Direct numerical simulation of low-Reynolds-number flow past arrays of rotating spheres

2015 ◽  
Vol 765 ◽  
pp. 396-423 ◽  
Author(s):  
Qiang Zhou ◽  
Liang-Shih Fan
Keyword(s):  
Reynolds Number ◽  
Drag Force ◽  
Lift Force ◽  
Immersed Boundary ◽  
Particle Rotation ◽  
Volume Fractions ◽  
Reynolds Number Flow ◽  
Lattice Boltzmann Simulations ◽  
Random Arrays ◽  
Simulation Results

AbstractImmersed boundary-lattice Boltzmann simulations are used to examine the effects of particle rotation, at low particle Reynolds numbers, on flows in ordered and random arrays of mono-disperse spheres. The drag force, the Magnus lift force and the torque on the spheres, are determined at solid volume fractions up to the close-packed limits of the arrays. The rotational Reynolds number based on the angular velocity and the diameter of the spheres is used to characterize the rotational movement of spheres. The results show that the normalized Magnus lift force produced by particle rotation is approximately in direct proportion to the rotational Reynolds number, while the normalized drag force and torque acting on spheres are barely affected by this number. The Magnus lift force is negligible relative to the magnitude of the drag force when the rotational Reynolds number is low. However, it can be very significant, and even larger than the drag force, as the rotational Reynolds number increases up to $O(10^{2})$, especially for low solid volume fractions. Based on the simulation results, relations for the Magnus lift force and the torque for both ordered arrays and random arrays of rotating spheres at solid volume fractions from zero to close-packed limits are formulated. Further, the drag force relations in the literature are revised based on existing theories and the present simulation results for both arrays of spheres.

Study the Influence of Position and the Angle of the Winglets on MITE Micro Air Vehicle

2010 ◽  
Author(s):  
Babak Ganji ◽  
Romina Sadr-Eshkevari
Keyword(s):  
Reynolds Number ◽  
Drag Force ◽  
Lift Force ◽  
Aerodynamic Characteristics ◽  
Flow Solver ◽  
Structured Grid ◽  
Lateral Angle ◽  
Reynolds Number Flow ◽  
Air Vehicle ◽  
Number Flow

In recent years, small aircraft has been thoroughly studied and superior designs have been extensively developed. The aerodynamic design of micro aerial vehicles (MAVs), the most important small aircrafts, in Low-Reynolds number flow (LRNF) has become one of the main concerns to the profession. LRNF is mostly influenced by the airfoil design. Similar to all aircrafts, vertical elevons and winglets play an important role in the aerodynamics of MAVs. On this basis, the present study aimed to assess the effect of lateral angle alterations of the two vertical winglets in the aerodynamics of micro tactical expendable (MITE) in LRNF. A finite element flow solver (FEFS) based on structured grid was employed for studying the aerodynamic characteristics of MITE. The findings of the present study suggest that with the gradual increase in cant angle φ, lift force decreases and drag force remains unchanged. Also with the increase of lateral angle θ, drag force increases significantly and negligible changes are observed in lift force. Vertical elevons play an important role in the control of MITE. Also the effect of Reynolds number on aerodynamic coefficients is discussed.

Moderate-Reynolds-number flows in ordered and random arrays of spheres

2001 ◽  
Vol 448 ◽  
pp. 243-278 ◽  
Author(s):  
REGHAN J. HILL ◽  
DONALD L. KOCH ◽  
ANTHONY J. C. LADD
Keyword(s):  
Reynolds Number ◽  
Drag Force ◽  
Volume Fraction ◽  
Reynolds Numbers ◽  
Hydrodynamic Dispersion ◽  
Fluid Inertia ◽  
Volume Fractions ◽  
Moderate Reynolds Number ◽  
Random Arrays ◽  
Arrays Of Spheres

Lattice-Boltzmann simulations are used to examine the effects of fluid inertia, at moderate Reynolds numbers, on flows in simple cubic, face-centred cubic and random arrays of spheres. The drag force on the spheres, and hence the permeability of the arrays, is calculated as a function of the Reynolds number at solid volume fractions up to the close-packed limits of the arrays. At Reynolds numbers up to O(102), the non-dimensional drag force has a more complex dependence on the Reynolds number and the solid volume fraction than suggested by the well-known Ergun correlation, particularly at solid volume fractions smaller than those that can be achieved in physical experiments. However, good agreement is found between the simulations and Ergun's correlation at solid volume fractions approaching the close-packed limit. For ordered arrays, the drag force is further complicated by its dependence on the direction of the flow relative to the axes of the arrays, even though in the absence of fluid inertia the permeability is isotropic. Visualizations of the flows are used to help interpret the numerical results. For random arrays, the transition to unsteady flow and the effect of moderate Reynolds numbers on hydrodynamic dispersion are discussed.

