FIGURE 4 - uploaded by Mohsen Daghooghi
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(Colour online) Visualization of relative vorticity (vorticity relative to undisturbed flow) and streamlines around the ellipsoid in a suspension with ? = 0.058, Ar = 2, Re = 0.01. (a) Minimum angular velocity, ? = 0; (b) maximum acceleration, ? = ?/4; (c) maximum angular velocity, ? = ?/2; (d) maximum deceleration, ? = 3?/4.
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We investigate the rheological properties of a suspension of neutrally buoyant rigid ellipsoids by fluid–structure interaction simulations of a particle in a periodic domain under simple shear using the curvilinear immersed-boundary (CURVIB) method along with a quaternion–angular velocity technique to calculate the dynamics of the particle’s motion...
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... figure 4 the out-of-plane vorticity contours and streamlines around the ellipsoid are visualized in the symmetric midplane (plane perpendicular to the vorticity vector and passing the centre of the ellipsoid) for different phases in a suspension with Re = 0.01 and φ = 0.058. The background plane is coloured by the relative out-of-plane vorticity (vorticity relative to the undisturbed flow), where dark and bright colours indicate positive and negative vorticity regions, respectively. ...
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... background plane is coloured by the relative out-of-plane vorticity (vorticity relative to the undisturbed flow), where dark and bright colours indicate positive and negative vorticity regions, respectively. Figure 4(a) shows the ellipsoid at θ = 0, where the angular velocity is minimum ( figure 3a), and we can clearly see the closed streamline region around the ellipsoid. The existence of this region was shown numerically by Kossack & Acrivos (1974) and experimentally verified by Poe & Acrivos (1975) for spheres and cylinders. ...
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... existence of this region was shown numerically by Kossack & Acrivos (1974) and experimentally verified by Poe & Acrivos (1975) for spheres and cylinders. The other instances visualized in figure 4 show that the closing streamline region would collapse by rotation of the ellipsoid. As we can see in figure 4(b-d), when the ellipsoid is not aligned with the flow, the curvature of the body twists the streamlines and disturbs the closing region around the particle. ...
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... other instances visualized in figure 4 show that the closing streamline region would collapse by rotation of the ellipsoid. As we can see in figure 4(b-d), when the ellipsoid is not aligned with the flow, the curvature of the body twists the streamlines and disturbs the closing region around the particle. In figure 4(a), we see that a negative vorticity region is formed at both poles of the particle, i.e. the flow in these regions rotates in a direction opposite to the undisturbed shear flow. ...
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... we can see in figure 4(b-d), when the ellipsoid is not aligned with the flow, the curvature of the body twists the streamlines and disturbs the closing region around the particle. In figure 4(a), we see that a negative vorticity region is formed at both poles of the particle, i.e. the flow in these regions rotates in a direction opposite to the undisturbed shear flow. In contrast, when the particle reaches the maximum angular velocity (see figure 4c), negative vorticity regions are formed near the sides of the particle. ...
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... figure 4(a), we see that a negative vorticity region is formed at both poles of the particle, i.e. the flow in these regions rotates in a direction opposite to the undisturbed shear flow. In contrast, when the particle reaches the maximum angular velocity (see figure 4c), negative vorticity regions are formed near the sides of the particle. At θ = π/4 and θ = 3π/4, (Figure 4b,d, respectively), we can observe that the curvature of flow changes at the poles, i.e. the direction of vorticity changes at the poles. ...
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... contrast, when the particle reaches the maximum angular velocity (see figure 4c), negative vorticity regions are formed near the sides of the particle. At θ = π/4 and θ = 3π/4, (Figure 4b,d, respectively), we can observe that the curvature of flow changes at the poles, i.e. the direction of vorticity changes at the poles. ...
