Viscous dissipation of a power law fluid in axial flow between isothermal eccentric cylinders

We study the temperature distribution of a power law fluid in a pressure-driven axial flow between isothermal eccentric cylinders in bipolar cylindrical coordinates. We begin our analysis by writing the equation of energy in bipolar cylindrical coordinates. We then obtain a dimensionless algebraic analytic solution for temperature profiles under a steady, laminar, incompressible and fully developed flow [Eq. (64)]. We find that the dimensionless temperature profile depends upon the radius ratio of the inner to outer cylinders, the eccentricity, the angular position, and the power law exponent n. The temperature is a strong function of the gap between the cylinders. The temperature profiles are flat in the middle of the gap and then, near the wall, suddenly drop to the wall temperature.     

Equilibrium shapes of a drop pendant in an electrostatic field

The stationary shapes of a conducting fluid drop in the gap between the plates of a plane capacitor are studied. The drop is held on the upper plate by the surface tension forces. The self-consistent problem of the determination of the drop shape and the charge distribution over its surface is solved. Estimates are obtained for the maximum volume of the stationary drop at the given fluid parameters and electric field strength.     

Level‐set based numerical simulation of a migrating and dissolving liquid drop in a cylindrical cavity

In the present paper the dissolution of a binary liquid drop having a miscibility gap and migrating due to thermo‐solutal capillary convection in a cylindrical cavity is studied numerically. The interest in studying this problem is twofold. From a side, in the absence of gravity, capillary migration is one of the main physical mechanisms to set into motion dispersed liquid phases and from the other side, phase equilibria of multi‐component liquid systems, ubiquitous in applications, often exhibit a miscibility gap. The drop capillary migration is due to an imposed temperature gradient between the cavity top and bottom walls. The drop dissolution is due to the fact that initial composition and volume values, and thermal boundary conditions are only compatible with a final single phase equilibrium state. In order to study the drop migration along the cavity and the coupling with dissolution, a previously developed planar two‐dimensional code is extended to treat axis‐symmetric geometries. The code is based on a finite volume formulation. A level‐set technique is used for describing the dynamics of the interface separating the different phases and for mollifying the interface discontinuities between them. The level‐set related tools of redistancing and off‐interface extension are used to enhance code resolution in the critical interface region. Migration speeds and volume variations are determined for different drop radii. Copyright © 2004 John Wiley & Sons, Ltd.     

An Approximate Lie Group Investigation into the Spreading of a Liquid Drop on a Slowly Dropping Flat Plane

The approximate Lie group method is used to investigate the evolutionof the free surface of a thin liquid drop on a slowly dropping flat plane. Surfacetension effects are ignored. A group classification is performed to determine the rateat which the plane drops. An approximate group invariant solution is then calculatedfor the free surface of an evolving liquid drop on the slowly dropping flat plane. Animportant parameter in the solution is the initial angle of the plane. For small anglesthere is no significant difference in the drop profile. For larger angles, changes in thedrop profile and rate of spreading are significant.     

Liquid flow in a gap between a cylinder and a wall in motion

The results of an experimental investigation and calculations of the location of the minimum pressure point are presented for the case, when a cylindrical body moves along a wall in the presence of a small gap. The pressure on the cylindrical body surface is measured in the confusor and diffuser regions. It is shown that with decrease in the gap the minimum pressure point is displaced toward the minimum gap line, with increase in the pressure drop. An increase in the velocity of the motion at a constant gap leads only to a pressure increase in the diffuser region, while the location of the minimum pressure point remains the same. It is established that an increase in the inner cylinder radius moves the minimum pressure location away from the minimum gap line. The formation of two return flow regions in the confusor and diffuser regions near the cylindrical surface is detected. It is shown that the return flow in the pressure drop region reaches the stage of incipient cavitation bubbles. The results obtained can be useful in lubrication theory, as well as in medicine and biology.     

GROUND EFFECT OF FLOW AROUND AN ELLIPTIC CYLINDER IN A TURBULENT BOUNDARY LAYER

The flow characteristics around an elliptic cylinder with an axis ratio of AR=2 located near a flat plate were investigated experimentally. The elliptic cylinder was embedded in a turbulent boundary layer whose thickness is larger than the cylinder height. For comparison, the same experiment was carried out for a circular cylinder having the same vertical height. The Reynolds number based on the height of the cylinder cross-section was 14000. The pressure distributions on the cylinder surface and on the flat plate were measured for various gap distances between the cylinder and the plate. The wake velocity profiles behind the cylinder were measured using hot-wire anemometry. In the near-wake region, the vortices are shed regularly only when the gap ratio is greater than the critical value of G/B=0·4. The critical gap ratio is larger than that of a circular cylinder. The variation of surface pressure distributions on the elliptic cylinder with respect to the gap ratio is much smaller than that on the circular cylinder. This trend is more evident on the upper surface than the lower one. The surface pressures on the flat plate recover faster than those for the case of the circular cylinder at downstream locations. As the gap ratio increases, the drag coefficient of the cylinder itself increases, but the lift coefficient decreases. For all gap ratios tested in this study, the drag coefficient of the elliptic cylinder is about half that of the circular cylinder. The ground effect of the cylinder at small gap ratio constrains the flow passing through the gap, and restricts the vortex shedding from the cylinder, especially in the lower side of the cylinder wake. This constraint effect is more severe for the elliptic cylinder, compared to the circular cylinder. The wake region behind the elliptic cylinder is relatively small and the velocity profiles tend to approach rapidly to those of a flat plate boundary layer     

