**1. Introduction**

Generally, a wing or tail of an aircraft will be damped by damping when the speed of it is low; when the speed of flight exceeds a certain value, small disturbance will cause vibration divergence and the structure to collapse in a matter of seconds or even tens of milliseconds. This phenomenon is called flutter. Flutter is the most important subject in aeroelasticity. It is a kind of self-excited vibration which can maintain the constant amplitude oscillation under the interaction of elastic force, inertia force and aerodynamic force when the lifting surface moves at a certain

speed in the air flow. At this time, the damping (g) equals 0. Due to the existence of system damping (g < 0), the vibration of the aircraft soon attenuates or even disappears completely with a small flight speed after being disturbed, but when the flight speed increases to a certain value, the amplitude caused by the disturbance just keeps the same. This speed is called the critical flutter speed, the vibration frequency at this time is called the critical flutter frequency and g = 0. In order to prevent flutter, the critical flutter velocity must be larger than the maximum flight velocity under all flight conditions and there must be some margin. **Figure 1** taken from a Chinese book written by Liu, C., F. and Qiu, J. [1] is an example of the wing flutter calculation: when the speed of flight, VCR, is 850 m/s, the wing is in constant amplitude vibration, and if the speed of flight is less than or greater than it, the wing vibration will attenuate or disperse.

Classical flutter calculations in frequency domain are performed using either the K method proposed by Bisplinghof, R. L., and Ashley, H. [2] or the P-K method proposed by Hassig, H. [3] and Lawrence, J. A., and Jackson, P. [4]. The K method is generally very fast and quite simple, but it has a downfall in that sometimes the frequency and damping values "loop" around themselves and generate multi-value frequency and damping as a function of velocity. The K method solution is only valid when g = 0 and the structural motion is neutrally stable and matches the aerodynamic motion with the neutral stability. The P-K method is acknowledged to provide more accurate modal damping values after the K method. Gradually, the P-K method has become one of the most widely used methods in aeroelastic engineering. After that, the p method, proposed by Abel, I. [5], improves the damping and frequency trends by taking into account the effect of nonzero damping by means of generalized aerodynamic forces, which are approximately valid for the damping-frequency area under consideration. At the end of the 1990s, the *μ* method studied by Lind, R., and Brenner, M. [6], was used to fitting procedures to transform the aerodynamics to the state space. At the beginning of the new century, a g method proposed by P. C. Chen [7] is used in the analytic property of unsteady aerodynamics and a damping perturbation approach. These two methods of P-K method and g method are different in the

**Figure 1.** *The wing flutter calculation, VCR = 850 m/s.*

### *Verification and Validation of Supersonic Flutter of Rudder Model for Experiment DOI: http://dx.doi.org/10.5772/intechopen.98384*

equation form, but they share the same stability criterion, i.e., an eigen root of aeroelastic equation is solved and the root with positive real part indicates flutter. Additionally, the g method uses a reduced-frequency sweep technique to search for the roots of the flutter solution and a predictor corrector scheme to ensure the robustness of the sweep technique. The g method includes a first-order damping term in the flutter equation which is rigorously derived from the Laplace-domain aerodynamics. And then, an improved g method proposed by Ju Qiu and Qin Sun [8], increases a second-order damping term in the flutter equation. It is also valid in the entire reduced frequency domain and up to the second order of damping. Recently, the H method proposed by Michaël H. L. [9], automatically extends the aerodynamic data obtained for purely oscillatory motions to damping and diverging oscillatory motions by means of a direct harmonic interpolation method, thereby improving the prediction of damping and frequencies. This procedure may assist the aeroelastician in making improved estimates of aerodynamic damping at g < 0 conditions to support flight flutter testing and probably offers potential for flight control system design or analysis. Brian P. Danowsky and etc. [10] showed that three different flutter suppression controllers were designed using a flight-test-validated aeroelastic aircraft model. The flight tests demonstrated that the flutter boundary could be successfully expanded using active control. Eli [11] indicated that AFS (Active flutter suppression) technology had the potential to lead to significant weight savings and performance gains.

In the new and challenging field of energy harvesting through fluid–structure instabilities, such as analysis in time domain, the coupled-mode flutter mechanism has been recently scrutinized. A lot of complicated aeroelastic characteristics are predicted by a structural-aerodynamic fully-coupled formulation, such as rotorcraft written by Bernardini G., Serafini J., Molica Colella M., and Gennaretti M. [12], a transport wing's wingtip introduced by Peng Cui and Jinglong Han [13], a transonic wing analyzed by Xiang Zhao, Yongfeng Zhu and Sijun Zhang [14]. Francisco Palacios, Michael R. Colonno, and etc. [15] showed an integrated platform for multi-physics simulation and design, e.g. flutter predictions by a loosely-coupled method, remained open source and serves as a starting point for new capabilities that will hopefully be contributed by users in both academic and industrial environments. Most recently, Leclercq T., Peake N., and de Langre E. [16] pointed out that flutter did not prevent drag reduction by reconfiguration. Eirikur Jonsson [17] put flutter and post-flutter constraints into the process of the aircraft design optimization. Sergey Shitov and Vasily Vedeneev [18] investigated the flutter boundaries of rectangular panels simply supported at all edges, and used potential flow theory to calculate the unsteady pressure.

