Local Piston Theory Research Articles

Effect of Model Fidelity on High-Speed Aeroelastic Behavior of a Cantilever Plate

Turbulence, flow separation, and shock dynamics challenge the modeling and analysis of high-speed aeroelastic behavior. Motivated by this, the importance of modeling the fidelity of the flow is explored in the aeroelastic response of a cantilever plate in an Ma=2.0 separating turbulent flow using unsteady Reynolds-averaged Navier–Stokes (URANS) and URANS-enriched local piston theory (LPT). Structural modeling assumptions are also evaluated using both linear and nonlinear representations. Close agreement in the predicted aeroelastic steady state is observed. However, large discrepancies in the dynamic aeroelastic response predictions are found and ultimately linked to the neglect of deformation-induced cavity pressure fluctuations and dynamic flow separation in the LPT model. Interestingly, the dynamic flow separation induces a fluid-driven limit cycle oscillation in the postflutter regime. Furthermore, structural nonlinearity is not found to have a strong impact on the conditions and configurations considered.

Experimental and Numerical Flutter Analysis Using Local Piston Theory with Viscous Correction

Due to the maneuver and overload requirements of aircraft, it is inevitable that supersonic fins experience high angles of attack (AOAs) and viscous effects at high altitudes. The local piston theory with viscous correction (VLPT) is introduced and modified to account for the 3-dimensional effect. With the contribution of the explicit aerodynamic force expression and enhanced surface spline interpolation, a tightly coupled state-space equation of the aeroelastic system is derived, and a flutter analysis scheme of relatively small computational complexity and high precision is established with a mode tracking algorithm. A wind tunnel test conducted on a supersonic fin confirms the validity of our approach. Notably, the VLPT predicts a more accurate flutter boundary than the local piston theory (LPT), particularly regarding the decreasing trend in flutter speed as AOA increases. This is attributed to the VLPT’s ability to provide a richer and more detailed steady flow field. Specifically, as the AOA increases, the spanwise flow evolves into a gradually pronounced spanwise vortex, yielding an additional downwash and energizing the boundary layer, which is not captured by LPT. This indicates that the precision of LPT/VLPT significantly depends on the accuracy of steady flow results.

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.

Efficient Prediction of the Temperature History of a Hypersonic Vehicle Throughout the Mission Trajectory with an Aerodynamic Thermal Load Element

This work introduces an efficient approach for aero-thermo-mechanical analysis to predict the temperature history of a hypersonic vehicle during its full mission trajectory. The approach uses a recently proposed aerodynamic thermal load element, in which the effects of aerodynamic pressure and aerodynamic heating are efficiently considered using local piston theory and the Eckert reference temperature method, respectively. This element is implemented as a user-subroutine in commercial software to handle realistic models for the aero-thermo-mechanical analysis, such as the X-43A. A finite element model of the X-43A is constructed for a benchmark test. Using the model, an aero-thermo-mechanical analysis is carried out while considering the full mission trajectory of the X-43A. The predicted temperature results are compared with recorded flight test data from the X-43A. Additionally, the aero-thermo-mechanical behavior of the hypersonic vehicle is investigated according to various parameters. The investigation confirms that the approach can be efficiently used in the design of hypersonic vehicles with considerable savings in computational cost.

Effects of structural thermal boundary conditions on hypersonic aerothermoelasticity of all-movable control surface

Structural thermal boundary conditions are usually simplified in the aerothermoelastic analysis. However, it will influence the heat transfer, the temperature distribution, and the structure stiffness, which have effects on the accurate prediction of the aerothermoelastic characteristics. In this study, an aerothermoelastic framework for hypersonic vehicles is developed, and the effects of structural thermal boundary conditions on aerothermoelasticity of all-movable control surface are investigated. The Reynold’s averaged Navier–Stokes equations are solved by computational fluid dynamics method to obtain the thermal environment. The transient heat transfer, the thermal stress, and the structure mode are analyzed by using finite element method. Finally, the local piston theory is used to calculate the unsteady aerodynamic force, and aeroelastic characteristics are analyzed in the state space. Aerothermoelastic characteristics of three different structural thermal boundaries are investigated in detail, including aerodynamic heating only on control surface; aerodynamic heating on both the control surface and the shaft; and aerodynamic heating on the control surface, the shaft, and the body. The results show that the heat transfer process, the temperature distribution, the thermal stresses, and the natural frequencies of the structure are influenced significantly by structural thermal boundary conditions especially in the shaft. Furthermore, the aerothermoelastic stability margin is affected ultimately.

