Convective heat exchange of a viscoplastic fluid with temperature-dependent rheological characteristics during structural flow in a circular pipe

Heat exchange in a viscoplastic liquid moving in a circular pipe is investigated, taking into account the dependence of plastic viscosity and ultimate shear stress on temperature. A system of motion, energy, and continuity equations transformed under the assumption that the Pe and Pr numbers are much greater than 1 is solved on a computer by the method of finite differences using iterations. Results of the numerical solutions for the exponential form of the dependences of the rheological characteristics on temperature are analyzed in detail. A comparison of the numerical solutions with well-known theoretical solutions in particular cases and also with experimental data indicates their high precision.     

Convective motions in a porous ring sector

Gravitational filtration convection of an incompressible fluid in ring sectors is studied. The bifurcation and development of families of convective regimes are studied using equations in polar coordinates and a finite-difference scheme that preserves the cosymmetry of the original problem. The occurrence of instability for trapezoidal and semiring areas is analyzed for stationary states.     

The settling of spheres in a viscoplastic fluid

Results on the variation in the steady settling velocity of spheres with a time interval between experiments in a 0.3 wt% aqueous Carbopol-941 dispersion are reported. Spheres made of stainless steel, brass, ceramics and soda lime glass ranging in nominal diameter from 1/4 to 3/8 in. were used. In each experiment, four identical spheres were permitted to settle in quick succession and the time interval between such sets was varied systematically. It was found that four spheres were sufficient to reach an asymptotic settling velocity which did not change with the addition of more spheres to the set. The dependence of the drag coefficient on a modified Reynolds number based on this asymptotic settling velocity was found to be consistent with that from prior work. The steady terminal settling velocity of the first sphere was found to decrease with increasing time intervals between experiments. The results are consistent with the hypothesis of network damage caused by shear with subsequent healing.     

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.     

Deformation of a Bingham viscoplastic fluid in a plane confuser

A review is given to and comprehensive numerical-analytic study is carried out of the problem of steady Bingham viscoplastic flow in a plane confuser. The solution is constructed in the first approximation with the yield stress as a small parameter and the solution of the Jeffery-Hamel problem (steady radial motion of an incompressible viscous material in a plane confuser) as the zero-order approximation. The numerical analysis is based on the modified accelerated-convergence method proposed earlier by the authors. The bifurcations of the deformation pattern occurring when the parameters reach some critical values are discussed and commented on. The asymptotic boundaries of the rigid zones that appear at infinity upon perturbation of the yield stress are determined __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 4, pp. 3–45, April 2006.     

Convective instability of a rotating fluid

A physical system may be in thermodynamic equilibrium when participating as a whole in uniform rotational motion [1]. In particular, mechanical equilibrium of a liquid in a cavity rotating about a stationary axis with the constant angular velocity (solid-body rotation of the liquid) is possible. If the liquid is uniform in composition and isothermal, then such equilibrium, as shown in [2], is stable for all . However, in the case of a nonuniformly heated liquid, stability of the solid-state rotation is, generally speaking, impossible.The appearance of two steady-state force fields is associated with uniform rotation: the centrifugal field and the Coriolis force field. The former field forces the liquid elements which are less heated and therefore more dense to move away from the axis of rotation, displacing the less dense liquid layers (centrifugation). If we maintain in the liquid a temperature gradient which prevents the establishment of equilibrium stratification of the liquid, then with a suitable value of this gradient (the magnitude obviously depending on ) undamped flows—convection—will develop in the liquid. Thus, while in conventional gravitational convection the gravity field is the reason for the appearance of the Archimedes buoyant forces, in the rotating cavity the mixing of the nonuniformly heated liquid is caused by the centrifugal field. As soon as the convective flows arise the Coriolis forces come into play. Account for the latter, as is shown below, prevents reducing in a trivial fashion the study of convective stability of rotating liquid to the well-studied problems of gravitational convection.     

Flow of a Viscoplastic Fluid on a Rotating Disk

ＦＬＯＷＯＦＡＶＩＳＣＯＰＬＡＳＴＩＣＦＬＵＩＤＯＮＡＲＯＴＡＴＩＮＧＤＩＳＫＦａｎＣｈｕｎ（范椿）（ＩｎｓｔｉｕｉｅｏｆＭｅｃｈａｎｉｃｓ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ）（ＲｅｃｅｉｖｅｄＮｏｖ．２０，１９９２；Ｃｏｍｍｕｎｉｃａｔ...     

