In this paper, we study the fluid-structure interaction (FSI) of a three-dimensional (3D) flexible membrane immersed in an unsteady separated flow at moderate Reynolds numbers. We employ a body-conforming variational FSI solver based on the recently developed partitioned iterative scheme for the coupling of turbulent fluid flow with nonlinear structural dynamics. Of particular interest is to understand the flow-excited instability of a 3D flexible membrane as a function of the non-dimensional mass ratio, Reynolds number and aeroelastic number. For a wide range of the parameters, we examine two distinctive stability regimes of fluid-membrane interaction: deformed-steady state (DSS) and dynamic balance state (DBS). We propose stability phase diagrams to demarcate the DSS and DBS regimes for the parameter space of mass ratio vs. Reynolds number and mass ratio vs. aeroelastic number. Based on the aeroelastic mode analysis, we observe a frequency synchronization between the vortex shedding frequency and the membrane vibration frequency which leads to self-sustained vibrations in the dynamic balance state. To characterize the origin of the frequency lock-in, we derive an approximate analytical formula for the nonlinear natural frequency by considering the added mass effect and employing a large deflection theory for a simply supported rectangular membrane. Through our systematic high-fidelity numerical investigation, we find that the onset of the membrane vibration and the mode transition has a dependence on the frequency lock-in between the natural frequency of the tensioned membrane and the vortex shedding frequency or its harmonics. These findings on the fluid-elastic instability of membranes have implications for the design and development of control strategies for membrane wing-based unmanned systems and drones.
The unsteady aerodynamic thrust and aeroelastic response of a two-dimensional membrane airfoil under prescribed harmonic motion are investigated computationally with a high-order Navier-Stokes solver coupled to a nonlinear membrane structural model. The effects of membrane prestress and elasticity are examined parametrically for selected plunge and pitch-plunge motions at a chord-based Reynolds number of 2500. The importance of inertial membrane loads resulting from the prescribed flapping is also assessed for pure plunging motions. This study compares the period-averaged aerodynamic loads of …
Reynolds-number-dependent entrance bias in temperature polarization of lab-scale membrane distillation
Zachry Department of Civil and Environmental Engineering, Texas A&M University（德克萨斯农工大学扎克里土木与环境工程学院）；School of Sustainable Engineering and the Built Environment, Arizona State University（亚利桑那州立大学可持续工程与环境学院）
Microorganisms are rarely found in Nature swimming freely in an unbounded fluid. Instead, they typically encounter other organisms, hard walls, or deformable boundaries such as free interfaces or membranes. Hydrodynamic interactions between the swimmer and nearby objects lead to many interesting phenomena, such as changes in swimming speed, tendencies to accumulate or turn, and coordinated flagellar beating. Inspired by this class of problems, we investigate locomotion of microorganisms near deformable boundaries. We calculate the speed of an infinitely long swimmer close to a flexible surface…
The wake behind a cube with a face normal to the flow was investigated experimentally in a water tunnel using laser induced fluorescence visualisation (LIF) and particle image velocimetry (PIV) techniques. Measurements were carried out for moderate Reynolds numbers between 100 and 400 and in this range a sequence of two flow bifurcations was confirmed. Values for both onsets were determined in the framework of Landau`s instability model. The measured longitudinal vorticity was separated into three components corresponding to each of the identified regimes. It was shown that the vorticity assoc…
Breakup of liquid drops occurs in several natural and industrial settings. Fully resolved Volume of Fluid based simulations presented in this study reveal the complete flow physics and droplet dynamics that lead to the breakup of a drop in a particular mode. We have investigated the effects of density ratio and Reynolds number on the dynamics of drop deformation and subsequent breakup. A density ratio-Weber number phase plot is presented that indicates the variation in the deformation of the drop at various density ratios and Weber numbers. We show that the breakup dynamics of the droplets at …
In view of new experimental data the instability against adiabatic nonaxisymmetric perturbations of a Taylor-Couette flow with an axial density stratification is considered in dependence of the Reynolds number Re of rotation and the Brunt-Väisälä number Rn of the stratification. The flows at and beyond the Rayleigh limit become unstable between a lower and an upper Reynolds number (for fixed Rn). The rotation can thus be too slow or too fast for the stratorotational instability. The upper Reynolds number above which the instability decays, has its maximum value for the potential flow (driven b…
