Session R13: Multiphase Flow VII

Modeling of Sulfuric Acid Condensation on Heat Exchanger Cooling Fins

Sulfuric acid corrosion on metallic heat exchanger cooling fins can cause serious blockage problem and stop the normal operation of heat exchangers. Corrosion rates are strongly dependent on surface film pH value. Therefore, a multi-physics computational framework was developed to predict the liquid film formed on solid surface and the pH distribution. Such a model can be used for better understanding of acid condensation from multi-species system. In this work, first, from S to H$_{2}$SO$_{4}$, formation of sulfuric acid in gas phase during combustion and cooling process was investigated with detailed chemistry mechanisms. The amount of SO$_{2}$ and SO$_{3}$ that plays important role in acid condensation process was calculated. Then, multi-component condensation process was modeled to produce a liquid film of acid and water solution condensed on solid surface that has low temperature. pH value was obtained based on the concentration of the acid. The above work provides critical information for corrosion analysis for heat exchangers.   

Reduced model for multi-component condensation

An extremely efficient reduced model for multi-component condensation is presented. The Becker-D\"oring (BD) equations are approximated by the General Dynamic Equation (GDE) in the supercritical region. The subcritical and critical regions are replaced by a source point that injects clusters into the supercritical region. The location and strength of the source point are determined from local estimates of the Gibbs free energy function, and the diffusion term in a corresponding Fokker-Planck equation. The result is a curve in composition space with Dirac delta function character in planes perpendicular to the curve. Integral properties of the GDE and BD solutions compare well for a typical two-component nucleation pulse experiment and computational effort is reduced by five orders of magnitude.   

Modeling of moving contact lines on electrically charged heated surfaces

Local fluid flow and heat transfer near moving contact lines on heated surfaces is usually described by mathematical models incorporating the effects of evaporation, surface tension, thermocapillarity, and disjoining pressure due to London-van der Waals forces. However, this description is not accurate for the cases when electric charges in the liquid and on the heated surface are present, which is usually the case in applications involving water and liquid metals. We develop a model which incorporates the electrostatic effects into the standard lubrication-type model of a contact line on a heated surface. The gas phase above the liquid is assumed to be pure vapor and the macroscopically dry region of the solid is covered with an adsorbed film. The local liquid-vapor interface shapes and the apparent contact angle are described as functions of the temperature and the charge density at the solid surface.   

Sustained inertial-capillary oscillations and jet formation in displacement flow in a tube

We study inertial effects in the displacement of a fluid in a capillary by a more viscous fluid using a level-set method. Various flow regimes are identified with a Reynolds and a capillary number as the main parameters. At relatively low Reynolds number, the meniscus forms a steady shape, and the interfacial curvature at the tube centre could change from being concave to convex upon increasing the Reynolds number. Beyond a critical Reynolds number, a quasi-steady solution is no longer found for sufficiently small contact angle values (less than 80 degrees): instead, the interface undergoes non-dampened periodic oscillations and, at even larger values of the Reynolds number, quasi-periodically, and the interface evolves from simple wavy shapes to complex shapes with multiple wavy units. Beyond a second critical Reynolds number, the liquid forms a jet and the meniscus advances with a nearly constant speed which decreases with Re. This is also observed at large contact angle values. In a developing jet, however, the interface shape remains partially quasi-steady, near the contact line region and the tube centre. The flow behaviour is shown to be robust over a range of other governing parameters, including the capillary number and the slip length.   

Bubbles in an isotropic homogeneous turbulent flow

Bubbly turbulent flow plays an important role in many engineering applications and natural phenomena. In this kind of flows the bubbles are dispersed in a turbulent flow and they interact with the turbulent structures. The present study focuses on the motion and hydrodynamic interaction of a single bubble in a turbulent environment. In most previous studies, the effect of bubbles on the carrier fluid was analyzed, under the assumption that the bubble size was significantly smaller that the smallest turbulence length scale. An experimental study of the effect of an isotropic and homogeneous turbulent flow on the bubble shape and motion was conducted. Experiments were performed in an isotropic turbulent chamber with nearly zero mean flow, in which a single bubble was injected. The fluid velocity was measured using the Particle Image Velocimetry (PIV) technique. The bubble deformation was determined by video processing of high-speed movies. The fluid disturbances on the bubble shape were studied for bubbles with different sizes. We will present experimental data obtained and discuss the differences among these results to try to understand the bubble - turbulence interaction mechanisms.   

