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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Vortex methods for separated flows

The numerical solution of the Euler or Navier-Stokes equations by Lagrangian vortex methods is discussed. The mathematical background is presented in an elementary fashion and includes the relationship with traditional point-vortex studies, the convergence to smooth solutions of the Euler equations, and the essential differences between two- and three-dimensional cases. The difficulties in extending the method to viscous or compressible flows are explained. The overlap with the excellent review articles available is kept to a minimum and more emphasis is placed on the area of expertise, namely two-dimensional flows around bluff bodies. When solid walls are present, complete mathematical models are not available and a more heuristic attitude must be adopted. The imposition of inviscid and viscous boundary conditions without conformal mappings or image vortices and the creation of vorticity along solid walls are examined in detail. Methods for boundary-layer treatment and the question of the Kutta condition are discussed. Practical aspects and tips helpful in creating a method that really works are explained. The topics include the robustness of the method and the assessment of accuracy, vortex-core profiles, timemarching schemes, numerical dissipation, and efficient programming. Calculations of flows past streamlined or bluff bodies are used as examples when appropriate.

Spalart, Philippe R.↗
NASA NTRS2020

Evolution of an Atmospheric Kármán Vortex Street From High‐Resolution Satellite Winds: Guadalupe Island Case Study

Vortex streets formed in the stratocumulus‐capped wake of mountainous islands are the atmospheric analogues of the classic Kármán vortex street observed in laboratory flows past bluff bodies. The quantitative analysis of these mesoscale unsteady atmospheric flows has been hampered by the lack of satellite wind retrievals of sufficiently high spatial and temporal resolution. Taking advantage of the cutting‐edge Advanced Baseline Imager, we derived kilometer‐scale cloud‐motion winds at 5‐min frequency for a vortex street in the lee of Guadalupe Island imaged by Geostationary Operational Environmental Satellite‐16. Combined with Moderate Resolution Imaging Spectroradiometer data, the geostationary imagery also provided accurate stereo cloud‐top heights. The time series of geostationary winds, supplemented with snapshots of ocean surface winds from the Advanced Scatterometer, allowed us to capture the wake oscillations and measure vortex shedding dynamics. The retrievals revealed a markedly asymmetric vortex decay, with cyclonic eddies having larger peak vorticities than anticyclonic eddies at the same downstream location. Drawing on the vast knowledge accumulated about laboratory bluff body flows, we argue that the asymmetric island wake arises from the combined effects of Earth's rotation and Guadalupe's nonaxisymmetric shape resembling an inclined flat plate at low angle of attack. However, numerical simulations will need to establish whether or not the selective destabilization of the shallow atmospheric anticyclonic eddies is caused by the same mechanisms that destabilize the deep columnar anticyclones of laboratory flows, such as three‐dimensional vertical perturbations due to centrifugal or elliptical instabilities.

Horváth, Á.↗
NASA NTRS1981

Computation of separated flows by a vortex-tracing algorithm

Numerical solutions for two-dimensional, time-dependent, separated flows around bodies are obtained, using a new version of the vortex method. This method provides an efficient representation of flows involving large regions of separation. The modifications incorporated in the new version, which improve its accuracy, versatility, and computing speed, are described. The computer cost is only of the order of the 3/2 power on N, instead of N-squared, for each step with N vortices. Arbitrary shapes can be treated; a conformal mapping is not required. Special attention is paid to the viscous character of the solution and to the accurate computation of the pressure distribution at the body surface. The vortex solution for the outer flow is coupled to an inner solution for the attached part of the boundary layer. Numerical results are presented for several bluff bodies exhibiting dependence on Reynolds number, for stationary airfoils under steady or transient conditions and for oscillating airfoils, including dynamic stalls. These results are compared with other available results, analytical or experimental, and demonstrate the enhanced reliability and accuracy of the improved method.

