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NASA NTRS1991

The optical analogy for vector fields

This paper develops the optical analogy for a general vector field. The optical analogy allows the examination of certain aspects of a vector field that are not otherwise readily accessible. In particular, in the cases of a stationary Eulerian flow v of an ideal fluid and a magnetostatic field B, the vectors v and B have surface loci in common with their curls. The intrinsic discontinuities around local maxima in absolute values of v and B take the form of vortex sheets and current sheets, respectively, the former playing a fundamental role in the development of hydrodyamic turbulence and the latter playing a major role in heating the X-ray coronas of stars and galaxies.

Parker, E. N.↗

NASA NTRS1961

Annular Internal-External-Expansion Rocket Nozzles for Large Booster Applications

For large-thrust booster applications, annular rocket nozzles employing both internal and external expansion are investigated. In these nozzles, free-stream air flows through the center as well as around the outside of the exiting jet. Flaps for deflecting the rocket exhaust are incorporated on the external-expansion surface for thrust-vector control. In order to define nozzle off-design performance, thrust vectoring effectiveness, and external stream effects, an experimental investigation was conducted on two annular nozzles with area ratios of 15 and 25 at Mach 0, 2, and 3 in the Lewis 10- by 10-foot wind tunnel. Air, pressurized to 600 pounds per square inch absolute, was used to simulate the exhaust flow. For a nozzle-pressure-ratio range of 40 to 1000, the ratio of actual to ideal thrust was essentially constant at 0.98 for both nozzles. Compared with conventional convergent-divergent configurations on hypothetical boost missions, the performance gains of the annular nozzle could yield significant orbital payload increases (possibly 8 to 17 percent). A single flap on the external-expansion surface of the area-ratio-25 annular nozzle produced a side force equal to 4 percent of the axial force with no measurable loss in axial thrust.

Connors, James F.↗

NASA NTRS1985

Analysis of the inflow layer and air-sea interactions in Hurricane Frederic (1979)

The current study is attempting to overcome the problem of uncertain heights of the satellite winds. The effective heights of the satellite wind vectors were determined. Satellite, aircraft, rawinsonde and surface wind measurements were integrated into a three dimensional analysis of the storm in flow layer over water. Similar analyses of the thermodynamic field in the inflow layer were conducted. Diagnostic budget analyses of moisture, sensible heat kinetic energy and momentum in the inflow layer were conducted. Air-sea interactions were also examined.

Frank, W. M.↗

NASA NTRS1986

Measurement of leading edge vortices from a delta wing using a three component laser velocimeter

An investigation of the flow field above a 75-deg swept delta wing at a 20.5-deg angle of attack is described. The experiment was performed in the NASA Langley Basic Aerodynamic Research Tunnel (BART) using an orthogonal three-component laser velocimeter. Preliminary laser velocimeter results show velocity vectors in the cross flow plane at x/c = 0.5, revealing the formation of the primary and secondary vortices over the upper surface of the wing.

Meyers, James F.↗

NASA NTRS1996

Surface Tension Driven Convection Experiment (STDCE)

This document reports the results obtained from the Surface Tension Driven Convection Experiment (STDCE) conducted aboard the USML-1 Spacelab in 1992. The experiments used 10 cSt silicone oil placed in an open circular container that was 10 cm wide and 5 cm deep. Thermocapillary flow was induced by using either a cylindrical heater placed along the container centerline or by a CO2 laser. The tests were conducted under various power settings, laser beam diameters, and free surface shapes. Thermistors located at various positions in the test section recorded the temperature of the fluid, heater, walls, and air. An infrared imager was used to measure the free surface temperature. The flow field was studied by flow visualization and the data was analyzed by a PTV technique. The results from the flow visualization and the temperature measurements are compared with the numerical analysis that was conducted in conjunction with the experiment. The compared results include the experimental and numerical velocity vector plots, the streamline plots, the fluid temperature, and the surface temperature distribution.