Naturally, for every simulation and every test, it is desired to produce a model that could be accurate, studied by Samuel C. Mclntosh Jr., Robert E. Reed Jr. T. and William P. Rodden [19], so as to permit meaningfully calculated and experimental comparisons and to provide data for evaluating new theoretical or numerical techniques for treating aeroelastic problems. The studies of all cases suggest that at increased airspeeds the aircraft may develop unstable oscillations leading to a catastrophic failure, described by Jieun Song, Seung Jin Song and Taehyoun Kim [20], Jie Zeng and Sunil L. Kukreja [21], Thomas Andrianne and Grigorios Dimitriadis [22]. At all times, on one hand, there exist analytical models and tools that allow estimating the onset of the dynamic instability, but they are often subject to modeling uncertainties and limitations that can produce inaccurate, unreliable results. On the other hand, the test data are a direct reflection of the actual aircraft, to some degree, and hence can be used with confidence. Also, it is a common and required practice in aerospace industry to conduct flight flutter tests and validate the simulation effect of the analysis model before aircraft enter into service.

Since the beginning of the century, American Society of Mechanical Engineers guide to Verification and Validation (V&V) defined the goal of V&V process as to develop standards for assessing the correctness and credibility of modeling and simulation in computational science. According to the paper, for Validation, and Predictive Capability in Computational Engineering and Physics, written by William L. Oberkampf, Timothy G. Trucano, Charles Hirsch [23], a proposed question was how confidence in modeling and simulation should be critically assessed. Verification and validation (V&V) of computational simulations are the primary methods for building and quantifying this confidence. Briefly, verification is the assessment of the accuracy of the solution to a computational model. Validation is the assessment of the accuracy of a computational simulation by comparison with experimental data. In verification, the relationship of the simulation to the real world is not an issue. In validation, the relationship between computation and the real world, i.e., experimental data, is the issue. Furthermore, Verification is defined as following: the process of determining that a model implementation accurately represents the developer's conceptual description of the model and the solution to the model, while Validation means that the process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended uses of the model. Supanee Arthasartsri and He Ren [24], in A380 Aircraft Reliability Program also pointed out that the validation is a process determining whether the mathematical model describes sufficiently well the reality with respect to the decision to be made, which includes requirement validation and product validation, whereas, the purpose of Validation is to ensure that the requirements for a product are sufficiently correct and complete to achieve safety and to satisfy the needs of the customer within program constraints (e.g. cost, schedule). The Product Validation is to check if product meets the implicit needs of the customer. It is also to ensure the final product meets the requirement, for example, airworthiness certification of commercial aircraft. Additionally, V & V method was described in Guide for Verification and Validation in Computational Solid Mechanics, written by Schwer L. E. and etc. [25].

In **Figure 2**, it is evident to see the test has not been involved in the first stage of the V&V process, Verification and only is employed in the second step, Validation.

When V & V technique is widely used to aerospace engineering, civil engineering, auto engineering, etc., it obtains fruitful achievements. For instance, the example of V&V method implementation on GP7200 by Engine Alliance, which the results of reliability before entry into service exceeded the expectation requirements from FAA. With the entry into service of Airbus A380, the application of validation and verification method in safety and reliability program has been proven successful. The other example is Validation and Verification of the Lunar Atmosphere Dust Environment Explorer (LADEE) mission models and software. This program identified and prioritized a set of V&V technologies that significantly reduced the development cost and compressed the development schedule of emerging safety critical flight control systems. It is predicted that it could also be applied to other aerospace system design and to other industry that require the high level of safety and V&V Method would be used to provide the confidence in the results from simulation.

The present research uses V & V technologies to handle the flutter problem of the rudder. There is, however, a significant difference, that is to say, the experimental data were added to modify the simulated models, besides codes and software verification.

In the Verification process, the stiffness of the rudder axis could be adjusted during the flight or the experiment. The accuracy of the flutter-prediction results of these methods heavily depends on how good the model or mode estimations are.

*Verification and Validation of Supersonic Flutter of Rudder Model for Experiment DOI: http://dx.doi.org/10.5772/intechopen.98384*

**Figure 2.**

*Verification and Validation's activities and products.*

Therefore, the modes of the rudder directly influencing flutter speeds become very critical. In order to obtain a precise model to simulate two cases of supersonic flutter, the appropriate axis structures were provided by optimization process. Unlike traditionally aeroelastic systems of maximum performance and minimum weight, studied by Melike Nikbay, and Muhammet N. Kuru, [26], the objective was a minimal 1-order or 2-order error which was a ratio of test eigenvectors and calculated ones, constraints were the first and second natural frequencies, and design variables were stiffness of the different rudder axles. Finally, modes of the first bending and second twisting of the rudder were found out in Case one, and

these of the first torsion and second bending were extracted in Case two. In addition, it focused on finding a right analysis model by optimization method, according to experimental data of mode shapes studied by Zimmerman, N. H., and Weissenburer, J. T. [27]. Test investigations were first presented, followed by verifying the structural model and mode by optimization. Although two flutter cases both had the same flutter mechanism, classical bending-torsion flutter, they had their own critical flutter points, respectively.

The present work also aims at a deeper understanding of the phenomena by characterizing the tight interaction between the unsteady flow patterns in the flow-field and the response of the structure. After numerical aeroelastic simulations were finished, the test data were employed to validate flutter prediction to confirm the observed critical velocity and coupled-mode flutter in the validation stage of V& V technologies.