Direct numerical simulations are carried out to investigate the flow features responsible for secondary tones arising in trailing-edge noise at moderate Reynolds numbers. Simulations are performed for a NACA 0012 airfoil at freestream Mach numbers 0.1, 0.2 and 0.3 for angle of incidence 0 deg. and for Mach number 0.3 at 3 deg. angle of incidence. The Reynolds number based on the airfoil chord is fixed at $Re_c=10^5$. Flow configurations are investigated where noise generation arises from the scattering of boundary layer instabilities at the trailing edge. Results show that noise emission has a…
A study of fully developed plane turbulent channel flow subject to spanwise system rotation through direct numerical simulations is presented. In order to study both the influence of the Reynolds number and spanwise rotation on channel flow, the Reynolds number $Re = U_b h/ν$ is varied from a low 3000 to a moderate $31\,600$ and the rotation number $Ro = 2 Ωh/U_b$ is varied from 0 to 2.7, where $U_b$ is the mean bulk velocity, $h$ the channel half gap and $Ω$ the system rotation rate. The mean streamwise velocity profile displays also at higher $Re$ the characteristic linear part with a slope …
The effect of thermophoresis on the impaction of particles on a cylinder is investigated for different particle sizes, particle conductivities, temperature gradients and for Reynolds numbers between 100 and 1600. Simulations are performed using the Pencil Code, a high-order finite difference code. An overset-grid method is used to precisely simulate the flow around the cylinder. The ratio of particles impacting the cylinder and the number of particles inserted upstream of the cylinder is used to calculate an impaction efficiency. It is found that both the particle conductivity and the temperat…
We study compressible turbulent flow in a circular pipe, at computationally high Reynolds number. Classical related issues are addressed and discussed in light of the DNS data, including validity of compressibility transformations, velocity/temperature relations, passive scalar statistics, and size of turbulent eddies.Regarding velocity statistics, we find that Huang's transformation yields excellent universality of the scaled Reynolds stresses distributions, whereas the transformation proposed by Trettel and Larsson (2016) yields better representation of the effects of strong variation of den…
Dynamics of a liquid drop falling through a quiescent medium of another liquid is investigated in external uniform electric field. The electrohydrodynamics of a drop is governed by inherent deformability of the drop (defined by capillary number), the electric field strength (defined by Masson number) and the surface charge convection (quantified by electric Reynolds number). Surface charge convection generates nonlinearilty in a electrohydrodynamics problem by coupling the electric field and flow field. In Stokes limit, most existing theoretical models either considered weak charge convection …
A numerical study of stably stratified flows past spheres at Reynolds numbers $Re=200$ and $Re=300$ is reported. In these flow regimes, a neutrally stratified laminar flow induces distinctly different near-wake features. However, the flow behaviour changes significantly as the stratification increases and suppresses the scale of vertical displacements of fluid parcels. Computations for a range of Froude numbers $Fr\in [0.1,\infty]$ show that as Froude number decreases, the flow patterns for both Reynolds numbers become similar. The representative simulations of the lee-wave instability at $Fr=…
Large Eddy Simulations of a flow at a moderate Reynolds number over and around a three-dimensional hill have been performed. The main aim of the simulations was to study the effects of various inflow conditions (boundary layer thickness and laminar versus turbulent boundary layers) on the flow behind the hill. The main features of the flow behind the hill are similar in all simulations, however various differences are observed. The topology of the streamlines (friction lines) on the surface adjacent to the lower wall was found to be independent of the inflow conditions prescribed and comprised…
A fundamental problem in the field of turbulent skin-friction drag reduction is to determine the performance of the available control techniques at high values of the Reynolds number $Re$. We consider active, predetermined strategies based on spanwise forcing (oscillating wall and streamwise-traveling waves applied to a plane channel flow), and explore via Direct Numerical Simulations (DNS) up to $Re_τ=2100$ the rate at which their performance deteriorates as $Re$ is increased. To be able to carry out a comprehensive parameter study, we limit the computational cost of the simulations by adjust…
Effect of high and low Reynolds number is studied on low frequency vibrational modes of a spherical virus embedded in the aqueous medium. We have used an analytical approach based on fluid dynamic and classical Lamb theory to calculate the vibrational modes of a virus with material parameters of lysozyme crystal in water. The obvious size effect on the vibrational modes is observed. The estimated damping time which is of the order of picosecond varies with Reynolds number and shows a high value for a critical Reynolds number. The stationary eigenfrequency regions are observed for every quantum…
A direct numerical simulation of an oblique shock wave impinging on a turbulent boundary layer at Mach number 2.28 is carried out at moderate Reynolds number, simulating flow conditions similar to those of the experiment by Dupont et al. (2006). The low-frequency shock unsteadiness, whose characteristics have been the focus of considerable research efforts, is here investigated via the Morlet wavelet transform. Owing to its compact support in both physical and Fourier spaces, the wavelet transformation makes it possible to track the time evolution of the various scales of the wall-pressure flu…