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Citations
... 14 When moving through a system, the particle's shape, size, and density will play a significant role in its dynamics as well as kinematics (location and orientation). 15 Furthermore, the orientation of a non-spherical particle locally affects the shear flow, which, in turn, affects the motion/orientation of particles, i.e., fluid-particle interaction, 16 that ultimately determines the rheology of the particle-fluid system. Similarly, when a particle is near a wall, there is a particle-fluid-wall interaction that determines the dynamics of the particle in conjunction with local flow dynamics. ...
... When coupling the DEM to the computational fluid dynamic (CFD) solver, i.e., CFD-DEM methods, 23,34 the hydrodynamic forces that dictate the motion of particles in DEM are required. There are two ways to obtain forces on the particle from the fluid: (a) Particle-resolved simulations: directly compute the forces on the particle when the grid size is much smaller than the particle size, 35 i.e., flow around the particle is resolved using methods that can handle moving boundaries in the flow, such as immersed boundary (IB) methods, 16 fictitious domain methods, 36 and level set methods, 37 or (b) force-coupling simulations: the hydrodynamic forces on a particle are determined by using empirical formulas when the computational domain is much larger than the particle, and the effect of particles on the flow is handled by incorporating reaction forces in the flow equations. 38,39 For example, the force-coupling method has been used for fluidized beds 2 and cyclone 3 applications, while particle-resolved has been used for particle flow through a microchannel. ...
The resting dynamics of non-spherical particles on a flat surface can be considered the last phase in settling a particle, which has yet to be fully investigated. This last phase for the non-spherical particle is numerically investigated, for the first time, using a sharp-interface immersed boundary method coupled with a kinematic-based collision model. The collision model guarantees a realistic, stable/settled position of non-spherical-shaped particles, contrary to alternative models that implement a repulsive penalty force. In the simulations, a single particle is released with a constant velocity downwards close to the wall until the collision occurs. Hydrodynamic moments alter the settling dynamics depending on the Reynolds number (Re) by opposing the gravity-driven motion of particles. It was observed that the settling trajectories/angles were generally not affected for each particle, but their rate of change, i.e., angular velocities, reduced as the Reynolds number decreased. A simplified model for the hydrodynamic moment was explored based on a modified Stokes drag moment for spherical particles, which includes a shape factor Kn for relating non-spherical particles to spherical ones. It was found that using the projected area of non-spherical particles provided the best overall scaling to find their equivalent spheres because it provided the lowest Kn values. In addition, Kn was found to deviate from the constant theoretical value because of the build-up pressure between the particle and the wall which changed with Re. A linear relation between the mean Kn and Re was found to be a good approximation. This work demonstrates how particle-resolved simulations can provide the data required for developing simplified models for non-spherical particles.
... (1) and (2)], in the presence of a solid barricade for flow, are solved using the sharp interface Curvilinear Immersed Boundary (CurvIB) method developed by Borazjani et al. 44 and Ge et al. 46 The method has been fully validated and applied to a variety of FSI problems such as vortexinduced vibrations, 8,47 biomedical applications, 48-50 self-propelled aquatic swimming, 51-54 and particle-flow interaction. 55,56 For completeness, a brief explanation has been provided here. The fluid solver employs a finite volume discretization approach with a staggered grid arrangement with pressure in cell center and contravariant velocities in face center. ...
The flow induced transverse vibration of a cylinder with an attached flexible and elastic plate is investigated numerically over a range of reduced velocities (Ur) using an in-house fluid solver based on curvilinear immersed boundary method strongly coupled with an open-source finite element based structural solver. It was observed that an attached elastic plate of width 0.1D and length L = D suppresses large vibrations of the cylinder, but one with length L = 2D, contrary to previous studies, amplifies vibrations up to five times of an isolated cylinder. Three regimes were observed: vortex induced vibration (VIV), suppression, and galloping. In VIV regime for 3 {less than or equal to} Ur {less than or equal to} 7, lock-in was observed where the vortex shedding frequency from the plate-cylinder system was seen to slightly increase relative to that of static cylinder-plate system to match with the natural frequency of the cylinder and plate. For 7 < Ur {less than or equal to} 9, the cylinder-plate system was pushed into suppression regime wherein its displacement was nullified because of lack of vorticity interaction and out-of-phase deformation. Beyond Ur = 9, the cylinder-plate system vibrated in the galloping regime wherein it shed and generated forces as an asymmetric body creating an angle of attack with the incoming flow. The vibration amplitude of the cylinder was higher in the galloping regime, but the vibrations of the plate were more intense (higher amplitude and mode) in the VIV regime. New vortex patterns were observed in the VIV and galloping regimes ranging from 2S mode till 2T mode.
