Liquid film circumferential asymmetry prediction in horizontal annular two-phase flow

This study considers the prediction of the degree of asymmetry in the circumferential distribution of the liquid film in the tube cross section of horizontal annular gas–liquid two-phase flow, endemic of the lower region of this flow regime near the stratified-wavy flow transition boundary. Focusing on disturbance waves as the predominant mechanism for transporting the liquid in the annular film from the bottom to the top of the tube to counterbalance the draining effect of gravity, a new prediction method for the degree of asymmetry in the annular liquid film is proposed that outperforms existing correlations. Flow pattern maps for horizontal gas–liquid two-phase flow of frequent use in the design of evaporators and condensers can thus be explicitly updated to account for both symmetric and asymmetric annular flows. The underlying experimental database contains 184 measured liquid film circumferential profiles, corresponding to 1276 local liquid film thickness measurements collected from 15 different literature studies for tube diameters from 8.15 mm to 95.3 mm.     

Development of a PLIC-VOF method for the dynamic simulation of entry region flow in a laminar falling film

The present work describes a numerical procedure to simulate the development of hydrodynamic entry region in a gravity-driven laminar liquid film flow over an inclined plane. It provides a better insight into the physics of developing film in entry region. A novel numerical approach is proposed which has the potential to provide solutions for the complex physics of liquid film spreading on solid walls. The method employs an incompressible flow algorithm to solve the governing equations, a PLIC-VOF method to capture the free surface evolution and a continuum surface force (CSF) model to include the effect of surface tension. To account for the moving contact line on the solid substrate, a precursor film model based wall treatment is implemented. Liquid film flow has been simulated for the Reynolds number range of 5 ≤ Re ≤ 37.5, and the predicted results are found to agree well with the available analytical and experimental data.     

Effective and efficient characterization of lubrication flow over soft coatings

This work models the fluid-structure interactions associated with separating a solid from a soft elastic film in a liquid environment. One side of the soft film is permanently attached to a rigid substrate. The ensuing liquid flow and elastic deformations are derived by considering a system of partial differential equations, that govern the mechanics of the separation process. A finite element based computational scheme is developed to solve the governing equations and predict the resultant forces acting on the solid. It is shown that the resulting forces are influenced by the elasticity of the film for an initial duration and by the viscosity of the liquid at larger times. The proposed model is utilized to shed insights into the mechanics of the separation process in constrained-surface stereolithography process.

     

Effects of a countercurrent gas flow on falling-film mode transitions between horizontal tubes

A liquid film falling between horizontal tubes is known to take the form of droplets, jets or sheets, depending on the liquid flow rate; the form of the flow is the so-called “falling-film mode”. Although previously neglected in studies of mode transition, a countercurrent gas flow often exists in falling-film heat exchangers, and its effect on the liquid flow might be important: it could impact the flow regime, lead to local “dryout,” and decrease the heat transfer rate. Experiments are conducted to explore the effects of a countercurrent gas flow and liquid feeding length on falling-film mode transitions for a liquid flowing over horizontal tubes. The effects on mode transition are shown to depend on fluid properties and are explained in terms of unsteadiness and film thickness. In general, transition hysteresis is reduced with an increasing gas velocity. A correlation is developed to predict the countercurrent gas flow effects on falling-film mode transitions. The liquid feeding length can affect mode transitions in quiescent surroundings and when a countercurrent gas flow imposed.     

Local film thickness and temperature distribution measurement in wavy liquid films with a laser-induced luminescence technique

Heat transfer in falling liquid film systems is enhanced by waviness. Comprehension of the underlying kinetic phenomena requires experimental data of the temperature field with high spatiotemporal resolution. Therefore a non-invasive measuring method based on luminescence indicators is developed. It is used to determine the temperature distribution and the local film thickness simultaneously. Results are presented for the temperature distribution measurement in a laminar-wavy water film with a liquid side Reynolds number of 126 flowing down a heated plane with an inclination angle of 2° at two positions in flow direction. The measured temperature distributions are used to calculate the local heat transfer coefficient for solitary waves at two positions in flow direction.     

