Numerical simulation on gas-droplet flow characteristics and spray evaporation process in CFB-FGD tower

Nozzle arrangement in the nozzle spray system has a significant impact on the gas-droplet flow characteristics and the temperature distribution within the circulating fluidized bed flue gas desulphurization (CFB-FGD) tower, which is critical to the SO₂ removal efficiency. The effects of spray direction, nozzle number and nozzle spray angle on gas-droplet distribution and temperature distribution inside the FGD tower are investigated with numerical simulation based on a Eulerian-Lagrangian mathematical model. An optimal nozzle arrangement scheme is proposed to improve the contact between gas and water droplets and the flue gas temperature distribution. Results show that upward spray direction is beneficial to the interaction between water droplets, improving gas-droplet flow characteristics and spray evaporation process, and water droplets number trapped by tower wall could be reduced in the water droplets evaporation. With the increase in nozzle number, it is conducive to the contact between flue gas and water droplets to increase the evaporation efficiency of water droplets, as well as the uniformity of temperature distribution inside the tower. With nozzle spray angle increases from 30° to 120°, flue gas velocity decreases, water droplets number trapped by the tower wall increases. The temperature distribution at different cross-section is the most uniform when the nozzle spray angle is 60°.     

Evaporation of Ultra-thin Liquid Films into Air

We develop a mathematical model of evaporation of a thin liquid film into air under the action of disjoining pressure. The rate of evaporation is found from the numerical solution of the diffusion equation with specified local vapor concentration near the film surface, assumed equal to its equilibrium value. Evolution of the film is studied for two commonly used disjoining pressure models using a simplified formulation which neglects thermal gradients present in the system. The results are then compared to numerical simulations of coupled systems of equations describing heat conduction in the liquid and solid phases and diffusion of vapor through air. Conditions are formulated at which disjoining pressure suppresses evaporation.     

低压环境固着盐水液滴蒸发析晶过程实验研究

实验研究了低压环境下固着盐水液滴在不同基底表面(铜、载玻片和聚四氟乙烯)的蒸发析晶过程,分析了表面性质和环境压力的影响。结果表明,低压环境下易在接触线处析出白色盐晶。铜表面由于表面能较大,接触面上覆盖盐晶体,液滴蒸发过程接触直径几乎不变,接触角逐渐减小。在载玻片表面,当环境压力较高时,液滴蒸发造成接触线收缩,伴随盐晶体的生长和移动接触角波动。在聚四氟乙烯表面,接触面处易产生气泡,气泡的生长和爆裂导致接触角明显波动。Pe数可以揭示液滴蒸发过程外部传质扩散和内部离子扩散的相对大小。研究成果有助于指导海水淡化的工业应用。     

Crack behavior in a high contact ratio spur gear tooth and its effect on mesh stiffness

The efficiency of high contact ratio (HCR) gearing can be achieved by proper selection of gear geometry for increased load capacity and smoother operation despite of their high sliding velocities. The prediction of variation in mesh stiffness of HCR gearing is critical as the average number of teeth being in contact is high at a given time as compared to conventional low contact ratio (LCR) gearing. In this paper, linear elastic fracture mechanics (LEFM) based finite element method is used to perform the crack propagation path studies of HCR spur gear having tooth root crack for two gear parameters viz. backup ratio and pressure angle. A total potential energy model has been adopted to analytically estimate the mesh stiffness variation. The results depict the mesh stiffness reduction in the presence of the crack. The percentage change in mesh stiffness with increasing crack length is an important parameter in fault diagnosis of geared transmission. Higher the percentage change in mesh stiffness, easier to detect the fault. Two gear parameters viz. back-up ratio and pressure angle has been studied and the effect of crack length on mesh stiffness have been outlined. With the increase of deterioration level gears having lower back-up ratio fault can be detected at an early stage, similarly, chances for early fault detection is more for gears having higher pressure angle.     

Multi-scale Numerical Modeling of Radial Heat Transfer in Grooved Heat Pipe Evaporators

It is well known that small-scale effects near contact lines have a crucial importance on the radial heat transfer within a grooved heat pipe evaporator. This paper studies this problem using a multi-scale model which is composed of two parts, macroscopic and microscopic. At the macroscopic scale, we solve the heat conduction problem for the solid and the liquid phases, using a finite-element method. In order to avoid the classical singularity problem at the contact line, in addition to taking the solid thermal conductivity into account, we do not impose the saturation temperature but a mixed condition along the interface. The coupling with the microscopic scales is achieved using a correlation for the apparent contact angle, obtained from a lubrication-type theory developed for the contact line region, and taking into account the variation of the saturation temperature with the disjoining pressure and with the meniscus curvature. Our results show a strong influence of this apparent contact angle on the heat transfer within the heat pipe, for two different geometries and as a function of the heat flux.     