Ostrach, S.↗

NASA NTRS1980

Performance improvement of delta wings at subsonic speeds due to vortex flaps

Subsonic wind tunnel tests were conducted to determine performance improvements possible from the use of leading edge vortex flaps (LEVF) on delta wings. Various flap sizes and deflection angles were examined and lift-to-drag ratio improvements of up to 40% were found at moderate angles of attack on 60 deg and 75 deg swept wings. The LEVF is concluded to be effective in moving the wing's leading edge vortex onto the flaps, tilting the vortex-induced force vector forward to produce a thrust or reduce the wing's drag while maintaining attached flow and lift on the wing's upper surface.

Marchman, J. F., III↗

NASA NTRS2015

The Prediction of Scattered Broadband Shock-Associated Noise

A mathematical model is developed for the prediction of scattered broadband shock-associated noise. Model arguments are dependent on the vector Green's function of the linearized Euler equations, steady Reynolds-averaged Navier-Stokes solutions, and the two-point cross-correlation of the equivalent source. The equivalent source is dependent on steady Reynolds-averaged Navier-Stokes solutions of the jet flow, that capture the nozzle geometry and airframe surface. Contours of the time-averaged streamwise velocity component and turbulent kinetic energy are examined with varying airframe position relative to the nozzle exit. Propagation effects are incorporated by approximating the vector Green's function of the linearized Euler equations. This approximation involves the use of ray theory and an assumption that broadband shock-associated noise is relatively unaffected by the refraction of the jet shear layer. A non-dimensional parameter is proposed that quantifies the changes of the broadband shock-associated noise source with varying jet operating condition and airframe position. Scattered broadband shock-associated noise possesses a second set of broadband lobes that are due to the effect of scattering. Presented predictions demonstrate relatively good agreement compared to a wide variety of measurements.

Miller, Steven A. E.↗

NASA NTRS1991

Analysis and representation of complex structures in separated flows

We discuss our recent work on extraction and visualization of topological information in separated fluid flow data sets. As with scene analysis, an abstract representation of a large data set can greatly facilitate the understanding of complex, high-level structures. When studying flow topology, such a representation can be produced by locating and characterizing critical points in the velocity field and generating the associated stream surfaces. In 3D flows, the surface topology serves as the starting point. The 2D tangential velocity field near the surface of the body is examined for critical points. The tangential velocity field is integrated out along the principal directions of certain classes of critical points to produce curves depicting the topology of the flow near the body. The points and curves are linked to form a skeleton representing the 2D vector field topology. This skeleton provides a basis for analyzing the 3D structures associated with the flow separation. The points along the separation curves in the skeleton are used to start tangent curve integrations. Integration origins are successively refined to produce stream surfaces. The map of the global topology is completed by generating those stream surfaces associated with 3D critical points.

Helman, James↗

NASA NTRS1994

The Determination of Forces and Moments on a Gimballed SRM Nozzle Using a Cold Flow Model

