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At least 91 records · Page 5

Selection principles and pattern formation in fluid mechanics and nonlinear shell theory

Research accomplishments are summarized and publications generated under the contract are listed. The general purpose of the research was to investigate various symmetry breaking problems in fluid mechanics by the use of structure parameters and selection principles. Although all of the nonlinear problems studied involved systems of partial differential equations, many of these problems led to the study of a single nonlinear operator equation of the form F(w, lambda, gamma) = 0, (w is an element of H), (lambda is an element of R1), (gamma is an element of R1). Instead of varying only the load parameter lambda, as is often done in the study of such equations, one of the main ideas used was to vary the structure parameter gamma in such a way that stable solutions were obtained. In this way one determines detailed stability results by making use of the structure of the model equations and the known physical parameters of the problem. The approach was carried out successfully for Benard-type convection problems, Taylor-like problems for short cylinders, rotating Couette-Poiseuille channel flows, and plane Couette flows. The main focus of the research was on wave theory of vortex breakdown in a tube. A number of preliminary results for inviscid axisymmetric flows were obtained.

Sather, Duane P.↗

Flowmeter evaluation for on-orbit operations

Various flowmetering concepts were flow tested to characterize the relative capabilities and limitations for on-orbit fluid-transfer operations. Performance results and basic operating principles of each flowmetering concept tested are summarized, and basic considerations required to select the best flowmeter(s) for fluid system application are discussed. Concepts tested were clamp-on ultrasonic, area averaging ultrasonic, offset ultrasonic, coriolis mass, vortex shedding, universal venturi tube, turbine, bearingless turbine, turbine/turbine differential-pressure hybrid, dragbody, and dragbody/turbine hybrid flowmeters. Fluid system flowmeter selection considerations discussed are flowmeter performance, fluid operating conditions, systems operating environments, flowmeter packaging, flowmeter maintenance, and flowmeter technology. No one flowmetering concept tested was shown to be best for all on-orbit fluid systems.

Baird, R. S.↗

Simulation of a three-dimensional vortex breakdown

The breakdown of a vortex flow in a tube is studied for a slightly diverging tube by means of a numerical solution of the Navier-Stokes equations for a quasi-stationary, incompressible, laminar flow. Numerical results are compared to experiments of Faler and Leibovich. The numerical data display features similar to the experimental results concerning breakdown conditions, location, and structure.

Liu, C. H.↗

A numerical method for prediction of compressible turbulent flows with closure models

A new computer code to solve the time averaged Navier-Stokes equations is developed. Many of the state-of-the-art numerical techniques and algorithms have been tested and implemented in the program in order to achieve a better numerical accuracy and code efficiency. Various turbulence models are tested for a wide range of flows. The initial focus has been on two-equation eddy-viscosity models, which are the most advanced available in current compressible flow codes. The long term goal will be to test Reynolds-Stress models and to explore their performance in the high Mach number range. Although testing and improvement of turbulence models for supersonic and hypersonic flows is the primary objective of this research, part of the effort has been devoted to analyzing the vortex breakdown phenomena using new computer programs. Some preliminary results on the breakdown of a vortex flow in a tube are reported. Present calculations are restricted to two dimensional flow geometry.

Huang, P. G.↗

Swirling flows in streamtubes of variable cross section.

The behavior of vortex flow at high swirls is investigated. The problem was first formulated in the method of weighted residuals, using Bessel functions as approximating functions. Convergent solutions require a large number of steps in the axial direction and do not seem to offer an advantage over traditional methods. As the results do not differ substantially from those of the zeroth approximation (the solution for 'cylindrical' flow), this approximation is then explored and discussed in more detail. It is used to derive a relationship predicting a critical radius for which stagnation on the axis (vortex breakdown) can be expected for a given swirl. Flow patterns with open and closed vortex bubbles are explored. At high swirls, even minute variations in outer streamtube radius have profound effects on the flow. Vortex breakdown bubbles in divergences, tubes, and free flows can be explained.

Bossel, H. H.↗

Numerical study of transient flow phenomena in shock tunnels

Computational fluid dynamics (CFD) was used to study some transient flow features that can occur during the startup process of a shoch tunnel. The investigation concentrated on two areas: (1) the flow near the endwall of the driven tube during shock reflection and (2) the transient flow in the nozzle. The driven tube calculations were inviscid and focused on the study of a vortex system that was seen to form at the driven tube's axis of symmetry. The nozzle flow calculations examined viscous and inviscid effects during nozzle startup. The CFD solutions of the nozzle flows were compared with experimental data to demonstrate the effectiveness of the numerical analysis.

