Piston Theory Research Articles

Flutter and Limit-Cycle Oscillations of a Panel Using Unsteady Potential Flow Aerodynamics

The potential aerodynamic theory is implemented to model the flow over a flexible panel. The present study compares the more complete unsteady version of the potential flow theory with its simplification known as the linear piston theory for different Mach numbers and the two- and three-dimensional aerodynamic models. The piston theory is “local” in space and time because it assumes the pressure at a spatial point and time only depends on the panel deformation at the same point and time. The full potential flow model includes the effect of the past history of the panel deformation and the spatial distribution of the panel deformation on the pressure at any instant in time and at any point in space. Aeroelastic analysis is made to trace the flutter onset critical condition based on the limit cycle oscillation amplitudes, and the results are compared with the more traditional implementation using piston theory. Conclusions are made based on the use and application of this more complete aerodynamic theory, particularly for near-transonic and hypersonic flow regimes. Subsonic results are also presented in this study.

Correlation of supersonic wind tunnel measurements with a nonlinear aeroelastic theoretical/computational model of a thin plate

Supersonic wind tunnel test data is compared with a nonlinear aeroelastic computational model, considering a freestream flow with Mach nearly 2, coupled cavity, and no-shock impingement. The measurements include Limit Cycle Oscillations (LCO) for the given set of flow and structural parameters. The effect of a static pressure differential, temperature differential, and the type of LCO is also studied: periodic or chaotic. A fully coupled aero-thermal–acoustic–elastic analysis was carried out, where the strong dependency of the dynamic instability upon the in-plane boundary stiffness was discovered. Associated with aerodynamic and acoustic formulations, the nonlinearities from the structure are found to be the strongest factor determining the occurrence and character of LCO. At the same time, the cavity effect was found to be negligible for this experimental configuration. Additionally, a comparison analysis was performed on the aerodynamic model for this flow condition between the Linear Piston Theory and the Full Potential Aerodynamics. The calculation of the critical flutter boundary was also performed in terms of the static pressure differential between the cavity pressure and the panel surface pressure, presenting regions where the panel is in static deformation due to the pressure differential versus LCO response. The comparison with the analytical model showed good agreement with the measured data, achieving a similar panel displacement at three-quarters of the panel length as well as the expected behavior of periodicity or chaos for specific values of temperature and static pressure differential.

Numerical aeroelastic flutter prediction of variable stiffness laminated panels with curvilinear fiber in supersonic flow

The flutter behaviour of layered structure has been investigated in this research considering the curved fibre instead of the conventional type of fibre directions (uni/multiple directional types). Due to the change in angles, the influences of fibre directions on the final properties of the laminated structure results in variable stiffness. The effective properties of composite in conjunction with the aeroelastic loading under the supersonic flow have been computed numerically. The numerical responses are calculated through an in-house MATLAB code prepared from the higher-order displacement polynomial and isoparametric finite element formulation. The aeroelastic loading effect is incorporated via the standard first-order Piston theory. The necessary comparison and convergence tests are performed to show the model's accuracy. Further, the influential parameters (geometry and material) with and without fibre directional effects are examined and discussed in detail.

Numerical study on the nonlinear characteristics of shock induced two-dimensional panel flutter in inviscid flow

For an aeroelastic system of a two-dimensional elastic panel subjected to an impinging inviscid oblique shockwave, the nonlinear flutter characteristics are affected by many factors such as shock impingement location, cavity pressure and initial perturbation. The effects of the above factors on the variation of system bifurcation type and dynamic behaviors are investigated numerically. A low-fidelity computational method coupled with local piston theory and van Karman plate model, and a high-fidelity computational method coupled with Euler equations and finite element model are used for fluid-structure interaction simulations. Two sets of new findings are unveiled. First, either the variation of shock impingement location or cavity pressure can induce the aeroelastic system to transition between a subcritical bifurcation and a supercritical bifurcation. For some cases, the system bifurcation characteristics exhibit strong sensitivity to these two factors. Second, it is found that in addition to the limit cycle oscillation in the form of a combination of the second and third structural modes, multiple stable limit cycle oscillations due to the coupling of higher-order modes can be triggered by suitable initial perturbations. These limit cycle oscillations have high frequencies and amplitudes, which suggest a higher risk of structural fatigue failure.

