Parametric constraints with application to optimization for flutter using a continuous flutter constraint
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An investigation has been made utilizing a three-blade, 10-foot- diameter, supersonic-ty-pe propeller to determine propeller flutter characteristics. The particular flutter characteristics of interest were (1) the effect of stall flutter on a propeller operating in positive and negative thrust, (2) the effect of stall flutter on a propeller operating with the thrust axis inclined, and (3) the variation of vibratory blade shear stresses as the stall flutter boundary is penetrated and exceeded. Thrust and power measurements were made for all test conditions. Wake and inflow surveys were made when appropriate, to define the thrust and torque distributions and the magnitude of the inflow velocity. Stress measurements were made simultaneously to obtain the propeller flutter and bending response. It was found when operating both in the positive and negative thrust regions that, for most cases after the onset of flutter, the magnitude of the flutter stresses at first increased rapidly with section blade angle P, after which further increases in 0 resulted in only a moderate increase or a reduction in stress. Thrust-axis inclination up to the limit of the tests (angle of attack of 15 deg and dynamic pressure of 40 psf) appeared to have no effect on stall flutter. The stall flutter stresses were found to be directly associated with the section thrust characteristics of the blades. The onset of flutter was found to occur simultaneously with the divergence of the section thrust variation with blade angle from linearity for stations outboard of the blade 0.8-radius station. The maximum flutter stresses appeared to be a function of the maximum section thrust obtained at or in the vicinity of the blade 0.8-radius station. In an attempt to correlate two-dimensional airfoil data with three-dimensional data to predict the stall angle of attack (divergence of the section thrust) of the blade sections, it was found that no consistent correlation could be obtained. Also, a knowledge of the inflow conditions appeared to be insufficient to account for differences in airfoil characteristics between the two-dimensional and the three-dimensional cases.
High energy-density turbomachines, like the SSME turbopumps, utilize labyrinth seals, also referred to as knife-edge seals, to control leakage flow. The pressure drop for such seals is order of magnitude higher than comparable jet engine seals. This is aggravated by the requirement of tight clearances resulting in possible unfavorable fluid-structure interaction of the seal system (seal flutter). To demonstrate these characteristics, a benchmark case of a High Pressure Oxygen Turbopump (HPOTP) outlet Labyrinth seal was studied in detail. First, an analytical assessment of the seal stability was conducted using a Pratt & Whitney legacy seal flutter code. Sensitivity parameters including pressure drop, rotor-to-stator running clearances and cavity volumes were examined and modeling strategies established. Second, a concurrent experimental investigation was undertaken to validate the stability of the seal at the equivalent operating conditions of the pump. Actual pump hardware was used to construct the test rig, also referred to as the (Flutter Rig). The flutter rig did not include rotational effects or temperature. However, the use of Hydrogen gas at high inlet pressure provided good representation of the critical parameters affecting flutter especially the speed of sound. The flutter code predictions showed consistent trends in good agreement with the experimental data. The rig test program produced a stability threshold empirical parameter that separated operation with and without flutter. This empirical parameter was used to establish the seal build clearances to avoid flutter while providing the required cooling flow metering. The calibrated flutter code along with the empirical flutter parameter was used to redesign the baseline seal resulting in a flutter-free robust configuration. Provisions for incorporation of mechanical damping devices were introduced in the redesigned seal to ensure added robustness
Results of a study of the development of flutter modules applicable to automated structural design of advanced aircraft configurations, such as a supersonic transport, are presented. Automated structural design is restricted to automated sizing of the elements of a given structural model. It includes a flutter optimization procedure; i.e., a procedure for arriving at a structure with minimum mass for satisfying flutter constraints. Methods of solving the flutter equation and computing the generalized aerodynamic force coefficients in the repetitive analysis environment of a flutter optimization procedure are studied, and recommended approaches are presented. Five approaches to flutter optimization are explained in detail and compared. An approach to flutter optimization incorporating some of the methods discussed is presented. Problems related to flutter optimization in a realistic design environment are discussed and an integrated approach to the entire flutter task is presented. Recommendations for further investigations are made. Results of numerical evaluations, applying the five methods of flutter optimization to the same design task, are presented.
