† Corresponding author. E-mail:
Accurate aerodynamic measurements in the hypersonic flow of large aircraft models in tunnels have practical significance, but pose a significant challenge. Novel aerodynamic force measurement methods have been proposed,but lack theoretical support. The forms of the force signals techniques for signal processing and calculation of aerodynamics are especially problematic. A theoretical study is conducted to investigate the dynamic properties based on models of the draw-rod system and slender rods. The results indicate that the inertia item can be neglected in the rod governing equation; further, the solutions show that the signals of each rod are a combination of aerodynamic signals (with a constant value) and sine signals, which can be verified by experimental shock tunnel results. Signal processing and aerodynamics calculation techniques are also found to be achievable via the flat part of the signals.
Accurate aerodynamic measurements in the hypersonic flow of an in-tunnel full-scale aircraft model are important,[1] but are challenging. The measurement of a full-scale aircraft model requires a sufficiently large wind tunnel platform with excellent free stream quality and an innovative support form for the model.
The shock tunnel is an important piece of ground equipment in the aerospace research field. The current tunnel limits the size of the aircraft model,[2,3] but can be used to provide a high total pressure and a high total temperature at relatively low cost. The traditional shock tunnel is only capable of satisfying the measurement of models several hundred millimeters in length, which renders experiments on full-scale models impossible.[4–7] The long-test-duration hypersonic detonation-driven shock tunnel[8] (JF12 shock tunnel) allows full-scale model measurement; the exit diameter of its nozzle is 2.5 m and the diameter of its test section is 3.5 m. It is capable of reproducing pure air flow with Mach numbers from 5–9 at altitudes of 25–50 km.
An effective support form is also crucial for aerodynamic measurements of a full-scale aircraft model in the shock tunnel. As a typical piece of impulse equipment, the running time of the shock tunnel is very short, generally between approximately 2 and 100 ms,[4,5] which makes the accurate measurement of the aerodynamic force of any model extremely difficult. A running time of several minutes was reported for the conventional tunnel;[9] this duration was found to be far longer than the vibration period of a force measurement structure. Further, the effects of damping were very apparent and the initial vibrations of the force measurement system were decayed. The whole structure can reach the force equilibrium state resulting in quasi-static (and thus highly accurate) measurements. In the shock tunnel, conversely, vibrations, balance, and support of the model are triggered by the impulse force due to the strong primary shock[10–14] during nozzle start-up. The damping effects can be neglected as the order of the magnitude of the test time is identical to that of the force measurement structure period. To this effect, aerodynamic force balance usage is a dynamic measurement process.
Several periods of signals are essential for dynamic signal processing and aerodynamics calculation. Individual signals sensed by the balance form a combination of signals corresponding to the aerodynamic force and vibration. Removal of the vibrational signals represents an essential and critical step processing force signals in the shock tunnel. Several periods (typically more than three) of signals should be tested to ensure accuracy. However, the natural frequencies of a measurement system rely heavily on the support form. More periods of signals would enhance the accuracy of peeled-off vibrational signals.[15,16] Thus, the support form of the model largely determines the overall accuracy of force measurements.
Rear sting supports are the most commonly used support forms in shock tunnels.[17–25] However, the cantilever-beam type limits the frequency, so the mass of the model is limited to a few hundred grams and the length magnitude within the millimeter level. The mass of a full-scale aircraft model is close to 1000 kg. The vibrational frequencies markedly decrease as the model mass increases in these setups. The equation of the frequency for the spring-vibrator model suggests that
Researchers have recently developed a novel aerodynamic force measurement method for large aircraft models in the JF12 shock tunnel.[25] The applicable model mass is about 300–1000 kg and its length is about 3–5 m. The aircraft model used to explore this method was hung via the draw-rod system (Fig.
![]() | Fig. 1. (color online) (a) Force analysis prior to tunnel testing. (b) Force analysis during testing. |
The preliminary study on this novel aerodynamic measurement method merits some further clarification. The forms of the force signals, for example, are unclear. Effective removal of vibrational signals depends heavily on the signal forms, which are closely related to the overall feasibility and the accuracy of the method. The technique for obtaining the aerodynamics from the force signals should also be further explored. Theoretical support still has these two essential problems. In this study, the theory of static force vectors was investigated in this regard as a series of basic dynamic measurement concepts. Further assessment under the structural dynamics theory was also conducted to investigate the working process of the draw-rod system in the shock tunnel. A few relevant theoretical solutions were proposed, as discussed below.