... Particles non-spherical shape is key to study the dispersion of pollen and seeds [3], the lifecycle of diatom plankton [4] and sediment transport in rivers [5]. Besides, the addition of fibres in a fluid flow can significantly alter the suspension rheology [6,7]. ...
Non-spherical particles transported by an anisotropic turbulent flow preferentially align with the mean shear and intermittently tumble when the local strain fluctuates. Such an intricate behaviour is here studied for inertialess, rod-shaped particles embedded in a two-dimensional turbulent flow with homogeneous shear. A Lagrangian stochastic model for the rods angular dynamics is introduced and compared to the results of direct numerical simulations. The model consists in superposing a short-correlated random component to the steady large-scale mean shear, and can thereby be integrated analytically. To reproduce the single-time orientation statistics obtained numerically, it is found that one has to properly account for the combined effect of the mean shear, for anisotropic velocity gradient fluctuations, and for the presence of persistent rotating structures in the flow that bias Lagrangian statistics. The model is then used to address two-time statistics. The notion of tumbling rate is extended to diffusive dynamics by introducing the stationary probability flux of the rods unfolded angle. The model is found to reproduce the long-term effects of an average shear on the mean and the variance of the fibres angular increment. Still, it does not reproduce an intricate behaviour observed in numerics for intermediate times: the unfolded angle is there very similar to a L\'evy walk with distributions of increments displaying intermediate power-law tails.
... The non-spherical shape plays an important role in the study of the dispersion of pollen and seeds (Sabban et al. (2017)), the dynamics of ice clouds (Heymsfield (1977)), the lifecycle of diatom plankton (Musielak et al. (2009)) and sediment transport in rivers (Vercruysse et al. (2017)). Moreover, the addition of fibres in a fluid flow can significantly alter the suspension rheology (Butler and Snook (2018); Daghooghi and Borazjani (2015)). In (a) prolate ellipsoid with λ > 1 corresponds to rigid rod; (b) spherical particle with λ = 1 and (c) oblate ellipsoid with λ < 1 corresponds to rigid disk. ...
The motion of small non- spherical particles suspended in a turbulent flow is relevant for a large variety of natural and industrial applications such as aerosol dynamics in respiration, red blood cells motion, plankton dynamics, ice in clouds, combustion, to name a few. Anisotropic particles react on turbulent flows in complex ways, which depend on a wide range of parameters (shape, inertia, fluid shear). Inertia-free particles, with size smaller than the Kolmogorov length, follow the fluid motion with an orientation generally defined by the local turbulent velocity gradient. Therefore, this thesis is focused on the dynamics of these objects in turbulence exploiting stochastic Lagrangian methods. The development of a model that can be used as predictive tool in industrial computational fluid dynamics (CFD) is highly valuable for practical applications in engineering. Models that reach an acceptable compromise between simplicity and accuracy are needed for progressing in the field of medical, environmental and industrial processes.The formulation of a stochastic orientation model is studied in two-dimensional turbulent flow with homogeneous shear, where results are compared with direct numerical simulations (DNS). Finding analytical results, scrutinising the effect of the anisotropies when they are included in the model, and extending the notion of rotational dynamics in the stochastic framework, are subjects addressed in our work. Analytical results give a reasonable qualitative response, even if the diffusion model is not designed to reproduce the non-Gaussian features of the DNS experiments.The extension to the three-dimensional case showed that the implementation of efficient numerical schemes in 3D models is far from straightforward. The introduction of a numerical scheme with the capability to preserve the dynamics at reasonable computational costs has been devised and the convergence analysed. A scheme of splitting decomposition of the stochastic differential equations (SDE) has been developed to overcome the typical instability problems of the Euler–Maruyama method, obtaining a mean-square convergence of order 1/2 and a weakly convergence of order 1, as expected. Finally, model and numerical scheme have been implemented in an industrial CFD code (Code_Saturne) and used to study the