scholarly journals Dynamic Behaviours of a Filament in a Viscoelastic Uniform Flow

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 90
Author(s):  
Jingtao Ma ◽  
Fang-Bao Tian ◽  
John Young ◽  
Joseph C. S. Lai
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Critical Reynolds Number ◽  
Major Effect ◽  
Uniform Flow ◽  
Weissenberg Number ◽  
Immersed Boundary ◽  
Flapping Motion ◽  
Drag And Lift ◽  
Boltzmann Method

The dynamic behaviours of a filament in a viscoelastic uniform flow were investigated by an immersed boundary-lattice Boltzmann method. The effects of the Reynolds numbers (Re, ranging from 10 to 200) and the Weissenberg number (Wi, ranging from 0 to 1.2) on the filament flapping motion and the drag and lift coefficients on the filament were studied. It was found that a higher inertial effect (larger Re) promotes the flapping motion of the filament. In addition, the major effect of the viscoelasticity of the Giesekus fluid is to decrease the critical Reynolds number for the flapping motion of the filament and to promote the flapping motion. The drag coefficient on the filament in a Giesekus uniform flow decreases with the increase of Wi at low Re (Re<100), and experiences oscillations with similar amplitudes at all Wi at a sufficiently high Re (Re>100). In contrast, the viscoelasticity of the FENE-CR fluid increases the critical Reynolds number at lower Wi (Wi<0.8), and shows little influence on the critical Reynolds number at higher Wi (Wi≥0.8). In addition, the viscoelasticity of the FENE-CR fluid hinders the flapping motion of the filament, and increases the drag coefficient on the filament at low Re (Re<100).

Dynamics of a macroscopic elastic fibre in a polymeric cellular flow

2017 ◽  
Vol 817 ◽  
pp. 388-405 ◽  
Author(s):  
Qiang Yang ◽  
Lisa Fauci
Keyword(s):  
Reynolds Number ◽  
Viscoelastic Fluid ◽  
Relaxation Times ◽  
Elastic Fibre ◽  
Weissenberg Number ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Reynolds Number Flow ◽  
Number Flow ◽  
Multiple Cells

We study the dynamics and transport of an elastic fibre in a polymeric cellular flow. The macroscopic fibre is much larger than the infinitesimal immersed polymer coils distributed in the surrounding viscoelastic fluid. Here we consider low-Reynolds-number flow using the Navier–Stokes/Fene-P equations in a two-dimensional, doubly periodic domain. The macroscopic fibre supports both tensile and bending forces, and is fully coupled to the viscoelastic fluid using an immersed boundary framework. We examine the effects of fibre flexibility and polymeric relaxation times on fibre buckling and transport as well as the evolution of polymer stress. Non-dimensional control parameters include the Reynolds number, the Weissenberg number, and the elasto-viscous number of the macroscopic fibre. We find that large polymer stresses occur in the fluid near the ends of the fibre when it is compressed. In addition, we find that viscoelasticity hinders a fibre’s ability to traverse multiple cells in the domain.

scholarly journals Drag and lift forces on clean spherical and ellipsoidal bubbles in a solid-body rotating flow

2011 ◽  
Vol 682 ◽  
pp. 434-459 ◽  
Author(s):  
MARIE RASTELLO ◽  
JEAN-LOUIS MARIÉ ◽  
MICHEL LANCE
Keyword(s):  
Aspect Ratio ◽  
Drag Coefficient ◽  
Solid Body ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Uniform Flow ◽  
Rotating Flow ◽  
Wide Range ◽  
Spherical Bubbles ◽  
Drag And Lift

A single bubble is placed in a solid-body rotating flow of silicon oil. From the measurement of its equilibrium position, lift and drag forces are determined. Five different silicon oils have been used, providing five different viscosities and Morton numbers. Experiments have been performed over a wide range of bubble Reynolds numbers (0.7 ≤ Re ≤ 380), Rossby numbers (0.58 ≤ Ro ≤ 26) and bubble aspect ratios (1 ≤ χ ≤ 3). For spherical bubbles, the drag coefficient at the first order is the same as that of clean spherical bubbles in a uniform flow. It noticeably increases with the local shear S = Ro−1, following a Ro−5/2 power law. The lift coefficient tends to 0.5 for large Re numbers and rapidly decreases as Re tends to zero, in agreement with existing simulations. It becomes hardly measurable for Re approaching unity. When bubbles start to shrink with Re numbers decreasing slowly, drag and lift coefficients instantaneously follow their stationary curves versus Re. In the standard Eötvös–Reynolds diagram, the transitions from spherical to deformed shapes slightly differ from the uniform flow case, with asymmetric shapes appearing. The aspect ratio χ for deformed bubbles increases with the Weber number following a law which lies in between the two expressions derived from the potential flow theory by Moore (J. Fluid Mech., vol. 6, 1959, pp. 113–130) and Moore (J. Fluid Mech., vol. 23, 1965, pp. 749–766) at low- and moderate We, and the bubble orients with an angle between its minor axis and the direction of the flow that increases for low Ro. The drag coefficient increases with χ, to an extent which is well predicted by the Moore (1965) drag law at high Re and Ro. The lift coefficient is a function of both χ and Re. It increases linearly with (χ − 1) at high Re, in line with the inviscid theory, while in the intermediate range of Reynolds numbers, a decrease of lift with aspect ratio is observed. However, the deformation is not sufficient for a reversal of lift to occur.

