Study of a family of supersonic inlet systems.
Large scale axisymmetric inlet systems performance capabilities, reviewing theoretical and experimental programs
Cubbison, R. W.↗
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Study of a family of supersonic inlet systems.
Large scale axisymmetric inlet systems performance capabilities, reviewing theoretical and experimental programs
Cubbison, R. W.↗
ADAM - An axisymmetric duct aeroacoustic modeling system
ADAM is an acronym for Axisymmetric Duct Aeroacoustic Modeling and is the name of an interconnected system of computer programs for integrated aerodynamic and acoustic analysis of aeroengine nacelles. The system consists of a streamtube curvature program for determination of the mean flow and a set of finite element codes for solution of the acoustic propagation problem. Use of the system is facilitated by interactive graphics for viewing aerodynamic and acoustic fields throughout their solution domains. This paper describes the capabilities and structure of the present system and discusses experience gained in the sample problems. Possible future enhancements to the system are also outlined.
Abrahamson, A. L.↗
Numerical experiments on the oscillations of a rotating, axisymmetric galaxy
Modes of oscillation in six rotating, axisymmetric N-body systems are studied in a sequence of self-consistent, three-dimensional numerical experiments. The experimental systems are realizations of theoretical models of galaxies which are stellar-dynamical counterparts of uniformly rotating polytropes of index equal to 0.5. The ratio of the rotational kinetic energy to the gravitational potential energy ranges from 0.13 to 0.20. The systems oscillate axisymmetrically; the oscillations are interpreted as superpositions of a mode of radial pulsation and a Kelvin-like mode of oscillation. The experimental frequencies of these modes agree very well with theoretical predictions. When these modes are suppressed, the states of the experimental systems are very steady. The systems are dynamically unstable with respect to a toroidal mode when the ratio of the rotational kinetic energy to the gravitational potential energy exceeds a value lying between 0.16 and 0.17.
Miller, R. H.↗
A generalized orthogonal coordinate system for describing families of axisymmetric and two-dimensional bodies
A generalized curvilinear orthogonal coordinate system is presented which can be used for approximating various axisymmetric and two-dimensional body shapes of interest to aerodynamicists. Such body shapes include spheres, ellipses, spherically capped cones, flat-faced cylinders with rounded corners, circular disks, and planetary probe vehicles. A set of transformation equations is also developed whereby a uniform velocity field approaching a body at any angle of attack can be resolved in the transformed coordinate system. The Navier-Stokes equations are written in terms of a generalized orthogonal coordinate system to show the resultant complexity of the governing equations.
Gnoffo, P. A.↗
On the nonlinear characteristics of the axisymmetric flow regime: Cylindrical and spherical systems
The physical relationship between steady axisymmetric flows that might be observed in the atmosphere and in laboratory vessels is investigated theoretically. This is accomplished by comparing both the nonlinear structure and the thermal forcing mechanisms in two truncated spectral models of flow in the atmosphere and the rotating laboratory cylinder, respectively. Under statically stable conditions, the response of the internally forced spherical model (which is developed here from a set of new orthonormal basis functions) exhibits steady behavior different from that in the externally forced cylindrical model. Two regions of multiple steady solutions occur in the cylindrical model, under stable conditions, that are not found in the spherical one. The possible physical relevance of these multiple solutions is investigated by determining their location in parameter space with respect to the classical Hadley-Rossby transition curve. The results suggest that the wave flow regime, in an annulus, might develop catastrophically when an upper symmetric flow ceases to exist.
Higgins, R. W.↗
Performance characteristics from Mach 2.58 to 1.98 of an axisymmetric mixed-compression inlet system with 60-percent internal contraction
Performance test from Mach 2.58 to 1.98 of axisymmetric mixed-compression inlet system with 60 percent internal contraction
Cubbison, R. W.↗
Performance summary of a two-dimensional and an axisymmetric supersonic-inlet system
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Sorensen, N. E.↗
ADAM: An Axisymmetric Duct Aeroacoustic Modeling system
An interconnected system of computer programs for analyzing the propagation and attenuation of sound in aeroengine ducts containing realistic compressible subsonic mean flows, ADAM was developed primarily for research directed towards the reduction of noise emitted from turbofan aircraft engines. The two basic components are a streamtube curvature program for determination of the mean flow, and a finite element code for solution of the acoustic propagation problem. The system, which has been specifically tailored for ease of use, is presently installed at NASA Langley Reseach Center on a Control Data Cyber 175 Computer under the NOS Operating system employing a Tektronix terminal for interactive graphics. The scope and organization of the ADAM system is described. A users guide, examples of input data, and results for selected cases are included.
