Bubble dynamics of a single condensing vapor bubble in a subcooled pool boiling system with a centrally heated cylindrical tank has been studied in the Rayleigh number range
Pool boiling is a complex nonlinear dynamic process. The microscopic aspects of boiling process, for example, embryo nucleation and surface roughness determine its nature largely. The microscopic effects eventually exhibit in a macroscopic behavior. Further, boiling is a highly stochastic process and the precise prediction of the location and time of the generation, collapse, coalescence is difficult with the present status of knowledge. The condensation of bubbles in subcooled boiling systems is extremely important for studying the hydrodynamics during subcooled pool boiling. The simple reason for this is that condensation changes the shape and size of the bubbles. When a bubble is formed at the interstitial site in the case of nucleate boiling the bubble grows to a certain diameter and then departs from the interstitial site. As the bubble departs from the nucleation site, it tends to slide along the hot surface and detaches from the surface. The bubble then does not necessarily follow a straight path but moves near or away from the wall. In addition to experimental investigations, Computational Fluid Dynamics (CFD) is useful to obtain better understanding of bubble dynamics.
Experimental investigations on dynamics of single vapor bubbles condensing in a subcooled boiling liquid have been carried out by Voloshko and Vurgaft [
The unavailability of data on the bubble dynamics in pool boiling systems is the main motivation of the current work. Further, the hydrodynamics of bubbles in subcooled boiling systems have been studied by bubbles being formed on a horizontal plate. The dynamics of bubbles on vertical tube are; however, different from the one on a horizontal plate. The flow generated due to heating of a vertical tube is different than the one on horizontal plate. Another important aspect is the Rayleigh numbers considered in this work. It may be noted that this range of Rayleigh numbers has not been investigated for subcooled pool boiling. The current work is an effort to develop a CFD model and validate the results with experiments.
The experimental setup is similar to the one used by Ganguli et al. [
(a) Schematic of a dimensionless rectangular enclosure with leftside wall heated. (b) Schematic of a vertical rectangular enclosure with leftside wall heated and a bubble patched at the interstice.
A digital video camera (Photron Fastcam 10KC, Resolution 512 × 480 pixels) together with halogen lamp (located at the opposite side of the camera) was used for taking pictures of the condensate films. All signals except video images were processed using the data acquisition system, consisting of A/D converter and a PC. The video images were analyzed by means of MATLAB software. All the instruments were calibrated before testing.
In this study, the VOF method [
The following assumptions were made for the study. Vapor (steam) and liquid (water) phases were considered as incompressible fluids. No internal mass source are assumed. Hence the source terms for liquid and vapor have been considered to be equal. Bubble generation and behavior is a stochastic phenomenon. Yet the bubble generation at the same interstitial site has been tracked for the single bubble analysis, and the effect of other bubbles on the single bubble has been neglected. The bubble on the tube surface slides on the surface vertically upward for some distance and lifts off. The shear due to the thermal boundary layer as soon as it is developed is assumed to be constant for the lifecycle of the bubble since very little change in velocity gradients occurs in 500 ms which is the maximum time period for any bubble to travel the vertical distance under consideration.
A two-phase model has been formulated in the Euler-Euler framework using VOF approach. The VOF model is a surface-tracking technique applied to a fixed Eulerian mesh. It is designed for two or more immiscible fluids where the position of the interface between the fluids is of interest. In the VOF model, the fluids share a single set of momentum equations and the volume fraction of each of the fluids in each computational cell is tracked throughout the domain. The field for all variables and properties is shared by the phases and represent volume-averaged values, as long as the volume fraction of each of the phases is known at each location. In each control volume the volume fractions of all the phases sum up to unity. Thus the variables and properties in any given cell are either purely representative of one of the phase, or representative of a mixture of the phases depending upon the volume fraction values. In other words, if the
Based on the local value of
The term on the right-hand side of (
The terms on the right-hand side of (
Further, the properties appearing in the transport equations are determined by the presence of the component phase in each control volume. In the present vapor-liquid system the volume fraction of the liquid is being tracked, the density and viscosity in each cell are given by (
A single set of Navier-Strokes equation for an incompressible Newtonian flow was solved.
