NO PLIF Study of Hypersonic Transition Over a Discrete Hemispherical Roughness Element

Nitric oxide (NO) planar laser-induced fluorescence (PLIF) has been use to investigate the hypersonic flow over a flat plate with and without a 2-mm (0.08-in) radius hemispherical trip. In the absence of the trip, for all angles of attack and two different Reynolds numbers, the flow was observed to be laminar and mostly steady. Boundary layer thicknesses based on the observed PLIF intensity were measured and compared with a CFD computation, showing agreement. The PLIF boundary layer thickness remained constant while the NO flowrate was varied by a factor of 3, indicating non-perturbative seeding of NO. With the hemispherical trip in place, the flow was observed to be laminar but unsteady at the shallowest angle of attack and lowest Reynolds number and appeared vigorously turbulent at the steepest angle of attack and highest Reynolds number. Laminar corkscrew-shaped vortices oriented in the streamwise direction were frequently observed to transition the flow to more turbulent structures

Hamiltonian flows on null curves

The local motion of a null curve in Minkowski 3-space induces an evolution equation for its Lorentz invariant curvature. Special motions are constructed whose induced evolution equations are the members of the KdV hierarchy. The null curves which move under the KdV flow without changing shape are proven to be the trajectories of a certain particle model on null curves described by a Lagrangian linear in the curvature. In addition, it is shown that the curvature of a null curve which evolves by similarities can be computed in terms of the solutions of the second Painlev\'e equation.Comment: 14 pages, v2: final version; minor changes in the expositio

Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations

We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence of isoperiodic deformations, at each step of which a real double point is "unpinched" to produce a new pair of branch points and therefore a solution of higher genus. We prove that every step in this process corresponds to a cabling operation on the previous curve, and we provide a labelling scheme that matches the deformation data with the knot type of the resulting filament.Comment: 33 pages, 5 figures; submitted to Journal of Nonlinear Scienc

A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow

Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time simulation of smoke. Here we introduce a time-discrete evolution equation for arbitrary closed polygons in 3-space that is a discretisation of the localised induction approximation of filament motion. This discretisation shares with its continuum limit the property that it is a completely integrable system. We apply this polygon evolution to a significant improvement of the numerical algorithms used in Computer Graphics.Comment: 15 pages, 3 figure

Ricci Solitons and Einstein-Scalar Field Theory

B List has recently studied a geometric flow whose fixed points correspond to static Ricci flat spacetimes. It is now known that this flow is in fact Ricci flow modulo pullback by a certain diffeomorphism. We use this observation to associate to each static Ricci flat spacetime a local Ricci soliton in one higher dimension. As well, solutions of Euclidean-signature Einstein gravity coupled to a free massless scalar field with nonzero cosmological constant are associated to shrinking or expanding Ricci solitons. We exhibit examples, including an explicit family of complete expanding solitons which can be thought of as a Ricci flow for a complete Lorentzian metric. The possible generalization to Ricci-flat stationary metrics leads us to consider an alternative to Ricci flow.Comment: 17 pages, 1 figure; Revised version (organizational changes, other minor revisions and corrections, citations corrected and added), to appear in CQ

Multiple Velocity Profile Measurements in Hypersonic Flows Using Sequentially-Imaged Fluorescence Tagging

Nitric-oxide planar laser-induced fluorescence (NO PLIF) was used to perform velocity measurements in hypersonic flows by generating multiple tagged lines which fluoresce as they convect downstream. For each laser pulse, a single interline, progressive scan intensified CCD (charge-coupled device) camera was used to obtain two sequential images of the NO molecules that had been tagged by the laser. The CCD configuration allowed for sub-microsecond acquisition of both images, resulting in sub-microsecond temporal resolution as well as sub-mm spatial resolution (0.5-mm horizontal, 0.7-mm vertical). Determination of axial velocity was made by application of a cross-correlation analysis of the horizontal shift of individual tagged lines. A numerical study of measured velocity error due to a uniform and linearly-varying collisional rate distribution was performed. Quantification of systematic errors, the contribution of gating/exposure duration errors, and the influence of collision rate on temporal uncertainty were made. Quantification of the spatial uncertainty depended upon the signal-to-noise ratio of the acquired profiles. This velocity measurement technique has been demonstrated for two hypersonic flow experiments: (1) a reaction control system (RCS) jet on an Orion Crew Exploration Vehicle (CEV) wind tunnel model and (2) a 10-degree half-angle wedge containing a 2-mm tall, 4-mm wide cylindrical boundary layer trip. The experiments were performed at the NASA Langley Research Center's 31-Inch Mach 10 Air Tunnel

High-Speed PLIF Imaging of Hypersonic Transition over Discrete Cylindrical Roughness

In two separate test entries, advanced laser-based instrumentation has been developed and applied to visualize the hypersonic flow over cylindrical protrusions on a flat plate. Upstream of these trips, trace quantities of nitric oxide (NO) were seeded into the boundary layer. The protuberances were sized to force laminar-to-turbulent boundary layer transition. In the first test, a 10-Hz nitric oxide planar laser-induced fluorescence (NO PLIF) flow visualization system was used to provide wide-field-of-view, high-resolution images of the flowfield. The images had sub-microsecond time resolution. However these images, obtained with a time separation of 0.1 sec, were uncorrelated with each other. Fluorescent oil-flow visualizations were also obtained during this test. In the second experiment, a laser and camera system capable of acquiring NO PLIF measurements at 1 million frames per second (1 MHz) was used. This system had lower spatial resolution, and a smaller field of view, but the images were time correlated so that the development of the flow structures could be observed in time

Classical and Quantum Integrability of 2D Dilaton Gravities in Euclidean space

Euclidean dilaton gravity in two dimensions is studied exploiting its representation as a complexified first order gravity model. All local classical solutions are obtained. A global discussion reveals that for a given model only a restricted class of topologies is consistent with the metric and the dilaton. A particular case of string motivated Liouville gravity is studied in detail. Path integral quantisation in generic Euclidean dilaton gravity is performed non-perturbatively by analogy to the Minkowskian case.Comment: 27 p., LaTeX, v2: included new refs. and a footnot

Evaluating Microcounseling Training

An evaluation research design was developed as an attempt to provide a more satisfactory approach to microcounseling training program evaluation. Trainee performance was measured three times during a counseling practicum, with microcounseling training occurring between the second and third observations. Trainee performance was compared to a predetermined standard for counselor behavior. Results were analyzed for both the differences between observations, and the degree of similarity to the model. Counseling behavior of trainees after microcounseling training was significantly different from their behavior prior to the training. After training they were more like the standard. The trainees performed less like the standard after some counseling experience, but before receiving microcounseling training.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66901/2/10.1177_0193841X8300700206.pd