Three-dimensional Poiseuille Flow Research Articles

Nonmodal and modal analyses of a flow through inhomogeneous and anisotropic porous channel

A study of nonmodal and modal stability analyses of a three-dimensional Poiseuille flow through a channel is performed where the bounding walls are partially covered by inhomogeneous and anisotropic porous layers. The evolution equations corresponding to normal velocity and normal vorticity are derived for fluid and porous layers to decipher the transient disturbance energy growth. The modal stability analysis reveals that the anisotropy parameter has a stabilizing impact, while the coefficient of inhomogeneity shows a peculiar behaviour on the most unstable shear mode. The nonmodal stability analysis predicts that the transient disturbance energy growth exists and attenuates with the increase in the value of the anisotropy parameter and larger values of the coefficient of inhomogeneity; however, it intensifies for smaller values of the coefficient of inhomogeneity.

Study on the binding focusing state of particles in inertial migration

In this paper, the inertial migration of particles in a periodic straight channel is studied numerically based on the immersed boundary-lattice Boltzmann method in two-dimensional and three-dimensional Poiseuille flow. In the model, on considering the inertial migration of particles, the interaction of a soft particle and a hard particle that are similar in size is studied. We observe an interesting particle interaction phenomenon named the binding focusing state (BFS). That is, when the focused soft particle gets close to the hard particle, both particles will switch their original runways, and then run together on a new equilibrium position. To investigate the characteristics of the BFS, the effects of the soft particle deformability, the Reynolds numbers and the initial particle positions on the BFS are studied in detail. The soft particle deformability and Reynolds numbers can affect the formation of the BFS. Moreover, the streamline and pressure around the particles are analyzed to show the formation laws of the BFS; this is more intuitive and aids in understanding the BFS.

Optimized transportation meshfree method and its apllication in simulating droplet surface tension effect

Owing to challenges encountered by mesh-based CFD methods when simulating large material deformation, a number of meshfree methods have been presented. The optimized transportation meshfree method is a newly developed meshfree method, but it inherits the advantage of the finite element method in boundary treatment and thus having great potential applications in surface tension effect simulation. By adding the surface tension potential into the Lagrangian, the resulting generalized force acts on fluid surfaces exactly. The axial symmetry treatment is also discussed. By simulating several benchmark cases such as two- and three-dimensional Poiseuille flow, static and vibrating drop and drop deformation, the advantages like precision and convergence of the optimized transportation meshfree method in simulating surface tension effect are verified.

Convergence analysis of inertial lift force estimates using the finite element method

We conduct a convergence analysis for the estimation of inertial lift force on a spherical particle suspended in flow through a straight square duct using the finite element method. Specifically, we consider the convergence of an inertial lift force approximation with respect to a range of factors including the truncation of the domain, the resolution of the tetrahedral mesh and the boundary conditions imposed at the (truncated) ends of the domain. Additionally, we compare estimates obtained via the Lorentz reciprocal theorem with those obtained via a direct integration of fluid stress over the particle surface. 
 