Experiments on the flow of a thin liquid film over a horizontal stationary and rotating disk surface

Experiments on characterization of thin liquid films flowing over stationary and rotating disk surfaces are described. The thin liquid film was created by introducing deionized water from a flow collar at the center of an aluminum disk with a known initial film thickness and uniform radial velocity. Radial film thickness distribution was measured using a non-intrusive laser light interface reflection technique that enabled the measurement of the instantaneous film thickness over a finite segment of the disk. Experiments were performed for a range of flow rates between 3.0 lpm and 15.0 lpm, corresponding to Reynolds numbers based on the liquid inlet gap height and velocity between 238 and 1,188. The angular speed of the disk was varied from 0 rpm to 300 rpm. When the disk was stationary, a circular hydraulic jump was present in the liquid film. The liquid-film thickness in the subcritical region (downstream of the hydraulic jump) was an order of magnitude greater than that in the supercritical region (upstream of the hydraulic jump) which was of the order of 0.3 mm. As the Reynolds number increased, the hydraulic jump migrated toward the edge of the disk. In the case of rotation, the liquid-film thickness exhibited a maximum on the disk surface. The liquid-film inertia and friction influenced the inner region where the film thickness progressively increased. The outer region where the film thickness decreased was primarily affected by the centrifugal forces. A flow visualization study of the thin film was also performed to determine the characteristics of the waves on the free surface. At high rotational speeds, spiral waves were observed on the liquid film. It was also determined that the angle of the waves which form on the liquid surface was a function of the ratio of local radial to tangential velocity.     

Experimental study on axial development of liquid film in vertical upward annular two-phase flow

Accurate measurements of the interfacial wave structure of upward annular two-phase flow in a vertical pipe were performed using a laser focus displacement meter (LFD). The purpose of this study was to clarify the effectiveness of the LFD for obtaining detailed information on the interfacial displacement of a liquid film in annular two-phase flow and to investigate the effect of axial distance from the air–water inlet on the phenomena. Adiabatic upward annular air–water flow experiments were conducted using a 3 m long, 11 mm ID pipe. Measurements of interfacial waves were conducted at 21 axial locations, spaced 110 mm apart in the pipe. The axial distances from the inlet (z) normalized by the pipe diameter (D) varied over z/D = 50–250. Data were collected for predetermined gas and liquid flow conditions and for Reynolds numbers ranging from Re_G = 31,800 to 98,300 for the gas phase and Re_L = 1050 to 9430 for the liquid phase. Using the LFD, we obtained such local properties as the minimum thickness, maximum thickness, and passing frequency of the waves. The maximum film thickness and passing frequency of disturbance waves decreased gradually, with some oscillations, as flow developed. The flow development, i.e., decreasing film thickness and passing frequency, persisted until the end of the pipe, which means that the flow might never reach the fully developed state. The minimum film thickness decreased with flow development and with increasing gas flow rate. These results are discussed, taking into account the buffer layer calculated from Karman’s three-layer model. A correlation is proposed between the minimum film thickness obtained in relation to the interfacial shear stress and the Reynolds number of the liquid.     

Nonlinearwaves in a liquid film-gas flow system

The instability and regular nonlinear waves in the film of a heavy viscous liquid flowing along the wall of a round tube and interacting with a gas flow are investigated. The solutions for the wave film flows are numerically obtained in the regimes from free flow-down in a counter-current gas stream to cocurrent upward flow of the film and the gas at fairly large gas velocities. Continuous transition from the counter-current to the cocurrent flow via the state with a maximum amplitude of nonlinear waves and zero values of the liquid flow rate and the phase velocity is investigated. The Kapitsa-Shkadov method is used to reduce a boundary value problem to a system of evolutionary equations for the local values of the layer thickness and the liquid flow rate.     

Deformation of the Free Surface in a Moving Locally-Heated Thin Liquid Layer

Liquid film flow on a vertical surface is studied experimentally and theoretically under the determining influence of the thermocapillary forces. In the two-dimensional steady-state case the shape of the film surface is calculated numerically within the thin layer approximation with allowance for the temperature dependence of the viscosity of the liquid and redistribution of the heat flux in the heating element. A local heat source was used in the experiments to produce temperature gradients up to 10 K/mm on the liquid surface. The film thickness was determined by means of the schlieren method with reflection. The relative thickness of the roller in the upper heater edge zone, characteristic of the formation of regular structures, is measured. The thickness is h/h ₀=1.32 ±0.07, which agrees satisfactorily with the results of numerical calculations.     

