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At least 361 records · Page 20

A solution to the Navier-Stokes equations based upon the Newton Kantorovich method

An implicit finite difference scheme based on the Newton-Kantorovich technique was developed for the numerical solution of the nonsteady, incompressible, two-dimensional Navier-Stokes equations in conservation-law form. The algorithm was second-order-time accurate, noniterative with regard to the nonlinear terms in the vorticity transport equation except at the earliest few time steps, and spatially factored. Numerical results were obtained with the technique for a circular cylinder at Reynolds number 15. Results indicate that the technique is in excellent agreement with other numerical techniques for all geometries and Reynolds numbers investigated, and indicates a potential for significant reduction in computation time over current iterative techniques.

Davis, J. E.↗

Numerical solution of the compressible Navier-Stokes equations using density gradients as additional dependent variables

Numerical solution of two dimensional, time dependent, compressible viscous Navier-Stokes equations about arbitrary bodies was treated using density gradients as additional dependent variables. Thus, six dependent variables were computed with the SOR iteration method. Besides formulation for pressure gradient terms, a formulation for computing the body density was presented. To approximate the governing equations, an implicit finite difference method was employed. In computing the solution for the flow about a circular cylinder, a problem arose near the wall at both stagnation points. Thus, computations with various conditions were tried to examine the problem. Also, computations with and without formulations are compared. The flow variables were computed on 37 by 40 field first, then on an 81 by 40 field.

Kwon, J. H.↗

Analysis of strong-interaction dynamic stall for laminar flow on airfoils

A compressible Navier-Stokes solution procedure is applied to the flow about an isolated airfoil. Two major problem areas were investigated. The first area is that of developing a coordinate system and an initial step in this direction has been taken. An airfoil coordinate system obtained from specification of discrete data points developed and the heat conduction equation has been solved in this system. Efforts required to allow the Navier-Stokes equations to be solved in this system are discussed. The second problem area is that of obtaining flow field solutions. Solutions for the flow about a circular cylinder and an isolated airfoil are presented. In the former case, the prediction is shown to be in good agreement with data.

Gibeling, H. J.↗

Numerical solution of the Navier-Stokes equations for blunt nosed bodies in supersonic flows

A time dependent, two dimensional Navier-Stokes code employing the method of body fitted coordinate technique was developed for supersonic flows past blunt bodies of arbitrary shapes. The bow shock ahead of the body is obtained as part of the solution, viz., by shock capturing. A first attempt at mesh refinement in the shock region was made by using the forcing function in the coordinate generating equations as a linear function of the density gradients. The technique displaces a few lines from the neighboring region into the shock region. Numerical calculations for Mach numbers 2 and 4.6 and Reynolds numbers from 320 to 10,000 were performed for a circular cylinder with and without a fairing. Results of Mach number 4.6 and Reynolds number 10,000 for an isothermal wall temperature of 556 K are presented in detail.

Warsi, Z. U. A.↗

Plasma research in electric propulsion at Colorado State University

The effect of electron bombardment ion thruster magnetic field configurations on the uniformity of the plasma density and the ion beam current density are discussed. The optimum configuration is a right circular cylinder which has significant fields at its outer radii and one end but is nearly field free within the cylinder and at the extraction grid end. The production and loss of the doubly charged ions which effect sputtering damage within thrusters are modeled and the model is verified for the mercury propellant case. Electron bombardment of singly charged ions is found to be the dominant double ion production mechanism. The low density plasma (approx. one million elec/cubic centimeter which exists in the region outside of the beam of thrust producing ions which are drawn from the discharge chamber is discussed. This plasma is modeled by assuming the ions contained in it are generated by a charge exchange process in the ion beam itself. The theoretical predictions of this model are shown to agree with experimental measurements.

