Michihisa Tsutahara

Fluid dynamic effects of grooves on circular cylinder surface

It is shown that a groove on the surface of a circular cylinder affects movement of the separation point backward and reduces draw even at Reynolds numbers of about a few thousand. Several types of circular-arc cross-section grooves are studied using flow visualisations and numerical simulations. Whether these grooves are effective depends strongly on their positions, and the most effective positions are about 80 deg, measured from the foremost point. When they are effective, cavity flows are developed inside the grooves. This effect corresponds to that of dimples on golf balls and will explain unique characteristics of the drag curve.

Wake of a rotating circular cylinder

Flow about a rotating circular cylinder is one of the classical problems of fluid mechanics. The Karman vortex street in the wake of a still circular cylinder is one of the most well-known phenomena in fluid mechanics. It is of interest how the vortex street is affected by the rotation of the cylinder. It is so far known by experiments that the Strouhal number of vortex shedding becomes larger as the rotating speed becomes higher and that the meandering of the wake due to the Karman vortex street disappears when the rotating speed of the cylinder is high enough, that is, when the spin parameter, which is defined as the ratio of the peripheral speed of the cylinder surface of the uniform velocity, is about 2. The Reynolds number in which these experiments have been done is of order 104-105 so that it is rather high. Kimura and Tsutahara simulated these phenomena by the discrete vortex method. Their simulation corresponds to very high Reynolds number flows because the diffusion of the vorticity is neglected. For a rather wide range of the Reynolds number, the initial stage of the flows about rotating circular cylinders has been studied numerically and experimentally by Badr and Dennis and Badr and Coutanceau. Who state that at a Reynolds number of 103 a periodic variation appears in the time variation of the lift for the flow at the spin parameter of unity, but no periodic variation appears for the flow at a spin parameter of 3. However, the effect of the Reynolds number on these phenomena has never been explicitly described. In this study, the effect of the rotation of the cylinder and that of the Reynolds number are investigated by experiments and numerical simulations.

Transverse instability of surface solitary waves

The linear stability of finite-amplitude surface solitary waves with respect to long-wavelength transverse perturbations is examined by asymptotic analysis for small wavenumbers of perturbations. The sufficient condition for the transverse instability is explicitly derived

Numerical analysis of a weak shock wave propagating in a medium using lattice boltzmann method (LBM)

This study introduced a lattice Boltzmann computational scheme capable of modeling thermo hydrodynamic flows with simpler equilibrium particle distribution function compared with other models. The equilibrium particle distribution function is the local Maxwelian equilibrium function in this model, with all the constants uniquely determined. The characteristics of the proposed model is verified by calculation of the sound speeds, and the shock tube problem. In the lattice Boltzmann method,a thermal fluid or compressible fluid model simulates the reflection of a weak shock wave colliding with a sharp wedge having various angles θw. Theoretical results using LBM are satisfactory compared with the experimental result or the TVD.

Numerical simulation of sound generation in a mixing layer by the finite difference lattice Boltzmann method

We simulated aerodynamic sound in a two-dimensional mixing layer using the finite difference lattice Boltzmann method (FDLBM). We introduced a finite difference scheme, called the dispersion relation preserving (DRP) scheme, into the FDLBM to carry out an accurate simulation of aerodynamic problems. The scheme is designed such that the dispersion relation of the finite difference scheme is the same as that of the original partial differential equations and is useful for acoustic simulations. A turbulent flow field was simulated by large-eddy simulation (LES), using the Smagorinsky model, and the results were compared with those from a direct simulation based on the Navier-Stokes equations to confirm the usefulness of this method. The combination of the FDLBM and the DRP scheme was shown to be very effective for direct simulations of aerodynamic sound.

