Separation of micro and sub-micro diamagnetic particles in dual ferrofluid streams based on negative magnetophoresis

In the present study, we numerically demonstrate an approach for separation of micro and sub-micro diamagnetic particles in dual ferrofluid streams based on negative magnetophoresis. The dual streams are constructed by an intermediate sheath flow, after which the negative magnetophoretic force induced by an array of permanent magnets dominates the separation of diamagnetic particles. A simple and efficient numerical model is developed to calculate the motions of particles under the action of magnetic field and flow field. Effects of the average flow velocity, the ratio of sheath fluid flow to sample fluid flow, the number of the magnet pair as well as the position of magnet pair are investigated. The optimal parametric condition for complete separation is obtained through the parametric analysis, and the separation principle is further elucidated by the force analysis. The separation of smaller micro and sub-micro diamagnetic particles is finally demonstrated. This study provides an insight into the negative magnetophoretic phenomenon and guides the fabrication of feasible, low-cost diagnostic devices for sub-micro particle separation.     

Deuteriodifluoromethylation and gem‐Difluoroalkenylation of Aldehydes Using ClCF2H in Continuous Flow

The deuteriodifluoromethyl group (CF₂D) represents a challenging functional group due to difficult deuterium incorporation and unavailability of precursor reagents. Herein, we report the use of chlorodifluoromethane (ClCF₂H) gas in the continuous flow deuteriodifluoromethylation and gem‐difluoroalkenylation of aldehydes. Mechanistic studies revealed that the difluorinated oxaphosphetane (OPA) intermediate can proceed via alkaline hydrolysis in the presence of D₂O to provide α‐deuteriodifluoromethylated benzyl alcohols or undergo a retro [2+2] cycloaddition under thermal conditions to provide the gem‐difluoroalkenylated product.     

A NUMERICAL PROCEDURE FOR PREDICTING MULTIPLE SOLUTIONS OF A SPHERICAL TAYLOR–COUETTE FLOW

A new numerical procedure for predicting multiple solutions of Taylor vortices in a spherical gap is presented. The steady incompressible Navier–Stokes equations in primitive variables are solved by a finite- difference method using a matrix preconditioning technique. Routes leading to multiple flow states are designed heuristically by imposing symmetric properties. Both symmetric and asymmetric solutions can be predicted in a deterministic way. The current procedure gives very fast convergence rate to the desired flow modes. This procedure provides an alternative way of finding all possible stable steady axisymmetric flow modes.     

ON THE STRUCTURE OF STEADY FLOW THROUGH DUAL-INTAKE ENGINE PORTS

The influence of intake port design on the flow field in a dual-intake valve engine was investigated using computational fluid dynamics, in order to study the effect of inlet port design on the in-cylinder flow. A detailed 3D computational grid incorporating all the features of the Ford Zetec production engine inlet ports, valves and cylinder head was initially created and the flow structure modelled at 5 and 10 mm valve lifts under steady flow conditions. Comparisons of computational results with experimental data obtained by laser Doppler anemometry indicate that the flow characteristics have been predicted well in most regions. Flow generated by different intake port designs was also simulated by introducing air into the cylinder at different directions to the inlet valve axes and the effects of port deactivation, throttling and exhaust gas recirculation were examined. The implications of the results for intake port design are discussed.     

NUMERICAL SIMULATION OF THREE-DIMENSIONAL INCOMPRESSIBLE FLOW BY A NEW FORMULATION

A new mathematical formulation, called the pseudovorticity–velocity formulation, of the three-dimensional incompressible Navier–Stokes equations is presented as an alternative to the vorticity–velocity approach. For the model lid-driven cavity flow problem in two and three dimensions, combined with an explicit mixed spectral /finite different numerical scheme the proposed formulation is found to be efficient and very accurate as compared with the results available in the literature. In particular, the simulation results demonstrate an attractive feature of the present formulation compared with the vorticity–velocity approach, namely that the divergence-free condition of the velocity field can always be achieved on a non-staggered mesh.     

