Computational Fluid Dynamics/computational Structural Dynamics Research Articles

Numerical studies on the aeroelasticity of a shipboard helicopter rotor during engagement and disengagement with ship motions using CFD/CSD coupling approach

When the shipboard helicopter rotor engages and disengages on a ship deck, due to the influence of wind-over-deck environment and ship airwake, the heterogeneity of rotor airload is large. This large heterogeneity leads to the fluctuation of blade deflection which changes the aerodynamic forces and causes danger of over deflection. To investigate the aeroelasticity of a rotor blade and find the rule of deflection and the deformed blade aerodynamic force in the rotor/ship coupling flow field, we establish a loose computational fluid dynamics/computational structural dynamics (CFD/CSD) coupling model. This coupling model simulates the aeroelastic characteristics of the shipboard helicopter rotor during engagement and disengagement with ship motions. In the simulation, the CFD solver is based on Reynolds-averaged Navier-Stokes (RANS) equations and the CSD solver is based on the moderate deflection beam model. We compare the results with the experimental data and verify the effectiveness of the simulation. Through the analysis of the flow field, blade deflection, and aerodynamic forces under various wind-over-deck conditions at different positions, we find in certain cases, that the elastic deflection has a significant impaction the blade aerodynamic force. As the wind direction anglesincrease, the rotor blade is more likely to have a large negative elastic twist deflection, causing drop of aerodynamic forces and danger of over deflection.

Three dimensional aeroelastic analyses considering free-play nonlinearity using computational fluid dynamics/computational structural dynamics coupling

Most of the previous studies on free-play aeroelasticity were based on the linear aerodynamic theory, which cannot consider the aerodynamic nonlinear effects. This paper proposes a framework of computational fluid dynamics/computational structural dynamics (CFD/CSD) coupling approach that can deal with the three dimensional aeroelastic problems with both the free-play nonlinearity and the aerodynamic nonlinearity. The fictitious mass method is used to construct the reduced structural equations of motion and the switching point is detected using the bisection method. The adaptive time step obtained by the bisection method is returned to the CFD solver so that both the structural and the fluid equations are integrated using the same time step. An all-movable wing with free-play at the root is considered for numerical studies. Results demonstrate the CFD/CSD coupling method can predict the stable limit cycle oscillation (LCO) effectively. The initial condition study shows that the LCO behavior is subcritical and the hysteresis response can be predicted in time domain effectively by the presented method. The viscous effect is shown to increase the LCO boundary and shift the LCO amplitude to a larger velocity in transonic regime. The LCO boundary is determined from subsonic to transonic Mach numbers. The transonic dip in LCO boundary is found by the CFD/CSD coupling method, but the equivalent linearization with doublet lattice method fails to predict this phenomenon. From the results of this study, the LCO boundary is shown to be 43.5% below the flutter boundary at most.

Fuel efficiency optimization of high-aspect-ratio aircraft via variable camber technology considering aeroelasticity

In this study, variable camber technology is applied to improve the fuel efficiency of high-aspect-ratio aircraft with aeroelasticity considered. The nonlinear static aeroelastic analyses are conducted for CFD/CSD (computational fluid dynamics/computational structural dynamics) numerical simulations. The RBF (radial basis function) method is adopted for the transmission of aerodynamic loads and structural displacements, the diffusion smoothing method is employed for grid deformation in each iteration of CFD/CSD coupling, and the FFD (free-form deformation) method is introduced for the parameterization of variable camber wing. Based on the aerodynamic characteristic curves under different cambers, the discrete variable camber control matrix for the high-aspect-ratio aircraft during the cruise phase is established. The Fibonacci method is employed to optimize the fuel efficiency by utilizing the control matrix. The results indicate that the drag during the cruise phase is reduced obviously and the fuel efficiency is improved evidently comparing to the original configuration.

