Flow Drag Force Research Articles

Numerical simulation of flow around rectangular cylinders

We recently reported the experimental results of lift and drag forces, base pressure and Strouhal number of rectangular cylinders against Reynolds numbers and the side ratios of a model, measured in a wind tunnel and found the interesting fluid-characteristics and phenomena of flow. Then, we have calculated flows around rectangular cylinders in the range of low Reynolds numbers of 150 to 800 by a finite difference method (FDM) and flows at high Reynolds numbers by a discrete vortex method (DVM), to gain a better insight into the detailed flow characteristics. The results simulated by FDM successfully indicate the existence of the critical range of Reynolds number where the value of Strouhal number changes, accompanied with a drastic change of flow pattern. At high Reynolds numbers, we have computed flows around rectangular cylinders with different side ratios from 0.6 to 8 by DVM and succeeded in a simulation of the phenomenon that the value of Strouhal number abruptly changes when the side ratio of a model is 2.8 or 6, as the critical value. The computed results of flow pattern, base pressure, drag force and Strouhal number show a good agreement with the experimental ones.

A Numerical Analysis of Flow around Rectangular Cylinders

By a finite difference method, flows around cylinders with rectangular cross sections of various width-to-height ratios of 0.4 to 8 have been computed in the range of Reynolds numbers of l00 to 1200. We have successfully simulated some interesting phenomena whereby flow around the cylinder of the B/H ratio of 2 changes to a fully separated flow at a Reynolds number of 800, while for the cylinder of the B/H ratio of 2.8, a fully separated flow changes to an alternate reattachment one at a Reynolds number of 1200 with the lapse of time, two components with different Strouhal frequencies appear in a flow field around the cylinder of the B/H ratio of 6 at a Reynolds number of 800, and the flow pattern critically changes when the B/H ratio is 2.8 and 6 at Reynolds numbers of 500 to 1200. It is clarified by a numerical simulation that the component with a high Strouhal frequency is induced by vortices separated from the trailing edges and that the low Strouhal component is due to the oscillation of flow over the side walls accompanied by a movement of separation bubbles. Finally, the computed results of flow patterns, base pressure, drag force and Strouhal number show a good agreement with the experiments.

A numerical analysis of flow around rectangular cylinders.

By a finite difference method, flows around cylinders with rectangular cross sections of various width-to-height ratios of 0.4 to 8 have been computed in the range of Reynolds numbers of l00 to 1200. We have successfully simulated some interesting phenomena whereby flow around the cylinder of the B/H ratio of 2 changes to a fully separated flow at a Reynolds number of 800, while for the cylinder of the B/H ratio of 2.8, a fully separated flow changes to an alternate reattachment one at a Reynolds number of 1200 with the lapse of time, two components with different Strouhal frequencies appear in a flow field around the cylinder of the B/H ratio of 6 at a Reynolds number of 800, and the flow pattern critically changes when the B/H ratio is 2.8 and 6 at Reynolds numbers of 500 to 1200. It is clarified by a numerical simulation that the component with a high Strouhal frequency is induced by vortices separated from the trailing edges and that the low Strouhal component is due to the oscillation of flow over the side walls accompanied by a movement of separation bubbles. Finally, the computed results of flow patterns, base pressure, drag force and Strouhal number show a good agreement with the experiments.

Viscous attenuation of acoustic waves in suspensions

A model for attenuation of acoustic waves in suspensions is proposed that includes an energy loss due to viscous fluid flow around spherical particles. The expression for the complex wavenumber is developed by considering the partial pressures acting on the solid and fluid phases of the suspension. This is shown to be equivalent to the results of the Biot theory for porous media in the limiting case where the frame moduli vanish. Unlike earlier applications of the limiting case Biot theory, however, a value for the attenuation coefficient is developed from the Stokes flow drag force on a sphere instead of attempting to apply a permeability value to a suspension. Accurate modeling of observed phase velocities from suspensions of spherical polystyrene particles in water and oil and successful inversion for kaolinite properties using attenuation and velocity data from kaolinite suspensions at 100 kHz show that this viscous dissipation model is a good representation of the effects controlling the propagation of acoustic waves in these suspensions. The viscous effects are shown to be significant for only a limited range of solid concentration and frequency by the reduced accuracy of the model for attenuation in a kaolinite suspension at 1 MHz.

Creeping flow of dilute polymer solutions past cylinders and spheres

A dilute polymer solution is modelled as a suspension of dumbbells with finite extensibility. Time-dependent numerical calculations are performed of flow part cylindrical and spherical surfaces at low Reynolds number. A finite-difference scheme is employed in which the evolution in time of the dumbbells is followed from an initially unstretched equilibrium. Results are calculated with (i) a no-slip, and (ii) a zero-tangential-stress boundary condition at the body surface. At large Deborah number, D, the polymer is most highly stretched in thin regions of fluid close to and downstream of stagnation points of the flow. The most important region dynamically is found to be at the rear of the obstacle. Numerical refinements in space and time are included in order properly to resolve this fine-scale structure. Numerically stable results are obtained for values of D up to 16, and show that the flow field and drag force on the obstacle tend toward finite values at large D. Experimental measurements of the drag on a falling rigid sphere, and the velocity distribution around it, are compared with the numerical results for the no-slip boundary. Observations of bubble behaviour are discussed in the light of the results for the slip boundary.