Flutter of carbon-based nanohybrid composite panels

Recently, carbon-based composite aerospace and mechanical structures have considerable attention due to their great material and mechanical properties. Carbon nanotubes (CNTs) or graphene platelets (GPLs) reinforcements for different matrices are common for the design of modern multilayer structures. In the present paper, the supersonic flutter of nanohybrid composite multilayer panels is examined and discussed. The nanohybrid multilayer panel is made of different technologically justified configurations of polymer layers reinforced by CNTs and GPLs The effective material properties of each CNTs and GPLs layer are determined according to two well-established homogenization techniques: the Mori–Tanaka scheme and the modified Halpin–Tsai model, respectively. Reddy’s third-order shear deformation theory is applied to avoid determining shear correction factors for different distributions of material properties. Hamilton’s principle and the first-order piston theory are applied to formulate aeroelastic coupled equations of motion of the panel. The numerical meshless method is employed to discretize dynamic equations and find generalized multi-parametric characteristic equations functionally dependent on the parameters of the structure with different boundary conditions. The accuracy of the obtained solution and results is examined by comparing the determined natural frequency and critical aerodynamic pressure with those obtained in previous studies. Then, a comprehensive parametric study is carried out to show the effects of hybridization of different distribution patterns of CNTs and GPLs, weight fractions, total layer number, and aspect ratio of hybrid composite panels on the flutter bounds. Results show that the present method provides a highly effective general numerical model for flutter analysis of hybrid nanocomposite panels with different boundary conditions for all thickness categories including thick plates. Moreover, an optimization nanoparticles distribution for the flutter of the nanohybrid composite panel has been obtained.

Nonlinear static/dynamic behaviors of composite curved panels with piezoelectric patches in supersonic airflow

The nonlinear aeroelastic static deflection and dynamic response of the composite curved panel with rectilinear- and curvilinear-fiber lay-up configurations under supersonic flow are investigated. The geometrical nonlinear effect of the composite curved panel is depicted by the Von-Karman strain and the aerodynamic load is incorporated through the nonlinear third-order piston theory. The Newton-Raphson method is employed to determine the static deflection of the composite curved panel and the four-order Runge-Kutta method is for the dynamic response, respectively. After examining the accuracy of the established mechanical model through numerical comparisons with existing literatures, the parametric studies focusing on panel curvature, high-order piston aerodynamic force, fiber angle orientation, temperature rise, locations and applied voltages of the piezoelectric patch on nonlinear static deformation and dynamic response are investigated. The results are deliberated in detail, and it is observed that the panel curvature and fiber angle orientation significantly affect the aeroelastic static deflection and dynamic response of the curved panel under thermal environment. Moreover, high-order aerodynamic force enlarges the static deflection and dynamic response of the curved panels with a large curvature whereas the impact of applied voltages of the piezoelectric patch will be weaker.

Effects of porosity distribution and piezoelectric layers on natural frequencies and unsteady aerodynamic pressure of smart thick porous plates

In this paper, the effects of porosity distribution and piezoelectric layers on the natural frequencies and flutter aerodynamic pressure of smart thick porous plates in supersonic airflow are studied. Based on the third-order shear deformation plate theory and first-order piston theory, thick functionally graded porous plates embedded by piezoelectric layers are investigated. The effective porous material properties, such as Young’s modulus and mass density are considered to vary along the thickness direction. The aeroelastic governing equations of motion are obtained using Hamilton’s principle and Maxwell’s equation. By applying Galerkin’s approach, the partial differential governing equations are transformed into a set of ordinary differential equations. The results indicate that the unsteady aerodynamic pressure and natural frequencies decrease as the porosity coefficient increases. Furthermore, the symmetric porosity distribution predicts the highest unsteady aerodynamic pressure and natural frequencies for porous plates. Besides, the results show that the porous plate enclosed by piezoelectric layers in open circuit condition has higher flutter aerodynamic pressure and natural frequencies than the similar plate in closed circuit condition.

