Kyoji Yamamoto

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.

Thermophoresis of a spherical particle in a rarefied gas of a transition regime

A theoretical study is made of thermophoresis of a solid sphere in a rarefied gas in which a uniform temperature gradient and a uniform velocity at infinity exist. The analysis is carried out on the basis of the linearized Bhatnager–Gross–Krook (BGK) equation, from which simultaneous integral equations for the density, flow velocity, and temperature are derived. These equations are solved numerically over a wide range of Knudsen numbers covering the area from the slip flow to the nearly free molecular flow. A formula for the variation of the thermophoretic force acting on the sphere versus the Knudsen number is obtained for any value of thermal conductivity of the sphere when there is no imposed flow at infinity. The thermophoretic velocity of a suspended sphere in a gas is also calculated. The flow patterns as well as the distributions of temperature are shown.

Experimental study of the flow in a helical circular tube

The effect of torsion on the flow in a helical tube of circular cross-section is experimentally investigated over a range of Reynolds numbers from about 500 to 20000. Three cases of dimensionless curvature δ were studied, i.e. δ=0.01, 0.05 and 0.1. The torsional parameter β0, which is defined as with dimensionless torsion τ, was considered for seven cases between 0.45 and 1.72. The results reveal rather large effect of torsion on the flow: the friction factor of the flow at a fixed δ deviates from that of the toroidally curved tube without torsion as β0 increases, and it decreases toward that of the straight tube as β0 further increases. It is also found that the torsion has a destabilizing effect on the flow. The critical Reynolds number at the onset of turbulence varies with β0 and has a minimum at β0 ⋍ 1.3. The minimum critical Reynolds number at δ = 0.1 is about 800.

Characteristics of reflected gas molecules at a solid surface

The Couette flow and a thermal problem of a rarefied nitrogen gas between two platinum walls are considered to investigate the characteristics of the reflected gas molecule at a solid surface. The analysis is based on the molecular dynamics (MD) method for the gas-wall interaction together with the direct simulation Monte-Carlo (DSMC) method for the motion of gas molecules. The accommodation coefficients of momentum, translational, and rotational energies of the molecule are obtained. The velocity and rotational energy distributions of the molecule at the wall surface are also obtained. It is found that the Maxwell-type distribution function consisting of specular and diffuse reflections well describes the distribution function of the reflected molecules if the accommodation coefficient involved is chosen properly. It is also found that the flow and temperature fields subject to the Maxwell-type reflection conditions decomposed into each direction of the space coordinates result in good agreements with th...

Visualization of the flow in a helical pipe

The secondary flow structure in a helical pipe with large torsion is investigated by using a numerical calculation of a fluid particle trajectory and an experiment using a smoke visualization technique. Good agreement is obtained between the experiment and the numerical calculation. The secondary flow in a cross-section is transformed from a two counter-rotating vortices structure to a one-recirculation structure with increase of the torsion of the pipe at a constant Dean number. The line dividing two vortices varies its direction from horizontal to vertical as the torsion increases.

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.

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.

Natural Convection about a Heated Sphere in a Porous Medium

The natural convection about a heated sphere in an unbounded region of porous medium is studied theoretically when the induced flow by buoyancy is slow and hence conduction dominates over convection. A uniformly valid asymptotic solution is obtained by straightforward expansion in terms of a small parameter which represents the effect of convection. It is shown that the effect of the convection of the heat flux from the sphere is of the order of square of the small parameter.

Flow through a Porous Wall with Convective Acceleration

This paper deals with the flow in very porous media when the convective acceleration of the flow cannot be neglected. The governing equations are taken to be a generalized Darcys law which takes the convection term into account in the porous region and Eulers equation in the pure fluid region. Two types of flow are investigated in detail: One is a one-dimensional flow streaming into or out of a plane porous wall with a tangential component of velocity to the surface and the other is a two-dimensional stagnation point flow through a porous wall. It is found that vorticity is created when the flow crosses the surface of the wall obliquely. It is also shown that there may be the case in which the usual Darcys law is inaccurate to describe the flow even when the permeability of the porous medium is very small.

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.