 References M. S. Alnaes, J. Blechta, J. Hake, A. Johansson, B. Kehlet, A. Logg, C. Richardson, J. Ring, M. E. Rognes, and G. N. Wells. The FEniCS project version 1.5. Arch. Numer. Software, 3(100):923, 2015. doi:10.11588/ans.2015.100.20553. D. Di Carlo. Inertial microfluidics. Lab Chip, 21:30383046, 2009. doi:10.1039/B912547G. C. Geuzaine and J.-F. Remacle. Gmsh: A 3-d finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Meth. Eng., 79(11):13091331, 2009. doi:10.1002/nme.2579. B. Harding. A study of inertial particle focusing in curved microfluidic ducts with large bend radius and low flow rate. In Proc. 21st Australasian Fluid Mechanics Conference, number 603, 2018. URL https://people.eng.unimelb.edu.au/imarusic/proceedings/21/Contribution_603_final.pdf. B. Harding, Y. M. Stokes, and A. L. Bertozzi. Effect of inertial lift on a spherical particle suspended in flow through a curved duct. J. Fluid Mech., accepted, 2019. URL https://arxiv.org/abs/1902.06848. A. J. Hogg. The inertial migration of non-neutrally buoyant spherical particles in two-dimensional shear flows. J. Fluid Mech., 272:285318, 1994. doi:10.1017/S0022112094004477. K. Hood, S. Lee, and M. Roper. Inertial migration of a rigid sphere in three-dimensional Poiseuille flow. J. Fluid Mech., 765:452479, 2015. doi:10.1017/jfm.2014.739. N. Nakagawa, T. Yabu, R. Otomo, A. Kase, M. Makino, T. Itano, and M. Sugihara-Seki. Inertial migration of a spherical particle in laminar square channel flows from low to high reynolds numbers. J. Fluid Mech., 779:776793, 2015. doi:10.1017/jfm.2015.456. T.-W. Pan and R. Glowinski. Direct simulation of the motion of neutrally buoyant balls in a three-dimensional poiseuille flow. C. R. Mecanique, 333(12):884895, 2005. doi:10.1016/j.crme.2005.10.006. C. Taylor and P. Hood. A numerical solution of the navier-stokes equations using the finite element technique. Comput. Fluids, 1(1):73100, 1973. doi:10.1016/0045-7930(73)90027-3. M. E. Warkiani, G. Guan, K. B. Luan, W. C. Lee, A. A. S. Bhagat, P. Kant Chaudhuri, D. S.-W. Tan, W. T. Lim, S. C. Lee, P. C. Y. Chen, C. T. Lim, and J. Han. Slanted spiral microfluidics for the ultra-fast, label-free isolation of circulating tumor cells. Lab Chip, 1:128137, 2014. doi:10.1039/C3LC50617G. B. H. Yang, J. Wang, D. D. Joseph, H. H. Hu, T.-W. Pan, and R. Glowinski. Migration of a sphere in tube flow. J. Fluid Mech., 540:109131, 2005. doi:10.1017/S0022112005005677. L. Zeng, S. Balachandar, and P. Fischer. Wall-induced forces on a rigid sphere at finite reynolds number. J. Fluid Mech., 536:125, 2005. doi:10.1017/S0022112005004738.

Molecular dynamic simulation of Copper and Platinum nanoparticles Poiseuille flow in a nanochannels

In this paper, simulation of Poiseuille flow within nanochannel containing Copper and Platinum particles has been performed using molecular dynamic (MD). In this simulation LAMMPS code is used to simulate three-dimensional Poiseuille flow. The atomic interaction is governed by the modified Lennard–Jones potential. To study the wall effects on the surface tension and density profile, we placed two solid walls, one at the bottom boundary and the other at the top boundary. For solid–liquid interactions, the modified Lennard–Jones potential function was used. Velocity profiles and distribution of temperature and density have been obtained, and agglutination of nanoparticles has been discussed. It has also shown that with more particles, less time is required for the particles to fuse or agglutinate. Also, we can conclude that the agglutination time in nanochannel with Copper particles is faster that in Platinum nanoparticles. Finally, it is demonstrated that using nanoparticles raises thermal conduction in the channel.

Inertial migration of a rigid sphere in three-dimensional Poiseuille flow

AbstractInertial lift forces are exploited within inertial microfluidic devices to position, segregate and sort particles or droplets. However, the forces and their focusing positions can currently only be predicted by numerical simulations, making rational device design very difficult. Here we develop theory for the forces on particles in microchannel geometries. We use numerical experiments to dissect the dominant balances within the Navier–Stokes equations and derive an asymptotic model to predict the lateral force on the particle as a function of particle size. Our asymptotic model is valid for a wide array of particle sizes and Reynolds numbers, and allows us to predict how focusing position depends on particle size.