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 Vortex-induced vibration of a transversely rotating sphere

2018 ◽  
Vol 847 ◽  
pp. 786-820 ◽  
Author(s):  
Methma M. Rajamuni ◽  
Mark C. Thompson ◽  
Kerry Hourigan
Keyword(s):  
Reynolds Number ◽  
Drag Force ◽  
Rotation Rate ◽  
Lift Force ◽  
Oscillation Amplitude ◽  
Fluid Viscosity ◽  
Sphere Diameter ◽  
Force Coefficient ◽  
Vortex Induced Vibration ◽  
Rotation Rates

The effects of transverse rotation on the vortex-induced vibration (VIV) of a sphere in a uniform flow are investigated numerically. The one degree-of-freedom sphere motion is constrained to the cross-stream direction, with the rotation axis orthogonal to flow and vibration directions. For the current simulations, the Reynolds number of the flow, $Re=UD/\unicode[STIX]{x1D708}$, and the mass ratio of the sphere, $m^{\ast }=\unicode[STIX]{x1D70C}_{s}/\unicode[STIX]{x1D70C}_{f}$, were fixed at 300 and 2.865, respectively, while the reduced velocity of the flow was varied over the range $3.5\leqslant U^{\ast }~(\equiv U/(f_{n}D))\leqslant 11$, where, $U$ is the upstream velocity of the flow, $D$ is the sphere diameter, $\unicode[STIX]{x1D708}$ is the fluid viscosity, $f_{n}$ is the system natural frequency and $\unicode[STIX]{x1D70C}_{s}$ and $\unicode[STIX]{x1D70C}_{f}$ are solid and fluid densities, respectively. The effect of sphere rotation on VIV was studied over a wide range of non-dimensional rotation rates: $0\leqslant \unicode[STIX]{x1D6FC}~(\equiv \unicode[STIX]{x1D714}D/(2U))\leqslant 2.5$, with $\unicode[STIX]{x1D714}$ the angular velocity. The flow satisfied the incompressible Navier–Stokes equations while the coupled sphere motion was modelled by a spring–mass–damper system, under zero damping. For zero rotation, the sphere oscillated symmetrically through its initial position with a maximum amplitude of approximately 0.4 diameters. Under forced rotation, it oscillated about a new time-mean position. Rotation also resulted in a decreased oscillation amplitude and a narrowed synchronisation range. VIV was suppressed completely for $\unicode[STIX]{x1D6FC}>1.3$. Within the $U^{\ast }$ synchronisation range for each rotation rate, the drag force coefficient increased while the lift force coefficient decreased from their respective pre-oscillatory values. The increment of the drag force coefficient and the decrement of the lift force coefficient reduced with increasing reduced velocity as well as with increasing rotation rate. In terms of wake dynamics, in the synchronisation range at zero rotation, two equal-strength trails of interlaced hairpin-type vortex loops were formed behind the sphere. Under rotation, the streamwise vorticity trail on the advancing side of the sphere became stronger than the trail in the retreating side, consistent with wake deflection due to the Magnus effect. This symmetry breaking appears to be associated with the reduction in the observed amplitude response and the narrowing of the synchronisation range. In terms of variation with Reynolds number, the sphere oscillation amplitude was found to increase over the range $Re\in [300,1200]$ at $U^{\ast }=6$ for each of $\unicode[STIX]{x1D6FC}=0.15$, 0.75 and 1.5. The VIV response depends strongly on Reynolds number, with predictions indicating that VIV will persist for higher rotation rates at higher Reynolds numbers.

Moderate-Reynolds-number flow in a wall-bounded porous medium

2002 ◽  
Vol 453 ◽  
pp. 315-344 ◽  
Author(s):  
REGHAN J. HILL ◽  
DONALD L. KOCH
Keyword(s):  
Reynolds Number ◽  
Unsteady Flow ◽  
Reynolds Numbers ◽  
Steady Flows ◽  
Reynolds Number Flow ◽  
Periodic Arrays ◽  
Fundamental Frequencies ◽  
Lattice Boltzmann Simulations ◽  
Moderate Reynolds Number ◽  
Domain Consistency

The transition to unsteady flow and the dynamics of moderate-Reynolds-number flows in unbounded and wall-bounded periodic arrays of aligned cylinders are examined using lattice-Boltzmann simulations. The simulations are compared to experiments, which necessarily have bounding walls. With bounding walls, the transition to unsteady flow is accompanied by a loss of spatial periodicity, and the temporal fluctuations are chaotic at much smaller Reynolds numbers. The walls, therefore, affect the unsteady flows everywhere in the domain. Consistency between experiments and simulations is established by examining the wake lengths for steady flows and the fundamental frequencies at higher Reynolds numbers, both as a function of the Reynolds number. Simulations are used to examine the velocity fluctuations, flow topologies, and the fluctuating forces on the cylinders.