Spalart, P. R.↗
NASA NTRS1995

Fast Multipole Methods for Three-Dimensional N-body Problems

We are developing computational tools for the simulations of three-dimensional flows past bodies undergoing arbitrary motions. High resolution viscous vortex methods have been developed that allow for extended simulations of two-dimensional configurations such as vortex generators. Our objective is to extend this methodology to three dimensions and develop a robust computational scheme for the simulation of such flows. A fundamental issue in the use of vortex methods is the ability of employing efficiently large numbers of computational elements to resolve the large range of scales that exist in complex flows. The traditional cost of the method scales as Omicron (N(sup 2)) as the N computational elements/particles induce velocities at each other, making the method unacceptable for simulations involving more than a few tens of thousands of particles. In the last decade fast methods have been developed that have operation counts of Omicron (N log N) or Omicron (N) (referred to as BH and GR respectively) depending on the details of the algorithm. These methods are based on the observation that the effect of a cluster of particles at a certain distance may be approximated by a finite series expansion. In order to exploit this observation we need to decompose the element population spatially into clusters of particles and build a hierarchy of clusters (a tree data structure) - smaller neighboring clusters combine to form a cluster of the next size up in the hierarchy and so on. This hierarchy of clusters allows one to determine efficiently when the approximation is valid. This algorithm is an N-body solver that appears in many fields of engineering and science. Some examples of its diverse use are in astrophysics, molecular dynamics, micro-magnetics, boundary element simulations of electromagnetic problems, and computer animation. More recently these N-body solvers have been implemented and applied in simulations involving vortex methods. Koumoutsakos and Leonard (1995) implemented the GR scheme in two dimensions for vector computer architectures allowing for simulations of bluff body flows using millions of particles. Winckelmans presented three-dimensional, viscous simulations of interacting vortex rings, using vortons and an implementation of a BH scheme for parallel computer architectures. Bhatt presented a vortex filament method to perform inviscid vortex ring interactions, with an alternative implementation of a BH scheme for a Connection Machine parallel computer architecture.

Koumoutsakos, P.↗
NASA NTRS1984

Body-turbulence interaction

The paper reviews the area of body-turbulence interaction with particular emphasis upon the influence of the body upon an incident turublent field. Cases considered include two-dimensional (high and low fineness ratio, porous, and impervious) and three-dimensional bodies in-stream, adjacent to, and attached to walls. Particular physics common to several geometric and incident flow configurations include (1) eddy severing at relatively sharp leading edges, (2) production of vorticity of the opposite sense on bluff bodies, and (3) body region production of control vortices which affect the incident turbulence field for the order of 100 boundary-layer thicknesses downstream. The major local effects of the body upon the incident turbulent field include (1) a blocking effect, (2) influence of the body momentum deficit/near wake, (3) distortion due to the body time-averaged flow field, and (4) unsteady body circulation. The review may be of particular interest for turbulence alteration/control using fixed geometry in applications such as drag reduction, separation control, noise reduction, and augmentor optimization.

Bushnell, D. M.↗
NASA NTRS2010

Triaxial Swirl Injector Element for Liquid-Fueled Engines

A triaxial injector is a single bi-propellant injection element located at the center of the injector body. The injector element consists of three nested, hydraulic swirl injectors. A small portion of the total fuel is injected through the central hydraulic injector, all of the oxidizer is injected through the middle concentric hydraulic swirl injector, and the balance of the fuel is injected through an outer concentric injection system. The configuration has been shown to provide good flame stabilization and the desired fuel-rich wall boundary condition. The injector design is well suited for preburner applications. Preburner injectors operate at extreme oxygen-to-fuel mass ratios, either very rich or very lean. The goal of a preburner is to create a uniform drive gas for the turbomachinery, while carefully controlling the temperature so as not to stress or damage turbine blades. The triaxial injector concept permits the lean propellant to be sandwiched between two layers of the rich propellant, while the hydraulic atomization characteristics of the swirl injectors promote interpropellant mixing and, ultimately, good combustion efficiency. This innovation is suited to a wide range of liquid oxidizer and liquid fuels, including hydrogen, methane, and kerosene. Prototype testing with the triaxial swirl injector demonstrated excellent injector and combustion chamber thermal compatibility and good combustion performance, both at levels far superior to a pintle injector. Initial testing with the prototype injector demonstrated over 96-percent combustion efficiency. The design showed excellent high -frequency combustion stability characteristics with oxygen and kerosene propellants. Unlike the more conventional pintle injector, there is not a large bluff body that must be cooled. The absence of a protruding center body enhances the thermal durability of the triaxial swirl injector. The hydraulic atomization characteristics of the innovation allow the design to be rapidly scaled from small in-space applications [500-5,000 lbf (2.2 22.2 kN)] to large thrust engine applications [80,000 lbf (356 kN) and beyond]. The triaxial injector is also less sensitive to eccentricities, manufacturing tolerances, and gap width of many traditional coaxial and pintle injector designs. The triaxial-injector injection orifice configuration provides for high injection stiffness. The low parts count and relatively large injector design features are amenable to low-cost production.

