Numerical simulation on an interaction of a vortex street with an elliptical leading edge using an unstructured grid

An algorithm for a time accurate incompressible Navier–Stokes solver on an unstructured grid is presented. The algorithm uses a second order, three‐point, backward difference formula for the physical time marching. For each time step, a divergence free flow field is obtained based on an artificial compressibility method. An implicit method with a local time step is used to accelerate the convergence for the pseudotime iteration. To validate the code, an unsteady laminar flow over a circular cylinder at a Reynolds number of 200 is calculated. The results are compared with available experimental and numerical data and good agreements are achieved. Using the developed unsteady code, an interaction of a Karman vortex street with an elliptical leading edge is simulated. The incident Karman vortex street is generated by a circular cylinder located upstream. A clustering to the path of the vortices is achieved easily due to flexibility of an unstructured grid. Details of the interaction mechanism are analysed by investigating evolutions of vortices. Characteristics of the interactions are compared for large‐ and small‐scale vortex streets. Different patterns of the interaction are observed for those two vortex streets and the observation is in agreement with experiment. Copyright © 2004 John Wiley & Sons, Ltd.     

Computations of flow over a flexible plate using the hybrid Cartesian/immersed boundary method

A hybrid Cartesian/immersed boundary code is developed and applied to interactions between a flexible plate and a surrounding fluid. The velocities at the immersed boundary (IB) nodes are reconstructed by interpolations along local normal lines to an interface. A new criterion is suggested to distribute the IB nodes near an interface. The suggested criterion guarantees a closed fluid domain by a set of the IB nodes and it is applicable to a zero‐thickness body. To eliminate the pressure interpolation at the IB nodes, the hybrid staggered/non‐staggered grid method is adapted. The developed code is validated by comparisons with other experimental and computational results of flow around an in‐line oscillating cylinder. Good agreements are achieved for velocity profiles and vorticity and pressure contours. As applications to the fluid–structure interaction, oscillations of flexible plate in a resting fluid and flow over a flexible plate are simulated. The elastic deformations of the flexible plate are modelled based on the equations of motion for plates considering the fluid pressure as the external load on the plate. Two non‐dimensional parameters are identified and their effects on the damping of the plate motion are examined. Grid convergence tests are carried out for both cases. Copyright © 2007 John Wiley & Sons, Ltd.     

Simulation of compressibility of entrapped air in an incompressible free surface flow using a pressure-based method for unified equations

A pressure-based method is developed to solve the unified conservation laws for incompressible and compressible fluids. A polytropic law is used to model the compressibility of a gas and decouple the energy equation. The pressure field is calculated by solving a single-pressure Poisson equation for the entire flow domain. The effects of the compressibility of the gas are reflected in the source term of the Poisson equation. The continuities of pressure and normal velocity across a material interface are achieved without any additional treatment along the interface. To validate the developed method, the oscillation of a water column in a closed tube due to the compression and expansion of air in the tube is simulated. The computed time history of the pressure at the end wall of the tube is in good agreement with other computational results. The free drop of a water column in a closed tank is simulated. The time history of the pressure at the center of the bottom of the tank shows good agreement with other reported results. The developed code is applied to simulate the air cushion effect of entrapped air in a dam break flow. The computed result is in good agreement with other experimental and computational results until the air is entrapped. As the entrapped air pocket undergoes rapid pulsation, the pressure field of water around the air pocket oscillates synchronously.     

Simulation of free surface flows using the flux‐difference splitting scheme on the hybrid Cartesian/immersed boundary method

In this study, a method is developed to simulate the interaction between free surface flows and moving or deforming boundaries using the flux‐difference splitting scheme on the hybrid Cartesian/immersed boundary method. At each physical time step, the boundary is defined by an unstructured triangular surface grid. Immersed boundary (IB) nodes are distributed inside an instantaneous fluid domain based on edges crossing the boundary. At an IB node, dependent variables are reconstructed along the local normal line to the boundary. Inviscid fluxes are computed using Roe's flux‐difference splitting scheme for immiscible and incompressible fluids. The free surface is considered as a contact discontinuity in the density field. The motion of free surface is captured without any additional treatment along the fluid interface. The developed code is validated by comparisons with other experimental and computational results for a piston‐type wave maker, impulsive motion of a submerged circular cylinder, flow around a submerged hydrofoil, and Rayleigh–Taylor instability. The developed code is applied to simulate wave generation due to a continuously deforming bed beneath the free surface. The violent motion of a free surface caused by sloshing in a spherical tank is simulated. In this case, the free surface undergoes breakup and reconnection. Copyright © 2011 John Wiley & Sons, Ltd.     

Internal wave computations using the ghost fluid method on unstructured grids

Two‐layer incompressible flows are analysed using the ghost fluid method on unstructured grids. Discontinuities in dynamic pressure along interfaces are captured in one cell without oscillations. Because of data reconstructions based on gradients, the ghost fluid method can be adopted without additional storages for the ghost nodes at the expense of modification in gradient calculations due to the discontinuity. The code is validated through comparisons with experimental and other numerical results. Good agreements are achieved for internal waves generated by a body moving at transcritical speeds including a case where upstream solitary internal waves propagate. The developed code is applied to analyse internal waves generated by a NACA0012 section moving near interfaces. Variations of the lift acting on the body and configurations of the interfaces are compared for various distances between the wing and the interface. The effects of the interface are compared with the effects of a solid wall. Copyright © 2004 John Wiley & Sons, Ltd.     

Oxidative degradation of reducing carbohydrates to ammonium formate with H(2)O(2) and NH(4)OH

Oxidation of various carbohydrates into ammonium formate was investigated in the presence of hydrogen peroxide and ammonium hydroxide. Most of the examined carbohydrates except nonreducing sugars were efficiently converted into ammonium formate under environment friendly and mild conditions in aqueous media.