orientational and rotational behaviour of anisotropic inertia-free particles in an applicative prototype of inhomogeneous turbulence, i.e. a turbulent channel flow. This real application has faced two issues of the modelling: the numerical implementation in an industrial code, and whether and to which extent the model is able to reproduce the DNS experiments. The stochastic Lagrangian model for the orientation in the CFD code reproduces with some limits the orientation and rotation statistics of the DNS.The results of this study allows to predict the orientation and rotation of aspherical particles, giving new insight into the prediction of large scale motions both, in two-dimensional space, of interest for geophysical flows, and in three-dimensional industrial applications.
... Furthermore, not only few works have turned their attention to investigate inertia effects in diluted and semidiluted (Verberg and Koch 2006;Krüger et al. 2014;Daghooghi and Borazjani 2015;Husband and Gadala-Maria 1987) or concentrated suspensions flows (Linares-Guerrero et al. 2017;Kulkarni and Morris 2008) but also the majority has neglected buoyancy effects. The first studies about particle migration between streamlines that considered inertia effects have been conducted by Segre and Silberberg (1961), Segre and Silberberg (1962), and Segre and Silberberg (1963) in Poiseuille flow. ...
The current work puts forward a numerical study of non-colloidal suspension flows in a parallel-plate geometry. The inhomogeneous Euler-Euler model applied to the continuity and momentum equations is used to solve the two-phase flow problem. The aim is at the investigation of particle motion in the suspensions flow and its consequence on the measured apparent viscosity. In contrast with prior works that dealt with neutrally buoyant flows, buoyancy is now taken into account. Good agreement was obtained between measured and computed particle distributions. Analysis of this distribution reveals that not only the particle motion but also the apparent viscosity depends on whether the lower or the upper plate is rotating. Comparisons between buoyant and non-buoyant flows were performed to understand the reasons behind the particle motion. Numerical experiments were conducted by rotating the upper or lower parallel plates and varying Reynolds number, particle volume fraction, density ratio and particle size. It can be anticipated that the particle motion in buoyant flows is mainly driven by a combination of gravity and a secondary flow perpendicular to the main circumferential flow.
... This error will be accumulated over time resulting in a skewing effect on the shape of the object [35]. In order to circumvent this problem and following our previous method [36], a quaternion vector is used instead of a rotational matrix to represent the orientation of the body in 3-D space [37]. Quaternions use four parameters to describe the three degrees of freedom of any arbitrary rotation. ...
... In fact, this method can be implemented in any discrete element model to obtain a more accurate and realistic final equilibrium state of a particle on the wall. In addition, this numerical scheme will be coupled to our immersed boundary method [6,36] to simulate sedimentation of rigid particles in a viscous fluid in the future. Time series of the collision procedure and resting of an irregular particle on a rigid wall is shown. ...
A discrete model is proposed for settling of an arbitrary-shaped particle onto a flat surface under the gravitational field. In this method, the particle dynamics is calculated such that (a) the particle does not create an overlap with the wall and (b) reaches a realistic equilibrium state, which are not guaranteed in the conventional discrete element methods that add a repulsive force (torque) based on the amount of overlap between the particle and the wall. Instead, upon the detection of collision, the particle’s kinematics is modified depending on the type of contact, i.e., point, line, and surface types, by assuming the contact point/line as the instantaneous center/line of rotation for calculating the rigid body dynamics. Two different stability conditions are implemented by comparing the location of the projection of the center of mass on the wall along gravity direction against the contact points to identify the equilibrium (stable) state on the wall for particles with multiple contact points. A variety of simulations are presented, including smooth surface particles (ellipsoids), regular particles with sharp edges (cylinders and pyramids) and irregular-shaped particles, to show that the method can provide the analytically-known equilibrium state.