Vibration of a thin panel exposed to ramp-induced shock-boundary layer interaction at Mach 2

Flight vehicles that operate in the supersonic regime can be subject to adverse fluid–structure interactions due to their lightweight design. The presence of geometric obstructions such as control surfaces or fins can induce shocks that can interact with the boundary layer, leading to flow separation. This work investigates experimentally the interaction between a compliant panel in a Mach 2 flow under a compression ramp-induced shock-wave/boundary-layer interaction (SBLI). Thin brass panels of different thickness are investigated in a wind tunnel. Tests are performed both with and without a 20° compression ramp installed. This direct comparison allows characterization of the effect of the SBLI on the system dynamics. High-speed stereoscopic digital image correlation (DIC) and fast-response pressure sensitive paint (PSP) are used to obtain simultaneous measurements of full field deformation and surface pressure of the panels. The panel vibration is dominated by the first bending mode. Despite the forcing of the separation shock foot, the presence of the SBLI does not significantly modify the operational deflection shape, frequency, and amplitude of the dominant vibration mode, beyond what is observed for the no-SBLI case. On the other hand, analysis of the shock foot motion shows that the shock primarily oscillates at the first natural frequency of the panel. This leads to the conclusion that the shock foot oscillation is driven by the panel vibration in a one-way coupling mechanism. The SBLI does modify the higher modes, which is likely due to localized forcing by the separation shock foot. Full-field surface pressure predictions are made using first order piston theory. Results show that the fluid–structure interaction is dominated by the large region of attached flow upstream of the shock foot.

Temperature- and moisture-dependent aeroelastic stability of graphene platelet reinforced nanocomposite lattice sandwich plates subjected to supersonic flow

In this work, we investigate the aero-thermo-elastic properties of graphene platelet (GPL)-reinforced nanocomposite lattice sandwich plates with pyramidal truss cores under supersonic airflow by considering the temperature- and moisture-dependent properties for the first time. GPLs in the face sheets are uniformly distributed or in graded form, and the trusses of the lattice cells are uniformly reinforced by GPLs. The effective modulus of elasticity of the GPL-reinforced nanocomposite is obtained using the Halpin–Tsai model, while the rule of mixture is used to estimate the Poisson's ratio and mass density of nanocomposite. Through the stress and deformation analysis of a pyramidal cell, the equivalent transverse shear modulus of a lattice-sandwich-core layer is determined; then, the composite lattice sandwich plate is transformed into a three-layered-sandwich structure. The kinematic relationships of the face sheets and lattice core layer are established using Kirchhoff plate theory and first-order shear deformation theory, respectively. The aerodynamic load resulting from the supersonic flow is obtained using piston theory. The equations of motion governing the flutter behaviors of simply supported sandwich plates under supersonic flow are derived with the help of a standard Lagrange process and assumed mode method. A comprehensive parameter study is conducted to explore the effects of temperature, moisture, GPL distribution pattern, and GPL weight fraction on the aero-thermo-elastic flutter characteristics of the nanocomposite lattice sandwich plates.

