Study of the thermocapillary effect on a wavy falling film using a fiber optical thickness probe

The wave flow of a water film down a vertical plate with a 150×150 mm heater has been experimentally studied. The effect of the heat flux on the film flow leads to the formation of periodically flowing rivulets and thin film between them due to the action of thermocapillary forces in spanwise direction. The local film thickness between rivulets is measured by means of a noncontact fiber optical probe. As the heat flux grows, the average film thickness continuously decreases but upon reaching about 50% of the initial thickness, the film spontaneously breaks down. It is found that the decrease of the wave amplitude between rivulets is caused by the reduction of the local Reynolds number and is in a qualitative agreement with the laws of the hydrodynamics for the isothermal case. That is, no appreciable effect of streamwise thermocapillary forces on the wave amplitudes is detected. The experimental results are in good agreement with recently published data obtained by the capacitance method.     

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.     

Thermal characteristics of a high heat flux micro-evaporator

Our purpose is to design a high heat flux micro-evaporator that can remove more than 100 W/cm². For this purpose a thin liquid film is evaporized. The liquid film is stabilized in micro-channels by capillary forces. The micro-channels are fabricated by chemical etching on silicon to reduce thermal resistance. For the experiments, the channel plate is heated by an ITO thin film heater deposited on the opposite side of the channel plate. Influence of heat flux, coolant flow rate, and inlet temperature on the temperature of the heater element are investigated. Water is used as working fluid. A maximal heat flux of 125 W/cm² could be achieved for water inlet temperature of 90 °C and flow rate of 1.0 mL/min. The temperature of the heater element is kept constant at about 120 °C with fluctuations within 8 °C. The measured pressure drop is less than 1000 Pa.     

Thermocapillary convection in a liquid layer with a quasi-point heat source in the substrate

By the method of tracer particles the velocity field of thermocapillary convection in a thin layer of silicone oil, excited by a quasi-point heat source in the rigid substrate, is investigated as a function of the layer thickness, the temperature of the heater, and the liquid viscosity. The vertical velocity distributions are plotted in several cross-sections at different distances from the vortex axis. A novel method of measuring the profile of the thermocapillary depression, based on mirror reflection from the free liquid surface of radiation scattered by a tracer particle, is proposed. The central segment of the profile of the thermocapillary depression is obtained for different values of the layer thickness, the liquid viscosity and the heater temperature.     

Measurement of locally heated liquid film thickness by a double-fiber optical probe

An experimental investigation of thermocapillary deformations in a film of 10% ethyl alcohol solution in water, flowing down a plate with a heater of length 6.7 mm and width 68 mm, is performed. Heating of the film results in the formation of a horizontal liquid bump at the top edge of the heater. On the heater the flow divides into vertical rivulets with a thin film between them. Film deformations in the bump and the thin film between the rivulets are investigated. Local film thickness is measured by means of a double-fiber optical probe. The method is based on the dependence of the intensity of reflected light on the distance between the probe and the reflecting surface. The measurement results are compared to those previously obtained using the schlieren method. The experiment is controlled by three parameters. They are, with their respective values, the plate inclination angle (4–90°), the Reynolds number (0.15–62) and the heat flux density (0–4.5 W/cm²).     

Stability of a vertical liquid film with consideration of the marangoni effect and heat exchange with the environment

The stability of a free vertical liquid film under the combined action of gravity and thermocapillary forces has been studied. An exact solution of the Navier-Stokes and thermal conductivity equations is obtained for the case of plane steady flow with constant film thickness. It is shown that if the free surfaces of the film are perfectly heat insulated, the liquid flow rate through the cross section of the layer is zero. It is found that to close the model with consideration of the heat exchange with the environment, it is necessary to specify the liquid flow rate and the derivative of the temperature with respect to the longitudinal coordinate or the flow rate and the film thickness. The stability of the solution with constant film thickness at small wave numbers is studied. A solution of the spectral problem for perturbations in the form of damped oscillations is obtained.     

Intensification of Heat Transfer in a Downward Liquid-Film Flow

Heat transfer in a film flow of the FC-72 dielectric liquid down a vertical surface with an embedded 150×150 mm heater is experimentally examined in the range of Reynolds numbers Re = 5–375. A chart of liquid-film flow modes is constructed, and characteristic heat-transfer regions are identified. Data on the dependence of heater-wall temperature and local heat flux at the axis of symmetry of the heater on the longitudinal coordinate are obtained. Local and mean heat-transfer coefficients are calculated. It is shown that enhanced heat transfer is observed in the region where rivulets starts forming in the low-Reynolds-number liquid-film flow.     

