Subcooled Region Research Articles

A phenomenological model for boiling heat transfer and the critical heat flux in tubes containing twisted tapes

New critical heat flux (CHF) and boiling heat transfer data were obtained in the subcooled and low quality regions using refrigerant 113. These data were obtained in a 0.61 cm round tube containing a twisted tape having a twist ratio of 6.25. The new CHF data, plus water data from the literature, were compared to a modified version of the CHF predictive model based on bubble crowding and coalescence in the bubbly layer [Weisman and Pei, Int. J. Heat Mass Transfer26, 1463–1478 (1983), Weisman and Illeslamlou, Fusion Tech.13, 654—659 (1988)]. Reasonably good predictions were obtained within the range of the model. It was also found that the Yang and Weisman [Int. J. Multiphase Flow17, 77–94 (1991)] extension of the CHF model to boiling heat transfer held for swirling flow.

Experimental and Analytical Evaluations on Critical Heat Flux Under One Sided Heating Condition for Fusion Applications

AbstractIt is one of key issues to predict a critical heat flux (CHF) with the highly subcooled flow boiling and the CHF margin for the promising design of plasma facing components for the next generation fusion machines such as an International Thermonuclear Experimental Reactor and a Fusion Experimental Reactor. In particular, divertor plate is subjected to severe heat loads under a condition for one side heating. Because of no correlations predicting CHF for the highly subcooled flow region with heating on one side of the divertor plate, experimental data which were obtained under one sided heating condition have been evaluated by various existing CHF correlations which are based on a condition for uniform circumferential heating. As results, experimental CHF data of the straight tube are relatively good agreement with some correlations within an accuracy of −20 to +10 %, but no correlations are available in the CHF prediction of the externally-finned tube. Further experiments are necessary to evaluate...

Melting of ice in a porous medium heated from below

A numerical study is made of the melting of ice heated from below in a cavity filled with a porous medium, using the time-dependent form of the governing equations. The natural convection in the liquid phase, the conduction in the subcooled ice region, and the effect of density inversion of water are incorporated into the numerical simulation. The primary characteristics of the melting process, i.e. the onset of convection, the flow pattern in the melt, the heat transfer rate, and the interface position, are studied in terms of the Rayleigh number, the Stefan number, the aspect ratio of the cavity, and the density inversion of water. Principal findings indicate that the initial cellular pattern formed just after the onset of convection passes through several intermediate forms in its transition to a final steady state. Each change in the convection pattern is accompanied by a sudden increase in the heat transfer rate and in the displacement velocity of the solid-liquid interface. A local maximum in the heat transfer rate is exhibited shortly after the establishment of the new convection pattern.

Density-wave oscillations in parallel channels - an analytical approach

Density wave oscillations in parallel channel systems are analytically investigated. A new model is presented, from which explicit expressions are obtained for the stability limits and periods of oscillation of a two-identical channel system. The two modes correspond to the channels oscillating in-phase or out-of-phase, in both cases with the same amplitude. A two-channel system with a power skew is then analyzed with two different approaches. In the first approach a pertubative methods is used, which shows that the normal modes are no longer the in-phase and out-of-phase ones. In the second approach of a fourth order eigenvalue problem is solved with a computer. For different power skews the stability thresholds, amplitude ration and phase difference between the oscillations of the variables of the two channels and the periods of oscillation are obtained. It is also shown that larger power skews make the system more unstable, except in the very low inlet subcooling region.

Simple functions for the fast approximation of light water thermodynamic properties

Thermalhydraulic systems analysis and simulation requires the fast and accurate generation of light water thermodynamic properties. An approach suggested in the past is the use of simple, non-linear functions to give approximations to the properties. Such functions have been developed and are presented here. The range of use is from 0.085 MPa to 21.3 MPa, and from 90°C to 450°C. In the subcooled and superheated regions the error for enthalpy, entropy and specific volume is usually much less than 1%. This error is based on comparisons to the latest internationally accepted formulation for the thermophysical properties of steam and water. These simple analytic functions provide an alternative to the use of linear interpolation algorithms and complex transcendental equations to generate light water thermodynamic properties. They are well suited to be made into computer subprograms, yet they are simple enough to be used with programmable calculators.

A Semianalytic Method for the Solution of the Steady-State Steam Generator Equations

A model was developed for steady-state steam generator analysis for purposes of continuous on-line data validation, plant state verification, and fault identification. The basic features of this model are as follows: 1. The water (steam) temperature in the subcooled and superheated regions is written as a quadratic function of enthalpy and the system equations are solved analytically. 2. The same equations are also solved analytically in the nucleate and film boiling regions. 3. The departure from nucleate boiling quality is determined from the iterative solution of a transcendental equation. These features allow the use of large nodes in each region and the direct determination of the region boundaries. Applications to typical steam generator problems showed computation times of 0.025 s. The analysis of four Energy Technology Engineering Center experiments showed very good agreement between model predictions and measurements.

Critical heat flux in narrow tubes under uniform heating condition. Experimental data at near zero qualities.