Numerical Analysis of Unsteady Flow in the Weis-Fogh Mechanism by the 3D Discrete Vortex Method With GRAPE3A

The three-dimensional flows in the Weis-Fogh mechanism are studied by flow visualization and numerical simulation by a discrete vortex method. In this mechanism, two wings open, touching their trailing edges (fling), and rotate in opposite directions in the horizontal plane. At the fling stage, the flow separates at the leading edge and the tip of each wing. Then they rotate, and the flow separates also at the trailing edges. The structure of the vortex systems shed from the wings is very complicated and their effect on the forces on the wings have not yet been clarified. Discrete vortex method, especially the vortex stick method, is employed to investigate the vortex structure in the wake of the two wings. The wings are represented by lattice vortices, and the shed vortices are expressed by discrete three-dimensional vortex sticks. in this calculation, the GRAPE3A hardware is used to calculate at high speed the induced velocity of the vortex sticks and the viscous diffusion of fluid is represented by the random walk method. The vortex distributions and the velocity field are calculated. The pressure is estimated by the Bernoulli equation, and the lift and moment on the wing are also obtained.

Evolution of viscous flow around a suddenly rotating circular cylinder in the lattice Boltzmann method

Abstract The lattice Boltzmann method is a numerical scheme in which a fluid is considered to consist of many particles that collide with each other and move on a regular lattice discretizing the space uniformly. In spite of the high ability of numerical accuracy, this method has not been used to simulate the flow around the body with a moving curved surface. In order to study the practical computation in this method, we present a numerical study of the initial development with time of the two-dimensional viscous incompressible flow around a circular cylinder which suddenly starts rotation about its axis with a constant angular velocity ω and translation with a constant speed U from rest. In the boundary condition, the particle distributions at boundaries are determined on the assumption of a state of local equilibrium. The Reynolds numbers are taken as 200 and 500, and the ratios of peripheral velocity to the moving speed of the cylinder are 0.5 and 1.0. The results by this method agree well with numerical ones which Badr and Dennis have obtained through Fourier analysis, and also with experimental results by Coutanceau and Menard.

The finite-difference lattice Boltzmann method and its application in computational aero-acoustics

The application of the finite-difference lattice Boltzmann method in computational aero-acoustics is reviewed, mainly on the basis of the work of the author and his colleagues. Some models of thermal and isothermal fluids are described and the constraints for recovering the Euler equations and the Navier–Stokes equations are described. The arbitrary Lagrangian Eulerian technique is used for high Mach number flows and for simulations of moving bodies. A model of gas–liquid two-phase fluid is introduced in which the density difference is 800 times and the sound velocity difference is 4 times. Some applications of aero-acoustic problems are briefly described and the simultaneous simulation of underwater sound and sound propagating in air is also presented. The difference between the thermal model and the isothermal model is shown in the aero-acoustic problems.

Direct simulation of sound and underwater sound generated by a water drop hitting a water surface using the finite difference lattice Boltzmann method

The sound and underwater sound emitted from a water drop colliding with a water surface are simulated by a new model of the finite difference lattice Boltzmann method. The two-particle immiscible fluid model is modified to simulate sound in the gas phase and underwater simultaneously. In the very early stage after the collision, sounds propagating into the gas and liquid phases are successively detected, and the effects of drop shape and gas bubbles are also observed.

Numerical Prediction of Acoustic Sounds Occurring by the Flow Around a Circular Cylinder

Acoustic sounds generated by uniform flow around a two-dimensional circular cylinder at Re=150 are simulated by applying the finite difference lattice Boltzmann method. A third-order-accurate up-wind scheme is used for the spartial derivatives. A second-order-accurate RungeKutta scheme is also used for time marching. Very small acoustic pressure fluctuation, with same frequency as that of Karman vortex street, is compared with pressure fluctuation around a circular cylinder. The propagation velocity of acoustic sound shows that acoustic approaching the upstream, due to the Doppler effect in uniform flow, slowly propagates. For the downstream, on the other hand, it quickly propagates. It is also apparent that the size of sound pressure is proportional to the central distance τ-1/2 of the circular cylinder.