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NASA NTRS1989

The evolution of cooling flows - Self-similar cooling waves

Similarity solutions are presented for the time-dependent evolution of cooling flows. A cooling flow expands when the cooling time computed from the initial gas distribution increases with radius. If certain simplifying conditions are met, the evolution of the resulting cooling wave becomes self-similar. The similarity solutions obtained here assumed subsonic flow, which is valid in the outer parts of observed cooling flows; they are matched to transonic accretion solutions valid in the central parts. The models are applied to the cooling flow onto M87, with unsatisfactory agreement at small radius. A local linear stability analysis shows that the similarity solution suffers isobaric thermal instability, suggesting that the neglect of star formation may be responsible for the poor agreement. The similarity solution suggests that the cooling flow around M87 was more vigorous in the past.

Bertschinger, Edmund↗

NASA NTRS1994

McIntosh active-region class similarities and suggestions for mergers

McIntosh active-region classifications reported during a five-year period were examined to determine similarities among the classes. Two methods were used extensively to determine these similarities. The number of transitions among classes were used to determine the most frequent transitions out of each class, and the alternative classes reported for the same region by different sites were used to establish which classes were neighboring classes. These transition frequencies and neighboring classes were used to identify classes that could be eliminated or merged with other classes. Class similarities were used to investigate the relative importance of several pairs of decisions that occur within a single McIntosh parameter. In particular, the redundancy of parameters in some classes was examined, and the class similarities were used to identify which of these parameters could be eliminated. Infrequently reported classes were also considered, and suggestions for mergers were made when similarities between classes could be identified.

Bornmann, P. L.↗

NASA NTRS1998

Self-Similar Compressible Free Vortices

Lie group methods are used to find both exact and numerical similarity solutions for compressible perturbations to all incompressible, two-dimensional, axisymmetric vortex reference flow. The reference flow vorticity satisfies an eigenvalue problem for which the solutions are a set of two-dimensional, self-similar, incompressible vortices. These solutions are augmented by deriving a conserved quantity for each eigenvalue, and identifying a Lie group which leaves the reference flow equations invariant. The partial differential equations governing the compressible perturbations to these reference flows are also invariant under the action of the same group. The similarity variables found with this group are used to determine the decay rates of the velocities and thermodynamic variables in the self-similar flows, and to reduce the governing partial differential equations to a set of ordinary differential equations. The ODE's are solved analytically and numerically for a Taylor vortex reference flow, and numerically for an Oseen vortex reference flow. The solutions are used to examine the dependencies of the temperature, density, entropy, dissipation and radial velocity on the Prandtl number. Also, experimental data on compressible free vortex flow are compared to the analytical results, the evolution of vortices from initial states which are not self-similar is discussed, and the energy transfer in a slightly-compressible vortex is considered.

vonEllenrieder, Karl↗

NASA NTRS1976

Similarity theory of the buoyantly interactive planetary boundary layer with entrainment

A similarity model is developed for the vertical profiles of turbulent flow variables in an entraining turbulent boundary layer of arbitrary buoyant stability. In the general formulation the vertical profiles, internal rotation of the velocity vector, discontinuities or jumps at a capping inversion and bulk aerodynamic coefficients of the boundary layer are given by solutions to a system of ordinary differential equations in the similarity variable. To close the system, a formulation for buoyantly interactive eddy diffusivity in the boundary layer is introduced which recovers Monin-Obukhov similarity near the surface and incorporates a hypothesis accounting for the observed variation of mixing length throughout the boundary layer. The model is tested in simplified versions which depend only on roughness, surface buoyancy, and Coriolis effects by comparison with planetary-boundary-layer wind- and temperature-profile observations, measurements of flat-plate boundary layers in a thermally stratified wind tunnel and observations of profiles of terms in the turbulent kinetic-energy budget of convective planetary boundary layers. On balance, the simplified model reproduced the trend of these various observations and experiments reasonably well, suggesting that the full similarity formulation be pursued further.