The critical heat flux in narrow tubes with 1-3 mm inside diameter was investigated for the exit equilibrium qualities from subcooled to quality regions using water at ambient pressure. In the subcooled region, critical heat flux increased with the decrease of the tube inside diameter, and in the quality region, vice versa. Further, the critical heat flux for the 2 and 3 mm inside diameter tubes was confirmed to increase with the increase of qualities in the near zero quality region. This means the existence of a minimum in the critical heat flux in the region. These characteristics were explained qualitatively with the difference of the mechanisms of the critical heat flux between subcooled and quality regions.

Flow instabilities in a natural circulation bailing channel. 3rd report Validity of homogeneous flow model for instability analysis.

The main purpose of this paper is to examine the validity of a homogeneous flow model to predict the onset of the density-wave oscillation in a natural circulation boiling channel. Seven different homogeneous flow models are tested. The major differences among them relate to how to treat the heat capacity in the subcooling region and the frictional coefficient. The analytical results obtained by these models are compared with the experimental data. As a result, it was made clear that the best model is the one considering the effect of the heat capacity in the subcooling region up to the subcooled boiling boundary and ignoring the transient changes of the frictional coefficient.

A heat transfer model for volumetrically heated nuclear debris beds

The thermal response of a fixed porous volumetrically heated debris bed is analyzed. The Modified Dispersion-Concentric Model (D-C model) is used in the analysis of forced flow cooling through a volumetrically heated fixed porous debris bed. The fundamental equations are based on the assumptions of dispersed plug flow and concentric intra-particle temperature profiles. The model is theoretically sound provided that a large axial effective fluid thermal dispersion coefficient is assumed. The fundamental equations are rather simple and can be easily solved in terms of temperature profiles for the solid and fluid phases. The theoretical model for the temperature profile for the fluid phase in the subcooled liquid region and in the superheated vapor region compares well with existing experimental measurements.

Remarks on the choice of a stiff ordinary differential equation solver

This paper discusses several aspects of the solution of fluid-flow problems. A model problem is described which captures several of the salient characteristics of such problems. The model problem is derived from the one-dimensional Euler equations. It corresponds to the subcooled liquid region of a three-region reactor steam-generator model. The defining partial differential equations are discretized spatially using the method of pseudo-characteristics. The resulting system of ordinary differential equations (ODEs) is then solved by the method of lines using each of several available ODE solvers. In addition to demonstrating that fluid-flow problems can be solved effectively using adaptive mathematical software, the results also illustrate the typical performance of each solver as well as the relative merits of special solver features (e.g. automatic method switching and exploitation of problem sparsity or bandedness). The model problem is also modified and used to illustrate several commonly observed characteristics of fluid-flow models. The results illustrate the potential effect on solver performance of characteristics such as inaccurate water property calculations. Consequently, they explain apparent anomalies often attributed incorrectly to poor solver design and algorithmic implementation. The results also support the choice of the sparse ODE solver LSODES for the solution of fluid-flow problems.

Validity of homogeneous flow model for instability analysis

The main objective of this paper is to present the validity of using a homogeneous flow model which predicts density-wave oscillation of water in a natural-circulation boiling-fluid channel. The seven different homogeneous flow models presented here are all based on linearized approximation, and the transient responses of the pressure drop as to the inlet flow rate are calculated by the Laplace transformation technique. The major differences between these seven models are in their heat capacities in the subcooling region and in their frictional coefficients. The test results using the analytical models are then compared with the data obtained from two different apparatuses: one apparatus is for the data in the region up to 2.94 MPa of pressure, and a second larger apparatus in the region up to 11.8 MPa of pressure. Furthermore, they are evaluated with some other authors' work to make the generalization. The model which best predicts the onset of oscillation is finally selected by carefully comparing the results of these comparisons.

Critical Heat Flux on a Horizontal Cylinder in an Upward Subcooled and Low-Quality Two-Phase Crossflow

An experimental investigation has been conducted to determine the low-velocity critical heat flux (CHF) behavior on a single horizontal tube in a subcooled and low-quality two-phase crossflow of R-113. Data were obtained over a range of velocities (up to 0.3 m/s), subcooling (0 to 14 K), and qualities (0 < x < +30 percent) at two pressures. There was a linear decrease in the CHF with increasing quality up to about 10 percent quality; then, due to a flow regime transition, the CHF remained relatively constant. A correlation has been developed which predicted well the subcooled and low-quality region CHF condition in the linearly decreasing portion of the curve. Data from the literature are also predicted well.

A FOUR-PARAMETER EXTENSION OF MODIFIED LEE-KESLER EQUATION OF STATE

A modified Lee-Kesler equation of state has been proposed to improve the accuracy for the subcooled and saturated liquid regions of normal fluids. It is further extended to polar fluids by the addition of a fourth parameter X. The extended equation has been found to be reliable over a wide vapor and liquid regions for polar fluids and it is easy for computer use. Fourteen kinds of normal fluids and twelve kinds of polar fluids have been tested. The total average absolute deviations for the normal fluids and polar fluids are 0.79% and 1.68% over the range of Tr = 0.3 to 4 and Pr - 0.01 to 10.

