Ultra-low Reynolds Number Research Articles

A simple analytic model for predicting the wicking velocity in micropillar arrays

Hemiwicking is the phenomena where a liquid wets a textured surface beyond its intrinsic wetting length due to capillary action and imbibition. In this work, we derive a simple analytical model for hemiwicking in micropillar arrays. The model is based on the combined effects of capillary action dictated by interfacial and intermolecular pressures gradients within the curved liquid meniscus and fluid drag from the pillars at ultra-low Reynolds numbers {boldsymbol{(}}{{bf{10}}}^{{boldsymbol{-}}{bf{7}}}{boldsymbol{lesssim }}{bf{Re}}{boldsymbol{lesssim }}{{bf{10}}}^{{boldsymbol{-}}{bf{3}}}{boldsymbol{)}}. Fluid drag is conceptualized via a critical Reynolds number: {bf{Re}}{boldsymbol{=}}frac{{{bf{v}}}_{{bf{0}}}{{bf{x}}}_{{bf{0}}}}{{boldsymbol{nu }}}, where v0 corresponds to the maximum wetting speed on a flat, dry surface and x0 is the extension length of the liquid meniscus that drives the bulk fluid toward the adsorbed thin-film region. The model is validated with wicking experiments on different hemiwicking surfaces in conjunction with v0 and x0 measurements using Water {boldsymbol{(}}{{bf{v}}}_{{bf{0}}}{boldsymbol{approx }}{bf{2}},{bf{m}}{boldsymbol{/}}{bf{s}}{boldsymbol{,}},{bf{25}},{boldsymbol{mu }}{bf{m}}{boldsymbol{lesssim }}{{bf{x}}}_{{bf{0}}}{boldsymbol{lesssim }}{bf{28}},{boldsymbol{mu }}{bf{m}}{boldsymbol{)}}, viscous FC-70 {boldsymbol{(}}{{boldsymbol{v}}}_{{bf{0}}}{boldsymbol{approx }}{bf{0.3}},{bf{m}}{boldsymbol{/}}{bf{s}}{boldsymbol{,}},{bf{18.6}},{boldsymbol{mu }}{bf{m}}{boldsymbol{lesssim }}{{boldsymbol{x}}}_{{bf{0}}}{boldsymbol{lesssim }}{bf{38.6}},{boldsymbol{mu }}{bf{m}}{boldsymbol{)}} and lower viscosity Ethanol {boldsymbol{(}}{{boldsymbol{v}}}_{{bf{0}}}{boldsymbol{approx }}{bf{1.2}},{bf{m}}{boldsymbol{/}}{bf{s}}{boldsymbol{,}},{bf{11.8}},{boldsymbol{mu }}{bf{m}}{boldsymbol{lesssim }}{{bf{x}}}_{{bf{0}}}{boldsymbol{lesssim }}{bf{33.3}},{boldsymbol{mu }}{bf{m}}{boldsymbol{)}}.

Thermophoresis-Assisted Microscale Magnus Effect in Optical Traps

The Magnus effect, commonly observed on the macroscale, has been considered to be negligible at the microfluidic limit. However, the thermophoretic effect at the microscale leads to a strong lift force that acts on the optically trapped and heated microparticles rotating in a liquid flow. This thermophoresis-assisted Magnus effect is experimentally observed and explained through the inhomogeneity of temperature distribution in the flow around the absorbing microparticles rotated by magnetic forces within the limit of ultralow Reynolds numbers.

