2.1 Multi-body dynamics

This refers to the ability to construct a model by arbitrarily interconnecting modelling elements, each with their own degrees of freedom, and using iterative numerical methods to solve the resulting fully coupled dynamic system. This has the advantage of eliminating the derivation and programming of the fully coupled equations, thereby reducing model development time and eliminating the potential for human error. While the iterative solution method is less computationally efficient than the explicit formulation that could be achieved with a manual derivation, the speed of modern computers has largely eliminated this disadvantage.

2.2 Blade element and finite element methodologies

Using a blade element model, detailed rotor aerodynamics and blade- and hub-retention dynamics can be accurately modelled. The blade element model is computationally efficient and has been extensively used for flight dynamics and handling qualities analysis as well as full rotorcraft flight simulation^{(Reference He, Goericke and Lee1,Reference He, Goericke and Kang2)} . The finite element method significantly improves the rotor structural dynamics modelling by considering the nonlinear blade elasticity, which is important for vibratory loads prediction^{(Reference Saberi, Jung and Anastassiades3)}.

2.3 Unsteady airloads

Both blade element and finite element models are integrated with unsteady aerodynamics models, including dynamic stall for detailed blade section airloads evaluation^{(Reference He and Du Val4)}. In addition, modules are provided for blade element ducted fan modelling that include the effect of fan/duct interaction^{(Reference He and Xin5)}.

2.4 Viscous vortex particle method

The viscous VPM is a first-principle-based rotor/wing wake dynamics solution. It provides an accurate and computationally efficient method for complicated and/or novel rotor/wing wake and interference modelling^{(Reference He and Zhao6-Reference He and Rajmohan11)}. VPM currently does not run in real time and is used in an offline mode.

2.5 Interface to computational fluid dynamics codes

In recent years, first-principle-based rotorcraft aerodynamics methods (i.e. Navier-Stokes-based CFD airloads solvers) have been interfaced with FLIGHTLAB to offer a coupled CFD/CSD solution^{(Reference Rajmohan, Zhao and He8)}.

2.6 Flight and engine controls

To support full-flight rotorcraft modelling, modules are provided (such as gains, integrators, switches, transfer functions, etc.) to simulate flight control systems, ranging from simple mechanical controls with a Stability Augmentation System (SAS) to full digital fly-by-wire/light systems with integrated primary and automatic flight control systems.

2.7 Engines and drivetrain

Modules are provided for the modelling of the power turbine and gas generator with the applied turbine and gas generator torques obtained from thermodynamic tables as a function of rotational speed and fuel flow. Options for both quasi-static and dynamic modelling of the thermodynamics are provided. Modelling of the rotational speed degree of freedom of the power turbine and gas generator includes their inertia, the torque output of the thermodynamic tables, and the reaction torque of the rotors, as applied through the drivetrain. Control modules (such as gains, switches, math elements, transfer functions, etc.) are also provided for modelling engine fuel control and fuel dynamics. The drivetrain model includes the transmission, clutch, main rotor shaft, and tail rotor shaft.

Additional modules provide modelling capabilities of landing gears, fuel system, internal and external cargo, and more. The research reported in the references has underpinned the developments illustrated in Fig. 1.

