S. George Bankoff

A Critical Review of the Flooding Literature

Countercurrent flow of a gas and a liquid in direct contact with each other is, of necessity, gravity dominated. That is, in the absence of electromagnetic force fields, thermocapillary effects, or concentration-capillary effects, countercurrent flow can be sustained only as a result of the difference in the gravitational force per unit volume on the gas and on the liquid. If the gas and liquid are simultaneously introduced into a porous medium or into a vertical or inclined pipe, the gas tends to rise relative to the liquid. If conditions allow complete separation, it is possible to maintain steady countercurrent flow in which the liquid discharges at the bottom while the gas flows out from the top. The countercurrent flow is opposed by interfacial friction between the phases, which always seems to increase monotonically as the relative countercurrent mean velocity of the phases increases. Hence, for a given geometry and liquid-gas pair, there is a maximum relative velocity that can be sustained in countercurrent flow. This point is known as the onset of flooding. Further increases in gas or liquid input ratas result in only partial delivery of the liquid out of the bottom. Eventually, if the gas velocity becomes sufficiently high, none of the liquid is delivered at the bottom, and fully cocurrent upward flow is established. If the liquid is being introduced from an upper plenum, none will penetrate into the pipe or porous medium when this second critical gas velocity is reached.

Dynamics of a condensing liquid film under conjoining'disjoining pressures

The dynamics of a condensing apolar ultrathin liquid film is studied in the framework of long-wave theory in the cases of both horizontal and slightly tilted solid coated surfaces. When condensation is slow, the film on a horizontal substrate passes through the stages of hole opening driven by the “reverse reservoir effect,” hole closing, eventual thickness equilibration and further spatially uniform growth of the condensate. When condensation is faster and the resistance to phase change is lower, secondary droplet(s) may emerge within the hole. During the film evolution the thickness of the microlayer covering the hole remains practically constant due to the “reverse reservoir effect.” The total heat flux across the condensate film is found to decrease with the absolute value of the condensation constant. When the solid substrate is tilted, the film dynamics exhibits the formation of multidrop structures and their coarsening along with the stages typical for the horizontal case. The increase of the tilt ...

Non-isothermal spreading of a thin liquid film on an inclined plane

A thin layer of liquid advancing over a dry, heated, inclined plate is studied. A lubrication model with contact line motion is derived. The plate is at constant temperature, and the surface Biot number is specified. The steady-state solution is obtained numerically. In addition, the steady-state solution is studied analytically in the neighbourhood of the contact line. A linear stability analysis about the steady state is then performed. The effects of gravity, thermocapillarity and contact line motion are discussed. In particular, we determine a band of unstable wavenumbers, and the maximum growth rate as a function of these parameters.

Nonlinear dynamics in horizontal film boiling

This paper uses thin-film asymptotics to show how a thin vapour layer can support a liquid which is heated from below and cooled from above, a process known as horizontal film boiling. This approach leads to a single, strongly-nonlinear evolution equation which incorporates buoyancy, capillary and evaporative effects. The stability of the vapour layer is analysed using a variety of methods for both saturated and subcooled film boiling. In subcooled film boiling, there is a stationary solution, a constant-thickness vapour film, which is determined by a simple heat-conduction balance. This is Rayleigh–Taylor unstable because the heavier liquid is above the vapour, but the instability is completely suppressed for sufficient subcooling. A bifurcation analysis determines a supercritical branch of stable, spatially-periodic solutions when the basic state is no longer stable. Numerical branch tracing extends this into the strongly-nonlinear regime, revealing a hysteresis loop and a secondary bifurcation to a branch of travelling waves which are stable under certain conditions. There are no stationary solutions in saturated film boiling, but the initial development of vapour bubbles is determined by directly solving the time-dependent evolution equation. This yields important information about the transient heat transfer during bubble development.

Formation of a dry spot in a horizontal liquid film heated from below

Abstract This study deals with the formation of a dry spot in a non-boiling thin film of ethanol on a horizontal surface upon slowly increasing the heat flux from an embedded nichrome strip. Appreciable thinning of the film occurred prior to rupture, and is associated with the appearance of Benard-type convective cells. The threshold heat flux for appearance of a dry spot is greater than for disappearance, presumably due to contact angle hysteresis and/or the temperature gradients in the heater strip in the vicinity of the triple interface. A quasi-static stability analysis is given, based upon the equilibrium shape of a semi-infinite drop on a heated surface.

Electrohydrodynamics of Thin Flowing Films

Thin films of oil flowing down a nearly-vertical plate were subjected to a strong normal electrostatic field. Steady-state height profiles were measured by fluorescence imaging. For electrode potentials less than that required to produce an instability, the two-dimensional response of the interface was < 1%. Calculations of the fluid height coupled with the electric field solution were identical to uncoupled calculations for electric fields below the stability threshold. Pressure profiles under the film and three-dimensional effects are also discussed.

Thermal singularities in film rupture

Long‐wave approximation for the spatiotemporal evolution of thermal and evaporative instabilities of a thin liquid film lying on a ‘‘thick’’ solid substrate is considered. It is shown that accounting for a nonzero thermal resistance of the solid eliminates the emergence of temperature, heat and mass flux singularities at the rupture point.

The effect of heat conduction in the vapor on the dynamics of downflowing condensate

A vapor fills the gap between two vertical plates, one hot and one cold. The temperatures are adjusted so that condensate forms on the cold wall. It is the dynamics of the system that is examined. The paper extends the one-sided model of evaporation–condensation to account the heat conduction in the vapor phase, which turns out to be important in many condensation problems. For the considered flow, both vapor recoil and Marangoni effect are stabilizing; as a result, the condensate becomes unstable at nonzero Reynolds numbers in contrast to the usual film flow down a vertical wall. A nonlinear evolution equation is derived and analyzed for the interaction of viscous shear and evaporation–condensation. It turns out that the one-sided model of heat and mass transfer gives a very good description of the initial stage of thin-film growth; in later stages, however, the heat conduction through the vapor becomes important when the film is sufficiently thick.

Molten fuel-coolant interaction phenomena with application to carbide fuel safety

Abstract This paper reviews the major phases occurring during an energetic molten fuel/coolant interaction (MFCI), the categories of interaction and modes of contact between molten fuel and liquid coolant, the film boiling destabilization and collapse mechanisms, and the important fragmentation mechanisms of the melt. Two major models that describe the processes involved in an MFCI event are discussed: the spontaneous nucleation model and the pressure detonation model. Finally, the MFCI experiments involving carbide fuel and liquid sodium are reviewed and the potential for an energetic interaction between molten carbide fuel and liquid sodium is discussed. Recommendations are given for future work on MFCI phenomena relative to the carbide fuel/sodium system.

Control of Linear Time-Invariant Systems with Plant Disturbances and Incomplete Measurements

This paper is concerned with the estimation and control of linear systems with unknown disturbances entering the system at specified points. The assumption that systems experience some sort of disturbance input which is not known a priori and which cannot be directly measured on-line is true for most cases. These disturbances may be due to environmental effects or modeling approximations. As examples one can cite load fluctuations in regulators, changes in wind velocity and direction in aircraft; raw material variations in chemical processes, etc. Estimators designed by conventional techniques fail exactly to reconstruct the state when such disturbances are present. In this case the designer is forced to use output feedback or an unknown-biased estimate of the state variables in his control law, which may result in failure to meet the closed-loop specifications.