Flow patterns past two circular cylinders in proximity

Flow patterns past two nearby circular cylinders of equal diameter immersed in the cross-flow at low Reynolds numbers (Re ? 160), were numerically studied using an immersed boundary method. We considered all possible arrangements of the two cylinders in terms of the distance between the two cylinders and the inclination angle of the line connecting the cylinder centers with respect to the direction of the main flow. Ten distinct flow patterns were identified in total based on vorticity contours and streamlines, which are Steady, Near-Steady, Base-Bleed, Biased-Base-Bleed, Shear-Layer-Reattachment, Induced-Separation, Vortex-Impingement, Flip-Flopping, Modulated Periodic, and Synchronized-Vortex-Shedding. Collecting all the numerical results obtained, we propose a general flow-pattern diagram for each Re, and a contour diagram on vortex-shedding frequency for each cylinder at Re = 100. The perfect symmetry implied in the geometrical configuration allows one to use these diagrams to identify flow pattern and vortex-shedding frequencies in the presence of two circular cylinders of equal diameter arbitrarily positioned in physical space with respect to the main-flow direction.     

A multiple-layer σ-coordinate model for simulation of wave-structure interaction

A 3D multiple-layer σ-coordinate model has been developed to simulate surface wave interaction with various types of structures including submerged structures, immersed structures, and floating structures. This model is the extension of the earlier model [Lin P, Li CW. A σ-coordinate three-dimensional numerical model for surface wave propagation. Int J Numer Methods Fluid 2002;38(11):1045-68] that solves Navier-Stokes equations in the transformed σ-coordinate, which is especially efficient for simulation of wave propagation over varying topography. By introducing the layered σ-coordinates, the present model overcomes the difficulty encountered by the earlier model in calculating waves past a depth discontinuity, e.g., a submerged rectangular breakwater. Furthermore, with the employment of 3-layer σ-coordinate the present model is able to simulate flow interaction with an immersed body or a floating body. The new model is validated against an established Volume-Of-Fluid (VOF) model [Lin P, Liu PL-F. A numerical study of breaking waves in the surf zone. J Fluid Mech 1998;359:239-64] for the 2D solitary wave interaction with a submerged, immersed, or floating rectangular obstacle. For the solitary wave interaction with a submerged breakwater, the numerical results are also compared to the experimental data by Zhuang and Lee [A viscous rotational model for wave overtopping over marine structure. In Proc 25th Int Conf Coast Eng, ASCE, 1996. p. 2178-91] and very good agreements have been obtained for velocities in the vortex behind the structure. Finally, the present model is used to simulate 3D wave interaction with a Very Large Floating Structure (VLFS) above a submerged shoal. It is proved that the model is an accurate and efficient numerical tool to investigate different wave-structure interactions problems.     

Simulating flows with moving rigid boundary using immersed-boundary method

The present study is to apply the immersed-boundary method to simulate 2- and 3-D viscous incompressible flows interacting with moving solid boundaries. Previous studies indicated that for stationary-boundary problems, different treatments inside the solid body did not affect the external flow. However, the relationship between internal treatment of the solid body and external flow for moving-boundary problems was not studied extensively and is investigated here. This is achieved via direct-momentum forcing on a Cartesian grid by combining “solid-body forcing” at solid nodes and interpolation on neighboring fluid nodes. The influence of the solid body forcing within the solid nodes is first examined by computing flow induced by an oscillating cylinder in a stationary square domain, where significantly lower amplitude oscillations in computed lift and drag coefficients are obtained compared with those without solid-body-forcing strategy. Grid-function convergence tests also indicate second-order accuracy of this implementation with respect to the L¹ norm in time and the L² norm in space. Further test problems are simulated to examine the validity of the present technique: 2-D flows over an asymmetrically-placed cylinder in a channel, in-line oscillating cylinder in a fluid at rest, in-line oscillating cylinder in a free stream, two cylinders moving with respect to one another, and 3-D simulation of a sphere settling under gravity in a static fluid. All computed results are in generally good agreement with various experimental measurements and with previous numerical simulations. This indicates the capability of the present simple implementation in solving complex-geometry flow problems and the importance of solid body forcing in computing flows with moving solid objects.     

