On asymptotic analysis of gaseous squeeze-film bearings
Asymptotic analysis for obtaining steady state solution of time dependent gas lubrication equation, of diffusion type, for gaseous squeeze film bearings
DIFFUSION COEFFICIENT↗
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Numerical studies of motion of vortex filaments - Implementing the asymptotic analysis
A computational code is developed for the integro-differential equations governing the motion of the centerlines of vortex filaments submerged in a background potential flow. These equations, which are derived from the method of matched asymptotic analysis, include the effect of the decaying large-magnitude circumferential and axial velocity components in the vortical cores. Numerical examples are presented to assess the effect of a large axial velocity and that of nonsimilar initial profiles in the vortical cores. The initial configurations of the filaments are chosen so as to fulfill the basic assumption of the asymptotic analysis, which is that the effective vortical core size is much smaller than all the other length scales in the flowfield, e.g., the radius of curvature and the interfilament distance. The computations are continued until the basic assumption is no longer valid, that is when the merging or intersection of filaments has begun. A classification of the various types of local or global merging or intersection of filaments is made and demonstrated by numerical examples. It is then shown that the asymptotic solution not only provides the initial data but also can be used to formulate the appropriate boundary conditions for the numerical solution of a merged region.
Liu, C. H.↗
An asymptotic analysis of supersonic reacting mixing layers
The purpose of this paper is to present an asymptotic analysis of the laminar mixing of the simultaneous chemical reaction between parallel supersonic streams of two reacting species. The study is based on a one-step irreversible Arrhenius reaction and on large activation energy asymptotics. Essentially it extends the work of Linan and Crespo to include the effect of free shear and Mach number on the ignition regime, the deflagration regime and the diffusion flame regime. It is found that the effective parameter is the product of the characteristic Mach number and a shear parameter.
Jackson, T. L.↗
An asymptotic analysis for large deflections of pressurized shallow spherical membrane shells.
Large deflections of symmetrically loaded shallow membrane shells of revolution, considering existence of boundary layer near edges and using asymptotic analysis
ASYMPTOTIC METHOD↗
Asymptotic modal analysis and statistical energy analysis
Asymptotic Modal Analysis (AMA) is a method which is used to model linear dynamical systems with many participating modes. The AMA method was originally developed to show the relationship between statistical energy analysis (SEA) and classical modal analysis (CMA). In the limit of a large number of modes of a vibrating system, the classical modal analysis result can be shown to be equivalent to the statistical energy analysis result. As the CMA result evolves into the SEA result, a number of systematic assumptions are made. Most of these assumptions are based upon the supposition that the number of modes approaches infinity. It is for this reason that the term 'asymptotic' is used. AMA is the asymptotic result of taking the limit of CMA as the number of modes approaches infinity. AMA refers to any of the intermediate results between CMA and SEA, as well as the SEA result which is derived from CMA. The main advantage of the AMA method is that individual modal characteristics are not required in the model or computations. By contrast, CMA requires that each modal parameter be evaluated at each frequency. In the latter, contributions from each mode are computed and the final answer is obtained by summing over all the modes in the particular band of interest. AMA evaluates modal parameters only at their center frequency and does not sum the individual contributions from each mode in order to obtain a final result. The method is similar to SEA in this respect. However, SEA is only capable of obtaining spatial averages or means, as it is a statistical method. Since AMA is systematically derived from CMA, it can obtain local spatial information as well.
Dowell, Earl H.↗
Asymptotic analysis of dissipative waves with applications to their numerical simulation
Various problems involving the interplay of asymptotics and numerics in the analysis of wave propagation in dissipative systems are studied. A general approach to the asymptotic analysis of linear, dissipative waves is developed. It was applied to the derivation of asymptotic boundary conditions for numerical solutions on unbounded domains. Applications include the Navier-Stokes equations. Multidimensional traveling wave solutions to reaction-diffusion equations are also considered. A preliminary numerical investigation of a thermo-diffusive model of flame propagation in a channel with heat loss at the walls is presented.
