Introduction to Droplet-Based Millifluidic Chemistry Using a Macroscopic-Droplet Generator

A recent assessment of available direct numerical simulation (DNS) data from turbulent boundary layer flows (Schlatter & Örlü,J. Fluid Mech., vol. 659, 2010, pp. 116–126) showed surprisingly large differences not only in the skin friction coefficient or shape factor, but also in their predictions of mean and fluctuation profiles far into the sublayer. While such differences are expected at very low Reynolds numbers and/or the immediate vicinity of the inflow or tripping region, it remains unclear whether inflow and tripping effects explain the differences observed even at moderate Reynolds numbers. This question is systematically addressed by re-simulating the DNS of a zero-pressure-gradient turbulent boundary layer flow by Schlatteret al. (Phys. Fluids, vol. 21, 2009, art. 051702). The previous DNS serves as the baseline simulation, and the new DNS with a range of physically different inflow conditions and tripping effects are carefully compared. The downstream evolution of integral quantities as well as mean and fluctuation profiles is analysed, and the results show that different inflow conditions and tripping effects do indeed explain most of the differences observed when comparing available DNS at low Reynolds number. It is further found that, if transition is initiated inside the boundary layer at a low enough Reynolds number (based on the momentum-loss thickness)${\mathit{Re}}_{\theta } \lt 300$, all quantities agree well for both inner and outer layer for${\mathit{Re}}_{\theta } \gt 2000$. This result gives a lower limit for meaningful comparisons between numerical and/or wind tunnel experiments, assuming that the flow was not severely over- or understimulated. It is further shown that even profiles of the wall-normal velocity fluctuations and Reynolds shear stress collapse for higher${\mathit{Re}}_{\theta } $irrespective of the upstream conditions. In addition, the overshoot in the total shear stress within the sublayer observed in the DNS of Wu & Moin (Phys. Fluids, vol. 22, 2010, art. 085105) has been identified as a feature of transitional boundary layers.

For a number of manmade and natural flyers the aerodynamics of low Reynolds number plays a crucial role. Active study of birds and insects is growing rapidly for development of Micro Air Vehicles (MAVs). MAVs are capable of performing tasks like surveillance, environmental monitoring and threat assessment in hostile environment. When compared to general civilian aircrafts MAVs fly at low Reynolds number regime of 105 or lower. A considerable change of aerodynamic characteristics is seen between aircrafts that operate in low and high Reynolds number regimes. Low Reynolds number flyers are sensitive to wing gust and deformation because of being lightweight and operating at low speeds. The birds have nature’s finest locomotion system when it comes to maneuvering effectively through space. This review paper will assist further studies in the field of low Reynolds number flyers that can be used for future development on MAVs. A holistic review of past two decades of research work and studies done on low Reynolds number flyers has been presented in this paper. The Theoretical, Experimental and Numerical techniques followed by researchers have been highlighted so that the study on biological and manmade flyers can be systematically presented. It was found that researchers preferred Numerical and Experimental techniques while conducting aerodynamic analysis of low Reynolds number flyers. An attempt has been made in this paper to fill the research gap that is there in mimicking the flight of animals and thus developing man-made systems having higher efficiency.

This study uses computational methods to analyze fluid flow characteristics NACA 4415 in ultra-low, low, and moderate Reynolds number categories. The turbulence model chosen is the standard k-ε. The ultra-low Reynolds number used is 5×10^3, while the Reynolds number for the low category is 4.17×10^4. For the moderate category, the Reynolds number is 3×10^6. The variation of the grid being tested is the grid with the number of elements 5×10^4, 10^5 and 2×10^5. The grid with the number of elements 2×10^5 gives the best results. At the ultra-low Reynolds number, there is no stall condition. The stall condition at the low Reynolds number is AoA=12°. At the moderate Reynolds number, the stall occurs at AoA=18°. The largest Cl is in the moderate Reynolds number. Meanwhile, the smallest Cd is at the ultra-low Reynolds number. Based on the analysis of pressure contours, velocity contours and velocity streamlines, the fluid flow patterns seen are not much different. However, there is a significant difference in their values.