Muss, Jeff↗
NASA NTRS1976

A low speed self streamlining wind tunnel

A two dimensional test section in a low speed wind tunnel is producing flow conditions free from wall interference. The test section has flexible top and bottom walls, and rigid sidewalls from which the models are mounted spanning the tunnel. All walls are unperforated, and the flexible walls are positioned by screw jacks. To eliminate wall interference, the wind tunnel itself supplies the information required in this streamlining process, when run with the model present. Measurements taken at the flexible walls are used by the tunnel computer to check wall contours. When the static pressure distribution in the test section along a contoured flexible wall matches that computed for an imaginary flow field passing over the outside of the same contour, the wall is a streamline in an infinite flow field and the test section flow is free from wall interference. A series of iterations brings the walls from straight to streamlines. Illustrative aerodynamic data is presented, taken on a bluff body and a lifting wing.

Goodyer, M. J.↗
NASA NTRS1977

A field study of wind over a simulated block building

A full-scale field study of the wind over a simulated two-dimensional building is reported. The study develops an experiment to investigate the structure and magnitude of the wind fields. A description of the experimental arrangement, the type and expected accuracy of the data, and the range of the data are given. The data are expected to provide a fundamental understanding of mean wind and turbulence structure of the wind field around the bluff body. Preliminary analysis of the data demonstrates the reliability and completeness of the data in this regard.

Frost, W.↗
NASA NTRS1977

Sources of low-level wind shear around airports

Some potential sources of low-level wind shear in and around airports and their likely effects are probed and analyzed. Wind shear over flat terrain with near-homogeneous surface properties (roughness, specific heat), the turning layer, shear flows over inhomogeneous terrain (airport + urban areas), thunderstorms, turbulent flowfields over bluff bodies (individual buildings), and recirculating wake flow downstream of three-dimensional block bodies are among the topics covered. Overshoot or undershoot of runways, and induced moments (pitch, roll, yaw) in takeoff and landing, and other potential hazards traceable to wind shear patterns at low heights are discussed, with emphasis on mean flow or steady-state wind shear (time-averaged, say 2-min averaged, wind fields). Wind tunnel studies and V/STOL operations are included in the study.

Fichtl, G. H.↗
NASA NTRS1977

Vortices induced in a stagnation region by wakes - Their incipient formation and effects on heat transfer from cylinders

Horseshoe-like vortices, induced by wakes in the stagnation region of bluff bodies, are proposed as an efficient mechanism for augmentation of convective heat transfer. The vortex 'flow module' induced by single or multiple wakes, which had not been observed previously, was first documented and the resulting flow field was studied using various visualization techniques and hot-wire anemometry. In an attempt to understand the driving force behind this flow module, the conditions at which incipient formation of the vortices occurs were investigated. Existence of such a threshold is essential and was hitherto an open question in analytical studies of stability of flow in stagnation region. Finally, effects of the flow module on heat transfer from a cylinder were measured.

Nagib, H. M.↗
NASA NTRS1978

Some features of a wake tone flow field

An experimental investigation of a two-dimensional model of bluff body wake-surface interaction noise examines the changes in the flow field associated with changes in sound generated. Results show three distinct flow regimes separated by large differences in wake structure. In the first, with the surface in the near wake, discrete frequency sound is totally suppressed. At greater separation distances an amplified discrete frequency tone, a wake tone, is generated with the frequency a function of the separation distance. The final regime, with the surface in the far wake, is similar to a wake with no surface interaction.