Mathematical modeling of moving contact lines in heat transfer applications

We provide an overview of research on the mathematical modeling of apparent contact lines in non-isothermal systems conducted over the past several decades and report a number of recent developments in the field. The latter involve developing mathematical models of evaporating liquid droplets that account not only for liquid flow and evaporation, but also for unsteady heat conduction in the substrate. The droplet is placed on a flat heated solid substrate and is assumed to be in contact with a saturated vapor. Furthermore, we discuss a careful comparison between mathematical models and experimental work that involves simultaneous measurement of shapes of evaporating droplets and temperature profiles in the solid substrate. The latter is accomplished using thermochromic liquid crystals. Applications to new research areas, such as studies of the effect of evaporation on fingering instabilities in gravity-driven liquid films, are also discussed.     

Ti—5Al,5Sn合金冷坩埚感应熔炼过程中Al和Sn元素的挥发研究

利用所建立模型研究了Ｔｉ－５Ａｌ－２,５Ｓｎ合金感应凝壳熔炼（ＩＳＭ）过程中Ａｌ、Ｓｎ元素的挥发控制方式,并在此基础上研究了熔体温度和真空室压和对Ａｌ、Ｓｎ挥发速率的。结果表明,实际熔炼条件下Ａｌ、Ｓｎ的挥发都由界面挥发反应单一控制,真空室压力对挥发速率的影响具有明显的临界值,当压力低于此临界值时,挥发速率几乎没有什么粉经,两当压力高于此值时,挥发速率迅速降低。     

On the asymptotic analysis of surface-stress-driven thin-layer flow

It has been demonstrated experimentally that thin liquid layers may be applied to a solid surface or substrate if a temperature gradient is applied which results in a surface tension gradient and surface traction. Two related problems are considered here by means of the long-wave or lubrication theory. In the first problem, an improved estimate of the applied liquid coating thickness for a liquid being drawn from a bath is found through asymptotic and numerical matching. Secondly, the theory is extended to consider substrates that are not perfectly wetted but exhibit a finite equilibrium contact angle for the coating liquid. This extension incorporates the substrate energetics using a disjoining pressure functional. Unsteady flows are calculated on a substrate of nonuniform wettability. The finite contact angle value required to stop stress-driven flow is predicted and the resulting steady profiles are compared with experimental results for several values of the applied stress.     

Wetting of MgO and α-Al2O3 by molten Mg: a model of droplet with high vapor pressure

The wetting of MgO and α-Al₂O₃ polycrystalline plates by molten Mg in purified argon was studied between 973 and 1273?K using an improved sessile drop method. The MgO/Mg system is basically non-reactive while Al₂O₃/Mg is reactive. The common features in the non-reactive and reactive systems are the high tendency for oxidation and the high evaporation rate of Mg. It is shown that wetting kinetics in both systems is governed by the evaporation and pinning phenomenon leading to contact angle versus time curves passing through a minimum: the apparent contact angle first decreases and then increases. The intrinsic contact angle should be estimated using the initial value (advancing contact angle) and the maximum value just before the disappearance of the droplet caused by Mg evaporation (receding contact angle).     

Meniscus and viscous forces during separation of hydrophilic and hydrophobic smooth/rough surfaces with symmetric and asymmetric contact angles

Adhesive or repulsive forces contributed by both meniscus and viscous forces can be significant and become one of the main reliability issues when the contacting surfaces are ultra smooth, and the normal load is small, as is common for micro/nano devices. In this study, both meniscus and viscous forces during separation for smooth and rough hydrophilic and hydrophobic surfaces are studied. The effects of separation distance, initial meniscus height, separation time, contact angle and roughness are presented. Meniscus force decreases with an increase of separation distance, whereas the viscous force has an opposite trend. Both forces decrease with an increase of initial meniscus height. An increase of separation time, initial meniscus height or a decrease of contact angle leads to an increase of critical meniscus area at which both forces are equivalent. An increase in contact angle leads to a decrease of attractive meniscus force but an increase of repulsive meniscus force (attractive or repulsive dependent on hydrophilic or hydrophobic surface, respectively). Contact angle has a limited effect on the viscous force. For asymmetric contact angles, the magnitude of the meniscus force and the critical meniscus area are in between the values for the two angles. An increase in the number of surface asperities (roughness) leads to an increase of meniscus force; however, its effect on viscous force is trivial. A slightly attractive force is observed for the hydrophobic surface during the end stage of separation though the magnitude is small. The study provides a fundamental understanding of the physics of the separation process and it can be useful for control of the forces in nanotechnology applications.     