Hoffert, M. I.↗

NASA NTRS1979

Application of the principle of similarity fluid mechanics

Possible applications of the principle of similarity to fluid mechanics is described and illustrated. In correlating thermophysical properties of fluids, the similarity principle transcends the traditional corresponding states principle. In fluid mechanics the similarity principle is useful in correlating flow processes that can be modeled adequately with one independent variable (i.e., one-dimensional flows). In this paper we explore the concept of transforming the conservation equations by combining similarity principles for thermophysical properties with those for fluid flow. We illustrate the usefulness of the procedure by applying such a transformation to calculate two phase critical mass flow through a nozzle.

Hendricks, R. C.↗

NASA NTRS1984

Eigenvalue similarity rules for symmetric cross-ply laminated plates

Symmetric cross-ply laminated plates are analyzed by employing a previously presented affine stretching process, some material constant definitions from Tsai (1964), and by gneralizing existing similarity rules. As examples, similarity rules are employed to find the frequency spectrum of a cross-ply symmetric plate from the corresponding isotropic solution, and a similarity solution is presented for the vibration of an axially loaded, simply supported cross-ply symmetric plate. Buckling similarity rules are also presented.

Brunelle, E. J.↗

NASA NTRS1987

Engineering analysis of slender-body aerodynamics using Sychev similarity parameters

The similarity parameters deduced by Sychev for inviscid hypersonic flow over slender bodies are reviewed and used to correlate flowfield, surface-pressure, normal-force and center-of-pressure data for supersonic flow over thin slender wings and smooth slender bodies at low-to-high angles of attack. Although Sychev expected similarity to hold only for hypersonic freestream and cross flows, it is demonstrated empirically that similarity holds for any value of cross-flow Mach number if the axial flow component is supersonic. It is also shown for thin wings that similarity holds for much larger values of aspect ratio than Sychev supposed. A one-term power-law expression is found to fit all of the normal-force correlations which suggests that it may be possible to develop a simple semi-empirical method for estimating the aerodynamic characteristics of arbitrary slender airframes.

Hemsch, Michael J.↗

NASA NTRS1987

Similarity networks as a knowledge representation for space applications

Similarity networks are a powerful form of knowledge representation that are useful for many artificial intelligence applications. Similarity networks are used in applications ranging from information analysis and case based reasoning to machine learning and linking symbolic to neural processing. Strengths of similarity networks include simple construction, intuitive object storage, and flexible retrieval techniques that facilitate inferencing. Therefore, similarity networks provide great potential for space applications.

Bailey, David↗

NASA NTRS1987

On self-similarity of crack layer

The crack layer (CL) theory of Chudnovsky (1986), based on principles of thermodynamics of irreversible processes, employs a crucial hypothesis of self-similarity. The self-similarity hypothesis states that the value of the damage density at a point x of the active zone at a time t coincides with that at the corresponding point in the initial (t = 0) configuration of the active zone, the correspondence being given by a time-dependent affine transformation of the space variables. In this paper, the implications of the self-similarity hypothesis for qusi-static CL propagation is investigated using polystyrene as a model material and examining the evolution of damage distribution along the trailing edge which is approximated by a straight segment perpendicular to the crack path. The results support the self-similarity hypothesis adopted by the CL theory.

Botsis, J.↗

NASA NTRS1988

Isothermal magnetostatic atmospheres. II - Similarity solutions with current proportional to the magnetic potential cubed

The paper presents a family of isothermal magnetostatic atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model J is directed along the x-axis, where x is the horizontal ignorable coordinate. The current J is taken to be proportional to the cube of the magnetostatic potential A and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. A range of similarity solution examples are displayed depending on the values of the similarity parameters. Each similarity parameter corresponds to a symmetry of the underlying nonlinear elliptic equation for A. The similarity parameters also determine the source currents for the potential field solution of the family. The solutions show the interplay between the gravitational force, the J & B force (B, magnetic field induction) and the gas pressure gradient.

