Low Reynolds Number Flow Regime Research Articles

Energy harvesting in a flow-induced vibrating flapper with biomimetic gaits

Energy harvesting from flow induced vibrations (FIV) in flexible bodies offer opportunities for power generation in biomimicking robotic devices and is an active area of research. The focus of this study is on investigating the underlying physics and qualitatively analysing the energy extraction scenarios in similar structural systems, comprising of a flexible piezoelectric flapper in a low Reynolds number flow regime. A high-fidelity three-way fully coupled fluid–structure–electric energy solver is developed in-house to study the energy harvesting capabilities of such a flapper, its hydrodynamic characteristics and the associated unsteady flow-field. The results indicate that the flapper deformation profiles at the most efficient harvesting regimes, resemble the propulsion gaits of natural swimmers. Investigations on the effects of a sinusoidal heaving actuation reveal no significant impact on the harvested power at the high yield (high power output) regime, identified under the passive condition showing biomimetic gait. This study provides mechanics based insights that is expected to be useful for bio-inspired designs of FIV based harvesters.

Smart hybrid VIV control of a linearly sprung cylinder using an internal semi-active NES-based vibration absorber coupled with two active rotating wake-control rods

Extensive two dimensional CFD simulations were carried out to investigate the hybrid active/semi-active cross-flow vortex induced vibration (VIV) suppression of a flexibly-mounted circular cylinder. The cylinder is equipped with two smart actively rotating control rods that are symmetrically oriented 120° apart in the near-wake region in real-time collaboration with an internally-fitted semi-active NES-based vibration absorber in the low Reynolds number flow regime (Re=100) over a typical range of lock-in reduced flow velocities (3≤U∗≤10). The control rods function as flow control actuators by enforcing the desired momentum injection into the near-wake region, while the semi-active structural control is realized by switching the nonlinear absorber force between some minimum and maximum values consistent with certain control logics. Selected multi-input-multi-output (MIMO) feedback control laws are introduced into the coupled transient dynamic simulation framework through a manually hooked user defined function (UDF) subroutine. The modified active rotating rod control system equipped with passive NES is found to be fairly successful in overall mitigation of the time response amplitudes (i.e., up to 56% reduction in the cylinder displacements, 78% reduction in the lift amplitudes, and 8% reduction in the drag coefficients as compared to the hybrid passive system). Similarly, notable reductions are obtained when a modified continuous feedback control strategy is directly applied in the NES-based semi-active vibration absorber (i.e., up to 55% in the displacements, and up to 11% in the drag coefficients). Moreover, the superior performance of proposed smart hybrid active/semi-active VIV control system in comparison to the hybrid passive system is demonstrated (i.e., up to 68% reduction in the displacements, 61% in the lift amplitudes, and 12% in the drag coefficient). Lastly, the key novelties, advantages, practical limitations, and trade-offs of the proposed numerical model are briefly pointed out in regard to the real-world marine/offshore applications and forthcoming investigations.

Nonlinear vortex dynamic analysis of flow-induced vibration of a flexible splitter plate attached to a square cylinder

Flow-induced vibration (FIV) of a flexible splitter plate attached to a square cylinder in laminar flow is investigated using a two-way fluid-structure interaction (FSI) simulation. The Reynolds number based on the edge length of the square cylinder is fixed at Re = 332.6. Numerical results show that the vortex structure falling off on both sides of the square cylinder will excite the vibration of the flexible plate. There is a noticeable phase difference between the flexible plate's hydrodynamic load (lift) and the vertical vibration displacement of the end of the plate. It is also found that there is a pronounced hysteresis effect on the vortex shedding on both sides of the square cylinder due to the action of the flexible plate. The viscous dissipation term dominates the vorticity transport in low Reynolds number flow regimes. The viscous dissipation term reflects the flow trend of the flow field to a certain extent. The results obtained are insightful to the design of FSI-based ocean engineering structures using flexible plates.

Experimental Fluid Dynamic Characterization of Serrated Rotors for Drone Propulsion

The present study reports an experimental investigation regarding one of the most effective and most studied passive control technique in literature to mitigate the noise pollution radiating by a small drone: the Serrated Trailing Edge (STE). 23 quiet propellers have been designed and manufactured in order to identify the most silent configuration. An aeroacoustic pre-qualification of the designed propellers has been performed by means of microphone measurements within the anechoic chamber of Niccolò Cusano University. Then, an aeroacoustic and fluid dynamic characterization of the most performing configuration has been carried out by means of load cell, microphone and PIV measurements in the anechoic wind tunnel facility of TUDelft University of Technology in order to investigate the mechanism that stands behind the noise mitigation. With this purpose, the aerodynamic and aeroacoustic performance and even the velocity and vorticity field along the blade of STE propellers have been characterized. Particular attention is devoted to the fluid-dynamic aspects related to the low Reynolds number flow regime. Results show that serrations seems to modify the wake velocity and the tip voretx intensity resulting in a lower acoustic emission.

