The two-fluid model has been extensively used in modeling boiling
flow of water, however, there are few equivalent studies of
boiling flow of cryogenic liquids. In the present study the
two-fluid model was implemented in the OpenFOAM source code by
incorporating closure correlations, which more adjustable for
cryogenic liquids. Then boiling flow of liquid nitrogen in a
vertical tube was numerically simulated using the modified basic
model. In order to include the boiling effect, several different
subroutines which model evaporation and condensation phenomena
were attached to the solver. Comparison with experimental data
shows that the modified model is satisfactorily improved in
accuracy. This study demonstrated that the following parameters
and models are important for accurate prediction: the bubble
diameter frequency departure, the bubble diameter distribution
and the active site nucleation density, among which, the active
site nucleation density has the most significant influence.

Numerical Simulation of Heat Transfer During Boiling Flow of Cryogenic Fluid in Vertical Tube

A numerical study of the Couette–Taylor–Poiseuille two-phase flow is presented in this work. The proposed mathematical model takes into account the nonstationarity and three-dimensionality of the process of medium motion and rotation of the surface of the inner cylinder, as well as surface tension and the action of gravity. The developed numerical technique was tested on the solution of the problem of Couette–Taylor single-phase flow, which is the limiting case of a two-phase flow, when the volume concentration of the gas phase is zero. Two regimes of a two-phase flow are obtained. At low Reynolds numbers, a stratified flow regime is observed. In the second regime of two-phase flow, the gas phase is localized along a helical line along the surface of the inner cylinder. It is shown that the dimensionless torque increases when the gas phase is added to the flow.

Numerical Simulation of Couette–Taylor–Poiseuille Two-Phase Flow

The problem of the viscous incompressible fluid flow between two
coaxial cylinders is considered in the case when the inner
cylinder is rotates and the outer cylinder is stationary. The
process of fluid flow is simulated by solving the
three-dimensional Navier–Stokes equations. The computational
algorithm is based on the finite volume method. The dependences of
the dimensionless viscous torque from the Reynolds number and the
radius ratio are established.

Numerical Simulation of Laminar Taylor–Couette Flow

In the paper flows of shock waves in multiphase media are described. Gas suspensions are considered as a multiphase medium—liquid drops or solid particles suspended in a gas. In this work, a continual approach in mathematical modeling of the dynamics of multiphase media is applied. The continual approach involves solving the complete hydrodynamic system of equations for each of the mixture components. The system of equations for the dynamics of each phase includes equation of continuity of density (average density for the dispersed phase), equations of conservation of momentum and energy. The carrier medium is described as a viscous, compressible heat-conducting gas. The mathematical model takes into account the velocity and thermal interaction of the phases of the mixture. The system of equations was solved by the MacCormack explicit finite-difference method of the second order of accuracy. To obtain a monotonic numerical solution, a nonlinear correction scheme was applied to the grid function. The influence of parameters of a disperse phase on speed and the shape of the reflected shockwave was numerically studied in the paper. Results of numerical calculations of the distribution of a shock wave from clean gas to a gas suspension, with the subsequent reflection from a firm surface, are given. Calculations allowed to establish that the intensity of a shock wave, reflected from a firm surface, in a gas suspension increases with a decrease of the number of dispersed particles. It is established that in polydisperse gas suspensions existence of fine fraction leads to an increase in the intensity of the reflected shock wave.

Numerical Modeling of the Shock Waves Reflection from a Firm Surface in Mono- and Polydisperse Gas Suspensions

Features of Swirling Flow in a Container with a Rotating Bottom

The results of numerical modeling of hydrodynamics and heat and mass transfer at boiling of subcooled liquids in conditions of forced flow in vertical heated pipes are presented. The mathematical model is based on the use of Euler’s description of mass, motion and energy conservation for liquid and gas phases, recorded within the framework of the theory of interacting continua. The turbulent characteristics of the fluid are calculated using a modified model of transfer of components of the Reynolds stress tensor, taking into account the presence of the gaseous phase in the medium. For an approximate calculation of the heat transfer coefficient for bubble boiling of a liquid near the heat-generating wall, generalized empirical dependences are used, taking into account the various mechanisms of heat transfer in a two-phase vapor-liquid medium. Comparison of the results of numerical modeling with experimental data has shown that the proposed approach allows to simulate bubble boiling modes in a wide range of pressure values, mass flow rates, heating modes of subcooled liquids during forced turbulent fluid flow in vertical pipes.

Numerical Simulations of Subcooled Boiling Flow in Vertical Pipe at High Pressure

Complex hydrodynamic behavior of circulating fluidized beds makes their scale-up very complicated. In particular, large-scale lateral solids segregation causes a complex two-phase flow pattern which influences significantly their performance. This article discusses the advanced hydrodynamic model developed for circulating fluidized beds based on the two-fluid concept. In this model, the kinetic theory of granular flows (KTGF) was used to solve gas–solids flow behavior. To model the influence of direct particle-particle collisions the kinetic theory for granular flow was applied based on the Chapman–Enskog theory of dense gases. For model validation purposes, a cold flow circulating fluidized bed was employed in which solid particles was transported with air as fluidizing agent. The validity of the presented model has been tested with experimental data and information available in the literature, for both gas–particle and liquid–particle systems.

Mathematical Modelling of Gas Flow with Heavy Solid Particles Based on Eulerian Approach

General two-dimensional models were derived and solved numerically for the thermoacoustical convection that is generated in a compressible fluid by rapid heating of one of the vertical enclosing walls. In the cases considered, the left wall temperature is raised rapidly (impulsively or gradually) while the right wall is held at a specified temperature. The top and the bottom walls of the considered enclosure are thermally insulated. The numerical solutions of the full Navier–Stokes equations were obtained by employing a highly accurate flux-corrected transport algorithm for the convection terms and by a central differencing scheme for the viscous and diffusive terms. It is numerically established that the magnitude of the power of pressure waves associated with the thermoacoustic effect, and the resulting flow pattern is strongly influenced by the difference in wall temperatures (values of overheating) and the speed of the wall heating process.

B. A. Snigerev

Papers

Numerical Simulation of Heat Transfer During Boiling Flow of Cryogenic Fluid in Vertical Tube

Numerical Simulations of Subcooled Boiling Flow in Vertical Pipe at High Pressure

Mathematical Modelling of Gas Flow with Heavy Solid Particles Based on Eulerian Approach

Numerical Study of Thermoacoustic Waves in a Cavity under Rapid Wall Heating