While there has been much recent progress in simulating nonlinear aeroelastic systems, and in predicting many of the aeroelastic phenomena of concern in transport aircraft design (i.e. transonic flutter buckets), the utility of a simulation in generating an understanding of the flutter behavior is limited. This is due in part to the high cost of generating these simulations; and the implied limitation on the number of conditions that can be analyzed, but there are also some difficulties introduced by the very nature of a simulation. Flutter engineers have traditionally worked in the frequency domain, and are accustomed to describing the flutter behavior of an airplane in terms of its V-G and V-F (or Q-G and Q-F) plots and flutter mode shapes. While the V-G and V-F plots give information about how the dynamic response of an airplane changes as the airspeed is increased, the simulation only gives information about one isolated condition (Mach, airspeed, altitude, etc.). Therefore, where a traditional flutter analysis can let the engineer determine an airspeed at which an airplane becomes unstable, while a simulation only serves as a binary check: either the airplane is fluttering at this condition, or it is not. In this document, a new technique is described in which system identification is used to easily extract modal frequencies and damping ratios from simulation time histories, and shows how the identified parameters can be used to determine the variation in frequency and dampin,o ratio as the airspeed is changed. This technique not only provides the flutter engineer with added insight into the aeroelastic behavior of the airplane, but it allows calculation of flutter mode shapes, and allows estimation of flutter boundaries while minimizing the number of simulations required.
Flight flutter tests were conducted on an experimental airplane which resulted in the successful prediction of a limited amplitude stabilizer flutter at supersonic speeds. The flutter obtained was unusual in that fore and aft bending of the stabilizer carry-through structure contributed to the flutter condition. During flight tests the impending flutter condition was observed from force per unit amplitude, damping coefficient, and frequency measurements. A description is given of the physical and operational characteristics of the test equipment and telemetering facilities. A flutter analysis using measured modes and incompressible two-dimensional strip air forces yielded a conservative flutter speed. Sled tests of a similar stabilizer configuration had lead to the conclusion that flutter would not be encountered. Certain overall conclusions are reached regarding this particular flight flutter testing program and the need for a concerted research effort in this field.
This paper documents an invited presentation given to The Boeing Company, Seattle, Washington, on September 9, 1997. The audience consisted of structural dynamic and flight test engineers from the Boeing Commercial Airplane Group who were interested in discussing research which may be applied to future flight flutter test programs. A method to compute robust flutter margins is described which is a significant departure from traditional methods. This method uses the structured singular value, mu, to compute a flutter margin which directly accounts for modeling errors such that a worst-case flutter margin is computed with respect to those errors. This method may be applied in several ways. A post-flight application uses data sets from multiple test points to compute worst-case flutter margins and a worst-case flight envelope. An on-line implementation computes flutter margins at each test point to track the flutter margins during a flight test. This on-line implementation is the basis for a flutterometer flight test tool that displays the distance to flutter at a given test point. Such a tool was not previously possible using traditional flutter flight test analysis methods. The F/A-18 System Research Aircraft was used to demonstrate these applications using flight data recorded from test points throughout the flight envelope.
Panel-flutter tests have been made at transonic and supersonic speeds With particular reference to buckled curved panels with longitudinal stringers. Other panel configurations were also tested in an attempt to determine effects of skin thickness, curvature, stringers, buckling, pressure differential, and Mach number on the dynamic pressure necessary to start flutter. For buckled curved panels with longitudinal stringers, the dynamic pressure required to start flutter was increased by increasing the skin thickness and increasing the pressure differential across the panel. There was no apparent effect of Mach number variation from 1.3 to 2.0. None of the curved panels failed because of flutter although the dynamic pressure at the start of flutter was exceeded by a factor of 3 in many cases. curved panels and four flat panels failed because of flutter. The flat panels fluttered at lower dynamic pressures than the curved panels and four flat panels failed because of flutter.