Hagstrom, Thomas↗
Asymptotic analysis of numerical wave propagation in finite difference equations
An asymptotic technique is developed for analyzing the propagation and dissipation of wave-like solutions to finite difference equations. It is shown that for each fixed complex frequency there are usually several wave solutions with different wavenumbers and the slowly varying amplitude of each satisfies an asymptotic amplitude equation which includes the effects of smoothly varying coefficients in the finite difference equations. The local group velocity appears in this equation as the velocity of convection of the amplitude. Asymptotic boundary conditions coupling the amplitudes of the different wave solutions are also derived. A wavepacket theory is developed which predicts the motion, and interaction at boundaries, of wavepackets, wave-like disturbances of finite length. Comparison with numerical experiments demonstrates the success and limitations of the theory. Finally an asymptotic global stability analysis is developed.
Giles, M.↗
On asymptotic analysis of gaseous squeeze-film bearings.
HF gaseous squeeze film bearing asymptotically analyzed by considering internal and edge regions separately
GASEOUS DIFFUSION↗
Asymptotic analysis with reduced chemistry for the burning of n-heptane droplets
The method of rate-ratio asymptotics is used with reduced chemistry to analyze the flame structure and extinction of an isolated n-heptane droplet burning under quasisteady, spherically symmetrical conditions. The outer transport zones are described by the classical Burke-Schumann solution. The inner reaction zone consists of a thin layer, on the rich side of the flame, where the fuel is consumed, and on the lean side, a broader but still asymptotically thin oxidation layer, where H2 and CO are consumed. Special attention is given to differences in predictions of extinction conditions, caused by different chemical-kinetic approximations in the reduced chemistry, including fuel-chemistry effects through molecules containing more than one carbon atom. From the analysis, extinction diameters for n-heptane droplets are estimated for different pressures and ambient oxygen concentrations. The results show that extinction diameters are extremely sensitive to the number of radicals consumed in breaking down each fuel molecule.
Card, J. M.↗
Asymptotic analysis of force-free magnetic fields of cylindrical symmetry
It is known from computer calculations that if a force-free magnetic-field configuration is stressed progressively by footpoint displacements, the configuration expands and approaches the open configuration with the same surface flux distribution, and, in the process, the energy of the field increases progressively. Analysis of a simple model of force-free fields of cylindrical symmetry leads to simple asymptotic expressions for the extent and energy of such a configuration. The analysis is carried through for both spherical and planar source surfaces. According to this model, the field evolves in a well-behaved manner with no indication of instability or loss of equilibrium.
Sturrock, P. A.↗
A WKB asymptotic analysis of baroclinic instability
A modest extension of conventional WKB methods of solving second-order differential equations asymptotically is developed and applied to the problem of baroclinic instability. Accurate results are obtained for the Charney problem using simple expressions. More important, the present expressions can be used immediately for a wide variety of basic velocity profiles.
Lindzen, R. S.↗
An asymptotic analysis of a general class of signal detection algorithms
For applications to the problem of radio frequency interference identification, or in the search for extraterrestrial intelligence, it is important to have a basic understanding of signal detection algorithms. A general technique for assessing the asymptotic sensitivity of a broad class of signal detection algorithms is given. In these algorithms, the decision is based on the value of X sub 1 + X sub 2...+ X sub n where the X sub 1's are obtained by sampling and preliminary processing of a physical process.
Mceliece, R. J.↗
Effect of the thickness variation and initial imperfection on buckling of composite cylindrical shells: Asymptotic analysis and numerical results by BOSOR4 and PANDA2
This study is an extension of a previous investigation of the combined effect of axisymmetric thickness variation and axisymmetric initial geometric imperfection on buckling of isotropic shells under uniform axial compression. Here the anisotropic cylindrical shells are investigated by means of Koiter's energy criterion. An asymptotic formula is derived which can be used to determine the critical buckling load for composite shells with combined initial geometric imperfection and thickness variation. Results are compared with those obtained by the software packages BOSOR4 and PANDA2.