Effects of surface topography on low Reynolds number droplet/bubble flow through a constricted passage

This paper is an attempt to study the effects of surface topography on the flow of a droplet (or a bubble) in a low Reynolds number flow regime. Multiphase flows through a constricted passage find many interesting applications in chemistry and biology. The main parameters that determine the flow properties such as flow rate and pressure drop and govern the complex multiphase phenomena such as drop coalescence and breakup in a straight channel flow are the viscosity ratio, droplet size, and ratio of the viscous forces to the surface tension forces (denoted by the capillary number). However, in flow through a constricted passage, in addition to the above-mentioned parameters, various other geometric parameters such as constriction ratio, length, shape of the constriction, phase angle, and spacing between the constrictions also start playing an important role. Most of the studies done on the problem of drop flow through a constricted passage have aimed to understand the role of physical parameters, with some studies extending their analysis to understand the variation of one or two geometric parameters. However, no study could be found, which explicitly evaluates the role of surface topography. An attempt has been made to unify the current literature as well as analyze the effect of the geometric parameters by understanding the physics and mechanisms involved. The non-dimensional numbers that govern this problem are then identified using the scaling analysis.

The Importance of a Filament-like Structure in Aerial Dispersal and the Rarefaction Effect of Air Molecules on a Nanoscale Fiber: Detailed Physics in Spiders' Ballooning.

Many flying insects utilize a membranous structure for flight, which is known as a "wing." However, some spiders use silk fibers for their aerial dispersal. It is well known that spiders can disperse over hundreds of kilometers and rise several kilometers above the ground in this way. However, little is known about the ballooning mechanisms of spiders, owing to the lack of quantitative data. Recently, Cho et al. discovered previously unknown information on the types and physical properties of spiders' ballooning silks. According to the data, a crab spider weighing 20 mg spins 50-60 ballooning silks simultaneously, which are about 200 nm thick and 3.22 m long for their flight. Based on these physical dimensions of ballooning silks, the significance of these filament-like structures is explained by a theoretical analysis reviewing the fluid-dynamics of an anisotropic particle (like a filament or a high-slender body). (1) The filament-like structure is materially efficient geometry to produce (or harvest, in the case of passive flight) fluid-dynamic force in a low Reynolds number flow regime. (2) Multiple nanoscale fibers are the result of the physical characteristics of a thin fiber, the drag of which is proportional to its length but not to its diameter. Because of this nonlinear characteristic of a fiber, spinning multiple thin ballooning fibers is, for spiders, a better way to produce drag forces than spinning a single thick spider silk, because spiders can maximize their drag on the ballooning fibers using the same amount of silk dope. (3) The mean thickness of fibers, 200 nm, is constrained by the mechanical strength of the ballooning fibers and the rarefaction effect of air molecules on a nanoscale fiber, because the slip condition on a fiber could predominate if the thickness of the fiber becomes thinner than 100 nm.

Design of Supercritical Low-Reynolds-Number Airfoils for Fixed-Wing Flight on Mars

Aerodynamic shape optimization for the high-subsonic low-Reynolds number flow regime represents an area of on-going research. The interaction between supercritical compressible flow and laminar boundary layer separation is not well understood due to the high challenges associated with setting up relevant experimental work. However, in the design of future fixed wing aircraft for flight in extra-terrestrial atmospheres, such flow conditions might commonly occur. The present study presents a family of single-point and multi-point optimized airfoils designed for high-subsonic flight at a high-lift condition in the Martian atmosphere. A gradient based optimizer is used, with a second-order finite-volume flow solver and a second-order continuous adjoint solver for determining surface sensitivities with respect to the objective function of minimizing drag. Both fully turbulent and transitional flow are considered, to evaluate the impact on the resulting design and to stress the importance of continuing research to develop robust shape optimization including laminar boundary layer and transition prediction. Both on-design and off-design conditions are evaluated, the airfoils obtained when considering transition effects demonstrating good overall performance.

On the Role of Size Differences in Synchronized Motion of Magnetic Particles in Fluid: A Study on Trimers

Synchronized motion and pattern formation of magnetic particle aggregates in variable magnetic field is of growing interest from the point of view of both fundamental science and its applications. In this article, the role of size differences in synchronized motion of magnetic particles under external rotating magnetic field at low Reynolds number flow regimes is considered. Several different motion regimes are observed in simulations as a function of particle size differences and field rotation rate. Simulation indicates phase-like transitions between different motion regimes when particle size differences become significant. It is also shown that particle size differences permit the possibility of locomotion for particle aggregates which cannot be observed for uniform particle sizes.