The superposition of forces and moments is based on the principle of equilibrium within three dimensional force systems i.e., the static theory. It is generally applied in low-speed tunnels with a wire-support system.[27,28] In this study, we also found that it is related to the dynamic aerodynamic measurements.
Before testing the tunnel, the resultant forces and gravity of the model were considered to be in equilibrium as shown in Fig.
The aerodynamic force measurements in the shock tunnel are a dynamic process. Thus, the force measurement theory of the draw-rod system in a shock tunnel is characterized by structural dynamics. The dynamic properties of the aircraft model and rods can be investigated separately. The ultimate objective of applying dynamic theory is to obtain the aerodynamic force with the measured signals of each rod.
The vibration of the whole system can be roughly divided into two stages corresponding to the test process: the forced impulse stage and the steady vibration stage.Signals can be efficiently acquired during steady vibration of the draw-rod system. The following basic assumptions were applied:
The vibration of the whole system can be simplified as a multidegree-of-freedom structure as describedby[29]
The natural frequencies were determined via the properties of the force measurement structure, which can be solved via the following free vibration equation:
Let
The rods used in the tests are uniform and have equal cross sections. The dynamic process belongs to one-dimensional and longitudinal vibration and can be expressed as follows:[29]
Natural frequencies:[29]
Normal modes:
Generalized force:
Normal coordinate:
Displacement solution:
The magnitude analysis was conducted for each term in Eq. (
Signal processing is a crucial issue[19–21] inherent to the force measurement in shock tunnels. The signal compositions for each rod in the draw-rod system were determined as described above; the methods of dynamic signals in rod processing were then established to calculate the aerodynamics.
The sinusoidal signals can be removed via signal processing (e.g., the LDSE method). The generalized displacement given in Eq. (
Thus, the method to obtain the aerodynamics is complete. Each experimental signal contains a flat signal and some sine signals. Numerical methods such as LDSE, as mentioned above, can be applied to extract sine signals as vibrational signals. The frequencies of sine signals are equal to the natural frequencies of the structure. The remaining parts of signals are the flat signals which correspond to a constant force as the inner forces of the rods. The superposition of forces and moments can then be applied, where the constant forces of each rod are similar to the static force
The signals of the inner forces are a combination of a constant value (flat signals) and some sine signals. Figure
![]() | Fig. 2. (color online) (a) Experimental signals of the rods at tail; (b) compositions of CH9 signals (corresponding to the rod at tail). |
The theory that sine signal frequencies equal the natural frequencies of the structure was also validated by experiments. The natural frequencies were measured by knocking experiments. The signals were acquired by accelerometers. The Fourier analysis was applied to measure the natural frequencies. Figure
In this study, theoretical support was established for a novel aerodynamic force measurement method applicable to large aircraft models for JF12 shock tunnel tests. The draw-rod system and slender rods were modeled and verified numerically.
A physical model was set up for the draw-rod system, and its dynamic properties were analyzed via structural dynamics. A detailed order analysis was also conducted to simplify the vibrational equation of the rods. We found that the inertia force of the rods is much smaller than the outer excitation force. The signals of each rod were identified as a combination of a constant value (flat signal) and sine signals. The experimental results also support this theoretical conclusion.
A method for signal processing and aerodynamics calculation was also proposed here, in which each experimental signal contains a flat signal and some sinusoidal signals. The sine signal frequencies are equal to the natural frequencies of the structure. Vibrational signals can be removed; the remainders are flat signals, which can be converted to a constant force as the inner forces of the rods. The resultant inner constant forces based on the superposition of forces and moments are equal to the aerodynamic forces. These theoretical predictions were validated by experimental tests in an actual shock tunnel.
In the future, we plan to further investigate the interference induced by the rods on aerodynamic measurements.
[1] | |
[2] | |
[3] | |
[4] | |
[5] | |
[6] | |
[7] | |
[8] | |
[9] | |
[10] | |
[11] | |
[12] | |
[13] | |
[14] | |
[15] | |
[16] | |
[17] | |
[18] | |
[19] | |
[20] | |
[21] | |
[22] | |
[23] | |
[24] | |
[25] | |
[26] | |
[27] | |
[28] | |
[29] | |
[30] |