Raymond E. Gordnier

Unsteady vortex structure over a delta wing

The structure of the shear layer which emanates from the leading edge of a 76-deg sweep delta wing and forms the primary vortex is investigated numerically. The flow conditions are Mv_ = 0.2, Re = 50,000 and angle of attack of 20.5 deg. Computational results are obtained using a Beam-Warming-t ype algorithm. The existence of a Kelvin-Helmholtz-type instability of the shear layer which emanates from the leading edge of the delta wing is demonstrated. A description is provided of the three-dimensional, unsteady behavior of the smallscale vortices associated with this instability. The numerical results are compared qualitatively with experimental flow visualizations exhibiting a similar behavior.

Transonic flutter simulations using an implicit aeroelastic solver

Flutter computations are presented for the AGARD 445.6 standard aeroelastic wing configuration using a fully implicit, aeroelastic Navier-Stokes solver coupled to a general, linear, second-order structural solver. This solution technique realizes implicit coupling between the fluids and structures using a subiteration approach. Results are presented for two Mach numbers, M∞ = 0.96 and 1.141. The computed flutter predictions are compared with experimental data and with previous Navier-Stokes computations for the same case. Predictions of the flutter point for the M∞ = 0.96 case agree well with experimental data. At the higher Mach number, M∞ = 1.141, the present computations overpredict the flutter point but are consistent with other computations for the same case. The sensitivity of computed solutions to grid resolution, the number of modes used in the structural solver, and transition location is investigated. A comparison of computations using a standard second-order accurate central-difference scheme and a third-order upwind-biased scheme is also made.

Compact Difference Scheme Applied to Simulation of Low-Sweep Delta Wing Flow.

Computational simulations are presented of the flow over a 50-deg sweep delta wing for angles of attack a = 5,10, and 15 deg. The full Navier-Stokes equations are solved using a sixth-order compact differencing scheme coupled with an eighth-order low-pass spatial filter to provide numerical stability

Numerical simulation of delta-wing roll

Abstract 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.

Computation of Limit-Cycle Oscillations of a Delta Wing

This paper presents computational simulations of limit cycle oscillations of a cropped delta wing. A newly developed aeroelastic solver which couples a well validated Navier-Stokes code with a nonlinear nite element method for the von Karman plate equations is employed. Previous computations using a linear structural modal solver to model the delta wing produced limit cycle oscillations with significantly larger amplitudes than the experimentally measured limit cycle response. The present computations with the nonlinear structural model produce limit cycle amplitudes commensurate with the experimental measurements. The computations presented in the paper demonstrate that the geometric nonlinearities in the structural model provide the proper nonlinear mechanism for the development of the limit cycle response observed in the experiments.

Numerical Simulation of the Impingement of a Streamwise Vortex on a Plate

Abstract The flow field generated by the impingement of a della-wing vortex on a plate is examined computationally. The flow is simulated by solving the unsteady, three-dimensional Navier-Slokes equations on an overset grid system using a time accurate, implicit Beam and Warming algorithm. Comparison of the computed solutions for two levels of mesh resolution indicates that no additional flow features appear with grid refinement. Both the mean and unsteady flow structures are examined. Over the delta wing the (low exhibits a spiral vortex breakdown induced by the plate. Underneath the plate a highly unsteady, large-scale (owl-type) stall region is formed and results in the shedding of hairpin-like vortical structures. On the top surface of the plate a shallow separation region also exists outboard of the vortex impingement location. These separated flow features result from the spanwise variation in effective angle of attack created by the incoming vortex system. Also present over the upper surface is a m...