CFD/CSD-based flutter prediction method for experimental models in a transonic wind tunnel with porous wall

To predict the flutter dynamic pressure of a wind tunnel model before flutter test, an accurate Computational Fluid Dynamics/Computational Structural Dynamics (CFD/CSD)-based flutter prediction method is proposed under the conditions of a 2.4 m × 2.4 m transonic wind tunnel with porous wall. From the CFD simulations of the flows through an inclined hole of this wind tunnel, the Nambu’s linear porous wall model between the flow rate and the differential pressure is extended to the porous wall with inclined holes, so that the porous wall can be conveniently modeled as a boundary condition. According to the flutter testing approach for the current wind tunnel, the steady CFD calculation is conducted to achieve the required inlet Mach number. A time-domain CFD/CSD method is then employed to evaluate the structural response of the experimental model, and the critical flutter point is obtained by increasing the dynamic pressure step by step at a fixed Mach number. The present method is applied to the flutter calculations for a vertical tail model and an aircraft model tested in the current transonic wind tunnel. For both models, the computed flutter characteristics agree well with the experimental results.

Aeroelastic Simulation Using CFD/CSD Coupling Based on Precise Integration Method

Aeroelasticity studies the interaction between the aerodynamic loads and the flexible structures, and has gained much attention in the design of modern aircraft. Most of the existing computational fluid dynamics/computational structural dynamics (CFD/CSD) coupling approaches are based on Runge–Kutta method, central difference method, linear multi-step method and so on, which are conditionally stable and are unsuitable for the stiff problem that requires a very small time step to solve. In this paper, the precise integration method (PIM) formula is derived for the structural modal equations and then the PIM-based CFD/CSD coupling method is presented. The three-dimensional AGARD wing 445.6 and a sweptback wing are considered here for aeroelastic studies. The flutter results demonstrate that the presented method is comparable in accuracy to the traditional strong coupling method and has better numerical stability property than some exiting improved methods. For the static aeroelastic analyses, applying a large damping ratio to the structural equations helps to obtain the equilibrium quickly but may lead to the stiff problem, which was seldom discussed before. The results show that the presented PIM-based coupling method can overcome the stiff problem arising in static aeroelastic systems and is more efficient than the traditional coupling approach based on Runge–Kutta method, especially when a large damping ratio is applied.

UH-60A Rotor Analysis with an Accurate Dual-Formulation Hybrid Aeroelastic Methodology

Dual-solver hybrid methodologies that couple fluid solvers in different regions of the flowfield have been developed to accelerate convergence with minimal compromises in accuracy. A new dual-solver hybrid analysis framework that addresses some of the major shortcomings of prior dual-solver hybrid methodologies has been developed through an academic–industry partnership. In this effort, one of the hybrid solvers, comprising of a computational fluid dynamics–computational structural dynamics (CFD-CSD) solver coupled with a Lagrangian wake-panel module, is assessed. The hybrid solver’s ability to replicate the accuracy of the more expensive CFD-CSD approach and its ability to capture the physics of the rotor system are presented. The criteria that have been evaluated include integrated aerodynamic performance quantities, structural loads and moments, and near-body wakes. If the best practices extracted from this analysis are applied, the analysis with a reduced off-body CFD mesh is able to predict forward-flight rotor behavior that is within 4% of a full CFD simulation with up to 70% cost savings. This accuracy has been assessed on both high-speed and high-thrust flight conditions and has been quantitatively verified for aerodynamic, structural, and hub variables of interest at a number of radial blade stations for a frequency range of 0–16/rev.

Numerical analysis on flutter of Busemann-type supersonic biplane airfoil

The Busemann-type supersonic biplane can effectively reduce the wave drag through shock interference effect between airfoils. However, considering the elastic property of the wing structure, the vibration of the wings can cause the shock oscillation between the biplane, which may result in relative aeroelastic problems of the wing. In this research, fluid–structure interaction characteristics of the Busemann-type supersonic biplane at its design condition have been studied. A theoretical two-dimensional structure model has been established to consider the main elastic characteristics of the wing structure. Coupled with unsteady Navier–Stokes equations, the fluid–structure dynamic system of the supersonic biplane is studied through the two-way computational fluid dynamics/computational structural dynamics (CFD/CSD) coupling method. The biplane system has been simulated at its design Mach number with different nondimensional velocities. Different initial disturbance has been applied to excite the system and the effects of the position of the mass center on the system’s aeroelastic stability is also discussed. The results reveal that the stability of the airfoil in supersonic biplane system is decreased compared with that of the airfoil isolated in supersonic flow and such stability reduction effect should be given due attention in practical design.

