Interaction and “apparent” reconnection of 3D vortex tubes via direct numerical simulations

We present evidence of: “binding” of anti-parallel vortex tube segments; strong noncircular core development; evolution of new secondary finger-like vortex structures: and finally “apparent” vortex reconnections due to entanglement. The latter three processes are not present in Biot-Savart filament simulations.     

Entrance flow of a yield-power law fluid

In the present work we have obtained the numerical solution of the momentum equation for a Yield-Pseudoplastic power-law fluid flowing in the entrance region of a tube. The accuracy of the numerical results is checked by comparing the asymptotic values of friction coefficients and velocity profiles with the corresponding results from the analytical solutions for the fully-developed region. The results of the entrance flow solution for the power-law exponent equal to unity (Bingham fluid) are also in agreement with the numerical solution for a Bingham fluid. Detailed results are presented for wide ranges of yield numbers and power law exponents.

Nomenclature

Nomenclature a constant - D diameter - F dimensionless pressure gradient in (4.3) - f _x friction factor in (5.1) - f _app total friction factor in (5.2) - K entrance pressure drop coefficient - n power law exponent - p pressure - r radial co-ordinate - R radius of a tube - Re Reynolds number (5.3) - s rate of shear, u/r - u axial velocity - average velocity - v velocity in radius direction - x axial co-ordinate - y normal co-ordinate - Y yield number in (4.4) - z dimensionless axial distance =(x/D)/Re - z ₁ 1/z Greek Symbols plug flow radius in (4.6) - _eff effective viscosity - density - shear stress - _y yield stress - dimensionless stream function     

Diffusion flux to a distorted gas bubble at large Reynolds numbers

The diffusion flux to a distorted gas bubble situated in a uniform viscous incompressible fluid flow is determined for large Reynolds and Péclet numbers and finite Weber numbers. The bubble has the shape of an ellipsoid of revolution, oblate in the flow direction, making it possible to use the flow field derived by Moore [1] in the form of a two-term expansion with respect to the flow parameter =R^–1/2 (R is the Reynolds number; the zeroth term of the expansion corresponds to potential flow). The dependence of the diffusion flux onto the bubble surface on the Weber and Reynolds numbers is determined. The results of Winnikow [2] and Sy and Lightfoot [3] are thus generalized to the case of finite Weber numbers and a broader range of Reynolds numbers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 70–76, July–August, 1976.     

Equations and forms of motion of a jet flowing onto a liquid

A nonlinear theory is constructed for a thin jet of nonviscous, incompressible, weightless fluid flowing from a nozzle onto the surface of an immobile heavy liquid. The theory is asymptotically (over jet thickness) more accurate than that presented in [1]. Forms of the flow are studied as functions of nozzle, jet, and heavy liquid parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 20–28, November–December, 1976.     

Slow motions of a rigid sphere in incompressible viscoelastic fluids

Problems concerned with the force of resistance and the moment of forces acting from the side of a viscoelastic fluid on a sphere moving with acceleration are considered in a linear formulation. Fairly simple relations are obtained for a fluid with a single relaxation time or a single after-action time. A discussion of the asymptotic expressions is given for a fluid with a large number of times.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 9–16, March–April, 1976.     

Analysis of biaxial-fatigue damage at elevated temperatures

Two-level cumulative-damage fatigue tests were conducted on tubular 304 stainless-steel specimen under biaxial-strain conditions at elevated temperatures. Effects of temperature, biaxiality and sequence of straining were investigated. The experimental results are forwarted with a new approach that utilizes the Miner cumulative-damage rule. This approach has shown that fatigue damage at elevated temperatures of 538°C (1000°F) and 649°C (1200°F) accelerates and decelerates as a result of time of exposure to a given loading sequence. The effect of biaxiality is shown through the behavior of the material under axial and shear-strain components. The axial (tensile) strain component has shown to be the severest detrimental damaging component when compared to a shear-strain component. A damage mechanism emerges from the interaction of temperature and loading sequence. Its significance can be observed only when a certain life ratio has been exhausted.     

Strain-gage-stability measurements for years at 75°C in air

The authors have evaluated the performance of three types of metal-foil strain gages for two and a half years at a constant temperature of 75°C in air. The studies included polyimide-backed and phenolic-glass-backed gages with copper-nickel foil (constantan) and glass-fiber-rein-forced epoxy-phenolic-resin-backed gages with nickel-chromium foil (modified Karma). All gages were tested in a three-wire-lead, single-active-gage Wheatstone bridge system at nominal mechanical-strain levels of 0, +1000 and ?1000 μm/m. The polyimide-backed constantan gages used in Installation No. 1 typically zero-shifted more than +200 μm/m after 30 days' testing at 75°C. The phenolic-glass-backed constantan gages used in Installation No. 2 zero-shifted ?40 to +20 μm/m after 30 days and +270 to +350 μm/m after 900 days. The glass-fiber-reinforced, epoxyphenolic-resin-backed Karma gages used in Installation No. 3 zero-shifted about +5 μm/m after 30 days, and +20 to +45 μm/m after 900 days. The Karma gages used in Installation No. 3 performed better than the other two types of gages. The measured results for the Karma gages appeared to be independent of the adhesives, test-part material, and mechanical-strain levels that we tested. The high stability and low zero drifts of this gage at 75°C allowed us to reliably correct the measured static-strain data on actual test parts.     

Vibrations of a gas-filled spherical cavity in pseudoplastic and dilatant liquids

Questions of the dynamics of bubbles in a liquid are connected with problems of cavitation [1]. In connection with cavitation phenomena in non-Newtonian media, in particular in polymeric liquids [2, 3], a study is made of the pulsations of a bubble in a polymeric liquid with an exponential rheological law. The equation of the motion of the boundary of the gas cavity is integrated numerically; here, the cases of pseudo-plastic and dilatant liquids are discussed separately. The results obtained can be used in the analysis of acoustical cavitation in aqueous solutions of polymers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 146–148, January–February, 1975.     

Convective motions in a porous medium heated from below

Convective motions in a porous medium filling a horizontal cylinder with a cross section of arbitrary shape and heated from below are studied. The small-parameter method is used to obtain infinitely many stationary motions forming a one-parameter family. For small values of the parameter, all of these motions are stable with respect to small perturbations. The article also discusses the case of heating which is not strictly vertical. It is found that in this case only one stationary motion is stable.     

Steady-state motion of a plate with a discontinuous mass

An “exact” solution employing the normal mode approach is presented for the steady-state motion of a plate of arbitrary shape and with arbitrary boundary conditions that is provided with a discontinuous mass. The plate is viscously damped and the excitation is furnished in the form of distributed and/or concentrated loads that vary sinusoidally. The rigid mass, which may act as a vibration damper, can be applied to any point in the structure. Experimental studies with a mechanical model corroborate the theoretical results. Results of the analysis are applied to cantilever and simply-supported square plates subjected to base excitation and discrete loads. The effects of all system parameters, including damper location and mass ratio, mode shapes, viscous damping, and excitation frequency are determined. It is found that the system under consideration is an efficient device for reducing the vibration of plates, particularly cantilevered ones.