Identification using novel input types

The use of Schroder-sweep input response data for unsteady aerodynamic modeling was demonstrated in [31] for the first time. In this work, Murphy.et.al. used Schroder-sweep input response data from water tunnel tests to estimate the parameters of a simplified linear indicial model of normal force coefficient. In this section, the approach and advantages of using a VVM for identification of unsteady aerodynamic loads using the test data with Schroder-sweep inputs are presented.

uN(t) = N X 1 A sin(kωt + φk) (5.7) φk+1− φk = πk2 N (5.8)

Schroeder sweep is a wide-band input that consist of combination of multiple sine waves [100]. A typical Schroeder sweep input is given by Eq.(5.7). The frequency of each sine is an integral multiple of the base frequency ω, and it has N sine wave components. These sine waves have phase φk as given in Eq.(5.8). This makes the peak- to-peak amplitude of the input to be minimum and Root-Mean-Square to be maximum simultaneously, as first proved by Schroeder in [100]. This ensures that the input power is maximum to obtain best signal-to-noise ratio, while variation of amplitudes remains practical. Its unique advantage is that a single test can provide systems response data for multiple harmonic inputs. However, the use of data for the purpose of estimation depends on the linear or nonlinear nature of systems response for the input conditions.

For a chosen Schroeder-sweep input, if the response of CZ(t) or Cm(t) is found to be linear, it can be used for estimation of the first-kernel state parameters of VVM. This can be done by adopting an approach similar to the two-step regression method used with small amplitude forced oscillation test data. Using the Schroder-sweep input response of the force or moment coefficient, we can estimate in-phase and out-of-phase derivatives at multiple frequencies. This is done by taking a Fourier transform of the response at the component frequencies of the Schroeder-sweep input. Thus, it is possible to estimate a(α0), K1(α0) from a single Schroeder input test with three-five component frequencies. This is more efficient than performing SAFO tests with one frequency at a time.

0.5 1 1.5 2 2.5 3 3.5 4 −10 0 10 α 0.5 1 1.5 2 2.5 3 3.5 4 −100 0 100 α ’ 0.5 1 1.5 2 2.5 3 3.5 4 −500 0 500 α ’’

Fig. 5.6. A Schroder-sweep input with maximum amplitude A = 20o_{, component frequencies f =}

0.25, 0.5, 0.75, 1, 1.25Hz, proposed for dynamic wind tunnel tests.

aerodynamics, we can consider a two or three state VVM. The parameter estimation is done by output-error method. As demonstrated in the case of Cm of F16XL, using VVM approach we can get satisfactory results by appropriate choice of number of states. It is not necessary to classify the wind tunnel test data as small amplitude and large amplitude because VVM gets inherently tuned to match linear and nonlinear unsteady aerodynamics, valid for the maximum input used in experiments. This implies that one can choose a Schroeder sweep input of appropriate amplitude and bandwidth, and use output-error method for estimation of model parameters of an aerodynamic coefficient.

Here is an example of Schroeder-sweep input which is suitable for advanced pre- programmable dynamic test rig which can implement a desired anlge of attack trajectory shape. For a Schroder-sweep, assume that the maximum amplitude is A = 20 deg, component frequencies are f = 0.25, 0.5, 0.75, 1, 1.25Hz, and sampling rate is 100Hz. Then the input to the WT model is defined in Fig.(5.6). In this input, note that the maximum pitch-rate is 100 deg /s, and pitching acceleration is 520 deg /s2_{. Currently} available forced oscillation test rigs are capable of implementing fast model maneuvers. For example, the NASA-LaRC forced oscillation test rig has capability to implement maximum pitch rate of 260 deg /s, and pitch acceleration of 2290 deg /s2. However, these

are usually mechanically geared for harmonic inputs and cannot implement other dynamic maneuvers.

Note that, this single input covers a range of amplitudes and a bandwidth, which is likely to be sufficient for modeling. Thus, using Schroeder-sweep tests and VVM approach is a good combination for modeling, and a promising idea for the future.

5.4.5.2 Other dynamic input

Step and ramp motions inputs are other wide-band inputs which can be useful in identification. Their spectrum is usually defined by a two or three term Fourier Series. Even though, the trajectory of angle of attack used in experiments may not be exactly like a step or ramp, it is still possible to correlate the spectrum of input to the output using the advanced spectrum correlation methods available in literature [49]. In this case the arguments presented for Schroeder sweep input still hold good and a similar approach applies. Thus, use of step and ramp inputs is also a promising proposition for novel dynamic wind tunnel tests.

W.Silva presented use of phased impulse inputs for estimation of unsteady aero- dynamic impulse responses using CFD outputs and wind tunnel test data [56]. The parameter functions of VVM can be estimated more easily than the Volterra kernel shapes. The method given in [56] is useful for estimation of only first and second kernels. However, a VVM structure with three states can also be estimated by this method and this significantly enhances the models capability.