Abrahamson, A. L.↗
Application of a numerical orthogonal coordinate generator to axisymmetric blunt bodies
An application of a simple numerical technique which allows for the rapid construction of orthogonal coordinate systems about axisymmetric blunt bodies is presented. This technique can generate orthogonal meshes which have unequally spaced points in two directions. Relations are given for the numerical generation of the metric coefficients. Body shapes ranging from simple analytical bodies to complex reverse curvature bodies are presented together with their orthogonal coordinate systems. The relatively good accuracy of the technique is shown in tabular data describing coordinate line slopes and metric coefficients. The predictor-corrector numerical method used to generate these results is both simple in concept and easy to program, so that the application of the technique should be broader than the results presented.
Graves, R. A., Jr.↗
Numerical experiments on the stability of disklike galaxies
It is noted that the stability properties of available galactic models are not consistent with presumptions based on observation and that axisymmetric disk systems with velocity dispersions like those of the Galaxy display major changes in form on a dynamical time scale. A report is given on a series of numerical experiments carried out as part of a systematic search for purely self-consistent disk galaxy models that might undergo little change over the time of several galactic rotations. The stability problem is reviewed, the method and calculations used are described, and initial conditions are outlined. The problem of estimating growth rates is discussed, and growth rates are evaluated for various disturbances. Experimental results are presented concerning growths of axisymmetric disturbances in 'cold' systems as well as disturbances with m = 1, 2, and 3. It is found that m = 2 disturbances are the most virulent and should dominate when all m values are allowed, but that the most rapidly growing disturbances are inhibited when several m values are allowed.
Miller, R. H.↗
Angular distribution of particle fluxes in rotating systems
Charged-particle pitch-angle distributions at one point on a magnetic drift surface in a rapidly rotating axisymmetric mirroring system (such as Jupiter's magnetosphere would be in the absence of the 10-deg dipole tilt) are related to those at another point by Liouville's theorem. If the distribution function in the rotating frame is gyrotropic; i.e., if it is independent of the phase angle of the gyration, it is gyrotropic at all points on that drift surface. Examples are given of 'pancake', 'dumbbell', and isotropic distributions when they are observed from the nonrotating frame at different points on a drift surface.
Northrop, T. G.↗
Application of a numerically generated orthogonal coordinate system to the solution of inviscid axisymmetric supersonic flow over blunt bodies
A numerically generated orthogonal coordinate system (with the body surface and shock wave as opposite boundaries) was applied with a time asymptotic method to obtain steady flow solutions for axisymmetric inviscid flow over several blunt bodies including spheres, paraboloids, ellipsoids, hyperboloids, hemisphere cylinders, spherically blunted cones, and a body with a concavity in the stagnation region. Comparisons with experimental data and with the results of other computational methods are discussed. The numerically generated orthogonal coordinate system is described and applications of the method to complex body shapes, particularly those with concave regions, are discussed.
Hamilton, H. H., II↗
On the three-dimensional shapes of elliptical galaxies
The paper considers the hypothesis that elliptical galaxies are oblate axisymmetric objects flattened by rotation. It was found that (1) rotation does not flatten axisymmetric elliptical galaxies appreciably and elliptical galaxy models can rotate rapidly and yet show little flattening, (2) several systems remained axisymmetric when the quantity t used as a measure of rotation was greater than 0.14, and (3) models with similar shapes can have quite different internal dynamics.
Miller, R. H.↗
Turbojet-exhaust-nozzle secondary-airflow pumping as an exit control of an inlet-stability bypass system for a Mach 2.5 axisymmetric mixed-compression inlet
The throat of a Mach 2.5 inlet that was attached to a turbojet engine was fitted with large, porous bleed areas to provide a stability bypass system that would allow a large, stable airflow range. Exhaust-nozzle, secondary-airflow pumping was used as the exit control for the stability bypass airflow. Propulsion system response and stability bypass performance were obtained for several transient airflow disturbances, both internal and external. Internal airflow disturbances included reductions in overboard bypass airflow, power lever angle, and primary-nozzle area, as well as compressor stall. Nozzle secondary pumping as a stability bypass exit control can provide the inlet with a large stability margin with no adverse effects on propulsion system performance.
