Two-phase couette flow

A study is made of plane laminar Couette flow, in which foreign particles are injected through the upper boundary. The effect of the particles on friction and heat transfer is analyzed on the basis of the equations of two-fluid theory. A two-phase boundary layer on a plate has been considered in [1, 2] with the effect of the particles on the gas flow field neglected. A solution has been obtained in [3] for a laminar boundary layer on a plate with allowance for the dynamic and thermal effects of the particles on the gas parameters. There are also solutions for the case of the impulsive motion of a plate in a two-phase medium [4–6], and local rotation of the particles is taken into account in [5, 6]. The simplest model accounting for the effect of the particles on friction and heat transfer for the general case, when the particles are not in equilibrium with the gas at the outer edge of the boundary layer, is Couette flow. This type of flow with particle injection and a fixed surface has been considered in [7] under the assumptions of constant gas viscosity and the simplest drag and heat-transfer law. A solution for an accelerated Couette flow without particle injection and with a wall has been obtained in [6]. In the present paper fairly general assumptions are used to obtain a numerical solution of the problem of two-phase Couette flow with particle injection, and simple formulas useful for estimating the effect of the particles on friction and heat transfer are also obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–46, May–June, 1976.     

Numerical investigation of two-phase rotating flow

Finite difference solutions of the two-fluid equations of motion for a particle (droplet)-fluid mixture in a rotating finite axisymmetric cylinder are presented. The numerical method, which can be regarded as an extension of the Harlow & Amsden approach, employs forward time and centred space discretization and treats implicitly the pressure, Coriolis and volume flux terms. The computed flow fields are examined via a detailed comparison to previous analytic approximations, which illuminates both the physical and numerical aspects and the validity of these approximations.     

Stability of nonisothermal couette flow

A study is made of the loss of stability of the stationary flow of a viscous fluid between two heated rotating cylinders. The linearized stability problem is studied in the Boussinesq approximation. The perturbations are assumed to be periodic in the time, and also in the axial and azimuthal directions. The neutral curves are calculated numerically. The ranges of variation of the parameters of the problem are found, and in them the most dangerous perturbations (in the class of spatially periodic perturbations) are those without rotational symmetry.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 167–170, January–February, 1980.I thank V. I. Yudovich for constant interest in the work.     

Secondary regimes in couette flow

We consider the asymptotic solutions of secondary steady flows in a fluid contained between cylinders rotating in the same direction for large Reynolds numbers.The existence of secondary axisymmetric steady flows in a fluid contained between cylinders rotating in the same direction was shown in [1, 2]. In the following we present the asymptotic behavior of such solutions for the case of large Reynolds numbers. The construction follows the scheme suggested in [3].     

Experimental investigation of horizontal forced-vibration effect on air-water two-phase flow

In order to investigate the potential seismic vibrations effect on two-phase flow in an annular channel, experimental tests with air-water two-phase flow under horizontal vibrations were carried out. A low-speed eccentric-cam vibration module capable of operating at motor speed of 45–1200 rpm (f = 0.75–20 Hz) was attached to an annular channel, which was scaled down from a prototypic BWR fuel sub-channel with inner and outer diameters of 19.1 mm and 38.1 mm, respectively. The two-phase flow was operated in the ranges of 〈j_f〉 = 0.25–1.00 m/s and 〈j_g〉 = 0.03–1.46 m/s with 27 flow conditions, and the vibration amplitudes controlled by cam eccentricity (E) were designed for the range of 0.8–22.2 mm. Ring-type impedance void meters were utilized to detect the area-averaged time-averaged void fraction under stationary and vibration conditions. A systematic experimental database was built and analyzed with effective maps in terms of flow conditions (〈j_g〉-〈j_f〉) and vibration conditions (E-f and f-a), and the potential effects were expressed by regions on the maps. In the 〈j_g〉-〈j_f〉 maps, the void fraction was found to potentially decrease under vibrations in bubbly flow regime and relatively lower liquid flow conditions, which may be explained by the increase of distribution parameter. Whereas and the void fraction may increase at the region closed to bubbly-to-slug transition boundary under vibrations, which may be explained by the changes of drift velocity due to flow regime change from bubbly to slug flows. No significant change in void fraction was found in slug flow regime under the present test conditions.     

Experimental investigation of horizontal two-phase flow by an electrodiffusion method

The results of an experimental investigation of the local mean and fluctuating friction at the wall of a horizontal tube are presented for the case where a gas-liquid stream flows in the tube with a wide range of regime parameters. The electrodiffusion method is used for measuring the friction. Curves of the tangential stresses along the perimeter of the tube as well as along its length are constructed, permitting an objective determination of certain flow regimes. The experimental results are compared with those of the existing computational methods.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 101–108, March–April, 1973.     

