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31.
    
On the basis of the Helmholtz decomposition, a grid‐free numerical scheme is provided for the solution of unsteady flow in hydraulic turbines. The Lagrangian vortex method is utilized to evaluate the convection and stretch of the vorticity, and the BEM is used to solve the Neumann problem to define the potential flow. The no‐slip boundary condition is satisfied by generating vortex sticks at the solid surface. A semi‐analytical regularization technique is applied to evaluate the singular boundary surface integrals of the potential velocity and its gradients accurately. The fast multipole method was extended to evaluate the velocity and velocity gradients induced by the discretized vortex blobs in the Lagrangian vortex method. The successful simulation for the unsteady flow through a hydraulic turbine's runner has manifested the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   
32.
    
The paper presents a semi‐implicit algorithm for solving an unsteady fluid–structure interaction problem. The algorithm for solving numerically the fluid–structure interaction problems was obtained by combining the backward Euler scheme with a semi‐implicit treatment of the convection term for the Navier–Stokes equations and an implicit centered scheme for the structure equations. The structure is governed either by the linear elasticity or by the non‐linear St Venant–Kirchhoff elasticity models. At each time step, the position of the interface is predicted in an explicit way. Then, an optimization problem must be solved, such that the continuity of the velocity as well as the continuity of the stress hold at the interface. During the Broyden, Fletcher, Goldforb, Shano (BFGS) iterations for solving the optimization problem, the fluid mesh does not move, which reduces the computational effort. The term ‘semi‐implicit’ used for the fully algorithm means that the interface position is computed explicitly, while the displacement of the structure, velocity and the pressure of the fluid are computed implicitly. Numerical results are presented. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   
33.
Airfoil performance degradation in heavy rain has attracted many aeronautical researchers’ eyes. In this work, a two-way momentum coupled Eulerian–Lagrangian approach is developed to study the aerodynamic performance of a NACA 0012 airfoil in heavy rain environment. Scaling laws are implemented for raindrop particles. A random walk dispersion approach is adopted to simulate raindrop dispersion due to turbulence in the airflow. Raindrop impacts, splashback and formed water film are modeled with the use of a thin liquid film model. The steady-state incompressible air flow field and the raindrop trajectory are calculated alternately through a curvilinear body-fitted grid surrounding the airfoil by incorporating an interphase momentum coupling term. Our simulation results of aerodynamic force coefficients agree well with the experimental results and show significant aerodynamic penalties at low angles of attack for the airfoil in heavy rain. An about 3° rain-induced increase in stall angle of attack is predicted. The loss of boundary momentum by raindrop splashback and the effective roughening of the airfoil surface due to an uneven water film are testified to account for the degradation of airfoil aerodynamic efficiency in heavy rain environment.  相似文献   
34.
    
In this paper, we describe a numerical model to simulate the evolution in time of the hydrodynamics of water storage tanks, with particular emphasis on the time evolution of chlorine concentration. The mathematical model contains several ingredients particularly designed for this problem, namely, a boundary condition to model falling jets on free surfaces, an arbitrary Lagrangian–Eulerian formulation to account for the motion of the free surface because of demand and supply of water, and a coupling of the hydrodynamics with a convection–diffusion–reaction equation modeling the time evolution of chlorine. From the numerical point of view, the equations resulting from the mathematical model are approximated using a finite element formulation, with linear continuous interpolations on tetrahedra for all the unknowns. To make it possible, and also to be able to deal with convection‐dominated flows, a stabilized formulation is used. In order to capture the sharp gradients present in the chlorine concentration, particularly near the injection zone, a discontinuity capturing technique is employed. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   
35.
    
Herein, the modified Lagrangian vortex method (LVM), a hybrid analytical‐numerical algorithm per se, is devised to simulate the process of vortex formation and shedding from the sharp edge of a zero‐thickness vertical plate under linear water‐wave attack. Application of the Helmholtz decomposition facilitates a convenient switch between the inviscid‐ and viscous‐flow models, thereby enabling easy incorporation of vorticity effects into the potential‐flow calculations for the viscous‐dominated region. In evaluating the potential‐flow component, making good use of the quickly convergent technique with singular basis functions, correctly capturing the singular behavior in velocity fields near the tip of the plate, leads to a considerable reduction of computational burdens and to 12‐decimal‐place accuracy. The viscous correction is carried out via the meshless LVM with improved boundary conditions. Comparisons with previously published results show good agreement. Simulations of vortex generation and evolution illuminate the ability of the present method, and provide a supplement to pertinent experimental works. The hybrid scheme proposed herein allows flexibility for the former LVM and convenience in the code development. Such a compromise fits particularly well for the high‐resolution modeling of sharp‐edged vortex shedding without heavy numerical developments. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   
36.
    
This paper presents a new approach for the detection and treatment of colloidal particle collisions. It has been developed in the framework of Lagrangian approaches where a large number of particles is explicitly tracked. The key idea is to account for the continuous trajectories of both colliding partners during a time step that is not restricted. Unlike classical approaches which consider only the distances between a pair of particles at the beginning and at the end of each time step (or assume straight-line motion in between), we model the whole relative, and possibly diffusive, trajectory. The collision event is dealt with using the probability that the relative distance reaches a minimum threshold (equal to the sum of the two particle radii). In that sense, the present paper builds on the idea of a previous work. However, in this first work, the collision event was simulated with a simplified scheme where one of the collision partners was removed and re-inserted randomly within the simulation domain. Though usually applied, this treatment is limited to homogeneous situations. Here, an extension of the stochastic model is proposed to treat more rigorously the collision event via a suitable evaluation of the time and spatial location of the collision and an adequate calculation of subsequent particle motion. The resulting collision kernels are successfully compared to theoretical predictions in the case of particle diffusive motion. With these promising results, the feasibility of simulating the collisional regime over a whole range of particle sizes (even nanoscopic) and time steps (from a ballistic to a purely diffusive regime) with a numerical method of reasonable computational cost has been confirmed. The present approach thus appears as a good candidate for the simulation of the agglomeration phenomenon between particles also in complex non-homogeneous flows.  相似文献   
37.
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.  相似文献   
38.
A linearized plane pendulum with the slowly varying mass and length of string and the suspension point moving at a slowly varying speed is presented as an example of a simple 1D mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. The expression for the pendulum geometric phase is obtained by three different methods. The pendulum is shown to be canonically equivalent to the damped harmonic oscillator. This supports the mathematical conclusion, not widely accepted in physical community, of no difference between the dissipative and Hamiltonian 1D systems.  相似文献   
39.
40.
A class of twisted special Lagrangian submanifolds in T~*R~n and a kind of austere submanifold from conormal bundle of minimal surface of R~3 are constructed.  相似文献   
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