Michael L. Corradini

Modeling high-speed viscous liquid sheet atomization

Abstract A linear stability analysis is presented for a liquid sheet that includes the effects of the surrounding gas, surface tension and the liquid viscosity on the wave growth process. An inviscid dispersion relation is used to identify the transition from a long wavelength regime to a short wavelength regime, analogous to the first and second wind induced breakup regimes of cylindrical liquid jets. This transition, which is found to occur at a gas Weber number of 27/16, is used to simplify the viscous dispersion relation for use in multi-dimensional simulations of sheet breakup. The resulting dispersion relation is used to predict the maximum unstable growth rate and wave length, the sheet breakup length and the resulting drop size for pressure-swirl atomizers. The predicted drop size is used as a boundary condition in a multi-dimensional spray model. The results show that the model is able to accurately predict liquid spray penetration, local Sauter mean diameter and overall spray shape.

Vapor explosions in light water reactors: A review of theory and modeling

Abstract A vapor explosion is a physical event in which a hot liquid (fuel) rapidly fragments and transfers its internal energy to a colder, more volatile liquid (coolant); in so doing, the coolant vaporizes at high pressures and expands, doing work on its sorroundings. In present day fission reactors, if complete and prolonged failure of normal and emergency coolant flow occurs, fission product decay heat would cause melting of the reactor materials. In postulated severe accident analyses vapor explosions are considered if this molten “fuel” contacts residual water in-vessel or ex-vessel, because these physical explosions have the potential of contributing to reactor vessel failure and possibly containment failure and release of radioactive fission products. Vapor explosions are also a real concern in industrial processes where a hot fluid can contact a colder volatile fluid, e.g., foundries for aluminum and steel, paper pulping mills, LNG operations. The vapor explosion is commonly divided into four phases of heat transfer: (1) quiescent mixing of fuel and coolant, (2) triggering of the explosion, (3) explosion escalation and propagation, and (4) expansion and work production. This work provides a comprehensive review of vapor explosion theory and modeling in these four areas. Current theories and modeling have led to a better understanding of the overall process, although some specific fundamental issues are either not well understood or require experimental verification of theoretical hypotheses. These key issues include the extent of fuel-coolant mixing under various contact modes, the basic fuel fragmentation mechanism, and the effect of scale on the mixing process coupled to the explosion propagation and efficiency. Current reactor safety concerns with the vapor explosion are reviewed in light of these theories and models.

A diffusion layer model for steam condensation within the AP600 containment

Abstract Steam condensation plays a key role in removing heat from the atmosphere of the Westinghouse AP600 containment in case of a postulated accident. A model of steam condensation on containment surfaces under anticipated accident conditions is presented and validated against an extensive and sound database. Based on the diffusion layer theory and on the use of the heat/mass transfer analogy, one can deal with large temperature gradients across the gaseous boundary layer under high mass flux circumstances. The thermal resistance of the condensate film, as well as its wavy structure, have also been considered in this model. As compared to Anderson et al. (1998) (Experimental analysis of heat transfer within the AP600 containment under postulated accident conditions. Nucl. Eng. Des. (submitted)) experimental database, an average error lower than 15%, within the experimental confidence range, has demonstrated its remarkable accuracy. In particular, the model has shown a good response to the influence of primary variables in steam condensation (i.e. subcooling, noncondensable concentration and pressure), providing a mechanistic explanation for effects such as the presence of light noncondensable gas (i.e. helium as a simulant for hydrogen) in the gaseous mixture. In addition, the model has been contrasted against correlations used in safety analysis (i.e. Uchida, Tagami, Kataoka, etc.) and occasionally to Dehbi’s database. This cross-comparison has pointed out several shortcomings in the use of these correlations and has extended the model validation to other databases.

Modeling of Small-Scale Single Droplet Fuel/Coolant Interactions

In this paper a model for small-scale single droplet fuel/coolant interactions (FCIs) is proposed, which considers the growth of a coolant vapor/liquid interfacial disturbance into a coolant liquid jet during the collapse of the vapor film surrounding the fuel. This results in the encapsulation of the jet as coolant drops beneath the fuel surface and leads to fragmentation of the fuel. In this model, the FCI process is divided into four stages: film boiling around a molten fuel droplet in an infinite coolant pool, film collapse and coolant jet formation, coolant jet penetration and entrapment in the fuel, and rapid evaporation of entrained coolant and fragmentation of the fuel. The process repeats itself cyclically from the second stage. For the single-droplet experiments performed previously, the model predicts the qualitative trends of steam bubble growth and collapse, the final size of fuel fragments, and time scale for the fuel fragmentation.

Experimental analysis of heat transfer within the AP600 containment under postulated accident conditions

Abstract The new AP600 reactor designed by Westinghouse uses a passive safety system relying on heat removal by condensation to keep the containment within the design limits of pressure and temperature. Even though some research has been done so far in this regard, there are some uncertainties concerning the behavior of the system under postulated accident conditions. In this paper, steam condensation onto the internal surfaces of the AP600 containment walls has been investigated in two scaled vessels with similar aspect ratios to the actual AP600. The heat transfer degradation in the presence of noncondensable gas has been analyzed for different noncondensable mixtures of air and helium (hydrogen simulant). Molar fractions of noncondensables/steam ranged from (0.4–4.0) and helium concentrations in the noncondensable mixture were 0–50% by volume. In addition, the effects of the bulk temperatures, the mass fraction of noncondensable/steam, the cold wall surface temperature, the pressure, noncondensable composition, and the inclination of the condensing surface were studied. It was found that the heat transfer coefficients ranged from 50 to 800 J s −1 K −1 m −2 with the highest for high wall temperatures at high pressure and low noncondensable molar fractions. The effect of a light gas (helium) in the noncondensable mixture were found to be negligible for concentrations less than approximately 35 molar percent but could result in stratification at higher concentrations. The complete study gives a large and relatively complete data base on condensation within a scaled AP600 containment structure, providing an invaluable set of data against which to validate models. In addition, specific areas requiring further investigation are summarized.

