fully converged solutions was 17.1 hours.

4.1.5 Surface pressure predictions

Due to the lack of experimental surface pressure measurements, a comparison between HMB3 and CFD data published by Kaul et al^{(Reference Kaul24)} using the OVERFLOW2 solver is shown in Fig. 14. Three radial stations were considered (r/R = 0.72, 0.83, and 0.94), and the collective pitch angle was 10°. The surface pressure coefficient is computed based on the local velocity at each radial station:

(3) $$\begin{equation} C_P=\frac{P-P_{\infty }}{1/2 \rho _\infty (\Omega r)^2} \end{equation}$$

CFD results using HMB3 correspond to the coarse grid (18.6 million cells for the three blades) where the k-ω SST turbulence model^{(Reference Menter50)} was employed, while Kaul’s results were obtained with a grid size of 35 million cells using the Spalart-Allmaras turbulence model^{(Reference Spalart and Allmaras25)}. Despite that small variation on the predicted peak C_P is seen by the different numerical simulations, a fair agreement is found for all radial stations. Regarding the radial stations r/R = 0.72 and r/R = 0.83, it is clear that the suction peak does not exceed the critical C* _P values (Equation (4)), while the most outboard section (r/R = 0.94) reaches sonic conditions.

(4) $$\begin{equation} {C^*_P}=\frac{2}{\gamma ({M_{{\rm tip}}\frac{r}{R}})^2}\bigg [\bigg ({\frac{2+(\gamma -1){(M_{{\rm tip}}\frac{r}{R})^2}}{\gamma +1}}\bigg )^{\frac{\gamma }{\gamma -1}}-1\bigg ]. \end{equation}$$

4.1.6 Sectional loads

Figure 15 shows the distribution of sectional thrust and torque coefficients along the rotor radius for collective pitch angles from 3° to 13°. The influence of the tip vortex on the tip region (from 90% R to 100% R) is visible in terms of loading and torque coefficients. It is interesting to note that the torque coefficient is significantly decreased in the tip region (r/R > 0.90) as consequence of the change on the planform due to the twist and aerofoil sections.

Figure 15. Blade sectional thrust coefficient (left) and torque coefficient (right) for the full-scale XV-15 rotor in helicopter mode.

4.1.7 Aeroacoustic analysis

The Helicopter Ffowcs Williams-Hawkings (HFWH) code is used here to predict the mid and farfield noise on the full-scale XV-15 main rotor. This method solves the Farassat 1A formulation (also known as retarded-time formulation) of the original Ffowcs Williams-Hawkings FW-H equation^{(Reference Ffowcs-Williams and Hawkings54)}, which is mathematically represented by:

(5) $$\begin{eqnarray} 4 \pi a_{0}^2(\rho ({\bf x},{\bf t})-\rho _0) &=& \frac{\partial }{\partial t}\int \frac{\rho _0 u_n}{r} \delta (f)\frac{\partial f}{\partial \mathrm{x_j}}\, \mathrm{dS(y)} -\frac{\partial }{\partial \mathrm{x_i}} \int \frac{P_{ij}}{r}\delta {(f)}\frac{\partial f}{\partial \mathrm{x_j}}\, \mathrm{dS(y)}\nonumber\\ &&+\,\frac{\partial ^2}{\partial \mathrm{x_i}\mathrm{x_j}} \int \frac{T_{ij}({\bf y},{\bf t-r/c})}{r}\, \mathrm{dV(y)}. \end{eqnarray}$$

where T_ij = ρu_iu_j + P_ij − c ²(ρ − ρ₀)δ _ij is known as the Lighthill stress tensor^{(Reference Lighthill55)}, which may be regarded as an “acoustic stress”. The first and second terms on the right-hand of Equation (5) are integrated over the surface f, whereas the third term is integrated over the volume V in a reference frame moving with the body surface. The first term on the right-hand, represents the noise that is caused by the displacement of fluid as the body passes, which known as thickness noise. The second term accounts for noise resulting from the unsteady motion of the pressure and viscous stresses on the body surface, which is the main source of loading, blade-vortex-interaction, and broadband noise^{(Reference Brentner and Farassat56)}. If the flowfield is not transonic or supersonic, these two source terms are sufficient^{(Reference Brentner and Farassat56)}. The sound is computed by integrating the Ffowcs Williams-Hawkings equation on an integration surface placed away from the solid surface. The time-dependent pressure signal that appears in Equation (5) is obtained by transforming the flow solution from the blade reference frame to the inertial reference frame. This acoustic-code has been previously employed for three-dimensional rotor hover predictions such the S-76 rotor (See Jimenez and Barakos^{(Reference Jimenez and Barakos43)}), showing a good correlation with the theory^{(Reference Gopalan and Shmitz57,Reference Gopalan and Shmitz58)} .