The Solid Rocket Motor Air Flow Facility (SAF) at NASA Marshall Space Flight Center was used to characterize the flow in the critical aft end and nozzle of a solid propellant rocket motor (SRM) as part of the design phase of development. The SAF is a high pressure, blowdown facility which supplies a controlled flow of air to a subscale model of the internal port and nozzle of a SRM to enable measurement and evaluation of the flow field and surface pressure distributions. The ASRM Aft Section/Nozzle Model is an 8 percent scale model of the 19 second burn time aft port geometry and nozzle of the Advanced Solid Rocket Motor, the now canceled new generation space Shuttle Booster. It has the capability to simulate fixed nozzle gimbal angles of 0, 4, and 8 degrees. The model was tested at full scale motor Reynolds Numbers with extensive surface pressure instrumentation to enable detailed mapping of the surface pressure distributions over the nozzle interior surface, the exterior surface of the nozzle nose and the surface of the simulated propellant grain in the aft motor port. A mathematical analysis and associated numerical procedure were developed to integrate the measured surface pressure distributions to determine the lateral and axial forces on the moveable section of the nozzle, the effective model thrust and the effective aerodynamic thrust vector (as opposed to the geometric nozzle gimbal angle). The nozzle lateral and axial aerodynamic loads and moments about the pivot point are required for design purposes and require complex, three dimensional flow analyses. The alignment of the thrust vector with the nozzle geometric centerline is also a design requirement requiring three dimensional analyses which were supported by this experimental program. The model was tested with all three gimbal angles at three pressure levels to determine Reynolds number effects and reproducibility. This program was successful in demonstrating that a measured surface pressure distribution could be integrated to determine the lateral and axial loads, moments and thrust vector alignment for the scaled model of a large space booster nozzle. Numerical results were provided which are scaleable to the full scale rocket motor and can be used as benchmark data for 3-D CFD analyses.

Whitesides, R. Harold↗

NASA NTRS2004

Transition from Pool to Flow Boiling: The Effect of Reduced Gravity

Applications of boiling heat transfer in space can be found in the areas of thermal management, fluid handling and control, power systems, on-orbit storage and supply systems for cryogenic propellants and life support fluids, and for cooling of electronic packages for power systems associated with various instrumentation and control systems. Recent interest in exploration of Mars and other planets, and the concepts of in-situ resource utiliLation on Mars highlights the need to understand the effect of gravity on boiling heat transfer at gravity levels varying from 1>= g/g(sub e) >=10(exp -6). The objective of the proposed work was to develop a mechanistic understanding of nucleate boiling and critical heat flux under low and micro-gravity conditions when the velocity of the imposed flow is small. For pool boiling, the effect of reduced gravity is to stretch both the length scale as well as the time scale for the boiling process. At high flow velocities, the inertia of the liquid determines the time and the length scales and as such the gravitational acceleration plays little role. However, at low velocities and at low gravity levels both liquid inertia and buoyancy are of equal importance. At present, we have little understanding of the interacting roles of gravity and liquid inertia on the nucleate boiling process. Little data that has been reported in the literature does not have much practical value in that it can not serve as a basis for design of heat exchange components to be used in space. Both experimental and complete numerical simulations of the low velocity, low-gravity nucleate boiling process were carried out. A building block type of approach was used in that first the growth and detachment process of a single bubble and flow and heat transfer associated with the sliding motion of the bubble over the heater surface after detachment was studied. Liquid subcooling and flow velocity were varied parametrically. The experiments were conducted at 1 g(sub e), while varying the orientation of surface with respect to the gravity vector. In the laboratory experiments, holographic interferometry was used to obtain data on velocity and temperature fields associated with a bubble prior to, and after detachment and during sliding motion. A test rig for conducting experiments in the KC-135 was developed, but experiments could not be conducted due to the unavailability of the aircraft prior to completion of the project. Numerical simulations modeling the micro and macro regions of the bubble were carried out in three dimensions. The results of the experiments were used to validate analytical/numerical models.

Dhir, Vijay K.↗

NASA NTRS1979

A viscous flow analysis of the tip vortex generation process

A viscous primary-secondary flow analysis designed for numerical solution by forward marching integration is applied to the tip vortex generation problem. Equations governing streamwise momentum, streamwise vorticity, and a gas law are solved in conjunction with equations governing scalar and vector surface potentials for the secondary velocities. The numerical method used combines a consistently split linearized block implicit (LBI) scheme for parabolic equations and a scalar iterative ADI scheme for elliptic equations. Computed results are presented for a wing of rectangular planform immersed in a high Reynolds number stream at 6 degrees incidence. The physical mechanism for generation of the tip vortex, as revealed by the analysis and computations, is discussed. Detailed flow results for the case of 6 degree incidence are included.