... The method is fully parallelized using Message Passing Interface (MPI) and Portable, Extensible Toolkit for Scientific Computation (PETSc) [48]. It has been fully validated [46,[49][50][51] and applied to a wide range of applications: vortex induced vibrations [52,53], aquatic locomotion [54][55][56][57][58][59][60][61][62][63], cardiovascular flows [64][65][66][67][68][69][70], sediment transport [71], large-eddy simulations and flow control [72][73][74][75], rheology [76,77], and copepods [4]. In the next section, some of the copepod simulations using this method are presented and discussed. ...
Copepods are small aquatic creatures which are abundant in oceans as a major food source for fish, thereby playing a vital role in marine ecology. Because of their role in the food chain, copepods have been subject to intense research through different perspectives from anatomy, form-function biology, to ecology. Numerical simulations can uniquely support such investigations by quantifying: (i) the force and flow generated by different parts of the body, thereby clarify the form-function relation of each part; (ii) the relation between the small-scale flow around animal and the large-scale (e.g., oceanic) flow of its surroundings; and (iii) the flow and its energetics, thereby answering ecological questions, particularly, the three major survival tasks, i.e., feeding, predator avoidance, and mate-finding. Nevertheless, such numerical simulations need to overcome challenges involving complex anatomic shape of copepods, multiple moving appendages, resolving different scales (appendage-, animal- to large-scale). The numerical methods capable of handling such problems and some recent simulations are reviewed. At the end, future developments necessary to simulate copepods from animal- to surrounding-scale are discussed.
... The domain is periodic in x-and z-directions, and the walls at the top and bottom move with velocities U w and −U w , respectively, which gives a constant shear rate of γ = 2U w /L x . As in prior work [105,106], the particle Reynolds number, defined as Re = ρ fγ a 2 /µ f , is set to 10. A penalty spring constant of κ = 10 4 g/(cm · s) 2 is used, and the time step size is set to ∆t = 0.05 h finest . ...
... Fig. 19(c) shows the angular velocity ω z =θ with respect to the orientation of the prolate ellipsoid. The results obtained from our simulation are compared with two other numerical studies, one using a curvilinear immersed boundary approach [106] and the second one using a force coupling method [105]. ...
This paper introduces a sharp interface method to simulate fluid-structure interaction (FSI) involving arbitrary rigid bodies immersed in viscous incompressible fluids. This approach, which we refer to as an immersed Lagrangian-Eulerian (ILE) method, integrates aspects of partitioned and immersed FSI formulations by solving separate momentum equations for the fluid and solid domains, as in a partitioned formulation, while also using non-conforming discretizations of the moving fluid and structure, as in an immersed formulation. A Dirichlet-Neumann coupling scheme is used, in which the motion of the immersed solid is driven by fluid traction forces evaluated along the fluid-structure interface, and the motion of fluid along that interface is constrained to match the solid velocity, so as to enforce the no-slip condition. To develop an efficient numerical method, we introduce a penalty approach that weakly imposes the no-slip condition along the fluid-solid interface. In the coupling strategy, a separate discretization of the fluid-structure interface is tethered to the volumetric solid mesh via stiff spring-like penalty forces. Our fluid-structure interaction scheme relies on a recently developed immersed interface method (IIM) for discrete geometries, which enables the accurate determination of both velocities and stresses along the fluid-structure interface. The effectiveness of this straightforward FSI methodology is extensively tested against benchmark computational and experimental studies in two and three spatial dimensions, including for geometries with non-smooth features. Unlike commonly used partitioned methods, which can suffer from so-called added mass effect instabilities, our methodology avoids subiterations between fluid and solid solvers or complex handling of the fluid pressure, and it retains stability for models involving extremely low, nearly equal, equal, and high solid-fluid density ratios. Our empirical results indicate that this is a robust approach to FSI that is applicable to models with a very broad range of density ratios.