This paper presents an efficient numerical method for the flows past airfoils at very low Reynolds numbers, which are of interest for the micro-aircraft applications and the unmanned air vehicles (UAV). The flows at very low Reynolds numbers are dominated by viscous effects and by very thick boundary layers, with few computational or experimental results available for airfoils. The present analysis is based on a pseudo-time integration method using artificial compressibility to accurately solve the Navier-Stokes equations. This is done in a rectangular computational domain obtained by a coordinate transformation fiom the physical flow domain around the airfoil. The method uses a central differencing scheme on a stretched staggered grid in the computational domain. This method is first successfully validated for the flows with multiple separation regions past a downstream-facing step by comparison with previous experimental and computational results at very low Reynolds numbers between 400 and 1200. Then the method is used to obtain solutions for several NACA airfoils at very low Reynolds numbers between 400 and 6000. The present airfoil solutions are validated by comparison with the numerical results obtained by Kunz & Kroo for Reynolds numbers between 1000 and 6000 (no results were available for Reynolds numbers smaller than 1000). A very good agreement has been found between the two sets of results. The decrease in the low Reynolds number was found to lead to a marked increase in the pressure coefficient on the airfoil, which is more pronounced towards the trailing edge and for thinner airfoils.

Fluid flow, heat transfer and entropy generation characteristics of micro-pipes are investigated computationally by considering the simultaneous effects of pipe diameter, wall heat flux and Reynolds number in detail. Variable fluid property continuity, Navier-Stokes and energy equations are numerically handled for wide ranges of pipe diameter (d = 0.50–1.00 mm), wall heat flux (q''= 1000–2000 W/m2) and Reynolds number (Re = 1 – 2000), where the relative roughness is kept constant at e/d = 0.001 in the complete set of the scenarios considered. Computations indicated slight shifts in velocity profiles from the laminar character at Re = 500 with the corresponding shape factor (H) and intermittency values (γ) of H = 3.293→3.275 and γ = 0.041→0.051 (d = 1.00→0.50 mm). Moreover, the onset of transition was determined to move down to Retra = 1,656, 1,607, 1,491, 1,341 and 1,272 at d = 1.00, 0.90, 0.75, 0.60 and 0.50 mm, respectively. The impacts of pipe diameter on friction mechanism and heat transfer rates are evaluated to become more significant at high Reynolds numbers, resulting in the rise of energy loss data at the identical conditions as well. In cases with low pipe diameter and high Reynolds number, wall heat flux is determined to promote the magnitude of local thermal entropy generation rates. Local Bejan numbers are inspected to rise with wall heat flux at high Reynolds numbers, indicating that the elevating role of wall heat flux on local thermal entropy generation is dominant to the suppressing function of Reynolds number on local thermal entropy generation. Cross-sectional total entropy generation is computed to be most influenced by pipe diameter at high wall heat flux and low Reynolds numbers.

The square lattice tower with tubular members (SLTTM) is widely used in civil engineering. Wind load is the primary factor affecting the stability of these structures. This paper presents the wind loads of the SLTTM at different Reynolds numbers (Re) through wind tunnel testing and large eddy simulation (LES). A series of wind tunnel tests with four segment models were first conducted to discuss the effects of wind direction, turbulence intensity, and solidity ratio on the aerodynamic force under low and subcritical Reynolds numbers. The LES method was subsequently employed to determine the aerodynamic force coefficient at Re = 191–1.34 × 106 in both the smooth and uniform turbulent wind fields. The results from wind tunnel tests indicate that the mean and fluctuating drag coefficients at low Reynolds numbers are somewhat different from those at subcritical Reynolds numbers. The solidity ratio and wind direction exert a notable influence on the mean drag coefficient, whereas their impact on the fluctuating drag coefficient is relatively minimal. As the turbulence intensity increases, both the mean and fluctuating drag coefficients exhibit a notable rise. The results of the LES at Re = 191–1.34 × 106 show that an increase in turbulence intensity can markedly elevate the fluctuating drag coefficient. However, the effect on the mean drag coefficient is found to depend on the Reynolds number range. The Reynolds number effect on the mean and fluctuating drag coefficients of the SLTTM may be primarily attributed to the members without and with a shielding effect, respectively.