Optimization of Biomimetic Propulsive Kinematics of a Flexible Foil Using Integrated Computational Fluid Dynamics–Computational Structural Dynamics Simulations

A computational methodology, which combines a computational fluid dynamics (CFD) technique and a computational structural dynamics (CSD) technique, is employed to design a deformable foil whose kinematics is inspired by the propulsive motion of the fin or the tail of a fish or a cetacean. The unsteady incompressible Navier–Stokes equations are solved using a second-order accurate finite difference method and an immersed-boundary method to effectively impose boundary conditions on complex moving boundaries. A finite element-based structural dynamics solver is employed to compute the deformation of the foil due to interaction with fluid. The integrated CFD–CSD simulation capability is coupled with a surrogate management framework (SMF) for nongradient-based multivariable optimization in order to optimize flapping kinematics and flexibility of the foil. The flapping kinematics is manipulated for a rigid nondeforming foil through the pitching amplitude and the phase angle between heaving and pitching motions. The flexibility is additionally controlled for a flexible deforming foil through the selection of material with a range of Young's modulus. A parametric analysis with respect to pitching amplitude, phase angle, and Young's modulus on propulsion efficiency is presented at Reynolds number of 1100 for the NACA 0012 airfoil.

Aeroacoustic Analysis of a Lift-Offset Coaxial Rotor Using High-Fidelity CFD/CSD Loose Coupling Simulation

This paper presents the aeroacoustic analysis of a lift-offset coaxial rotor in high-speed forward flight using the high-fidelity computational fluid dynamics/computational structural dynamics (CFD/CSD) loose coupling software Helios. Acoustic simulations are performed using the software PSU-WOPWOP at eight microphones positioned below the coaxial rotor. The total power of the three speed cases—100, 150, and 200 kt—is validated against flight-test data and shows good agreement. A series of parametric studies is also conducted to investigate the effect of lift offset, flight speed, and rotor-to-rotor separation distance on acoustics of the coaxial rotor. Strong blade-crossover and self-blade–vortex interaction events of the coaxial rotor, which are major sources of loading noise, are captured via high-fidelity CFD simulations in all speed cases. Highly impulsive acoustic pressure signals are identified in all simulation cases, and the magnitude of mid-frequency sound pressure level (SPL) increases significantly with increasing flight speed and lift offset. The strength of mid-frequency SPL, on the other hand, is reduced significantly as the rotor-to-rotor separation distance increases at 100 kt. However, the higher speed cases do not show a significant reduction in mid-frequency SPL with increasing separation distance.

Rotor Airload and Acoustics Prediction Based on CFD/CSD Coupling Method

An advanced airload and noise prediction method based on computational fluid dynamics/computational structural dynamics (CFD/CSD) coupling for helicopter rotor has been developed in this paper. In the present method, Navier-Stokes equation is applied as the governing equation, and a moving overset grid system is generated in order to account for the blade motions in rotation, flapping and pitching. The blade structural analysis is based on 14-DOF Euler beam model, and the finite element discretization is conducted on Hamilton's variational principle and moderate deflection theory. Aerodynamic noise is calculated by Farassat 1A formula derived from FW-H equation. Using the developed method, numerical example of UH-60A is performed for aeroelastic loads calculation in a low-speed forward flight, and the calculated results are compared with both those from isolated CFD method and available experimental data. Then, rotor noise is emphatically calculated by CFD/CSD coupling method and compared with the isolated CFD method. The results show that the aerodynamic loads calculated from CFD/CSD method are more satisfactory than those from isolated CFD method, and the exclusion of blade structural deformation in rotor noise calculation may cause inaccurate results in low-speed forward flight state.

Numerical study on influence of single control surface on aero elastic behavior of forward-swept wing

In order to study the influence of elastic forward-swept wing (FSW) with single control surface, the computational fluid dynamics/computational structural dynamics (CFD/CSD) loose coupling static aero elastic numerical calculation method was adopted for numerical simulation. The effects of the elastic FSW with leading- or trailing-edge control surface on aero elastic characteristics were calculated and analysed under the condition of high subsonic speed. The result shows that, the deflection of every single control surface could change the aero elastic characteristics of elastic FSW greatly. Compared with the baseline model, when leading-edge control surface deflected up, under the condition of small angles of attack, the aerodynamic characteristics was poor, but the bending and torsional deformation decreased. Under the condition of moderate angles of attack, the aerodynamic characteristics was improved, but bending and torsional deformation increased; When leading-edge control surface deflected down, the aerodynamic characteristics was improved, the bending and torsional deformation decreased/increased under the condition of small/moderate angles of attack. Compared with the baseline model, when trailing-edge control surface deflected down, the aerodynamic characteristics was improved. The bending and torsional deformation increased under the condition of small angles of attack. The bending deformation increased under the condition of small angles of attack, but torsional deformation decreases under the condition of moderate angles of attack. So, for the elastic FSW, the deflection of trailing-edge control surface play a more important role on the improvement of aerodynamic and elastic deformation characteristics.