3.1 Overview

The FLIGHTLAB Development System has been used by a variety of organisations to simulate and analyse the behaviour of a wide range of existing aircraft and to support the design and testing of new and unique aircraft configurations. The unique configurations include tail sitters, tiltrotors, compound rotorcraft, coaxial rotorcraft, autogyros, and distributed propulsion aircraft. A selective fidelity modelling capability allows for reduction in the computational intensity by reducing the modelling sophistication for phenomena that are of secondary importance to the application. For example, rigid body structural modelling may be used in real-time training applications where structural loads are not being directly investigated. Validation is an essential activity to ensure the modelling fidelity is sufficient to support the required application. The level of modelling typically used for performance and handling qualities analysis includes blade element rotors with finite state dynamic inflow modelling of both the inflow at the rotor and for downwash interference effects on the fuselage and empennage^{(Reference He, Goericke and Kang2,Reference He and Du Val4,Reference Strope, Borden and Harding12)} . Structural modelling of the rotor for these applications uses either rigid body, modal elastic or finite element representations^{(Reference Saberi, Jung and Anastassiades3)}. For detailed design and analysis, the flow field is modelled using VPM to capture the interactional aerodynamics of all vorticity producing elements^{(Reference He and Zhao6-Reference He and Rajmohan11)}. Interfacing to CFD codes provides high-fidelity modelling of the airloads^{(Reference Rajmohan, Zhao and He8)}. For structural loads analysis, finite element modelling of the rotor is used and a modal representation of the fuselage, obtained from a NASTRAN model, is used to couple the modal fuselage response with a full finite element NASTRAN model of the fuselage. Table 1 provides examples of the selective fidelity modelling options typically used for various modelling and simulation applications.

Table 1 Examples of selective fidelity modelling options applied to achieve required fidelity for different applications

The following sections discuss these validation efforts, including example plots comparing simulation and test data. The discussion also addresses the modelling and simulation challenges in each area and the model enhancements that were required to achieve an acceptable level of correlation with the test data.

3.2 Performance

Performance prediction is a basic necessity for any modelling and simulation tool. It requires trimming the model at a range of flight conditions and aircraft configurations and recording control settings, engine power, rotor thrust and torque, and other essential parameters. The software uses an iterative gradient approach to trim that can be carried out to any desired level of accuracy. The trim process can be difficult at the edge of the flight envelope due to discontinuities in the aerodynamics. The trim process has been enhanced to address this problem and provides a robust trim across the flight envelope. A detailed study of the ability of FLIGHTLAB models to accurately predict rotorcraft performance was conducted and reported in Reference He, Goericke and KangRef. 2. A number of modelling enhancements were made during this study to improve the performance prediction. Enhancements include modification to the inflow modelling, the addition of stall delay, the addition of wake decay, and modelling of rotor interference effects on the empennage. These enhancements and the associated validation effort are described in Reference He, Goericke and KangRef. 2 and summarised below.

Prediction of the power required for performance estimates is affected by inflow modelling accuracy, particularly at hover and low-speed flight conditions. The Peters and He finite state dynamic wake model, described in Reference Peters and HeRef. 13, is used for induced velocity modelling for performance predictions. The finite-state dynamic wake model uses a mathematical series representation of both radial and azimuthal inflow variation. Comparisons against test data were performed for two different orders of the dynamic wake series approximation; 3 states and 15 states. Increasing the order of the series approximation affects the power estimation accuracy as shown in Fig. 2^{(Reference He, Goericke and Kang2)}. This figure plots power coefficient (C_P) vs. thrust coefficient (C_T) for a UH-60 helicopter in ground effect and overlays test data with both a 3-state and a 15-state dynamic wake model. The dynamic wake model includes ground effect using a three-dimensional potential source.

Figure 2. Effect of inflow model order on hover performance^{(Reference He, Goericke and Kang2)} Pres. Alt (ft): 3111 Whl. Ht. (ft. AGL): 5.0 F.S.C.G. (in): 347.1.

The rotor blade planform and twist for this vehicle were distributed toward an optimum inflow distribution for good hover performance. The blade element model used for analysis accurately represents the detailed blade platform and twist and therefore, it gives reasonably good prediction even with a 3-state wake model. But the 3-state model prediction does deviate from the measured data at higher lifting conditions due to the increasingly nonuniform variation of the induced inflow. That is why the higher-order finite state wake model (15 states) improved the results at the higher thrust region. While a 6-state model was not tested in this study, it may provide a good compromise between the 3- and 15-state results and it is still very computationally efficient.