Li, Yi-Wei↗
Asymptotic Analysis of Premixed N-alkane Cool Flame Propagation
A simplified chemical-kinetic cool-flame mechanism for n-alkanes developed recently is applied to premixed laminar cool-flame deflagrations. The present contribution derives the structure of the associated freely propagating cool premixed flame controlled by the low-temperature chemistry and develops formulas for calculating the corresponding laminar burning velocity. Application of activation-energy asymptotics reveals finite-rate chemistry without heat release occurring throughout the preheat zone and leakage of both fuel and oxygen through the thin heat-release zone, there being zones of consumption of an intermediate species on each side of the heat-release zone, thicker than that zone but still thin compared with the preheat-zone thickness. Predicted laminar burning velocities are compared with recently reported measurements for n-dodecane, performed in a newly deigned high-pressure ignition apparatus, resulting in reasonable agreement.
Cool flames↗
Asymptotic Analysis of Premixed N-alkane Cool Flame Propagation
A simplified chemical-kinetic cool-flame mechanism for n-alkanes developed recently is applied to premixed laminar cool-flame deflagrations. The present contribution derives the structure of the associated freely propagating cool premixed flame controlled by the low-temperature chemistry and develops formulas for calculating the corresponding laminar burning velocity. Application of activation-energy asymptotics reveals finite-rate chemistry without heat release occurring throughout the preheat zone and leakage of both fuel and oxygen through the thin heat-release zone, there being zones of consumption of an intermediate species on each side of the heat-release zone, thicker than that zone but still thin compared with the preheat-zone thickness. Predicted laminar burning velocities are compared with recently reported measurements for n-dodecane, performed in a newly deigned high-pressure ignition apparatus, resulting in reasonable agreement.
cool flames↗
Asymptotic analysis of corona discharge from thin electrodes
The steady discharge of a high-voltage corona is analyzed as a singular perturbation problem. The small parameter is the ratio of the length of the ionization region to the total gap length. By this method, current versus voltage characteristics can be calculated analytically.
Durbin, P. A.↗
Asymptotic analysis for the burning of n-heptane droplets using a four-step reduced mechanism
A four-step reduced mechanism is obtained from a minimal chemical-kinetic description, where the effects of the elementary rates are treated as parameters in the expressions for the global rates. This mechanism is used to analyze the extinction characteristics of a single n-heptane droplet burning under quasi-steady, spherically symmetrical conditions. The reaction layer consists of a merged inner zone, on the fuel-rich side of the flame, where fuel and H atoms are consumed thereby producing H2 and CO along with H2O and CO2, and an oxygen-consumption zone, on the fuel-lean side, where H2 and CO are oxidized to produce additional H2O and CO2 along with H radicals. For the inner zone, a parameter mu is identified which describes the ratio of the thickness of a fuel-consumption layer to that of an H-recombination layer. Analytical solutions for the rate of scalar dissipation at extinction are obtained in the limiting cases of mu tending to 0 and mu tending to infinity. From the results of the analysis, extinction diameters for n-heptane droplets are estimated for different pressures and ambient oxygen concentrations.
Card, J. M.↗
Asymptotic modal analysis of a rectangular acoustic cavity excited by wall vibration
Asymptotic modal analysis, a method that has recently been developed for structural dynamical systems, has been applied to a rectangular acoustic cavity. The cavity had a flexible vibrating portion on one wall, and the other five walls were rigid. Banded white noise was transmitted through the flexible portion (plate) only. Both the location along the wall and the size of the plate were varied. The mean square pressure levels of the cavity interior were computed as a ratio of the result obtained from classical modal analysis to that obtained from asymptotic modal analysis for the various plate configurations. In general, this ratio converged to 1.0 as the number of responding modes increased. Intensification effects were found due to both the excitation location and the response location. The asymptotic modal analysis method was both efficient and accurate in solving the given problem. The method has advantages over the traditional methods that are used for solving dynamics problems with a large number of responding modes.
Peretti, Linda F.↗