... Computer simulations provide an ideal testing ground for exploring theoretical models. The motion of spheroidal and ellipsoidal colloids in shear flows is attracting attention lately, with authors studying the impact of particle inertia, 19,20 of fluid inertia, 21 of both inertias, [22][23][24][25] of weak Brownian noise, 26 and of the combination thereof. 27 The hydrodynamic contributions to the motion are accounted for by the explicit solution of time-varying flow and stress fields, or by analytic approximation in the form of mobility and resistance matrices. ...
... 31 The emphasis in most of these studies is on the dynamics of the particles, e.g., the phase behavior and chaos of the tumbling orbits 20,22,32,33 or the segregation of chiral particles in a shear flow, 34 while some studies also explored the resulting intrinsic viscosities of dilute suspensions of these particles. 17,24,26,35,36 Freely available packages like BEST 37 and HYDRO++ 38 readily calculate the mobility matrices of arbitrarily shaped colloids and their intrinsic viscosities at zero shear rate. 39,40 Our objective is to explore the intrinsic viscosity, in particular, the interplay between shear flow and Brownian motion that gives rise to shear thinning for elongated colloids. ...
A numerical study is presented on the intrinsic viscosities of sheared dilute suspensions of nonspherical Brownian colloidal particles. The simulations confirm theoretical predictions on the intrinsic viscosities of highly oblate and highly prolate spheroids in the limits of weak and strong Brownian noise (i.e., for low and high Péclet numbers). Numerical data and fit functions are provided covering the entire shear-thinning regime, for spheroids ranging from highly oblate to highly prolate. The tumbling motion and intrinsic viscosities of a hemispherical cap and a helix are briefly discussed.
... To handle the complex shape and motion of LV, a curvilinear immersed boundary (CURVIB) method 53,59,20 is used which has been extensively validated for a variety of complex flow problems 54,60 and implemented in various applications such as cardiovascular flows 61,42,43 , aquatic motions and vortex dynamics 62,63 and rheology of suspensions 64,65 . The 3D reconstructed surfaces of LV from 2D-echo which are meshed using triangular elements are given to the flow solver as an input for each time step to classify the background domain's nodes into fluid, boundary, and solid using an efficient ray tracing algorithm 20 which can handle thick, closed-surface bodies. ...
Image-based computational fluid dynamics (CFD) has emerged as a powerful tool to study cardiovascular flows while 2D echocardiography (echo) is the most widely used non-invasive imaging modality for diagnosis of heart disease. Here, echo is combined with CFD, i.e., an echo-CFD framework, to study ventricular flows. To achieve this, our previous 3D reconstruction from multiple 2D-echo at standard cross-sections is extended by 1) reconstructing valves (aortic and mitral valves) from 2D-echo images and the superior wall; 2) optimizing the location and orientation of the surfaces to incorporate the physiological assumption of fixed apex as a reference (fixed) point for reconstruction; and 3) incorporating several smoothing algorithms to remove the nonphysical oscillations (ringing) near the basal section observed in our previous study. The main parameters of the reconstructed left ventricle (LV) are all within the physiologic range. Our results show that the mitral valve can significantly change the flow pattern inside the LV during the diastole phase in terms of ring vortex formation/propagation as well as the flow circulation. In addition, the abnormal shape of unhealthy LV can drastically change the flow field during the diastole phase. Furthermore, the hemodynamic energy loss, as an indicator of the LV pumping performance, for different test cases is calculated which shows a larger energy loss for unhealthy LV compared to the healthy one.