Natural convection of a viscoplastic fluid in vertical circular channels

In contrast to a Newtonian fluid, a viscoplastic fluid can be in a state of mechanical equilibrium when heat is supplied from the side. Therefore, natural convection in a viscoplastic fluid heated from the side occurs only when the determining parameters exceed certain threshold values. The threshold conditions for the onset of convection for a flat vertical layer have been investigated several times [1–4]. The present paper is an investigation of the conditions of occurrence of plane-parallel natural convection of a viscoplastic fluid in regions with cylindrical symmetry: in a vertical annular layer and in a vertical circular tube.     

Convective self-oscillations near an air-bubble surface in a horizontal rectangular channel

The concentration convection in an isothermal fluid near an air bubble clamped between the vertical walls of a horizontal channel with a rectangular cross-section is studied experimentally and numerically. The channel is filled with an aqueous solution of a surfactant with a nonuniform concentration. As a result of the competition between the gravitational convection in the cavity volume and the Marangoni convection near the bubble surface, an oscillation flow regime is established. This regime is observed experimentally over several hours. In the numerical experiment, the oscillations are obtained in the presence of an initial horizontal surfactant concentration gradient. Against the background of gravitational convection, short bursts of Marangoni convection with ten times greater intensity are observed. The convective flow patterns and the oscillation periods obtained experimentally and numerically are in fairly good agreement.     

Hydrodynamic stability of Poiseuille flow of a viscoplastic non-Newtonian fluid

The hydrodynamic stability of Poiseuille flow of a viscoplastic fluid is investigated. The flow is shown to be stable for infinitesimal disturbances.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 152–154, November–December, 1974.In conclusion the authors thank S. A. Regirer for critical remarks.     

Convective instability of a fluid in two-layer saturated strata

The problem of convective instability of a fluid in a system consisting of two horizontal porous strata with different permeabilities and a permeable common boundary is considered. The problem is investigated in parametric form as a function of the stratum thickness ratio and stratum permeabilities. As distinct from a uniform stratum, in this case the neutral curve can have one or two minima depending on the relationship between the parameters. The case of two minima is characterized by the condition of loss of stability of the fluid in the system as a whole and in the thinner stratum with greater permeability. These minima correspond to significantly different wave numbers. Makhachkala. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 165–169, January–February, 1999.     

Convective stability of fluid in a rotating horizontal annulus

The convective stability of quasi-equilibriumof a fluid layer formed by two horizontal coaxial cylindrical surfaces which have different temperatures and rotate at the same angular velocity about the axis of symmetry is investigated theoretically and experimentally. Consideration is carried out from the standpoint of thermal vibrational convection caused by the average lifting force generated as a result of vibrations of a nonisothermal fluid with respect to the cavity. The vibrations are induced by an external field. The action of the centrifugal force field is also taken into account. Stability of mechanical quasi-equilibrium with respect to monotonic plane perturbations, which are, as shown experimentally, the most dangerous, is studied within the framework of the linear analysis. The stability boundaries are constructed for layers of various relative thickness in the plane of control parameters, the centrifugal and vibrational Rayleigh numbers. The thresholds of excitation of two-dimensional convective structures obtained experimentally are in good agreement with the theoretical ones.     

Slow motions of a solid in a continuously stratified fluid

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 55–60, March–April, 1991.     

Very slow flow of Bingham viscoplastic fluid around a circular cylinder

Numerical simulations have been used to study the flow of a Bingham viscoplastic fluid around a circular cylinder in an infinite medium with negligible inertia effects. Papanastasiou's regularisation technique has been adopted to approximate the model. The case corresponding to preponderant plasticity effects has been particularly studied and convergence of the solutions examined in detail. The flow kinematics and stresses have been determined. The rigid zones have been identified and characterised. At large Oldroyd numbers, when plasticity effects become preponderant, a viscoplastic boundary layer appears around the cylinder. The characteristics of this viscoplastic boundary layer are quantified. The results are compared with existing theoretical results, concerning particularly the predictions of the viscoplastic boundary layer theory and the plasticity theory.