Numerical simulation of the modulated flow pattern for vertical upflows by the phase separation concept

The multiphase heat transfer could be enhanced by creating thin liquid film on the wall. The phase separation concept is called due to the separated flow paths of liquid and gas over the tube cross section to yield thin liquid film. Our proposed heat transfer tube consists of an annular region close to the wall and a core region, interfaced by a suspending mesh cylinder in the tube. The heat transfer tube is a multiscale system with micron scale of mesh pores, miniature scale of annular region and macroscale of tube diameter and length. Great effort has been made to link from micron scale to macroscale. The Volume of Fluid (VOF) method simulates air/water two-phase flow for vertical upflow. The three-dimensional system was successfully converted to a two-dimensional one by using three equivalent criteria for mesh pores. The non-uniform base grid generation and dynamic grid adaption method capture the bubble interface. The numerical results successfully reproduce our experimental results. The numerical findings identify the following mechanisms for the enhanced heat transfer: (a) counter-current flow exists with upward flow in the annular region and downward flow in the core region; (b) void fractions are exact zero in the core region and higher in the annular region; (c) the liquid film thicknesses are decreased to 1/6–1/3 of those in the bare tube section; (d) the gas–liquid mixture travels much faster in the annular region than in the bare tube; (e) three-levels of liquid circulation exists: meter-scale bulk liquid circulation, moderate-scale liquid circulation around a single-elongated-ring-slug-bubble, and microliquid circulation following the ring-slug-bubble tails. These liquid circulations promote the fluid mixing over the whole tube length and within the radial direction. The modulated parameters of void fractions, velocities and liquid film thicknesses in the annular region and three-levels of liquid circulation are greatly beneficial for the multiphase heat transfer enhancement.     

An analytical investigation into filmwise condensation on a horizontal tube in a porous medium with suction at the tube surface

An analytical investigation is performed into the problem of steady filmwise condensation flow over the outside surface of a horizontal tube embedded in a porous medium with suction at the tube surface. As in classical film condensation problems, an assumption is made that the condensate and vapor layers meet at a common boundary rather than being separated by an intermediary two-phase zone. Furthermore, it is assumed that the condensate film has constant properties and conforms to Darcy’s law within the porous medium. By introducing an effective suction function to represent the effect of the wall suction on the thickness of the liquid film, both the local condensate film thickness and the local Nusselt number are derived using a simple numerical shooting method. The analytical results indicate that the mean Nusselt number depends on the Darcy number, the Jakob number, the Rayleigh number and the suction parameter. Furthermore, it is found that the local Nusselt number has a maximum value at the upper surface of the horizontal tube and reduces toward zero at the lower surface as a result of the finite thickness of the condensate layer.     

Calculating liquid droplets settling on a cylinder in gas-liquid spray flow

Adding atomized liquid to air flowing around a cylinder gives an appreciable increase in heat transfer by forming a liquid film on the cylinder surface. The heat transfer coefficient depends upon the amount of liquid forming the film, which is limited by two phenomena: droplet deflection from the liquid film on the surface and droplets not striking the cylinder. This paper presents a method of calculating the quantity of liquid droplets settling on a cylinder surface in a gas-liquid spray flow. A coefficient $\text{k}$, the volume ratio of the liquid entering the film to the amount of liquid directed at the cylinder, is introduced. $\text{k}$ values were calculated by means of numerical computation and the theory verified experimentally. The calculation method permits estimation of the dependence of the amount of liquid settling on a cylinder on the droplet diameter distribution parameters and on the linear gas velocity     

Chebyshev finite difference approach to modeling the thermoviscosity effect in a power-law liquid film on an unsteady stretching surface

The effect of thermoviscosity (temperature-dependent viscosity) on the heat transfer in a power-law liquid film over an unsteady stretching sheet is investigated. Similarity analysis is used to transform the governing equations for mass, momentum and energy into a system of ordinary differential equations, which contain a thermoviscosity parameter θ_r, unsteadiness parameter S, generalized Prandtl number Pr and power-law index n. The film thickness, the temperature distributions, the local heat transfer rate, and the local skin-friction coefficient were obtained using the Chebyshev finite difference method (ChFD). The results show that thermoviscosity significantly increases the film thickness and the local heat transfer rate while decreasing the local skin-friction coefficient as θ_r → 1. It is found that liquids with a higher power-law index will have a larger film thickness and a higher free-surface temperature, which indicate a lower local heat transfer rate, ?θ′(0).     