Passive flow control mechanism in a bio-inspired corrugated hydrofoil

Corrugated hydrofoils are lately getting attention because of their superior aerodynamic performance compared to engineered hydrofoils at low Reynolds numbers (Re). A particle image velocimetry (PIV) based study on corrugated hydrofoil is conducted here to understand the flow dynamics around it at ultralow Reynolds numbers (Re = 280–11,700). Seven different angles of attack (α) are considered in this study ranging from − 15° to 15°. Load cell measurements are undertaken to obtain the force coefficients and further these are compared with the results obtained from PIV data using wake survey method. The wake velocity profiles are examined to understand the variation in force coefficients in a better way. Vortices are found to be trapped in the valley of the corrugations. The lift coefficient increases as the number of vortices increases on the top (suction) surface. A temporal analysis of the data shows that the partially merged co-rotating vortices give higher lift as compared to the fully merged vortices. The maximum aerodynamic performance is obtained at − 5° angle of attack for Re = 6760. The asymmetry in the geometry combined with asymmetry in the flow helps create relatively high lift for a corrugated wing. The performance of positive and negative angles of attack are compared and it is found that the fluctuation in lift coefficient is comparatively higher. It is hypothesized that the merging of trapped vortices with each other gives the effect of fluid roller bearings; this fluid roller bearing produces a travelling wave, which avoids the formation of boundary layer, thereby leading to high gliding ratio. These detailed results, covering the entire Reynolds number and angle of attack range of dragonfly flight, provide useful insights into the secret of dragonfly flight which will help in better design of micro air vehicles.

Aerodynamic study of the corrugated airfoil at ultra-low Reynolds number

In this study, Aeshna cyanea dragonfly forewing mid-cross-section corrugated airfoil was simulated at ultra-low Reynolds number. The corrugated airfoil was compared with its smooth counterpart to study the effect of the corrugations upon the aerodynamic performance. Unsteady two-dimensional laminar flow was solved using FLUENT. This study was divided into gliding phase and flapping phase. In the gliding phase, the corrugated airfoil produced a higher lift force with respect to the profiled airfoil at both tested Reynolds numbers ([Formula: see text], [Formula: see text]) with comparable drag coefficient for all the tested angles of attack. In the flapping phase, both the corrugated airfoil and the flat-plate have a very similar flow behavior which yields a very similar aerodynamic performance at Re[Formula: see text]. A structural analysis was performed to compare the corrugated airfoil with the flat-plate. The analysis revealed the superiority of the corrugated airfoil over the flat-plate in decreasing the deflection under the applied load. The reduced frequency was varied to study its impact on the aerodynamic performance. By increasing the reduced frequency, the thrust and the lift forces increased by [Formula: see text]% and [Formula: see text]%, respectively. Any increase in the reduced frequency will increase lift and thrust forces, but the propulsive efficiency will deteriorate.

Aerodynamic shape optimization of airfoils at ultra-low Reynolds numbers

The flow over NACA 0008 airfoil is studied computationally in the ultra-low Reynolds number regime Re ∈ [1000, 10000] for various angles of attack α ∈ [0°, 8°]. The laminar flow separation occurs even at low angles of attack in this Reynolds number regime. The lift curve slope is far reduced from the inviscid thin airfoil theory value of Cl,α = 2π. Significant increase in the values of drag coefficient is seen with a decrease in Re. Lift-to-drag ratios are consequently very low. An adjoint-based aerodynamic shape optimization methodology is employed to obtain improved aerodynamic characteristics in the ultra-low Re regime. Three different objective functions are considered, namely, (i) minimization of drag coefficient, Cd, (ii) maximization of lift coefficient, Cl, and (iii) maximization of lift-to-drag ratio, (Cl/Cd). Significant improvement in each of the objective functions is obtained.

Numerical Validation of NACA 0009 Airfoil in Ultra-Low Reynolds Number Flows

Validation of the sectional airfoil performance is necessary to test a propeller. This study presents a numerical validation of the computational fluid dynamics (CFD) method for testing a symmetric NACA airfoil called NACA 0009. An ultra-low Reynolds number of 20000 is assumed and investigated. The implementation is performed using a commercial CFD solver ANSYS Fluent. The obtained results are compared with experimental data obtained from literature. A coarse grid is adopted as meshing technique and a realizable k-ε turbulence model, which has provided the best results, is assumed. Results show favourable prediction for most of the considered angles of attack. Thus, an overall reliable model has been developed.