Pumping flow model in a microchannel with propagative rhythmic membrane contraction

A pumping flow model in a microchannel with a single attached membrane subjected to propagative contraction is presented in this article. The lubrication theory is used to approximate the induced flow field at a low Reynolds number flow regime. A well-posed expression for the wall profile is derived to describe the membrane propagative mode of rhythmic contractions. Unlike our previously derived pumping model “nonpropagative” where at least two membranes that operate with time-lag are required to produce unidirectional flow, the present results demonstrate that an inelastic channel with a single membrane contraction that operates in a “propagative” mode can produce unidirectional flow and work as a micropump. The model can be used to understand flow transport in many biological systems including but not limited to insect respiration, urine flow, and fluid dynamics of duodenum and intestine. The present pumping paradigm is relatively easy to fabricate and is expected to be useful in many biomedical applications.

Transition to chaos in the flow-induced vibration of a pitching–plunging airfoil at low Reynolds numbers: Ruelle–Takens–Newhouse scenario

This study focuses on numerically analyzing the transition from periodic to chaotic dynamics in the fluid-elastic response of a 2-dof flexibly-mounted airfoil with chord-wise rigidity. The computational framework is composed of a high fidelity Navier–Stokes solver, weakly coupled with a structural model having geometric nonlinearity represented by cubic order stiffness terms. A low Reynolds number flow regime and a very low structure-to-fluid added mass ratio have been considered to simulate the flying conditions of very light-weight unmanned devices. A bifurcation analysis of the system, in the absence of actuation or control forces, is undertaken with the wind velocity as the control parameter. The route to chaos – identified to be the Ruelle–Takens–Newhouse quasi-periodic route – is established for the first time for a flexible pitch–plunge flapping system. Robust nonlinear time series analysis techniques have been implemented to characterize different complex dynamical states present in the system.

Letter: A note on flow characterization of the FX63-137 airfoil at low Reynolds number using oil-film interferometry technique

The Wortmann FX 63-137 airfoil has been extensively studied and used in a low Reynolds number flow regime due to its excellent aerodynamic performance with high lift and soft-stall characteristics. In this work, a laminar separation bubble (LSB) on the upper surface of the FX63-137 airfoil is experimentally studied at low Reynolds numbers of 200 000, 300 000, and 500 000 with different angles of attack via the oil-film interferometry (OFI) technique. The flow features, such as laminar separation, reattachment, turbulent separation, and laminar-turbulent transition, on the upper surface were clearly captured. Furthermore, the characteristics of the reverse flow and reattached flow of LSB were also exhibited evidently. Compared with oil flow visualization, the OFI technique is much easier to use, is less time-consuming, and provides for more indistinct flow features over the airfoil surface.

Effect of thermal buoyancy on a fluid flowing past a pair of side-by-side square bluff-bodies in a low-Reynolds number flow regime

In this research article, we have analyzed the effect of thermal stratification of shear layers due to mixed convection heat transfer past a pair of side-by-side square cylinders in a confined domain, an extended part of our recent study [A. Sanyal and A. Dhiman, “Wake interactions in a fluid flow past a pair of side-by-side square cylinders in presence of mixed convection,” Phys. Fluids 29, 103602 (2017)]. Investigations from the studies of instantaneous and time-averaged isotherms revealed the actual stretches of the temperature gradient in streamwise and transverse extents at Re = 1–40, Ri = 0–1, s/d = 0.7–10, and Pr = 50. The effects of “baroclinic production,” embedded in the transport of vorticity, were rigorously analyzed through the determination of local period-averaged vorticity flux at a certain cross section in the near-field downstream. The study also revealed the underlying flow physics pertaining to the variations in period-averaged wall vorticity and the local Nusselt number. The transport of vorticity has been explained in terms of the vortex structure formulations, and because of the absence of any such similar studies for multiple bluff-body arrangements, the study has been thoroughly correlated from the cases of single bluff-body flow. In an attempt to control several flow regimes by slightly changing the flow and thermal parameters, it is found that chaotic flow cannot exist beyond a certain value of s/d. However, an abnormality was noted in terms of the flow bifurcations at s/d = 1.5 at the juncture of flow transition from unseparated to a separated steady flow for the first time and this is solely attributed to the effect of thermal buoyancy in the flow field.

Flexible flapping wings can exhibit quasi-periodic motion!