An updated three-zone heat transfer model for slug flow boiling in microchannels

This work proposes a novel physics-based model for the fluid mechanics and heat transfer associated with slug flow boiling in horizontal circular microchannels to update the widely used three-zone model of Thome et al. (2004). The heat transfer model has a convective boiling nature and predicts the time-dependent variation of the local heat transfer coefficient during the cyclic passage of a liquid slug, an evaporating elongated bubble and a vapor plug. The capillary flow theory, extended to incorporate evaporation effects, is applied to estimate the bubble velocity along the channel. A liquid film thickness prediction method also considering bubble proximity effects, which may limit the radial extension of the film, is included. The minimum liquid film thickness at dryout is set to the channel wall roughness. Theoretical heat transfer models accounting for the thermal inertia of the liquid film and for the recirculating flow within the liquid slug are utilized. The heat transfer model is compared to experimental data taken from three independent studies. The 833 slug flow boiling data points cover the fluids R134a, R245fa and R236fa, and channel diameters below 1 mm. The proposed evaporation model predicts more than 80% of the database to within ±30%. It demonstrates a stronger contribution to heat transfer by the liquid slugs and correspondingly less by the thin film evaporation process compared to the original three-zone model. This model represents a new step towards a complete physics-based modelling of the bubble dynamics and heat transfer within microchannels under evaporating flow conditions.     

An experimental test of equations predicting the load bearing capacity of squeeze films of elastico-viscous liquid

A form of squeeze film apparatus was recently described in which the movement of one plate towards the other was simulated by the continuous volume generation of liquid over the plate area. The liquid exuded from a large number of holes in the lower plate surface and formed a “continous flow” version of squeeze film apparatus with no moving parts [1]. A later paper gave derivations of equations from which squeeze film load bearing capacity could be evaluated, taking into account viscous, inertial and normal stress effects in the liquid film [2].In order to find the total load in a squeeze film system, it was necessary to obtain the relationship between the first normal stress difference and shear rate for the liquid in use, using an experimental method. At high shear rates, the jet thrust method provided these data [3,4] and from them the load bearing capacity of squeeze films of hot, polymer-thickened oil were predicted [2].A more complete test of the method is possible with a highly elastic liquid because considerable load enhancement due to extra stress is present at moderate deformation rates in squeeze film systems [1,5,6,7]. Thus a 0.1 per cent aqueous polyacrylamide solution gives well-defined load enhancement and (quite independently) the jet thrust method gives the relationship between normal stress and shear rate from which predictions of load enhancement may be made. Furthermore, convergent nozzles may be used in the jet thrust apparatus [3] to measure the stress development in an elastic liquid which is being simulateneously sheared and stretched, a situation which more closely resembles the squeeze film case than that of steady shear.     

Can Moderately Rarefied Gas Transport Through Round and Flat Tight Channels of Fractured Porous Media be Described Accurately?

We study the generation and flow of foam through rough-walled, fractured marble rocks that mimic natural fracture systems in carbonate reservoirs. Flow was isolated to the fracture network because of the very low rock permeability of the marble samples and foam generated in situ during co-injection of surfactant solution and gas. The foam apparent viscosities were calculated at steady pressure gradients for a range of gas fractions, and similar to foam flow in porous media, we identified two flow regimes for foam flow in fractures: a high-quality flow regime only dependent on liquid velocity and a low-quality flow regime determined by the gas and liquid velocities. Variations in local fluid saturation during co-injection were visualized and quantified using positron emission tomography combined with computed tomography.

     

Evaporation of Falling and Shear-Driven Thin Films on Smooth and Grooved Surfaces

One of the most important tasks in development of modern gas turbine combustors is the reduction of NO_x emissions. An effective way to reduce the NO_x emission is using the lean premixed prevaporization (LPP) concept. An important phenomenon taking place in LPP chambers is the evaporation of thin fuel films. To increase the fuel evaporation rate, the use of microstructured walls has been suggested. The wall microstructures make use of the capillary forces to evenly distribute the liquid fuel over the wall, so that the appearance of uncontrolled dry patches can be avoided. Moreover, the wall structures promote the thin film evaporation characterized by ultra-high evaporation rates. An experimental setup was built for the investigation of thin liquid films falling down on the outer surface of vertical tubes with either a smooth or structured surface. In the first testing phase water is used, fuel like liquids will be used later on. The thin film can be heated from both sides, by hot oil flowing inside the tube, and by hot compressed air flowing in co-current direction to the thin film. The film is partly evaporated along the flow. Results for the wavy film structure at different Reynolds numbers are reported. For theoretical investigations a model describing the hydrodynamics and heat transfer due to evaporation of the gravity- and shear-driven undisturbed liquid film on structured surfaces was developed. For low Reynolds numbers or low liquid mass fluxes the wall surface is only partly covered with liquid and the heat transfer is shown to be governed by the evaporation of the ultra-thin film in the vicinity of the three-phase contact line. A numerical model for the solution of a two-dimensional free-surface flow of a liquid film over a structured wall was also developed. The Navier–Stokes equations are solved using the Volume of Fluid (VOF) technique. The energy equation is included in the model. The model is verified by comparison with data from the literature showing favorable agreement. In particular, the proposed model predicts the formation of capillary waves observed in the experiments. The model is used to investigate the flow of liquid on a structured wall. This calculation is the first step towards the modeling of a three-dimensional wavy flow of a gravity- and shear-driven film along a wall with longitudinal grooves. It is found that due to the Marangoni effect, a circulating flow arises within the cavity, thereby leading to an enhancement in the evaporation rate.     

