Vijay K. Dhir

Effect of Surface Wettability on Active Nucleation Site Density During Pool Boiling of Water on a Vertical Surface

Pool boiling of saturated water at 1 atm pressure has been investigated. In the experiments, copper surfaces prepared by following a well-defined procedure were used. The cumulative number density of the cavities and their shapes were determined with an optical microscope. The surface had a mirror finish and had a surface Ra (centerline average) value of less than 0.02 μm. The wettability of the surface was changed by controlling the degree of oxidation of the surface. In the experiments with the primary surface, the wall heat flux and superheat were determined with the help of thermocouples embedded in the test block. The density, spatial distribution, local distribution, and nearest-neighbor distance distribution of active nucleation sites in partial and fully developed nucleate boiling were determined from still pictures.

Heat transfer and pressure drop in narrow rectangular channels

Recently, with the advent of more powerful electronic chips and the miniaturization of electronic circuits and other compact systems, a great demand exists for developing efficient heat removal techniques to accommodate these high heat fluxes. With this objective in mind, both single-phase forced convection and subcooled and saturated nucleate boiling experiments have been performed in small rectangular channels using FC-84 as test fluid. The test section used in these experiments consisted of five parallel channels with each channel having the following dimensions: hydraulic diameter (Dh)=0.75 mm and length to diameter ratio (L/Dh)=409.8. The experiments were performed with the channels oriented horizontally and uniform heat fluxes applied at the top and bottom surfaces. The parameters that were varied during the experiments included the mass flow rate, inlet liquid subcooling, and heat flux. In each of the experiments conducted, the temperature of both the liquid and the wall were measured at various locations along the flow direction. Based on the measured temperatures, pressure drops, and the overall energy balance across the test section, the heat transfer coefficients for both single-phase forced convection and flow boiling has been calculated. Additionally, in these experiments, the single- and two-phase pressure drop across the channels was also measured. A correlation has been developed for two-phase flow pressure drop under subcooled and saturated nucleate boiling conditions. Furthermore, two new correlations are proposed – one for subcooled flow boiling heat transfer and the other for saturated flow boiling heat transfer.

Numerical Simulation of Film Boiling Near Critical Pressures With a Level Set Method

Attempts have recently been made to numerically simulate film boiling on a horizontal surface. It has been observed from experiments and numerical simulations that during film boiling the bubbles are released alternatively at the nodes and antinodes of a Taylor wave. Near the critical state, however, hydrodynamic transition in bubble release pattern has been reported in the literature. The purpose of this work is to understand the mechanism of the transition in bubble release pattern through complete numerical simulation of the evolution of the vapor-liquid interface. The interface is captured by a level set method which is modified to include the liquid-vapor phase change effect. It is found from the numerical simulation that at low wall superheats the interface moves upwards, bubbles break off, and the interface drops down alternatively at the nodes and antinodes. However, with an increase in wall superheat, stable vapor jets are formed on both the nodes and antinodes and bubbles are released from the top of the vapor columns. The numerical results are compared with the experimental data, and visual observations reported in the literature are found to be in good agreement with the data.

Onset of Nucleate Boiling and Active Nucleation Site Density During Subcooled Flow Boiling

The partitioning of the heat flux supplied at the wall is one of the key issues that needs to be resolved if one is to model subcooled flow boiling accurately. The first step in studying wall heat flux partitioning is to account for the various heat transfer mechanisms involved and to know the location at which the onset of nucleate boiling (ONB) occurs. Active nucleation site density data is required to account for the energy carried away by the bubbles departing from the wall. Subcooled flow boiling experiments were conducted using a flat plate copper surface and a nine-rod (zircalloy-4) bundle. The location of ONB during the experiments was determined from visual observations as well as from the thermocouple output. From the data obtained it is found that the heat flux and wall superheat required for inception are dependent on flow rate, liquid subcooling, and contact angle. The existing correlations for ONB underpredict the wall superheat at ONB in most cases. A correlation for predicting the wall superheat and wall heat flux at ONB has been developed from the data obtained in this study and that reported in the literature. Experimental data are within630 percent of that predicted from the correlation. Active nucleation site density was determined by manually counting the individual sites in pictures obtained using a CCD camera. Correlations for nucleation site density, which are independent of flow rate and liquid subcooling, but dependent on contact angle have been developed for two ranges of wall superheat—one below 15°C and another above 15°C. @DOI: 10.1115/1.1471522#

Framework for a Unified Model for Nucleate and Transition Pool Boiling

An area and time-averaged model for saturated pool boiling heat fluxes has been developed. In the model, which is valid in the upper end of nucleate boiling and in transition boiling, the existence of stationary vapor stems at the wall is assumed. The energy from the wall is conducted into the liquid macro/micro thermal layer surrounding the stems and is utilized in evaporation at the stationary liquid-vapor interface. The heat transfer rate into the thermal layer and the temperature distribution in it are determined by solving a two-dimensional steady-state conduction equation. The evaporation rate is given by the kinetic theory. The heater surface area over which the vapor stems exist is taken to be dry. Employing experimentally observed void fractions, not only the nucleate and transition boiling heat fluxes but also the maximum and minimum heat fluxes are predicted from the model. The maximum heat fluxes obtained from the model are valid only for surfaces that are not well wetted and includes the contact angle as one of the parameters.