scholarly journals Lattice Boltzmann simulations of low-Reynolds-number flows past fluidized spheres: effect of inhomogeneities on the drag force

2017 ◽  
Vol 833 ◽  
pp. 599-630 ◽  
Author(s):  
Gregory J. Rubinstein ◽  
Ali Ozel ◽  
Xiaolong Yin ◽  
J. J. Derksen ◽  
Sankaran Sundaresan
Keyword(s):  
Reynolds Number ◽  
Drag Force ◽  
Lattice Boltzmann ◽  
Volume Fraction ◽  
Low Reynolds Number ◽  
Particle Volume Fraction ◽  
Spherical Particles ◽  
Particle Volume ◽  
Lattice Boltzmann Simulations ◽  
Low Reynolds

The formation of inhomogeneities within fluidized beds, both in terms of the particle configurations and flow structures, have a pronounced effect on the interaction force between the fluid and particles. While recent numerical studies have begun to probe the effects of inhomogeneities on the drag force at the particle scale, the applicability of prior microscale constitutive drag relations is still limited to random, homogeneous distributions of particles. Since an accurate model for the drag force is needed to predict the fluidization behaviour, the current study utilizes the lessons of prior inhomogeneity studies in order to derive a robust drag relation that is both able to account for the effect of inhomogeneities and applicable as a constitutive closure to larger-scale fluidization simulations. Using fully resolved lattice Boltzmann simulations of systems composed of fluid and monodisperse spherical particles in the low-Reynolds-number (Re) regime, the fluid–particle drag force, normalized by the ideal Stokes drag force, is found to significantly decrease, over a range of length scales, as the extent of inhomogeneities increases. The extent of inhomogeneities is found to most effectively be quantified through one of two subgrid-scale quantities: the scalar variance of the particle volume fraction or the drift flux, which is the correlation between the particle volume fraction and slip velocity. Scale-similar models are developed to estimate these two subgrid measures over a wide range of system properties. Two new drag constitutive models are proposed that are not only functions of the particle volume fraction and the Stokes number ($St$), but also dependent on one of these subgrid measures for the extent of inhomogeneities. Based on the observed, appreciable effect of inhomogeneities on drag, these new low-Re drag models represent a significant advancement over prior constitutive relations.

Relationship Between Macroscopic Rheological Properties and Microstructure of a Dilute Suspension by a Two-Way Coupling Numerical Scheme

2019 ◽  
Author(s):  
Tomohiro Fukui ◽  
Misa Kawaguchi ◽  
Koji Morinishi
Keyword(s):  
Reynolds Number ◽  
Rheological Properties ◽  
Numerical Scheme ◽  
Lift Force ◽  
Flow Direction ◽  
Spatial Arrangement ◽  
Suspended Particles ◽  
Spherical Particles ◽  
Particle Rotation ◽  
Axis Position

Abstract The rheological properties of a suspension depend on particle shape, spatial arrangement of the particles and hydrodynamic interactions as well as the concentration of the particles. So far, we proposed a two-way coupling numerical scheme to evaluate the effects of particle rotation on the rheological properties. This particle rotation decreases the fluid resistance. However, these studies were conducted on the condition that suspended particles were homogeneously distributed. Therefore, the particles in this study are randomly scattered in a suspension for better practical applications. Pressure-driven suspension flow simulations were conducted to consider the effects of inertia on the relationship between spatial arrangement of the particles and the rheological properties of a suspension. The channel width and axial length were set 400 μm and 1620 μm, respectively, and periodic boundary conditions were applied in the flow direction. The rigid spherical particles whose diameter was 20 μm were randomly scattered in the channel as an initial condition. The concentration of the suspension was set 1.02% for dilute assumption, and the suspension flows with the Reynolds number from 2 to 128 were reproduced in order to investigate the inertial effects of the suspended particles on the rheological properties. The rheological properties of the suspension were evaluated in terms of power-law index (non-Newtonian index). The velocity profile of a suspension for low Reynolds number conditions exhibited almost parabolic. This indicates the suspension behaves as a Newtonian fluid. For higher Reynolds number conditions, on the other hand, the lift force on the particles increased and they migrated toward the equilibrium y-axis position, where the lift force is zero. These changes in the y-axis position of the particles caused a change in microstructure of the suspension, which were followed by a change in macroscopic rheological properties. Owing to these microstructure changes, the non-Newtonian (thixotropic) properties were enhanced as the Reynolds number increased.

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