Sanders, B. W.↗
Application of PML Absorbing Boundary Conditions to the Benchmark Problems of Computational Aeroacoustics
Accurate numerical non-reflecting boundary conditions are important in all the proposed benchmark problems of the Second Workshop. Recently, a new absorbing boundary condition has been developed using Perfectly Matched Layer (PML) equations for the Euler equations. In this approach, a region with a width of a few grid points is introduced adjacent to the non-reflecting boundaries. In the added region, Perfectly Matched Layer equations are constructed and applied so that the out-going waves are absorbed inside the layer with little reflection to the interior domain. It will be demonstrated in the present paper that the proposed absorbing boundary condition is quite general and versatile, applicable to radiation boundaries as well as inflow and outflow boundaries. It is also easy to implement. The emphasis of the paper will be on the application of the PML absorbing boundary condition to problems in Categories 1, 2, and 3. In Category 1, solutions of problems 1 and 2 are presented. Both problems are solved using a multi-domain polar grid system. Perfectly Matched Layer equations for a circular boundary are constructed and their effectiveness assessed. In Category 2, solutions of problem 2 are presented. Here, in addition to the radiation boundary conditions at the far field in the axisymmetric coordinate system, the inflow boundary condition at the duct inlet is also dealt with using the proposed Perfectly Match Layer equations. At the inlet, a PML domain is introduced in which the incident duct mode is simulated while the waves reflected from the open end of the duct are absorbed at the same time. In Category 3, solutions of all three problems are presented. Again, the PML absorbing boundary condition is used at the inflow boundary so that the incoming vorticity wave is simulated while the outgoing acoustic waves are absorbed with very little numerical reflection. All the problems are solved using central difference schemes for spatial discretizations and the optimized Low-Dissipation and Low-Dispersion Runge-Kutta scheme for the time integration. Issues of numerical accuracy and efficiency are also addressed.
Hu, Fang Q.↗
A Two-dimensional Cartesian and Axisymmetric Study of Combustion-acoustic Interaction
This paper describes a study of a lean premixed (LP) methane-air combustion wave in a two-dimensional Cartesian and axisymmetric coordinate system. Lean premixed combustors provide low emission and high efficiency; however, they are susceptible to combustion instabilities. The present study focuses on the behavior of the flame as it interacts with an external acoustic disturbance. It was found that the flame oscillations increase as the disturbance amplitude is increased. Furthermore, when the frequency of the disturbance is at resonance with a chamber frequency, the instabilities increase. For the axisymmetric geometry, the flame is found to be more unstable compared to the Cartesian case. In some cases, these instabilities were severe and led to flame extinction. In the axisymmetric case, several passive control devices were tested to assess their effectiveness. It is found that an acoustic cavity is better able at controlling the pressure fluctuations in the chamber.
Hood, Caroline↗
Buoyancy-driven flows of a radiatively participating fluid in a vertical cylinder heated from below
The effect of radiative energy transport on the onset and evolution of natural convective flows is studied in a Rayleigh-Benard system. Steady, axisymmetric flows of a radiatively participating fluid contained in a rigid-walled, vertical cylinder which is heated on the base, cooled on top, and insulated on the side wall are calculated by using the Galerkin FEM. Bifurcation analysis techniques are used to investigate the changes in the flow structure due to internal radiation. The results of this two-parameter study - where the Rayleigh number, Ra and optical thickness, tau, are varied - apply to fluids ranging from opaque to nearly transparent with respect to IR radiation. For any nonopaque fluid, internal radiation eliminates the static state that without radiation, exists for all values of the Rayleigh number. This heat transfer mechanism also destroys a symmetry of the system that relates clockwise and counterclockwise flows. The connectivity between characteristic flow families and the range of Ra where families are stable are found to depend greatly on tau. Results demonstrate the inadequacy of characterizing the behavior of this system using simple notions of radiative transfer in optically thick or thin media; the nonlinear interaction of radiation and flow are far more complicated than these asymptotic limits would imply.
Salinger, A. G.↗