Mechanistic Prediction of Nucleate Boiling Heat Transfer–Achievable or a Hopeless Task?

Over the last half of the twentieth century, a number of purely empirical and mechanism-based correlations have been developed for pool nucleate boiling. Empirical correlations differ from each other substantially with respect to the functional dependence of heat flux on fluid and surface properties, including gravity. The mechanism-based correlations require knowledge of the number density of active sites, bubble diameter at departure, and bubble-release frequency. However, because of the complex nature of the subprocesses involved, it has not been possible to develop comprehensive models or correlations for these parameters. This, in turn, has led to the pessimistic view that mechanistic prediction of nucleate boiling is a hopeless task. However, there is an alternative to the past approaches¯complete numerical simulation of the boiling process. Value of this approach for bubble dynamics and associated heat transfer is shown through excellent agreement of predictions with data obtained on microfabricated surfaces on which active nucleation sites can be controlled.

Wall Heat Flux Partitioning During Subcooled Flow Boiling: Part 1—Model Development

In this work a mechanistic model has been developed for the wall heat flux partitioning during subcooled flow boiling. The premise of the proposed model is that the entire energy from the wall is first transferred to the superheated liquid layer adjacent to the wall. A fraction of this energy is then utilized for vapor generation, while the rest of the energy is utilized for sensible heating of the bulk liquid. The contribution of each of the mechanisms for transfer of heat to the liquid—forced convection and transient conduction, as well as the energy transport associated with vapor generation has been quantified in terms of nucleation site densities, bubble departure and lift-off diameters, bubble release frequency, flow parameters like velocity, inlet subcooling, wall superheat, and fluid and surface properties including system pressure. To support the model development, subcooled flow boiling experiments were conducted at pressures of 1.03 ‐3.2 bar for a wide range of mass fluxes ~124‐926 kg/m 2 s!, heat fluxes ~2.5‐90 W/cm 2 ! and for contact angles varying from 30° to 90°. The model developed shows that the transient conduction component can become the dominant mode of heat transfer at very high superheats and, hence, velocity does not have much effect at high superheats. This is particularly true when boiling approaches fully developed nucleate boiling. Also, the model developed allows prediction of the wall superheat as a function of the applied heat flux or axial distance along the flow direction. @DOI: 10.1115/1.1842784#

Study of lateral merger of vapor bubbles during nucleate pool boiling

The bubble dynamics and heat transfer associated with lateral bubble merger during transition from partial to fully developed nucleate boiling is studied numerically. Complete Navier-Stokes equation in three dimensions along with the continuity and energy equations are solved using the SIMPLE method. The liquid vapor interface is captured using the Level-Set technique. Calculations are carried out for multiple bubble mergers in a line and also in a plane and the bubble dynamics and wall heat transfer are compared to that for a single bubble

Shape of a Vapor Stem During Nucleate Boiling of Saturated Liquids

The transport processes occurring in an evaporating two-dimensional vapor stem formed during saturated nucleate boiling on a heated surface are modeled and analyzed numerically. From the heater surface heat is conducted into the liquid macro/microthermal layer surrounding the vapor stems and is utilized in evaporation at the stationary liquid-vapor interface. A balance between forces due to curvature of the interface, disjoining pressure, hydrostatic head, and liquid drag determines the shape of the interface. The kinetic theory and the extended Clausius-Clapeyron equation are used to calculate the evaporative heat flux across the liquid-vapor interface. The vapor stem shape calculated by solving a fourth-order nonlinear ordinary differential equation resembles a cup with a flat bottom. For a given wall superheat, several metastable states of the vapor stem between a minimum and maximum diameter are found to be possible. The effect of wall superheat on the shape of the vapor stem is parametrically analyzed and compared with limited data reported in the literature.

A hydrodynamic model for two-phase flow through porous media

Abstract A hydrodynamic model has been developed to predict void fraction and pressure gradient for one-dimensional two-phase flow through porous media. The model includes discussion of flow regimes and their relationship with flow and porous layer configurations. The particle-gas drag, particle-liquid drag and liquid-gas interfacial drag are then evaluated theoretically from the flow configuration associated with each flow regime. The above drag models are then employed in conjunction with force balances on the two phases to obtain the void fraction and pressure gradient as functions of liquid and gas superficial velocities. Results are found to agree very favorably with existing experimental data obtained in both co-current and counter-current flow conditions. It has also been found that this hydrodynamic model is capable of fully describing essential features of the flooding phenomenon observed in counter-current flow of immiscible fluids. Furthermore, counter-current flooding limits predicted using this hydrodynamic model are found to agree well with existing correlations in the literature. Seemingly conflicting experimental observations reported by various authors on the behavior of void fractions and pressure drops near the flooding limit can also be resolved by the present model.