Viscous Condition Research Articles

The wave-vector-frequency spectrum of pressure on a smooth plane in turbulent boundary-layer flow at low Mach number

Properties of the wave-vector-frequency spectrum of fluctuating pressure on a smooth planar wall in turbulent boundary-layer flow at low Mach number are reviewed. In the low but incompressive wave-number range, where ω/c≲K≲max(δ−1,U∞/ω), consistent with the Kraichnan–Phillips hypothesis for inviscid flow, the dependence would be expected to be as K2, but no experimental substantiation exists. In a higher subconvective range where δ−1≲K≲ω/U∞, most pertinent experiments suggest that the spectrum is instead wave-number-white. In the acoustic domain a peak is predicted at K=ω/c. A mean-shear contribution proportional to the square of streamwise wave number appears predominant in the convective domain. An explicit model spectrum is specified that conforms in an appropriate domain to the principle of wall similarity and corresponds to boundary-layer velocity spectra that are planar isotropic in a convected frame. The model potentially encompasses the entire inviscid domain, including the acoustic range. An alternative model exhibits a factorable dependence on the wave-number components. In the acoustic range, the model forms are totally unvalidated by experiment. In the convective domain, the state of determination suffices for many applications, but a preference between model forms and assured choice of parameter values awaits further analysis and perhaps certain further measurements. An addendum based on recent work suggests that the wall pressure at low but incompressive wave numbers may be dominated by a wave-vector-white contribution originating in the viscous wall condition.

Surface void nucleation under the power-law creep condition in an Al-3 at. pct Mg solid solution alloy

In this study, under the viscous glide creep condition of Al-3 at. pct Mg solid solution alloy, which is the power-law creep condition with stress exponent n=3, [9,10] surface void nucleation due to GBM (grain boundary migration) and evaporation of magnesium is investigated

Approximate analytical solutions for viscous shear flows past a circular cylinder.

The two-dimensional flow of an incompressible viscous fluid past a circular cylinder placed in a uniform shear field is analytically solved with different Oseen's velocity fields considered to avoid the "Garstang paradox". The general solutions of the corresponding velocity consist of the nonsymmetric solution to the Oseen equations and one to the equations of the perfect fluids for shear flows past a circular cylinder. The constants of the above are determined by the viscous condition on a circular cylinder. On the basis of these solutions, the expansion formulae of the stream function, Ψ, and the vorticity, ζ, are obtained up to the fourth power of the Reynolds number, Re. The flow patterns for values of a shear parameter, ε, in the range 0≤ε≤0.5 are depicted by utilizing these expansion formulae. They are shown with good results at low Re. Also, the expansion formulae of the lift, moment, and pressure distribution are obtained up to the fourth power of Re. Lastly, successive approximations for the ε-term based on the above solutions are carried out and discussed in the same manner as in the previous paper.

Numerical Calculation of Flow Driven by a Ceiling Fan

ABSTRACT Anumerical model was developed to calculate flow driven by a ceiling fan. Solutions were obtained for Reynolds numbers (Re*) of 500 to 1500 and three vorticity boundary conditions. Simulated velocity profiles below the fan were similar in shape to the velocity profile measured below an actual ceiling fan (Timmons and Baughman, 1985). Solutions with a viscous sublayer slip condition (VSSC), based on the assumption that the vorticity at the wall boundary is the vorticity at the edge of the viscous sublayer in a turbulent boundary layer, gave velocity profiles near the floor which matched profiles measured by Timmons and Baughman. A zero vorticity slip condition (ZVSC) and the no-slip condition were also used in the numerical model. Flow patterns obtained from solutions with the ZVSC and VSSC showed floor jets and recirculating eddies similar to those photographed in a cylindrical enclosure with a suspended fan.

