Hybrid integral transform analysis of supercooled droplets solidification

The freezing phenomena in supercooled liquid droplets are important for many engineering applications. For instance, a theoretical model of this phenomenon can offer insights for tailoring surface coatings and for achieving icephobicity to reduce ice adhesion and accretion. In this work, a mathematical model and hybrid numerical–analytical solutions are developed for the freezing of a supercooled droplet immersed in a cold air stream, subjected to the three main transport phenomena at the interface between the droplet and the surroundings: convective heat transfer, convective mass transfer and thermal radiation. Error-controlled hybrid solutions are obtained through the extension of the generalized integral transform technique to the transient partial differential formulation of this moving boundary heat transfer problem. The nonlinear boundary condition for the interface temperature is directly accounted for by the choice of a nonlinear eigenfunction expansion base. Also, the nonlinear equation of motion for the freezing front is solved together with the ordinary differential system for the integral transformed temperatures. After comparisons of the solution with previously reported numerical and experimental results, the influence of the related physical parameters on the droplet temperatures and freezing time is critically analysed

Residence time control in micromixers with vortex shedding

Residence time control is an important indicator of micromixer design. When using vortex shedding to enhance mixing efficiency in a micromixer, the relationship between residence time and vortex shedding becomes important; if residence time is shorter than shedding time, the fluid elements flow through the channel too quickly with no contribution of vortex shedding to mixing. Both residence time and vortex shedding depend on geometrical and flow parameters and hence in order to optimize micromixer design the effect of these parameters on mixing need to be well understood. Furthermore, the onset of vortex shedding in confined flows such as those encountered in micromixers need be elucidated. In this work, the flow field past a single cylindrical pin in a microchannel is studied experimentally using a high-speed PIV system. The effects of confinement on vortex formation are examined. Vortex shedding was observed for a channel height of two pin diameters and the shedding frequency increased with increasing lateral confinement (i.e. upon decrease in channel width at the same pin diameter). Therefore, controlling residence time via wake oscillations in pin microchannels is highly dependent on confinement

An improved lumped model for freezing of a freely suspended supercooled water droplet in air stream

This work deals with the mathematical modeling of the transient freezing process of a supercooled water droplet in a cold air stream. The aim is to develop a simple yet accurate lumped-differential model for the energy balance for a freely suspended water droplet undergoing solidification, that allows for cost effective computations of the temperatures and freezing front evolution along the whole process. The complete freezing process was described by four distinct stages, namely, supercooling, recalescence, solidification, and cooling. At each stage, the Coupled Integral Equations Approach (CIEA) is employed, which reduces the partial differential equation for the temperature distribution within the spherical droplet into coupled ordinary differential equations for dimensionless boundary temperatures and the moving interface position. The resulting lumped-differential model is expected to offer improved accuracy with respect to the classical lumped system analysis, since boundary conditions are accounted for in the averaging process through Hermite approximations for integrals. The results of the CIEA were verified using a recently advanced accurate hybrid numerical-analytical solution through the Generalized Integral Transform Technique (GITT), for the full partial differential formulation, and comparisons with numerical and experimental results from the literature. After verification and validation of the proposed model, a parametric analysis is implemented, for different conditions of airflow velocity and droplet radius, which lead to variations in the Biot numbers that allow to inspect for their influence on the accuracy of the improved lumped-differential formulation

Approximation error model (AEM) approach with hybrid methods in the forward-inverse analysis of the transesterification reaction in 3D-microreactors

This work advances the approximation error model approach for the inverse analysis of the biodiesel synthesis using soybean oil and methanol in 3D-microreactors. Two hybrid numerical-analytical approaches of reduced computational cost are considered to offer an approximate forward problem solution for a three-dimensional nonlinear coupled diffusive-convective-reactive model. First, the Generalized Integral Transform Technique (GITT) is applied using approximate non-converged solutions of the 3D model, by adopting low truncation orders in the eigenfunction expansions. Second, the Coupled Integral Equations Approach (CIEA) provides a reduced mathematical model for the average concentrations, which leads to inherently approximate solutions. The AEM approach through the Bayesian framework is illustrated in the simultaneous estimation of kinetic and diffusion coefficients of the transesterification reaction. For this purpose, the fully converged GITT results with higher truncation orders for the 3D partial differential model are employed as reference results to define the approximations errors. The results highlight that either the non-converged solutions via GITT or the reduced model solution obtained via CIEA, when taking into account the model error, are robust and cost-effective alternatives for the inverse analysis of nonlinear convection–diffusion-reaction problems

Probing vortex-shedding at high frequencies in flows past confined microfluidic cylinders using high-speed microscale particle image velocimetry

Vortex-shedding from micropins has the potential to significantly enhance and intensify scalar transport in microchannels, for example by improving species mixing. However, the onset of vortex-shedding and the mixing efficiency are highly sensitive to the confinement imposed by the microchannel walls. In this work, the time dependent flow past a cylindrical pin in microchannels with different levels of confinement was studied experimentally. The onset of vortex-shedding in such flows is associated with high, kilohertz range frequencies that are difficult to resolve using conventional laser-based microscale particle image velocimetry (μPIV) techniques. Hence, in this study, a high-speed μPIV technique was implemented in order to obtain time-resolved measurements of the velocity fields downstream of the micropin to estimate the corresponding vortex-shedding frequencies and quantify the mixing in the pin wake. The vertical confinement (pin length to diameter ratio) was found to delay the onset of vortex-shedding. When vortex-shedding was present, the shedding frequency and the corresponding Strouhal numbers were found to be greater in channels with higher lateral confinement for the same Reynolds number. Finite-time Lyapunov exponent analysis was performed on the acquired velocity fields to estimate the mixing performance. The results clearly illustrated the significant enhancement in both the mixing in the wake and the mass flux across the centerline of the wake induced by vortex-sheddin

