Kyoji Kamemoto

On contribution of advanced vortex element methods toward virtual reality of unsteady vortical flows in the new generation of CFD

The purpose of this paper is to explain the attractive applicability of the advanced vortex element methods and their contribution to the beginning of the new generation of CFD, with introduction of epoch-making application of the methods to simulation of unsteady flows around bluff bodies and virtual operation of fluid machinery. The vortex methods have been developed and applied for analysis of complex, unsteady and vortical flows in relation to problems in a wide range of industries, because they consist of simple algorithm based on physics of flow. Nowadays, applicability of the vortex element methods to various engineering problems has been developed and improved dramatically and it has become encouragingly clear that the vortex methods have so much interesting features that they provide easy-to-handle and completely grid-free Lagrangian calculation of unsteady and vortical flows without use of any RANS type turbulent models. In this paper, the mathematical background and numerical procedure of a vortex method developed by the group of the present author are briefly explained, and topics of calculated flows around bluff bodies, an oscillating airfoil, a swimming fish, virtual operation of fluid machinery (pumps and water turbines) are introduced.

Numerical simulation of flow around a sphere with vortex blobs

Abstract A vortex model of a blob method (which is one of the vortex methods proposed before) is modified to take into account the viscous effect. The modified method was applied to simulation of a flow around a sphere using the Boundary Element Method. The surface of the sphere was represented by the distributed source panels. The continuous distribution of vorticity over the surface of the sphere was replaced by a number of vortex blobs. All the blobs were allowed to flow at their own convective velocities, and the boundary layer separation was expected to be naturally represented by their convective motion. As a result of this calculation, the boundary layer separation from the surface was reasonably simulated in the initial stage of a starting flow.

Interactive flow around two circular cylinders of different diameters at close proximity. Experiment and numerical analysis by vortex method

Experimental investigations and numerical analysis were carried out to clarify the behavior of an interactive flow around two circular cylinders with different diameters. In particular, the reattachment that the separated shear layer from the main cylinder reattaches on the rear surface by Coanda effect was noted. The results obtained were as follows. Intermittency of the reattachment was found in the present numerical calculation, and was confirmed experimentally. The calculated values of time-averaged fluid forces agreed well with those of experiments, and the qualitative characteristics of calculated Strouhal numbers were coincident with those of experiment.

Vortex shedding from an oscillating circular cylinder in a uniform flow

Abstract In this study, the vortex shedding from a circular cylinder in forced oscillation in the direction of a uniform flow was investigated by visualizing water flows around it at Reynolds numbers of 260–2460. It was observed that the frequency of vortex shedding from the oscillating cylinder tends to be equal to n times the cylinders oscillation frequency ( n = 0.5, 1, 2, 3,…), even if the oscillation frequency is smaller than the natural Karman vortex frequency. This tendency can be considered a sort of “lock-in” phenomenon, and its features vary with both oscillation amplitude and Reynolds number. It was also known that flows of vortex shedding wakes in the lock-in states can be classified into three typical patterns depending on the lock-in frequency ratio n ( n = 0.5, 1, 2, 3,…). At the lock-in states of n = 2, 3,…, a set of vortices are shed with shorter and longer periods during one cycle of cylinder oscillation. At the lock-in state of n = 1, a twin vortex street is formed; twin vortices are also formed at n = 0.5, but a Karman vortex street appears instead of the twin vortex street. When the vortex shedding is out of a lock-in state, the flow pattern of the wake becomes very complex. Although the instantaneous vortex shedding frequency varies with the change of relative velocity in one cycle of the cylinder oscillation, the rate of variation of the vortex shedding frequency is greater than that of the relative flow velocity. Even if the oscillation frequency is as small as about 10% of the Karman vortex frequency, the vortex shedding shows a tendency to deviate from the state of so-called quasi-steady vortex shedding.

A Grid-Free Lagrangian Approach of Vortex Method and Particle Trajectory Tracking Method Applied to Internal Fluid-Solid Two-Phase Flows

We have developed a numerical simulation scheme combining a vortex method and a particle trajectory tracking method, which is applicable to internal unsteady two-phase flows. It is a completely grid-free Lagrangian-Lagrangian simulation, which is able to simulate the primary effect of vortical flow on the unsteady particle motion and dispersion. It can handle unsteady high Reynolds number flows. So far, no one has applied this kind of method internal multiphase flows, though many industrial multiphase flows are internal. In this study, internal liquid-solid two-phase flows in a vertical channel and a mixing tee have been calculated by the new method, in which use of the vortex introduction model enables the simulation of the dynamic behavior of separation or reattachment. In the mixing tee, solid particle phenomena such as depositions or particle-wall collisions have been simulated and measured. Numerical results based on simple two-dimensional flow and one-way model show good agreement with the experimental data. The results show that turbulent vortices dominate particle motion. It has been shown that the present method can be useful in the design of industrial multiphase flows with particle mixing, dispersion, deposition, and particle-wall collision because it is possible to simulate the effect of turbulent vortices on the particle motion.