Flow of a viscous fluid in a closed cavity in the presence of slip effects

Slip at the wall is observed in the flow of non-Newtonian fluids [1–4] and rarefied gases [5]. The most complete information on the phenomenon is obtained in capillary viscosimetry. For small radii of the capillaries and in porous media the slip effect is manifested even for Newtonian fluids (water, kerosene, for example) [6]. Experiments [2, 4] show that the influence of the entrance section can be ignored if the length of the capillary exceeds its radius by about 100 times. For the measurement of the rheological characteristics of high-viscosity fluids the use of long capillaries is difficult, and it is necessary to calculate the two-dimensional flow at the entrance section with allowance for slip. The need for such calculations also arises, for example, when one is choosing the optimal parameters of the screw devices employed in the processing of polymers [7]. Two-dimensional flows of a viscous incompressible fluid are frequently calculated with the flow function ψ and vorticity ϕ=− Δψ used as variables [8–14]. The expressions for the vorticity on the boundary are usually obtained from the viscous no-slip condition [8, 9]. In the present paper, expressions are obtained for the vorticity on a wall in the presence of slip. The obtained expressions are used to solve a test problem on the flow of a viscous incompressible fluid in a cavity.

On the numerical modeling of an oldroyd-type constitutive equation

A one-dimensional coupled set of equations consisting of appropriate forms of an equation of motion and a three-constant Oldroyd constitutive equation, used in the description of certain non-Newtonian flows, has been modeled using a finite-difference technique. These one-dimensional equations may be applicable along the centerline of a symmetric almost parallel flow field, where extensive molecular stretching occurs, with the restrictions of zero pressure gradient and zero shear. Mainly, this article differs from previous numerical work on these equations, such as Townsend's work on a four-constant Oldroyd equation, in that the nonlinear convection terms, which did not appear in this earlier work due to the parallel flow being considered, are now present. In comparison with the full set of equations, it is seen that the structure of the motion and constitutive equation used retain the essential characteristics of the complete set. In the equations, the time and spatial derivatives of both velocity and stress were centered so that in the Newtonian limit of zero relaxation and retardation times, the motion equation would reduce to Burgers' equation with the diffusion term time lagged. Stability of the differencing scheme for the constitutive equation dictated that the convective derivative of the deformation rate be time lagged with respect to the convective derivative of the stress. A von Neumann stability analysis was performed on the model equation yielding restrictions on Δt based on the usual viscous condition and, in addition, on the convective inertial and elastic propagation velocities, and also on the time scale of the straining motion. As a test for the proposed scheme an initial-boundary-value problem was formulated. An analytic steady-state solution to the problem can be obtained in Lagranian coordinates if a constant velocity and a linear stress-deformation rate condition are assumed at the inflow to the flow field. This analytic solution, expressed in Eulerian coordinates, was then used as a check for the iterated steady-state solution.

Classification of polymer-low molecular liquid systems according to their physical condition

A scheme for the classification of polymer-low molecular liquid systems according to their physical condition is considered: the viscous flow condition, gels, plasticized polymers and dispersions are included. Particular attention is paid to the origin of the systems, which, in the case of heterogeneous formations, has a decisive effect on their properties and behaviour.

Flow of Gas through Porous Media in the Region between Molecular and Viscous Condition

Experiments on the flow of gases through porous Pyrex disks at pressures in the range of a few mm Hg are described. For air, hydrogen, and carbon dioxide the specific flow is found to be given by Q=A(MT)12+BηTp̄+CM12{1−exp[α0−βT12]p̄}The significance of this result is discussed.

STREPTOCOCCUS MUCILAGINOSUSKULKA, COSBIE AND WALKER (Spec, nov.)

Particulars are given of the isolation, characteristics and classification of a catalase-negative, tetrad-forming streptococcus, which was obtained from a ropy beer. The most distinctive feature of this organism is its propensity to render beer extremely viscous, not only under anaerobic but also under aerobic conditions, and this propensity has persisted over a period of five years, during which the organism has been cultivated in the laboratory. In its principal characteristics it differs so markedly from those beer streptococci which have been described previously, and indeed, from other non-pathogenic streptococci concerning which particulars have been published, that it is to be regarded as a new species. The habit of producing a very viscous condition both in bottled beer and in beer in cask renders it particularly virulent as a beer disease organism.