Mechanism of frequency lock-in in vortex-induced vibrations at low Reynolds numbers

In this study, a CFD-based linear dynamics model combined with the direct Computational Fluid Dynamics/Computational Structural Dynamics (CFD/CSD) simulation method is utilized to study the physical mechanisms underlying frequency lock-in in vortex-induced vibrations (VIVs). An identification method is employed to construct the reduced-order models (ROMs) of unsteady aerodynamics for the incompressible flow past a vibrating cylinder at low Reynolds numbers ($Re$). Reduced-order-model-based fluid–structure interaction models for VIV are also constructed by coupling ROMs and structural motion equations. The effects of the natural frequency of the cylinder, mass ratio and structural damping coefficient on the dynamics of the coupled system at$Re=60$are investigated. The results show that the frequency lock-in phenomenon at low Reynolds numbers can be divided into two patterns according to different induced mechanisms. The two patterns are ‘resonance-induced lock-in’ and ‘flutter-induced lock-in’. When the natural frequency of the cylinder is in the vicinity of the eigenfrequency of the uncoupled wake mode (WM), only the WM is unstable. The dynamics of the coupled system is dominated by resonance. Meanwhile, for relatively high natural frequencies (i.e. greater than the eigenfrequency of the uncoupled WM), the structure mode becomes unstable, and the coupling between the two unstable modes eventually leads to flutter. Flutter is the root cause of frequency lock-in and the higher vibration amplitude of the cylinder than that of the resonance region. This result provides evidence for the finding of De Langre (J. Fluids Struct., vol. 22, 2006, pp. 783–791) that frequency lock-in is caused by coupled-mode flutter. The linear model exactly predicts the onset reduced velocity of frequency lock-in compared with that of direct numerical simulations. In addition, the transition frequency predicted by the linear model is in close coincidence with the amplitude of the lift coefficient of a fixed cylinder for high mass ratios. Therefore, it confirms that linear models can capture a significant part of the inherent physics of the frequency lock-in phenomenon.

An Aero-Thermo-Elasticity Method Applied on the Supersonic Aircraft Model

Coupling between the vibration frequencies and the unsteady aerodynamic will reduce the flutter speed and ride quality through the aerodynamic heat transfer. As the flight speed improved, the aeroelastic analysis has become an essential means of aircraft design. The method of aero-thermo-elastic (ATE) analysis is coupled with aircraft aeroelastic analysis and thermal deformation, and is more realistic reflection of the actual flight of the aircraft. In this paper, an ATE analysis of aircraft adopted by computational fluid dynamics/computational structural dynamics (CFD/CSD) methods, and compared with the traditional analysis, to provide analytical tools for the supersonic aircraft design.

Rotor Aeroelastic Stability Analysis Using Coupled Computational Fluid Dynamics/Computational Structural Dynamics

Computational fluid dynamics/computational structural dynamics (CFD/CSD) coupling was successfully applied to the rotor aeroelastic stability problem to calculate lead–lag regressing mode damping of a hingeless rotor in hover and forward flight. A direct time domain numerical integration of the equations in response to suitable excitation was solved using a tight CFD/CSD coupling. Two different excitation methods—swashplate cyclic pitch and blade tip lead–lag force excitations—were investigated to provide suitable blade transient responses. The free decay transient response time histories were postprocessed using the moving-block method to determine the damping as a function of the rotor operating conditions. Coupled CFD/CSD analysis results are compared with the experimentally measured stability data obtained for a 7.5-ft-diameter Mach-scale hingeless rotor model as well as stability predictions using the comprehensive analysis Rotorcraft Comprehensive Analysis System (RCAS). The coupled CFD/CSD predictions agreed more closely with the experimental lead–lag damping measurements than RCAS predictions based on conventional aerodynamic methods, better capturing key features in the damping trends.

