Tomoya Nakajima

Asymptotic solutions for two-dimensional low Reynolds number flow around an impulsively started circular cylinder

The unsteady flow field of an incompressible viscous fluid around an impulsively started cylinder with slow motion is studied in detail. Integral expressions are derived from the nonlinear vorticity equation, and are solved by the method of matched asymptotic expansions. To complete the matching process five regions are necessary and their regions are essentially governed by the following relations: (i) the initial flow is unsteady Stokes flow (I), (ii) the early transient flow near the cylinder is steady Stokes flow (II), but the far-field flow is unsteady Stokes flow (III), so that Stokes-Oseen-like matching is necessary, and (iii) as time increases the inertia terms become significant far downstream; thus the far flow is unsteady Oseen flow (IV), but the flow near the cylinder is steady Stokes flow (V), so that the matching of the Stokes-Oseen equations is necessary. The asymptotic analytical solutions are given for five flow fields around a circular cylinder. Also presented are the drag coefficient, the vorticity, and the streamline. The drag coefficient is verified quantitatively by comparing with earlier theories of the initial flow and the steady flow.

Numerical Simulation of Gas-Liquid Two-Phase Flow in a Horizontally Placed Hydrophobic Rectangular Channel (Part 2, Influence of Abrupt Contraction)

Abstract This paper computationally visualizes two-phase flow patterns through a horizontally placed hydrophilic or hydrophobic rectangular channel with an abrupt contraction. The rectangular duct used in this study has a thickness narrower than the Laplace constant so that the surface tension governs the fluid system rather than the inertia force. In particular, the computed bubble behavior at the abrupt contraction seemed to be a similar nature against the preliminary experimental result.

Two-Dimensiona flow Near Nozzle of Air-Cusion Pad. Discrete Vortex Method.

The purpose of the present paper is to determine numerically the effect of the shape of the nozzle of the air-cushion pad on the flow behavior near the nozzle. In the present paper, a new technique applied to the vortex method is proposed for case of calculations of various nozzle shapes : the fundamental shape of the nozzle is mapped conformally and the panel method is applied to various shapes of the nozzle exit in the mapping plane. The numerical calculation is compared with previous experimental results. Numerical results show that the velocity distribution at the nozzle exit agrees fairly well with experimental one and the global feature of streamlines is similar to experimental ones. The pressure distribution on the surface of strips oscillates remarkably due to the existence of discrete vortices near their surface, but it is pointed out that the flow is steady, in a sense of time average, except a few early stages and the pressure gap between the cushion chamber and the outside of the jet is shown.