Response of floating grains on a capillary Faraday wave in the dense limit

When macroscopic grains float on a water-air interface, they aggregate into a static cluster due to attractive gravity-induced capillary interaction between the grains. Here we study what happens when the grains in the cluster are excited using capillary Faraday waves with a wavelength comparable to the grain size. The grains are found to exhibit cooperative motion in domains which tend to become larger as the particle concentration $\phi$ increases towards the jamming point. We measure the average grain velocity and the velocity-velocity correlations of the grains in space and time as a function of $\phi$ and the driving amplitude $a$.   

Breakup of particle clumps on liquid surfaces

In this talk we describe the mechanism by which clumps of some powdered materials breakup and disperse on a liquid surface to form a monolayer of particles. We show that a clump breaks up because when particles on its outer periphery come in contact with the liquid surface they are pulled into the interface by the vertical component of capillary force overcoming the cohesive forces which keep them attached, and then these particles move away from the clump. In some cases, the clump itself is broken into smaller pieces and then these smaller pieces break apart by the aforementioned mechanism. The newly-adsorbed particles move away from the clump, and each other, because when particles are adsorbed on a liquid surface they cause a flow on the interface away from themselves. This flow may also cause particles newly-exposed on the outer periphery of the clump to break away. Since millimeter-sized clumps can breakup and spread on a liquid surface within a few seconds, their behavior appears to be similar to that of some liquid drops which can spontaneously disperse on solid surfaces.   

Surface shear viscosity effects on the damping of oscillations in millimetric liquid bridges

The damping rate of the small free oscillations in a non-cylindrical, axi-symmetric liquid bridge between two circular disks is calculated and compared with some previous experimental measurements using hexadecane in a millimetric liquid bridge. Current theories, accounting for viscous damping in both the boundary layers attached to the disks and the bulk, underestimated the measured damping by a $O$(1) quantity. Calculations based on the full Navier-Stokes equations are also in disagreement with the experimental results. These discrepancies are essentially eliminated in this work considering the effect of the surface shear viscosity (whose value results from empirical fitness), which could be due to the presence of a contaminating monolayer. Some conclusions are extracted in connection with surface wave damping in micro-fluidic devices.   

Optimized evaporation from a microchannel heat sink

Two-phase heat transfer devices, benefiting the unique thermal capacities of phase- change, are considered as the top choice for a wide range of applications involving cooling and temperature control. Evaporation and condensation in these devices usually take place on porous structures. It is widely accepted that they improve the evaporation rates and the overall performance of the device. The liquid menisci formed on the pores of a porous material can be viewed as the active sites of evaporation. Therefore, quantifying the rate of evaporation from a single pore can be used to calculate the total evaporation taking place in the evaporator given the density and the average size of the pores. A microchannel heat sink can be viewed as an structured porous material. In this work, an analytical model is developed to predict the evaporation rate from a liquid meniscus enclosed in a microchannel. The effects of the wall superheat and the width of the channel on the evaporation profile through the meniscus are studied. The results suggest that there is an optimum size for the width of the channel in order to maximize the thermal energy absorbed by the unit area of the heat sink as an array of microchannels.   

Numerical simulation of heat transfer provided by an impinging droplet train

A detailed investigation of the parameters that affect cooling within the thermal boundary layer created by a stream of impinging HFE-7100 droplets striking a pre-wetted and heated surface is performed. After the initial transient has ended, the flow enters a quasi-steady state in which the liquid crown formed during continuous droplet impact remains nearly stationary. Factors including initial film thickness, surface tension, droplet velocity, volumetric flow-rate and droplet frequency are categorized as either contributing to changing the thickness of the thermal boundary layer or as non-contributing parameters. Additionally, an analytical solution for the growth of the thermal boundary layer is proposed, using a crown propagation model, to describe the flow within the boundary layer. The analytical model shows good agreement with numerical results and incorporates the influence of the previously identified parameters.