We study laminar forced convection mass transfer to single layer arrays of equidistantly and non-equidistantly spaced micro-spheres. We report average Sherwood numbers as a function of geometry and flow conditions, for open frontal area fractions between 0.04 and 0.95, Schmidt numbers between 0.7 and 10, and Reynolds numbers (based on micro-sphere diameter and the free stream velocity) between 0.1 and 100. For equidistantly spaced arrays of micro-spheres we propose a general analytical expression for the average Sherwood number as a function of the Reynolds number, Schmidt number and the open frontal area fraction, as well as asymptotic scaling rules for small and large Reynolds. For all studied Schmidt numbers, equidistant arrays exhibit decreasing average Sherwood numbers for decreasing open frontal area fractions at low Reynolds numbers. For high Reynolds numbers, the Sherwood number approaches that of a single spheres in cross-flow, independent of the open frontal area fraction. For equal open frontal area fractions, the Sherwood number in non-equidistant arrays is lower than in equidistant arrays for intermediate Reynolds numbers. For very low and high Reynolds numbers, non-uniformity does not influence mass transfer.

An Eppler 817 (E817) hydrofoil was studied experimentally using two dimensions two components Particles Image Velocimetry (PIV) measurements. Both statistical and time-resolved series were used to study the effect of Reynolds number and angle of attack on the flow topologies and dynamics. Vortex shedding modes were observed over a range of low chord-based Reynolds numbers 400 ≤ Rec ≤ 20000 and four angles of attack ( α = 2◦, 6◦, 12◦ and 30◦). Those Reynolds numbers are scarce documented on such hydrofoil as they are far from usual operating conditions. However, those low Reynolds numbers allowed us to observe Reynolds number based transitions of the vortex shedding modes at a given angle of attack. The data were acquired on both an extruded 2D hydrofoil and a 3D "T-shaped" hydrofoil, composed of a vertical shaft (e.g. rudder on a boat) holding the horizontal lifting surface. The latter was used to investigate the influence of both the 3D shape and surface proximity on the hydrofoil’s behaviour through three different depths, ranging from 3.5 to 0.875 chords. Additional measurements from a 6-axis loads sensor were used to characterize the loss of performance due to the free-surface proximity.

Systematic flow measurements of profile and mixing losses were made across the blade pitches of a linear turbine cascade at low and moderate Reynolds numbers. The effect of Reynolds number on mixing behavior and development of the wake downstream of the trailing edge were investigated by means of traverse results at different planes downstream of the cascade. The experimental loss data were compared with predictions of theoretical boundary layer flow methods and of computational fluid dynamics (CFD) analyses. Several turbulence models available in commercial CFD tools and in the open CFD code OpenFOAM were considered for the present case study. It was found that substantial deviations between the numerical predictions and the experimental data occurred. These deviations may be attributed to the fact that at low Reynolds numbers, laminar and transitional boundary layer flows and flow separation phenomena became relevant. Based on the experimental two-dimensional loss data, the validity of simple Reynolds number scaling rules was assessed.

The flow field around pairs of small particles moving and rotating in a shear flow close to a wall at low but finite Reynolds number (Re) is computed as a function of time by means of the lattice-Boltzmann technique. The total force and torque acting on each particle is computed at each time step and the position of the particles is updated. By considering the lift force and the disturbances induced by the particles, the trajectories of the pair of particles are explained as a function of the distances from the wall and the Reynolds number. It is shown that when particles are positioned in a particular form, they collide forming strings. In particular, we are interested in particle-bridge formation in shear flows, and two collided particles (a string) can be considered as a nucleus of a particle bridge.