Tokarcik-Polsky, Susan↗

Three-dimensional Navier-Stokes calculations of multiple interacting vortex rings

Results from a finite-difference Navier-Stokes code for three-dimensional, unsteady, vortical flows in unbounded domains are presented and analyzed in this paper. The vortical flows presented are representative of vortex rings and other closed vortical tubes or structures in fluid mechanics. Such structures are important elements in fluid flows such as jets, atmospheric turbulence, and the far-field wakes of aircraft, and studies of their interaction may aid in an understanding of complex fluid flows. The paper demonstrates that computational methods can be used as a viable alternative or supplement to experimental techniques for studying the physics of vortex flows. The separate visualization of vortex stretching, convection, and diffusion is presented in this paper for a single elliptical vortex ring.The calculations employ a truncated series expansion technique to simulate the unbounded nature of the fluid flow with a finite computational domain, which is a more accurate technique than the conventional freestream boundary specification. The numerical divergence of the three-dimensional vorticity field is considered as a useful estimate of truncation error, and the use of a kinetic energy decay law as a calculation check is demonstrated. Results from the Navier-Stokes code are presented for the unsteady motion of two and four vortex rings along parallel axes, and the results agree qualitatively with experimental flow visualization.

Chamberlain, J. P.↗

Combination of Kinematics with Flow Visualization to Compute Total Circulation

A method is described in which kinematics is exploited to compute the total circulation of a vortex from relatively simple flow visualization experiments. There are several advantages in the technique, including the newly acquired ability to calculate the changes in strength of a single vortex as it evolves. The main concepts and methodology are discussed in a general way for application to vortices which carry along with them definable regions of essentially irrotational fluid; however, the approach might be generalized to other flows which contain regions of concentrated vorticity. As an illustrative example, an application to the study of the transient changes in total circulation of individual vortex rings as they travel up a tube is described, taking into account the effect of the tube boundary. The accuracy of the method, assessed in part by a direct comparison with a laser Doppler measurement is felt to be well within experimental precision for vortex rings over a wide range of Reynolds numbers.

Brasseur, J. G↗

Head-on parallel blade-vortex interaction

An experimental and computational study was carried out to investigate the parallel head-on blade-vortex interaction (BVI) and its noise generation mechanism. A shock tube, with an enlarged test section, was used to generate a compressible starting vortex which interacted with a target airfoil. The dual-pulsed holographic interferometry (DPHI) technique and airfoil surface pressure measurements were employed to obtain quantitative flow data during the BVI. A thin-layer Navier-Stokes code (BV12D), with a high-order upwind-biased scheme and a multizonal grid, was also used to simulate numerically the phenomena occurring in the head-on BVI. The detailed structure of a convecting vortex was studied through independent measurements of density and pressure distributions across the vortex center. Results indicate that, in a strong head-on BVI, the opposite pressure peaks are generated on both sides of the leading edge as the vortex approaches. Then, as soon as the vortex passes by the leading edge, the high-pressure peak suddenly moves toward the low-peak-reducing in magnitude as it moves--simultaneously giving rise to the initial sound wave. In both experiment and computation, it is shown that the viscous effect plays a significant role in head-on BVIs.

Lee, Soogab↗

Navier-Stokes calculations for unsteady three-dimensional vortical flows in unbounded domains

Finite-difference Navier-Stokes calculations for unsteady, three-dimensional, incompressible, viscous flows induced by initial vorticity distributions are presented and discussed in this paper. The initial vorticity distributions are assumed to be embedded in a flow field of infinite extent that is quiescent at infinity. These vorticity distributions are typical of vortex rings and other closed vortical tubes or structures. Such structures are important elements in fluid flows such as jets, atmospheric convection and the far-field wakes of aircraft; studies of their interaction may aid in an understanding of complex fluid flows. The calculations employ a method recently proposed by Ting to approximate the infinite-domain boundary value problem with a finite boundary computational domain, and this method is shown to yield accurate three-dimensional results for reasonable expenditures of computer time. Because of the efficiency of the boundary condition technique and the resulting Navier-Stokes code, a 16-bit minicomputer with virtual memory was capable of performing the calculations for the unsteady motion of two obliquely colliding vortex rings. The results of these calculations are presented in the paper.

Chamberlain, J. P.↗

An experimental and theoretical study of the flow phenomena within a vortex sink rate sensor

Tests were conducted to obtain a description of the flow field within a vortex sink rate sensor and to observe the influence of viscous effects on its performance. The characteristics of the sensor are described. The method for conducting the test is reported. It was determined that for a specific mass flow rate and the geometry of the vortex chamber, the flow in the vortex chamber was only affected, locally, by the size of the sink tube diameter. Within the sink tube, all three velocity components were found to be higher for the small sink tube diameters. As the speed of rotation of the sensor was increased, the tangential velocities within the vortex chamber, as well as in the sink tube, increased in proportion to the speed of rotation.