Geology of the Samoan Islands

The geology of the Samoan archipelago is described, especially Tutuila where detailed work was done, and the geologic literature is reviewed. Tutuila was built by five volcanoes over two and possibly three parallel rifts trending N. 70° E. A caldera 6 miles across, formed by collapse of the top of the Pago volcano, is described, and its bounding fault is mapped. Pago Pago Bay is a drowned river valley cut by a stream along the curved base of the caldera wall. A thick series of tuffs and differentiated lavas partly filled the caldera. Several bulbous trachyte domes in a highly viscous condition pushed through these tuffs to the surface. One of them dragged upward with it for hundreds of feet a thick section of basalts. About 600 dikes and 40 faults are recorded. Several of the dikes are unusual; two contain oriented dunite xenoliths, and one contains bedded ash. Drilling shows that the fringing reefs of Tutuila are chiefly bedded calcareous sand and silt and not coral colonies. Upolu is a deeply eroded mass of Pliocene lavas surrounded by a drowned barrier reef and partly buried by late Pleistocene and Recent lavas. Upolu was submerged so rapidly in late Pleistocene time that only narrow and interrupted fringing reefs grew on the steep shores of Pliocene rocks while a wide barrier reef developed on the gentle slopes of the flat-lying Pleistocene lavas. The absence of a continuous reef on Tutuila also is due to rapid submergence. Brief observations are recorded for the rest of the islands. The geologic histories of the various islands of the entire group are similar.

OBSERVATIONS ON THE STRUCTURE OF PROTOPLASM BY AID OF MICRODISSECTION

1. Protoplasm is an emulsion colloid normally in the sol state. 2. The density of protoplasm varies from the very liquid state of young Fucus oögonia and embryos and of streaming protoplasm in myxomycetes and pollen tubes, to the quite viscous condition found in mature and resting eggs of marine organisms. 3. There is a rapid increase in viscosity of the Fucus egg during the last stages of its ripening, which is, on fertilization, followed by a return to the liquid consistency characteristic of active, growing proptolasm. 4. The plasma membrane is a definite morphological structure, constantly and repeatedly capable of repair through the conversion of the fluid protoplasm into a hyaline layer of greater molar concentration. This film of gel is exceedingly elastic, pliable and glutinous. 5. The surface layer, like the interior cytoplasm, seems to be capable of alteration with changes in environment. 6. The capacity for membrane-formation is one of the last essential properties of the living substance to be lost. It is lost only at death. 7. The kind of membrane formed is apparently identical with the parent membrane (except in the case of escaped protoplasm from cells which possess a cellulose wall). 8. The formation of a membrane is probably a purely physical process, but is dependent upon the physiological condition of the protoplasm. It is not dependent upon the surrounding medium. 9. The amount of physical disturbance that protoplasm can be subjected to before showing signs of injury varies from that of the immature Fucus ovum, where it is exceedingly great, to that of the ripe egg where it is very slight, often no more than a touch sufficing to cause disorganization. 10. Gelation of the plasma always takes place in time and is hurried by dissection. It is accompanied by degeneration. 11. Normal protoplasm is at all times non-miscible in water. Miscibility of the plasma is an unfailing criterion of degeneration. 12. Dissolution of the Fucus ovum is the result of the disorganized cytoplasmic matrix going into solution with the surrounding water. This mixing may take place with the rapidity of an explosion, or slowly, and then either continuously or spasmodically. 13. The disintegration of the egg plasm is frequently localized, in that certain regions of the contents continue dissemination of the granules from the beginning, while others join in later, and still others never take part. This indicates a gross structure of the egg plasm, i. e., the protoplasm is composed of many centers of activity in which different chemical reactions take place separated by protective partitions. 14. That any definite and permanent arrangement of the colloidal particles exists seems unlikely. Whatever structure, gross or ultimate, protoplasm may possess is secondary to chemical activity upon which the life of the organism depends.

III. Notes of researches on the acids of the lactic series.—No. V. Action of zinc upon a mixture of ethyl oxalate and amyl iodide

When a mixture of equivalent proportions of ethyl oxalate and amyl iodide is digested with granulated zinc at 70° C., the zinc is gradually dissolved, while much hydride of amyl and amylene are given off. The mixture finally assumes a viscous or semisolid condition, and, when treated with water, produces a further quantity of hydride of amyl, which distils off at a gentle heat. On the subsequent application of a higher temperature, water, accompanied by amylic alcohol, amyl iodide, and an ethereal liquid, distils over, the three latter forming a mixture, the separation of which into its component parts presents rather formidable difficulties. After drying with chloride of calcium, this oily mixture begins to boil at about 132° C.; the product first passing over consists principally of amylic alcohol, mixed with amyl iodide.