In this paper, we have proposed a modified Marker-And-Cell (MAC) method to investigate the problem of an unsteady 2-D incompressible flow with heat and mass transfer at low, moderate, and high Reynolds numbers with no-slip and slip boundary conditions. We have used this method to solve the governing equations along with the boundary conditions and thereby to compute the flow variables, viz. $u$-velocity, $v$-velocity, $P$, $T$, and $C$. We have used the staggered grid approach of this method to discretize the governing equations of the problem. A modified MAC algorithm was proposed and used to…
We investigate properties of the scale dependence and cross-scale transfer of kinetic energy in compressible three-dimensional hydrodynamic turbulence, by means of two direct numerical simulations of decaying turbulence with initial Mach numbers M = 1/3 and M = 1, and with moderate Reynolds numbers, R_lambda ~ 100. The turbulent dynamics is analyzed using compressible and incompressible versions of the dynamic spectral transfer (ST) and the Karman-Howarth-Monin (KHM) equations. We find that the nonlinear coupling leads to a flux of the kinetic energy to small scales where it is dissipated; at …
Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim of this paper is to present a variant (obtained via a weighted residual approach) of the averaged one-dimensional model derived by Stewart et al. "Local and global instabilities of flow in a flexible-walled channel," Eur. J. Mech. B/Fluids 28, 541-557 (2009)]. The asymptotic expansions for small Reynolds numbers of these two models, compared to the exact so…
The evaporation of dispersed, liquid droplets in jet-sprays occurs in several industrial applications and in natural phenomena. Despite the relevance of the problem, a satisfactory comprehension of the mechanisms involved has not still be achieved because of the wide range of turbulent scales and the huge number of droplets involved. In this context, we address a DNS of a turbulent jet spray at relatively high Reynolds number, i.e. Re=10,000. We focus on the effect of the jet Re on the evaporation process and the preferential segregation of droplets, comparing the outcomes also with a DNS at l…
We study the effects of fluid-particle and particle-particle interactions in a three-dimensional monodispersed reactor with unstable fluidization. Simulations were conducted using the Immersed Boundary Method (IBM) for particle Reynolds numbers of 20-70 with an Archimedes number of 23600. Two different flow regimes were identified as a function of the particle Reynolds number. For low particle Reynolds numbers ($20 < Re_p < 40$), the porosity is relatively low and the particle dynamics are dominated by interparticle collisions that produce anisotropic particle velocity fluctuations. The relati…
We study the laminar and turbulent channel flow over a viscous hyper-elastic wall and show that it is possible to sustain an unsteady chaotic turbulent-like flow at any Reynolds number by properly choosing the wall elastic modulus. We propose a physical explanation for this effect by evaluating the shear stress and the turbulent kinetic energy budget in the fluid and elastic layer. We vary the bulk Reynolds number from 2800 to 10 and identify two distinct mechanisms for turbulence production. At moderate and high Reynolds numbers, turbulent fluctuations activate the wall oscillations, which, i…
According to a recent theory \cite{Li14}, when the Reynolds number is large, fully developed turbulence is caused by short term unpredictability (rough dependence upon initial data); when the Reynolds number is moderate, often transient turbulence is caused by chaos (long term unpredictability). This article aims at studying chaos in plane Couette flow at moderate Reynolds number. Based upon the work of L. van Veen and G. Kawahara \cite{VK11} on a transversal homoclinic orbit asymptotic to a limit cycle in plane Couette flow, we explore symbolic dynamics and chaos near the homoclinic orbit. Ma…
The emerging field of deformable microfluidics widely employed in the Lab-on-a-Chip and MEMS communities offers an opportunity to study a relatively under-examined physics. The main objective of this work is to provide a deeper insight into the underlying coupled fluid-solid interactions of a low-Reynolds-number fluid flow through a shallow deformable microchannel with ultra-low height-to-width ratios. The fabricated deformable microchannels of several microns in height and few millimeters in width, whose aspect ratio is about two orders of magnitude smaller than that of the previous reports, …
The flow past a fixed finite-length circular cylinder, the axis of which makes a nonzero angle with the incoming stream, is studied through fully-resolved simulations, from creeping-flow conditions to strongly inertial regimes. The investigation focuses on the way the body aspect ratio $χ$ (defined as as the length-to-diameter ratio), the inclination angle $θ$ with respect to the incoming flow and the Reynolds number $\text{Re}$ (based on the cylinder diameter) affect the flow structure past the body and therefore the hydrodynamic loads acting on it. The configuration $θ=0^\circ$ (where the cy…