Research on Panel Flutter Considering the Effect of Convective Active Cooling

The aeroelastic characteristics of the panel under the action of coolant are obviously different from the flutter characteristics of the traditional panel. In order to solve this problem, the dynamics model of the panel flutter was established in this paper based on von Karman’s large deformation theory and the Kirchhoff–Love hypothesis. The panel dynamics equations were discretized into constant differential equations with finite degrees of freedom by Galerkin’s method, and solved by the fourth Runge–Kutta method in the time domain. The nonlinear modified piston theory was used to predict the unsteady aerodynamic loads, and the accuracy of the flutter analysis model was verified. On this basis, the effects of the head-panel pressure of coolant, the pressure drop ratio, the coolant injection direction, and the inertial resistance and viscous resistance on panel stability and flight stability were investigated, respectively. The results showed that reducing the pressure drop ratio, and reducing or increasing the head-panel pressure (valuing away from the freestream pressure) can improve the critical dynamic pressure when bifurcation occurs. At M∞=5.0, the pressure drop ratio causes a 22.1% increment in the critical dynamic pressure. The influence of the coolant injection direction on the panel bifurcation is mainly influenced by the head-panel pressure. The inertial resistance slows down the convergence process of the panel response, increases the limit cycle amplitude, and reduces the critical dynamic pressure of the panel, while the viscous resistance plays the opposite role. Based on these conclusions, this paper finally proposes the suppression method of panel fluttering from head-panel pressure, inertial resistance, viscous resistance, etc.

Aerothermoelastic Analysis of Conical Shell in Supersonic Flow

The aerothermoelastic behavior of a conical shell in supersonic flow is studied in the paper. According to Love’s first approximation shell theory, the kinetic energy and strain energy of the conical shell are expressed and the aerodynamic model is established by using the linear piston theory with a curvature correction term. By taking the characteristic orthogonal polynomial series as the admissible functions, the mode function of conical shell under different boundary conditions can be obtained using the Rayleigh–Ritz method. Then, the dynamic model of the conical shell is derived by using the Lagrange equation. Based on the model, variations in the natural frequencies with respect to temperature and free-stream static pressure are analyzed. Additionally, the effects of the length-to-radius ratio, the thickness-to-radius ratio, and semi-vertex angle, as well as the thermal and aerodynamic loads on the aerothermoelastic stability of the structure are investigated in detail.

Nonlinear thermo-acoustic response and fatigue prediction of three-dimensional braided composite panels in supersonic flow

In this paper, a novel aerodynamic-acoustic coupling model to investigate the influence of aeroelastic effects on the thermo-acoustic response of three-dimensional, four-directional braided composite panel is proposed, and the fatigue life under the combined aerodynamic load and acoustic load is discussed by using a rainflow cycle counting method. Assuming that the fibers are transversely isotropic and the matrix is isotropic, the fiber inclination model was used to predict the effective stiffness matrices of the composite panels. The piston theory and Gaussian random acoustic excitation were used to simulate the aerodynamic load and acoustic load, the thermal load is assumed to be a uniform distribution in steady state, and the material properties are assumed to be independent of temperature. Based on the von-Karman strain–displacement relation, the governing equations of the panel were formulated, and the response solutions of the four sides simply supported panel were obtained using Galerkin method and Runge-Kutta method. The aeroelastic effect on the thermos-acoustic response of the braided composite panel was investigated in time and frequency domains, and the life of different load conditions was predicted. The results show that the aeroelastic not only transforms the movement form, but also affects fatigue life of the panel.

A Method for Predicting the Aeroelastic Response of Radial Turbomachines

AbstractAircraft intermittent combustion engines often incorporate turbochargers adapted from ground-based applications to improve their efficiency and performance. These turbochargers can operate at off-design conditions and experience blade failures brought on by aerodynamic-induced blade resonances. A reduced-order model of the aeroelastic response of general fluid–structural configurations is developed using the Euler–Lagrange equation informed by numerical data from uncoupled computational fluid dynamic (CFD) and computational structural dynamic calculations. The structural response is derived from a method of assumed-modes approach. The unsteady fluid response is described by a modified version of piston theory that approximates the local transient pressure fluctuation in conjunction with steady CFD solution data. The reduced-order model is first applied to a classical panel flutter scenario and found to predict a flutter boundary that compares favorably to the boundary identified by existing theory and experimental data. The model is then applied to the high-pressure turbine of a dual-stage turbocharger. The model predictions are shown to reliably determine the lack of turbine blade flutter and rudimentary damping comparisons are performed to assess the ability of the model to ascertain the susceptibility of the turbine to forced response. Obstacles associated with the current experimental state of the art that impinge upon further numerical validation are discussed.

