On the use of higher-order finite-difference schemes on curvilinear and deforming meshes

Recent progress in flapping wing aerodynamics and aeroelasticity

https://ntrs.nasa.gov/api/citations/20010018414/downloads/20010018414.pdf

Reduced-order modeling: new approaches for computational physics

This work investigates the application of a high-order finite difference method for compressible large-eddy simulations on stretched, curvilinear and dynamic meshes. The solver utilizes 4th and 6th-order compact-differencing schemes for the spatial discretization, coupled with both explicit and implicit time-marching methods. Up to 10th order, Pade-type low-pass spatial filter operators are also incorporated to eliminate the spurious high-frequency modes which inevitably arise due to the lack of inherent dissipation in the spatial scheme. The solution procedure is evaluated for the case of decaying compressible isotropic turbulence and turbulent channel flow. The compact/filtering approach is found to be superior to standard second and fourth-order centered, as well as third-order upwind-biased approximations. For the case of isotropic turbulence, better results are obtained with the compact/filtering method (without an added subgrid-scale model) than with the constant-coefficient and dynamic Smagorinsky models. This is attributed to the fact that the SGS models, unlike the optimized low-pass filter, exert dissipation over a wide range of wave numbers including on some of the resolved scales

Large-Eddy Simulation on Curvilinear Grids Using Compact Differencing and Filtering Schemes

The flowflelds surrounding a synthetic-jet actuating device are investigated numerically by direct simulation. Solutions are obtained to the unsteady compressible Navier-Stokes equations for both the interior of the actuator cavity and for the external jet flowfield. The interior results are generated on an overset deforming zonal mesh system, whereas the jet flowfield is obtained by a high-order compact-difference scheme. Newton-like subiterations are employed to achieve second-order temporal accuracy. Details of the computations are summarized, and the quality of the results is assessed via grid resolution and time-step size studies. Several aspects of the actuator configuration are investigated, including cavity geometry and Reynolds number. Differences between two-dimensional and three-dimensional external unsteady flowfields are elucidated, and comparison is made with experimental data in terms of the mean and fluctuating components of the jet velocity

Numerical investigation of synthetic-jet flowfields

This paper presents computations of the flowfield around an 80° sweep delta wing undergoing a constant roll-rate manoeuver from 0° to 45°. The governing equations for the problem are the unsteady, three-dimensional Navier-Stokes equations. The equations are solved using the implicit, approximately-factored algorithm of Beam-Warming. Fixed roll angle results are also presented and compared with experimental measurements to demonstrate the ability of the numerical technique to accurately capture the flowfield around a rolled delta wing. The dynamical behavior of the vortex position and strength, as well as its corresponding effect on surface pressure, lift and roll moment are described. A simple, quasi-static explanation of this vortex behavior based on effective angle of attack and sideslip angle is proposed.

Numerical simulation of delta-wing roll

High fidelity computational simulation of a membrane wing airfoil

Development of a three-dimensional viscous aeroelastic solver for nonlinear panel flutter

: The present paper highlights results derived from the application of a high-fidelity simulation technique to the analysis of low-Reynolds-number transitional flows over moving and flexible canonical configurations motivated by small natural and man-made flyers. This effort addresses three separate fluid dynamic phenomena relevant to small fliers, including: laminar separation and transition over a stationary airfoil, transition effects on the dynamic stall vortex generated by a plunging airfoil, and the effect of flexibility on the flow structure above a membrane airfoil. The specific cases were also selected to permit comparison with available experimental measurements. First, the process of transition on a stationary SD7003 airfoil section over a range of Reynolds numbers and angles of attack is considered. Prior to stall, the flow exhibits a separated shear layer which rolls up into spanwise vortices. These vortices subsequently undergo spanwise instabilities, and ultimately breakdown into fine-scale turbulent structures as the boundary layer reattaches to the airfoil surface. In a time-averaged sense, the flow displays a closed laminar separation bubble which moves upstream and contracts in size with increasing angle of attack for a fixed Reynolds number. For a fixed angle of attack, as the Reynolds number decreases, the laminar separation bubble grows in vertical extent producing a significant increase in drag. For the lowest Reynolds number considered (Re(sub c) = 10(exp 4)), transition does not occur over the airfoil at moderate angles of attack prior to stall. Next, the impact of a prescribed high-frequency small-amplitude plunging motion on the transitional flow over the SD7003 airfoil is investigated. The motion-induced high angle of attack results in unsteady separation in the leading edge and in the formation of dynamic-stall-like vortices which convect downstream close to the airfoil.

High-Fidelity Simulations of Moving and Flexible Airfoils at Low Reynolds Numbers (Postprint)

The present paper highlights results derived from the application of a high-fidelity simulation technique to the analysis of low-Reynolds-number transitional flows over moving and flexible canonical configurations motivated by small natural and man-made flyers. This effort addresses three separate fluid dynamic phenomena relevant to small fliers, including: laminar separation and transition over a stationary airfoil, transition effects on the dynamic stall vortex generated by a plunging airfoil, and the effect of flexibility on the flow structure above a membrane airfoil. The specific cases were also selected to permit comparison with available experimental measurements. First, the process of transition on a stationary SD7003 airfoil section over a range of Reynolds numbers and angles of attack is considered. Prior to stall, the flow exhibits a separated shear layer which rolls up into spanwise vortices. These vortices subsequently undergo spanwise instabilities, and ultimately breakdown into fine-scale turbulent structures as the boundary layer reattaches to the airfoil surface. In a timeaveraged sense, the flow displays a closed laminar separation bubble which moves upstream and contracts in size with increasing angle of attack for a fixed Reynolds number. For a fixed angle of attack, as the Reynolds number decreases, the laminar separation bubble grows in vertical extent producing a significant increase in drag. For the lowest Reynolds number considered \((Re_c = 10^4)\), transition does not occur over the airfoil at moderate angles of attack prior to stall. Next, the impact of a prescribed high-frequency small-amplitude plunging motion on the transitional flow over the SD7003 airfoil is investigated. The motioninduced high angle of attack results in unsteady separation in the leading edge and in the formation of dynamic-stalllike vortices which convect downstream close to the airfoil. At the lowest value of Reynolds number \((Re_c = 10^4)\), transition effects are observed to be minor and the dynamic stall vortex system remains fairly coherent. For \(Re_c = 4 \times 10^4\), the dynamic-stall vortex system is laminar at is inception, however shortly afterwards, it experiences an abrupt breakdown associated with the onset of spanwise instability effects. The computed phased-averaged structures for both values of Reynolds number are found to be in good agreement with the experimental data. Finally, the effect of structural compliance on the unsteady flow past a membrane airfoil is investigated. The membrane deformation results in mean camber and large fluctuations which improve aerodynamic performance. Larger values of lift and a delay in stall are achieved relative to a rigid airfoil configuration. For \(Re_c = 4.85 \times 10^4\), it is shown that correct prediction of the transitional process is critical to capturing the proper membrane structural response.

Raymond E. Gordnier

Papers

Numerical simulation of delta-wing roll

High fidelity computational simulation of a membrane wing airfoil

Development of a three-dimensional viscous aeroelastic solver for nonlinear panel flutter

High-Fidelity Simulations of Moving and Flexible Airfoils at Low Reynolds Numbers (Postprint)

High-fidelity simulations of moving and flexible airfoils at low Reynolds numbers