Wilbur, P. J.↗

Boundary-layer separation on isolated boattail nozzles

An angle of attack of 0 deg was investigated in the Langley 16 foot transonic tunnel at free-stream Mach numbers from 0.40 to 0.95 to study the phenomenon of separated flow on a series of circular-arc afterbodies. Both high-pressure air and solid circular cylinders with the cylinder diameter equal to the nozzle-exit diameter were used to simulate jet exhausts. The results indicate that boundary-layer separation is most extensive on steep boattails at high Mach numbers. The jet total-pressure ratio changes (jet total pressure to free-stream static pressure) affected the extent of separation very little; however, comparison of the separation data obtained by using the two jet-simulation techniques indicate that entrainment associated with the presence of a jet had a significant effect on the extent of separation. The solid-simulator separation data were also used to evaluate the predictions of eight separation criteria.

Abeyounis, W. K.↗

Experimental studies on the effects of a sting support on the pressure distribution around a spherical object

Experiments were conducted on a spherical object, 2.5 inches in diameter, to obtain the pressure distribution around its meridan plane. In most of the tests the sphere was provided with a tail consisting of a circular cylinder that was attached directly to the rear with its axis in alignment with the center of the sphere. In some tests the tail was removed and the sphere alone was tested for comparison purposes. The main object of the tests was to obtain information on tail interference with the pressure distribution. The results of the tests show that the pressure distribution was affected by the presence of the tail to a minor extent only, while major differences occurred with the variation of the Reynolds number. The experiments were performed both in an open as well as inside a closed wind tunnel under steady flow conditions at Reynolds numbers ranging from 0.91 to 2.6 x 100000.

Barna, P. S.↗

Effects of turbulence on laminar separation on aerodynamic surfaces such as airfoils and compressor blading

Activities report include (1) completion of measurements of turbulence amplification in flow about a circular cylinder; (2) initiation of the measurements of turbulence characteristics in flow about a single symmetric airfoil; and, (3) further examination of various matching numerical methods. Emphasis is placed on the experimental program conducted to obtain data on the amplification of the oncoming turbulence and its management.

Sadeh, W. Z.↗

An experimental study of sound radiation from hyperboloidal inlet ducts

Sound radiation from hyperboloidal inlet ducts which include a circular cylinder with plane baffle as a limiting case was investigated. Results include the polar angle variation of the pressure level and the phase of the radiated field for various frequencies and various modes incident which were produced using an electronically operated mode synthesizer. Good agreement with a rigorous theoretical prediction was found.

Clark, L. R.↗

A simplified computer program for the prediction of the linear stability behavior of liquid propellant combustors

A program for predicting the linear stability of liquid propellant rocket engines is presented. The underlying model assumptions and analytical steps necessary for understanding the program and its input and output are also given. The rocket engine is modeled as a right circular cylinder with an injector with a concentrated combustion zone, a nozzle, finite mean flow, and an acoustic admittance, or the sensitive time lag theory. The resulting partial differential equations are combined into two governing integral equations by the use of the Green's function method. These equations are solved using a successive approximation technique for the small amplitude (linear) case. The computational method used as well as the various user options available are discussed. Finally, a flow diagram, sample input and output for a typical application and a complete program listing for program MODULE are presented.

Mitchell, C. E.↗

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↗

Use of piezoelectric multicomponent force measuring devices in fluid mechanics

The characterisitics of piezoelectric multicomponent transducers are discussed, giving attention to the advantages of quartz over other materials. The main advantage of piezoelectric devices in aerodynamic studies is their ability to indicate rapid changes in the values of physical parameters. Problems in the accuracy of measurments by piezoelectric devices can be overcome by suitable design approaches. A practical example is given of how such can be utilized to measure rapid fluctuations of fluid forces exerted on a circular cylinder mounted in a water channel.

Richter, A.↗

Light scattering properties of spheroidal particles

In the present paper, the light scattering characteristics of spheroidal particles are evaluated within the framework of a scattering theory developed for a homogeneous isotropic spheroid. This approach is shown to be well suited for computing the scattering quantities of spheroidal particles of fairly large sizes (up to a size parameter of 30). The effects of particle size, shape, index of refraction, and orientation on the scattering efficiency factors and the scattering intensity functions are studied and interpreted physically. It is shown that, in the case of oblique incidence, the scattering properties of a long slender prolate spheroid resemble those of an infinitely long circular cylinder.