Inerter-Based Eigenvector Orientation Approach for Passive Control of Supersonic Panel Flutter

Inspired by the mass amplification property of inerters, an inerter-based passive panel flutter control procedure is developed and proposed. Formulations of aeroelastic equations of motion are based on the use of a wide-beam (flat panel) element stiffness equation subjective to supersonic flow using piston theory. The onset of flutter is analyzed using an eigenvector orientation approach, which may provide the advantage of lead time while the angle between eigenvectors of the first two coalescing modes reduces towards zero. The mass amplification effect of inerters is described and incorporated into the aeroelastic equation of motion of the passive actuation system for the investigation of flutter control. To demonstrate the potential applicability and usefulness of the proposed formulation and procedure, two numerical examples with one and two inerters, respectively, to optimally control the flutter of the panel modeled by wide-beam elements are presented. The results of the numerical simulation of the present examples demonstrate that the present inerter-based method can offset the onset of flutter to a higher level of aerodynamic pressure by optimizing the effective mass ratios and locations of inerters. In addition, this paper demonstrates that fundamental modes may be playing a role when identifying the optimal location of the inerters. It appears that the placement of the inerters may be more effective in controlling flutter at the highest amplitude of the mode shape along the wide beam. The procedure developed in this study may be of use for practical application for passive panel flutter control.

Supersonic flutter of variable stiffness circular cylindrical shells

Curvilinear reinforcement fibres allow to tailor the elastic properties of composite laminates in space, leading to Variable Stiffness Composite Laminates (VSCL). In this work, the aeroelastic stability of VSCL cylindrical shells under a supersonic airflow along the axial direction is analysed in order to verify if curvilinear fibres can be used to increase the flutter speed. A linear mathematical model for thin circular cylindrical VSCL shells is developed for that purpose. The aerodynamic pressure caused by the supersonic airflow is modelled recurring to the linearised piston theory. The p-version of the finite element method is used to transform the differential equations of motion from partial to ordinary. Using the latter, eigenvalue problems are defined to obtain the natural frequencies and mode shapes of vibration, and the critical flutter conditions. Various types of curvilinear fibre paths are explored, to find paths that result in higher values of critical flutter free stream pressure. The values are compared with the ones of conventional, constant stiffness, composite laminated shells.

Supersonic flutter characteristics of dielectric rectangular plate: The effects of magneto-aero-hydrodynamic interactions

This paper offers the authors’ views on critical magneto-aeroelastic behavior for dielectric rectangular isotropic plates. Magneto-aeroelastic stability and dynamic models are used to determine the total perturbed pressure caused by the incident flow of a perfectly conducting supersonic gas and a magnetic field as well as the critical flutter speed of flowing stream. The analytical description presented here is a generalization of the well-known pressure’s formula obtained on the basis of the “piston theory” of the classical theory of gas dynamics in the case of a magneto-hydrodynamic flow of elastic plates. Along with the analytical solutions, parametric studies are supplied to inform the reader about the influence of magnetic field on the flutter boundary.

Analytical and Numerical Simulation of Surface Pressure of an Oscillating Wedge at Hypersonic Mach Numbers and Application of Taguchi's Method

This paper aims to estimate the surface pressure of a wedge at hypersonic Mach numbers at a considerable angle of incidence. The Ghosh similitude, corresponding strip theory, and piston theory are used to determine the pressure distribution analytically, and the results are compared to those of the CFD analysis. The theory is valid when the shock wave is attached to the leading edge of the nose of the wedge. Pressure on the windward surface was considered in the analysis. The pressure on the Lee surface is neglected. The condition for the validity of the theory is that the Mach number M2 behind the shock wave is greater than 2.5. The parameters taken into account for the study are the wedge angle and Mach number. The range of wedge angle considered is from 5 to 25 degrees and the Mach number considered is from 5 to 15. The analytical and the CFD results are in good agreement. The findings indicate that the parameters like wedge angle and Mach number are influential parameters that influence the wedge surface static pressure. The surface static pressure rises with an increase in Mach number and wedge angle.

