On the droplet entrainment from gas-sheared liquid film

Abstract

We formulate the droplet entrainment detached from a thin liquid film sheared by a turbulent gas in a circular pipe. In a time-averaged sense, the film has a Couette flow with a mean velocity of um. Then, a roll wave of wavelength λ and phase velocity uc is formed destabilized through Kelvin–Helmholtz instability, followed by a ripple wave of wavelength λp due to Rayleigh–Taylor instability, wherein the vorticity thickness of the gas stream is consistently a characteristic length scale. Superposing the two types of waves in axial and transverse directions produces conical cusps as the root of ligaments, from which droplets are torn off. The droplet entrainment rate is derived as λpλucum, validated by recent experimental results.

Visualization of Coolant Liquid Film Dynamics in Hypergolic Bipropellant Thruster

“…We find the smooth film without the waves near the collision point until 3 mm downstream. The following wavy pattern shows the typical ripple wave, also reported by Kinney et al [16] and Cherdantsev et al [17] in the past, formed by superposing two types of instabilities; the Kelvin-Hermholtz instability along the axial direction is initiated by the liquid-gas velocity difference, and the following Rayleigh-Taylor instability in the transverse direction is stimulated by the acceleration of the wave crest [19]. The three-dimensional wavy film structure is clearly identified under the practical operating condition of bipropellant thrusters.…”

“…The film keeps evaporating from the liquid-gas interface; thus, the film front becomes thinner, heated a longer time after injection on the wall. Then, the viscous force inside the liquid film, inversely proportional to the film thickness assuming the Couette flow [19], becomes large downstream, leading to the deceleration of the film front. The deceleration of V front also indicates that the effect of thinning film on V front overcomes the acceleration of combustion gas from t 0 ms to 50 ms.…”

“…The film has instability waves of λ≈1 mm, much longer than the film thickness. The film Reynolds number is Re f V local h∕v ∼ 10, in which the effect of viscosity on the instability is insignificant, and λ is determined by boundary-layer thickness of the gas stream and density ratio of liquid to gas [19,33], whose values are consistent under the same chamber pressure. As the result, λ is independent of MR.…”

“…Cherdantsev et al [17] and Shinan et al [18] also observed the liquid film flow sheared by a high-velocity gas stream. Inoue and Maeda [19] succeeded in the comprehensive formulation describing the unstable liquid film dynamics. Stechman et al [20] tried to predict the film length based on heat transfer between the combustion gas and chamber wall.…”

Evaporation of Three-Dimensional Wavy Liquid Film Entrained by Turbulent Gas Flow

“…of a thin liquid film extending on a wall exposed to a fast gas flow is a general thermo-fluid issue in many practical situations, such as film-cooling technology [1][2][3], icing on aircraft wings [4][5][6], and drying of paints and cleaning solutions [7]. Past and recent studies including quantitative measurements [5,[8][9][10][11][12][13][14][15] provide a scenario that the turbulent gas flows over the initially smooth film, soon drives the film with complex wavy structures by Kelvin-Helmholtz (KH) instability as a roll wave, accelerates the wave crests producing transverse wave by Rayleigh-Taylor (RT) instability as a ripple wave, stretches ligaments, and eventually entrains droplets disintegrated by Plateau-Rayleigh instability, all in a sequential fashion. The waves intricately merge and break downstream [10,16] being a disturbance wave [5,13,17,18] with large amplitude.…”