Zhihua Xie

Numerical investigation of flow-induced rotary oscillation of circular cylinder with rigid splitter plate

Numerical results of fluid flow over a rotationally oscillating circular cylinder with splitter plate are presented here. Different from the previous examinations with freely rotatable assembly, the fluid and structure interactions are treated as a coupled dynamic system by fully considering the structural inertia, stiffness, and damping. The hydrodynamic characteristics are examined in terms of reduced velocity Ur at a relatively low Reynolds number Re = 100 for different plate lengths of L/D = 0.5, 1.0, and 1.5, where Ur = U/(Dfn), Re = UD/υ and fn = (κ/J)0.5/2π with U the free stream velocity, D the diameter of the circular cylinder, υ the fluid kinematic viscosity, fn the natural frequency, J the inertial moment, κ the torsional stiffness, and L the plate length. Contrast to the freely rotating cylinder/plate body, that is, in the limit of κ → 0 or Ur →∞, remarkable rotary oscillation is observed at relatively low reduced velocities. For the typical case with L/D = 1.0, the maximum amplitude may reach...

Large-eddy simulation of turbulent open-channel flow over three-dimensional dunes

A large-eddy simulation study has been undertaken to investigate the turbulent structure of open-channel flow over three-dimensional (3D) dunes. The governing equations have been discretized using the finite volume method, with the partial cell treatment being implemented in a Cartesian grid form to deal with the 3D dune topography. The simulated free surface elevations, mean flow velocities and Reynolds shear stress distributions have been compared with experimental measurements published in the literature. Relatively close agreement has been obtained between the two sets of results. The predicted mean velocity field and the associated turbulence structure are significantly different from those observed for flows over two-dimensional dunes. The effects of dune three-dimensionality are reflected in spanwise variations of mean flow fields, secondary currents and different distributions of vertical profiles of the double-averaged velocity. Furthermore, large-scale vortical structures, such as spanwise rollers and hairpin-like structures, are predicted in the simulations, with most of them being generated in the concave regions of the 3D dunes.

Numerical modelling of wind effects on breaking waves in the surf zone

Wind effects on periodic breaking waves in the surf zone have been investigated in this study using a two-phase flow model. The model solves the Reynolds-averaged Navier–Stokes equations with the k − 𝜖 turbulence model simultaneously for the flows both in the air and water. Both spilling and plunging breakers over a 1:35 sloping beach have been studied under the influence of wind, with a focus during wave breaking. Detailed information of the distribution of wave amplitudes and mean water level, wave-height-to-water-depth ratio, the water surface profiles, velocity, vorticity, and turbulence fields have been presented and discussed. The inclusion of wind alters the air flow structure above water waves, increases the generation of vorticity, and affects the wave shoaling, breaking, overturning, and splash-up processes. Wind increases the water particle velocities and causes water waves to break earlier and seaward, which agrees with the previous experiment.

A two-phase flow model for three-dimensional breaking waves over complex topography

A two-phase flow model has been developed to study three-dimensional breaking waves over complex topography, including the wave pre-breaking, overturning and post-breaking processes. The large-eddy simulation approach has been adopted in this study, where the model is based on the filtered Navier–Stokes equations with the Smagorinsky sub-grid model being used for the unresolved scales of turbulence. The governing equations have been discretized using the finite volume method, with the PISO algorithm being employed for the pressure–velocity coupling. The air–water interface has been captured using a volume of fluid method and the partial cell treatment has been implemented to deal with complex topography in the Cartesian grid. The model is first validated against available analytical solutions and experimental data for solitary wave propagation over constant water depth and three-dimensional breaking waves over a plane slope, respectively. Furthermore, the model is used to study three-dimensional overturning waves over three different bed topographies, with three-dimensional wave profiles and surface velocities being presented and discussed. The overturning jet, air entrainment and splash-up during wave breaking have been captured by the two-phase flow model, which demonstrates the capability of the model to simulate free surface flow and wave breaking problems over complex topography.

Numerical simulation of three-dimensional breaking waves and its interaction with a vertical circular cylinder

Wave breaking plays an important role in wave-structure interaction. A novel control volume finite element method with adaptive unstructured meshes is employed here to study 3-D breaking waves. The numerical framework consists of a “volume of fluid” type method for the interface capturing and adaptive unstructured meshes to improve computational efficiency. The numerical model is validated against experimental measurements of breaking wave over a sloping beach and is then used to study the breaking wave impact on a vertical circular cylinder on a slope. Detailed complex interfacial structures during wave impact, such as plunging jet formation and splash-up are captured in the simulation, demonstrating the capability of the present method.

A new unconditionally stable explicit scheme for the convection-diffusion equation with Robin boundary conditions

An alternating direction explicit (ADE) scheme to solve the unsteady convection–diffusion equation with Robin boundary conditions is presented and discussed in this paper. It was derived based on the local series expansion method and proved unconditionally stable by von Neumann stability analysis. Thereafter, the ADE scheme is compared with the conventional schemes, and a comparison between the amplification factor of all schemes and the exact one shows that the proposed scheme can simulate well both convection- and diffusion-dominated problems. Finally, the proposed method was validated by a numerical experiment which indicates that, for large cell Reynolds numbers, the proposed scheme, which has unconditional stability, is more accurate than implicit schemes and most explicit schemes. It is also shown that the proposed scheme is simple to implement, economical to use, effective for dealing with Robin boundary conditions and easy to apply to multidimensional problems.

Application of a three-point explicit compact difference scheme to the incompressible Navier-Stokes equations

A three-point explicit compact difference scheme with high order of accuracy for solving the unsteady incompressible Navier-Stokes equations was presented. Numerical solutions are obtained for the model problem of lid-driven cavity flow and are compared with benchmark solutions found in the literature. It is discovered that the proposed three point explicit compact scheme is not only simple to implement and economical to use, but also is effective to obtain high-order accurate solution in coarse grid systems.

A High Order Compact Difference Scheme for Solving the Unsteady Convection-Diffusion Equation

In practical engineering applications, convection diffusion equations are generally used to describe the transport processes involving fluid motion, heat transfer, astrophysics, oceanography, meteorology, semiconductors, hydraulics, pollutant & sediment transport and chemical engineering. In this paper, a high order compact difference scheme based on the fourth order compact difference scheme in spatial discretization and the fourth order Runge-Kutta method in time integration is proposed for the numerical simulation of the unsteady convection-diffusion equation. The validity and effectiveness of the proposed method is firstly tested by a two-dimensional convection-diffusion equation with a Gaussian pulse type concentration. The L 2 error norms are used to measure differences between the exact and numerical solutions and compared to those obtained by other methods. It is shown that the results obtained by proposed method agree very well with the analytical solutions and is more accurate than other methods. Then, a two-dimensional non-linear Burgers equation is used to validate the effectiveness of the proposed method used to solve the non-linear convection-diffusion equation, which also models well. Finally, the Taylor’s vortex problem is investigated by the proposed method and good agreement is obtained with the exact solutions. From the three test problems, it is shown that the proposed high order compact difference scheme is an efficient and accurate method to simulate the transport problems and also can be applied to many engineering problems.