Implicit LES Simulations of a Low Reynolds Number Flexible Membrane Wing Airfoil

This paper presents implicit LES simulations of a flexible membrane wing airfoil at a transitional/turbulent Reynolds number. The aerodynamics are simulated using a wellvalidated, sixth-order Navier-Stokes solver which is coupled with a one-dimensional finiteelement approach for the structural dynamic response of the membrane. The membrane airfoil geometry chosen corresponds to the experimental configuration of Rojratsirikul et al. 1 Computations on a coarse and refined mesh were performed to assess the impact of grid resolution on the computed solutions. A description of the unsteady fluid/structure interaction for angles of attack of = 8 and = 14 are presented indicating a close coupling between the unsteady flow behavior and the structural response. Initial comparisons of the computational results with available experimental data show good qualitative agreement. Issues with membrane structural modeling and the need for a more complete experimental characterization of the membrane structural properties are discussed. In order to address the technical challenges associated with successful MAV development, designers are looking to biological flight for inspiration. Successful development of these biomimetic MAV concepts will require significant advancements in the fundamental understanding of the unsteady aerodynamics of low Reynolds number fliers and the associated fluid-structure interactions. The inherent flexibility in the structural design of lightweight MAVs and the exploitation of that flexibility creates strong coupling between the unsteady fluid dynamics and the airframe structural response giving rise to tightly integrated, multidisciplinary physics. Conventional simplified analytical techniques and empirical design methods, although attractive for their eciency, may have limited applicability for these complicated, multidisciplinary design problems. Critical insight into the highly complex, coupled MAV physics calls for the exploitation of advanced multidisciplinary computational techniques. The focus of the present paper will be the simulation and analysis of aeroscience issues associated with a flexible membrane wing airfoil. The specific case to be considered corresponds to the experiments of Rojratsirikul, Wang and Gursul 1 where flow visualizations as well as PIV measurements have been carried out for a simple membrane wing. An implicit LES approach 2 is employed to compute the mixed laminar/transitional/turbulent flowfields present in the experiments of Rojratsirikul et al. The ILES approach exploits the properties of a well validated, robust, sixth-order Navier-Stokes solver. 3‐5 This aerodynamic solver is coupled with a one-dimensional finite element membrane structural model suitable for the highly nonlinear structural response associated with a flexible membrane airfoil. In a previous paper by Gordnier, 6 two-dimensional computations for very low Reynolds numbers (Re < 10 4 ) were performed for the same membrane wing configuration. The impact of various fluid and structural parameters including angle of attack, membrane elasticity, membrane pretension and Reynolds number were explored. The present work will extend these computations to the Reynolds number of the experiments of Rojratsirikul et al, Re = 48,500. At this Reynolds number the flow is transitional/turbulent and

Physical mechanisms for limit-cycle oscillations of a cropped delta wing

This paper presents simulations of limit-cycle oscillations of a cropped delta wing using a computational technique that implicitly couples a full Navier-Stokes solver to a linear structural solver. Computational results are compared with existing experimental measurements of the limit-cycle response of the delta wing. The limit-cycle oscillation is shown to consist primarily of a response of the first bending mode and the first torsional mode. Aerodynamic features of the limit cycle identified include a leading-edge vortex and a double shock structure. The leading edge vortex acts like an aerodynamic spring and provides the physical mechanism for the evolution of the limit cycle on the delta wing. Computations are repeated using the Euler equations to determine if the inviscid flow equations adequately simulate the observed limit cycle response.

Numerical Simulation of Limit-cycle Oscillations of a Cropped Delta Wing Using the Full Navier-Stokes Equations

This paper presents simulations of limit-cycle oscillations of a cropped delta wing using a computational technique that implicitly couples a full Navier-Stokes solver to a linear structural solver. Computational results are compared with existing experimental measurements of the limit-cycle response of the delta wing. The limit-cycle oscillation is shown to consist primarily of a response of the first bending mode and the first torsional mode. Aerodynamic features of the limit cycle identified include a leading-edge vortex and a double shock structure. The leading edge vortex acts like an aerodynamic spring and provides the physical mechanism for the evolution of the limit cycle on the delta wing. Computations are repeated using the Euler equations to determine if the inviscid flow equations adequately simulate the observed limit cycle response.

Implicit LES Simulations of a Flexible Flapping Wing

A high-order (up to 6th order) Navier-Stokes solver is coupled with a structural solver that decomposes the equations of three-dimensional elasticity into cross-sectional, smalldeformation and spanwise, large-deformation analyses for slender wings. The resulting high-fidelity aeroelastic solver is applied to the investigation of both a rigid and moderately flexible rectangular wing undergoing a pure plunging motion. Comparisons of the computed results demonstrate good agreement with available experimental measurements. A description of the complex interaction between the unsteady aerodynamics and the flexible wing structural dynamics is given. Connections between the results of this analysis and the enhanced aerodynamic loads for the flexible wing are made.