Asano, S.↗

Sunspots and the physics of magnetic flux tubes. III - Aerodynamic lift

The aerodynamic lift exerted on a magnetic flux tube by the asymmetric flow around the two sides of the tube is calculated as part of an investigation of the physics of solar flux tubes. The general hydrodynamic forces on a rigid circular cylinder in a nonuniform flow of an ideal fluid are derived from the first derivatives of the velocity field. Aerodynamic lift in a radial nonuniform flow is found to act in the direction of the flow, toward the region of increased flow velocity, while in a shear flow, lift is perpendicular to the free stream and directed toward increasing flow velocity. For a general, three dimensional, large-scale stationary incompressible equilibrium flow, an expression is also derived relating the lift per unit length to the dynamical pressure, cylinder radius and the gradient of the free-stream velocity. Evidence from an asymmetric airfoil in a uniform flow indicates that lift is enhanced in a real fluid in the presence of turbulence.

Parker, E. N.↗

An investigation of transonic turbulent boundary layer separation generated on an axisymmetric flow model

Experimental data are presented describing the transonic turbulent separated flow generated by an axisymmetric flow model. The model consisted of a circular-arc bump affixed to a straight circular cylinder aligned with the flow direction. Measurements of the mean velocity, turbulence intensity, and Reynolds shear stress profiles were made in the separated flow. These data revealed the dramatic changes in the shear stress levels as the flow passed from the interaction through to reattachment. Information on the behavior of the turbulence reaction to the imposed pressure gradients, as presented in this investigation, will be required for the development of the turbulence models used in predicting nonequilibrium turbulent flow fields.

Bachalo, W. D.↗

Evaluation of approximate methods for the prediction of noise shielding by airframe components

An evaluation of some approximate methods for the prediction of shielding of monochromatic sound and broadband noise by aircraft components is reported. Anechoic-chamber measurements of the shielding of a point source by various simple geometric shapes were made and the measured values compared with those calculated by the superposition of asymptotic closed-form solutions for the shielding by a semi-infinite plane barrier. The shields used in the measurements consisted of rectangular plates, a circular cylinder, and a rectangular plate attached to the cylinder to simulate a wing-body combination. The normalized frequency, defined as a product of the acoustic wave number and either the plate width or cylinder diameter, ranged from 4.6 to 114. Microphone traverses in front of the rectangular plates and cylinders generally showed a series of diffraction bands that matched those predicted by the approximate methods, except for differences in the magnitudes of the attenuation minima which can be attributed to experimental inaccuracies. The shielding of wing-body combinations was predicted by modifications of the approximations used for rectangular and cylindrical shielding. Although the approximations failed to predict diffraction patterns in certain regions, they did predict the average level of wing-body shielding with an average deviation of less than 3 dB.

Ahtye, W. F.↗

Coherent substructure of turbulence near the stagnation zone of a bluff body

The evolution of freestream turbulence in crossflow about a circular cylinder was studied in order to identify the existence of a coherent substructure which is the outcome of the amplification of freesteam turbulence by the stretching mechanism in diverging flow about a bluff body. Visualization of the flow events revealed the selective stretching of cross-vortex tubes and the emergence of an organized turbulent flow pattern near the cylinder stagnation zone. Significant amplification of the total turbulent energy of the streamwise fluctuating velocity was consistently monitored. Realization of selective amplification at scales larger than the neutral scale of the stagnation flow was indicated by the variation of the discrete streamwise turbulent energy. A most amplified scale, characteristic of the energy containing eddies within the coherent substructure and commensurate with the boundary-layer thickness, was detected. Penetration of the amplified turbulence into the cylinder boundary layer led to the retardation of separation and to a concurrent decrease in the drag coefficient at subcritical cylinder-diameter Reynolds numbers.

Sadeh, W. Z.↗

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.↗