截锥壳颤振分析的微分求积法

引入微分求积法(Differential Quadrature Method,简称DQM)对截锥壳气动弹性方程离散,采用一阶活塞理论气动力,运用特征值分析方法求解系统的颤振临界动压。研究了半顶角、径厚比、长径比等几何参数对颤振临界动压的影响。结果表明,DQM求解截锥壳气动弹性方程具有良好的精度和计算效率,结构产生1阶~2阶耦合型颤振的最低临界动压对应的周向波数较大,并因几何参数而异;颤振临界动压参数随半顶角的增大而减小,随着径厚比的增大而增大,随长径比的增大而减小。     

Jet printing of colloidal solutions – Numerical modeling and experimental verification of the influence of ink and surface parameters on droplet spreading

Ink jet printing of functional materials promises an efficient route for the manufacturing of future low cost and large-area electronics applications. The effect of capillary flow of thin liquid films, the control of droplet spreading by suitably influencing the wetting properties of surfaces, the rheology of the ink and the process design play a relevant role in improvement of ink jet printed patterns. This work presents the experimentally based numerical study of the shape of single ink jetted droplets controlled by homogeneous contact angle distributions. The dynamics of the fluid on the substrate surface is treated in the frame of the lubrication theory using the concept of a precursor film and modeling the equilibrium contact angle by a disjoining pressure. The model describes the spreading of axisymmetric droplets considering different material and process parameter configurations. It is shown that the spreading process can be modeled separately from the drying process within a certain range of contact angles.     

Influence of fluorinated self-assembled monolayer on wetting dynamics during evaporation of refrigerant–oil mixture on metal surface

Reducing wettability of a metal surface is a promising method for enhancing boiling heat transfer of refrigerant–oil mixture on the metal. As fluorinated self-assembled monolayer (F-SAM) coating is effective for wettability reduction, its influence on wetting dynamics including meniscus shape, contact angle, contact line velocity and rising liquid height during evaporation of refrigerant–oil mixture on metal surface were experimentally investigated. The refrigerant–oil mixture was prepared by R141b and NM56, the oil mass fraction ranged from 0 to 10 wt%, and the surface roughness ranged from 0.028 to 1.166 µm. The results show that during evaporation of refrigerant–oil mixture, the presence of F-SAM changes the evaporation mode to be constant contact line velocity followed by both constant contact angle and contact line velocity, while decreases the rising liquid height. The results suggest that larger surface roughness and higher oil mass fraction are preferred when using F-SAM to reduce surface wettability.     

Quantum Fingering of the Inverted Liquid-Crystal 4He Interface in the Field of Gravity

The simplest example of fingering occurs when a heavier liquid occupies the half-space above a lighter one. The fingers of the heavier liquid driven by gravity grow down, displacing the lighter liquid upward. The fingering of the superfluid phase into the ⁴He crystal facet below its roughening transition temperature can provide us an example of macroscopic quantum nucleation phenomena. Due to cusp-like singularity in the surface tension as a function of the facet orientation the crystal facet has a relative stability and its fingering is accompanied by overcoming some critical nucleation barrier. The barrier height is proportional to the square of the facet step energy and depends on a ratio of the facet size to the capillary length. At sufficiently low temperatures the thermal activation mechanism for the interface fingering is replaced with the quantum one associated with the penetration through the nucleation barrier.      

加肋斜度对加肋壳稳定性的影响

本文从正交各向异性假设出发,推导了肋骨具有斜度时环加肋圆柱壳总体失稳的临界水压公式,并且用有限元分析软件ＡＬＧＯＲ进行了验证。在公式推导的过程中,考虑了加肋的实际分布情况,并编制了计算程序,对半圆环界面加肋圆柱壳和圆管加肋圆柱壳的临界水压进行了比较。算例表明,在消耗相同材料的情况下,半圆环加肋圆柱壳具有较好的抗水压性能;肋骨斜度增加,临界水压下降。     

Effect of a supersonic counterflow jet on blunt body heat transfer rates for oncoming high enthalpy flow

Heat transfer reduction studies, in the presence of a supersonic counterflow jet from the stagnation point of a 60-deg apex angle blunt cone, are conducted in a free piston driven hypersonic shock tunnel, HST3, to verify the effectiveness of this technique for high enthalpy flows. For flow of Mach number 8 with stagnation enthalpy of 5 MJ/kg, it has been observed that the heat transfer rate at some location decreases initially with increase in the injection pressure ratio until the critical injection pressure ratio is reached. A forty-five percent reduction in heat transfer rate near the stagnation point has been measured for the critical injection pressure ratio, equal to 14.91. A further increase in the injection pressure ratio reduces the overall percentage heat transfer reduction. The dependence of fluidic spike length on percentage heat transfer reduction has been confirmed. Published in Inzhenerno-Fizicheskii Zhurnal, Vo. 82, No. 1, pp. 3–7, January–February, 2009.     

