摘要:

A two‐dimensional cylinder is subjected to frequency‐modulated excitation in the cross‐stream direction. Transition from a locked‐in response to a completely destabilized response can be attained by lowering the value of modulation frequency while all other parameters are maintained constant. This transition involves progression through a series of identifiable states including lock‐in at the modulation frequency, period doubling at the modulation frequency, and spectral‐broadened response.

ISSN:0899-8213    

DOI:10.1063/1.858004

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

Through analyzing a simple solution of the axisymmetric Stokes equations for slow viscous flow, it is possible to show how placing a finite body between a source and sink tends to expand the domain through which the exchange of mass takes place, whereas placing it on the same side tends to contract this domain.

ISSN:0899-8213    

DOI:10.1063/1.858005

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

The method of matched asymptotic expansions is used to solve for the free surface of a thin liquid drop draining down a vertical wall under gravity. The analysis is based on the smallness of the surface tension term in the lubrication equation. In a region local to the front of the drop, where the surface curvature is large, surface tension forces are significant. Everywhere else, the surface curvature is small, and surface tension plays a negligible role. A numerical time‐marching scheme, which makes no small surface tension assumptions, is developed to provide a datum from which to gauge the accuracy of the small surface tension theory. Agreement between the numerical scheme and the small surface tension theory is good for small values of surface tension. Extension to the propagation of drops by spinning and by blowing with a jet of air is also discussed. It is shown that there are inherent similarities between all three spreading mechanisms.

ISSN:0899-8213    

DOI:10.1063/1.858006

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

The problem of transport of a reactive solute in a porous medium by convection and diffusion is studied for the case in which the solute particles undergo a first‐order chemical reaction on the surface of the bed. Assuming that the geometry is periodic, the method of homogenization is applied, showing explicitly that the effective equation is given by a Kramers–Moyal expansion, i.e., a partial differential equation of infinite order in which thenth term is the product of thenth gradient of the mean concentration by annth‐order constant tensor. The effective values of reactivity, solute velocity, diffusivity, and of all the tensorial coefficients in the expansion are independent of the initial solute distribution and are expressed in terms of Peclet’s and Damkohler’s numbers, Pe=aV/Dand Da=ak/D, respectively, whereais the cell size,Vis the solvent mean velocity,Dis the solute molecular diffusivity, andkis the surface reactivity, showing that they are independent of the initial solute distribution. Since the ratio between two successive terms in the effective equation equals the small ratio &egr; between the micro‐ and macrolength scales, truncating the expansion after thenth term allows us to find the effective concentration up toO(&egr;n) terms.The impact of this fact is exemplified, showing that in the case of a solute flowing in a pipe with small Damkohler number Da, the effective concentration can be determined up toO(Da) terms only if the effective equation includes the skewness term. When Pe and Da are either small or large, after determining a two‐parameter expansion of the solution, it is shown that the ratios between the diffusion, convection, and reaction macroscopic characteristic time scales cannot always be inferred through a naive dimensional analysis at the microscale. For example, when Da≫1 we find that the effective reaction rate tends to a constant value, independent of Da. When Pe≫1, Taylor‐like dispersion, proportional to Pe2, is obtained when the mean flow is perpendicular to any vector of the reciprocal lattice. If this condition is not satisfied, the result strongly depends on the magnitude of the volume fraction of the bed particles &Fgr;. If Pe−3≪&Fgr;≪1, then the main mechanism causing dispersion is convection alone and the effective diffusivity is proportional to Pe; on the contrary, when &Fgr;≪Pe−3, the effective diffusivity tends to a constant value independent of Pe.

ISSN:0899-8213    

DOI:10.1063/1.858007

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

Many similarity solutions have been found for the equations of one‐dimensional (1‐D) hydrodynamics. These special combinations of variables allow the partial differential equations to be reduced to ordinary differential equations, which must then be solved to determine the physical solutions. Usually, these reduced ordinary differential equations are solved numerically. In some cases it is possible to solve these reduced equations analytically to obtain explicit solutions. In this work a collection of analytic solutions of the 1‐D hydrodynamics equations is presented. These can be used for a variety of purposes, including (i) numerical benchmark problems, (ii) as a basis for analytic models, and (iii) to provide insight into more complicated solutions.