Introduction I wing design it is very important to determine the maximum lift coefficient as accurately as possible, since this lift coefficient corresponds to the stall speed that is the minimum speed at which controllable flight can be maintained. Any further increase in angle of incidence will increase flow separation on the wing upper surface, resulting in a loss of lift and a large increase in drag. Despite the significant advances in computational fluid dynamics, our ability to predict the maximum lift coefficient and poststall behavior of single airfoils, wings, multielement airfoils, or wings is still not satisfactory. The chief culprit is the lack of an accurate turbulence model to represent flows with extensive separation. Inaccuracies of numerical solutions of the conservation equations at these flow conditions, as well as difficulties in modeling of flow near the trailing edge of an airfoil or wing, add to this dilemma. Recently Cebeci et al. described an interactive boundary-layer method, together with the e approach to the calculation of transition, for predicting stall and poststall behavior of airfoils at low and high Reynolds numbers. The turbulence model was based on the Cebeci-Smith algebraic eddy-viscosity formulation with improvements for strong pressure gradient effects and transitional flows at low Reynolds numbers. Comparison of calculated results for incompressible flows indicated good agreement with experiment for a wide range of Reynolds numbers. Preliminary calculations for low-Mach-number flows with this interactive method that applies compressibility corrections to the panel method also indicated good agreement with data and showed that at a Mach number of 0.30, the compressibility effect on (Q)max was not negligible. The ability of the calculation method of Ref. 1 to predict the effect of ice on airfoil stall at high Reynolds numbers is examined here, and the results are presented in the following section. The interactive boundary-layer method previously developed for iced airfoils and coupled to the LEWICE code for predicting ice shapes' is replaced with the calculation method of Ref. 1. Appropriate changes are made to this method, including roughness effects due to ice, and the results are presented in the following section.

Micromixing process in microfluidic devices has been broadly employed in bio-, nano-, and environmental technologies using either miscible or immiscible liquids. However, there are limited experimental studies investigating the mixing process of different densities and viscosities liquids in relation to microfluidics. Therefore, the mixing process of propan-2-ol and water, water and sodium chloride solution, propan-2-ol and sodium chloride solution were experimented and reported at 5 ≤ Re ≤ 50 in T-junction and offset T-junction microchannels. For miscible mixing experiments, i.e. propan-2-ol and water, water and sodium chloride solution, both microchannels show mixing index for each Reynolds number is directly proportional to the mixing time. At low Reynolds number, higher molecular diffusion takes place while at low flow rate, the residence time of fluid is high. The mixing performance is relatively good at high Reynolds number of 40 and 50 due to the significant convection which is caused by the effect of stretching and thinning of liquid lamellae. For immiscible propan-2-ol and sodium chloride solution mixing, offset T-junction microchannel offers better mixing performance than T-junction microchannel at both low and high Reynolds number. The chaotic mixing happened at the intersection of the T-junction microchannel due to the direct interaction of two liquids entering the junction at high momentum.

The effect of the crystallographic form of MnO2 on the kinetics of oxygen reduction and evolution reaction

By modelling the magnetic source term in transporting equation of turbulent kinetic energy in a term by term manner, a nonlinear-eddy-viscosity k-ω model suitable for arbitratry magnetic field orientation was proposed at low magnetohydrodynamic Reynolds number assumption. In the present model, Kenjeres-Hanjalic model and Songs nonlinear viscosity model were employed to close the vblocity-electric field correlations and the turbulent normal stresses respectively. The relaminarization process was modeled by the low Reynolds number k-ω model meanwhile. The model was then validated with DNS and experiment results. The relative error was below 5% for the velocity profile and 10% for the friction coefficient, proving the applicability of the present model for engineering applications.

Investigation of hydrodynamic/biomass growth coupling in a pilot scale granular bioreactor at low pore Reynolds number