Turbulent flow in converging nozzles,part one:boundary layer solution

The boundary layer integral method is used to investigate the development of the turbulent swirling flow at the entrance region of a conical nozzle. The governing equations in the spherical coordinate system are simplified with the boundary layer as- sumptions and integrated through the boundary layer. The resulting sets of differential equations are then solved by the fourth-order Adams predictor-corrector method. The free vortex and uniform velocity profiles are applied for the tangential and axial velocities at the inlet region, respectively. Due to the lack of experimental data for swirling flows in converging nozzles, the developed model is validated against the numerical simulations. The results of numerical simulations demonstrate the capability of the analytical model in predicting boundary layer parameters such as the boundary layer growth, the shear rate, the boundary layer thickness, and the swirl intensity decay rate for different cone angles. The proposed method introduces a simple and robust procedure to investigate the boundary layer parameters inside the converging geometries.

Research on Design Method of the Full Form Ship with Minimum Thrust Deduction Factor

In the preliminary design stage of the full form ships, in order to obtain a hull form with low resistance and maximum propulsion efficiency, an optimization design program for a full form ship with the minimum thrust deduction factor has been developed, which combined the potential flow theory and boundary layer theory with the optimization technique. In the optimization process, the Sequential Unconstrained Minimization Technique（SUMT） interior point method of Nonlinear Programming（NLP） was proposed with the minimum thrust deduction factor as the objective function. An appropriate displacement is a basic constraint condition, and the boundary layer separation is an additional one. The parameters of the hull form modification function are used as design variables. At last, the numerical optimization example for lines of after-body of 50000 DWT product oil tanker was provided, which indicated that the propulsion efficiency was improved distinctly by this optimal design method.

COMPUTER COMPUTATION OF THE METHOD OF MULTIPLE SCALES-DIRICHLET PROBLEM FOR A CLASS OF SYSTEM OF NONLINEAR DIFFERENTIAL EQUATIONS

The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations . The asymptotic expansions of solution were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application of the method of boundary layer with multiple scales .

ON THE FINITE DIFFERENCE METHODS FOR TWO DIMENSIONAL TURBULENCE BOUNDARY LAYER

In this paper,the author first establishes the general finite difference formula for the governing equations of the turbulent average velocities in a steady two dimensional incompressible fluid boundary layer-inner layer.Next, three key parameters of the difference scheme are determined respectively by several simple flow models with known analytical solutions.Finally a special five points difference system is given and its application value is showed by a numerical example for the vertical velocity distribution in an Ekman's layer.

RATIONAL SPECTRAL COLLOCATION METHOD FOR A COUPLED SYSTEM OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS

A, novel collocation method for a coupled system of singularly perturbed linear equations is presented. This method is based on rational spectral collocation method in barycentric form with sinh transform. By sinh transform, the original Chebyshev points are mapped into the transformed ones clustered near the singular points of the solution. The results from asymptotic analysis about the singularity solution are employed to determine the parameters in this sinh transform. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method.

VARIABLE MESH FINITE DIFFERENCE METHOD FOR SELF-ADJOINT SINGULARLY PERTURBED TWO-POINT BOUNDARY VALUE PROBLEMS

A numerical method based on finite difference method with variable mesh is given for self-adjoint singularly perturbed two-point boundary value problems. To obtain parameter- uniform convergence, a variable mesh is constructed, which is dense in the boundary layer region and coarse in the outer region. The uniform convergence analysis of the method is discussed. The original problem is reduced to its normal form and the reduced problem is solved by finite difference method taking variable mesh. To support the efficiency of the method, several numerical examples have been considered.

Sliding Mode Control of T-Shaped Pedestrian Channel

The study of pedestrian evacuation in channels with different structures is important among optimizing through efficiency,avoiding accidents and designing passageway.It is of significant reference to set up a specific model on account of the real traffic system and design an appropriate controller to apply on it.This paper establishes a macroscopic model for T-shaped channel with a number of controlled entrances basing on the law of mass conservation.Then,with the method of cascade,a kind of sliding mode controller is designed to achieve the control target of avoiding the blocking and maximizing the pedestrian flow of the whole model,the stability of the system is proved by the Lyapunov stability theory,and the boundary layer method is applied to restrain the chattering of the controller.Finally,simulation results show the efficiency of the sliding mode controller and the improvement brought by the boundary layer method.

Numerical simulation of the sticking process of glass-microparticles to a fiat wall to represent pollutant-particles treatment in a multi-channel cyclone

Ultrafine particles are dangerous to human health and are usually difficult to separate from airflow because of their low inertia, which helps them to stick easily to surfaces because of adhesive forces. This characteristic provides opportunities for adhesive ultrafine particle separation by designing air-cleaning devices that exploit the sticking ability. To understand governing effects in such air-cleaning devices, which can be designed as multi-channel cyclones, the sticking of adhesive spherical glass particles under oblique impact has been investigated numerically by using the discrete element method. An adhesive dissipative contact model was applied by implementing different interaction forces for various-sized ultraflne pollutant particles. Normal loading is represented by the elastic Hertz contact model, whereas viscous damping is described by the modified nonlinear Tsuji model. The influence of deformation- dependent adhesive forces for a range of ultrafine particle sizes is illustrated during the sticking process. Dissipative oscillations during the sticking process were observed because of the influence of viscous damping forces.