The dynamics of a flexible flapping wing is investigated by modelling it as a coupled nonlinear fluid-structure interaction (FSI) system in the low Reynolds number flow regime in accordance to the flight of flapping wing micro air vehicles (MAVs). A bifurcation analysis, by varying the free-stream wind velocity (U∞) as the control parameter, revealed the presence of a new dynamics in the form of a quasi-periodic attractor in the flapping wing motion. The structural and aerodynamic nonlinearities present in the system cause a supercritical Hopf bifurcation, where stable limit cycle oscillation emerges from fixed point response beyond a critical value of the free-stream velocity. Further increasing the control parameter, another bifurcation named Neimark-Sacker bifurcation takes place and as a result, the flapping wing exhibits quasi-periodic motion. The presence of Neimark-Sacker bifurcation in the flapping flow-field dynamics is an interesting find and the present work focuses on it's associated dynamical behaviour. Various dynamical system tools like frequency spectra, phase space, Poincaré section, first return map have been implemented successfully to confirm the presence of quasi-periodicity.

A Ghost-Valve micropumping paradigm for biomedical applications

To present a novel micropumping “Ghost-Valve” principle that can be useful for many of biomedical applications. This pumping mechanism is inspired by microscale internal flow motions within insect tracheal networks, which is observed to be induced by localized rhythmic wall contractions. A mathematical analysis based on the lubrication theory is given to govern this internal flow motions and to derive expressions of velocity stream function, pressure distributions, and net flow rate in a microchannel having two contracting sites. The derived flow velocity stream function suggests that, there exist contraction-induced stagnation planes “Ghost-Valves” in the neighbourhoods of channel collapsing sites. The dynamics (locations, birth/death) of these ghost valves have shown to be strong function of the assigned wall motion protocol, which can be tuned to control flow transport along the axial direction and produce unidirectional net flow. An inelastic microchannel subjected to a zero pressure drop and undergoes localized rhythmic wall contractions can work as a micropump. The minimum requirement for this paradigm to produce a unidirectional net flow is; A channel with at least two contracting membranes that move with a distinct time-lag with respect each other. The presented ghost-valve pumping model is expected to function efficiently in the low Reynolds number flow regime. Therefore, it yields a potential usefulness in many of biomedical microdevices for drug delivery, point-of-care testing, and cardiac assistance devices.

A221 光異性化反応を利用した低レイノルズ数流れの熱流動制御(OS-7: 電子機器・デバイスの熱工学的課題と熱流動現象(4))

Viscoelastic fluids in low Reynolds number flow regime have important potential for heat transfer performance in contrast to Newtonian fluuids. To provide a high efficiency heat exchanger, the authors are aiming at controlling the heat transfer rate actively, in particular, with photo-rheological fluids (PRFs) which include photoisomer, the rheological properties of which can be tuned by light. The viscoelasticity of the fluids as a working fluid of heat transfer becomes weaker as the exposure time increases. As a result of the experiment, both relaxation time and pressure loss penalty were decreased with UV irradiation. The corresponding heat transfer rate also has a decreasing trend as the exposure time is lengthened more. These changes are supposed to be caused by weaker viscoelasticity of the aqueous solution that may significantly influence flow structure, as OMCA, one component of the solute used in the present study, undergoes a photo-isomerization.

A bioinspired pumping model for flow in a microtube with rhythmic wall contractions

Inspired by respiratory system in insects, in particular the rhythmic wall contractions found in insect's tracheal tubes, we propose a bioinspired pumping model that can work particularly well in the low Reynolds number flow regime. Incompressible, viscous flow transport in a fluid-filled axisymmetric, inelastic tube with rhythmic wall contractions is modeled using the lubrication theory. The wall contractions are prescribed via a tube profile with two indentation sites that can move with time lags with respect to each other. The analytical model is validated using the method of fundamental solutions based on the Stokeslets-meshfree computational method. The velocity field, pressure and time averaged net flow rate induced in a complete contraction cycle are calculated. Results demonstrate that an inelastic tube with at least two contracting spots can produce unidirectional flow and working as pumping mechanism. The physical insight of this pumping model can be explained as follows: when the first constriction starts to increase with time while second constriction is slight, the resulting flow is distributed almost equally up and downstream. Now, if second constriction becomes large, then the flow resistance on the downstream side is larger during the decreasing phase of the first constriction, so less flow is drawn back upstream. Therefore, a unidirectional flow with net flow transport is produced.