Turbulent condensation on a cold wall in the presence of a noncondensable gas

A condensation model for forced and natural convection is derived by extending the Reynolds-Colburn analogy for heat and momentum transfer to mass and momentum transfer. The model is compared to the steady-state data of Uchida and Tagami and found to be in reasonable agreement with the forced convection data when an imposed velocity of 2 m/s is assumed. The natural convection model has the same functional dependence on Grashof number (h /SUB tot/ aboutGr /SUP -0.37/ ) as the data of Akers.

Heat Transfer and Fluid Flow Characteristics in Supercritical Pressure Water

A series of integral heat transfer measurements in a square annular flow passage was performed for bulk water temperatures of 175―400°C with upward mass velocities of 300 kg/m 2 s and 1000 kg/m 2 s and heat fluxes of 0, 200 kW/m 2 , and 440 kW/m 2 , all at a pressure of 25 MPa. Mean and turbulent velocities measured with a two-component laser Doppler velocimetry system along with simulations using the computational fluid dynamics (CFD) code FLUENT were used to explain the deterioration and enhancement of heat transfer in supercritical pressure water. At low mass velocities, the integral heat transfer measurements exhibited large localized wall temperature spikes that could not be accurately predicted with Nusselt correlations. Detailed mean and turbulent velocities along with FLUENT simulations show that buoyancy effects cause a significant reduction in turbulent quantities at a radial location similar to what is the law of the wall region for isothermal flow. At bulk temperatures near the pseudocritical temperature, high mass velocity integral heat transfer measurements exhibited an enhanced heat transfer with a magnitude dependent on the applied heat flux. Measured mean and turbulent velocities showed no noticeable changes under these conditions. FLUENT simulations show that the integrated effects of specific heat can be used to explain the observed effects. The experimentally measured heat transfer and local velocity data also serve as a database to compare existing CFD models, such as Reynolds-averaged Navier-Stokes (RANS) equations and possibly even large Eddy simulations (LES) and direct numerical simulations (DNS). Ultimately, these measurements will aid in the development of models that can accurately predict heat transfer to supercritical pressure water.

Physical Mechanisms for Atomization of a Jet Spray: A Comparison of Models and Experiments

Because combustion in direct injection engines is strongly influenced by the details of the fuel spray in thes engines, the authors have begun a broad research effort of jet breakup experiments and modelling of these high pressure sprays. The main objective of this effort is to better understand fuel injection from the study of the spray-jet breakup process and the associated fuel-oxidant mixing. The focus of this paper is the development of specific models for atomization of the spray-jet. These models are then compared to each other and to preliminary data from the spray-jet breakup experiments. Initial results indicate that KIVA with this proposed spray model shows good agreement with low pressure data (69 MPa) but underestimates spray penetration for higher pressures (104 MPa).

Condensation in the presence of noncondensable gases

Abstract An experimental investigation to examine the effects of surface orientation on the condensation of steam in the presence of noncondensable gas is reported. An air-steam mixture was directed into a rectangular flow-channel over a condensing aluminum surface that has a painted surface finish. The mixture flow was concurrent in all the tests with condensate flow. In this series of experiments, the orientation of the condensing surface was varied from 0–90° (plate surface was facing downwards at 0°), with a variable air-steam mass fraction of 0–0.87, and a mixture velocity of 1–3 m/s. The heat transfer coefficient was measured in addition to making visual observations of the condensation process. It was found that the heat transfer coefficient varied from 100 to 600 W/m2 K with the mass fraction of 0.87-0.24 and the maximum heat transfer coefficient of 6200 W/m2 K was measured with mass fraction of ∼ 0 . By tilting the condensing surface from the horizontal to vertical position, the heat transfer coefficient decreased 15 to 25% depending on the mass fraction. With a higher vapor content the effect of the orientation was smaller. This dependence was attributed to the existence of interfacial structure (droplets and ridges) that promoted heat transfer at small inclination angles, when the angle was increased the interface became smoother and heat transfer rates decreased. Heat transfer rates were also observed to increase with flow velocity, vapor content and pressure. The results are compared with some previously published data and a proposed condensation model that showed reasonable agreement with the data trends.

Lithium alloy chemical reactivity with reactor materials: current state of knowledge

Abstract Experimental work and supporting analysis have been conducted by Westinghouse Hanford Company and the University of Wisconsin on lithium-lead alloy chemical reactivity. This work is in support of the U.S. Department of Energy Fusion Safety Program through EG&G Idaho Inc. These studies involve experiments with lithium-lead (17Li83Pb) and its interactions with air, nitrogen, carbon dioxide, concrete, steam and water. The work at Westinghouse Hanford has been done to characterize potential safety concerns associated with the use of this alloy as a breeding abd/or coolant material in fusion reactors. These activities primarily involve large and small scale integral experiments. The work at Wisconsin has focused on lithium alloy/water interactions and is concerned with the chemical kinetics in small scale separate effects tests. In addition this work has been complemented by larger scale more prototypic tests and associated analyses at JRC Ispra. This paper discusses recent results and the status of our knowledge.