Local Piston Theory as an Alternative to Mesh Deformation: Slender Wing/Body Configurations

The suitability of local piston theory for modeling static loads on a deforming low-aspect-ratio wing in the presence of aerodynamic interference is investigated. Predictions using Euler-based local piston theory are compared to Euler solutions for the deformed geometry. Moderate to large deformations are investigated for the leeside wing on a cruciform wing/body configuration. It is shown that local piston theory is suitable even for large deformations, with the perturbation downwash/Mach number supersonic, provided that the loading induced by deformation is not dominated by interaction with body vortices or other sources of aerodynamic interference. Second-order local piston theory is recommended for deformations producing downwash/Mach numbers approaching sonic. The influence of the choice of piston theory coefficients is in producing an estimation band for the local piston theory load prediction, with insignificant influence on the load slope in the present investigation. In conclusion, local piston theory is put forward as a viable alternative to mesh deformation toward reduction of the computational cost of aerodynamic load prediction for static aeroelasticity, provided that perturbation loads are dominated by local twist and not by vortex interaction.

Local Piston Theory with Viscous Correction and Its Application

This paper introduces a local piston theory with viscous correction for the prediction of hypersonic unsteady aerodynamic loads at high attitudes and large Mach numbers. A semi-empirical relation accounting for the viscous interaction effects to determine the effective shape is proposed. The method is validated by applying to thin airfoils at various Mach numbers, angles of attack, and operating altitudes. Sample two- and three-dimensional aerodynamic forces calculations are conducted demonstrating this method. Furthermore, flutter boundary predictions for a two-dimensional airfoil and pitching-in-damping derivative evaluations for a three-dimensional waverider configuration are performed with this unsteady aerodynamic model. Compared with the Euler-based local piston theory, this model performs much better at high altitudes for a wide range of Mach numbers, angles of attack, and shapes. Results suggest the feasibility of using the effective shape of hypersonic vehicles to efficiently and accurately obtain the unsteady aerodynamic characteristics in hypersonic flow environment.

Aerodynamic Optimization for Hypersonic Wing Design Based on Local Piston Theory

Optimization of aerodynamic shapes using numerical methods has always been of engineering interest. This paper presents a highly efficient aerodynamic optimization method for hypersonic wings based on local piston theory. The objective of the optimization is to improve the aerodynamic characteristics of original airfoils or wings generated from NACA0012 while satisfying constraints on structure requirements. In the optimization procedure, a genetic algorithm is employed for optimum search, the Hicks–Henne bump function is used for airfoil geometrical modification, and local piston theory is used for unsteady pressure perturbations caused by geometrical modification from the baseline. Because unsteady pressure perturbations at supersonic or hypersonic conditions could be calculated by local piston theory based on initial flowfield results in the optimum searching process, only one steady-state solution without any use of moving or deforming grids is required. Therefore, the optimization method described in this paper is an extremely efficient technique that combines the advantages of steady computational fluid dynamics and the local piston theory and thus has very low computational cost in an optimum search process. Optimization results of airfoils and wings, including single and multipoint optimization for a flat wing without any sweep, and backswept wing, demonstrate the effectiveness and efficiency of the aerodynamic optimization method for hypersonic wings.

Generalized Formulation and Review of Piston Theory for Airfoils

The present work presents a brief review of some of the notable contributions to piston theory and of its theoretical basis. A generalized formulation of piston theory is given, applicable to both local and classical piston theory. A consistent generalized formulation of the downwash equation is given, accounting for arbitrary motion in the plane of the airfoil. The formulation reduces to established downwash equations through appropriate definition of the cylinder orientation. The theoretical range of validity of classical piston theory is examined, and the relative accuracy of a number of approximate theories encapsulated by the formulation as applied to a planar wedge is considered. The relative importance of higher order terms in piston theory is examined, with the significance of recent literature extending the fidelity of the first-order term highlighted. It is subsequently suggested that current implementations of local piston theory may be improved through the use of a first-order term of suitable accuracy.