高超声速溢流冷却实验研究

高超声速溢流冷却是一种新型的飞行器热防护方法,基本思想为:在高热流区布置溢流孔,控制冷却液以溢流方式流出,之后通过飞行器表面摩阻作用展布为液膜,形成热缓冲层以降低飞行器表面热流. 目前,溢流冷却技术还处于探索阶段,实现工程应用前还需开展大量的实验验证和机理研究工作. 本文首次开展溢流冷却的实验研究工作,采用热流测量、液膜厚度测量及液膜流动特性观测技术,搭建了完善的溢流冷却风洞实验平台,对溢流冷却热防护性能和高超声速条件下液膜流动规律进行了初步研究. 研究表明:(1) 高超声速流场中通过溢流能够在飞行器表面形成液膜并有效隔离外部高温气流,可降低飞行器表面热流率;(2) 楔面上的液膜前缘流动是一个逐渐减速的过程,增加冷却液流量液膜厚度变化不明显,但液膜前缘运动速度增大;(3) 液膜层存在表面波,在时间和空间方向发生演化,导致液膜厚度的微弱扰动;(4) 液膜层存在横向展宽现象,即液膜层宽度大于溢流缝宽度. 原因是液膜层与流场边界层条件不匹配,存在压力梯度,迫使冷却液向低压区流动,从而展宽液膜层,并且流量越高,横向展宽现象越明显.      

Counter-current gas–liquid flow in a vertical narrow channel—Liquid film characteristics and flooding phenomena

Results are reported of an experimental investigation of gas–liquid counter-current flow in a vertical rectangular channel with 10 mm gap, at rather short distances from liquid entry. Flooding experiments are carried out using air and various liquids (i.e., water, 1.5% and 2.5% aqueous butanol solutions) at liquid Reynolds numbers Re_L < 350. Visual observations and fast recordings suggest that the onset of flooding at low Re_L (<250) is associated with liquid entrainment from isolated waves, whereas “local bridging” is dominant at the higher Re_L examined in this study. Significant reduction of flooding velocities is observed with decreasing interfacial tension, as expected. Instantaneous film thickness measurements show that under conditions approaching flooding, a sharp increase of the mean film thickness, of mean wave amplitude and of the corresponding RMS values takes place. Film thickness power spectra provide evidence that by increasing gas flow the wave structure is significantly affected; e.g., the dominant wave frequency is drastically reduced. These data are complemented by similar statistical information from instantaneous wall shear stress measurements made with an electrochemical technique. Power spectra of film thickness and of shear stress display similarities indicative of the strong effect of waves on wall stress; additional evidence of the drastic changes in the liquid flow field near the wall due to the imposed gas flow, even at conditions below flooding, is provided by the RMS values of the wall stress. A simple model is presented for predicting the mean film thickness and mean wall shear stress under counter-current gas–liquid flow, below critical flooding velocities.     

Numerical study on the effect of initial flow velocity on liquid film thickness of accelerated slug flow in a micro tube

Numerical simulation of air–water slug flows accelerated from steady states with different initial velocities in a micro tube is conducted. It is shown that the liquid film formed between the gas bubble and the wall in an accelerated flow is significantly thinner than that in a steady flow at the same instantaneous capillary number. Specifically, the liquid film thickness is kept almost unchanged just after the onset of acceleration, and then gradually increases and eventually converges to that of an accelerated flow from zero initial velocity. Due to the flow acceleration, the Stokes layer is generated from the wall, and the instant velocity profile can be given by superposition of the Stokes layer and the initial parabolic velocity profile of a steady flow. It is found that the velocity profile inside a liquid slug away from the bubble can be well predicted by the analytical solution of a single-phase flow with acceleration. The change of the velocity profile in an accelerated flow changes the balance between the inertia, surface tension and viscous forces around the meniscus region, and thus the resultant liquid film thickness. By introducing the displacement thickness, the existing correlation for liquid film thickness in a steady flow (Han and Shikazono, 2009) is extended so that it can be applied to a flow with acceleration from an arbitrary initial velocity. It is demonstrated that the proposed correlation can predict liquid film thickness at Re < 4600 within the range of ±10% accuracy.