An immersed boundary technique for simulating complex flows with rigid boundary

A new immersed boundary (IB) technique for the simulation of flow interacting with solid boundary is presented. The present formulation employs a mixture of Eulerian and Lagrangian variables, where the solid boundary is represented by discrete Lagrangian markers embedding in and exerting forces to the Eulerian fluid domain. The interactions between the Lagrangian markers and the fluid variables are linked by a simple discretized delta function. The numerical integration is based on a second-order fractional step method under the staggered grid spatial framework. Based on the direct momentum forcing on the Eulerian grids, a new force formulation on the Lagrangian marker is proposed, which ensures the satisfaction of the no-slip boundary condition on the immersed boundary in the intermediate time step. This forcing procedure involves solving a banded linear system of equations whose unknowns consist of the boundary forces on the Lagrangian markers; thus, the order of the unknowns is one-dimensional lower than the fluid variables. Numerical experiments show that the stability limit is not altered by the proposed force formulation, though the second-order accuracy of the adopted numerical scheme is degraded to 1.5 order. Four different test problems are simulated using the present technique (rotating ring flow, lid-driven cavity and flows over a stationary cylinder and an in-line oscillating cylinder), and the results are compared with previous experimental and numerical results. The numerical evidences show the accuracy and the capability of the proposed method for solving complex geometry flow problems both with stationary and moving boundaries.     

Parallel unstructured multigrid simulation of 3D unsteady flows and fluid-structure interaction in mechanical heart valve using immersed membrane method

In this work, a second-order accurate immersed membrane method (IMM) is adopted to simulate the fluid-structure interaction phenomena in the mechanical heart valves (MHVs). The leaflets of the MHV are immersed in the fluid flows and move on top of the fixed fluid mesh. The blood flow is computed by a 3D parallel unstructured multigrid implicit finite-volume Navier-Stokes solver for incompressible flows. The opening and closing phases of a St. Jude 29 mm MHV are computed under pulsatile inflow to investigate the blood-leaflet interactions. The results show that the moment generated by the fluid pressure is the major cause for the valve motions, while the moment due to the fluid shear stresses is almost negligible. It is also observed that near the end of the opening phase the valve opening speed decelerates, so the valve leaflets have a cushioning effect and avoid a sudden impact on the hinges. For closing phase, jet flows are formed in the central channel and squeeze flows occur in the side channels near the fully closed positions.     

Particle mixing and reactive front motion in unsteady open shallow flow - Modelled using singular value decomposition

Passive and active tracers are used to examine particle mixing and reactive front dynamics in an open shallow flow of water past a circular cylinder. A quadtree grid based Godunov-type shallow water equation solver predicts the unsteady flow hydrodynamics of the wake behind the cylinder. The resulting periodic flow field consisting of a von Kármán vortex street is decomposed and stored over one oscillatory period using Singular Value Decomposition (SVD). Particles are advected according to the reconstructed flow field from the SVD modes, with continuous spatial velocity information obtained via bilinear interpolation. Passive particle dynamics driven by different SVD flow modes is investigated, and it is found that the flow field recovered from the mean flow and the first pair of time varying modes is adequate to represent the complicated dynamical properties induced by the original flow field. Active autocatalytic reaction, A + B → 2B, is incorporated into the particle advection model, assuming surface reaction. Active particles are found to trace out an expanded version of the unstable manifold of the chaotic saddle in the wake, in qualitative agreement with published analytical results. The numerical model is applicable to mixing and transport processes in more complicated shallow environmental flows.     