Shamroth, S. J.↗

NASA NTRS1983

An orthogonal coordinate grid following the three-dimensional viscous flow over a concave surface

Swept wings designed for laminar flow control exhibit both centrifugal and crossflow instabilities which produce streamwise vortices that can lead to early transition from laminar to turbulent flow in the presence of Tollmien-Schlichting waves. This paper outlines an iterative algorithm for generation of an orthogonal, curvilinear, coordinate grid following the streamlines of the three-dimensional viscous flow over a swept, concave surface. The governing equations for the metric tensor are derived from the Riemann-Christoffel tensor for an Euclidian geometry. Unit vectors along streamline, normal and binormal directions are determined. The governing equations are not solved directly, but are employed only as compatibility equations. The scale factor for the streamline coordinate is obtained by an iterative integration scheme on a 200 x 100 x 5 grid, while the other two scale factors are determined from definitions. Sample results are obtained which indicate that the compatibility equation error decreases linearly with grid step size. Grids smaller than 200 x 100 x 5 are found to be inadequate to resolve the grid curvature.

Dagenhart, J. R↗

NASA NTRS1979

Numerical solution of the Navier-Stokes equations for laminar, transonic flows

An implicit finite difference solution of the Navier-Stokes equations yielded time histories of the transonic laminar flow development about a circular cylinder and NACA-0018 airfoil. Reynolds numbers ranged from those corresponding to purely laminar flow to those corresponding to significant turbulence in the boundary layer. Body thermal conditions of an adiabatic wall and a specified body temperature were considered. Versatility in treating arbitrary bodies was incorporated by using numerically generated, body-fitted coordinate transformations. Solution of the simultaneous difference equations for the dependent variables was obtained using an accelerated Gauss-Seidel iterative scheme. Computational results are presented in the form of velocity vector fields, Mach number contours, aerodynamic coefficients, heat transfer rates at the body surface, and body temperature distributions. Truncation analyses of first and second derivative difference approximations resulted in general criteria for numerically generated coordinates so that flow near a body is more accurately represented.

Turner, L., III↗

NASA NTRS1995

Recent Developments in the Use of Liquid Crystal Coatings for Full-Surface Shear Stress Vector Measurements

Under normal white-light illumination and oblique observation, liquid crystal coating (LCC) color-change response to shear depends on both shear stress magnitude as well as the direction of the applied shear relative to the observer's line of sight. These color-change responses were quantified by subjecting a LCC to a wall-jet shear flow and measuring scattered-light spectra using a fiber optic probe and spectrophotometer. At any fixed shear stress magnitude, the maximum color change was measured when the shear vector was aligned with and directed away from the observer; changes in the relative in-plane view angle to either side of this vector/observer aligned position resulted in symmetric Gaussian reductions in measured color change. For this vector/observer aligned orientation, color change was found to scale linearly with increasing shear stress magnitude over an eight-fold range. Based on these results, a surface shear stress vector measurement methodology, involving multiple oblique-view observations of the test surface, was formulated. In the present paper, the experimental approach and data analysis procedure required to extend this vector measurement methodology to full-surface applications will be outlined and progress towards demonstrating this areal capability will be reviewed.

