Miguel R. Visbal

High-order-accurate methods for complex unsteady subsonic flows

Several issues related to the application of very high-order schemes for the finite difference simulation of the full Navier-Stokes equations are investigated. The schemes utilize an implicit, approximately factored time-integration method coupled with spatial fourth- and sixth-order compact-difference formulations and a filtering strategy of up to tenth order. For this last aspect a consistent optimization approach is developed to treat points near the boundary resulting in minimal degradation of accuracy. The problems investigated exhibit many of the challenging features of practical flows and include several with complications introduced by curvilinear meshes, viscous effects, unsteadiness, and three-dimensionality. The high-order method is observed to be very robust for every problem considered. The algorithm is demonstrated to be highly accurate compared to both second-order and upwind-biased methods. For several cases, particularly very-low-Mach-number flows, filtering is determined to be a superior alternative to scalar damping

Padé-type higher-order boundary filters for the Navier-Stokes equations

The use of procedures based on higher-order finite-difference formulas is extended to solve complex fluid-dynamic problems on highly curvilinear discretizations and with multidomain approaches. The accuracy limitations of previous near-boundary compact filter treatments are overcome by derivation of a superior higher-order approach. For solving the Navier-Stokes equations, this boundary component is coupled to interior difference and filter schemes with emphasis on Pade-type operators. The high-order difference and filter formulas are also combined with finite-sized overlaps to yield stable and accurate interface treatments for use with domain-decomposition strategies. Numerous steady and unsteady, viscous and inviscid flow computations on curvilinear meshes with explicit and implicit time-integration methods demonstrate the versatility of the new boundary schemes

Investigation of the flow structure around a rapidly pitching airfoil

A numerical study is presented for unsteady laminar flow past a NACA 0015 airfoil that is pitched, at a nominally constant rate, from zero incidence to a very high angle of attack. The flowfield simulation is obtained by solving the full two-dimensional compressible Navier-Stokes equations on a moving grid employing an implicit approximate-factorization algorithm. An evaluation of the accuracy of the computed solutions is presented, and the numerical results are shown to be of sufficient quality to merit physical interpretation. The highly unsteady flowfield structure is described and is found to be in qualitative agreement with available experimental observations. A discussion is provided for the effects of pitch rate and pitch axis location on the induced vortical structures and on the airfoil aerodynamic forces.

Large-Eddy Simulation of Supersonic Cavity Flowfields Including Flow Control

Large-eddy simulations of supersonic cavity flowfields are performed using a high-order numerical method. Spatial derivatives are represented by a fourth-order compact approximation that is used in conjunction with a sixth-order nondispersive filter. The scheme employs a time-implicit approximately factored finite difference algorithm, and applies Newton-like subiterations to achieve second-order temporal and fourth-order spatial accuracy. The Smagorinsky dynamic subgrid-scale model is incorporated in the simulations to account for the spatially underresolved stresses. Computations at a freestream Mach number of 1.19 are carried out for a rectangular cavity having a length-to-depth ratio of 5:1. The computational domain is described by 2.06×10 7 grid points and has been partitioned into 254 zones, which were distributed on individual processors of a massively parallel computing platform. Active flow control is applied through pulsed mass injection at a very high frequency, thereby suppressing resonant acoustic oscillatory modes

Accuracy and Coupling Issues of Aeroelastic Navier-Stokes Solutions on Deforming Meshes

An implicit time-accurate approach to aeroelastic simulation was developed with particular attention paid to the issues of time accuracy, structural coupling, grid-deformation strategy, and geometric conservation. A Beam ‐Warming, approximate-factored algorithm, modie ed to include Newton-like subiterations was coupled with a structural model, also in subiteration form. With a sufe cient number of subiterations, this approach becomes a fully implicit, e rst- or second-order-accurate aeroelastic solver. The solver was used to compute time-accurate solutions of an elastically mounted cylinder. The fully implicit coupling allowed the overall scheme to become second-order accurate in time, signie cantly reducing the workload for a given accuracy. A new algebraic grid deformation strategy was developed that preserves grid orthogonality near the surface under large deformations. Finally, the oscillatory behavior of an elastically mounted cylinder was reproduced accurately by the present approach, and results compared favorably to previous experiments and simulations.

High-Fidelity Simulation of Transitional Flows Past a Plunging Airfoil

This investigation addresses the simulation of the unsteady separated flows encountered by a plunging airfoil under low-Reynolds-number conditions (Rec 6 ◊ 10 4 ). The flow fields are computed employing a previously developed and extensively validated high-fidelity implicit large-eddy simulation (ILES) approach. In order to permit comparison with available experimental measurements, calculations are performed first for an SD7003 airfoil section at an angle of attack o = 4 plunging with reduced frequency k = 3.93 and nondimensional amplitude ho = 0.05. Under these conditions, it is demonstrated that for Rec = 10 4 , transitional effects are not significant and that the dynamic-stall vortices remain fairly coherent as they propagate along the airfoil. For Rec = 4 ◊ 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. A detailed description of this transition process near the leading edge is provided. The computed phased-averaged structures for both values of Reynolds number are found to be in good agreement with the experimental data. As a second example, the suppression of static stall at high angle of attack ( o = 14 ) is investigated using high-frequency small-amplitude vibrations (k = 10,ho = 0.005). At Rec = 6 ◊ 10 4 , separation is completely eliminated in a time-averaged sense, and the mean drag is reduced by approximately 40%. The instantaneous flow is characterized by the periodic generation of dynamic-stall vortices near the leading edge and by their subsequent transition as they convect close to the airfoil. For Rec = 10 4 , significant reduction of the timeaveraged separation region is still possible with transitional effects present in the aft-portion of the airfoil. For larger forcing amplitude (ho = 0.04,Rec = 10 4 ), a very intriguing regime emerges. The dynamic stall vortex moves around and in front of the leading edge and experiences a dramatic breakdown as it impinges against the airfoil. As a result, the phased-averaged flow displays no coherent vortices propagating along the airfoil upper surface. This new flow structure is also characterized in the mean by the existence of a strong jet in the near wake which manifests in a high value of net thrust. The present study demonstrates the importance of transitional effects for low-Reynolds-number maneuvering airfoils, as well as the suitability of the ILES approch for exploring such flow regime.