Smith, C. A.↗
NASA NTRS1979

A study of viscous cross-flow effects on circular cylinders at high Reynolds numbers

Results of experimental studies on viscous cross-flow over circular cylinders for Reynolds numbers from 0.15 x 10 to the 6th to 10.9 x 10 to the 6th at Mach numbers of less than 0.3 are presented and compared with previous work where possible. Results presented include the variation of static cross-flow drag coefficients with both Reynolds number and ratio of surface roughness to model diameter, the variation of Strouhal number with Reynolds number and the dynamic variation of surface static pressure coefficients with both angular position around the cylinder and Reynolds number. The effects of end-plates on flow around two-dimensional bluff-bodies and of tunnel blockage on drag measurements are also discussed.

James, W. D.↗
NASA NTRS1980

A dry-surface coating method for visualization of separation

A relatively simple and reasonably accurate dry-surface coating method for visualization of the separation line on a bluff body was devised and successfully tested. This technique is based on the color reaction of a dry film containing a pH indicator with an appropriate gas released in the body wake. The dry-surface coating method is effective at any Reynolds number and for both incident laminar and turbulent flows. It further supplies a colorful permanent of consistently good photographic quality of the separation line. The effectiveness and accuracy of this technique were tested in visualizing the separation angle on a circular cylinder in both laminar and turbulent crossflows at subcritical Reynolds numbers. Separation angles revealed by the visualization were within + or - 4 percent of their counterparts deduced from the mean wall pressure distribution.

Sadeh, W. Z.↗
NASA NTRS1980

Forebody and base region real-gas flow in severe planetary entry by a factored implicit numerical method. I - Computational fluid dynamics

A new code for the simulation of full (forebody and base region) flowfields about bluff bodies in the hypersonic regime of severe planetary entry is described. The present 'maximally conservative, maximally differenced' formulation of the unsteady compressible Navier-Stokes equations for 2-D axisymmetric 3-D flow is contrasted for stability with previous formulations of Viviand, Kutler, et al, and Thomas and Lombard. Discrete metric relations peculiar to the axisymmetric finite volume formulation are presented along with a general discussion of their relations to and consequences of failure to close computational cells. A computational mesh of curvilinear coordinate topology singular in the flow regime is presented that permits aligned capturing of the major physical features of the complex flowfield.

Lombard, C. K.↗
NASA NTRS1980

A visual investigation of turbulence in stagnation flow about a circular cylinder

A diagnostic visualization study of turbulence in stagnation flow around a circular cylinder was carried out to gain physical insight into the coherent structure of turbulence in flow around a bluff body advanced by the vorticity-amplification theory. The visualization was conducted at a cylinder-diameter Reynolds number of 8000 utilizing titanium dioxide white smoke for an approaching flow containing turbulence at scales larger than the neutral wavelength of the stagnation flow. Analyses of the flow events focused on tracing out the temporal and spatial evolution of a cross-vortex tube outlined by the entrained smoke filaments from its emergence near the stagnation zone through its penetration into the cylinder boundary layer.

Sadeh, W. Z.↗
NASA NTRS1981

Numerical solutions of atmospheric flow over semielliptical simulated hills

Atmospheric motion over obstacles on plane surfaces to compute simulated wind fields over terrain features was studied. Semielliptical, two dimensional geometry and numerical simulation of flow over rectangular geometries is also discussed. The partial differential equations for the vorticity, stream function, turbulence kinetic energy, and turbulence length scale were solved by a finite difference technique. The mechanism of flow separation induced by a semiellipse is the same as flow over a gradually sloping surface for which the flow separation is caused by the interaction between the viscous force, the pressure force, and the turbulence level. For flow over bluff bodies, a downstream recirculation bubble is created which increases the aspect ratio and/or the turbulence level results in flow reattachment close behind the obstacle.

Shieh, C. F.↗