In forward flight, the retreating blades experience reversed flow, which increases with speed and is the primary cause of stall encountered by the inboard blade sections, as discussed in Reference He, Goericke and KangRef. 2. The flow stall causes a large increase of rotor profile drag and hence, the power. But, the 3D flow due to rotor rotation can delay the blade stall and therefore, modelling the stall delay effect helps improve the prediction. This phenomena is also referred to as dynamic stall.

The stall delay model was developed analytically using a laminar 3D boundary-layer solution on a rotating wing^{(Reference Banks and Gadd14)} and the model introduces the delay in terms of both maximum lift angle-of-attack and the angle-of-attack corresponding to the drag divergence in stall. Enhancing the blade element with the 3D stall delay model helps improve the prediction. This effect is further addressed in Reference He, Goericke and KangRef. 2.

3.3 Stability

Stability validation includes tests for longitudinal static stability and lateral directional static stability. Longitudinal static stability requires varying the airspeed about a trim point and recording the attitudes and control settings required to achieve the specified airspeed. Lateral directional stability requires varying the sideslip about a trim point and recording the attitudes and control settings required to achieve the specified sideslip. The modelling and simulation challenge is to provide sufficient flexibility in the choice of trim variables and trim targets to conduct these specialised trim problems. For the longitudinal static stability prediction, the collective is fixed at the nominal trimmed state to follow the flight test procedure. For lateral/directional stability, the collective is varied to achieve trim. Figures 3(a) and 3(b)^{(Reference He, Goericke and Kang2)} show the results of these two stability tests for the UH-60 helicopter. The flight conditions for these tests are presented in the figure captions. The fit quality is dependent on multiple factors, including the fidelity of the rotor and interference modelling and the fidelity of the aerodynamic coefficient data for fuselage airloads, etc. The slope of these prediction lines for the simulated data agree well with the overlaid flight test data for the longitudinal stick, the pitch angle, and the horizontal stabilator (Hstab) in the longitudinal static stability case and for the lateral stick and roll angle in the lateral directional static stability case. The deviation of the slope in the pedal prediction line from that of the flight test data in the lateral directional static stability case is most likely due to deficiencies in the tail rotor modelling. This comparison was performed in 2005 when a Bailey rotor model was used for the tail rotor. The accuracy of the Bailey model degrades with forward flight speed and this could account for the discrepancy. Blade element tail rotor models are now used for improved forward flight predictions.

Figure 3. (a) Longitudinal static stability at 123 Kn. Pres. Alt (ft): 5220 G.W. (lb): 15260 F.S.C.G. (in): 360.3.

Figure 3. (b) Lateral directional static stability at 90 Kn. Pres. Alt (ft): 8524 G.W. (lb): 16785 F.S.C.G. (in): 364.4.

3.4 Control response

Validation of a model's dynamic response to control inputs is performed by initialising the model to the test conditions, driving the model with the recorded time history of controls, and comparing the model response with recorded flight data. This is typically done for a range of flight conditions and vehicle configurations. The modelling and simulation challenge is that any modelling error will propagate rapidly due to the open loop nature of this test so the test is generally limited to relatively short durations. Sufficient response duration, however, is required to assure that at least one full cycle of the longest frequency dynamics mode is fully captured. A set of representative controllability validation results are presented for hover in Figs. 4(a) and 4(b) and for forward flight in Figs. 5(a) and 5(b)^{(Reference He, Goericke and Kang2)}. The slight pitch attitude change prior to the control input is due to the level of tolerance assigned in the trim process. Modelling enhancements provided since this 2005 paper would significantly improve the correlation and have, in fact, resulted in the model passing FAA Level D certification requirements⁽¹⁹⁾. These enhancements include adjusting the inflow influence matrices of the Peters-He finite state inflow model based on results from the Viscous VPM, deriving fuselage aero data tables from CFD modelling, utilising a blade element tail rotor, etc. In addition, the off-axis response modelling has been significantly improved by the addition of the manoeuvre wake deformation to the dynamic wake modelling methodology. Also note the inconsistency between measured z-axis acceleration and measured z-axis velocity in Fig. 5(b). The velocity test data was derived from air data sensors and is less accurate than accelerometer data. This test data was collected in the mid-1980s before kinematic consistency testing was commonly applied to processing of test data.

