Transonic flutter analysis using a fully coupled density based solver for inviscid flow

This paper focuses on the coupling between the high fidelity aerodynamic model for the flow field and the modal analysis of a typical wing section to carry out flutter analysis. This coupled aeroelastic model is implemented in one of the most widely used open source CFD codes called OpenFOAM. The model is designed to calculate the structural displacement in the time domain based on the free vibration modes of the structure by constructing the numerical model directly from the modal analysis. Essentially a second order ordinary differential equation is solved for each mode as a function of the generalised coordinates. A density based solver using central difference scheme of Kurganov and Tadmor is used to model the flow field. Two main cases of transonic flow over NACA 64A010 are modelled for a forced pitching oscillation airfoil and a self-sustained aerofoil respectively. The self-sustained two degrees of freedom case is modelled for three different possibilities covering damped, neutral and divergent oscillations. Predicted results show very good agreement with the numerical and experimental data available in the literature

An Efficient Euler Method to Predict Shock Migration on a Straked Delta Wing Design

In support of the Air Force Office of Scientific Research, this project sought to identify the significance of nonlinear aerodynamic phenomena in regards to LCO of a straked delta wing design. Previous works include unsteady Navier-Stokes aeroelastic analysis of various wing designs and flight test of F-16 transonic LCO with interest focused on oscillatory SITES behavior. The research presented within this investigation further expanded the understanding of unsteady aerodynamics by performing aeroelastic analysis of a wing oscillated in pitch with an Euler-based, boundary layer coupled numerical method (ZEUS). The wing was tested for a multitude of LCO parameters such as median AoA, oscillation amplitude, oscillation frequency, Mach number, and the type of numerical solver used. Computed pressure data sets were analyzed along the wing\u27s surface at 4 chordwise stations along the wing\u27s span. Results indicate that oscillatory shock migration occurs in response to the pitching motion of the wing. ZEUS has the capability to run either a fully inviscid solution or a boundary layer coupled solution (BLC). While the use of both methods found shock migration to occur, the BLC solution predicted more significant shock migration. The inviscid solution predicted more aggressive shocks located further aft on the wing than the BLC solution. In regards to oscillation amplitude, increasing the amplitude resulted in a greater range of shock migration than lower amplitude cases. Both oscillation frequencies tested did not show any noteworthy differences. The aforementioned findings support the theory that potential oscillatory shock migration can occur during certain cases of transonic LCO. In addition, it was concluded that based on the flow solver used (ZEUS), shock movement during LCO is not purely a function of viscosity (SITES), although the modeling of viscous effects does affect the range of shock migration

Dynamic Aeroelastic Analysis of Wing/Store Configurations

Limit-cycle oscillation, or LCO, is an aeroelastic phenomenon characterized by limited amplitude, self-sustaining oscillations produced by fluid-structure interactions. In order to study this phenomenon, code was developed to interface a modal structural model with a commercial computational fluid dynamics program. LCO was simulated for a rectangular wing, referred to as the Goland+ wing. It was determined that the aerodynamic nonlinearity responsible for LCO in the Goland+ wing was the combination of strong trailing-edge and lambda shocks which periodically appear and disappear. This mechanism limited the flow of energy into the structure which quenched the growth of the flutter, resulting in a steady LCO. Under-wing and tip stores were added to the Goland+ wing to determine how stores affected limit-cycle oscillation. It was found that aerodynamic store shapes affect LCO in two off-setting ways: under-wing stores interfere with the airflow on the lower surface of the wing which decreases LCO amplitudes, whereas, aerodynamic forces on both under-wing and tip stores directly increase LCO amplitudes

Structural dynamics branch research and accomplishments to FY 1992

This publication contains a collection of fiscal year 1992 research highlights from the Structural Dynamics Branch at NASA LeRC. Highlights from the branch's major work areas--Aeroelasticity, Vibration Control, Dynamic Systems, and Computational Structural Methods are included in the report as well as a listing of the fiscal year 1992 branch publications

Forced response prediction for industrial gas turbine blades

A highly efficient aeromechanical forced response system is developed for predicting resonant forced vibration of turbomachinery blades with the capabilities of fully 3-D non-linear unsteady aerodynamics, 3-D finite element modal analysis and blade root friction modelling. The complete analysis is performed in the frequency domain using the non linear harmonic method, giving reliable predictions in a fast turnaround time. A robust CFD-FE mesh interface has been produced to cope with differences in mesh geometries, and high mode shape gradients. A new energy method is presented, offering an alternative to the modal equation, providing forced response solutions using arbitrary mode shape scales. The system is demonstrated with detailed a study of the NASA Rotor 67 aero engine fan rotor. Validation of the forced response system is carried out by comparing predicted resonant responses with test data for a 3-stage transonic Siemens industrial compressor. Two fully-coupled forced response methods were developed to simultaneously solve the flow and structural equations within the fluid solver. A novel closed-loop resonance tracking scheme was implemented to overcome the resonant frequency shift in the coupled solutions caused by an added mass effect. An investigation into flow-structure coupling effects shows that the decoupled method can accurately predict resonant vibration with a single solution at the blade natural frequency. Blade root-slot friction damping is predicted using a modal frequency-domain approach by applying linearised contact properties to a finite element model, deriving contact Droperties from an advanced semi-analytical microslip model. An assessment of Coulomb and microslip approaches shows that only the microslip model is suitable for predicting root friction damping

