5. Framework test cases

#### 5.1. Multidimensional discrete gust loads simulation

The aim of this test case is to demonstrate the use of simulation frameworks such as CA<sup>2</sup> LM for assessing the impact of multidimensional discrete gust modelling on conventional gust loads practices seen in industry. The prediction and control of aircraft gust loads is a key step in aircraft design development and certification. The methodology to model realistic discrete and continuous atmospheric disturbances has been derived based on many years of flight testing and operational data [37]. Hoblit [23] covers a concise but thorough overview of the historical development of gust and turbulence modelling in whereas a detailed discussion of current industry practices can be found in [35]. However, the methods to date simplify the process of calculating gust loads by neglecting spanwise variations in the gust/turbulence fields. This case study demonstrates the application of the CA<sup>2</sup> LM framework for studying gust profiles that have spanwise variations. Atmospheric disturbances are usually added through the use of velocity fields. For each aerodynamic station, the wind or gust velocities can be added to the rigid-body translation, rotation and elastic structural dynamics in a local nodal axis system to compute local changes to angle of attack and flow velocities. If gusts are defined as a velocity field, the gust model should also use the aerodynamic station layout and aircraft attitude to apply a penetration effect.

With the development of HALE UAV aircraft, the lack of spanwise non-uniform velocity distributions was identified as critical both for realistic and theoretical modelling purposes. The gust profiles specified in certification requirements [37, 38] implicitly assume that a uniform velocity distribution causes the highest internal loads and therefore, are the only cases that need to be investigated. Therefore, Defense Advanced Research Projects Agency (DARPA) focused on the derivation of a modified discrete gust model to account for the extra dimensional term and led to the expression of the discrete gust velocity Vdg to be defined by:

$$V\_{dg}\left(\mathbf{x}\_d, y\_d\right) = V\_{dg} f\_{\mathbf{x}}(\mathbf{x}\_d, H\_{\mathbf{x}}) f\_{\mathbf{y}}\left(y\_d, H\_{\mathbf{y}}\right) \tag{23}$$

where:

LM

LM framework for studying

parameters used by the aerodynamic model, closing the main calculation loop. Similarly, the adequate gravity contribution can be computed with position (or altitude) and applied to the

Figure 8. Aircraft flexible structure overlaid with aerodynamic profiles and control surfaces for pilot input visualisation.

Appropriate inputs, usually on aircraft control surface and thrust, should be linked to the model in the correct format. Control surface dynamics can be implemented for higher fidelity. As each module is included in the simulation framework, correct integration testing must be conducted to verify that each modules are behaving as expected. Therefore, as the complexity of the framework increases, thorough testing also requires more effort. It can also be really helpful to have visual aids and illustrations of the simulation. For example, an illustration of aerodynamic station and structural node positions updated with structural flexibility at each time step can be found in Figure 8 and is very useful to visualise the modelled aircraft.

The aim of this test case is to demonstrate the use of simulation frameworks such as CA<sup>2</sup>

for assessing the impact of multidimensional discrete gust modelling on conventional gust loads practices seen in industry. The prediction and control of aircraft gust loads is a key step in aircraft design development and certification. The methodology to model realistic discrete and continuous atmospheric disturbances has been derived based on many years of flight testing and operational data [37]. Hoblit [23] covers a concise but thorough overview of the historical development of gust and turbulence modelling in whereas a detailed discussion of current industry practices can be found in [35]. However, the methods to date simplify the process of calculating gust loads by neglecting spanwise variations in the gust/turbulence

gust profiles that have spanwise variations. Atmospheric disturbances are usually added through the use of velocity fields. For each aerodynamic station, the wind or gust velocities can be added to the rigid-body translation, rotation and elastic structural dynamics in a local

structural model.

64 Flight Physics - Models, Techniques and Technologies

5. Framework test cases

5.1. Multidimensional discrete gust loads simulation

fields. This case study demonstrates the application of the CA<sup>2</sup>

$$f\_x = \frac{1}{2} \left( 1 - \cos\left(\frac{\pi x\_d}{H\_x}\right) \right) \tag{24}$$

and fy is the corresponding sinusoidal function. Vdo is the gust intensity, Hx and Hy are the longitudinal and lateral gust gradients respectively and xd and yd are the longitudinal and lateral positions of the interest point in the discrete gust reference frame. Specifications to the range of both gust gradients can be made using similar hypothesis as before, ranging from 9 to 107 m.<sup>2</sup> An illustration of the multidimensional discrete gust velocity field is given in Figures 9 and 10.

This type of model was implemented as a feature within the CA<sup>2</sup> LM framework and applied to a conventional long range flexible aircraft configuration known as the AX-1. A study investigating the impact of such an approach to gust loads prediction for conventional aircraft was then carried out [39] using a sinusoidal lateral distribution as follows:

Figure 9. From a 1D to 2D discrete gust definition using coupled sinusoidal variation functions.

<sup>2</sup> In fact, it is necessary to push the higher end of the gradient spectrum so as to reach a minimum of 12.5 times the maximum aerodynamic chord of the vehicle and/or reach the peak maximum of the evaluated quantity with respect to the various conditions.