A comparison with theory was conducted in terms of total noise predictions. Analytical solutions are based on the work of Gopalan et al^{(Reference Gopalan and Shmitz57,Reference Gopalan and Shmitz58)} and have been successfully employed in the helicopter community^{(Reference Kusyumov, Mikhailov, Garipova, Batrakov and Barakos59)}. The key idea is to convert the FW-H integral equations to an explicit algebraic expressions. Figure 16 shows a comparison of the theoretical and numerical total noise given in dB, as a function of the radial distance in the rotor disk plane. Three collective pitch angles were selected for this study (θ₇₅ = 7°, 10°, 13°), which cover medium and high thrust using the coarse grid. The results show a fair agreement between theory and the predicted total noise for all collective pitch angles, although small differences were found at radial distance lower than 2R. In fact, this supports the idea that this theory is only valid at radial distance above 3R.

Figure 16. Total noise in dB as function of the normalised radial distance r/R at the tip plane of the full-scale XV-15 rotor.

Table 11 shows the effect of the collective pitch angle when increased from 7° to 10° and 13° degrees on the thrust coefficient, FoM, and total noise. It is clearly seen that the thrust coefficient linearly increases with the collective, whilst the FoM presents a drop of almost 2%. As expected, the sound pressure level (SPL) correlates in a linear fashion with the collective.

Table 11 Effect of the collective collective pitch angle on the thrust coefficient, FoM, and total noise in SPL for the full-scale XV-15 rotor

4.1.9 Sectional loads

Propeller radial loading distributions are shown in Fig. 18 in terms of sectional thrust and torque coefficients along the rotor radius. For this case, results with the coarse grid were used. A low collective pitch angles (θ₇₅ = 26°), a negative predicted loadings is observed covering up to 40% R. In fact, the inboard part of the propeller is acting as a windmill (power is absorbed from the flow) mainly due to the negative angle of the attack seen by those aerofoils. Consequently, this leads to a low propeller efficiency for this flight cruise condition. For high collective pitch angles (θ₇₅ = 28° and 28.8°), however, both inner and outer parts act as a propeller, providing a high efficiency.

Figure 18. Blade sectional thrust coefficient (left) and torque coefficient (right) for the full-scale XV-15 rotor in aeroplane mode.

4.1.10 Surface pressure predictions

Figure 19 presents predicted pressure coefficient contours for the XV-15 upper blade at the computed advance ratio, where the C_P is computed based on the local velocity. Results at low thrust coefficient confirm the idea that the inboard part of the rotor is under-loaded. As the collective pitch angle increased, contours of C_P at outboard part of the blade indicates a more uniform propeller load distributions.

Figure 19. Contours of surface pressure coefficient for the XV-15 rotor blade.

4.1.11 Flowfield details

Flowfield visualisation of the rotor wake for the full-scale XV-15 rotor blade in propeller mode using the Q criterion^{(Reference Jeong and Hussain51)} is given in Fig. 20. Contours of surface pressure coefficient are also included. Despite that a coarse grid size was used as background (2.6 million cells), the wake development shows a well-preserved first and second passage of the vortex. Moreover, the interaction between blade and vortex typically encountered in hovering rotors is not presented here. In fact, the downstream convection of the rotor wake at M _∞ = 0.182, results in a much less complex wake.

Figure 20. Wake visualisation of the propeller wake using Q-criterion shaded by contours of C_P at blade pitch angle of θ₇₅ = 26 ^o (left) and θ₇₅ = 28.8 ^o (right).