With the advent of CFD methods for nonlinear unsteady aerodynamics of delta-wing configurations, it is envisaged that such inputs which are not possible in a wind tunnel test, can now be used for identification using VVM much more efficiently.

5.5

Summary

VVM of longitudinal coefficients of GTA was integrated with 6DOF equations of motion for simulation and analysis. It was shown that the longitudinal unsteady aerodynamic loads significantly effect the frequency and stability of the Short-period mode, using the tools from linear systems analysis. VVM was compared to Volterra series based modeling approaches, Indicial theory based approaches and the ONERA dynamic stall model, to present its similarities and adaptations to these successful approaches. Further, VVM is amenable to identification using variety of input types due to its harmonic input response properties.

Chapter 6

Analysis and Modeling of Abrupt Wing

Stall

6.1

Introduction

The flight envelope boundary at high angle-of-attack and high sub-sonic Mach number is restricted by nonlinear and unsteady aerodynamics which drastically affect the aircraft’s stability and handling qualities. The aerodynamic phenomenon is usually reflected by onset of unintended rolling motion about body axis and is termed as Abrupt Wing Stall (AWS) [5]. This flight envelope boundary is of specific importance for a high- performance aircraft as it is used in a high-speed turn maneuver. However, due to lack of understanding of aerodynamics and safety concerns, this part of the envelope is conservatively curtailed for all the high-performance aircraft [101].

At high angle-of-attack and high subsonic Mach number shock pockets are formed on the upper surface of a delta-wing. These have two or three equilibrium flow-conditions, and can abruptly switch between them. This causes the flow on wings to be asymmetric and unsteady. In terms of aerodynamic loads, it causes static hysteresis in rolling moment versus side-slip, and loss of roll damping in the sense of traditional aero-derivative formulation. The asymmetric flow on the wings and its unsteady nature are visualized in the condensation pattern on the F-18E aircraft in flight as presented in Fig.(6.1). The resulting flight dynamics can exhibit different types of lateral instability, like slow roll-off (heavy wing), rapid rolling to a non-zero bank angle (wing-drop) and periodic body-axis rolling motion (wing-rock).

The unsteady aerodynamics at high angle-of-attack and high sub-sonic Mach number is different from that at low Mach number due to presence of a strong nonlinearity in Clvs. β. As discussed in previous chapters, VVM is not suitable for modeling such bifurcations in dynamics. Hence, a different approach for modeling the unsteady variation of Cl(t) as witnessed in AWS conditions is presented in this chapter.

Fig. 6.1. Asymmetric flow and its disappearance in a moment, as seen in the natural condensation pattern that appears on F-18E aircraft wing during flight at AWS conditions [5].

The topic is not widely stated in literature. A recent research program on this subject was pioneered by NASA-Langley Research Center with industry collaborators, as summarized in [5]. The papers from this program provide a good overview of AWS modeling and analysis technology. The phenomena is investigated using wind tunnel tests, flight tests, mathematical modeling and piloted simulation studies. The final approach that evolved is based on use of static and FTR test data for development of an aerodynamic model. They also presented a semi-empirical model based on piloted flight simulation evaluation studies. Both the models are qualitatively sufficient for flight simulation studies. Some of these concepts developed in the NASA AWS program are summarized in the next section.

The aerodynamic modeling approaches developed in the NASA AWS program are not generic for application to modeling AWS of other delta-wing aircraft. Other modeling approaches proposed in literature for modeling similar aerodynamic phenomena cannot be used either. Hence, a comprehensive approach to model unsteady rolling moment coefficient using static and FTR wind tunnel test data is presented in this chapter. The proposed model is called Bifurcational Model of Aerodynamic Asymmetry (BMAA). This model is in the form of differential equations and can be integrated with a 6DOF simulation framework easily. It has number of parameters which can be tuned to match the rolling moment coefficient from experimental data.

In Section 6.2, the literature on experimental studies in wind tunnel tests and modeling methods are summarized, to indicate the principles of modeling AWS phenomena. In Section 6.3, a semi-empirical criteria is presented for determining the angle-of-attack and Mach number conditions for occurrence of AWS using Free-to-roll wind tunnel test data. In Section 6.4, BMAA structure and its estimation process using static and Free-to-roll wind tunnel test data are presented. This model is used to perform closed-loop simulation studies of GTA, in order to examine its effect on flight dynamics, in Section 6.5.

Fig. 6.2. Variation inClversusβ obtained from β-sweep tests on F35 aircraft, left figure in AWS Angle-

of-attack region, right figure just before entering in AWS Angle-of-attack [103].