穿透现象和液滴形状的关系

拍摄了下落水滴周期性形变的照片，穿透现象（指水滴和水面碰撞后变成环状，穿入水中，直到池底）是在水滴为扁椭球形状或接近扁椭球形状时和水面碰撞发生的．表面张力是改变水滴形状的手段     

Visualization of the impact of water drops on a hot surface: effect of drop velocity and surface inclination

The behaviour of one drop impinging on a hot surface by varying the surface temperature, the drop velocity and the position of the surface (horizontal and a inclined 45°) both at a temperature below and above the Leidenfrost temperature has been experimentally evaluated, estimating the temperature at which the drop rebounds. A large influence on the drop velocity has been evidenced. The inclination of the surface decreases the critical value of the temperature above which the surface is not rewetted.     

The optimal drop shape for vortices generated by drop impacts: the effect of surfactants on the drop surface

Subsurface vortices are frequently created when a falling drop strikes a flat water surface. Prior work has demonstrated that the shape of the drop at the point of impact is critical in determining how deep or how fast the resulting vortex will penetrate into the water bulk. In the present study, the details of this phenomena are explored by using surfactants to vary surface tension. Specifically, Triton X-100 monolayers are created on the surface of the drop, and on the flat water surface. The results of these experiments suggest that there is no single optimal drop shape resulting in best vortex penetration. Rather, the data suggest that the optimal shape depends on the surface tension of the falling drop. An attempt is made to reconcile contradictory results in the literature using this result.

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ATOMIZATION OF A LIQUID DROP BY PULSATION

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Phase-field modeling of interfacial dynamics in emulsion flows: Nonequilibrium surface tension

A weakly nonlocal phase-field model is used to define the surface tension in liquid binary mixtures in terms of the composition gradient in the interfacial region so that, at equilibrium, it depends linearly on the characteristic length that defines the interfacial width. Contrary to previous works suggesting that the surface tension in a phase-field model is fixed, we define the surface tension for a curved interface and far-from-equilibrium conditions as the integral of the free energy excess (i.e., above the thermodynamic component of the free energy) across the interface profile in a direction parallel to the composition gradient. Consequently, the nonequilibrium surface tension can be widely different from its equilibrium value under dynamic conditions, while it reduces to its thermodynamic value for a flat interface at local equilibrium. In nonequilibrium conditions, the surface tension changes with time: during mixing, it decreases as the inverse square root of time, while in the linear regime of spinodal decomposition, it increases exponentially to its equilibrium value, as nonlinear effects saturate the exponential growth. In addition, since temperature gradients modify the steepness of the concentration profile in the interfacial region, they induce gradients in the nonequilibrium surface tension, leading to the Marangoni thermocapillary migration of an isolated drop. Similarly, Marangoni stresses are induced in a composition gradient, leading to diffusiophoresis. We also review results on the nonequilibrium surface tension for a wall-bound pendant drop near detachment, which help to explain a discrepancy between our numerically determined static contact angle dependence of the critical Bond number and its sharp-interface counterpart from a static stability analysis of equilibrium shapes after numerical integration of the Young-Laplace equation. Finally, we present new results from phase-field simulations of the motion of an isolated droplet down an incline in gravity, showing that dynamic contact angle hysteresis can be explained in terms of the nonequilibrium surface tension.     

Modeling of a Dynamic Magneto-Fluid Seal in the Presence of a Pressure Drop

The ferrohydrodynamic problem, with a disconnected free surface, of the stability of an annular magneto-fluid seal under the action of centrifugal forces and a pressure drop is solved numerically. The effect of the shaft speed on the critical pressure drop is investigated in relation to the volume of the magneto-fluid plug, the magnetic field strength, the magnetic properties of the fluid, the gap width, and the shaft radius. The flow pattern and the thermal power released in the sealing layer are studied.     

Experimental comparison between the effect of electrical discharge and the effect of surface heating on Mach 2 rarefied airflow over a flat plate

This study describes the experimental investigation of the effect of a negative DC glow discharge on a Mach 2 rarefied airflow around a flat plate. More precisely, we will show a comparison between two experiments. In the first one we will observe the effect of discharge by Pitot probe measurement. This discharge is created by applying negative DC potential difference between two electrodes flush mounted on the surface of a quartz flat plate placed in Mach 2 rarefied airflow. The electrodes are arranged in the spanwise direction. In the second experiment, electrodes are removed and replaced with a surface heater. The pressure profiles obtained by a glass Pitot tube are presented, and a comparison between the plasma effect and the surface heater effect is made, for the same surface temperature and in thermal equilibrium, with the aim of identifying the origin of the observed effect. For both experiments, surface heating causes a decrease in the boundary layer stagnation pressure, while increasing the boundary layer thickness, with the effects becoming larger for higher mean surface temperature. The effects due to the plasma actuator seem to be larger over the active electrode.     