Figure 4. (a) Longitudinal step in hover. Pres. Alt (ft): 5373 G.W. (lb): 15950 F.S.C.G. (in): 359.4.

Figure 4. (b) Pedal step in hover. Pres. Alt (ft): 5742 G.W. (lb): 15750 F.S.C.G. (in): 359.3.

Figure 5. (a) Lateral impulse in forward flight (92.0 Kn). Pres. Alt (ft): 4736 G.W. (lb): 16780 F.S.C.G. (in): 362.7.

Figure 5. (b) Collective step in forward flight. Pres. Alt (ft): 5944 G.W. (lb): 15600 F.S.C.G. (in): 351.4.

3.5 Manoeuvre loads

The ability of a model to predict manoeuvre loads accurately is essential to the use of the model in support of design and flight testing. Table 2 presents the types of manoeuvres typically used in helicopter flight tests for loads analysis^{(Reference Strope, Gassaway, Spires and Kacvinsky15)}.

Table 2 Flight test manoeuvres for loads analysis

As mentioned in the previous section, the use of a prescribed control-time history to drive the model results in rapid propagation of any modelling errors due to the open-loop nature of the control. The sensitivity of the manoeuvre loads to vehicle attitude makes this particularly problematic for manoeuvre loads prediction. This problem is addressed by using a virtual pilot model that uses feedback to track the time history of handling qualities parameters such as load factor. The prescribed control and virtual pilot can be combined as a feed-forward and feedback controller to further improve tracking of flight data.

A validation of manoeuvre load predictions on a UH-60M model was reported in Reference Strope, Gassaway, Spires and KacvinskyRef. 15, where three different methods of predicting manoeuvre loads were examined.

1. (1) Driving the model open loop from the flight test control time history

2. (2) Augmenting the flight test control history with a virtual pilot model that used handling qualities targets for the required manoeuvre

3. (3) Using only the virtual pilot model for the prescribed manoeuvre

The first approach could not replicate the handling qualities targets of roll attitude and load factor with sufficient accuracy to estimate manoeuvre loads. The second approach was more effective in predicting manoeuvre loads since it augmented the open-loop flight-test control time history with the feedback virtual pilot model, thereby tracking the handling qualities targets more accurately.

When there is a need for predicting manoeuvre loads in the absence of flight test data, the third method is the only available approach since it does not utilise the flight test control history. The paper concluded that matching test data for roll attitude and load factor for the rolling pull-out manoeuvre that was investigated is critical to matching peak manoeuvre loads and that running the virtual pilot control alone with these targets generated peak loads very near those measured in the flight test. This approach was subsequently used to predict the flight-test manoeuvre loads for the UH-60M aircraft in advance of flight tests.

A fourth approach, which was not investigated, is to use inverse simulation, where the time history of the trajectory is input and the controls and loads are output. This approach requires an iterative gradient search for the controls as opposed to the time-marching feedback control approach of a virtual pilot model.

No specific prediction error tolerance requirement for manoeuvring loads prediction exists, as far as the authors are aware. But, there is always a safety margin factor built in the design process, so it can tolerate certain load prediction errors in practice.

3.6 Aeroelastic stability

Aeroelastic effects can impact the dynamics of an aircraft and must therefore be properly modelled in a VE tool. The modelling and simulation challenge is to determine the necessary modelling sophistication to accurately capture the damping of the aeroelastic modes. This requires first validating the finite element structural model against structural deformation test data and then determining the level of sophistication of the wake modelling required to accurately reproduce the damping in aeroelastic test data.