Effect of vertical heat transfer on thermocapillary convection in an open shallow rectangular cavity

In order to understand the effect of the vertical heat transfer on thermocapillary convection characteristics in a differentially heated open shallow rectangular cavity, a series of two- and three-dimensional numerical simulations were carried out by means of the finite volume method. The cavity was filled with the 1cSt silicone oil (Prandtl number Pr = 13.9) and the aspect ratio ranged from 12 to 30. Results show that thermocapillary convection is stable at a small Marangoni number. With the increase of the heat flux on the bottom surface, thermocapillary convection transits to the asymmetrical bi-cellular pattern with the opposite rotation direction. The roll near the hot wall shrinks as the Marangoni number increases. At a large Marangoni number, numerical simulations predict two types of the oscillatory thermocapillary flow. One is the hydrothermal wave, which is dominant only in a thin cavity. The other appears in a deeper cavity and is characterized by oscillating multi-cellular flow. The critical Marangoni number for the onset of the oscillatory flow increases first and then decreases with the increase of the vertical heat flux. The three-dimensional numerical simulation can predict the propagating direction of the hydrothermal wave. The velocity and temperature fields obtained by three-dimensional simulation in the meridian plane are very close to those obtained by two-dimensional simulation.     

Effect of Thermocapillary Forces on the Initial Section of a Melt Film

The previous analysis of fields near the upper triple point of the floating–zone melting process is supplemented by the analysis of thermocapillary forces on the melt surface. It is shown that the effect of these forces is large in the general case, and a melt film with a macroscopic radius of curvature may be formed only if the temperature gradient over the melt surface and thermocapillary forces are small; in this case, the angular coordinates of the melt–film cross section are also small.     

Nonlinear vibrations of a vapor film in the presence of intense heat fluxes

Waves propagating along the interface between a thin vapor film and a liquid layer in the presence of a heat flux are investigated. The boundary conditions on the vapor-liquid phase surface take into account the temperature dependence of the pressure and the possibilities of formation of the metastable state of the superheated liquid and mass flow. Variations in the saturation pressure as functions of the temperature and mass flux lead to generation of weakly damped periodic waves of low amplitude whose velocity can be much higher than the velocity of the gravity waves. The waves ensure stability of the vapor film beneath the liquid layer in the gravity field. The finite-amplitude waves on the surface of the vapor film differ from the Stokes surface waves on the free surface of isothermal fluid. Instability regimes related with superheating of the liquid ant its explosive boiling when the amplitude of an initially small wave increases to infinity in a finite time can develop in a certain working-parameter regime.     

Experimental investigation into three-dimensional wavy liquid films under the influence of electrostatic forces

Three-dimensional interfacial waves that develop on the free surface of falling liquid films are known to intensify heat and mass transfer. In this context, the present paper studies the effect of electrostatic forces applied to a falling film of dielectric liquid on its three-dimensional nonlinear wave dynamics. Therefore, measurements of the local film thickness using a confocal chromatic imaging method were taken, and the complex wave topology was characterized through photography. The experiments show a complex interaction between the electric field and the hydrodynamics of the falling film, whereby electrostatic forces were found to both increase and decrease wave peak height in different regions of the wave. Additionally, an electrically induced breakup of the three-dimensional wave fronts, which leads to a locally doubled frequency in streamwise direction, is found. The ability to influence the wave topology demonstrated here opens the possibility to optimize heat transfer processes in falling liquid films.     

Computational analysis of convective instabilities in a liquid layer subjected to an inclined gradient of temperature

A 3D numerical study of convective instabilities in a horizontal liquid layer (silicone oil with a Prandtl number Pr = 102) with an upper free surface is presented. The liquid layer is subjected to an inclined gradient of temperature. The influence of both gravity and thermocapillary forces on the formation of convective patterns is studied for different values of the liquid layer depth. Numerical results are found to be in good agreement with experimental data of other authors.     

Equilibrium of a free nonisothermal liquid film

The equilibrium of a free weightless liquid film fixed over a planar contour and acted upon by thermocapillary forces is studied. Trends in the behavior of free liquid films are important for understanding the processes occurring in foams. The equilibrium equations for a nonisothermal weightless free film are derived for the two limiting cases: the temperature of the film is considered a known function of the coordinates; the free surface of the film is thermally insulated. For the plane and axisymmetric cases, the existence conditions for the solutions of the resulting nonlinear boundary-value problems are found and their properties are studied. For the general case, an approximate solution of the equilibrium problem is obtained provided that the analogue of the Marangoni number is small. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 16–29, May–June, 2007.     

Transient behavior of boiling bubbles generated on the small heater of a thermal ink jet printhead

The fundamental behavior of boiling bubbles generated on a small film heater used for thermal ink jet (TIJ) printers is investigated experimentally under the condition of a single pulse heating in a pool of water. The pulse power and the pulse width are varied in wide ranges that include the printing conditions. As the pulse power is increased or the pulse width increased at a fixed high pulse power, numerous fine bubbles appear simultaneously on the heater and then coalesce into a thin vapor film to grow to a vapor bubble, before collapsing at the center of the heater. For a long pulse width sequence, the coalesced bubble repeats the growth and collapse. Bubble behavior is also studied in the same heat flux range using a platinum film heater enabling surface temperature measurement. From a comparison of the two heaters, the dominant mechanism of nucleation on the TIJ heater is believed to be spontaneous nucleation at around the heating rate for printing. The dependence of the size and lifetime of the coalesced bubble on pulse power and pulse width are examined. Based on the analytical model presented by Asai [J. Heat Transfer 113 (1991) 973], the pressure impulse arising during the rapid evaporation of the superheated liquid, presumed to dominate the subsequent growth of the coalesced bubble, is estimated from the measured size of the coalesced bubble. The relationship between the pressure impulse and the superheat energy in the liquid is discussed.     