Webb, G. M.↗

NASA NTRS1992

Self-similar evolution of magnetized plasmas. I - Quasi-static solution

The concept of linear expansion suggested by Wei-Hong (1989 and 1990), describes the self-similar evolution of a magnetic structure. Linear expansion can be represented by a single function which connects the evolving physical parameters of the plasma with their initial values in explicit forms. A general self-similar dynamic equation, therefore, is derived. As the first step toward more general consideration, the quasi-static solution is investigated in this paper. It is shown that a gamma = 4/3 polytrope may evolve through consecutive equilibria if its magnetic field expands self-similarly. The change of the energy everywhere inside the plasma equals the work done by the internal plasma pressure and magnetic field for the expansion. For the special case of an expanding force-free magnetic field, the self-similar expansion is a clean expansion. No free magnetic energy is left anywhere inside the magnetic structure. The approximation in quasi-state modeling of a pressure confined magnetized plasmoid is analyzed.

Yang, Wei-Hong↗

NASA NTRS1950

An Analysis of the Applicability of the Hypersonic Similarity Law to the Study of Flow About Bodies of Revolution at Zero Angle of Attack

The hypersonic similarity law as derived by Tsien has been investigated by comparing the pressure distributions along bodies of revolution at zero angle of attack. In making these comparisons, particular attention was given to determining the limits of Mach number and fineness ratio for which the similarity law applies. For the purpose of this investigation, pressure distributions determined by the method of characteristics for ogive cylinders for values of Mach numbers and fineness ratios varying from 1.5 to 12 were compared. Pressures on various cones and on cone cylinders were also compared in this study. The pressure distributions presented demonstrate that the hypersonic similarity law is applicable over a wider range of values of Mach numbers and fineness ratios than might be expected from the assumptions made in the derivation. This is significant since within the range of applicability of the law a single pressure distribution exists for all similarly shaped bodies for which the ratio of free-stream Mach number to fineness ratio is constant. Charts are presented for rapid determination of pressure distributions over ogive cylinders for any combination of Mach number and fineness ratio within defined limits.

PRESSURE DISTRIBUTION - BODIES OF REVOLUTION↗

NASA NTRS2019

Fermi-GBM GRBs with Characteristics Similar to GRB 170817A

We present a search for gamma-ray bursts in the Fermi-GBM (Gamma Burst Monitor) 10-year catalog that show similar characteristics to GRB170817A, the first electromagnetic counterpart to a GRB (Gamma-Ray Burst) identified as a binary neutron star (BNS) merger via gravitational wave observations. Our search is focused on a nonthermal pulse, followed by a thermal component,as observed for GRB 170817A. We employ search methods based on the measured catalog parameters and Bayesian Block analysis. Our multipronged approach, which includes examination of the localization and spectral properties of the thermal component, yields a total of 13 candidates, including GRB170817A and the previously reported similar burst, GRB 150101B. The similarity of the candidates is likely caused by the same processes that shaped the gamma-ray signal of GRB170817A, thus providing evidence of a nearby sample of short GRBs resulting from BNS merger events. Some of the newly identified counterparts were observed by other space telescopes and ground observatories, but none of them have a measured redshift. We present an analysis of this subsample, and we discuss two models. From uncovering 13 candidates during a time period of 10 years we predict that Fermi-GBM will trigger on-board on about one burst similar to GRB170817A per year.

von Kienlin, A.↗

NASA NTRSDate not supplied

Evaluation of Preliminary Buffet Forcing Function Development based on Wind-Tunnel Tests of Geometrically-similar Models