Modeling blood flow in larger vessels using lattice-Boltzmann methods comes with a challenging set of constraints: a complex geometry with walls and inlet/outlets at arbitrary orientations with respect to the lattice, intermediate Reynolds number, and unsteady flow. Simple bounce-back is one of the most commonly used, simplest, and most computationally efficient boundary conditions, but many others have been proposed. We implement three other methods applicable to complex geometries (Guo, Zheng and Shi, Phys Fluids (2002); Bouzdi, Firdaouss and Lallemand, Phys. Fluids (2001); Junk and Yang Phy…
Non-equilibrium wall turbulence with mean-flow three-dimensionality is ubiquitous in geophysical and engineering flows. Under these conditions, turbulence may experience a counter-intuitive depletion of the turbulent stresses, which has important implications for modelling and control. Yet, current turbulence theories have been established mainly for statistically two-dimensional equilibrium flows and are unable to predict the reduction in the Reynolds stress magnitude. In the present work, we propose a multiscale model which explains the response of non-equilibrium wall-bounded turbulence und…
The effect of rotation is considered to become important when the Rossby number is sufficiently small, as is the case in many geophysical and astrophysical flows. Here we present direct numerical simulations to study the effect of rotation in flows with moderate Rossby numbers (down to Ro~0.1) but at Reynolds numbers large enough to observe the beginning of a turbulent scaling at scales smaller than the energy injection scale. We use coherent forcing at intermediate scales, leaving enough room in the spectral space for an inverse cascade of energy to also develop. We analyze the spectral behav…
Abrupt transition to turbulence may occur in pipe and channel flows at moderate flow rates, an unexpected event according to linear stability theory, and has been an open problem in fluid dynamics for more than a century. Extensive numerical simulations and statistical analyses of the plane-Poiseuille flow have been performed. A sequence of transition stages, which includes the equilibrium localized turbulence, the temporally persistent turbulence and the uniform turbulence, is identified. The spread of turbulent band is mainly caused by an oblique extension at moderate Reynolds numbers and ba…
Experiments in an extraordinary turbulent boundary layer called the sink flow, displaying a perfect streamwise invariance, show a wide extent of logarithmic scaling for moments of streamwise velocity up to order 12, even at moderate Reynolds numbers. This is in striking contrast to canonical constant-pressure turbulent boundary layers that show such comprehensive log scaling only at ultra-high Reynolds numbers. This demonstrates that ultra-high Reynolds number is not necessary for comprehensive log scaling to occur; while specific details of the sink flow are special, the relevance to general …
Direct numerical simulation of open-channel flow over a bed of spheres arranged in a regular pattern has been carried out at bulk Reynolds number and roughness Reynolds number (based on sphere diameter) of approximately 6900 and 120, respectively, for which the flow regime is fully-rough. The open-channel height was approximately 5.5 times the diameter of the spheres. Extending the results obtained by Chan-Braun et al. (J. Fluid Mech., vol. 684, 2011, 441) for an open-channel flow in the transitionally-rough regime, the present purpose is to show how the flow structure changes as the fully-rou…
At high Reynolds number, the interaction between two vortex tubes leads to intense velocity gradients, which are at the heart of fluid turbulence. This vorticity amplification comes about through two different instability mechanisms of the initial vortex tubes, assumed anti-parallel and with a mirror plane of symmetry. At moderate Reynolds number, the tubes destabilize via a Crow instability, with the nonlinear development leading to strong flattening of the cores into thin sheets. These sheets then break down into filaments which can repeat the process. At higher Reynolds number, the instabil…
We study the deformation and motion of an erythrocyte in fluid flows via a lattice Boltzmann method. To this purpose, the bending rigidity and the elastic modulus of isotropic dilation are introduced and incorporated with the lattice Boltzmann simulation, and the membrane-flow interactions on both sides of the membrane are carefully examined. We find that the static biconcave shape of an erythrocyte is quite stable and can effectively resist the pathological changes on their membrane. Further, our simulation results show that in shear flow, the erythrocyte will be highly flattened and undergo …
Immersed boundary methods are extensively used for simulations of dynamic solid objects interacting with fluids due to their computational efficiency and modelling flexibility compared to body-fitted grid methods. However, thin geometries, such as shells and membranes, cause a violation of the boundary conditions across the surface for many immersed boundary projection algorithms. Using a one-dimensional analytical derivation and multi-dimensional numerical simulations, this manuscript shows that adjustment of the Poisson matrix itself is require to avoid large velocity, pressure, and force pr…