Molecular-dynamics study of Poiseuille flow in a nanochannel and calculation of energy and momentum accommodation coefficients

We report a molecular-dynamics study of flow of Lennard-Jones fluid through a nanochannel where size effects predominate. The momentum and energy accommodation coefficients, which determine the amount of slip and temperature jumps, are calculated for a three-dimensional Poiseuille flow through a nano-sized channel. Accommodation coefficients are calculated by considering a " gravity"- (acceleration field) driven Poiseuille flow between two infinite parallel walls that are maintained at a fixed temperature. The Knudsen number (Kn) dependency of the accommodation coefficients, slip length, and velocity profiles is investigated. The system is also studied by varying the strength of gravity. The accommodation coefficients are found to approach a limiting value with an increase in gravity and Kn. For low values of Kn (<0.15), the slip length obtained from the velocity profiles is found to match closely the results obtained from the linear slip model. Using the calculated values of accommodation coefficients, the first- and second-order slip models are validated in the early transition regime. The study demonstrates the applicability of the Navier-Stokes equation with the second-order slip model in the early transition regime.

Linear feedback control of transient energy growth and control performance limitations in subcritical plane Poiseuille flow

Suppression of the transient energy growth in subcritical plane Poiseuille flow via feedback control is addressed. It is assumed that the time derivative of any of the velocity components can be imposed at the walls as control input and that full-state information is available. We show that it is impossible to design a linear state-feedback controller that leads to a closed-loop flow system without transient energy growth. In a subsequent step, state-feedback controllers—directly targeting the transient growth mechanism—are designed using a procedure based on a linear matrix inequalities approach. The performance of such controllers is analyzed first in the linear case, where comparison to previously proposed linear-quadratic optimal controllers is made; further, transition thresholds are evaluated via direct numerical simulations of the controlled three-dimensional Poiseuille flow against different initial conditions of physical interest, employing different velocity components as wall actuation. The present controllers are effective in increasing the transition thresholds in closed loop, with varying degree of performance depending on the initial condition and the actuation component employed.

Motion planning and trajectory tracking for three-dimensional Poiseuille flow

We present the first solution to a boundary motion planning problem for the Navier–Stokes equations, linearized around the parabolic equilibrium in a three-dimensional channel flow. The pressure and skin friction at one wall are chosen as the reference outputs as they are the most readily measurable ‘wall-restricted’ quantities in experimental fluid dynamics and also because they play a special role as performance metrics in aerodynamics. The reference velocity input is applied at the opposite wall. We find the exact (method independent) solution to the motion planning problem using the PDE (partial differential equation) backstepping theory. The motion planning solution results in open-loop controls, which produce the reference output trajectories only under special initial conditions for the flow velocity field. To achieve convergence to the reference trajectory from other (nearby) initial conditions, we design a feedback controller. We also present a detailed examination of the closed-form solutions for gains and the behaviour of the motion planning solution as the wavenumbers grow or the Reynolds number grows. Numerical results are shown for the motion planning problem.

On the motion of a neutrally buoyant ellipsoid in a three-dimensional Poiseuille flow

In previous articles, the authors introduced Lagrange multiplier based fictitious domain methods. Their goal in the present article is to apply a generalization of the above methods to simulate the motion of a neutrally buoyant ellipsoid in a three-dimensional Poiseuille flow and to investigate its rotational and orientational behavior via direct numerical simulations. We find distinctive states depending on the Reynolds number ranges and the shape of the ellipsoid.

Direct simulation of the motion of neutrally buoyant balls in a three-dimensional Poiseuille flow

In a previous article the authors introduced a Lagrange multiplier based fictitious domain method. Their goal in the present article is to apply a generalization of the above method to: (i) the numerical simulation of the motion of neutrally buoyant particles in a three-dimensional Poiseuille flow; (ii) study – via direct numerical simulations – the migration of neutrally buoyant balls in the tube Poiseuille flow of an incompressible Newtonian viscous fluid. Simulations made with one and several particles show that, as expected, the Segré–Silberberg effect takes place. To cite this article: T.-W. Pan, R. Glowinski, C. R. Mecanique 333 (2005).

