Mathematical modeling of dispersed media flows in the presence of nucleation, coagulation and phase transitions

2021 ◽  
Vol 102 (2) ◽  
pp. 14-24
Author(s):  
T.R. Amanbaev ◽  
◽  
G.E. Tilleuov ◽  
A. Zuparbekova ◽  
◽  
...  
Keyword(s):  
Phase Transitions ◽  
Saturation Temperature ◽  
Dimensional Model ◽  
Two Phase ◽  
One Dimensional ◽  
Dispersed Medium ◽  
Nucleation Model ◽  
Coagulation Equation ◽  
Media Flows ◽  
Vapor Temperature

A model of motion of a gas-dispersed medium in the presence of processes of nucleation, coagulation and phase transitions has been constructed. A homogeneous nucleation model is used to describe the nucleation process. It is believed that the process of cluster coagulation occurs due to their Brownian motion. The analysis of the solution of the coagulation equation in the particular case of monodisperse clusters in the presence of a source and sink of particles is carried out. To determine the rate of phase transitions the Hertz-KnudsenLangmuir formula is used. The calculations were carried out on the basis of a quasi-one-dimensional model within the equilibrium approximation (when the velocities and temperatures of the phases coincide). As a result of the study the main properties of the flow of a two-phase mixture in a channel in the presence of nucleation, coagulation, and phase transformations have been established. It is shown that the vapor temperature increases along the channel and reaches the saturation temperature at some distance from the channel entrance. Calculations have shown that the coagulation process has a rather strong effect on the distribution of cluster sizes along the channel.

One Dimensional Model for Rotating Channels in the Turbine System: Part 2 — Formulation and Validation for Film Condensation

2013 ◽  
Author(s):  
Murali Krishnan R. ◽  
Zain Dweik ◽  
Deoras Prabhudharwadkar
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Steam Turbine ◽  
Compressible Flow ◽  
Saturation Temperature ◽  
Film Condensation ◽  
Bulk Temperature ◽  
Dimensional Model ◽  
One Dimensional

This paper provides an extension of the previously described [1] formulation of a one-dimensional model for steady, compressible flow inside a channel, to the steam turbine application. The major challenge faced in the network simulation of the steam turbine secondary system is the prediction of the condensation that occurs during the engine start-up on the cold parts that are below the saturation temperature. Neglecting condensation effects may result in large errors in the engine temperatures since they are calculated based on the boundary conditions (heat transfer coefficient and bulk temperature) which depend on the solution of the network analysis. This paper provides a detailed formulation of a one-dimensional model for steady, compressible flow inside a channel which is based on the solution of two equations for a coupled system of mass, momentum and energy equations with wall condensation. The model also accounts for channel area variation, inclination with respect to the engine axis, rotation, wall friction and external heating. The formulation was first validated against existing 1D correlation for an idealized case. The wall condensation is modeled using the best-suited film condensation models for pressure and heat transfer coefficient available in the literature and has been validated against the experimental data with satisfactory predictions.

Numerical Simulation of Heat Transfer in a Closed Two-Phase Thermosiphon

2017 ◽  
Vol 743 ◽  
pp. 449-453
Author(s):  
Vladimir Arkhipov ◽  
Alexander Nee ◽  
Lily Valieva
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Phase Transitions ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Mathematical Modelling ◽  
Three Dimensional ◽  
Two Phase ◽  
One Dimensional ◽  
The Finite Difference Method

This paper presents the results of mathematical modelling of three–dimensional heat transfer in a closed two-phase thermosyphon taking into account phase transitions. Three-dimensional conduction equation was solved by means of the finite difference method (FDM). Locally one-dimensional scheme of Samarskiy was used to approximate the differential equations. The effect of the thermosyphon height and temperature of its bottom lid on the temperature difference in the vapor section was shown.

Structural phase transitions coupled with prominent dielectric anomalies and dielectric relaxation in a one-dimensional organic–inorganic hybrid compound [C3H4NS][CdCl3]

2015 ◽  
Vol 3 (33) ◽  
pp. 8535-8541 ◽  
Author(s):  
Guang-Quan Mei ◽  
Wei-Qiang Liao
Keyword(s):  
Phase Transitions ◽  
Dielectric Relaxation ◽  
Structural Phase ◽  
Structural Phase Transitions ◽  
Two Phase ◽  
Hybrid Compound ◽  
Inorganic Hybrid ◽  
One Dimensional

A one-dimensional organic–inorganic hybrid exhibits two phase transitions at 288 and 215 K, coupled with remarkable dielectric performances.

scholarly journals Calculation of Two-Phase Dispersed Droplet-In-Vapor Flows Including Normal Shock Waves

1978 ◽  
Vol 100 (3) ◽  
pp. 355-362 ◽  
Author(s):  
W. J. Comfort ◽  
T. W. Alger ◽  
W. H. Giedt ◽  
C. T. Crowe
Keyword(s):  
Shock Waves ◽  
Normal Shock ◽  
Vapor Flow ◽  
Dimensional Model ◽  
Two Phase ◽  
One Dimensional ◽  
Pressure Profiles ◽  
Pressure Equilibrium ◽  
Temperature And Pressure ◽  
Measured Pressure

A method for calculating quasi-one-dimensional, steady-state, two-phase dispersed droplet-in-vapor flow has been developed. The technique is applicable to both subsonic and supersonic single component flow in which normal shock waves may occur, and is the basis for a two-dimensional model. The flow is assumed to be inviscid except for droplet drag. Temperature and pressure equilibrium between phases is assumed, although this is not a requirement of the technique. Example calculations of flow in one-dimensional nozzles with and without normal shocks are given and compared with experimentally measured pressure profiles for both low quality and high quality two-phase steam-water flow.

Effects of interphase boundaries in Ginzburg–Landau one-dimensional model of two-phase states in clamped systems

2021 ◽  
Vol 129 (4) ◽  
pp. 044102
Author(s):  
Arkady P. Levanyuk ◽  
Sergey A. Minyukov ◽  
I. Burc Misirlioglu ◽  
M. Baris Okatan
Keyword(s):  
Dimensional Model ◽  
Two Phase ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Interphase Boundaries
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