Unsteady Cascade Aerodynamics in the Time Domain

A time domain numerical approach is carried out to enhance the understanding of three dimensional blade row aeroelastic characteristics under the parallel computation. The vibration energy of unsteady aerodynamic force on the entire blade row is investigated using numerical solution of 3-D Navier-Stokes equations, coupled with structure finite element models for the blades to identify modal shapes and the structural deformations simultaneously. Interactions between fluid and structure are dealt with in a coupled manner, based on the interface information exchange until convergence in each time step. With this approach good agreement between the numerical results and the experimental data is observed. The flutter mechanism is analyzed according to deformation of the blades. The effect of inter-blade phase angle (IBPA) is included in the analysis by releasing the hypothesis of constant phase angle between adjacent blades in the traveling wave model. The results illustrate fully three dimensional unsteady nonlinear behaviors, such as limit-cycle oscillation. It is shown that all blades flutter at the same mode and frequency, but not at the same amplitude and IBPA. The analysis of the influence of different tip clearance gaps on the flutter characteristics of the blade row is also performed.

For the design and certification of wind turbines, it is essential to provide fast and accurate unsteady aerodynamic load prediction models for the whole operational range of angle of attack, up to 180° for vertical-axis and 90° for horizontal-axis wind turbines. This work describes a computationally efficient unsteady forces prediction model based on a deep learning approach, namely the bidirectional long short-term memory (BiLSTM) algorithm, for an airfoil pitched over the full operational range of angles of attack up to 180°. No model has been developed to capture the unsteady forces at high angles of attack. Novel features based on operating conditions and the steady polars of the airfoil are used as inputs for the BiLSTM model. Direct measurements of steady and unsteady forces on a NACA 0021 airfoil model were conducted at reduced frequencies up to 0.075 and a Reynolds number of 120 000 in an open-jet wind tunnel for model learning and testing. The unsteady forces vary significantly from the steady values at high pitching amplitudes and post-stall angles, which, if not accounted for when simulating wind turbine performance, would result in inaccurate predictions. Furthermore, measurements revealed the effect of unsteady vorticity development and shedding on aerodynamic forces under forward and reverse flow conditions. The BiLSTM model is capable of capturing the underlying physics of unsteady aerodynamic forces under extreme operating conditions.

Unsteady aerodynamic models based on windtunnel forced oscillation test data and analyzed with a fuzzy logic algorithm arc incorporated into an F-16XL flight simulation code. The reduced frequency needed in the unsteady models is numerically calculated by using a limited prior time history of state variables in a least-square sense. Numerical examples arc presented to show the accuracy of the calculated reduced frequency. Oscillatory control inputs are employed to demonstrate the differences in the flight characteristics based on unsteady and quasi-steady aerodynamic models. Application of the unsteady aerodynamic models is also presented and the results are compared with one set of F16XIL longitudinal maneuver flight data. It is shown that the main differences in dynamic response are in the lateral-directional characteristics, with the quasi-steady model being more stable than the flight vehicle, while the unsteady model being more unstable. Similar conclusions can also be made in a simulated rapid sideslipping roll. To improve unsteady aerodynamic modeling, it is recommended to acquire test data with coupled motions in pitch, roll and yaw.

An introduction to entire functions

Introduction N methods for predicting generalized unsteady aerodynamic forces usually do not provide identical results. Experimental methods are rarely available to verify the accuracy of predicted generalized forces for complex configuration, and the flutter analyst must rely on calculated results. Convergence criteria generally are not available to enable the user to obtain the best results from a particular numerical method. This important issue was addressed recently by Rowe and Cunningham, and in a Comment by Stark followd by a Reply by Lottati. The usual way to tackle the accuracy of the method is by applying the code on several test cases and comparing these results against results obtained by other methods of computation (see Ref. 1). Another way is to use the existing relations for the aerodynamic forces developed on the configuration in direct and reverse flow. By comparison of the obtained results computed by direct and reverse flow, it is possible to assess the accuracy of the method. The general reverse-flow theorems for lifting-surface theory may also be applied to wings that undergo harmonic oscillation. The results of Ref. 1 emphasize the wavy character of the oscillatory pressure developed on an oscillating wing. The pressure distribution displayed in Ref. 1 aimed to alert users to the possible potential difficulties in obtaining an accurate solution due to the wavy character of the aerodynamic pressure on an oscillating wing. The pressure distribution becomes extremely wavy and more difficult to predict accurately as the reduced frequency k and the Mach number M get larger values. Reference 1 defined a wave number to assess the wayiness of the pressure distribution which might be useful in the estimation of relative difficulties in predicting converged aerodynamic forces. In this Note, the reverse-flow theorem will be applied to assess the accuracy of the computed unsteady aerodynamic forces for interference configuration. The computer program used to evaluate the unsteady aerodynamic forces on the configuration is the nonplanar piecewise continuous kernel function method (PCKFM).