Experimental evaluation of the migration of spherical particles in three-dimensional Poiseuille flow

Convective transport of 10 μm nearly neutrally buoyant spherical particles (polystyrene vinyl dibenzene) is studied in 220 μm and 530 μm diameter capillaries using an on-line particle detector of the electronic gate type. The detector, connected to the capillary outlet, monitors the elution and translates the passage of individual particles into pulsed signals. The measuring technique requires the use of an electrically conductive carrier liquid, such as physiological saline (0.9%NaCl). Passage times are registered for discrete capillary lengths varying between 0.25 m and 5 m. Mean particle and fluid velocities are used to calculate the preferential radius of particle transport. The equilibrium position of the particles is found to shift towards the capillary wall for higher Reynolds numbers, for longer and smaller capillaries, and for more dilute suspensions. However, the higher the particle to capillary diameter ratio, the more pronounced wall effects. Moreover, as the Stokes number is small (E-2), adhesion at the capillary walls turns out to be non-negligible and to have an impact on the final quantitative results.

三次元ポアズイユ流れにおける再層流化現象の直接数値シミュレーション(OS5 乱流現象の計測とシミュレーション)

三次元ポアズイユ流れにおける再層流化現象の直接数値シミュレーション(OS5 乱流現象の計測とシミュレーション)

The Moment Propagation Method for Advection–Diffusion in the Lattice Boltzmann Method: Validation and Péclet Number Limits

We numerically validate the moment propagation method for advection–diffusion in a lattice Boltzmann simulation against the analytic Taylor–Aris prediction for dispersion in a three-dimensional Poiseuille flow. Good agreement between simulation and theory is found, with relative errors smaller than 2%. The Péclet number limits on the moment propagation method are studied, and maximum parameter values are obtained. We show that a modification of the moment propagation method allows advection–diffusion simulations with higher Péclet numbers, in particular in the low Reynolds number limit.

Instability of the Hocking-Stewartson pulse and its implications for three-dimensional Poiseuille flow

The linear stability problem for the Hocking‐Stewartson pulse, obtained by linearizing the complex Ginzburg‐Landau (cGL) equation, is formulated in terms of the Evans function, a complex analytic function whose zeros correspond to stability exponents. A numerical algorithm based on the compound matrix method is developed for computing the Evans function. Using values in the cGL equation associated with spanwise modulation of plane Poiseuille flow, we show that the Hocking‐Stewartson pulse associated with points along the neutral curve is always linearly unstable due to a real positive eigenvalue. Implications for the spanwise structure of nonlinear Poiseuille problem between parallel plates are also discussed.

Bifurcations of Poiseuille flow between parallel plates: Three-dimensional solutions with large spanwise wavelength

The “spatial dynamics” approach is applied to the analysis of bifurcations of the three-dimensional Poiseuille flow between parallel plates. In contrast to the classical studies, we impose time periodicity as well as spatial periodicity with period 2π/α in the streamwise direction. However, we make no assumptions on the behavior in the spanwise direction, except the uniform closeness of the bifurcating solution to the basic flow. In an abstract setting it is shown how the dimension of the critical eigenspace of the spatial dynamics analysis can be uniquely determined from the classical linear stability problem. For the three-dimensional Poiseuille problem we are able to find all relevant coefficients from the analysis of the purely two-dimensional problem. Moreover, we are able to analyze precisely the influence of a spanwise pressure gradient and the associated spanwise mass flux. The study of the reduced problem shows that there are two different kinds of solutions (spirals and ribbons) which are 2αp/β periodic in the spanwise direction, as in the Couette-Taylor problem, and both of them bifurcate in the same direction.

Oscillations Due to the Transport of Microstructures

The aim of this paper is to report some improvements and some numerical tests of a model for convection of microstructures developed by McLaughlin, Papanicolaou and Pironneau [SIAM J. Appl. Math., 45 (1985), pp. 780–797]. This model was obtained by homogenization techniques. In particular, this paper gives a computational indication of the existence of oscillations in a macroscopic flow which evolves from an initial state with two well-separated length scales. This oscillatory behavior was formally predicted by McLaughlin et al. A simplified model including eddy viscosity terms is first obtained: This model is tested for a three-dimensional Poiseuille flow in which the mean flow is one-dimensional. Direct simulations and the simulations of the model are compared and good agreement is obtained in the behavior of both the mean velocity field and the kinetic energy of the microstructure.