Flow dynamics and mixing past pairs of confined microfluidic cylinders

Placing cylindrical obstacles in a micromixer is a promising means to enhance mass transport. However, there is still a lack of fundamental understanding on the effect of obstacle arrangement on the flow. The present work provides new experimental insights into confined inertia flows past two cylindrical pins, placed either in tandem or staggered arrangement in a Y-type micromixer, and their effect on mixing, through micro Particle Image Velocimetry (μPIV) and Laser Induced Fluorescence (μLIF) measurements. It is found that in such confined microfluidic environments, adding a second pin suppresses vortex-shedding for spacings less than 3.5-pin diameters in a tandem arrangement or 0.25-pin diameters in the staggered configurations. Vortex-shedding is found to enhance mixing in tandem configurations but not in staggered ones. The results highlight the important roles of both pin arrangement and flow instabilities in micromixer performance and can serve as a guide to micromixer design

Hybrid Approach in Microscale Transport Phenomena: Application to Biodiesel Synthesis in Micro-reactors

A hybrid engineering approach to the study of transport phenomena, based on the synergy among computational, analytical, and experimental methodologies is reviewed. The focus of the chapter is on fundamental analysis and proof of concept developments in the use of nano- and micro-technologies for energy efficiency and heat and mass transfer enhancement applications. The hybrid approach described herein combines improved lumped-differential modeling, hybrid numericalanalytical solution methods, mixed symbolic-numerical computations, and advanced experimental techniques for micro-scale transport phenomena. An application dealing with micro-reactors for continuous synthesis of biodiesel is selected to demonstrate the instrumental role of the hybrid approach in achieving improved design and enhanced performance

Mixing in flows past confined microfluidic cylinders: Effects of pin and fluid interface offsetting

Inserting obstacles such as cylindrical pins in a micromixer has the potential to significantly enhance scalar transport and improve species mixing between two co-flowing streams. However, it remains unclear how the mixing efficiency in confined microchannel flows is affected by the positioning of the fluid interface and the cylindrical pin with respect to the wall or to each other. The present work investigates the mixing induced by a single cylindrical pin placed at different gap distances from the wall of a Y-type micromixer. Two fluid interface positions are considered by mixing the fluid streams at different ratios; one located at the channel centreline and one shifted towards one of the walls. Micro particle image velocimetry (μPIV) is applied to investigate the velocity fields and streamline patterns for the different pin locations, and micro laser-induced fluorescence (μLIF) to acquire the instantaneous concentration fields and assess the mixing performance, utilising the intensity of segregation technique. Prior to the onset of vortex-shedding and when the fluid interface coincides with the channel centreline, slightly offsetting the pin from the centreline is found to yield the best mixing performance compared to centreline or near wall pin locations. However, when vortex-shedding is present, a centreline pin location exhibits the best mixing performance. The present measurements indicate that single micropins can enhance mixing, even in the absence of vortex-shedding, and when vortex-shedding occurs, they are most efficient when the pin axis and fluid interface are aligned

Innovative Metallic Microfluidic Device for Intensified Biodiesel Production

We present a strategy for intensified biodiesel production in a novel metallic microdevice. Additive manufacturing using Selective Laser Melting (SLM) was employed to build the metallic device consisting of multiple micro reactors monolithically integrated with multiple micro heat exchangers. This device allows high conversion rate of biodiesel production with concomitant use of the rejected heat from external source to enhance the reaction temperature and, thereby, its output. The biodiesel production was carried out using soybean oil, ethanol and NaOH as the catalyst. The influences of the reaction temperature and the residence time in the biodiesel production was examined. Biodiesel yield increased with the reaction temperature and a rate of conversion of 99.6% was achieved with a reactor residence time of less than 35 seconds. The work opens up a pathway to exploit waste heat to intensify biodiesel production and contribute significantly to global sustainability

Probing vortex-shedding at high frequencies in flows past confined microfluidic cylinders using high-speed microscale particle image velocimetry

Vortex-shedding from micropins has the potential to significantly enhance and intensify scalar transport in microchannels, for example by improving species mixing. However, the onset of vortex-shedding and the mixing efficiency are highly sensitive to the confinement imposed by the microchannel walls. In this work, the time dependent flow past a cylindrical pin in microchannels with different levels of confinement was studied experimentally. The onset of vortex-shedding in such flows is associated with high, kilohertz range frequencies that are difficult to resolve using conventional laser-based microscale particle image velocimetry (μPIV) techniques. Hence, in this study, a high-speed μPIV technique was implemented in order to obtain time-resolved measurements of the velocity fields downstream of the micropin to estimate the corresponding vortex-shedding frequencies and quantify the mixing in the pin wake. The vertical confinement (pin length to diameter ratio) was found to delay the onset of vortex-shedding. When vortex-shedding was present, the shedding frequency and the corresponding Strouhal numbers were found to be greater in channels with higher lateral confinement for the same Reynolds number. Finite-time Lyapunov exponent analysis was performed on the acquired velocity fields to estimate the mixing performance. The results clearly illustrated the significant enhancement in both the mixing in the wake and the mass flux across the centerline of the wake induced by vortex-shedding