A method for solving numerically the fully time-dependent two-dimensional Euler equations, applied to unsteady subsonic flow through vibrating turbomachine cascades with thin blades, is developed. The blades are assumed to vibrate at a constant interblade phase angle and the computed region is reduced to one blade passage, with the implementation of the interblade phase angle as a periodicity condition. The reliability of the method is validated by comparing it with an analytical flat plate theory, and the importance of radiative inlet and outlet boundary conditions for unsteady flow calculations is shown in an example. The method can be used to compute the aerodynamic force and damping coefficients acting on the blades and to investigate the propagation of unsteady disturbances through a cascade in flutter conditions.

Unsteady aerodynamic forces acting on oscillating blades of a transonic annular turbine cascade were investigated in both aerodynamic stable and unstable domains, using a Freon gas annular cascade test facility. In the facility, whole blades composing the cascade were oscillated in the torsional mode by a high-speed mechanical drive system. In the experiment, the reduced frequency K was changed from 0.056 to 0.915 with a range of outlet Mach number M2 from 0.68 to 1.39, and at a constant interblade phase angle. Unsteady aerodynamic moments obtained by two measuring methods agreed well. Through the moment data the phenomenon of unstalled transonic cascade flutter was clarified as well as the significance of K and M2 for the flutter. The variation of flutter occurrence with outlet flow velocity in the experiments showed a very good agreement with theoretical analysis.

Aiming at the difficulty of post-stall maneuvering control modeling and control of advanced aircraft under unsteady aerodynamics, a control method with high control accuracy and fast computation speed is proposed based on Radial Basis Function (RBF) network with minimum parameters learning (MPL) and dynamic surface control (DSC) method. Firstly, the aerodynamic characteristics of post-stall maneuvers are analyzed based on the experimental data of large-scale oscillation wind tunnels, and the key factors affecting the unsteady aerodynamic forces are obtained. Then, an accurate unsteady aerodynamic model is established based on the improved extreme learning machine (ELM) method. Secondly, the influence of unsteady aerodynamic forces on the control of post-stall maneuvers is considered. For the uncertainty of advanced aircraft model, high angle of attack flight control laws based on RBF-DSC are designed. In order to improve the calculation speed of the above control law and optimize the parameters, a post-stall maneuver control law method based on MPL-RBF-DSC is designed, and the stability of the method is proved. The coordinated allocation of the conventional aerodynamic surfaces and thrust vectors is realized based on the daisy chain method. Finally, the typical maneuver simulation of “Cobra” is carried out, which highlights the advantages of the design method in this paper, such as high control accuracy, short calculation time and strong robustness.

Unsteady aerodynamic forces on large, slender aerospace structures are established in wind-tunnel tests that employ a limited number of dynamic pressure sensors and use a correlation-based approach that, so far, cannot be directly verified. This paper describes a robust procedure based on frequency-specific correlation lengths, and it provides validation from an experiment on a generic, space vehicle model. The model was coated with unsteady pressure sensitive paint, which provided time histories of pressure fluctuations on a large number of points. At first, the entire dataset was integrated to determine the “true” unsteady forces. In the next step, progressively fewer points were used as “virtual sensors,” and the correlation-based procedure was applied to determine the “modeled” forces. By comparing the time histories and power spectra, it was observed that as few as 16 virtual sensors (four rings, with each containing four sensors and separated by half a diameter) were able to replicate the true fluctuations on a model segment with a reasonable accuracy. The modeled levels were typically higher, and they approached the true levels with an increase in the number of the virtual sensors. The procedure showed better agreement when pressure fluctuations were more coherent over a buffet zone.