Zeroth-order flutter prediction for cantilevered plates in supersonic flow

An aeroelastic prediction framework in MATLAB with modularity in the quasi-steady aerodynamic methodology is developed. Local piston theory (LPT) is integrated with quasi-steady methods including shock-expansion theory and the Supersonic Hypersonic Arbitrary Body Program (SHABP) as a computationally inexpensive aerodynamic solver. Structural analysis is performed using bilinear Mindlin–Reissner quadrilateral plate elements. Strong coupling of the full-order system and linearization of the modal-order system are implemented. The methodology is validated against published experimental data in the literature and benchmarked against Euler computation in the Edge CFD code. The flutter dynamic pressure is predicted to be within 10% of the experimental value for 140 times lower computational cost compared to CFD. Good agreement in other cases is obtained with the industry-standard ZONA7 and ZONA7U codes.

Integrated analysis on static/dynamic aeroelasticity of curved panels based on a modified local piston theory

A flow field modified local piston theory, which is applied to the integrated analysis on static/dynamic aeroelastic behaviors of curved panels, is proposed in this paper. The local flow field parameters used in the modification are obtained by CFD technique which has the advantage to simulate the steady flow field accurately. This flow field modified local piston theory for aerodynamic loading is applied to the analysis of static aeroelastic deformation and flutter stabilities of curved panels in hypersonic flow. In addition, comparisons are made between results obtained by using the present method and curvature modified method. It shows that when the curvature of the curved panel is relatively small, the static aeroelastic deformations and flutter stability boundaries obtained by these two methods have little difference, while for curved panels with larger curvatures, the static aeroelastic deformation obtained by the present method is larger and the flutter stability boundary is smaller compared with those obtained by the curvature modified method, and the discrepancy increases with the increasing of curvature of panels. Therefore, the existing curvature modified method is non-conservative compared to the proposed flow field modified method based on the consideration of hypersonic flight vehicle safety, and the proposed flow field modified local piston theory for curved panels enlarges the application range of piston theory.

Aeroservoelastic modeling and analysis of a canard-configured air-breathing hypersonic vehicles

Air-breathing hypersonic vehicles (HSVs) are typically characterized by interactions of elasticity, propulsion and rigid-body flight dynamics, which may result in intractable aeroservoelastic problem. When canard is added, this problem would be even intensified by the introduction of low-frequency canard pivot mode. This paper concerns how the aeroservoelastic stability of a canard-configured HSV is affected by the pivot stiffnesses of all-moveable horizontal tail (HT) and canard. A wing/pivot system model is developed by considering the pivot torsional flexibility, fuselage vibration, and control input. The governing equations of the aeroservoelastic system are established by combining the equations of rigid-body motion, elastic fuselage model, wing/pivot system models and actuator dynamics. An unsteady aerodynamic model is developed by steady Shock-Expansion theory with an unsteady correction using local piston theory. A baseline controller is given to provide approximate inflight characteristics of rigid-body modes. The vehicle is trimmed for equilibrium state, around which the linearized equations are derived for stability analysis. A comparative study of damping ratios, closed-loop poles and responses are conducted with varying controller gains and pivot stiffnesses. Available bandwidth for control design is discussed and feasible region for pivot stiffnesses of HT and canard is given.

Supersonic Flutter Analysis of Vehicles at Incidence Based on Local Piston Theory

Supersonic Flutter Analysis of Vehicles at Incidence Based on Local Piston Theory

Supersonic Flutter Analysis Based on a Local Piston Theory

DOI: 10.2514/1.37750 A highly efficient local-piston theory is presented for the prediction of inviscid unsteady pressure loads at supersonic and hypersonic speeds. A steady mean flow solution is first obtained by an Euler method. The classical pistontheoryismodifiedtoapplylocallyateachpointontheairfoilsurfaceontopofthelocalmean flowtoobtainthe unsteadypressureperturbationscausedbythedeviationoftheairfoilsurfacefromitsmeanlocationwithouttheneed of performing unsteady Euler computations. Results of two- and three-dimensional unsteady air loads and flutter predictions are compared with those obtained by the classical piston theory and an unsteady Euler method to assess theaccuracyandvalidityrangeinairfoilthickness, flightMachnumber,andangleofattackandwiththepresenceof blunt leading edges. The local-piston theory is found to offer superior accuracy and much wider validity range compared with the classical piston theory, with the cost of only a fraction of the computational time needed by an unsteady Euler method.