This section presents results for the validation of finite element structural modelling, modal reduction, and aeroelastic stability analysis that were reported in Reference Saberi, Jung and AnastassiadesRef. 3. In this reference, three separate tests were performed on the FLIGHTLAB implementation of the Hodges-Dowell nonlinear beam element^{(Reference Hodges and Dowell16)}.

• • The Hodges-Dowell nonlinear beam element has been validated for flap-lag-torsion deformation against the Princeton beam tests^{(Reference Dowell and Traybar17)}.

• • The modal reduction accuracy was tested by comparing hub vibratory loads for the full finite element model of the Lynx rotor with those obtained from different levels of modal reduction.

• • The coupled rotor-body aeromechanical stability analysis was validated by utilising a finite element model of the blade structure with different-order Finite-State Dynamic Inflow models and comparing the simulation results with experimental data from a scaled model of a hingeless rotor^{(Reference Bousman18)}.

The results of the aeromechanical stability analysis are shown in Fig. 6^{(Reference Saberi, Jung and Anastassiades3)}. This figure shows the comparison of predicted modal damping of the lag regressing mode, the body roll mode, and the body pitch mode with experimental results from the scaled model of a hingeless rotor. The dampings of these modes were obtained from the model by linearizing all degrees of freedom of the model, including body degrees of freedom, blade structural degrees of freedom, and inflow model degrees of freedom. Degrees of freedom in the rotating frame were transformed to multi-blade coordinates prior to the linearisation and the linearisation was performed at multiple rotor azimuths and averaged to obtain a constant coefficient representation of this periodic coefficient system. Eigenanalysis of the resulting linear model was then performed to obtain the damping of each mode.

Figure 6. FIGHTLAB finite element modelling of a scaled model of a hingeless rotor.

The experimental model^{(Reference Bousman18)} consisted of a rigid body for the fuselage, a shaft, and a hingeless rotor with three very stiff composite blades attached to the hub with steel flap and lead-lag flexures. The fuselage was mounted on spring-restrained pitch-and-roll gimbals. The experimental model is half scale to match the tip speed of the full-scale system. The arrangement effectively modelled an ideal rigid blade configuration with spring-restrained hinges. The experiment was designed to investigate the aeroelastic coupling effects of blades with the fuselage and it is widely used for methodology assessment.

The modal damping results shown in Fig. 6 are for various inflow models at zero degrees of collective pitch in zero wind. The model consists of a rigid body mass representing the fuselage, two pitch-and-roll springs representing the gimballed mount and a three-bladed rotor with blades attached to the hub with discrete flap and lead-lag hinges with spring components to represent the model flexure stiffness. Each blade includes five nonlinear beam elements. Comparisons were run for five different inflow models; uniform inflow and 3-, 6-, 10-, and 15-state Finite State Dynamic inflow models. The negative lag damping at the 750-RPM rotor speed is a result of the lag-regressing mode at resonance coupling with the body pitch-and-roll modes to produce an instability in the lag degree of freedom. The coupling is a function of the body pitch-and-roll frequencies, which are determined by the spring restraints on the body. The difference in the roll-and-pitch damping is due to the difference in the spring restraints and fuselage inertias in these axes. While all inflow models predicted the instability, the accuracy of the damping prediction improved successively with increased inflow states up to the 10-state inflow model. The 15-state inflow model did not show significant improvement over the10 state model, so the 10-state model is considered optimal for this analysis. The reason for the increase in fidelity in the damping prediction with inflow model order is due to the improved modelling of the non-uniform inflow distribution with increased inflow model order. Since there was zero relative wind in this test, the only non-uniform inflow effects are due to the elastic response of the blades and yet it can be seen that this small effect has a significant impact on the aeroelastic damping. This demonstrates the importance of modelling fidelity to achieve accurate analyses with VE.