Ground vehicles in high cross winds part II: Unsteady aerodynamic forces

The time-domain response of a corroding system with constant phase angle interfacial component: Application to steel in concrete

We carried out tests and analysis of flutter and vibration control of rectangular aluminum plate wing. The dimensions of the plate wing (420.0 X 140.0 X 1.0 mmt) were determined based on the wind tunnel size and blowing air velocity. The plate wing was driven by eight piezoceramic actuators bonded on the surfaces at the wing root part. Acceleration sensor was located at the wing tip and the signal was sent to digital signal processor through filters and control signal was sent to power amplifier. Amplified signal drove the piezoceramic actuator and suppressed vibration of the plate wing. System consist of structure, piezoceramic actuator and unsteady aerodynamic force was modeled into the standard form of modern control theory. Piezoceramic actuator's force was modeled using analogy of thermal analysis. Unsteady aerodynamic force in case of flutter control was calculated by DLM (frequency domain), then transformed to Roger's approximation for the purpose of time domain analysis. Full order control law consist of optimum regulator and Kalman's filter was reduced to low order law for practical use. First, we carried out the test for vibration control. In this case, structural damping ratio of the system increased remarkably in both case of gain control and reduced LQG control. Using gain control, that of the system increased up to 0.3. Second, we carried out the wind tunnel test of flutter control. Flutter speed at test increased about 2.9 m/s (10.8%, in calculation 12.2%) using reduced LQG controller.

Time domain modeling is a fascinating world which brings together several complex phenomena and methods of essential interest to engineers. This book is a reference guide which discusses the most advanced time-domain modeling methods and applications in electromagnetics and electrical engineering. The book starts by clearly explaining why time-domain modeling may be worth doing; then, it provides guidelines about why some choices must be made among the principal modeling approaches and next guides the reader through the state of the art in time domain modeling, concerning either numerical and analytical methods, and applications. Finally, it highlights areas for future time-domain modeling research. The book is a collection of chapters written by leading research groups in the fields, following a logical development set out by the editor. Topics covered include finite element methods in time domain with applications to low-frequency problems; transient analysis of scattering from composite objects using late-time stable TDIEs; the transmission-line modeling method, partial element equivalent circuit method in time-domain; unconditionally stable time-domain methods; time-domain linear macromodeling, analytical techniques for transient analysis; the application of the finite-difference time-domain (FDTD) technique to lightning studies; modeling of lightning and its interaction with overhead conductors; transient behaviour of grounding systems; and statistics of electromagnetic reverberation chambers and their simulation through time domain modeling.

The stability and safety of maglev trains are significantly affected by unsteady aerodynamic forces during high-speed operation. In this paper, we employ a time-delay feedback control strategy to suppress the nonlinear vertical vibrations of maglev train under periodic unsteady aerodynamic force. Firstly, the amplitude-frequency response equation of the maglev vehicle is derived using the multiple scales method, and the stability of the steady-state solutions is determined. Then, the influences of velocity feedback gain coefficient and velocity time delay on the nonlinear vibrations of the maglev vehicle are investigated. The optimal value range of the time delay is identified. The results demonstrate that the time delay feedback control can effectively suppress the nonlinear vibration of maglev vehicles and enhance their operational stability under the premise of reasonable selection of time delay parameters. The theoretical research presented in this paper can serve as a theoretical reference for the design, improvement, and optimization of control systems for high-speed maglev trains.

A new, and as yet unexplored, approach to passive flutter control is aerodynamic detuning, defined as designed passage-to-passage differences in the unsteady aerodynamic flow field of a rotor blade row. Thus, aerodynamic detuning directly affects the fundamental driving mechanism for flutter, i.e., the unsteady aerodynamic forces and moments acting on individual rotor blades. In this paper, a model to demonstrate the enhanced supersonic unstalled aeroelastic stability associated with aerodynamic detuning is developed. The stability of an aerodynamically detuned cascade operating in a supersonic inlet flow field with a subsonic leading edge locus is analyzed, with the aerodynamic detuning accomplished by means of nonuniform circumferential spacing of adjacent rotor blades. The unsteady aerodynamic forces and moments on the blading are defined in terms of influence coefficients in a manner that permits the stability of both a conventional uniformly spaced rotor configuration as well as the detuned nonuniform circumferentially spaced rotor to be determined. With Verdon’s uniformly spaced Cascade B as a baseline, this analysis is then utilized to demonstrate the potential enhanced aeroelastic stability associated with this particular type of aerodynamic detuning.