An experimental investigation of modes of flow under conditions of evaporation of liquid on a vertical heating surface

An experimental investigation is performed of the effect of temperature head on the flow of evaporating film of liquid, defined by the wetting line or by ribs, on a vertical heating surface. The experiments are performed under conditions of evaporation of R11 Freon in a medium of own vapor on a vertical copper plate, including the presence of ribbing. The visualization of flow is performed. Analysis is made of the effect of the evaporation intensity in the neighborhood of liquid-vapor-wall contact line on the conditions of film discontinuity and on the pattern of resultant streamer flow. It is demonstrated that, rather than spreading, the liquid in the case of streamer flow on the heating surface contracts downstream even for a close-to-zero equilibrium wetting angle. This is due to intense evaporation of liquid in the region of liquid-vapor-wall contact line, where the liquid film exhibits a minimal thickness, to the variation of curvature of the interface in this region, and to the emergence of thermal contact angle. The dependence of thermal contact angle on temperature head is determined. Dynamic measurements are performed of the local thickness of flowing films of liquid using a capacitance meter, and spectral analysis is performed of waves which arise because of instability of film flow on the evaporating film surface.     

Wetting and evaporation behaviors of molten Mg–Al alloy drops on partially oxidized α-SiC substrates

The wetting and evaporation behaviors of Mg–Al alloys over a full composition range on partially oxidized polycrystalline α-SiC substrates were studied in a flowing Ar atmosphere using an improved sessile drop method. The time dependence of the changes in contact angle and drop geometry was monitored and representative wetting stages were identified. The initial contact angles at 1173 K were 100° for pure Al and 76° for pure Mg, with the maximum value of 106° for the 7.6 mol.% Mg–Al alloy. The interfacial reaction and the evaporation of Mg led to the decrease in the apparent contact angle in the spreading stage and their respective contribution was evaluated. After the pinning of the triple line, the decrease in the contact angle resulted from the diminishing drop volume as a consequence of the Mg evaporation. The effects of Mg concentration on the wetting and evaporation behaviors were discussed. A mechanism for the time-dependent diminishing drop volume was proposed in light of the competition between the Mg evaporation and its diffusion from the drop bulk to the surface. Finally, the interfacial reaction was analyzed based on thermodynamic considerations.     

The interaction between the wellbore and pre-existing fractures

Down-hole imaging techniques have revealed that natural fractures can be reactivated in the vicinity of a wellbore. Fracture reactivation, however, has never been analysed in detail. In particular, no one has quantified the influence of in-situ state of stress, fracture friction angle, wellbore pressure, mud invasion in the fracture plane and fracture location on the short and long term stability of the fracture. We have therefore little knowledge of the importance of the phenomenon and of the conditions which lead to fracture reactivation.This work aims to quantify the influence of various controlling parameters on fracture instability. For this purpose, we have extended a method which was previously used to analyse the interaction of tensile cracks with the wellbore. The fluid invasion into the fracture is taken into account by assuming a length of invasion along which the fluid pressure is equal to the wellbore pressure.This work shows that fracture reactivation due to near wellbore effects is likely to occur although the fracture movement may not be easily detected. However the occurrence of this mechanism is quite sensitive to the fracture location with respect to the wellbore and to the fracture orientation. This work has also revealed the possibility of two length scales in fracture instability: the first length scale is related to the interaction of the wellbore with the fracture and the second one is related to fracture instability with respect to the far-field state of stress.     

Flutter of delaminated cross-ply laminated cylindrical shells

In this study, the instability of delaminated cross-ply thin laminated cylindrical shells and panels when subjected to supersonic flow parallel to its length edge is investigated. The delamination is parallel to the shell reference and it extends along the entire length of the cylindrical shell. The Love’s shell theory and Von-Karman–Donnell type of kinematic relations along with first-order potential theory have been employed to construct the aeroelastic equations of motion. The effects of several parameters such as length to radius ratio, delamination position, size and thickness on the critical values are discussed in the details. The results indicate that the presence of delamination reduced the overall stiffness of the structure and thereby decreases the flutter critical boundaries.