Tapered plastic multimode fiber sensor for salinity detection

A simple tapered plastic multimode (PMM) fiber optic sensor is proposed and demonstrated for continuous monitoring of salinity based on different concentration of sodium chloride (NaCl) in de-ionized water. The working mechanism of such device is based on the observed increment in the transmission of the sensor that is immersed in sodium chloride solution of higher concentration which also reflects an increase in its refractive index. The tapered PMM fiber is fabricated using heat-pulling method to achieve a waist diameter and a length of 0.187 mm and 5 mm, respectively. As the solution concentration varies from 0% to 12%, the output voltage of the sensor increases linearly from 0.109 mV to 1.142 mV with a sensitivity of 0.0024 mV/% and a linearity of more than 98%. The main advantages of this sensor are the feasibility of using PMM fiber which makes the sensor tougher, easier to fabricate and handle.     

Free-boundary method for the numerical solution of gas-dynamic equations in domains with varying geometry

A novel method is proposed for numerical solution of gas-dynamic equations on stationary Cartesian grids in domains containing solid impermeable and, in the general case, moving inclusions (objects). The suggested technique is based on the immersed boundary method, in which the computational domain (including solid objects) is covered by a single Cartesian grid and the calculation is carried out by the shock-capturing method over all cells. Under this approach, the influence of the solid inclusions on the flow of the gas medium is simulated by the introduction of specially selected mass, momentum, and energy fluxes into the right-hand side of the equations. The currently developed methods for the solution of this class of problems are surveyed and the advantages of the proposed approach are discussed. The method is verified by calculating some test problems that admit analytical solutions and it is used to solve the problem of supersonic flow around a blunt body. The results are compared with the calculation findings based on the standard curvilinear grid tied to the geometry of the body.     

A numerical study of flow past a cylinder with cross flow and inline oscillation

Two-dimensional fluid flow around an oscillating circular cylinder is studied numerically at different values of oscillation frequency and amplitude. A novel finite element method which uses discretization along the characteristic line is used for simulation. The solver is coupled to a mesh movement scheme using the Arbitrary Lagrangian-Eulerian (ALE) formulation to account for body motion in the flow field. Two cases of cylinder motion have been studied, cross flow and inline oscillation. In both cases, occurrence of lock on is investigated and the bounds of the lock on region are determined. A comparison of the numerical results with the experimental data indicates that 2D simulation is valid up to Re = 300. Beyond that, 3D effects appear. By using flow visualization, effect of a cylinder oscillation on the flow field and wake pattern has been studied. Also, variation of the mean drag coefficient against the oscillation parameters is discussed. The numerical results are in good agreement with the experimental data available in the literature.     

Analysis of an infinite multi-server queue with an optional service

This paper deals with an infinite-capacity multi-server queueing system with a second optional service (SOS) channel. The inter-arrival times of arriving customers, the service times of the first essential service (FES) and the SOS channel are all exponentially distributed. A customer may leave the system after the FES channel with a probability (1 − θ), or the completion of the FES may immediately require a SOS with a probability θ (0 ? θ ? 1). The formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix analytical approach. A cost model is developed to simultaneously determine the optimal values of the number of servers and the two service rates at the minimal total expected cost per unit time. Quasi-Newton method and Particle Swarm Optimization (PSO) method are employed to deal with the optimization problem. Under optimal operating conditions, numerical results are provided from which several system performance measures are calculated based on the assumed numerical values of the system parameters.     

Spectral regularization method for the time fractional inverse advection-dispersion equation

In this paper, we consider the time fractional inverse advection-dispersion problem (TFIADP) in a quarter plane. The solute concentration and dispersion flux are sought from a measured concentration history at a fixed location inside the body. Such problem is obtained from the classical advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α(0 < α < 1). We show that the TFIADP is severely ill-posed and further apply a spectral regularization method to solve it based on the solution given by the Fourier method. Convergence estimates are presented under a priori bound assumptions for the exact solution. Finally, numerical examples are given to show that the proposed numerical method is effective.     

