Numerical simulation of thin liquid films over a solid non-wettable substrate assuming lubrication approximation.

When a continuous film flows over a non-wettable surface, it may break up with the consequent formation of a dry-patch. The actual shape of the resulting water layer is of great interest in several engineering applications, such as in-flight icing simulations, finned dehumidifier behavior modeling, coating process and chemical absorption/distillation through structured packing. A 2D numerical solver for the prediction of film flow is presented. The lubrication approximation is assumed, allowing for the description of liquid film flowing down an inclinate plate, driven by both gravity and shear. The effects of contact line and surface wettability are introduced combining the precursor film model and the disjoining pressure terms. The capillary pressure, which is usually modeled through the small slope approximation, is here defined imposing the membranal equilibrium of the gas-liquid free-surface, in order to investigate higher values of the imposed equilibrium contact angle between liquid and solid substrate. The in-house solver is first validated with both experimental and numerical results, available in literature. Numerical simulations are then performed with the aim of studying the beahvior of liquids in absorption/distillation process through structured packing. The lubrication theory is finally extended to the most general case of a 3D curved substrate, allowing to investigate problems involving complex geometries and configurations. Thus, a liquid film flowing down a packing layer, which is a wrinked surface composing the packed column used in absorption process, is simulated. Such a problem has been investigated in literature by means of a fully 3D approach only, but the huge computational costs do not allow to investigate several configurations, resulting in a lack of knowledge of the hydrodinamics driving the liquid flowing through the packing layers. The full modeling of the capillary pressure and the extension to general curved substrates clearly put a new effort to the well known lubrication theory and allow to simulate phenomena, that were not covered by such a theory.When a continuous film flows over a non-wettable surface, it may break up with the consequent formation of a dry-patch. The actual shape of the resulting water layer is of great interest in several engineering applications, such as in-flight icing simulations, finned dehumidifier behavior modeling, coating process and chemical absorption/distillation through structured packing. A 2D numerical solver for the prediction of film flow is presented. The lubrication approximation is assumed, allowing for the description of liquid film flowing down an inclinate plate, driven by both gravity and shear. The effects of contact line and surface wettability are introduced combining the precursor film model and the disjoining pressure terms. The capillary pressure, which is usually modeled through the small slope approximation, is here defined imposing the membranal equilibrium of the gas-liquid free-surface, in order to investigate higher values of the imposed equilibrium contact angle between liquid and solid substrate. The in-house solver is first validated with both experimental and numerical results, available in literature. Numerical simulations are then performed with the aim of studying the beahvior of liquids in absorption/distillation process through structured packing. The lubrication theory is finally extended to the most general case of a 3D curved substrate, allowing to investigate problems involving complex geometries and configurations. Thus, a liquid film flowing down a packing layer, which is a wrinked surface composing the packed column used in absorption process, is simulated. Such a problem has been investigated in literature by means of a fully 3D approach only, but the huge computational costs do not allow to investigate several configurations, resulting in a lack of knowledge of the hydrodinamics driving the liquid flowing through the packing layers. The full modeling of the capillary pressure and the extension to general curved substrates clearly put a new effort to the well known lubrication theory and allow to simulate phenomena, that were not covered by such a theory

The Influence of Geometry on the Thermal Performance of Microchannels in Laminar Flow with Viscous Dissipation

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.Micro heat exchangers (MHXs) may achieve very high heat transfer coefficients thanks to their small dimensions and high Area-to-Volume ratio even in laminar flow. The main drawback of these devices is the high frictional losses – especially for liquid flows – that make viscous dissipation no longer negligible. In order to enhance heat transfer, modification of the channels’ cross-section is a viable strategy. In the present work the fully developed steady laminar flow of a Newtonian liquid through a microchannel subject to H1 boundary conditions in the presence of viscous dissipation is investigated. Entropy generation numbers and FG1a performance evaluation criterion are employed to assess the influence of smoothing the corners of an initially rectangular cross-section, with an aspect ratio ranging from 1 to 0.03 under four different types of geometrical constraints. The governing equations and the results are expressed in non-dimensional form, the intensity of viscous dissipation being exemplified by the Brinkman number, which is demonstrated to increase its maximum allowable value when corners are smoothed. The results are reported as a function of the non-dimensional radius of curvature Rc and aspect ratio and show that smoothing the corners almost invariably brings about a benefit for a fixed heated perimeter

Numerical Simulation of rivulet build up via lubrication equations

A number of engineering problems involve the evolution of a thin layer of liquid over a non-wettable substrate. For example, CO2 chemical absorption is carried out in packed columns, where ost-combustion CO2 flows up while liquid solvent falls down through a collection of corrugated sheets. Further application include, among others, in-flight icing simulations, moisture ondensation on de-humidifier fins, fogging build up and removal. Here, we present a development of an in-house code numerically solving the 2D lubrication equation for a film flowing down an nclined plate. The disjoining pressure approach is followed, in order to model both the contact line discontinuity and the surface wettability. With respect to the original implementation, the full odeling of capillary pressure terms according to Young- Laplace relation allows to investigate contact angles close to /2. The code is thus validated with literature numerical results, obtained by fully 3D approach (VOF), showing satisfying agreement despite a strong reduction in terms of computational cost. Steady and unsteady wetting dynamics of a developing rivulet are investigated and validated) under different load conditions and for different values of the contact angles