Goglia, G. L.↗

Rotor blade system with reduced blade-vortex interaction noise

A rotor blade system with reduced blade-vortex interaction noise includes a plurality of tube members embedded in proximity to a tip of each rotor blade. The inlets of the tube members are arrayed at the leading edge of the blade slightly above the chord plane, while the outlets are arrayed at the blade tip face. Such a design rapidly diffuses the vorticity contained within the concentrated tip vortex because of enhanced flow mixing in the inner core, which prevents the development of a laminar core region.

Leishman, John G.↗

An adaptive grid method for computing time accurate solutions on structured grids

The solution method consists of three parts: a grid movement scheme; an unsteady Euler equation solver; and a temporal coupling routine that links the dynamic grid to the Euler solver. The grid movement scheme is an algebraic method containing grid controls that generate a smooth grid that resolves the severe solution gradients and the sharp transitions in the solution gradients. The temporal coupling is performed with a grid prediction correction procedure that is simple to implement and provides a grid that does not lag the solution in time. The adaptive solution method is tested by computing the unsteady inviscid solutions for a one dimensional shock tube and a two dimensional shock vortex iteraction.

Bockelie, Michael J.↗

A numerical study of flow phenomena within a vortex sink rate sensor

A numerical investigation of a viscous incompressible fluid with constant properties within a vortex sink rate sensor is undertaken. A computer program was developed, for obtaining the numerical solution of the Navier-Stokes equations, assuming laminar flow, having general prescribed inlet conditions and axisymmetric boundary conditions. Computational results for various viscous flows and assorted boundary conditions have been obtained. In the vortex chamber, the radial momentum is conserved, whereas the axial momentum is negligible. In the sink region, the radial and tangential velocities, as well as the tangential vorticities, have significantly high values. In the sink tube, the radial momentum is negligible. The radial momentum within the vortex chamber is converted to the axial momentum in the sink tube. A change in the flow rate had an appreciable effect within the sensor and particularly near the sink tube entrance. As the flow rate was increased, both the tangential velocity and tangential vorticity increased rapidly. At the higher flow rates, vortices were produced at the corner of the entrance section of the sink tube.

Patel, D. K.↗

Partially ionized gas flow and heat transfer in the separation, reattachment, and redevelopment regions downstream of an abrupt circular channel expansion.

Heat transfer and pressure measurements obtained in the separation, reattachment, and redevelopment regions along a tube and nozzle located downstream of an abrupt channel expansion are presented for a very high enthalpy flow of argon. The ionization energy fraction extended up to 0.6 at the tube inlet just downstream of the arc heater. Reattachment resulted from the growth of an instability in the vortex sheet-like shear layer between the central jet that discharged into the tube and the reverse flow along the wall at the lower Reynolds numbers, as indicated by water flow visualization studies which were found to dynamically model the high-temperature gas flow. A reasonably good prediction of the heat transfer in the reattachment region where the highest heat transfer occurred and in the redevelopment region downstream can be made by using existing laminar boundary layer theory for a partially ionized gas. In the experiments as much as 90 per cent of the inlet energy was lost by heat transfer to the tube and the nozzle wall.

Back, L. H.↗

Vortices in spin-0 superfluids carry magnetic flux

Vortices in spin-0 superfluids generically carry magnetic fields inside their cores, so that even neutral superfluid vortices may be thought of as magnetic flux tubes. We give a systematic analysis of this ‘vortex magnetic effect’ using effective field theory, clarifying earlier literature on the subject. Furthermore, our analysis shows that in superfluid helium-4 the vortex magnetic effect may be large enough to be experimentally detectable.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Development and Breakdown of Goertler Vortices in High Speed Boundary Layers

The nonlinear development of G rtler instability over a concave surface gives rise to a highly distorted stationary flow in the boundary layer that has strong velocity gradients in both spanwise and wall-normal directions. This distorted flow is susceptible to strong, high frequency secondary instability that leads to the onset of transition. For high Mach number flows, the boundary layer is also subject to the second mode instability. The nonlinear development of G rtler vortices and the ensuing growth and breakdown of secondary instability, the G rtler vortex interactions with second mode instabilities as well as oblique second mode interactions are examined in the context of both internal and external hypersonic configurations using nonlinear parabolized stability equations, 2-D eigenvalue analysis and direct numerical simulation. For G rtler vortex development inside the Purdue Mach 6 Ludwieg tube wind tunnel, multiple families of unstable secondary eigenmodes are identified and their linear and nonlinear evolution is examined. The computation of secondary instability is continued past the onset of transition to elucidate the physical mechanisms underlying the laminar breakdown process. Nonlinear breakdown scenarios associated with transition over a Mach 6 compression cone configuration are also explored.

Li, Fei↗