Flutter Analysis of Compressor Blade Based on CFD/CSD

Based on the CFD/CSD (Computational Fluid Dynamics / Computational Structural Dynamics) algorithm, flutter characteristic and fluid structure interaction (FSI) problems of turbomachinery blades were studied in present paper. The three-dimensional unsteady Navier-Stokes equations and three-dimensional structural model were solved by the finite volume method and the finite element method, respectively. High accuracy in calculation and data exchange were gained by using load transfer, deformation tracking and synchronization between two solvers. The procedure successfully simulated the aeroelastic responses of a high performance fan rotor, NASA Rotor 67, over a range of operational conditions, and the results were compared with the experiment. The results show that the flutter mechanics of the compressor blade could be illustrated based on mean pressure and the distribution of cycle work, which is helpful for the decision of compressor stability.

Wing Flutter Simulations Using an Aeroelastic Solver Based on the Predictor—Corrector Scheme

An integrated computational fluid dynamics (CFD) and computational structural dynamics (CSD) method is developed here for the calculation and analysis of wing flutter in the time domain. The CFD solver is based on an unsteady multi-grid finite-volume algorithm for the Euler/Navier—Stokes equations on a multi-block structured grid. The CSD solver adopts a linear multi-step method to integrate the aeroelastic governing equations expressed in the modal space. A grid deformation method employing a radial basis function approach is introduced here to generate a dynamically moving grid. The solving procedure of an aeroelastic system is implemented with a predictor—corrector scheme in the physical time. By extrapolating the aerodynamic force, the hybrid predictor—corrector scheme is introduced to save the flow calculation right before the correcting step. The coupled CFD—CSD method is used to simulate wing flutter problems in the time domain in order to predict the stability of an aeroelastic system, which, in this paper, is fulfilled by finding the flutter boundaries. The calculation of the Isogai wing finds an S-shaped flutter boundary, which has been predicted by other studies. The obtained flutter boundary of the AGARD 445.6 wing shows a distinct transonic dip, which agrees well with the experiment result. Computational efficiency and accuracy using two predictor—corrector algorithms and a strong coupling algorithm are also compared.

Multi-Objective Design Exploration and Its Application to Regional-Jet Wing Design

A new approach, Multi-Objective Design Exploration (MODE), is presented to address multidisciplinary design optimization (MDO) problems using computational fluid dynamics-computational structural dynamics (CFD-CSD) coupling. MODE reveals the structure of the design space from the trade-off information and visualizes it as a panorama for Decision Maker. The present form of MODE consists of the Kriging Model, adaptive range multi objective genetic algorithms, analysis of variance and a self-organizing map. The main emphasis of this approach is visual data mining. An MDO system using high-fidelity simulation codes, a Navier-Stokes solver and NASTRAN has been developed and applied to a regional-jet wing design. Because the optimization system becomes very expensive computationally, only brief exploration of the design space has been performed. However, visual data mining results demonstrate that design knowledge can produce a good design even after brief design exploration.

Model-based simulation of the synergistic effects of blast and fragmentation on a concrete wall using the MPM

With the development of the material point method (MPM) that is an extension from computational fluid dynamics (CFD) to computational structural dynamics (CSD), a model-based simulation is performed in this paper to investigate the synergistic effects of blast and fragmentation on structural failure. As can be found from the open literature, the synergistic effects of blast and fragmentation have been usually simulated via a combined approach through an interface between CFD codes and CSD codes. As a consequence, numerical solutions are very sensitive to the choices of different time steps and spatial meshes for different physical phenomena, especially for the multi-physics involved in the initiation and evolution of structural failure. Hence, a coupled approach within a single computational domain seems to be necessary if objective results are needed. In this paper, a numerical procedure is proposed with the use of the MPM, so that different kinds of gradient and divergence operators could be discretized in a single computational domain without involving fixed mesh connectivity. To simulate the evolution of impact failure, the transition from continuous to discontinuous failure modes is identified via the bifurcation analysis. The potential of the proposed model-based simulation procedure is demonstrated through 1D and 2D isothermal cases including cased bomb expansion and fragmentation, blast wave expansion through a broken case, and blast and fragment impact on a concrete wall. The preliminary results obtained in this numerical study provide a better understanding of the synergistic effects on impact/blast-resistant structural design. An integrated experimental, analytical and computational effort is required to further improve the proposed procedure for general applications.