3.7 Induced velocity

The rotor-induced velocity is a predominating factor in all aspects of rotorcraft modelling. The vortex wake method, based on potential flow theory, is often used to model induced velocity, but it cannot predict transient wake behaviour, it does not include the effect of viscosity, it requires the use of empirical parameters, and it uses a grid-based formulation that induces an artificial numerical dissipation of the wake. VPM, based on the Navier-Stokes equations, includes viscosity, is completely physics based sono empirical parameters are required, and it uses a Lagrangian solution method that avoids the numerical dissipation of the grid-based solution method.

In Reference He and ZhaoRef. 6, comparisons were made between the induced velocity predictions of VPM, coupled with a FLIGHTLAB blade element rotor model, and measured data. This section summarises the validation results of Reference He and ZhaoRef. 6.

Comparisons were run at hover and forward-flight conditions for both steady-state and dynamic response cases. Figure 7 shows the comparison of simulated and measured downwash velocity for a two-bladed rotor in hover. Figure 8 shows the comparison of simulated and measured downwash velocity for a two-bladed rotor in forward flight at an advance ratio, Mu, of 0.095. For both the hover and forward-flight cases, the rotor is trimmed to a mean thrust coefficient of 0.0032 and the results are plotted at steady state. The measured downwash velocities were time averaged for comparison with the steady-state simulation results. The source data for both cases are referenced in Reference He and ZhaoRef. 6. Due to symmetry, the time-averaged hover downwash velocities in Fig. 7 are plotted vs. radial position only, for three vertical offsets from the rotor plane. For the forward-flight case, the time-averaged lateral component of the downwash velocities in Fig. 8(a) are plotted for a lateral cross-section at the rotor centre and each plot shows three vertical offsets from the rotor plane. In Fig. 8(b) the lateral component of the downwash velocities for three vertical offsets from the rotor plane are plotted for a lateral cross-section at 0.5 rotor radii behind the rotor centre. The hub coordinate frame, in which z is positive upward, y is positive to the right, and x is positive to the rear, is used for these plots. Downwash is defined as negative as it points to the negative z direction.

Figure 7. (a) Downwash velocity profile in hover for rotor vertical offset = -0.1R.

Figure 7. (b) Downwash velocity profile in hover for rotor vertical offset = -0.5R.

Figure 7. (c) Downwash velocity profile in hover for rotor vertical offset = -1.0R.

Figure 8. (a) Downwash velocity profiles in forward-flight for three vertical offsets at the rotor centre.

Figure 8. (b) Downwash velocity profiles in forward flight-for three vertical offsets at 0.5 rotor behind the rotor centre.

Figure 7, for the hover case, shows the initial wake contraction and the vortex decay and diffusion that occurs further downstream. Figure 8, for the forward-flight case, shows the downwash variation has a strong nonlinearity around both the advancing and retreating sides of the rotor plane, which implies strong rolled up tip vortices. The good correlation of simulation and test data, for both cases, demonstrate that VPM captures fundamental characteristics of the rotor vortex wake interaction, including wake contraction and tip-vortex roll-up, without any empirical modelling parameters. It also adequately predicts the physical wake diffusion in terms of the induced velocity decay.

3.8 Ground effects

Ground effects significantly impact rotor performance and trim and can impact nearby ground operations. Reference 9 reports the results of a study using the viscous VPM with a FLIGHTLAB aeromechanics rotorcraft model to predict ground effects. In order to incorporate ground effects into VPM, constraints must be satisfied at the ground boundary. There are two types of boundary conditions in fluid dynamics. One is the “non-penetration” condition, i.e., no air flow penetrates through the normal direction of the surface. All potential flow-based methods use a “mirror image wake” at the ground level to satisfy this type of boundary condition for the flow solution. The other boundary condition is the “non-slip condition” which enforces the zero flow velocity in all directions over the surface (both normal and tangential). The “non-slip” boundary condition at the ground surface is satisfied by the addition of vorticity at the ground surface to oppose ground-relative motion of the rotor downwash at the ground surface. Potential flow methods using the mirror image method only capture the non-penetration condition, not the non-slip condition (in the tangential direction). CFD methods use the non-slip condition. It should be noted that the non-slip constraint can also be applied to moving surfaces. VPM has the option to apply either boundary condition.

