This paper treats the numerical calculation of a steady two-dimensional viscous flow past a flexible membrane. Both edges of the membrane are fixed in the flow and its chord is set normal to the flow. The numerical ca...This paper treats the numerical calculation of a steady two-dimensional viscous flow past a flexible membrane. Both edges of the membrane are fixed in the flow and its chord is set normal to the flow. The numerical calculations of the Navier-Stokes equation based on a finite difference method and a relaxation method are carried out for several values of the membrane tension in cases when the Reynolds numbers are 5, 10 and 20. It is found that the membrane tension has a minimum value below which there is no steady shape of the membrane. Two different shapes of the membrane are possible at a given value of tension: the one is of small deformation, while the other a large deformation. There appear twin vortices in the concave region of the membrane shape if its deformation increases to a certain extent.展开更多
文摘This paper treats the numerical calculation of a steady two-dimensional viscous flow past a flexible membrane. Both edges of the membrane are fixed in the flow and its chord is set normal to the flow. The numerical calculations of the Navier-Stokes equation based on a finite difference method and a relaxation method are carried out for several values of the membrane tension in cases when the Reynolds numbers are 5, 10 and 20. It is found that the membrane tension has a minimum value below which there is no steady shape of the membrane. Two different shapes of the membrane are possible at a given value of tension: the one is of small deformation, while the other a large deformation. There appear twin vortices in the concave region of the membrane shape if its deformation increases to a certain extent.