Symmetric Versus Asymmetric Pitching of a Cycloidal Rotor Blade at Ultra-Low Reynolds Numbers

This paper provides a fundamental understanding of the unsteady aerodynamic phenomena on a cycloidal rotor blade operating with symmetric as well as asymmetric pitching at ultralow Reynolds numbers () by using a combination of experimental (force and flowfield measurements) and computational fluid dynamics (CFD) studies. The instantaneous blade fluid dynamic forces on a rotating cycloidal rotor blade were measured, which, along with particle image velocimetry (PIV) based flowfield measurements revealed the key fluid dynamic mechanisms acting on the blade. A two-dimensional CFD analysis of the cycloidal rotor was developed and systematically validated using both force and flowfield measurements. The CFD flow solution and PIV-measured flowfield correlated well, especially in the upper half of the circular blade trajectory, and both showed the formation and shedding of strong dynamic stall or leading-edge vortices at high pitch amplitudes, which is the reason for the stall delay and force enhancement. The dynamic virtual camber induced by the flow curvature decreased the blade lift in the upper half due to negative induced camber; however, the lift increased in the lower half due to positive camber. Therefore, introducing an asymmetry in pitch kinematics with higher pitch in the upper half and lower pitch in the bottom half counteracted this inherent lift asymmetry and improved efficiency through a more uniform lift production.

Force and flowfield measurements to understand unsteady aerodynamics of cycloidal rotors in hover at ultra-low Reynolds numbers

This paper provides a fundamental understanding of the unsteady fluid-dynamic phenomena on a cycloidal rotor blade operating at ultra-low Reynolds numbers (Re ∼ 18,000) by utilizing a combination of instantaneous blade force and flowfield measurements. The dynamic blade force coefficients were almost double the static ones, indicating the role of dynamic stall. For the dynamic case, the blade lift monotonically increased up to ±45° pitch amplitude; however, for the static case, the flow separated from the leading edge after around 15° with a large laminar separation bubble. There was significant asymmetry in the lift and drag coefficients between the upper and lower halves of the trajectory due to the flow curvature effects (virtual camber). The particle image velocimetry measured flowfield showed the dynamic stall process during the upper half to be significantly different from the lower half because of the reversal of dynamic virtual camber. Even at such low Reynolds numbers, the pressure forces, as opposed to viscous forces, were found to be dominant on the cyclorotor blade. The power required for rotation (rather than pitching power) dominated the total blade power.

Experimental Studies on a Mesoscale Cycloidal Rotor in Hover

This paper details the performance and flowfield measurements on a mesoscale cycloidal rotor (rotor radius of 1 in.), which operates at ultralow Reynolds numbers () and uses a design different from previous cycloidal rotor studies. The mesoscale rotor uses a cantilevered blade with a flat-plate airfoil and low-aspect-ratio elliptical blade planform. A three-component balance was developed to measure the vertical and sideward thrust, torque, and rotation frequency as the number of blades, pitch amplitude, and blade aspect ratio were varied. The studies showed that the highest efficiency was achieved with higher number of blades (4–6), high pitch amplitude (40–45 deg), and moderate aspect ratios. Phase-locked flowfield measurements were conducted using a particle image velocimetry (PIV) technique in two different orientations: chordwise and spanwise. PIV measurements show that the flowfield on the present mesoscale cycloidal rotor is highly three-dimensional and unsteady, characterized by the growth and shedding of leading-edge vortices and a trailing-edge vortex sheet similar to that seen on flapping wings; strong root and tip vortices that interact with each other to create an undulating wake; skewed inflow; and the strong interaction of the slip stream from the upper blade on the lower blade.

Numerical and experimental investigation of an airfoil design for a Martian micro rotorcraft

The present paper aims at investigating the impact of an airfoil design on the propulsion system for a Martian rotary wing micro air vehicle. The main challenge for flying on Mars is the atmosphere’s density and speed of sound that are significantly lower than on Earth. It leads to compressible ultra-low Reynolds number ([Formula: see text]) flows for a coaxial rotorcraft with a 30 cm diameter . Since those flows are unknown in the biosphere, numerical tools have not been validated yet. Therefore, the test section from a known depressurized experiment is simulated in 3D for solver assessment. XFoil, a program for the analysis of subsonic airfoil, is also evaluated in the Martian flow conditions for evaluating its ability to be used in an optimization process. Based on the XFoil’s performance evaluations, both the camber line and thickness distribution are optimized in 2D incompressible and compressible flows. Optimal shape is a highly cambered airfoil shifting the boundary layer separation downstream. For optimization assessment, airfoils from each optimization step are numerically evaluated with the validated solver showing that small variations in the airfoil design has little impact on the 2D aerodynamic performance. A compressible optimal airfoil is also proven to be more aerodynamically effective than the experimentally effective airfoils from literature. Finally, the impact of airfoil shapes on the 3D rotor performance is evaluated with a depressurized experimental campaign recreating the Martian atmosphere in terms of kinematic viscosity. The impact of gas composition is also assessed in subsonic flows.