Momentum equation is given below:
The CSF model of Brackbill et al. [
The geometric reconstruction scheme [
A model for phase change in the present study has been used to simulate the condensation phenomena, which describes the interphase heat transfer of intrinsic flows and considers the heat transfer processes on each side of the phase interface. Therefore, the mass exchange source terms in mass equations and latent heat transfer term in energy equation have been incorporated in the modeled equation through UDF. At the liquid-vapor interface, the temperature should be equal to the saturation temperature.
Heat content on vapor side across the interface is given by:
Similarly, the Heat Flux on the Liquid Side across the Interface is Given by:
The total mass transfer rate is the sum of each cell's mass transfer rate in the interface region. Let
The heat liberated due to condensation can also be expressed as:
From (
Turbulent kinetic energy is
The spatial derivatives in (
A 2D rectangular solution domain (
Sample grid of two dimensional (2D) cylindrical tank with left-hand wall heated.
The effect of time step on bubble size was investigated by performing the simulations with four different time steps (
In the present section we present the results of bubble movement and the lift force exerted on the bubble when a specific amount of heat input is provided. The present simulations have been provided after 60 seconds of run when the first bubble appears as per experimental observations. Rayleigh number (Ra) has been varied in the range
The grid used for the simulations is shown in Figure
Variation of axial velocity with dimensionless radial distance for various grid sizes. (a)
Figure
Axial velocity
In the case of subcooled boiling the effect of heat flux on the bubble diameter for a single bubble has been carried out in the present work. Figure
Variation of bubble diameter and maximum radial distance of bubble from the wall with Rayleigh number. ■ radial distance from the wall ♦ bubble diameter.
Velocity vectors showing the movement of the bulk fluid due to bubble movement.
Comparison of bubble movement with high-speed photography and VOF simulations. (a) Ra
Movement of the single bubble has been tracked both with the help of high-speed camera (125 frames/s) and 2D CFD simulations. For different heat inputs (
Dimensionless vertical distance
Bubble dynamics in subcooled pool boiling systems have been evaluated for (
Equivalent bubble diameter, mm
Total energy supplied to the system, kJ
Energy of fluid, kJ
Force because of the pressure jump at the interface, N
Gravitational constant, m
Generation of turbulence due to buoyancy,
Generation of turbulent kinetic energy due to mean velocity gradients (kg·
Column height, mm
Specific enthalpy as in energy equation in (
Identity matrix, (—)
Turbulent kinetic energy as in (
Thermal conductivity, W
Effective thermal conductivity, W
Thermal conductivity of liquid, W/mK
Thermal conductivity of vapor, W/m K
Total mass flow rate of steam, kg/s
Mass flow rate at the
Surface normal vector, (—)
Unit normal vector, (—)
Total pressure, Pa
Time averaged of total pressure, Pa
Condensation heat flux in (
Liquid heat flux across the interface, W/
Vapor heat flux across the interface, W/
Radius of the tank, m
Spatial co-ordinate in radial direction
Mass source in liquid phase, kW/
Mass source in qth phase, kW/
Mass source in vapor phase, kW/
Source term for energy equation, kg
Strain term in three spatial co-ordinates, N
Strain term, N
overall averaged strain term, N
Average of strain terms in two spatial co-ordinates, N
Time, s
Temperature, K
Time averaged value of temperature, K
Velocity vector, m/s
Time average of velocity, m/s
Volume of each cell,
Dissipation of turbulent kinetic energy in
Dissipation of turbulent kinetic energy in
Space co-ordinate in axial direction.
Constant used in (
Is constant used in
Constant
Effective viscosity, kg/ms
Constant
Latent heat of condensation for qth phase, kJ/kg
Volume fraction
Volume fraction of fluid, (—)
Volume fraction of fluid at jth cell, (—)
Volume fraction of the liquid phase, (—)
Surface curvature
Latent heat of condensation kJ/kg
Term used to calculation of shear stress component
Molecular viscosity, kg
Viscosity of liquid, kg/ms
Viscosity of vapor, kg/ms
Specific dissipation rate,
Density, kg
Density of liquid, kg/
Density of fluid, kg/
Density of vapour, kg/
Kinematics viscosity,
Turbulent viscosity,
Surface tension, N/m
Turbulent Prandtl number, (—)
Turbulent Prandtl number for kinetic energy equation, (—)
Shear stress, N
Averaged shear stress component, N/
Constant used in (
Effective
Axis indexes of spatial co-ordinates
Liquid
Phase
Vapor
Cylindrical space coordinate for radial direction
Turbulent
Cylindrical space coordinate for axial direction.