Influence of heat transfer on the aerodynamic performance of a plunging and pitching NACA0012 airfoil at low Reynolds numbers

The unsteady low Reynolds number aerodynamics phenomena around flapping wings are addressed in several investigations. Elsewhere, airfoils at higher Mach numbers and Reynolds numbers have been treated quite comprehensively in the literature. It is duly noted that the influence of heat transfer phenomena on the aerodynamic performance of flapping wings configurations is not well studied. The objective of the present study is to investigate the effect of heat transfer upon the aerodynamic performance of a pitching and plunging NACA0012 airfoil in the low Reynolds number flow regime with particular emphasis upon the airfoil's lift and drag coefficients. The compressible Navier–Stokes equations are solved using a finite volume method. To consider the variation of fluid properties with temperature, the values of dynamic viscosity and thermal diffusivity are evaluated with Sutherland's formula and the Eucken model, respectively. Instantaneous and mean lift and drag coefficients are calculated for several temperature differences between the airfoil surface and freestream within the range 0–100K. Simulations are performed for a prescribed airfoil motion schedule and flow parameters. It is learnt that the aerodynamic performance in terms of the lift CL and drag CD behavior is strongly dependent upon the heat transfer rate from the airfoil to the flow field. In the plunging case, the mean value of CD tends to increase, whereas the amplitude of CL tends to decrease with increasing temperature difference. In the pitching case, on the other hand, the mean value and the amplitude of both CD and CL decrease. A spectral analysis of CD and CL in the pitching case shows that the amplitudes of both CD and CL decrease with increasing surface temperature, whereas the harmonic frequencies are not affected.

Stokeslets-meshfree computations and theory for flow in a collapsible microchannel

We present both a theoretical model and Stokeslets-meshfree computations to study the induced flow motions and transport in a 2D microchannel with moving multiple prescribed dynamic collapses (contractions) along the upper wall. The channel is assumed to have a length that is much greater than its width, i.e., \({(\delta = W/L \ll1)}\) . The wall contractions are set to move with or without time (phase) lags with respect to each other. The theoretical analysis presented is based on the quasi-steady state approximations and the lubrication theory at the low Reynolds number flow regime. The meshfree numerical method is based on the method of fundamental solutions MFS, which uses a set of singularized force elements called Stokeslets to induce the flow motions. The flow field developments and structures induced by these wall contractions are given at various time snapshots during the collapsing cycle. The effect of the wall contractions amplitudes and the phase lags between individual contractions on the flow variables and on the time-averaged net flow over a complete cycle of contractions motions is studied. The present study is motivated by pumping mechanisms observed in insects, physiological systems that use multiple contractions to transport fluid, and the emerging novel microfluidic devices that mimic these systems.

Flow transport in a microchannel induced by moving wall contractions: a novel micropumping mechanism

A novel micropumping mechanism based on a theoretical model that describes flow transport in a microchannel induced by moving wall contractions in the low Reynolds number flow regime is presented. The channel is assumed to have a length that is much greater than its width (\({\delta = W/L \ll 1}\)) and the upper wall is subjected to prescribed, non-peristaltic, localized moving contractions. Lubrication theory for incompressible viscous flow at low Reynolds number (Re ~ δ) is used to model the problem mathematically and to derive expressions for the velocity components, pressure gradient, wall shear stress, and net flow produced by the wall contractions. The effect of contraction parameters such as amplitude and phase lag on the time-averaged net flow over a single cycle of wall motions is studied. The results presented here are supported by passive particle tracking simulations to investigate the possibility of using this system as a pumping mechanism. The present study is motivated by collapse mechanisms observed in entomological physiological systems that use multiple contractions to transport fluid, and the emerging novel microfluidic devices that mimic these systems.

Flow field characteristics study of a flapping airfoil using computational fluid dynamics

The flow field of a flapping airfoil in Low Reynolds Number (LRN) flow regime is associated with complex nonlinear vortex shedding and viscous phenomena. The respective fluid dynamics of such a flow is investigated here through Computational Fluid Dynamics (CFD) based on the Finite Volume Method (FVM). The governing equations are the unsteady, incompressible two-dimensional Navier-Stokes (N-S) equations. The airfoil is a thin ellipsoidal geometry performing a modified figure-of-eight-like flapping pattern. The flow field and vortical patterns around the airfoil are examined in detail, and the effects of several unsteady flow and system parameters on the flow characteristics are explored. The investigated parameters are the amplitude of pitching oscillations, phase angle between pitching and plunging motions, mean angle of attack, Reynolds number (Re), Strouhal number (St) based on the translational amplitudes of oscillations, and the pitching axis location ( x/ c). It is shown that these parameters change the instantaneous force coefficients quantitatively and qualitatively. It is also observed that the strength, interaction, and convection of the vortical structures surrounding the airfoil are significantly affected by the variations of these parameters.