Enhanced Diffusion of Passive Tracers in Active Enzyme Solutions.

Colloidal suspensions containing microscopic swimmers have been the focus of recent studies aimed at understanding the principles of energy transfer in fluidic media at low Reynolds number conditions. Going down in scale, active enzymes have been shown to be force-generating, nonequilibrium systems, thus offering opportunity to examine energy transfer at the ultralow Reynolds number regime. By monitoring the change of diffusion of inert tracers dispersed in active enzyme solutions, we demonstrate that the nature of energy transfer in these systems is similar to that reported for larger microscopic active systems, despite the large differences in scale, modes of energy transduction, and propulsion. Additionally, even an enzyme that catalyzes an endothermic reaction behaves analogously, suggesting that heat generation is not the primary factor for the observed enhanced tracer diffusion. Our results provide new insights into the mechanism of energy transfer at the molecular level.

Detailed Numerical Study on the Aerodynamic Behavior of a Gurney Flapped Airfoil in the Ultra-low Reynolds Regime

The addition of Gurney flap changes the nature of flow around airfoil by producing asymmetric Von- Karman vortex in its wake. Most of the investigations on Gurney flapped airfoils have modeled the flow using a quasisteady approach, resulting in time-averaged values with no information on the unsteady features of the flow. Among these, some investigations have shown that quasi-steady approach does a good job on predicting the aerodynamic coefficients and physics of flow. Previous studies on Gurney flap have shown that the calculated aerodynamic coefficients such as lift and drag coefficients from quasi-steady approach are in good agreement with the time averaged values of these quantities in time accurate computations. However, these investigations were conducted in regimes of medium to high Reynolds numbers where the flow is turbulent. Whether this is true for the regime of ultra-low Reynolds number is open to question. Therefore, it is deemed necessary to examine the previous investigations in the regime of ultra-low Reynolds numbers. The unsteady incompressible laminar flow over a Gurney flapped airfoil is investigated using three approaches; namely unsteady accurate, unsteady inaccurate, and quasisteady. Overall, all the simulations showed that at ultra-low Reynolds numbers quasi-steady solution does not necessarily have the same correlation with the time averaged results over the unsteady accurate solution. In addition, it was observed that results of unsteady inaccurate approach with very small time steps can be used to predict time-averaged quantities fairly accurate with less computational cost.

Design and Analysis of Passive Y-Type Micromixers for Enhanced Mixing Performance for Biomedical and Microreactor Application

In this paper, endeavor has been made to design and analyze different Y-type micromixers by characterizing the mixing and flow behavior in ultra-low Reynolds number region. The effects of different geometric and flow parameters on the mixing and pressure drop are studied through computational fluid dynamics (CFD) simulations using COMSOL Multiphysics software. The parameters investigated are obstacle geometry, obstacle arrangement, obstacle depth, aspect ratio (AR), entrance angle ([Formula: see text], Reynolds number (Re) and obstacle packing factor (OPF). The simulation results reveal that rectangular shaped obstacles in staggered arrangement gives the best mixing. Increasing obstacle depth and OPF increases both mixing and pressure drop whereas increasing entrance angle enhances mixing but has negligible effect on pressure drop. Also both the mixing and pressure drop performance enhances with decreasing AR and lower Reynolds number gives better mixing in the lower laminar flow region.

E-24 高粘度流体槽を用いた極低レイノルズ数二次元翼特性の評価

E-24 高粘度流体槽を用いた極低レイノルズ数二次元翼特性の評価

Dynamic Coupling at the Ångström Scale

AbstractWhile momentum transfer from active particles to their immediate surroundings has been studied for both synthetic and biological micron‐scale systems, a similar phenomenon was presumed unlikely to exist at smaller length scales due to the dominance of viscosity in the ultralow Reynolds number regime. Using diffusion NMR spectroscopy, we studied the motion of two passive tracers—tetramethylsilane and benzene—dissolved in an organic solution of active Grubbs catalyst. Significant enhancements in diffusion were observed for both the tracers and the catalyst as a function of reaction rate. A similar behavior was also observed for the enzyme urease in aqueous solution. Surprisingly, momentum transfer at the molecular scale closely resembles that reported for microscale systems and appears to be independent of swimming mechanism. Our work provides new insight into the role of active particles on advection and mixing at the Ångström scale.

