Nonlinear dynamics in horizontal film boiling

Abstract

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.

Dynamics of a vapor bubble on a heated substrate

“…A non-equilibrium evaporation equation for the interface, where both evaporation and condensation occur, was derived by Schrage [14], and is linearized to Eq. (26), as discussed by Panzarella et al [12]. Here T ¼ 0 and J ¼ 0 depicts an equilibrium state, T > 0 and J > 0 the evaporation, and T < 0 and J < 0 the condensation.…”

“…If we consider the variation of surface tension due to temperature change, a thermocapillary parameter would appears in the left-side of Eq. (22), as in the work by Panzarella et al [12]. The first term in Eq.…”

“…At the liquid-vapor interface z ¼ hðx; tÞ dimensionless boundary conditions for mass conservation, energy conservation, the equilibrium of normal stress and shear stress, continuous tangential velocity, continuous temperature and mass flux are imposed, as explained by Delhaye [4], Burelbach and Bankoff [2], and Panzarella et al [12].…”

“…Details for the derivation of the evolution are given in the work by Panzarella et al [12]. Interested readers may follow the analysis by noting that in the …”

“…The effect of the liquid-solid contact line is investigated in this study. Stability analysis ( [12], for example) of the vapor-liquid interface in film boiling also shows a spontaneous incipient rupture process of the vapor film. The liquid, upon touching the bottom (vaporfilm rupture), may either spread (toward transition boiling) or vaporize (toward film boiling), depending upon the competitive effects of evaporation and feeding from the liquid bulk above.…”