Vortex Method for the Analysis of Complex, Unsteady and Vortical Flows around a Swimming Fish

Although it is well known that the modes of undulatory locomotion of fish swimming provide high speed and high drive efficiency, it is hard to understand the propulsion mechanism of fish directly from living things. In the present study, in order to investigate hydrodynamic characteristics of the swimming modes, numerical simulation of flows around a deforming body of a rainbow trout which belongs to the kind of fish of subcarangiform undulatory swimmers was performed by using a Lagrangian vortex method. In this simulation, the basic configuration of the fish body is modeled with use of a NACA type airfoil, and the mode of undulatory motion is numerically given by a function obtained from observation of actual fish swimming. As a result of the present study, the relation between characteristics of propulsion force acting on the fish body and formation of complex vortex structures are clarified.

Application of a Vortex Method to Fluid Dynamics in Sports Science

This paper describes a pioneering work of practical application of an advanced vortex method in the field of fluid dynamics in sports science. The vortex method developed by the present authors is one of vortex element methods based on the Biot-Savart law, and it is known that the method provides a Lagrangian simulation of unsteady and vortical flows. In this study, in order to examine the applicability of the vortex method, three-dimensional, complex and unsteady flows around an isolated 100 m runner and a ski-jumper were calculated. Basic equations and mathematical treatment of the method are explained in this paper, and calculation conditions and panel data of deforming configuration of the athletes are described. As results of the present study, vortical and unsteady flow features around a runner and a ski-jumper are understood, and unsteady variation of aerodynamic forces corresponding to deformation of body configuration due to athletic motion are calculated. And, it is confirmed that the advanced vortex element method is a promising way to a grid-free Lagrangian large eddy simulation of unsteady and complex flows around dynamic bodies of athletes.Copyright

A GRID-FREE REDISTRIBUTION MODEL FOR A VORTEX METHOD AND TURBULENT FLOW ANALYSIS

This paper presents a new grid-free type of redistribution model for turbulent flow analysis, in which each vortex particle is redistributed into some elements in accordance with its stretching rate. The model is applied to an inclined collision of two vortex rings. Energy spectra are analyzed and compared with existing DNS data and results of experiments by Saddoughi & Veeravalli (1994). The energy cascade and dissipation process are reasonably simulated. In addition, the LES model proposed by Kiya & Izawa (1999) is applied to the proposed redistribution model. The results show that the analyzed energy spectra are in close agreement with the existing DNS data up to high wave number region.

Prediction of Aerodynamic Noise Radiated From a Vertical-Axis Wind Turbine

Unsteady flow field and flow induced noise of vertical axis wind turbine are numerically investigated. The flow field is numerically calculated by the vortex method with core-spreading model. This simulation obtains aerodynamic performance and aerodynamic forces. Aerodynamic noise is also simulated by using Ffowcs Williams-Hawkings equation with compact body and low-Mach number assumptions. Tip speed of rotor blades are not so high, then the contribution of the moving sound source is smaller than that of the dipole sound source. Since the maximum power coefficient of VAWT can be obtained at lower tip-speed ratio compared to the conventional, horizontal axis wind turbines, the aerodynamic noise from vertical axis wind turbine is smaller than that of the conventional wind turbines at the same aerodynamic performance. This result indicates that the vertical axis wind turbines are useful to develop low-noise wind turbines.Copyright

Recent Development of Lagrangian Vortex Method and Its Application into Fluid Machinery and Fluid Engineering

This paper is to introduce recent works of practical applications of vortex methods in the field of fluid machinery and fluid engineering, explaining the mathematical basis of the method based on the Biot-Savart law. It is pointed as one of the most attractive features of the vortex method that the numerical simulation using the method is considered to be a new and simple technique of large eddy simulation, because they consist of simple algorithm based on physics of flow of viscous fluid and it provides a completely grid-free Lagrangian calculation. As typical examples of simulation of complex flows, the internal flow of a mixed-flow pump calculated by the vortex method and the vortical flow around a flexible circular cylinder in a uniform stream which was simulated by a coupled structure and fluid analysis based on FEM and the vortex method are digested.