Dynamic Coupling at the Ångström Scale.

While momentum transfer from active particles to their immediate surroundings has been studied for both synthetic and biological micron-scale systems, a similar phenomenon was presumed unlikely to exist at smaller length scales due to the dominance of viscosity in the ultralow Reynolds number regime. Using diffusion NMR spectroscopy, we studied the motion of two passive tracers--tetramethylsilane and benzene--dissolved in an organic solution of active Grubbs catalyst. Significant enhancements in diffusion were observed for both the tracers and the catalyst as a function of reaction rate. A similar behavior was also observed for the enzyme urease in aqueous solution. Surprisingly, momentum transfer at the molecular scale closely resembles that reported for microscale systems and appears to be independent of swimming mechanism. Our work provides new insight into the role of active particles on advection and mixing at the Ångström scale.

Computational Aerodynamic Analysis of a Micro-CT Based Bio-Realistic Fruit Fly Wing.

The aerodynamic features of a bio-realistic 3D fruit fly wing in steady state (snapshot) flight conditions were analyzed numerically. The wing geometry was created from high resolution micro-computed tomography (micro-CT) of the fruit fly Drosophila virilis. Computational fluid dynamics (CFD) analyses of the wing were conducted at ultra-low Reynolds numbers ranging from 71 to 200, and at angles of attack ranging from -10° to +30°. It was found that in the 3D bio-realistc model, the corrugations of the wing created localized circulation regions in the flow field, most notably at higher angles of attack near the wing tip. Analyses of a simplified flat wing geometry showed higher lift to drag performance values for any given angle of attack at these Reynolds numbers, though very similar performance is noted at -10°. Results have indicated that the simplified flat wing can successfully be used to approximate high-level properties such as aerodynamic coefficients and overall performance trends as well as large flow-field structures. However, local pressure peaks and near-wing flow features induced by the corrugations are unable to be replicated by the simple wing. We therefore recommend that accurate 3D bio-realistic geometries be used when modelling insect wings where such information is useful.

Enhanced dispersion by elastic turbulence in porous media

We experimentally investigate hydrodynamic dispersion in elastic turbulent flows of a semi-dilute aqueous polymer solution within a periodic porous structure at ultra-low Reynolds numbers by particle tracking velocimetry. Our results indicate that elastic turbulence can be characterized by an effective dispersion coefficient which exceeds that of Newtonian liquids by several orders of magnitude and grows non-linearly with the Weissenberg number Wi. Contrary to laminar flow conditions, the velocity field, and thus the shear rate, is not proportional to the flow rate and becomes asymmetric at high Wi.

Optimization of Nano-Rotor Blade Airfoil Using Controlled Elitist NSGA-II

The aerodynamic performance of airfoil at ultra-low Reynolds number has a great impact on the propulsive performance of nano rotor. Therefore, the optimization of airfoil is necessary before the design of nano rotor. Nano rotor blade airfoil optimization is a multi-objective problem since the airfoil suffers a wide range of Reynolds number which increases the difficulty of optimization. In this paper, the airfoil of nano rotor was optimized based on the controlled elitist Non-dominated Sorting Genetic Algorithm II (NSGA-II) coupling with the parameterization method of Class function/Shape function Transformation technique (CST) and the multi-objectives function processing method of statistical definition of stability. An airfoil was achieved with the thickness of 2% and the maximum camber of 5.6% at 2/3 of chord. Airfoil optimized exhibits a good aerodynamic performance at ultra-low Reynolds number according to the computational results. And comparisons were carried out between the performance of the rotor designed with airfoil optimized and that of the rotor designed with AG38 airfoil, which showed that the airfoil optimized was suitable for rotor design.

803 極低レイノルズ数における2次元翼周りの可視化と翼特性の相関

803 極低レイノルズ数における2次元翼周りの可視化と翼特性の相関