Wave-Current Forces on Small Square Cylinders (Part I)

-Based on the extended Morison Equation and model tests, the in-line forces on small square cylinders caused by waves (regular and irregular) and currents are analyzed in detail in this paper. The hydrodynamic coefficient CD and Cu related to KC number and the effect of direction of wave incidence are also given, which can be used in engineering practice.

NUMERICAL COMPUTATION OF THE FLOW AROUND TWO SQUARE CYLINDERS ARRANGED SIDE-BY-SIDE

The numerical method is used to calculate the flow around two square cylinders arranged side-by-side and the mean and fluctuating aerodynamic forces, and Strouhal numbers and power spectrum of lift force and drag force are obtained. An improved MAC method proposed by Chen Suqin et al.,which uses three order upwind scheme to discretize the convection term and uses multigrid method to solve the Poisson equation for pressure is applied to simulate the flow around two square cylinders arranged side-by-side. Results show that the interference characteristic of two square cylinders arranged side-by-side is completely different with the different spacing ratio. When the spacing ratio is smaller than a certain critical value, the gap flow between two cylinders is biased to one side in a stable or unstable manner.

Two-Dimensional Simulation of the Navier-Stokes Equations for Laminar and Turbulent Flow around a Heated Square Cylinder with Forced Convection

Few studies jointly investigate thermal and turbulent effects. In general, these subjects are treated separately. The purpose of this paper is to use the Immersed Boundary Method (IBM) coupled with the Virtual Physical Model (VPM) to investigate incompressible two-dimensional Newtonian flow around a heated square cylinder at constant temperature on its surface with forced convection and turbulence. The VPM model dynamically evaluates the force that the fluid exerts on the immersed surface and the thermal exchange between both in the Reynolds numbers (Re) window 40 ≤ Re ≤ 5×103 . For simulations of turbulence the Smagorinsky and Spalart-Allmaras models are used. The first model uses the Large Eddy Simulation (LES) methodology and is based on the local equilibrium hypothesis for small scales associated with the Boussinesq hypothesis, such that the energy injected into the spectrum of the turbulence balances the energy dissipated by convective effects. The second model uses the concept Unsteady Reynolds Averaged Navier-Stokes Equations (URANS), with only one transport equation for turbulent viscosity, being calibrated in pressure gradient layers. The goal of this work is to analyse the combination of the heat-transfer phenomena with the turbulence for the thermo-fluid-structure interaction in a square cylinder. For this, it was developed a C/C++ code that requires low computational costs in regards to memory and computer facilities. It is observed that, with the increase of the Reynolds number, an increase of the drag coefficient occurs, as well as reinforces the influence of the pressure distribution downstream of the cylinder, which is strongly influenced by the formation and detachment of vortices on the upper and lower sides of the square cylinder.

LARGE EDDY SIMULATION AND SPECTRUM ANALYSIS OF FLOW AROUND TWO SQUARE CYLINDERS ARRANGED SIDE BY SIDE

Large eddy simulation cooperated with the second order full extension ETG(Euler-Taylor-Galerkin) finite element method was applied to simulate the flow around two square cylinders arranged side by side at a spacing ratio of (1.5.) The second order full extension ETG finite element method was developed by Wang and He. By means of Taylor expansion of terms containing time derivative, time derivative is replaced by space derivative. The function of it is equal to introducing an artificial viscosity term. The streamlines of the flow at different moments were obtained. The time history of drag coefficient, lift coefficient and the streamwise velocity on the symmetrical points were presented. Furthermore, the symmetrical problem of the frequency spectrum of flow around two square cylinders arranged side by side were studied by using the spectral analysis technology. The data obtained at the initial stage are excluded in order to avoid the influence of initial condition on the results. The power spectrums of drag coefficient, lift coefficient, the streamwise velocity on the symmetrical points were analyzed respectively. The results show that although the time domain process of dynamic parameters is non-symmetrical, the frequency domain process of them is symmetrical under the symmetrical boundary conditions.