Simulation of fish swimming and manoeuvring by an SVD-GFD method on a hybrid meshfree-Cartesian grid

In this paper we present the development of the Singular-Value Decomposition (SVD) based Generalized Finite Difference (GFD) method for the simulation of fluid-structure interaction (FSI) problems in a viscous fluid. The class of FSI problems is exemplified by the self-propulsion (swimming) and dynamic manoeuvring of deforming (undulating and flexing) bodies in a fluid medium. Computation is carried out on a hybrid grid comprising meshfree nodes around the undulating swimming body and Cartesian nodes in the background. The meshfree nodes are convected in tandem with the changing shape and motion of the swimming body. The resultant locomotion of the swimmer is governed by fully-coupled dynamic interaction between the deforming body and the fluid in accordance with Newton’s laws. Time integration of motion is carried out by a Crank-Nicolson based implicit iterative algorithm, which fully couples the changing position of the swimming body with the evolving flow field, for numerical stability. The numerical scheme is applied to the steady swimming/cruising and sharp turning manoeuvres of a two-dimensional carangiform fish. The Strouhal number approaches values for efficient steady swimming reported in Fish and Lauder (2006) and Triantafyllou and Triantafyllou (1993) [3] and [6] at high Reynolds number. An illustrative example shows the numerical carangiform swimmer executing a sharp turn through an angle of 70° from straight coasting within a space of about one body length. The results obtained are consistent with available literature. In steady swimming, the momentumless wake theoretically anticipated by Wu (2001) [57] is successfully reproduced here, as opposed to the inverse von Karman vortex street generally predicted by inviscid flow models. The momentumless wake, characterized by an aligned series of alternately-signed shed vortices, is symptomatic of a state of average equilibrium between drag acting on the body of the fish and thrust produced by its undulating tail fin. Guided swimming towards targets based on a simple feedback control scheme is also demonstrated.     

Analysis and control of the near-wake flow over a square-back geometry

A 3D numerical simulation, based on the Lattice Boltzmann method is carried out on the near-wake flow behind a generic square-back blunt body to analyze and establish a method to control the near-wake flow. The flow topology is described by the velocity and the pressure fields. The influence of the wake vortices on the aerodynamic drag is clarified and quantified. In order to reduce this drag, an active open-loop flow control is applied by continuous blowing devices distributed around the base periphery. The blowing effect on the behind body flow is a reduction of the wake section and of the total pressure loss in the wake and an increase of the static pressure on the base of the square body. This control leads to a significant drag reduction of ΔC_x = −29% with a blowing velocity of 1.5V₀. The efficiency is then studied, and we found that the most efficient control is obtained for a blowing velocity of 0.5V₀ and a jet angle of 45°. In this case, a 20% drag reduction is obtained, and the energy needed to control the system is seven times lower than the energy saved by the control.     

Cerebral arterial inflow assessment with F-FDG PET: Methodology and feasibility

Positron emission tomography (PET) with ¹⁸fluorodeoxyglucose (¹⁸F-FDG) is increasingly used in neurology. The measurement of cerebral arterial inflow (QA) using ¹⁸F-FDG complements the information provided by standard brain PET imaging. Here, injections were performed after the beginning of dynamic acquisitions and the time to arrival (t0) of activity in the gantry's field of view was computed. We performed a phantom study using a branched tube (internal diameter: 4 mm) and a ¹⁸F-FDG solution injected at 240 mL/min. Data processing consisted of (i) reconstruction of the first 3 s after t0, (ii) vascular signal enhancement and (iii) clustering. This method was then applied in four subjects. We measured the volumes of the tubes or vascular trees and calculated the corresponding flows. In the phantom, the flow was calculated to be 244.2 mL/min. In each subject, our QA value was compared with that obtained by quantitative cine-phase contrast magnetic resonance imaging; the mean QA value of 581.4 ± 217.5 mL/min calculated with ¹⁸F-FDG PET was consistent with the mean value of 593.3 ± 205.8 mL/min calculated with quantitative cine-phase contrast magnetic resonance imaging. Our ¹⁸F-FDG PET method constitutes a novel, fully automatic means of measuring QA.     