A conservative coupled finite difference-boundary element computational procedure for the simulation of turbulent magnetohydrodynamic flow in a straight rectangular duct at finite magnetic Reynolds number is presented. The flow is assumed to be periodic in the streamwise direction and is driven by a mean pressure gradient. The duct walls are considered to be electrically insulating. The co-evolution of the velocity and magnetic fields as described respectively by the Navier-Stokes and the magnetic induction equations, together with the coupling of the magnetic field between the conducting doma…
Extremum seeking control (ESC) and its slope seeking generalization are applied in a high-fidelity flow simulation framework for reduction of acoustic noise generated by a NACA0012 airfoil. Two Reynolds numbers are studied for which different noise generation mechanisms are excited. For a low Reynolds number flow, the scattering of vortex shedding at the airfoil trailing edge produces tonal noise while, for a moderate Reynolds number case, boundary layer instabilities scatter at the trailing edge leading to noise emission at multiple tones superimposed on a broadband hump. Different control se…
We derive analytical solutions for hydrodynamic sources and sinks to granular temperature in moderately dense suspensions of elastic particles at finite Reynolds numbers. Modeling the neighbor-induced drag disturbances with a Langevin equation allows an exact solution for the joint fluctuating acceleration-velocity distribution function $P\left(v^{\prime},a^{\prime};t\right)$. Quadrant-conditioned covariance integrals of $P\left(v^{\prime},a^{\prime};t\right)$ yield the hydrodynamic source and sink that dictate the evolution of granular temperature. Analytical predictions are in agreement with…
The energy extraction and vortex dynamics from the sinusoidal heaving and pitching motion of an elliptical hydrofoil is explored through large-eddy simulations (LES) at a Reynolds number of $50,000$. The LES is able to capture the time-dependent vortex shedding and dynamic stall properties of the foil as it undergoes high relative angles of attack. Results of the computations are validated against experimental flume data in terms of power extraction and leading edge vortex (LEV) position and trajectory. The kinematics for optimal efficiency are found in the range of heave amplitude $h_o/c=0.5-…
In this paper, we address a crucial point regarding the description of moderate to high Reynolds numbers aquatic swimmers. For decades, swimming animals have been classified in two different families of propulsive mechanisms based on the Reynolds number: the "resistive" swimmers, using local friction to produce the necessary thrust force for locomotion at low Reynolds number and the "reactive" swimmers, lying in the high Reynolds range, and using added mass acceleration (described by perfect fluid theory). However, inertial swimmers are also systems that dissipate energy, due to their finite s…
Shearing and rotational forces in fluids can significantly alter the transport of momentum.A numerical investigation was undertaken to study the role of these forces using plane Couette flow subject to rotation about an axis perpendicular to both wall-normal and streamwise directions. Using a set of progressively higher Reynolds numbers up to Re = 5200, we find that the torque for a given Re is a non-monotonic function of rotation number, Ro. For low-to-moderate turbulent Reynolds numbers we find a maximum that is associated with flow fields that are dominated by downstream vortices and calcul…
Natural fliers like bats exploit the complex fluid-structure interaction between their flexible membrane wings and the air with great ease. Yet, replicating and scaling the balance between the structural and fluid-dynamical parameters of unsteady membrane wings for engineering applications remains challenging. In this study, we introduce a novel bio-inspired membrane wing design and systematically investigate the fluid-structure interactions of flapping membrane wings. The membrane wing can passively camber and its leading and trailing edges rotate with respect to the stroke plane. We find opt…
KEY WORDS suspensions, inertial focusing, particle-laden flows, high Reynolds numbers SHORT SUMMARY The inertial migration of particles in square channel flows at the micro-scale has been deeply investigated in the last two decades. The well-known four equilibrium positions are located near the center of each channel face at moderate Reynolds numbers [1]. More recently, Miura et al. [2] revealed experimentally the presence of eight equilibrium positions in millimetric square channels for Reynolds numbers higher than 250. The aim of the present work is to extend these results obtained at millim…
Recent experiments found that a hot solid sphere that is able to sustain a stable Leidenfrost vapour layer in a liquid exhibits significant drag reduction during free fall. The variation of the drag coefficient with Reynolds number shows substantial deviation from the characteristic drag crisis behavior at high Reynolds numbers. Results obtained with liqiuds of different viscosities show that onset of the drag crisis depends on the viscosity ratio of the vapor to the liquid. The key feature of the vapour layer in facilitating tangential flow and in altering the behaviour of the boundary layer …