Simulation of Flow Around a Cube at Moderate Reynolds Numbers Using the Lattice Boltzmann Method

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Majid Hassan Khan ◽  
Atul Sharma ◽  
Amit Agrawal
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Lattice Boltzmann Method ◽  
Steady Flow ◽  
Flow Regime ◽  
Lattice Boltzmann ◽  
Reynolds Numbers ◽  
Side Force ◽  
Force Coefficients ◽  
Boltzmann Method

Abstract This article reports flow behavior around a suspended cube obtained using three-dimensional (3D) lattice Boltzmann method (LBM)-based simulations. The Reynolds number (Re) range covered is from 84 to 770. Four different flow regimes are noted based on the flow structure in this range of Re: steady axisymmetric (84 ≤ Re ≤ 200), steady nonaxisymmetric (215 ≤ Re ≤ 250), unsteady nonaxisymmetric in one plane and axisymmetric in the other plane (276 ≤ Re ≤ 300), and unsteady nonaxisymmetric in streamwise orthogonal planes (339 ≤ Re ≤ 770). Recirculation length and drag coefficient follow inverse trend in the steady flow regime. The unsteady flow regime shows hairpin vortices for Re ≤ 300 and then it becomes structureless. The nature of force coefficients has been examined at various Reynolds numbers. Temporal behavior of force coefficients is presented along with phase dependence of side force coefficients. The drag coefficient decreases with increase in Reynolds number in the steady flow regime and the side force coefficients are in phase. Drag coefficients are compared with established correlations for flow around a cube and a sphere. The side force coefficients are perfectly correlated at Re = 215 and they are anticorrelated at Re = 250. At higher Reynolds numbers, side force coefficients are highly uncorrelated. This work adds to the existing understanding of flow around a cube reported earlier at low and moderate Re and extends it further to unsteady regime at higher Re.

Study of flapping filaments using the immersed boundary-lattice Boltzmann method

2018 ◽  
Vol 89 (15) ◽  
pp. 3127-3136
Author(s):  
Zhengdao Wang ◽  
Yi Kun Wei ◽  
Yuehong Qian
Keyword(s):  
Reynolds Number ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Resonance Phenomenon ◽  
Discrete Equation ◽  
Immersed Boundary ◽  
Modified Method ◽  
Wide Range ◽  
Motion Characteristics ◽  
Boltzmann Method

In this study, flow over a flexible filament under a wide range of parameters is simulated using the immersed boundary-lattice Boltzmann method (IB-LBM). The leading end of the filament is fixed in the flow field and the trailing end is free to flap. To execute the simulation, we combine the IB-LBM and a semi-implicit discrete equation of force on the filament to better satisfy the boundary condition. After some numerical simulations validating the modified method, the motion of flexible filaments is examined with different dimensionless bending coefficients ([Formula: see text]) and Reynolds numbers ([Formula: see text]). From the trajectory of the flapping filament, different flapping modes are found. When the parameter is between that of two modes, the anti-resonance phenomenon is observed. Numerical results show that the dimensionless bending coefficient and Reynolds number both affect the flapping motion, but in different ways. The dimensionless bending coefficient mainly affects the mode of the flapping, while the Reynolds number mainly affects the perturbation to the filament motion, which is related to the motivation of this system. Some other motion characteristics, for example, the function of amplitude and perturbation propagation, are also discussed in this work.

A Numerical Study of Jet Propulsion of an Oblate Jellyfish Using a Momentum Exchange-Based Immersed Boundary-Lattice Boltzmann Method

2014 ◽  
Vol 6 (3) ◽  
pp. 307-326 ◽  
Author(s):  
Hai-Zhuan Yuan ◽  
Shi Shu ◽  
Xiao-Dong Niu ◽  
Mingjun Li ◽  
Yang Hu
Keyword(s):  
Reynolds Number ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Numerical Study ◽  
Mass Density ◽  
Density Ratio ◽  
Large Mass ◽  
Immersed Boundary ◽  
Momentum Exchange ◽  
Boltzmann Method

AbstractIn present paper, the locomotion of an oblate jellyfish is numerically investigated by using a momentum exchange-based immersed boundary-Lattice Boltzmann method based on a dynamic model describing the oblate jellyfish. The present investigation is agreed fairly well with the previous experimental works. The Reynolds number and the mass density of the jellyfish are found to have significant effects on the locomotion of the oblate jellyfish. Increasing Reynolds number, the motion frequency of the jellyfish becomes slow due to the reduced work done for the pulsations, and decreases and increases before and after the mass density ratio of the jellyfish to the carried fluid is 0.1. The total work increases rapidly at small mass density ratios and slowly increases to a constant value at large mass density ratio. Moreover, as mass density ratio increases, the maximum forward velocity significantly reduces in the contraction stage, while the minimum forward velocity increases in the relaxation stage.