The current state-of-the-art for launch vehicle buffet load estimation involves wind tunnel testing of highly instrumented rigid models and data processing of experimental unsteady pressure measurements to estimate the fluctuating aerodynamic loads. The model and instrumentation requirements to accomplish this type of testing are significant. The rigid model, in particular, must be built with relatively high geometric fidelity to approximate similar aerodynamic phenomena that will occur during the full-scale vehicle flight. Due to this requirement, several iterative wind tunnel tests are often required during the design maturation of the vehicle. For preliminary buffet load estimation, however, data from previous launch vehicle wind tunnel tests of geometrically similar models can be used to provide initial buffet environment estimates before a high geometric fidelity wind tunnel test has been conducted. In this paper, two components of this preliminary buffet estimation process are described: (1) assembly of buffet forcing functions from multiple data sources and (2) scaling of these buffet forcing functions to geometrically-similar components of a target vehicle configuration. The impacts of these estimation methods on the full-vehicle buffet forcing functions, including their longitudinal distribution along the vehicle, frequency-content at individual stations, and station-to-station coherence, are investigated. Considerations for using these methods to extrapolate wind tunnel data to geometrically similar models are also discussed.

Patrick S Heaney↗

NASA NTRSDate not supplied

Principles of Fluid Dynamic Similarity Analysis for Slosh Experiments

Most tank slosh test programs are not conducted with flight hardware in a flight-like environment due to cost and schedule constraints. Instead, subscale tanks are typically tested on the ground. If the “real”, flight liquid in the tank is a cryogenic propellant, sometimes a cryogen is used during testing, but more often a simulant liquid is used. Fluid dynamic similarity analysis, or “scaling analysis” as it is sometimes called, for slosh examines nondimensional numbers to determine which fluid dynamic regime(s) a tank is operating in. If the relevant nondimensional numbers of a scale tank test are similar enough to the real tank’s nondimensional numbers, then it is likely that the scale test data will be similar to what would be obtained with the real tank. This type of analysis is useful for guiding experiment design, test liquid selection, and for understanding the physical relevance of prior test data to a specific application. The authors have performed scaling analyses for many slosh test programs conducted in ground, parabolic flight, suborbital, and in-orbit environments. Basics of how to perform the analysis, along with select examples from ground and microgravity environments, are presented. Suggestions for various assumptions and compromises to make are discussed. Limitations and challenges are also discussed.

slosh↗

NASA NTRS1971

Similarity and generalized finite-difference solutions of parabolic partial differential equations.

Techniques are presented for obtaining generalized finite-difference solutions to partial differential equations of the parabolic type. It is shown that the advantages of similarity in the solution of similar problems are generally not lost if the solution to the original partial differential equations is effected in the physical plane by finite-difference methods. The analysis results in a considerable saving in computational effort in the solution of both similar and nonsimilar problems. Several examples, including both the heat-conduction equation and the boundary-layer equations, are given. The analysis also provides a practical means of estimating the accuracy of finite-difference solutions to parabolic equations.

Clausing, A. M.↗

NASA NTRS1974

Similarity constraints in testing of cooled engine parts

A study is made of the effect of testing cooled parts of current and advanced gas turbine engines at the reduced temperature and pressure conditions which maintain similarity with the engine environment. Some of the problems facing the experimentalist in evaluating heat transfer and aerodynamic performance when hardware is tested at conditions other than the actual engine environment are considered. Low temperature and pressure test environments can simulate the performance of actual size prototype engine hardware within the tolerance of experimental accuracy if appropriate similarity conditions are satisfied. Failure to adhere to these similarity constraints because of test facility limitations or other reasons, can result in a number of serious errors in projecting the performance of test hardware to engine conditions.

Colladay, R. S.↗

NASA NTRS1977

Application of differential similarity to finding nondimensional groups important in tests of cooled engine components

The method of differential similarity is applied to the partial differential equations and boundary conditions which govern the temperature, velocity, and pressure fields in the flowing gases and the solid stationary components in air-cooled engines. This procedure yields the nondimensional groups which must have the same value in both the test rig and the engine to produce similarity between the test results and the engine performance. These results guide the experimentalist in the design and selection of test equipment that properly scales quantities to actual engine conditions. They also provide a firm fundamental foundation for substantiation of previous similarity analyses which employed heuristic, physical reasoning arguments to arrive at the nondimensional groups.

Sucec, J.↗