Aeroelastic Analysis of a Wind Turbine Blade Using the Harmonic Balance Method

Most current wind turbine aeroelastic codes rely on the blade element momentum method with empirical corrections to compute aerodynamic forces on the wind turbine blades. While efficient, this method relies on experimental data and does not allow designers much flexibility for alternative blade designs. Unsteady solutions to the Navier-Stokes equations offer a significant improvement in aerodynamic modeling, but these are currently too computationally expensive to be useful in a design situation. However, steady-state solutions to the Navier-Stokes equations are possible with reasonable computation times. The harmonic balance method provides a way to represent unsteady, periodic flows through coupled a set of steady-state solutions. This method offers the possibility of unsteady flow solutions at a computational cost on the order of a few steady-state solutions. By coupling a harmonic balance driven aerodynamic model with a mode shape-based structural dynamics model, an efficient aeroelastic model for a wind turbine blade driven by the Navier-Stokes equations is developed in this dissertation. For wind turbine flows, turbulence modeling is essential, especially in the transition of the boundary layer from laminar to turbulent. As part of this dissertation, the Spalart-Allmaras turbulence model and the gamma-Re\_theta-t transition model are included in the aerodynamic model. This marks the first time that this transition model, turbulence model, and the harmonic balance method have been coupled to study unsteady wind turbine aerodynamics. Results show that the transition model matches experimental data more closely than a fully turbulent model for the onset of both static and dynamic stall. Flutter is of particular interest as turbines continue to increase in size, and longer and softer blades continue to enter the field. In this dissertation, flutter is investigated for the 1.5 MW WindPACT rotor blade. The aeroelastic model created, which incorporates the harmonic balance method and a fully turbulent aerodynamic model, is the first of its kind for wind turbine flutter analysis. Predictions match those of other aeroelastic models for the 1.5 MW WindPACT blade, and the first flapwise and edgewise modes are shown to dominate flutter for the rotor speeds considered

Transonic Aeroelastic Numerical Simulation in Aeronautical Engineering

A lower-upper symmetric Gauss-Seidel (LU-SGS) subiteration scheme is constructed for time-marching of the fluid equations. The Harten-Lax-van Leer-Einfeldt-Wada (HLLEW) scheme is used for the spatial discretization. The same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Through subiteration between the fluid and structural equations, a fully implicit aeroelastic solver is obtained for the numerical simulation of fluid/structure interaction. To improve the ability for application to complex configurations, a multiblock grid is used for the flow field calculation and transfinite interpolation (TFI) is employed for the adaptive moving grid deformation. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between the fluid and structure. The developed code was first validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. Then, the flutter character of a tail wing with control surface was analyzed. Finally, flutter boundaries of a complex aircraft configuration were predicted

Shock Migration on an Oscillating Straked Delta Wing Using an Unsteady Euler Solver

This research contributes to the understanding of Shock Induced Trailing Edge Separation (SITES) as a driver of Limit Cycle Oscillation (LCO) by performing a computational investigation of nonlinear aerodynamic phenomena on a straked delta wing in transonic flow, oscillating in pitch. ZEUS, an Euler-based aeroelastic solver with a boundary layer coupling scheme meant to capture viscous flow effects within the boundary layer, was used to analyze aerodynamic flow around the wing for various mean incidence angles, oscillation amplitudes, and Mach numbers within the transonic region. The dynamic characteristics of the airflow around the wing were investigated in order to characterize shock movement

Three dimensional frequency-domain solution method for unsteady turbomachinery flows

The three-dimensional calculation of unsteady flows is increasingly gaining importance in the prediction of turbomachinery flow problems. A three-dimensional Euler/Navier-Stokes solver incorporating the time-linearized method and the nonlinear harmonic method in the frequency domain has been developed for predicting unsteady turbomachinery flows. In the time-linearized method, the flow is decomposed into a steady part and a harmonic perturbation part. Linearization results in a steady flow equation and a time-linearized perturbation equation. A pseudo-time time-marching technique is introduced to time-march them. A cell centred finite volume scheme is employed for spatial discretization and the time integration involves a four stage Runge Kutta scheme. Nonreflecting boundary conditions are applied for far field boundaries and a slip wall boundary condition is used for Navier-Stokes calculations. In the nonlinear harmonic method, the flow is assumed to be composed of a time-averaged part and an unsteady perturbation part. Due to the nonlinearity of the unsteady equations, time-averaging produces extra unsteady stress terms in the time-averaged equation which are evaluated from unsteady perturbations. While the unsteady perturbations are obtained from solving the harmonic perturbation equation, the coefficients of perturbation equations come from the solution of time-averaged equation and this interaction is achieved through a strong coupling procedure. In order to handle flows with strong nonlinearity, a cross coupling of higher order harmonics through a harmonic balancing technique is also employed. The numerical solution method is similar to that used in the time-linearized method. The numerical validation includes several test cases involving linear and nonlinear unsteady flows with specific attention to flows around oscillating blades. The results have been compared with other well developed linear methods, nonlinear time-marching method and experimental data. The nonlinear harmonic method is able to predict strong nonlinearities associated with shock oscillations well but some limitations have also been observed. A three-dimensional prediction of unsteady viscous flows through a linear compressor cascade with 3D blade oscillation, probably the first of its kind, has shown that unsteady flow calculation in the frequency domain is able to predict three-dimensional blade oscillations reasonably well

An Aerothermoelastic Analysis Framework Enhanced by Model Order Reduction With Applications

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143034/1/6.2017-1601.pd