Structure of water in solutions in the subcooled region from freezing-point depressions

Hydrogen-bond structural temperatures were estimated for water in solutions of NaCl, Na2SO4, MgCl2 and MgSO4 for a wide concentration range and down to –21 °C. These temperatures are proportional to the molality, the constant of proportionality being a function of the intrinsic volumes and the charges of the ions. The differences in the volumes and entropies of ice and water in the solutions have been calculated and a constant-volume entropy identified. This entropy is a linear function of the solute concentration and has a value around 0.15 J g–1 K–1 at zero concentration. Possible origins of this entropy for pure water are considered.

Thermodynamic properties of water in the subcooled region. I

An equation is derived for the free energy difference between water and ice in the subcooled (supercooled) region. The calculated vapor pressure difference between ice and water agrees well with experimental measurements. The free energy difference estimated for water in the form of emulsion droplets and bulk water, although small varies significantly with temperature in the subcooled region and is shown to be proportional to the excess free energy arising from the surface effects inherent to the emulsion systems. The accuracy of emulsion data at temperatures below −20 °C therefore could be much lower than previously assumed. In turn this would distort the anomaly functions and give incorrect critical temperature estimates.

Thermodynamic properties of water in the subcooled region. II

The surface effect in fine capillaries is considered and an analysis made of the volumetric properties of water in the subcooled region, using emulsion, capillary, and bulk specific volume (v) data. The analysis indicates that the emulsion values of v are probably too large below 253 K and consequently the expansivity (α) values are too large numerically. Compressibility, heat capacity, and ultrasonic and refractive index data are used to estimate the expansivity in the subcooled region. All these data support conclusions from the analysis of v. Below 250 K the Cp/Cv ratios from emulsion data are much larger than those from ultrasonic data and those estimated from a variety of other data. The overall conclusion (from parts I and II) is that the question concerning the accuracy of emulsion data below 253 K must remain open at present.

An investigation of critical heat flux and surface rewet in flow boiling systems

A high thermal capacity copper test section placed at the end of a heating tube is used for investigating the critical heat flux and heat transfer characteristics during rewetting process for Freon-113 upward flow at mass velocities of 357, 627, 1035 and 1465 kg m −2 s −1. The critical heat flux coincides well with the maximum heat flux obtained by the transient cooling test. The wall superheat at the onset of rewetting changes greatly with the inlet quality, and ranges from 120 to 140°C in the subcooled and low quality region and from 60 to 80°C in the high quality region.

Critical heat flux in helical coils with a circumferential heat flux tilt toward the outside surface

A study of the forced-convection boiling of R-113 in electrically heated coils with a substantial heat flux tilt toward the outside of the coils is reported. The circumferentially local subcooled critical heat flux (CHF) with a flux tilt is increased or decreased, when compared to a coil without a flux tilt at the same bulk fluid condition, depending on the relative magnitudes of the flux tilt, mass velocity and ratio of tube diameter to coil diameter ( d/ D). Generally, there are increases in the local CHF with decreasing mass velocity and d/ D and with increasing flux tilt. The quality region CHF in a coil with a flux tilt is lower than the CHF in a coil without a flux tilt. The subcooled and quality region CHF condition (when unaffected by buoyancy) occurs at the inside surface of the coil and not at the location of highest heat flux. Operational problems, in particular upstream CHF conditions, may occur if a coiled tube is operated with low to moderate subcooling near the inlet and with moderately high heat fluxes.

Prediction Method of Flow Patterns in Subcooled and Low Quality Boiling Regions

A new parameter is proposed for prediction of the transition between flow patterns such as bubble, froth and annular flow, in both the subcooled and low quality regions of boiling flow. This parameter is derived from the theoretical calculation method of void fraction, which has been reported, on the assumption that the flow pattern transition occurs at a value of average void fraction over the cross section of the flow. A flow map is also presented which reasonably correlates the experimental results covering the following conditions ; pressure : 1∼98 ata, heat flux : 2×104∼5×106kcal/m2h, and mass velocity : 40∼5400kg/m2s.

A closed periodic condensation-evaporation cycle of an immiscible, gravity driven bubble

A closed periodic condensation-evaporation cycle of a two-phase vapour-liquid ‘bubble’ driven by gravity in an immiscible continuous phase with a vertical temperature profile is presented. The vertical column can also consist of two stratified layers of two different fluids of similar densities maintained at different temperatures. The cyclic motion of the bubble is due to latent heat transport and the ensuing differences in the relative densities. The immiscible liquid drop evaporates in a hot zone at the bottom, accelerates by buoyancy upward, reaches a subcooled region and reliquifies. Its motion is then reversed, with the heavier drop falling back toward the hot region. The characteristics of a Freon bubble-drop moving in water at various operating conditions are presented for transient and steady operations.