Control of Transitional and Turbulent Flows Using Plasma-Based Actuators

Abstract : An exploratory numerical study of the control of transitional and turbulent separated flows by means of asymmetric dielectric-barrier-discharge (DBD) actuators is presented. The flow fields are simulated employing an extensively validated high-fidelity Navier-Stokes solver which is augmented with both phenomenological and first-principles models representing the plasma-induced body forces imparted by the actuator on the fluid. Several applications are considered, including suppression of wing stall, control of boundary layer transition on a plate, control of laminar separation over a ramp, and turbulent separation over a wall-mounted hump. Effective suppression of stall over a NACA 0015 airfoil at moderate Reynolds numbers is demonstrated using either co-flow or counter-flow pulsed actuators with sufficiently high frequency. By contrast, continuous actuation (simulated by a steady body force in the phenomenological model) is found to provide little control of separation. For continuous actuator operation, the first-principles approach is needed in order to reproduce the benefits of the inherently unsteady force induced by the plasma actuator. The pulsed-modulated unsteady plasma force is found to be more effective than a monochromatic radio-frequency forcing. These results highlight the greater importance of transition and turbulence enhancement mechanisms rather than pure wall-jet momentum injection for the effective use of DBD devices. As a consequence, meaningful computations require the use of three-dimensional large-eddy simulation approaches capable of capturing the effects of unsteady forcing on the transitional/turbulent flow structure. For a laminar boundary layer developing along a flat plate, a counter-flow DBD actuator is shown to provide an effective on-demand tripping device.

Large-Eddy Simulation of Supersonic Compression-Ramp Flow by High-Order Method

A high-order method is used to perform large-eddy simulations of a supersonic compression-ramp flowfield. The procedure employs an implicit approximately factored finite difference algorithm, which is used in conjunction with a 10th-order nondispersive filter. Spatial derivatives are approximated by a sixth-order compact scheme, and Newton-like subiterations are applied to achieve second-order temporal accuracy. In the region of strong shock waves, the compact differencing of convective fluxes is replaced locally by an upwind-biased scheme. Both the Smagorinsky and dynamic subgrid-scale stress models are incorporated in the simulations. Details of the method are summarized, and a number of computations are carried out. Comparisons are made between the respective solutions as well as with available experimental data and with previous numerical results

Direct numerical simulations of flow past an array of distributed roughness elements

Direct numerical simulation was used to describe the subsonic flow past an array of distributed cylindrical roughness elements mounted on a flat plate. Solutions were obtained for element heights corresponding to a roughness-based Reynolds number (Re k ) of both 202 and 334. The numerical method used a sixth-order-accurate centered compact finite difference scheme to represent spatial derivatives, which was used in conjunction with a tenth-order low-pass Pade-type nondispersive filter operator to maintain stability. An implicit approximately factored time-marching algorithm was employed, and Newton-like subiterations were applied to achieve second-order temporal accuracy. Calculations were carried out on a massively parallel computing platform, using domain decomposition to distribute subzones on individual processors. A high-order overset grid approach preserved spatial accuracy on the mesh system used to represent the roughness elements. Features of the flowfields are described, and results of the computations are compared with experimentally measured velocity components of the time-mean flowfield, which are available only for Re k = 202. Flow about the elements is characterized by a system of two weak corotating horseshoe vortices. For Re k = 334, an unstable shear layer emanating from the top of the cylindrical element generated nonlinear unsteady disturbances of sufficient amplitude to produce explosive bypass transition downstream of the array. The Re k = 202 case displayed exponential growth of turbulence energy in the streamwise direction, which may eventually result in transition.

Structure of laminar juncture flows

A computational study of both steady and periodic laminar horseshoe vortex flows generated upstream of a cylinder/flat plate juncture is presented. The flowfields are simulated using the full three-dimensional unsteady Navier-Stokes equations and a time-accurate implicit algorithm. A new type of laminar horseshoe vortex topology is identified. For the case of a single primary vortex, this new topology is found to be independent of the computational grid and is also supported by recent experimental flow visualizations. The flat plate skin-friction portraits corresponding to the new and to the standard horseshoe vortex topologies are equivalent, pointing out the nonunique relation between the wall limiting streamline pattern and the three-dimensional flow above the plate. For the new topology, the foremost line of coalescense is an attachment rather than a separation line. This unusual feature illustrates the fact that convergence of skin-friction lines is a necessary but not sufficient condition for separation. As the Reynolds number increases, the flow topology evolves from a single to multiple primary horseshoe vortices, in agreement with experimental observations. At least two different types of triple horseshoe vortex systems are shown to be possible. Above a certain value of the Reynolds number, the juncture flow becomes unsteady and periodic at a frequency that increases with Reynolds number. The unsteady horseshoe vortex process upstream of the cylinder is found in qualitative agreement with experiment. Horseshoe vortices are periodically generated and convected toward the juncture. Vorticity intensification by vortex stretching, and the eruption of vorticity from the plate surface are observed.