Self-induced thermocapillary convection in film boiling heat transfer from a vertical surface in saturated conditions and viscous regimen

Self-induced thermocapillary convection and its significance with regard to film boiling heat transfer from a vertical saturated surface is discussed. Utilizing a simplified geometrical model, an analytical expression (multiplier factor) for the vapor film thickness and heat transfer coefficient corrected by thermocapillary phenomena was derived. The above equation is a new theoretical viewpoint for the enhancement in the heat transfer coefficient observed in the experimental data in the viscous regime and agree qualitatively with available experimental measurements made on R113 coolant.     

Simultaneous heat and mass transfer inside a vertical tube in evaporating a heated falling alcohols liquid film into a stream of dry air

A numerical study of the evaporation in mixed convection of a pure alcohol liquid film: ethanol and methanol was investigated. It is a turbulent liquid film falling on the internal face of a vertical tube. A laminar flow of dry air enters the vertical tube at constant temperature in the downward direction. The wall of the tube is subjected to a constant and uniform heat flux. The model solves the coupled parabolic governing equations in both phases including turbulent liquid film together with the boundary and interfacial conditions. The systems of equations obtained by using an implicit finite difference method are solved by TDMA method. A Van Driest model is adopted to simulate the turbulent liquid film flow. The influence of the inlet liquid flow, Reynolds number in the gas flow and the wall heat flux on the intensity of heat and mass transfers are examined. A comparison between the results obtained for studied alcohols and water in the same conditions is made.     

Forced-convection film condensation on a horizontal cylinder with wavy surface structure

The forced-convection film condensation on a horizontal cylinder with wavy surface structure was performed by boundary-layer-approximation. The local/mean heat fluxes were obtained for the effects of tube temperature, wave number, and wave amplitude. The mean heat flux increases with decreasing wavy amplitude and tube temperatures. Furthermore, when β = 20 and α = 0.005, the mean heat flux slightly increases from 1.1 to 3.6% compared with that of smooth tube, depending on tube temperature.     

Efficient reconstruction of local heat fluxes in pool boiling experiments by goal-oriented adaptive mesh refinement

In this paper, we consider the efficient estimation of local boiling heat fluxes from transient temperature measurements in the heater close to the heater surface. For accurate prediction, heat flux estimation is formulated as a transient three-dimensional (3D) inverse heat conduction problem (IHCP). This inverse problem is ill-posed and cannot be treated straightforwardly by established numerical methods. In order to obtain a regularized stable solution, a large-scale time-dependent PDE-constrained optimization problem has to be solved and an appropriate stopping criterion for the termination of the iterative solution process has to be chosen. Since the boiling heat flux is non-uniformly distributed on the heater surface due to the strong local activity of the boiling process, the use of a fixed uniform spatial discretization is not efficient. Instead, an adaptive mesh refinement strategy can be used to obtain an appropriate discretization which significantly reduces the total computational effort. In this work, we present an automatic algorithm incorporating an adaptive mesh refinement via a heat flux-based a-posteriori error estimation technique. The suggested algorithm can cope with both spatially point-wise or highly resolved temperature observations efficiently. It is applied to real measurement data obtained from two different types of pool boiling experiments. The numerical results show that the computational effort can be reduced significantly for given estimation quality. This adaptive IHCP solution technique can be also viewed as an efficient soft sensor to deduce unmeasurable local boiling heat fluxes.     

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.      

Periodic boiling in parallel micro-channels at low vapor quality

Based on experimental investigations the present study evaluates instability and heat transfer phenomenon under condition of periodic flow boiling of water and ethanol in parallel triangular micro-channels. Tests were performed in the range of hydraulic diameter 100–220 μm, mass flux 32–200 kg/m² s, heat flux 120–270 kW/m², vapor quality x = 0.01–0.08. The period between successive events depends on the boiling number and decreases with an increase in the boiling number. The initial film thickness decreases with increasing heat flux. When the liquid film reached the minimum initial film thickness CHF regime occurred. Temporal variations of pressure drop, fluid and heater temperatures were periodic. Oscillation frequency is the same for the pressure drop, for the fluid temperature at the outlet manifold, and for the mean and maximum heater temperature fluctuations. All these fluctuations are in phase. The CHF phenomenon is different from that observed in a single channel of conventional size. A key difference between micro-channel heat sink and single conventional channel is amplification of parallel-channel instability prior to CHF. The dimensionless experimental values of the heat transfer coefficient are presented as the Nusselt number dependence on the Eotvos number and the boiling number.