Forced convection heat transfer due to different inclination angles of splitter behind square cylinder

A numerical investigation is carried out to study the effect of splitter＇s inclination angle behind an inclined square cylinder on the forced convection heat transfer in a plan channel using the lattice Boltzmann method （LBM）. The simulations are conducted for the pertinent parameters in the following ranges： the Reynolds number Re=50-300, the gap ratio G/d = 2, and the splitter＇s inclination angle 8 = 0°-90°. The results show that with the increase in the angle of the splitter, the drag coefficient initially decreases and then increases. Moreover, the time-averaged Nusselt number at a certain angle increases noticeably.

Grid Convergence Property of Three-Dimensional Measurement-Integrated Simulation for Unsteady Flow behind a Square Cylinder with Karman Vortex Street

The purpose of this study was to clarify grid convergence property of three-dimensional measurement-integrated (3D-MI) simulation for a flow behind a square cylinder with Karman vortex street. Measurement-integrated (MI) simulation is a kind of the observer in the dynamical system theory by using CFD scheme as a mathematical model of the system. In a former study, two-dimensional MI (2D-MI) simulation with a coarse grid system showed a fairly good result in comparison with a 2D ordinary (2D-O) simulation, but the results were degraded with grid refinement. In this study, 3D-MI simulation and three-dimensional ordinary (3D-O) simulation were performed with three grid systems of different grid resolutions, and their grid convergence properties were compared. As a result, all 3D-MI simulations reproduced the vortex shedding frequency identical to that of the experiment, and the flow fields obtained were very close, within 5% difference between the results, while the results of the 3D-O simulations showed variation of the solution under convergence. It is shown that the grid convergence property of 3D-MI simulation is monotonic and better than that of 3D-O simulation, whereas those of 2D-O and 2D-MI simulations for streamwise velocity fluctuation are divergent. The solution of 3D-MI simulation with a relatively coarse grid system properly reproduces the basic three-dimensional structure of the wake flow as well as the drag and lift coefficients.

A New Method of Computing the Transient Response of a Dielectric Square Cylinder

The vulume intesral equation and Fourier transform are applied to solve thetransient response of a dielectric square cylinder. if the dielectric square cylinderis only two-dimensional inhoniogeneous and the source is three-dimensional,Fourier transformation is used to reduce the three-dimensional source into thesuperposition of two diniensional source.

Numerical simulation of viscous flow past an oscillating square cylinder using a CIP-based model

The flow past an in-line forced oscillating square cylinder at Reynolds number of 200 is studied using an in-house code, named constrained interpolation profile method developed in Zhejiang University （CIP-ZJU）. The model is established in the Cartesian coordinate system using the CIP method to discretise the Navier-Stokes equations. The fluid-structure interaction is treated as a multiphase flow of the liquid and solid phases to be solved simultaneously. An immersed boundary method is used to deal with the boundary of the solid body. The CFD model is first applied to the computation of the flow past a fixed square cylinder for its validation. Computations are then performed for the flow past a square cylinder oscillating in the streamwise direction. Considerable attention is paid to the symmetric and anti-symmetric modes of the vortex shedding in the oscillating square cylinder wake. Various oscillation amplitudes and frequencies are simulated and their effects on the vortex shedding modes are analyzed via Lissajous patterns of the unsteady lift coefficient. The relationship among the lift coefficient, the drag coefficient and the lock-on range is also investigated quantitatively.

RANS and hybrid LES/RANS simulations of flow over a square cylinder

Unsteady RANS(URANS),hybrid LES/RANS and IDDES simulations were conducted to numerically investigate the velocity field around,and pressures distribution and forces over a square cylinder immersed in a uniform,steady oncoming flow with Reynolds number Re=21,400.The vortex shedding responses in terms of Strouhal number,the pressure distribution,the velocity profile and the velocity fluctuations obtained by numerical simulations are compared with experimental data.Compared with 2D URANS simulation,3D simulations using hybrid LES/RANS and IDDES models provide more accurate prediction on the responses in the wake,including mean streamwise velocity profile and rms velocity fluctuations.This also results in more accurate prediction of time-averaged surface pressure coefficient on the rear surface obtained by 3D hybrid LES/RANS and IDDES simulations than by URANS simulation.When a hybrid LES/RANS model or IDDES model is used,a more accurate prediction for either pressure coefficient or velocity profile(especially in the far wake region)is not guaranteed by increasing the mesh resolution along the spanwise direction of the square cylinder.