Peter Griffith

The mechanism of heat transfer in nucleate pool boiling—Part I: Bubble initiaton, growth and departure

Abstract A criterion is developed for bubble initiation from a gas filled cavity on a surface in contact with a superheated layer of liquid. It is found that the temperature of bubble initiation on a given surface is a function of the temperature conditions in the liquid surrounding the cavity as well as the surface properties themselves. It is also found that the delay time between bubbles is a function of the bulk liquid temperature and the wall superheat, and is not constant for a given surface. By consideration of the transient conduction into a layer of liquid on the surface, a thermal layer thickness is obtained. With this thickness and a critical wall superheat relation for the cavity, a bubble growth rate is obtained. Bubble departure is considered and it is found that the Jakob and Fritz relation works as long as the true (non-equilibrium) bubble contact angle is used. At one gravity the primary effect of bubble growth velocity on bubble departure size is found to be due to contact angle changes.

On bubble growth rates

A simple general relation for bubble growth rates in a uniformly superheated liquid was derived. The relation is valid in both regions: inertia controlled and heat diffusion controlled growth, respectively. The derived relation is compared with the existing experimental results for bubble growth in a uniformly superheated liquid with very good agreement. The results are further extended to the bubble growth in a non-uniform temperature field which approximates the conditions present in a nucleate boiling from a heated surface.Abstract A simple general relation for bubble growth rates in a uniformly superheated liquid was derived. The relation is valid in both regions: inertia controlled and heat diffusion controlled growth, respectively. The derived relation is compared with the existing experimental results for bubble growth in a uniformly superheated liquid with very good agreement. The results are further extended to the bubble growth in a non-uniform temperature field which approximates the conditions present in a nucleate boiling from a heated surface.

Boiling and Evaporation in Small Diameter Channels

Since the 1950s, the research and industrial communities have developed a body of experimental data and set of analytical tools and correlations for two-phase flow and heat transfer in passages having a hydraulic diameter greater than about 6 mm. These tools include flow regime maps, pressure drop and heat transfer correlations, and critical heat flux limits, as well as strategies for robust thermal management of HVAC systems, electronics, and nuclear power plants. Designers of small systems with thermal management by phase change will need analogous tools to predict and optimize thermal behavior in the mesoscale and smaller sizes. Such systems include a wide range of devices for computation, measurement, and actuation in environments that range from office space to outer space as well as living systems. This paper examines important processes that must be considered when channel diameters decrease, including flow distribution issues in single, parallel, and split flows; flow instability in parallel passages; manufacturing tolerance effects; single-phase heat transfer; nucleation processes; boiling heat transfer and pressure drop; and wall conductance effects. The discussion focuses on engineering issues for the design of practical systems.

Drop size distributions and heat transfer in dropwise condensation

Abstract Drop distributions have been determined at atmospheric and low pressure for dropwise condensation on a smooth vertical copper surface promoted with di-octadecyl disulphide. Nucleation site densities of 200 × 10 6 sites/cm 2 were found. Significantly larger drop populations were found at atmospheric pressures than low pressures. By means of a heat transfer theory it was found that at atmospheric pressure, drop conduction was the limiting resistance while, at lower pressure, interfacial heat transfer was as important as drop conduction. The most important drops for heat transfer were found to be those less than ten microns in diameter. The distributions for this size range had to be inferred from the heat transfer measurements as the microscope and camera were unable to resolve drops this small.

Quantifying reactor safety margins part 1: An overview of the code scaling, applicability, and uncertainty evaluation methodology☆

Abstract In August 1988, the Nuclear Regulatory Commission (NRC) approved the final version of a revised rule on the acceptance of ECCS entitled “Emergency Core Cooling System; Revision to Acceptance Criteria.” The revised rule states an alternate ECCS performance analysis, based on best-estimate methods, may be used to provide more realistic estimates of plant safety margins, provided the licensee quantifies the uncertainty of the estimates and includes that uncertainty when comparing the calculated results with prescribed acceptance limits. To support the revised ECCS rule, the NRC and its contractors and consultants have developed and demonstrated a method called the Code Scaling, Applicability, and Uncertainty (CSAU) evaluation methodology. The CSAU methodology and an example application, described in this set of six papers, demonstrate that uncertainties in complex phenomena can be quantified. The methodology is structured, traceable, and practical, as is needed in the regulatory arena. It addresses in a comprehensive and systematic manner questions concerned with: (1) code capability to scale-up processes from test facility to full-scale nuclear power plant (NPP). (2) code applicability to safety studies of postulated accident scenario in a specified NPP, and (3) quantifying uncertainties of calculated results. The methodology combines a “top-down” approach to define the dominant phenomena with a “bottom-up” approach to quantify uncertainty. The methedology is able to address both: (1) uncertainties for which bias and distribution are quantifiable, and (2) uncertainties for which only a bounding value is quantifiable. The methodology is general, and therefore applicable to a variety of scenarios, plants, and codes. This paper provides an overview of the CSAU evaluation methodology and its application to a postulated cold-leg, large-break loss-of-coolant accident in a Westinghouse four-loop pressurized water reactor with 17 x 17 fuel. The code selected for this demonstration of the CSAU methodology was TRAC-PF1/MOD1, Version 14.3.