Reda, D. C.↗

NASA NTRS2013

ISSM: Ice Sheet System Model

In order to have the capability to use satellite data from its own missions to inform future sea-level rise projections, JPL needed a full-fledged ice-sheet/iceshelf flow model, capable of modeling the mass balance of Antarctica and Greenland into the near future. ISSM was developed with such a goal in mind, as a massively parallelized, multi-purpose finite-element framework dedicated to ice-sheet modeling. ISSM features unstructured meshes (Tria in 2D, and Penta in 3D) along with corresponding finite elements for both types of meshes. Each finite element can carry out diagnostic, prognostic, transient, thermal 3D, surface, and bed slope simulations. Anisotropic meshing enables adaptation of meshes to a certain metric, and the 2D Shelfy-Stream, 3D Blatter/Pattyn, and 3D Full-Stokes formulations capture the bulk of the ice-flow physics. These elements can be coupled together, based on the Arlequin method, so that on a large scale model such as Antarctica, each type of finite element is used in the most efficient manner. For each finite element referenced above, ISSM implements an adjoint. This adjoint can be used to carry out model inversions of unknown model parameters, typically ice rheology and basal drag at the ice/bedrock interface, using a metric such as the observed InSAR surface velocity. This data assimilation capability is crucial to allow spinning up of ice flow models using available satellite data. ISSM relies on the PETSc library for its vectors, matrices, and solvers. This allows ISSM to run efficiently on any parallel platform, whether shared or distrib- ISSM: Ice Sheet System Model NASA's Jet Propulsion Laboratory, Pasadena, California uted. It can run on the largest clusters, and is fully scalable. This allows ISSM to tackle models the size of continents. ISSM is embedded into MATLAB and Python, both open scientific platforms. This improves its outreach within the science community. It is entirely written in C/C++, which gives it flexibility in its design, and the power/speed that C/C++ allows. ISSM is svn (subversion) hosted, on a JPL repository, to facilitate its development and maintenance. ISSM can also model propagation of rifts using contact mechanics and mesh splitting, and can interface to the Dakota software. To carry out sensitivity analysis, mesh partitioning algorithms are available, based on the Scotch, Chaco, and Metis partitioners that ensure equal area mesh partitions can be done, which are then usable for sampling and local reliability methods.

Larour, Eric↗

NASA NTRS1981

A method for computation of inviscid three-dimensional flow over blunt bodies having large embedded subsonic regions

A computational technique for computing the three-dimensional inviscid flow over blunt bodies having large regions of embedded subsonic flow is detailed. Results, which were obtained using the CDC Cyber 203 vector processing computer, are presented for several analytic shapes with some comparison to experimental data. Finally, windward surface pressure computations over the first third of the Space Shuttle vehicle are compared with experimental data for angles of attack between 25 and 45 degrees.

Weilmuenster, K. J.↗

NASA NTRS1995

Study of compressible flow through a rectangular-to-semiannular transition duct

Detailed flow field measurements are presented for compressible flow through a diffusing rectangular-to-semiannular transition duct. Comparisons are made with published computational results for flow through the duct. Three-dimensional velocity vectors and total pressures were measured at the exit plane of the diffuser model. The inlet flow was also measured. These measurements are made using calibrated five-hole probes. Surface oil flow visualization and surface static pressure data were also taken. The study was conducted with an inlet Mach number of 0.786. The diffuser Reynolds based on the inlet centerline velocity and the exit diameter of the diffuser was 3,200,000. Comparison of the measured data with previously published computational results are made. Data demonstrating the ability of vortex generators to reduce flow separation and circumferential distortion is also presented.

Foster, Jeffry↗

NASA NTRS1985

The numerical simulation of steady transonic rotational flow using a dual potential formulation

A finite-difference method is presented that simulates steady transonic rotational flow of an inviscid fluid by representing the velocity field as the sum of scalar and vector potentials. This dual potential velocity decomposition extends the validity of the scalar (full) velocity potential to include vorticity. The inclusion of a vector potential also permits an alternate treatment of lift that does not require a circulation wake cut. This is accomplished by specifying the vector potential as a constant on the airfoil surface in order to satisfy a Kutta condition. The governing equations are solved as iteratively decoupled scalar equations using approximate factorization techniques, and the overall efficiency approaches that of the full potential equation. The governing equations are able to convect entropy and vorticity throughout the flow field and are equivalent to the Euler equations in continuous flow domains, however at shocks the Rankine-Hugoniot entropy jump must be supplied. An entropy correction method is presented and verified with transonic airfoil solutions of the Euler equations.

Chaderjian, N. M.↗