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Unsteady aerodynamic models are estimated for a given aircraft using dynamic wind tunnel test data. Small and large amplitude forced oscillation wind tunnel test data are primarily used for modeling the aerodynamic loads at stall. The rotary balance wind tunnel tests provide steady aerodynamic loads for conical motion, which is primarily of interest in the angle-of-attack range covering steep or flat spins [3]. Wind tunnel facilities for capturing such data are available in many organizations across the world, and have been in use for more than four decades. Hence, most of the experimental studies and estimation of the model parameters is done using this type of data for delta-wing configurations and some airfoils. A detailed description of all the important dynamic wind tunnel test methods and their comparative analysis for consistency of the data, are available in [3].

Other methods of obtaining data for estimation and validation of the unsteady aerodynamic model are flight tests and Computational Fluid Dynamics (CFD). There are two attempts presented in literature where the flight test data was used for estimation or validation of unsteady variation in normal force coefficient. Data from the flight tests done at TsAGI, Russia were used to validate the Goman-Khrabrov State-space model, which was estimated using wind tunnel data [11]. The second flight tests done at DLR, Germany on a C-160 aircraft were used for estimation of the parameters for a similar model structure [19, 26]. These results were good and so important to the research community that it forms the cover page of the popular textbook by Jategaonkar [71].

There are continuing efforts towards unsteady aerodynamics numerical simulations using CFD techniques. A significant progress has been made recently, for example the work in [80]. A comparative study of the CFD results with the flight test data was presented in [81]. However, these methods have not been shown to be effective for modeling any aircraft unsteady aerodynamic loads.

3.3.1

Forced Oscillation Wind Tunnel Test

Forced oscillation wind tunnel tests have been performed on many delta-wing configura- tions in order to model the unsteady variation of coefficients in the stall angle-of-attack

Fig. 3.5. Small amplitude forced oscillation wind tunnel test data for X31 aircraft [78].

regime. The rigs for performing this test are available in Central Aero-hydrodynamic Institute (Russia), ONERA (France), NASA-Langley Research Center (USA), Indian Institute of Science (India) etc. These rigs are designed to provide inputs to the model by changing α or β or φ. In this test, the models pitch-angle is varied in a sinusoidal manner at a particular amplitude and frequency. The tests are performed with different amplitude and frequency combinations to obtain responses in a variety of conditions. These tests are performed in two sets classified by the amplitude of input as, (i) Small Amplitude Forced Oscillation test (SAFO), and (ii) Large Amplitude Forced Oscillation test (LAFO).

Classically, small amplitude forced oscillation test data is reduced to in-phase and out- of-phase derivatives by numerical computation of the first two terms of the Fourier series expansion. This is possible because the aerodynamic coefficient variation is also found to be sinusoidal. The out-of-phase derivative which is commonly referred to as damping derivative, is incorporated as a table in an aero-database. However, in the stall angle-of- attack regime, it is found to be a strong function of frequency as shown in Fig.(3.5) for

Fig. 3.6. Large amplitude forced oscillation wind tunnel test data for F16XL, with sinusoidal inputs of amplitudes∆α = 10o_{, 35}o_{, maximum pitch-ratek}

max= 0.02, and α0= 36o[82].

pitching moment coefficient of X31 aircraft.

The variations in the normal force and pitching moment coefficients of F16XL in response to large amplitude sinusoidal inputs is shown in Fig.(3.6). In case of CL, the values for two input amplitudes differ by up to 0.5 in pitch down motion. In case of Cm, the oscillation cycle is twisted indicating aerodynamic damping and anti-damping. These figures show that the aerodynamic loads are also a strong function of input amplitudes. The power-spectrum-density maps of these coefficients showed that there are super- harmonics, which implies that the variations are also nonlinear in nature.

Similar observations have been made from the small and large amplitude forced oscillation tests for many delta-wing aircraft [4]. Therefore, the amplitude and frequency dependence of aerodynamic loads is a fundamental aerodynamic feature of any delta-wing configuration in the stall region.

3.3.2

Rotary Balance Rig

Rotary balance test is one of the oldest dynamic wind tunnel tests. In this test, the aircraft model is rotated about the wind axis at a steady rotation rate. The model is rotated over a range of non-dimensional rates corresponding to the likely coning rate in spin for the given aircraft configuration. The wind tunnel model motion is similar to steady stable spin of an aircraft, except that the radius of rotation is equal to zero. The test was conceived to characterize the aerodynamic loads on an aircraft in steady spin conditions. Hence, this data is primarily used to model aerodynamic loads in the spin angle-of-attack regime which is usually at much higher angle-of-attack than the stall conditions.

Fig. 3.7. NASA/Editics Rotary Balance Rig with WG16B research model installed [3].

from this data. Details of various rotary balance test rigs in different organizations across the world and their comparative analysis is presented in [3]. This data is not directly useful for unsteady modeling of longitudinal coefficients, but it is complementarily used in development of an aerodynamic model for the full angle-of-attack range of (₋₉₀o ₉₀o_].

3.3.3

Some Novel Rigs

Recently, novel rigs for performing wind tunnel tests in which model can be moved about multiple-axis and multiple degree-of-freedom have been developed at University of Bristol [83] and Indian Institude of Technology Kanpur [84]. The rig developed at Bristol is shown in Fig.(3.8). The rig can provide all degrees-of-freedom except the axial motion of the aircraft model. Hence, it can closely simulate the aircraft’s initial response and steady state response to external flow conditions. The rig has mechanism to restrict some of the degrees-of-freedom and to asses the aircraft’s dynamic response in specific axis. Thus, it is possible to undertake a variety of novel dynamic wind tunnel tests for high-fidelity unsteady modeling and its validation.

A wide-band input in the form of a Schroder-sweep was used for performing dynamic tests at NASA-Langley using Eidetics corporation water tunnel [44]. Such a method can save the need for repetitive tests with multiple frequencies, and save time and cost. It is also expected to show better correlation with load variations obtained from other tests as the data is representative of the system response over a bandwidth instead of some

Fig. 3.8. Five Degrees-of-freedom rig developed at the University of Bristol for dynamic wind tunnel tests [83].

discrete frequencies. This concept is discussed in Chapter 5.

A novel rig called the Dynamic-pitch-plunge-rig was developed in Virginia-Tech University, USA and used for modeling the unsteady variation of rolling moment coefficient of delta-wing configurations [33]. This method is a promising approach for obtaining coupled variation of different moment coefficients from wind tunnel experiments for the purpose of modeling.