Motion of non-wetting drop in constricted geometry

This work is a contribution to the study of deformation of a non-wetting drop transported under the combined effect of gravity and permanent fluid motion in a vertical channel. The deformation being caused during passage of the drop through a constriction formed by two spherical obstacles placed opposite in a vertical channel. For this purpose a three-dimensional computation is conducted in order to illustrate the behavior of the drop in the condition of non-wettability. The flow based on Navier–Stokes equation is solved numerically with volume of fluid (VOF) method. The corresponding simulations are carried out in view to analyse the behavior of the drop when it is forced to move between the obstacles for different values gap size until the breakup is obtained.     

Evolution of roughness on the surface of a strained elastic material due to stress-driven surface diffusion

The free energy of a stressed crystal is assumed to consist of elastic strain energy and surface energy, and the chemical potential for surface diffusion at constant temperature is obtained under this assumption. A gradient in chemical potential results in diffusive mass transport along the surface. The result is applied in considering the phenomena of instability of a flat surface in a stressed material under fluctuations in surface shape, and the transient evolution of surface roughness due to an initial perturbation in the nearly flat free surface of the material, both under plane strain conditions.     

Fluid flow and heat transfer in transitional boundary layers: effects of surface curvature and free stream velocity

Velocity and wall temperature measurements, over flat plate, concave and convex walls, were experimentally investigated in a low-speed wind tunnel with inlet velocities of 4 and 12 m/s encompassing the transitional region with streamwise distance Reynolds numbers from 3.15×10⁵ to 1.04×10⁶. As the velocity profiles, recorded by a semi-circular pitot tube and a digital constant-temperature hot-wire anemometer, were compared to exact Blasius profile and (1/7)th power law, experimental local Stanton numbers to analytical flat plate solution and turbulent correlation formula. Intermittency factors, derived from velocities and local Stanton numbers, were presented both in streamwise and pitchwise directions. It was found that the convex curvature delayed transition up to Re _x =1.04×10⁶, with a mean intermittency value of 0.61 and a shape factor of 1.81, where the similar intermittency and shape factors were determined at Re _x of 8.33×10⁵ and 4.25×10⁵ for the flat plate and concave wall, indicating the enhancing role of concave curvature on the transition mechanism. The thinner boundary layers of the concave surface resulted in higher intermittency values, corresponding to higher skin friction and Stanton numbers; moreover the lowest gap between the measured and derived Stanton numbers were also obtained over the concave surface. Destabilising role of the concave wall caused Stanton numbers to increase up to 22%, whereas the convex wall, due to its stabilising character, produced lower Stanton numbers by 12% with respect to those of the flat plate.     

Experimental investigation of the flow pattern,pressure drop and void fraction of two-phase flow in the corrugated gap of a plate heat exchanger

The two-phase flow in the corrugated gap created by two adjacent plates of a plate heat exchanger was investigated experimentally. One setup consisting of a transparent corrugated gap was used to visualize the two-phase flow pattern and study the local phenomena of phase distribution, pressure drop and void fraction. Saturated two-phase R365mfc and an air-water mixture were used as working fluids.In a second experimental setup, the heat transfer coefficients and the pressure drop inside an industrial plate heat exchanger during the condensation process of R134a are determined. Both experimental setups use the same type of plates, so the experimental results can be connected and a flow pattern model for the condensation in plate heat exchangers can be derived. In this work the results of the flow pattern visualization, the two-phase pressure drop in the corrugated gap and the void fraction analysis by measurement of the electrical capacity are presented. A new pressure drop correlation is derived, which takes into account different flow patterns, that appear during condensation. The mean deviation of the presented pressure drop model compared to the experimental data and data from other experimental works is 18.9%. 81.7% of the calculated pressure drop lies within ±30% compared to the experimental data.     

Motion of a spherical particle in a viscous nonisothermal fluid

The Stokes and Hadamard-Riabouchinsky formulas are generalized to the case of steady motion of a solid spherical particle or drop in an incompressible fluid whose viscosity depends exponentially on the temperature. It is shown that for finite temperature differences between the surface of the particle and the region far from it the drag is determined by an effective viscosity with value close to the geometric mean of the viscosity on the surface of the particle and far from it.     

平行间隙的热楔承载机理分析

本文研究了在4类表面温度边界条件下的热密度楔和热黏度楔对承载能力的影响,指出平行间隙内的油膜也具有承载能力,并与传统的几何楔进行了比较,分析了热密度楔和热黏度楔的关系及其重要性.除了用传统的表面温度差原理来解释平行间隙的承载机理外,还通过数值分析提出了1种补充理论,指出即使2个平行表面之间没有温度差但因油膜内部温度分布不均匀油膜也会产生承载力.