Figure 10. Visual display of the discrete gust velocity field for a given set of gust gradients used in the loads prediction loop.

$$f\_y = \cos\left(\frac{\pi y\_d}{H\_y}\right) \tag{25}$$

A sufficiently large number of realistic flight points compatible with the framework and implemented aircraft were used for this study. A number of gust gradients were used to allow a comparison between the conventional spanwise uniform velocity field and the multidimensional model of interest with enough fidelity. All simulations were made in an open loop system, where no correction to aircraft attitude is made. Two different approaches were used to scale the maximum gust intensity, keeping the core hypothesis of the certification requirements. This is justified by the very nature of the derivation of the original model, based on flight testing and loads data and not actual mapping of the gust velocity fields.

In both cases, the use of a multidimensional model led to lower gust structural wing root loads and vertical loads for an equivalent longitudinal gust gradient, as illustrated in Figure 11. In one case of velocity tuning methodology, some local loads extrema were higher than with the conventional model, possibly leading to higher occurrence numbers of specific load values. This also came to a cost in computation time, increasing by an order varying with Hy discretisation size the number of simulations required for a complete gust loads loop process.

Overall, these results were to be expected with the chosen spanwise distribution. Maximal gust intensity was centred on the fuselage in this study. But these results can vary quite dramatically with the selected fy distribution. If focused on matching the vertical load factor whilst keeping wingtip loads to the highest, this could lead to:

Figure 11. Time histories of wing root bending offset relative to trim for a given H<sup>x</sup> and various H<sup>y</sup> gradients.


#### 5.2. Aileron failure simulations

f <sup>y</sup> ¼ cos

on flight testing and loads data and not actual mapping of the gust velocity fields.

keeping wingtip loads to the highest, this could lead to:

loop.

66 Flight Physics - Models, Techniques and Technologies

A sufficiently large number of realistic flight points compatible with the framework and implemented aircraft were used for this study. A number of gust gradients were used to allow a comparison between the conventional spanwise uniform velocity field and the multidimensional model of interest with enough fidelity. All simulations were made in an open loop system, where no correction to aircraft attitude is made. Two different approaches were used to scale the maximum gust intensity, keeping the core hypothesis of the certification requirements. This is justified by the very nature of the derivation of the original model, based

Figure 10. Visual display of the discrete gust velocity field for a given set of gust gradients used in the loads prediction

In both cases, the use of a multidimensional model led to lower gust structural wing root loads and vertical loads for an equivalent longitudinal gust gradient, as illustrated in Figure 11. In one case of velocity tuning methodology, some local loads extrema were higher than with the conventional model, possibly leading to higher occurrence numbers of specific load values. This also came to a cost in computation time, increasing by an order varying with Hy discretisation size the number of simulations required for a complete gust loads loop process. Overall, these results were to be expected with the chosen spanwise distribution. Maximal gust intensity was centred on the fuselage in this study. But these results can vary quite dramatically with the selected fy distribution. If focused on matching the vertical load factor whilst

πyd Hy 

(25)

A control surface failure scenario is one of many failure cases that need to be considered for flight loads evaluation. Here the CA<sup>2</sup> LM framework is used for simulating a soft aileron failure where the port aileron undergoes an actuation failure and is forced to undergo a 15� amplitude limit cycle oscillation (LCO) whilst starboard aileron remains in the original trim setting. The dynamics of the aileron actuators are modelled through the transfer function:

$$\delta\_d(s) = \frac{-1.77s + 399}{s^2 + 48.2s + 399} \tag{26}$$

The main results obtained from the simulation of the AX-1 model are shown in Figure 12. The port aileron moves under a limit cycle oscillation at a constant frequency of 1.16 Hz, which corresponds to the first wing structural bending mode. The amplitude of this oscillation is set to �15� .

Figure 12. Example of AX-1 aileron cycle oscillation failure simulation results.

The frequency content of the roll rate p and yaw rate r signals show that the failure has excited a low frequency lateral-directional mode corresponding to periods of Tp = 10.24 s and Tr = 10.92 s in roll and yaw respectively. These correspond to the usual frequencies of the aircraft's Dutch roll mode. The highest peaks, just above 1 Hz, are the direct result of the simulated aileron forcing function. The load factor (n) only exhibits large transients when the aileron failure is initiated.

Figure 13 shows the frequency content of the wing root bending moment Mroot at different aileron excitation frequencies. At a frequency of 1.245 Hz, slightly higher than the frequency of the first structural mode of the wing (1.1634 Hz), the first aeroelastic mode appears and a resulting resonance is observed. Upon magnification (bottom right subfigure) another two peaks can be observed at 2.5 and 3 Hz. These correspond to aeroelastic modes associated with the 5th and 11th aircraft structural modes. At the frequency of 0.9 Hz, Mroot is higher than at the frequency of 1.1 Hz, which can be explained by the fact that the forcing function frequency is getting closer to rigid-body frequencies.

Simulations like this provide the insight loads engineers and flight control engineers need for exploring scenarios where a novel solution could be tested and design improvements can be made. Simulation frameworks such as CA<sup>2</sup> LM provide a rapid simulation capability needed especially at low technology readiness levels, where engineers and designers are interested in the impact of novel technologies such as folding wingtips, possible aircraft-pilot coupling scenarios [40] and flight loads during collision avoidance [6].

Figure 13. Wing root bending moment frequency spectrum for different aileron excitation.