Figure 9^{(Reference Zhao and He9)} shows a comparison of the simulated rotor wake in ground effect with experimental data obtained from a wind-tunnel test of a scaled four-bladed rotor in ground effects. The source data are referenced in Reference Zhao and HeRef. 9. A simulated rotor wake using only the non-penetration constraint (image ground) and a simulated rotor wake using the non-slip constraints (viscous ground) are compared with measured data to demonstrate the importance of applying the non-slip constraint. The plot shows the time-averaged outwash velocity, normalised by the nominal induced velocity in hover, at a lateral distance of twice the rotor radius from the rotor centre. The normalised outwash velocity is plotted as a function of Height Above Ground (HAG), normalised by the rotor radius.

Figure 9. Effect of the viscous ground on VPM-predicted time-averaged rotorwash at a radial station of 2.0R for an isolated rotor hovering at a Height Above Ground (HAG) of 0.5 R.

As seen in Fig. 9, the non-slip boundary condition matches the measurement data more closely than the non-penetration boundary condition, particularly in the region close to the ground. This is due to the introduction of the ground vorticity by implementing the non-slipboundary condition. It may be possible to further improve the correlation around 0.25R by using a smaller integration step. In Fig. 9, the normalised outwash at the ground surface is non-zero for all three cases. With the non-slip condition, the flow at the ground surface is zero in theory, but, due to the rapid reduction in outwash close to the surface, the numerical implementation can have errors and the referred paper discusses this in detail and also provides parametric studies on the numerical discretisation scheme that shows how to get the exact zero flow on the surface. For engineering analysis, however, this is less important. Note that even the measured data does not get the exact zero at the surface.

Additional comparisons of VPM predicted outwash with measured data are presented in Reference Zhao and HeRef. 9, including comparisons with CH-53E and XV-15 class rotorcraft. The comparisons show a good correlation.

3.9 Interactional aerodynamics

Interactional aerodynamics have a major effect on rotorcraft but it has traditionally been the least accurate element of rotorcraft simulation. Potential flow-based solution methods have been adopted in most interactional aerodynamics analyses. The potential flow methods, without considering the full flow physics such as air viscosity, etc., are insufficient to capture the fundamental aspects of flow interaction that usually involves large wake distortion and diffusion. Recent research and development of first-principle-based methods, such as VPM and Navier-Stokes-based CFD, has significantly improved the prediction accuracy. VPM now provides the first-principle physics-based modelling of the rotor wake required to address interactional aerodynamics modelling accurately.

The Rotorcraft industry has begun the design of transformational aircraft that will define aspects of the future of vertical flight aviation. These aircraft include tiltrotor, coaxial, and compound configurations with multiple rotors and ducted fans. The mutual interaction between the wakes, and other lifting surfaces, produced by these rotors and ducted fans significantly affects the performance, dynamics, loads, aeroelastic stability, and vibrations. The following sections address the validation of VPM-based interactional aerodynamic modelling for two modern configurations; coaxial, and compound. Validation of VPM for a tiltrotor configuration was given in Reference He and ZhaoRef. 7 but is not discussed here. The tiltrotor VPM results showed good correlation with the measured data.

3.9.1 Coaxial

This section summarises the results of Reference Zhao and HeRef. 10, which reports on an investigation into the use of VPM for coaxial rotor interactional aerodynamic modelling. As a first-principle modelling tool, VPM can properly model the mutual aerodynamic interaction of the upper and lower rotors. This validation effort also investigated enhancing the Finite-State Dynamic Inflow model with parameter modifications obtained from comparisons with the VPM results to obtain an enhanced Dynamic Wake model (DYW). The structure of the enhanced model is produced by coupling separate Dynamic Wake models for the two rotors through their off-rotor induced velocities. The parameters of these coupled Dynamic Wake models are then identified to match the results of the VPM wake. During the parameter identification process, the same rotor model was used in both the VPM simulation and the Dynamic Wake solution.