The effects of surface roughness and tunnel blockage on the flow past spheres

1974 ◽  
Vol 65 (1) ◽  
pp. 113-125 ◽  
Author(s):  
Elmar Achenbach
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Drag Coefficient ◽  
Critical Reynolds Number ◽  
Measurement Techniques ◽  
Flow Conditions ◽  
Number Range ◽  
Flow Past ◽  
Reynolds Number Range ◽  
Shedding Frequency

The effect of surface roughness on the flow past spheres has been investigated over the Reynolds number range 5 × 104 < Re < 6 × 106. The drag coefficient has been determined as a function of the Reynolds number for five surface roughnesses. With increasing roughness parameter the critical Reynolds number decreases. At the same time the transcritical drag coefficient rises, having a maximum value of 0·4.The vortex shedding frequency has been measured under subcritical flow conditions. It was found that the Strouhal number for each of the various roughness conditions was equal to its value for a smooth sphere. Beyond the critical Reynolds number no prevailing shedding frequency could be detected by the measurement techniques employed.The drag coefficient of a sphere under the blockage conditions 0·5 < ds/dt < 0·92 has been determined over the Reynolds number range 3 × 104 < Re < 2 × 106. Increasing blockage causes an increase in both the drag coefficient and the critical Reynolds number. The characteristic quantities were referred to the flow conditions in the smallest cross-section between sphere and tube. In addition the effect of the turbulence level on the flow past a sphere under various blockage conditions was studied.

Flexible ring flapping in a uniform flow

2012 ◽  
Vol 707 ◽  
pp. 129-149 ◽  
Author(s):  
Boyoung Kim ◽  
Wei-Xi Huang ◽  
Soo Jai Shin ◽  
Hyung Jin Sung
Keyword(s):  
Reynolds Number ◽  
Stable State ◽  
Uniform Flow ◽  
Bending Stiffness ◽  
Immersed Boundary ◽  
Number Range ◽  
Aspect Ratios ◽  
Reynolds Number Range ◽  
Internal Volume ◽  
Flexible Ring

AbstractAn improved version of the immersed boundary (IB) method for simulating an initially circular or elliptic flexible ring pinned at one point in a uniform flow has been developed. The boundary of the ring consists of a flexible filament with tension and bending stiffness. A penalty method derived from fluid compressibility was used to ensure the conservation of the internal volume of the flexible ring. At $\mathit{Re}= 100$, two different flapping modes were identified by varying the tension coefficient for a fixed bending stiffness, or by changing the bending coefficient for a fixed tension coefficient. The optimal tension and bending coefficients that minimize the drag force of the flexible ring were found. Visualization of the vorticity field showed that the two flapping modes correspond to different vortex shedding patterns. We observed the hysteresis property of the flexible ring, which exhibits bistable states over a range of flow velocities depending on the initial inclination angle, i.e. one is a stationary stable state and the other a self-sustained periodically flapping state. The Reynolds number range of the bistability region and the flapping amplitude were determined for various aspect ratios $a/ b$. For $a/ b= 0. 5$, the hysteresis region arises at the highest Reynolds number and the flapping amplitude in the self-sustained flapping state is minimized. A new bistability phenomenon was observed: for certain aspect ratios, two periodically flapping states coexist with different amplitudes in a particular Reynolds number range, instead of the presence of a stationary stable state and a periodically flapping state.

scholarly journals Deformation of a Capsule in a Power-Law Shear Flow

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Fang-Bao Tian
Keyword(s):  
Reynolds Number ◽  
Shear Rate ◽  
Shear Flow ◽  
Lattice Boltzmann Method ◽  
Power Law ◽  
Lattice Boltzmann ◽  
Immersed Boundary ◽  
Power Law Fluid ◽  
Boltzmann Method ◽  
Power Law Index

An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values.

Golf Ball Aerodynamics

1976 ◽  
Vol 27 (2) ◽  
pp. 112-122 ◽  
Author(s):  
P W Bearman ◽  
J K Harvey
Keyword(s):  
Reynolds Number ◽  
Wind Tunnel ◽  
Drag Coefficient ◽  
Critical Reynolds Number ◽  
Lift Coefficient ◽  
Golf Course ◽  
Aerodynamic Forces ◽  
Wide Range ◽  
Tunnel Technique ◽  
Smooth Sphere

SummaryA wind tunnel technique has been developed to measure the aerodynamic forces acting on golf balls over a wide range of Reynolds number and spin rate. Balls with round dimples and hexagonal dimples have been investigated. The dimples are found to induce a critical Reynolds number behaviour at a lower value of Reynolds number than that experienced by a smooth sphere and beyond this point, unlike the behaviour of a sand-roughened sphere, there is little dependence of the forces on further increases in Reynolds number. A hexagonally-dimpled ball has a higher lift coefficient and a slightly lower drag coefficient than a conventional round-dimpled ball. Trajectories are calculated using the aerodynamic data and the ranges are compared with data obtained from a driving machine on a golf course.

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