Flow-induced forces on two circular cylinders in proximity

Flow-induced forces on two nearby circular cylinders of equal diameter immersed in the cross flow at Re = 100 were numerically studied. We consider all possible arrangements of the two circular cylinders in terms of the distance between the two cylinders and the inclination angle of the line connecting the cylinder centers with respect to the direction of the main flow. It turns out that significant changes in the characteristics of flow-induced forces are noticed depending on how the two circular cylinders are positioned, resulting in quantitative changes of force coefficients on both cylinders. Collecting all the numerical results obtained, we propose contour diagrams for mean force coefficients and rms values of force coefficient fluctuations for each of the two cylinders. The perfect geometrical symmetry implied in the flow configuration allows one to use those diagrams to estimate flow-induced forces on two circular cylinders of equal diameter arbitrarily positioned in physical space with respect to the main flow direction.     

Finite difference-based lattice Boltzmann simulation of natural convection heat transfer in a horizontal concentric annulus

In this paper, a finite difference-based lattice BGK model for thermal flows is proposed based on the double-distribution function approach. We applied this model to simulate natural convection heat transfer in a horizontal concentric annulus bounded by two stationary cylinders with different temperatures. Velocity and temperature distributions as well as Nusselt numbers were obtained for the Rayleigh numbers ranging from 2.38 × 10³ to 1.02 × 10⁵ with the Prandtl number around 0.718. It is found that the numerical results are in good agreement with the experimental and numerical results reported in the literature.     

Lattice Boltzmann simulations to determine drag, lift and torque acting on non-spherical particles

The drag, lift and moment coefficients of differently shaped single particles have been determined as a function of the angle of incidence at particle Reynolds numbers between Re = 0.3 and 240 under different conditions. For this purpose simulations of the flow around these particles have been performed using the three-dimensional Lattice Boltzmann method. In the first case studied a particle is fixed in a uniform flow, in the second case the particle is rotating in a uniform flow to determine, among others, the Magnus lift force and in the third case the particle is fixed in a linear shear flow. In the first case six particle shapes are considered, i.e. a sphere, a spheroid, a cube, a cuboid and two cylinders with an axis ratio of 1 and 1.5, respectively. In the second and third case the sphere and the spheroid are considered. At the higher Re considered, the drag depends strongly on particle shape, the angle of incidence and particle rotation. The lift and the torque of both the sphere and the spheroid are strongly affected by particle rotation and fluid shear. For approximately Re ? 1, the shear induced lift for unbounded flow could not be simulated as the top and bottom wall have a significant influence in the current flow configuration. The shear induced lift of the sphere changes direction at approximately Re = 50 and the mean (over the orientation) shear induced lift of the spheroid changes direction at approximately Re = 90.     

Preliminary study on the accuracy of respiratory input impedance measurement using the interrupter technique

Respiratory input impedance contains information about the state of pulmonary mechanics in the frequency domain. In this paper the possibility of respiratory impedance measurement by interrupter technique as well as the accuracy of this approach are assessed. Transient states of flow and pressure recorded during expiratory flow interruption are simulated with a complex, linear model for the respiratory system and then used to calculate the impedance, including three states of respiratory mechanics and the influence of the measurement noise. The results of computations are compared to the known, theoretical impedance of the model. At 1 kHz sampling rate, the optimal time window lays between 100 and 200 ms and is centred around the pressure jump caused by the flow interruption. The proposed algorithm yields satisfactory accuracy in the range from 10 to 400 Hz, particularly to 150 Hz. Depending on the simulated respiratory system state, the error of calculated impedance (relative Euclidean distance between the vectors of computed and theoretical values), for the window of 190 ms, varies between 5.0% and 7.1%.     

On restraining the production of small scales of motion in a turbulent channel flow

Since most turbulent flows cannot be computed directly from the incompressible Navier-Stokes equations, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider nonlinear approximations of the convective term that preserve the symmetry and conservation properties. In particularly, the energy, enstrophy (in 2D) and helicity are conserved. The underlying idea is to restrain the convective production of small scales in an unconditional stable manner, meaning that the approximate solution cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. The resulting simulation method is successfully tested for a turbulent channel flow (Re_τ = 180 and 395).