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.

FORCES ON CYLINDERS IN COEXISTING FIELD OF REGULAR WAVES AND CURRENTS

Based on the linear wave theory, the lift force on the cylinder under the action of both regular waves and currents related to inline force and the resultant force has been investigated. The relationship between the hydrodynamic coefficients of resultant force Cf, of drag force Cd, of inertia force Cm and of lift force CL and the redefined KC number is reported. It is indicated that in a certain region of KC number, the influence of lift force on the resultant force can not be ignored.

WAVE CURRENT FORCE COEFFICIENTS ON INCLINED CYLINDER AND A NEW ESTIMATION METHOD

Based on the review of present force coefficients estimation methods, a new method in the frequency domain, revised cross-spectrum estimation method, is presented in this paper. Some experiments on the wave-current force on inclined cylinders are also described and the wave current force coefficients are estimated by the revised cross-spectrum estimation method. From the results, it is found that the wave and current directions have some regular effect on the coefficients. According to the results, some empirical formulas are obtained for converting the wave-current force coefficients on inclined cylinders into a unified coefficient. Comparisons show that the unified coefficients are in good agreement with other results.

Control of mean and fluctuating forces on a circular cylinder at high Reynolds numbers

A narrow strip is used to control mean and fluctuating forces on a circular cylinder at Reynolds numbers from 2.0 ×10^4 to 1.0 ×^ 10^5. The axes of the strip and cylinder are parallel. The control parameters are strip width ratio and strip position characterized by angle of attack and distance from the cylinder. Wind tunnel tests show that the vortex shedding from both sides of the cylinder can be suppressed, and mean drag and fluctuating lift on the cylinder can be reduced if the strip is installed in an effective zone downstream of the cylinder. A phenomenon of mono-side vortex shedding is found. The strip-induced local changes of velocity profiles in the near wake of the cylinder are measured, and the relation between base suction and peak value in the power spectrum of fluctuating lift is studied. The control mechanism is then discussed from different points of view.

Nonlinear effect on inertia component of wave forces on a cylinder

A series of experiments on wave forces on a cylinder have been carried out when inertia component isdominant for a small she cylinder. The influence of nonlinear effect on the inertia component of wave forces on a cylinder is analyzed. The applicable range of nonlinear wave theories, such as Stokes and cnoidal wave theories, in calculating wave forces on a cylinder is discussed. A correction method is suggested for linear wave theory in calculated waveforces on a cylinder under the nonlinear condition.

Wave-current force on horizontal cylinder

For the calculation of wave-current force on horizontal cylinder a modified Morison's equation is used. A redefined Keulegan- Carpenter number KC2 is determined for the horizontal cylinder in wave-current co-existing field. The force coefficients are well related to the redefined KC2 number. As to the comparison with the force on vertical cylinder, the characteristics of force on horizontal cylinder are quite similar to those on vertical cylinder, but the force coefficients for horizontal cylinder are larger than those for vertical cylinder. It is proved by the authors' calculation that the results of monochromatic wave can be used directly for the determination of irregular wave-current force on horizontal cylinder in time domain.

The influences of wall Lorentz force and field Lorentz force on the cylinder drag reduction

In this paper,the effects of Lorentz force on drag reduction for a circular cylinder have been studied experimentally and numerically.Based on its effects on drag reduction,the Lorentz force is found to be classified into two parts：one acts directly on the cylinder,named as the wall Lorentz force,and the other called the field Lorentz force acts on the fluid inside the boundary layer.The wall Lorentz force leads to the generation of a thrust,whereas the field Lorentz force results in drag increase.Since the former dominates the drag variation,the drag would reduce accordingly and even turn into negative （thrust） with the application of Lorentz force.

Erratum to:“An Approximate Method for Calculating the Fluid Force and Response of A Circular Cylinder at Lock-in” [China Ocean Engineering,22(3),2008,371-384]

Because of my carelessness,Eq.（1）in the paper "An approximate method for calculating the fluid force and response of a circular cylinder at lock-in"(China Ocean Engineering,22（3）,2008,pp.373)should be f’-1.0/U’-5.0=f’;-1.0/5.75f’;-5.0,not f’=U’/5.75. My apology is hereby given.

THE CALCULATION OF IN-LINE FORCE ON A VERTICAL CIRCULAR CYLINDER AND ANALYSIS OF HYDRODYNAMIC COEFFICIENTS C_D AND C_M IN WAVE-CURRENT CO-EXISTING FIELD

The purpose of this paper is to find some better methods for calculating in-line forces on a vertical circular cylinder and for analysing the hydrodynamic coefficients C_D and C_M in wave-current co-existing field. In this pa- per, in order to calculate hydrodynamic forces, the authors try to find a way of applying a great number of the re- sults about C_D and C_M for wave-only field in the case of wave-current co-existing field, and the results about C_D and C_M obtained in regular waves in the ease of irregular waves. Such a way may be of significance in engineering and further research.

SECOND ORDER DIFFRACTION FORCES ON HORIZONTAL CYLINDERS

The second order diffraction forces on a floating semicircular cylinder and a submerged circular cylinder are calculated using the method of Lighthill(ref.3). The first order potential is obtained by the multipole expansion and numerical results are provided.