Flutter characteristics for yaw angles between 15 deg and 90 deg were determined experimentally for two types of corrugation-stiffened panels: those with weak twisting stiffness and those with strong twisting stiffness. By mounting the panels on a remotely controlled turntable, good definition of the flutter boundaries was obtained by rotating the panels into and out of flutter. Flutter tests were conducted at M = 2 and M = 1.6. Before testing, vibration tests and analyses were also performed. The experimental flutter data is compared with flutter theory for orthotropic panels utilizing quasi-steady aerodynamics. Five different corrugated panels were tested consisting of one single skin panel having a length-to-width ratio of 5 on clamped supports and four different square double skin panels on discrete flexible supports. The investigation indicated that flutter speed for corrugated panels is highly dependent on yaw angle. Reasonable flutter correlation between analysis and test was obtained for moderate yaw angles, but extreme sensitivity to structural parameters made the correlation at large yaw angles uncertain.
A series of experiments was performed on a 1.8-m-diam model rotor in hover for the principal purpose of investigating the lead-lag stability of isolated bearingless rotors. Incidental to those tests, at least three types of pitch-flap flutter were encountered. Type 1 flutter occurred approximately at the second flap-mode frequency on both two-and three-bladed rotors for both small and large pitch angles and appeared to be a classic pitch-flap flutter. Type 2 flutter showed mostly torsional motion and was seen on both two- and three-bladed rotors. Type 3 flutter was a regressing flap flutter that occurred for only the three-bladed rotor configurations and appears to be a wake excited flutter. Although flutter occurred on a number of different configurations, no rotor parameters were identified that were clearly stabilizing or destabilizing.
The paper presents wind tunnel experimental flutter results, at transonic relative flows, for a 0.62-m diameter composite propfan model. A blade row that fluttered was tested alone, and with a stable aft counter-rotating blade row. The major objectives of the experiment were to study the effect of the second blade row on the row in flutter, and to investigate the flutter. Results show that the second row had a stabilizing effect. Two distinct flutter modes were found. For both flutter modes: flutter boundary, frequency, nodal diameter, and blade displacement data are given. The blade displacement data, obtained with an optical method, gives an indication of the flutter mode shape at a span near the blade tip.
A new method of calculating flutter boundaries of undamped aeronautical structures is presented. The method is an application of the weak transversality theorem used in catastrophe theory. In the first instance, the flutter problem is cast in matrix form using a frequency domain method, leading to an eigenvalue matrix. The characteristic polynomial resulting from this matrix usually has a smooth dependence on the system's parameters. As these parameters change with operating conditions, certain critical values are reached at which flutter sets in. Our approach is to use the transversality theorem in locating such flutter boundaries using this criterion: at a flutter boundary, the characteristic polynomial does not intersect the axis of the abscissa transversally. Formulas for computing the flutter boundaries and flutter frequencies of structures with two degrees of freedom are presented, and extension to multi-degree of freedom systems is indicated. The formulas have obvious applications in, for instance, problems of panel flutter at supersonic Mach numbers.
Modern fan designs have blades with forward sweep; a lean, thin cross section; and a wide chord to improve performance and reduce noise. These geometric features coupled with the presence of a shock wave can lead to flutter instability. Flutter is a self-excited dynamic instability arising because of fluid-structure interaction, which causes the energy from the surrounding fluid to be extracted by the vibrating structure. An in-flight occurrence of flutter could be catastrophic and is a significant design issue for rotor blades in gas turbines. Understanding the flutter behavior and the influence of flow features on flutter will lead to a better and safer design. An aeroelastic analysis code, TURBO, has been developed and validated for flutter calculations at the NASA Glenn Research Center. The code has been used to understand the occurrence of flutter in a forward-swept fan design. The forward-swept fan, which consists of 22 inserted blades, encountered flutter during wind tunnel tests at part speed conditions.