Laminar film condensation on the underside of horizontal and inclined surfaces

Abstract Heat-transfer rates in laminar film condensation on the underside of horizontal and inclined surfaces are predicted by assuming the condensate flow to be the quasi-steady result of a bounded instability. This assumption makes it possible to determine the final shape of the liquid-vapor interface, and thus predict the average heat-transfer coefficient. Measurements of the heat-transfer coefficient obtained by condensing Freon-113 were found to agree quite well with the values predicted by this method. Several distinct regimes of flow in the condensate film were observed. On the underside of horizontal surfaces, the interface is best described as a fully established Taylor instability. At slight angles of inclination there are three regimes of flow. Near the leading edge, the interface is smooth and waveless. Next there is a region of developing waves which are best described as elongated drops or longitudinal ridges. As the ridges grow in amplitude, drops form at the crests and subsequently fall from the surface. beyond the point at which drops first fall, a third regime exists which can be considered to be a fully developed state, independent of distance from the leading edge of the surface. At moderate angles of inclination and up to the vertical, “roll waves” appear a short distance from the leading edge.

The mechanism of heat transfer in nucleate pool boiling—Part II: The heat flux-temperature difference relation

Abstract The individual processes of bubble nucleation, growth and departure described in detail in Part I of this paper are used to predict the heat flux-temperature difference relation for one particular boiling experiment. The geometric idealizations made to evaluate the heat flux apply only in the isolated bubble regime. With only these idealizations, a knowledge of the surface nucleation properties, the bubble contact angle and the fluid properties is sufficient to predict the boiling performance of a surface. The comparison between the predicted and measured performance is quite good.

An integrated structure and scaling methodology for severe accident technical issue resolution : Development of methodology

Scaling has been identified as a particularly important element of the Severe Accident Research Program because of its relevance not only to experimentation, but also to analyses based on code calculations or special models. Recognizing the central importance of severe accident scaling issues, the United States Regulatory Commission implemented a Severe Accident Scaling Methodology (SASM) development program involving a lead laboratory contractor and a Technical Program Group to guide the development and to demonstrate its practicality via a challenging application. The Technical Program Group recognized that the Severe Accident Scaling Methodology was an integral part of a larger structure for technical issue resolution and, therefore, found the need to define and document this larger structure, the Integrated Structure for Technical Issue Resolution (ISTIR). The larger part of the efforts have been devoted to the development and demonstration of the Severe Accident Scaling Methodology, which is Component II of the ISTIR. The ISTIR and the SASM have been tested and demonstrated, by their application to a postulated direct containment heating scenario. The ISTIR objectives and process are summarized in this paper, as is its demonstration associated directly with the SASM. The objectives, processes and demonstration for the SASM are also summarized in the paper. The full body of work is referenced.

Quantifying reactor safety margins: Part 2, Characterization of important contributors to uncertainty

Abstract The NRC has issued a revised Emergency Core Coolant System (ECCS) rule which allows the use of best estimate computer codes for safety analysis, providing the uncertainty of the calculations are quantified and compared with acceptance limits contained in 10 CFR Part 50. To support the revised rule, the NRC and its contractors and consultants have developed and demonstrated a methodology to quantify uncertainty called Code Scaling, Applicability and Uncertainty (CSAU). The methodology consists of three primary elements containing 14 steps. The first element, “Requirements and Capabilities”, which contains the first six steps, is described and demonstrated in this paper. The objective of this element is to characterize the important contributors to uncertainty. The objective is accomplished by determining the applicability of a code to analysis of a transient in a Nuclear Power Plant (NPP) through comparison of the scenario- and plant-dictated requirements with the simulation capabilities of the code.

Gas-phase secondary flow in horizontal, stratified and annular two-phase flow

Abstract Experiments were performed and semi-empirical correlations were developed to both prove the existence of gas-phase secondary flow and to predict annular to stratified transition limits for isothermal and heated horizontal annular two-phase flows in pipes. At the low vapor velocities, where this transition from stratified flow occurs and the entrainment/deposition mechanism is insignificant, secondary flow in the vapor ccore plays the principal role in the full development of the liquid annulus. Direct measurements of secondary flow are presented along with a simple model to correlate its behavior. The secondary flow model is used in conjuction with the fluid mechanics of the film to derive a boundary model for the onset of annular flow in this transition region. The resulting boundary agrees well with both the thermal and isothermal transition data.