Natural convection in unsteady MHD couette flow

 The combined effect of natural convection and uniform transverse magnetic field on the couette flow of an electrically conducting fluid between two parallel plates for impulsive motion of one of the plates in discussed. Under the assumption of negligible induced magnetic field and applied magnetic field being fixed relative to the fluid or plate, the governing equations have been solved exactly, and the expressions for velocity and temperature field have been presented for two different cases. A comparative study is made between the velocity field for magnetic field fixed with respect to plate and magnetic field fixed with respect to fluid. Received on 12 July 1999     

An investigation of pressure transients in pipelines with two-phase bubbly flow

This paper presents a two-dimensional model for the analysis of the pressure transient of a two-phase homogeneous bubbly mixture flowing in a pipeline and the numerical integration using the centre implicit method (CIM). Experiments were conducted to confirm the proposed sonic speed equation of an air–water mixture for an air concentration of less than 1%. The 2D CIM model is compared with the method of characteristics (MoC) for a two-phase bubbly flow in a pipeline. The comparisons show that the proposed 2D CIM model generally gives good agreement with the method of characteristics.     

Experimental investigation of a developing two-phase bubbly flow in horizontal pipe

Experimental results for various water and air superficial velocities in developing adiabatic horizontal two-phase pipe flow are presented. Flow pattern maps derived from videos exhibit a new boundary line in intermittent regime. This transition from water dominant to water–gas coordinated regimes corresponds to a new transition criterion C_T = 2, derived from a generalized representation with the dimensionless coordinates of Taitel and Dukler.Velocity, turbulent kinetic energy and dissipation rate, void fraction and bubble size radial profiles measured at 40 pipe diameters for J_L = 4.42 m/s by hot film velocimetry and optical probes confirm this transition: the gas influence is not continuous but strongly increases beyond J_G = 0.06 m/s. The maximum dissipation rate, derived from spectra, is increased in two-phase flow by a factor 5 with respect to the single phase case.The axial evolution of the bubble intercept length histograms also reveal the flow organization in horizontal layers, driven by buoyancy effects. Bubble coalescence is attested by a maximum bubble intercept evolving from 2.5 to 4.5 mm along the pipe. Turbulence generated by the bubbles is also manifest by the 4-fold increase of the maximum turbulent dissipation rate along the pipe.     

Numerical analysis of the stability of nonisothermal couette flow

The stability of convective motion of a liquid between two rotating heated cylinders is investigated in the absence of external forces. The mathematical model for describing the convection is obtained from the general equations [1, 2] on the assumption that the density of the liquid, the thermal conductivity, the specific heat and the viscosity coefficients depend only on temperature, and that the work done by the pressure forces and the viscous dissipation are negligibly small. The thermal expansion coefficient of the liquid is not assumed to be small, which distinguishes the models in question from the classical Oberbeck-Boussinesq model [1, 3, 4]. Rostov-on-Don. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 70–76, September–October, 1988.     

Experimental investigation of the drag of simple bodies in a two-phase flow

In connection with their increasing use in technology, two-phase flows are being widely studied at the present time. However, computational methods for determining the parameters and influence of two-phase flows on constructional elements of machines, etc., are as yet inadequately developed. In addition, their further development in rational directions requires a large body of experimental data. It is therefore very important to extend the experimental investigations into two-phase flows. The present paper reports an experimental investigation into the aerodynamic drag of simple bodies in a two-phase flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 159–162, May–June, 1979.     

Characteristics of a viscoplastic material in the couette flow

A model governing a steady flow of a viscoplastic material between coaxial cylinders is proposed. Nonlinear velocity sensitivity typical of superplastic materials is taken into account. An algorithm of calculating the characteristics of the material is developed. The algorithm is based on the experimental data on moments and angular velocities of the rotating coaxial cylinders. The stability of the algorithm to errors in the initial data is estimated.     

Unsteady-state development of plane couette flow for viscoelastic fluids

Unsteady-state development of plane Couette flow for viscoelastic fluids is analyzed using a constitutive equation that can be obtained from molecular theory, in which the molecules are regarded as finitely extensible dumbbells. Typical features of the flow situation are as follows: (i) For a fluid with moderate elasticity, not only stress overshoot but also velocity overshoot are predicted. (ii) For suitable combinations of elasticity and gap width, and for some time intervals stress propagation and reflection phenomena are predicted. (iii) After a sufficient time has elapsed, the stress state behaves similarly to that corresponding to the start-up of a steady simple shear flow.