COMPUTATION OF DILUTE PARTICULATE LAMINAR FLOW OVER A BACKWARD-FACING STEP

Particle-laden flows are calculated for a classical laminar backward- facing step problem. The particle tracks are calculated using a recently developed exponential Lagrangian tracking scheme. The behaviour of the particle-laden flow is considered for various inlet for Reynolds number, Stokes numbers and void fractions. Doping the flow with low-Stokes-number particles has the effect of increasing the inlet inertia of the flow and this increases the strength of the recirculation behind the step. High-Stokes- number particles are dominated by gravitational effects which affect the flow accordingly. Differences between the single-phase flow and the particle-laden flows are therefore dependent on the Stokes number and increase linearly with void fraction.     

A NUMERICAL STUDY OF THE FLOW OVER ELLIPSOIDAL OBJECTS INSIDE A CYLINDRICAL TUBE

A numerical scheme is developed to obtain the flow field around one, two and five ellipsoidal objects inside a cylindrical tube. The scheme uses the Galerkin finite element technique and the primitive variable(u–v–p) formulation. The two-dimensional incompressible Navier–Stokes equations are solved numerically by using the direct mixed interpolation method. A Picard iteration scheme is used for the solution of the resulting system of non-linear algebraic equations. The computer code is verified by checking with known analytical solutions for the flow past a sphere. Results for the shear stress distributions along the ellipsoids, forces and drag coefficients are obtained for different geometric ratios and Reynolds numbers. Some of the intermediate computational results on the velocity fields developed are also reported.     

HIGH-ORDER-ACCURATE DISCRETIZATION STENCIL FOR AN ELLIPTIC EQUATION

The coefficients for a nine-point high-order-accurate discretization scheme for an elliptic equation ∇²u− γ²u=r₀ (∇² is the two-dimensional Laplacian operator) are derived. Examples with Dirichlet and Neumann boundary condtions are considered. In order to demonstrate the high-order accuracy of the method, numerical results are compared with exact solutions.     

METHOD–OF–LINES SOLUTION OF TIME–DEPENDENT TWO–DIMENSIONAL NAVIER–STOKES EQUATIONS

A novel approach to the development of a code for the solution of the time-dependent two-dimensional Navier–Stokes equations is described. The code involves coupling between the method of lines (MOL) for the solution of partial differential equations and a parabolic algorithm which removes the necessity of iterative solution on pressure and solution of a Poisson-type equation for the pressure. The code is applied to a test problem involving the solution of transient laminar flow in a short pipe for an incompressible Newtonian fluid. Comparisons show that the MOL solutions are in good agreement with the previously reported values. The proposed method described in this paper demonstrates the ease with which the Navier–Stokes equations can be solved in an accurate manner using sophisticated numerical algorithms for the solution of ordinary differential equations (ODEs).     

AN UNFACTORED IMPLICIT MOVING MESH METHOD FOR THE TWO-DIMENSIONAL UNSTEADY N–S EQUATIONS

An unfactored implicit time-marching method for the solution of the unsteady two-dimensional Reynolds-averaged thin layer Navier–Stokes equations is presented. The linear system arising from each implicit step is solved by the conjugate gradient squared (CGS) method with preconditioning based on an ADI factorization. The time-marching procedure has been used with a fast transfinite interpolation method to regenerate the mesh at each time step in response to the motion of the aerofoil. The main test cases examined are from the AGARD aeroelastic configurations and involve aerofoils oscillating rigidly in pitch. These test cases have been used to investigate the effect of various parameters, such as CGS tolerance and laminar/turbulent transition location, on the accuracy and efficiency of the method. Comparisons with available experimental data have been made for these cases. In order to illustrate the application of the mesh generator and flow solver to more general flows where the aerofoil deforms, results for an NACA 0012 aerofoil with an oscillating trailing edge flap are also shown.