Figure 10^{(Reference Zhao and He10)} shows the coefficient of thrust (CT) vs. coefficient of torque (CQ) plot of a coaxial rotor in hover. The three lines represent the measured wind-tunnel results, the VPM simulation results using VPM for the induced velocity, and the simulation results using the Augmented Dynamic Wake for the induced velocity. The aerodynamic interaction in a coaxial rotor is particularly strong due to the mutual interactions of the rotors and the interactions between the rotor wakes. VPM is well suited to capture these effects, as shown in Fig. 10. Figure 10 also shows that the augmented Dynamic Wake model provides good correlation with test data and may therefore be a useful tool for design and analysis given its state space formulation. As discussed in Reference Zhao and HeRef. 10, the correlation of the enhanced Dynamic Wake model with measured data is significantly improved over the Dynamic Wake model without enhancements.

Figure 10. Comparison of VPM, DYW, and test results for coaxial rotor.

Figure 11^{(Reference Zhao and He10)} shows the correlation of VPM predictions with test data for the KA32 helicopter coaxial rotor for three different advance ratios. The flight test data in this figure are the tip vortex trajectories digitised from a photograph. The shading of the VPM results represents the vorticity strength with the darker shading representing stronger vorticity. The circles show the tip vortex concentration region (black for VPM and red for test data), which can be viewed as the tip vortex path as well. The VPM results are seen to compare well with flight test results.

Figure 11. Comparison of VPM-predicted tip vortex trajectory with KA-32 flight test measurement at different advance ratios (CT=0.008).

3.9.2 Compound

In order to satisfy future rotorcraft mission requirements for speed, range, and payloads, the U.S. Army Future Vertical Lift programme is exploring compound configurations that may have multiple rotors, ducted fans, auxiliary wings, etc. These advanced configurations introduce additional aerodynamic lifting devices/surfaces that make aerodynamic interactions even more complex. A hybrid solver has been developed for full rotorcraft interactional aerodynamic modelling. The hybrid solver couples near-surface vorticity solvers (such as CFD) with the VPM, off-body, wake simulation and the aeromechanics model. This hybrid solver has been applied to model the aerodynamic interaction between the rotors, wings, fuselage, and empennage. The main rotor is modelled using the blade-element formulation with the VPM wake solution. The wing and tail surface are modelled with the lifting line that couples with the VPM wake solver. The fuselage is modelled using Navier-Stokes CFD solvers and is coupled with the rotor, wing, and tail surface. Simulation and wind-tunnel test results have been compared for validation in Reference He and RajmohanRef. 11. This section provides a qualitative summary from the results of Reference He and RajmohanRef. 11.

Figure 12^{(Reference He and Rajmohan11)} shows the wake interaction of a compound rotorcraft between the rotor, wing, fuselage, and tail at 120 Kn for two different wing positions. The rotor has a diameter of 108 inches and the wing is located directly under the rotor and has a span of 81 inches. The rotor-wake and the wing-tip vortices can be seen in the figure.

Figure 12. Rotorcraft wake with interaction between rotor, wing and horizontal tail at 120 Kn (mid and high positions).

Figure 13^{(Reference He and Rajmohan11)} shows the effect of the rotor-lift coefficient on the wing-lift coefficient for a range of fuselage angles of attack (α_f) and for two different wing positions. Comparing the zero angle-of-attack lines for both wing positions, it is seen that the closer the wing is to the rotor, the lower the resulting wing lift coefficient. The simulation results compare well with the wind-tunnel test results confirming the validity of using the hybrid simulation approach with VPM as a VE tool to evaluate designs where interactional aerodynamic effects are significant.

Figure 13. Effect of rotor on wing lift at 120 Kn (mid and high positions).