ISSN:0899-8213    

DOI:10.1063/1.858008

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

The bifurcation structure of two‐dimensional, pressure‐driven flows through a rectangular duct that is rotating about an axis perpendicular to its own is examined at a fixed Ekman number (Ek=&ngr;/b2&OHgr;) of 0.01. The solution structure for flow through a square duct (aspect ratio &ggr;=1) is determined for Rossby numbers (Ro=U/b&OHgr;) in the range of 0–5 using a computational scheme based on the arclength continuation method. The structure is much more complicated than reported earlier by Kheshgi and Scriven [Phys. Fluids28, 2968 (1985)]. The primary branch with two limit points in Rossby number and a hysteresis behavior between the two‐ and four‐cell flow structure that was computed by Kheshgi and Scriven is confirmed. An additional symmetric solution branch, which is disconnected from the primary branch (or rather connected via an asymmetric solution branch), is found. This has a two‐cell flow structure at one end, a four‐cell flow structure at the other and three limit points are located on the path. Two asymmetric solution branches emanating from symmetry breaking bifurcation points are also found for a square duct. Thus even within a Rossby number range of 0–5 a much richer solutions structure is found with up to five solutions at Ro=5. An eigenvalue calculation indicates that all two‐dimensional solutions develop some form of unstable mode by the time Ro is increased to 5.0. In particular, the four‐cell solution becomes unstable to asymmetric perturbations as found in a related problem of flow through a curved duct. The paths of the singular points are tracked with respect to variation in the aspect ratio using the fold following algorithm. A transcritical point is found at an aspect ratio of 0.815 and below which the four‐cell solution is no longer on the primary branch. When the channel cross section is tilted even slightly (1°) with respect to the axis of rotation, the bifurcation points unfold and the two‐cell solution evolves smoothly as Rossby number is increased. The four‐cell solutions then become genuinely disconnected from the primary branch. The uniqueness range in Rossby number increases with increasing tilt.

ISSN:0899-8213    

DOI:10.1063/1.858009

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

The induced flow of an incompressible, unbounded fluid is considered when a circular cylinder performs small transverse and torsional oscillations. An analytic solution, valid into the inner layer provides the necessary conditions for the matching with the numerical solution at the outer layer. The results are compared with those of the single transverse oscillation. It is shown that the torsional oscillation significantly affects the depth of the boundary layer and the position of the jet axis, especially when its amplitude becomes larger.

ISSN:0899-8213    

DOI:10.1063/1.858010

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

This study is concerned with the stability properties of laminar free‐shear‐layer flows, and in particular symmetric two‐dimensional wakes, for the supersonic through the hypersonic regimes. Emphasis is given to the use of proper wake profiles that satisfy the equations of motion at high Reynolds numbers. In particular the inviscid stability of a developing two‐dimensional wake is studied as it accelerates at the trailing edge of a splitter plate. The nonparallelism of the flow is a leading‐order effect in the calculation of the basic state, which is obtained numerically. Neutral stability characteristics are computed and the hypersonic stability is obtained by increasing the Mach number. It is found that the stability characteristics are altered significantly as the wake develops. Multiple modes (secondary modes) are found in the near wake that are closely related to the corresponding Blasius ones, but as the wake develops mode multiplicity is delayed to higher and higher Mach numbers. At a distance of about one plate length from the trailing edge, there is only one mode in a Mach number range of 0–20. The dominant mode emerging at all wake stations, and for high enough Mach numbers, is the so‐called vorticity mode that is centered around the generalized inflection point layer. The structure of the dominant mode is also obtained analytically for all streamwise wake locations and it is shown how the far‐wake limit is approached. Asymptotic results for the hypersonic mixing layer given by a tanh and a Lock distribution are also given.

ISSN:0899-8213    

DOI:10.1063/1.858011

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

High‐temperature effects alter the physical and transport properties of a gas, air in particular, due to vibrational excitation and gas dissociation, and thus the chemical reactions have to be considered in order to compute the flow field. Linear stability of high‐temperature boundary layers is investigated under the assumption of chemical equilibrium and this gas model is labeled here as ‘‘real gas model.’’ In this model, the system of stability equations remains of the same order as for the perfect gas and the effect of chemical reactions is introduced only through mean flow and gas property variations. Calculations are performed for Mach 10 and 15 boundary layers and the results indicate that real gas effects cause the first mode instability to stabilize while the second mode is made more unstable. It is also found that the second mode instability shifts to lower frequencies. There is a slight destabilizing influence of real gas on the Goertler instability as compared to the perfect gas results.

ISSN:0899-8213    

DOI:10.1063/1.858012

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

The statistics of stretching and stirring in time‐periodic chaotic flows is studied numerically by following the evolution of stretching ofO(105) points. The ratio between stretchings accumulated by each point at successive periods is referred to as a multiplier, and the total stretching is the product of multipliers. As expected, the mean stretching of the population increases exponentially whereas the probability density function of multipliers converges—in just two periods or so—to a time‐invariant distribution. There is, however, a considerable degree of order in the spatial distribution of stretching in spite of conditions of global chaos. The self‐correlation of multipliers shows as well considerable structure and often there are segregated populations of points: the largest population consists of points that experience extensive stretching, efficient stirring, and have a distribution of stretching values that evolves asymptotically—in about ten periods—into a limiting time‐invariant scaling distribution. The remaining points experience slow stretching and, although they also exhibit scaling behavior, are effectively segregated from the rest of the system in the time scale of our simulations.

ISSN:0899-8213    

DOI:10.1063/1.858013

出版商:AIP    

年代:1991

数据来源: AIP