The impact force on an elbow induced by traveling isolated liquid slugs in a horizontal pipeline is studied. A literature review reveals that the force on the elbow is mainly due to momentum transfer in changing the fluid flow direction around the elbow. Therefore, to accurately calculate the magnitude and duration of the impact force, the slug arrival velocity at the elbow needs to be well predicted. The hydrodynamic behavior of the slug passing through the elbow needs to be properly modeled too. A combination of 1D and 2D models is used in this paper to analyze this problem. The 1D model is used to predict the slug motion in the horizontal pipeline. With the obtained slug arrival velocity, slug length, and driving air pressure as initial conditions, the 2D Euler equations are solved by the smoothed particle hydrodynamics (SPH) method to analyze the slug dynamics at the elbow. The 2D SPH solution matches experimental data and clearly demonstrates the occurrence of flow separation at the elbow, which is a typical effect of high Reynolds flows. Using the obtained flow contraction coefficient, an improved 1D model with nonlinear elbow resistance is proposed and solved by SPH. The 1D SPH results show the best fit with experimental data obtained so far.

A new and efficient numerical model is proposed for simulating the acoustic wave propagation and scattering problems due to a complex geometry. In this model, the linearized Euler equations are solved by the finite-difference time-domain (FDT-D) method on an orthogonal Eulerian grid. The complex wall boundary represented by a series of Lagrangian points is numerically treated by the immersed boundary method (IBM). To represent the interaction between these two systems, a force field is added to the momentum equation, which is calculated on the Lagrangian points and interpolated to the nearby Eulerian points. The pressure and velocity fields are then calculated alternatively using FDTD. The developed model is verified in the case of acoustic scattering by a cylinder, for which the exact solutions exist. The model is then applied to sound wave propagation in a 2D vocal tract with area function extracted from MRI data. To show the advantage of present model, the grid points are non-aligned with the boundary. The numerical results have good agreements with solutions in literature. A FDTD calculation with boundary condition directly imposed on the grid points closest to the wall cannot give a reasonable solution.

Two Lagrangian models are developed for the accurate simulation of advection-diffusion transport in unsteady open channel flows. The first one is based on a second-order partial differential equation (PDE) for pollutant concentration (model I), and the second one is a first-order system with diffusive flux as another primary variable (model II). To solve the two models, the meshless smoothed particle hydrodynamics (SPH) method is employed. To enforce the inlet and outlet boundary conditions, an extrapolation scheme based on cubic spline is used. Numerical results are presented for tracer distributions with boundary layer in a uniform flow and are compared with analytical solutions. It is demonstrated that both the two models can accurately solve the advection-diffusion transport problems, for which numerical diffusion and disperse oscillation are often observed in most Eulerian schemes. Therefore, the Lagrangian particle models are efficient and accurate tools to predict advection dominated transport for water quality in river systems and for transport with a boundary layer.