Dynamic Wind Tunnel Testing Methods

Dynamic wind tunnel testing falls broadly under free-flight or forced oscillation tests.

There are other types of tests such as free-fall and free-spin that test extreme flight conditions but these are not as applicable here. A good overview of the various types is given by Owens et al [146] but the trade-off between free-flight and forced oscillation is given here. The Hexafly test vehicle has no rudder surfaces and is designed to be stable without them for the short duration of the hypersonic glide test. To fly stably about the lateral axes at low speeds would require rudder control with significant authority.

The high angles of attack, low inertia about the roll axis (I_xx), and non-zero off diagonal inertial components will lead to coupling between pitching motion and the lateral motion.

This complex interaction has been avoided in the present work by limiting the analysis of the dynamics to purely pitching motion as an initial study into subsonic stability of this unconventional hypersonic waverider design. The static analysis has shown good static stability properties in the lateral axes though dynamic behaviour in a real vehicle will likely be a challenging control problem for the reasons mentioned. Therefore, the type of free-flight testing considered here is the free-to-pitch only type. The model has one degree of freedom about the pitch axis and the control problem is then limited to elevon control of the pitch attitude only.

A key part of designing the test and model is the scaling parameters which allow the sub-scale results to be applied to full-scale flight predictions. The main scaling parame-ter for static testing is the Reynolds number which is defined for density (ρ), freestream

velocity (V∞), reference length (L_ref), and dynamic viscosity (µ) as ρV∞L_ref/µ [138].

Dynamic testing must also consider the Strouhal number, also known as the reduced oscillation frequency (ωLref/V ), the reduced linear acceleration (aLref/V²), the reduced angular acceleration ( ˙ΩL²_ref/V²), the Froude number (V²/L_refg), the relative density factor (m/ρL³_ref) and the relative mass moment of inertia (I/ρL⁵_ref) [146]. Where com-pressibility factors are considered Mach scaling is also required, however this is not the case here. It is clear that matching all of these scaling parameters simultaneously be-tween the sub-scale model and the full size vehicle is not possible as they conflict with each other. The reduced linear acceleration does not apply here as for both free-to-pitch and forced oscillation, the model translation is fixed and it does not linearly accelerate.

The Froude number is also considered less important as it is used to balance flow forces to gravitational force and in order to obtain the same trim angle of attack during test manoeuvres as at full flight. This is important for free flight tests but not as much for wind tunnel tests where the angle of attack can be varied without the requirement that lift be equal to weight. Dynamic tests of the F-16XL at high AoA have shown that the Strouhal number is important [146], as it enforces similitude of flow angles over the model surface during dynamic oscillatory manoeuvres [147]. The scaling factors that are focused on here are the Reynold’s number and the Strouhal number as they impact the aerodynamics of the test vehicles to the greatest degree.

Forced oscillation testing, as used in references [132], [148], [149] and [150], requires a wind tunnel mount that is capable of oscillating the test vehicle about the expected centre of rotation. The model must rotate about this point as the dynamics of the system cannot be transferred to a different point after the test has been completed as can be done with static forces and moments. The key aerodynamic feature to capture is the specific rate of change of the flow angles at different points on the vehicle during the rotational motion. The key difficulty for this work was accessing or developing this type of mount for the University of Sydney 3x4 wind tunnel. The main advantages of this type of test is that the manoeuvre frequency and amplitude can be directly selected allowing for matching of the Strouhal number to the full scale more easily. This allows the effect of the frequency and amplitude to be assessed independently. The model itself is also less complex without need for internal components and sensors. The mount interfaces to the model via a force measuring load cell similar to the static testing conducted in

Chapter 4. Most importantly, unstable flight states can be tested independent of any control system in the loop, allowing for the pure aerodynamic forces to be assessed. Free flight and free-to-rotate tests cannot assess the aerodynamics of unstable configurations without the flight control system active and although it is possible to do parameter estimation of the aerodynamic model from closed loop testing, it is much more difficult.

The limitations of forced oscillation testing are that it relies on numerical predictions of important frequencies such as that of the short period mode and the dutch roll mode to select test frequencies that are representative of the vehicle motion. The shape of the oscillatory motion is also constrained to the oscillation mechanism, usually sinusoidal in nature, on the assumption that the motion of the actual aircraft can be linearised about some trim condition. This may not be the case with highly non-linear flows and some element of the feel of the vehicle and behaviour under free flight is lost.

The free-to-pitch method requires a far more complicated wind tunnel model with ac-tuated control surfaces connected to a flight controller and on board sensors to measure the attitude and control surface states. The requirements are much closer to a full flight model although the availability of affordable high accuracy small scale components has made conducting this type of testing easier in recent years [151]. A gimbal system must be designed to attach the free-to-pitch model to the static mount in the wind tunnel.

Internal sensors are required to measure the angle of the gimbal and the control surfaces simultaneously, and the data must be stored to allow post processing of the damping characteristics. The model must, as far as possible, be scaled and weighted to be bal-anced around the centre of gravity and to have an inertia as close as possible as that required by the dynamic scaling factors to give a similar oscillation characteristic to the full vehicle. Linear regression techniques used here cannot separate the dynamics of a control system from the vehicle aerodynamics effectively as the controller would always be actively suppressing motion during a manoeuvre. Therefore the tests must be done of the open-loop response and cannot be done if the model is unstable in pitch. This forces the centre of gravity of the Hexafly-Int vehicle to be moved forward from the design centre of gravity referred to as CG_des in Chapter 4.

Despite the aforementioned limitations, the main advantage of free-to-pitch includes testing using the same mounting system as used for the static testing without the need for complex oscillation systems. If the inertial characteristics are similar then the observed

response to a control surface input will also be similar to that of the full vehicle including the actual shape of the rotational response over time. The use of the free-to-pitch method also allows a qualitative assessment of the ease of control in both open loop (pilot inputs only) and closed loop (controller active) modes. A controller can also be tuned to assess the requirements for controlling the closed loop response with software. Control sequence inputs can be automated to give step, doublet and 3-2-1-1 type manoeuvres among others. These are all broadband inputs and with a reasonable estimate of the short period frequency based on static testing results, can ensure that the short period mode is excited.

A free-to-pitch model as shown in Figure 5.1 has been developed for this work. The model freely rotates about the gimbal shown in blue, which is attached to the wind tunnel mount. Attempts to balance the geometric constraints with the various scaling requirements are described below. The data obtained from this model will be used to calculate a pitch damping derivative.

Figure 5.1: Free-to-pitch model (gimbal shown in blue)