Geometrically Nonlinear Aeroelastic Flutter Characteristic of Laminated Composite Shell Panels Under Supersonic Flow

The nonlinear aeroelastic flutter characteristics of laminated composite curved (flat and cylindrical) panels are reported in this paper by obtaining the finite element (FE) solutions under the supersonic flow. The panel model has been derived from the third-order shear deformation theory framework including full geometrical nonlinearity via Green–Lagrange strain. In contrast, the flutter due to aerodynamic loading is included via the first-order piston theory. The current predicted solution accuracy and their validations have been demonstrated by relating the free vibration frequency, coalescence frequency, and critical aerodynamic pressure with the available numerical data. The initial free vibration eigenvalue responses are compared with in-house experimental values. Finally, a few numerical examples are presented by varying parameters like the effect of fiber orientation, flow angle, end boundary conditions, aspect ratio, modular ratio, thickness ratio, and amplitude ratio on the supersonic flutter boundaries of shell panels. The critical aerodyanamic pressure for simply supported cross-ply flat panels increases by 42.85% when the amplitude ratio increases from 0 to 0.75.

Time-Varying Aeroelastic Modeling and Analysis of a Rapidly Morphing Wing

Advanced rotational variable-swept missile wings require the ability to rapidly deploy, retract and reach the designated position. Therefore, the establishment of an effective time-varying aeroelastic model of a rotating missile wing is the prerequisite for performing transient response analysis during the rapid morphing process. In this paper, the finite element model of the wing at the fixed configuration is combined with the floating frame method to describe the small elastic deformations and large rigid-body displacements of the wing, respectively. Combining the structural dynamic model with the supersonic piston theory, a nonlinear and time-varying aeroelastic model of a missile wing undergoing the rapid morphing process is established. A method for the real-time determination of the time-varying lifting surface during morphing is discussed. Based on the proposed aeroelastic equations of motion, the flutter characteristics of the wing at different sweep angles are obtained. The influences of the actuator spring constant, the damping ratio during the morphing and the post-lock stages, as well as the velocity quadratic term in the aeroelastic equations, on the transient responses of the system are studied. The simulation results show that the flutter characteristics of the wing are greatly influenced by the sweep angle. Moreover, the jumping phenomenon in flutter speed due to the switching of flutter modes is found with the increase of the sweep angle. The morphing simulations demonstrate that the transient aeroelastic responses mainly occur in the post-lock stage, so much more attention needs to be focused on the post-lock vibrations. In addition, under the given simulation parameters, the nonlinear quadratic velocity term has little effect on the transient responses of the system. This study provides an efficient method for predicting the transient aeroelastic responses of a rotational variable swept wing.

Aerothermoelastic analysis of GPL-reinforced composite lattice sandwich beams based on a refined equivalent model

For the first time, this paper investigates the temperature-dependent aerothermoelastic properties of nanocomposite pyramidal lattice sandwich beams in supersonic airflow. A nonuniform temperature distribution along the thickness is considered. The face sheets and core of the sandwich beam are fabricated from graphene platelet (GPL)-reinforced nanocomposites. A refined thermo-mechanical equivalent model is established to determine the effective shear modulus of the lattice core subjected to a nonuniform temperature distribution. Then, the core transforms into a continuum layer. Subsequently, the beams with lattice cores were modeled as equivalent sandwich structures composed of three continuum layers. The effective modulus of elasticity of the nanocomposites was calculated using the Halpin–Tsai micromechanics model combined with the mixture rule. The aerodynamic pressure was calculated using the first-order supersonic piston theory. The aerothermoelastic properties of the sandwich beam were investigated by analyzing the critical flutter aerodynamic pressure and time-dependent responses of structures. The influences of nonuniform temperature distribution, GPL reinforcements, and end restrictions on the flutter characteristics of beams are addressed using some parameter examples.