Her Mann Tsai

Calculation of Wing Flutter by a Coupled Fluid-Structure Method

An integrated computational fluid dynamics (CFD) and computational structural dynamics (CSD) method is developed for the simulation and prediction of flutter. The CFD solver is based on an unsteady, parallel, multiblock, multigrid finite volume algorithm for the Euler/Navier-Stokes equations. The CSD solver is based on the time integration of modal dynamic equations extracted from full finite element analysis. A general multiblock deformation grid method is used to generate dynamically moving grids for the unsteady flow solver. The solutions of the flowfield and the structural dynamics are coupled strongly in time by a fully implicit method. The coupled CFD-CSD method simulates the aeroelastic system directly on the time domain to determine the stability of the aeroelastic system. The unsteady solver with the moving grid algorithm is also used to calculate the harmonic and/or indicial responses of an aeroelastic system, in an uncoupled manner, without solving the structural equations. Flutter boundary is then determined by solving the flutter equation on the frequency domain with the indicial responses as input. Computations are performed for a two-dimensional wing aeroelastic model and the three-dimensional AGARD 445.6 wing. Flutter boundary predictions by both the coupled CFD-CSD method and the indicial method are presented and compared with experimental data for the AGARD 445.6 wing.

Unsteady Flow Calculations with a Parallel Multiblock Moving Mesh Algorithm

A novel parallel dynamic moving mesh algorithm designed for multiblock parallel unsteady flow calculations using body-fitted grids is presented. The moving grid algorithm within each block uses a method of arc-length-based transfinite interpolation, which is performed independently on local processors where the blocks reside. A spring network approach is used to determine the motion of the corner points of the blocks, which may be connected in an unstructured fashion in a general multiblock method. A smoothing operator is applied to the points of the block face boundaries and edges to maintain grid smoothness and grid angles. A multiblock parallel Euler/Navier-Stokes solver using multigrid and dual-time stepping is developed along with the moving mesh method. Computational results are presented for the unsteady flow calculations of airfoils and wings with deforming shapes as found in flutter simulations

A numerical study of transonic buffet on a supercritical airfoil

The flow of the BauerGarabedianKorn (BGK) No. 1 supercritical airfoil is investigated by the solution of the unsteady Reynolds-averagedNavierStokes equations with a two-equation lagged kωturbulent model.Two steady cases (M=0.71, α=1.396 deg and M=0.71, α=9.0 deg) and one unsteady case (M=0.71, α=6.97 deg), all with a far-stream Reynolds number of 20106, are computed. The results are compared with available experimental data. The computed shock motion and the evolution of the concomitant flow separation are examined. Space-time correlations of the unsteady pressure field are used to calculate the time for pressure waves to travel downstream within the separated region from the shock wave to the airfoil trailing edge and then back from the trailing edge to the shock outside the separated region. The reduced frequency so calculated agrees well with the computed buffet frequency, supporting the signal propagation mechanism for buffet proposed by Lee (Lee, B. H. K., Oscillation Shock Motion Caused by Transonic Shock Boundary-Layer Interaction, AIAA Journal, Vol. 28, No. 5, 1990, pp. 942944).

Numerical Investigation of Supersonic Nozzle Flow Separation

Separation of supersonic flow in a planar convergent–divergent nozzle with moderate expansion ratio is investigated by solving the Reynolds-averaged Navier–Stokes equations with a two-equation k-!turbulence model. The focus of the study is on the structure of the fluid and wave phenomena associated with the flow separation. Computations are conducted for an exit-to-throat area ratio of 1.5 and for a range of nozzle pressure ratios. The results are compared with available experimental data in a nozzle of the same geometry. The flow separates by the action of a lambda shock, followed by a succession of expansion and compression waves. For 1:5 < NPR < 2:4, the computation reveals the possibility of asymmetric flow structure. The computationally obtained asymmetric flow structuresareconsistentwithpreviousexperimental flowvisualizationsstudies.Inaddition,other flowfeaturessuch asshocklocationandwallpressuredistributionsarealsoingoodagreementwiththeexperimentaldata.Thepresent study provides new information that confirms earlier conjectures on the flow–wave structure relevant to the instability of the separated flow in convergent–divergent nozzles of moderate expansion ratio.

