Shinichiro Yanase

Dual solutions of the flow through a curved tube

Dual solutions, i.e. two-vortex and four-vortex solutions, and their stability of flow through a slightly curved circular tube are numerically investigated by the spectral method in the range 96 ≤ Dn ≤ 10000, where Dn is the Dean number. It is found that the two-vortex solution is stable in response to any small disturbances, while the four-vortex solution is unstable to asymmetric disturbances. Time evolution of the unsteady four-vortex flow is also studied by a numerical simulation of the Navier-Stokes equation when Dn = 1000. The four-vortex flow eventually turns into a two-vortex flow.

Statistical properties of MHD turbulence and turbulent dynamo

Statistical properties of MHD turbulence and the mechanism of turbulent dynamo are investigated by direct numerical simulations of three‐dimensional MHD equations. It is assumed that the turbulent field has a high symmetry and that the fluid has hyperviscosity and hypermagnetic diffusivity. An external force is exerted on the fluid as kinetic energy and helicity sources. The main concern of the present study is whether magnetic fields of scales comparable to the dominant fluid motions can be generated or not. It is shown that the turbulent dynamo is effective if hypermagnetic diffusivity is smaller than a critical value. The total energy spectrum is close to the k−5/3 power law in the inertial range. The energy transfer between kinetic and magnetic fields is discussed.

Laminar flows through a curved rectangular duct over a wide range of the aspect ratio

The laminar flow in a curved rectangular duct for a range of the aspect ratio 1 ≤ l ≤ 12 is investigated by use of the spectral method. The steady solutions are obtained using the Newton–Raphson method with the symmetry condition. As a result, five branches of steady solutions are found. Linear stability characteristics are also investigated for all the steady solutions. It is found that one steady solution is linearly stable for most of l, but two linearly stable steady solutions exist for a region of small l and there are several intervals of l where there is no linearly stable steady solution. We performed time-evolution calculations with and without the symmetry condition, and observed periodic oscillations with the symmetry condition and aperiodic time evolutions without the symmetric condition. Finally, the present results numerically suggest that what determines which solution is realizable may be the maximum of the momentum transfer in the cross section.

Torsion effect on the flow in a helical pipe

The effect of curvature and torsion on the flow in a helical pipe of circular cross-section is studied numerically by the spectral method. The calculations are carried out for 0 ≤ δ ≤ 0.6, 0 ≤ β0 ≤ 1.4 and 500 ≤ Dn ≤ 2000, where δ is the non-dimensional curvature, β0 the ratio of torsion to square root of curvature, and Dn the Dean number. The results obtained indicate large effects of torsion on the flow: The conventional two-vortex secondary flow is distorted to become almost one single recirculating cell when β0 0.8. The flux through the pipe at the given Dean number and curvature first decreases from that of the toroidally curved pipe as β0 increases from zero, reaches a minimum at β0 ≈ 0.8, and then increases to values larger than that of the toroidally curved pipe. The minimum value decreases as δ increases.

Rotating free-shear flows. Part 2. Numerical simulations

The three-dimensional dynamics of the coherent vortices in periodic planar mixing layers and in wakes subjected to solid-body rotation of axis parallel to the basic vorticity are investigated through direct (DNS) and large-eddy simulations (LES). Initially, the flow is forced by a weak random perturbation superposed on the basic shear, the perturbation being either quasi-two-dimensional (forced transition) or three-dimensional (natural transition). For an initial Rossby number R 0 (i) , based on the vorticity at the inflexion point, of small modulus, the effect of rotation is to always make the flow more two-dimensional, whatever the sense of rotation (cyclonic or anticyclonic). This is in agreement with the Taylor-Proudman theorem. In this case, the longitudinal vortices found in forced transition without rotation are suppressed. It is shown that, in a cyclonic mixing layer, rotation inhibits the growth of three-dimensional perturbations, whatever the value of the Rossby number. This inhibition exists also in the anticyclonic case for |R 0 (i) |≤1. At moderate anticyclonic rotation rates (R 0 (i) 1), the cyclonic side is composed of Kirmin vortices without longitudinal hairpin vortices. Kirmin vortices have disappeared from the anticyclonic side, which behaves like the mixing layer, with intense longitudinal absolute hairpin vortices. Thus, a moderate rotation has produced a dramatic symmetry breaking in the wake topology. Maximum destabilization is still observed for |R 0 (i) |≃2.5, as in the linear theory.

Stability of the flow in a helical tube

The flow in a helical tube of small curvature and its linear stability are theoretically investigated for a wide range of the torsion parameter β0, which is defined as β = λ/√2δ with the dimensionless torsion λ and curvature δ. It is shown that the torsion has a destabilizing effect on the flow. The critical Dean number at the onset of unstable flow first decreases as β0 increases, reaches a minimum at β0 ≈ 1.4, and then increases again. The minimum Dean number is about 600. The stability characteristics obtained are favorably compared with those in the previous experiment by Yamamoto et al., Fluid Dyn. Res. 16, 1995.

On the bifurcation of laminar flows through a curved rectangular tube

Bifurcating solutions are obtained for a flow through a slightly curved tube of rectangular cross-section. An aspect ratio of cross-section, γ, is changed over 1≦γ≦5 with the Dean number fixed to be 100. If γ<3.02, there is only a two-vortex solution. If γ≧3.02, there are dual solutions one of which is a two-vortex solution, the other is a four-vortex solution. Numerical solution of the unsteady Navier-Stokes equation at γ=4.9 shows that a two-vortex solution changes toward a four-vortex solution when it is disturbed by asymmetric disturbances.

Lattice Boltzmann simulation of blood cell behavior at microvascular bifurcations

Lattice Boltzmann simulations of a particulate suspension in plane Poiseuille flow and two-dimensional bifurcation flow are conducted to investigate the blood cell behavior at microvascular bifurcations. The simulation results of Poiseuille flow at a low hematocrit reveal that particles are concentrated between the centerline and the wall. This phenomenon indicates the occurrence of the Segre-Silberberg effect. On the other hand, as the hematocrit increases, this effect disappears and the number of particles flowing near the wall and the centerline increases. In the case of bifurcation flow, at a high bematocrit, the fractional particle flux to a daughter branch is almost similar to the fractional bulk flow to the same branch. However, at a low hematocrit, the fractional particle flux against the fractional bulk flow increases.

Flow Through a Rotating Curved Duct with Square Cross-Section

The incompressible viscous steady flow through a curved duct of square cross-section driven by a pressure gradient along the duct is considered. The rotation of the duct about the centre of the curvature is imposed to investigate the combined effects of rotation (Coriolis force) and curvature (centrifugal force) on the flow. The numerical calculations covering a wide range of rotational speed are carried out for the Dean numbers, D n , of 400, 642 and 800. When the rotation is in the same as the main flow direction, multiple solutions with 2-cell and 4-cell secondary flow patterns are obtained in case of D n =400 and 642, while only 4-cell solution is obtained in case of D n =800. When the rotation is opposite to the main flow direction, the 6-cell secondary flow pattern is obtained for D n =400, 642 and D n =800 with increasing the rotational speed gradually. For all cases, the total flux through the duct has a sharp peak, where the 6-cell pattern appears.

Transition from Steady to Chaotic States of Isothermal and Non-isothermal Flows through a Curved Rectangular Duct

Flows through a curved rectangular duct for the aspect ratio l =2 are numerically studied by use of the spectral method with and without a temperature difference between the vertical outer and inne...