Bifurcation analysis of liquid films over low wettability surfaces

Thin liquid layer evolution over a solid substrate and film instability phenomena are involved in a number of engineering applications: in chemical absorption through structured packing, the corrugated sheets are covered by the liquid solvent, offering an enhanced interface surface between the solvent and the gas solute; in coating process, the liquid pattern influences the resulting coating quality; in condensation over finned dehumidifier, heat transfer performances are influenced by the evolving liquid layer, which may arrange as a droplets population or an ensemble of rivulets. Here, the evolution of a liquid layer flowing down an inclined plate bounded by lateral walls, which is the simplest configuration describing hydrodynamics inside structured packing, is numerically investigated. An in-house code, previously developed and largely validated in case of film instability and rivulet buildup, is used in order to solve governing lubrication equations. The full implementation of capillary pressure allows to simulate contact angles up to 60 . Film break is observed due to instability induced by lateral walls, if the imposed liquid flow rate exceeds a critical value, leading to the formation of a rivulet pattern. Fixing the size of the investigated physical domain, the number of observed rivulets, which strongly influences the resulting wetted area, is traced as a function of the flow characteristics (identified by the Bond number), the substrate wettability and the liquid properties; the corresponding bifurcation diagram is presented

Optimised Electro-Osmotic Flow in Rectangular Microchannels with Smoothed Corners

Electro-osmotic flows are a means of circulating polar fluids through microchannels without resorting to mechanical pumping. The lack of moving parts, of noise and the ease of integration in silicon chips make them an interesting option for microchip cooling and miniaturized total analysis systems. This paper describes an optimization in terms of first- and second-law analysis of the cross-section of a microchannel subject to electro-osmotic flow. Starting from rectangular cross-sections of different aspect ratios, its corners are progressively smoothed and the resulting Poiseuille and Nusselt numbers computed. Performance evaluation criteria are then used to assess the change in, among others, heat transfer rate, temperature difference between wall and bulk fluid, and equivalent pumping power. The entropy number is also computed and the results commented. It is found that the latter criterion highlights a configuration of minimum entropy generation, whereas the trends of the heat transfer and temperature difference are opposite to that of the equivalent pumping power

Numerical simulation of shear driven film instability over heterogeneous surfaces via enhanced lubrication theory

The prediction of the transition between continuous film, ensemble of rivulets and moving droplets is crucial in applications such as in-flight icing on airfoil wings or a number of chemical reactors. Here, lubrication theory is used to numerically investigate the stability of a continuous liquid film, driven by shear, over a heterogeneous surface. The disjoining pressure is used to model surface wettability, while the full implementation of the film curvature allows to investigate contact angles up to 60◦. Different heterogeneous surface configurations occurring in real problems are investigated. An extended computational campaign records the transition from continuous film to rivulet regime and, if present, the further transition from rivulet to droplets at different flow conditions. A moving grid approach allows for accurate prediction of instability phenomena at low computational cost. The numerical results are successfully validated with experimental evidence in case of critical flow rate leading to a stable dry patch and compared with literature results involving the inherently multiscale in-flight icing phenomenon, providing useful statistical information, required to transfer the present detailed small-scale information into larger scale CFD computational approaches

Performance assessment of electro-osmotic flow of rectangular microchannels with smoothed corners

Microchannel heat sinks are a viable alternative to traditional thermal management systems when high fluxes over small surfaces are involved. To avoid high pressure drops especially when liquids are concerned, electro-osmotic flow, a phenomenon which is relevant at the microscales only, can be employed profitably. Joule heating, which occurs every time an electrical current is circulated through a conductor with finite electrical resistance, may hamper the application of electro-osmotic flows significantly; its effects must therefore be investigated, as should the influence of the entry length on the overall transport phenomena which occur in the microchannel, especially so since channels with uniform temperature at the walls tend to be somewhat short, to mitigate heat generation due to Joule heating. In this paper the transport phenomena occurring within a microchannel of rectangular cross-section with uniform wall temperature through which an electro-osmotic flow occurs is studied, while considering the flow fully developed hydrodynamically but thermally developing (Graetz problem). The corners are then smoothed progressively and the effect of this change in the shape of the cross-section over the non-dimensional dissipated power or temperature difference between wall and fluid is investigated using the performance evaluation criteria introduced by Webb. Correlations are suggested for the Poiseuille and Nusselt numbers for all configurations as are criteria to obtain the maximum allowable channel length, i.e. the length of the channel over which the walls start to cool the fluid, owing to Joule heating, in terms of the hydraulic diameter