Swarm Algorithm for Single- and Multiobjective Airfoil Design Optimization

Shape optimization of airfoils involves highly expensive, nonlinear objective(s) and constraint functions often with functional and slope discontinuity that limits the efficient use of gradient-based methods for its solution. Gradient-based methods are not capable of generating a set of pareto solutions as required in multiobjective problems as they work with a single solution and improve it through successive iterations. Population-based, zero-order, stochastic optimization methods are therefore an attractive choice for shape optimization problems as they are easy to implement and effective for highly nonlinear problems. We present a swarm algorithm that is applicable for optimization problems in general, but is here explored for airfoil design optimization studies

Vortical structures in a laminar V-notched indeterminate-origin jet

A flow visualization investigation using dye-injection and laser-induced fluorescence techniques has been carried out to understand the vortex dynamics resulting from a V-notched indeterminate-origin jet with two peaks and two troughs. The laminar jet (Re=2000) was studied under forcing and nonforcing conditions to investigate the resultant dynamics of coherent large- and small-scale flow structures. Present experimental observations indicated that the effects of the nozzle peaks and troughs differ from those reported previously. Instead of the peaks producing streamwise vortex pairs which spread outwards into the ambient fluid and the troughs generating similar vortex pairs but entraining ambient fluid into the jet flows as indicated by earlier studies, the present experimental observations showed that both peaks and troughs produce outward-spreading streamwise vortex pairs. Laser cross sections further showed that the subsequent formation of azimuthal ring vortices causes these streamwise vortex pairs t...

Aerodynamic Design of Turbine Blades Using an Adjoint Equation Method

Aerodynamic design of turbine blades using an adjoint equation method is studied. Two design cases are tested. The first one is an inviscid design case for a VKI turbine stator, and the design objective is to minimize the entropy generation rate of the blade subject to a prescribed blade loading. The second case is a viscous design case for a standard configuration 4 turbine stator. The design objective is to minimize the entropy generation rate subject to a prescribed mass-averaged exit flow angle. The penalty function method is applied to deal with the constrained optimization problems. A resultant cost function is defined as a weighted sum of the original cost function and the deviation from the constraint. The formulations of the adjoint systems are derived for both cases based on the flow governing equations and the design objectives. Numerical programs are implemented to perform the optimization design. For the inviscid design case, the method is able to effectively reduce the entropy generation rate while the constraint is precisely satisfied. Reduction of shock wave strength is also observed. For the viscous design case, results using the Baldwin-Lomax turbulence model and results using laminar flow solutions are presented. The program is effective for both transonic and subsonic conditions, which means the method is able to deal with friction effects in addition to reducing shock wave strength.

Application of Three-Dimensional Interfaces for Data Transfer in Aeroelastic Computations

A framework of requirements for uid-structure interfaces is presented and applied to evaluate the qualities of various transfer methods. The Constant-Volume Tetrahedron approach is compared with an inverse Boundary Element Method, both of which are threedimensional techniques. Advantages of these three-dimensional interfaces over conventional planar interpolation methods (such as the innite-plate spline interpolation) are demonstrated and discussed. Comparisons are based on geometric considerations as well as on results from aeroelastic computations. For utter calculations, the three-dimensional Euler equations are solved by a nite-v olume method coupled with a nite-dierence method for the modal structural equations. The Constant-Volume Tetrahedron approach is more easily implemented as the inverse Boundary Element Method. However, the application of elastic equilibrium in case of the BEM is more physically meaningful than the arbitrary constraint of a constant elemental volume. A detailed comparison of both approaches in terms of implementation and applicability is provided.

Flutter Simulation and Prediction with CFD-based Reduced-Order Model

The paper presents an approach for the simulating and predicting utter of complex congurations. One of the major diculties in direct numerical simulation is the extensive computational time required. A hybrid approach combining CFD and reduced-order model (ROM) on the other hand takes advantage of the accuracy of CFD-based computations and the eciency of a ROM model. In this work, the CFD-based aeroelastic computations involve a Cartesian-based Euler solver with embedded multi-grid sequencing for o w computations, using the small perturbation techniques to implement the unsteady boundary conditions on the stationary grid. The structural response of the system is computed using the mode superposition technique. Data communication between the non-matching uid and structure domains is performed using the Constant Volume Tetrahedron (CVT) interpolation method. For a given set of igh t conditions, the CFD solver is rst performed to compute the o w solutions for a prescribed input that are needed to construct the reducedorder model of the system. The ROM results are compared with the CFD-solver results. The prediction of utter boundary for the AGARD 445.6 wing is presented.

Stability of Vortex Pairs over Slender Conical Bodies: Analysis and Numerical Computation

DOI: 10.2514/1.33498 Analytical studies and computational fluid dynamics simulations are presented to study the formation and stability of stationary symmetric and asymmetric vortex pairs over slender conical bodies in an inviscid incompressible flow at high angles of attack. The analytical method is based on an eigenvalue analysis on the motion of the vortices under small perturbations. A three-dimensional time-accurate Euler code is used to compute five typical flowsstudiedbythe analytical methodon extraordinarily finegrids withstrict convergence criteria. Both the theory and the computation show that the vortices over a delta wing are stable and those over a wing–body configuration at the low angle of attack are symmetric and stable, but become asymmetric and bistable at higher angles of attack; that is, the vortices shift to one of two stable mirror-imaged asymmetric configurations. The computational results agree well with the analytical predictions, demonstrating the existence of a global inviscid hydrodynamic instability mechanism responsible for the asymmetry of separation vortices over slender conical bodies.