A fast three-dimensional vortex method for unsteady wake calculations

In the array design of the vertical axis wind turbines (VAWT), the wake effect of the upstream VAWT on the downstream VAWT needs to be considered. In order to simulate the velocity distribution of a VAWT wake rapidly, a new two-dimensional numerical method is proposed, which can make the array design easier and faster. In this new approach, the finite vortex method and vortex particle method are combined to simulate the generation and evolution of the vortex, respectively, the fast multipole method (FMM) is used to accelerate the calculation. Based on a characteristic of the VAWT wake, that is, the velocity distribution can be fitted into a power-law function, a new correction model is introduced to correct the three-dimensional effect of the VAWT wake. Finally, the simulation results can be approximated to the published experimental results in the first-order. As a new numerical method to simulate the complex VAWT wake, this paper proves the feasibility of the method and makes a preliminary validation. This method is not used to simulate the complex three-dimensional turbulent evolution but to simulate the velocity distribution quickly and relatively accurately, which meets the requirement for rapid simulation in the preliminary array design.

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Derivation of Vortex Method from Navier-Stokes Equations. Three-Dimensional Flow.

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B ◽

10.1299/kikaib.61.4257 ◽

1995 ◽

Vol 61 (592) ◽

pp. 4257-4262

Author(s):

Tomoya Nakajima ◽

Teruhiko Kida

Keyword(s):

Stokes Equations ◽

Three Dimensional ◽

Vortex Method ◽

Navier Stokes ◽

Three Dimensional Flow ◽

Navier Stokes Equations ◽

Dimensional Flow

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A New Three-Dimensional Vortex Method

Lecture Notes in Engineering - Supercomputers and Fluid Dynamics ◽

10.1007/978-3-642-82908-6_6 ◽

1986 ◽

pp. 62-76

Author(s):

S. Shirayama ◽

K. Kuwahara

Keyword(s):

Three Dimensional ◽

Vortex Method

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The role of rotary motion on vortices in reverse flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.728 ◽

2019 ◽

Vol 880 ◽

pp. 723-742 ◽

Cited By ~ 1

Author(s):

Luke R. Smith ◽

Yong Su Jung ◽

James D. Baeder ◽

Anya R. Jones

Keyword(s):

Vortex Dynamics ◽

Reverse Flow ◽

Three Dimensional ◽

Flow Region ◽

Vortex Method ◽

Forward Flight ◽

Vorticity Transport ◽

Rotating Wing ◽

Rotary Wing

The physics of a rotary wing in forward flight are highly complex, particularly when flow separation is involved. The purpose of this work is to assess the role of three-dimensional (3-D) vortex dynamics, with a focus on Coriolis forces, in the evolution of vortices in the reverse flow region of a rotating wing. High-fidelity numerical simulations were performed to recreate the flow about a representative rotating wing in forward flight. A vorticity transport analysis was performed to quantify and compare the magnitudes of 2-D flow physics, vortex tilting and Coriolis effects in the resulting flow fields. Three-dimensional vortex dynamics was found to have a very small impact on the growth and behaviour of vortices in the reverse flow region; in fact, the rate of vortex growth was successfully modelled using a simple 2-D vortex method. The small role of 3-D physics was attributed to the Coriolis and vortex tilting terms being approximately equal and opposite to one another. This ultimately lead to vortex behaviour that more closely resembled a surging wing as opposed to a conventional rotating wing, a feature unique to the reverse flow region.

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Numerical and Experimental Study of Flow Field between the Main Hull and Demi-Hull of a Trimaran

Journal of Marine Science and Engineering ◽

10.3390/jmse8120975 ◽

2020 ◽

Vol 8 (12) ◽

pp. 975

Author(s):

Cong Sun ◽

Chunyu Guo ◽

Chao Wang ◽

Lianzhou Wang ◽

Jianfeng Lin

Keyword(s):

Flow Field ◽

High Speed ◽

Light Transmission ◽

Transmission Rate ◽

Laser Sheet ◽

Three Dimensional ◽

Wake Flow ◽

Navier Stokes ◽

Unsteady Wake ◽

Real Flow

The interactions between the main hull and demi-hull of trimarans have been arousing increasing attention, and detailed circumferential flow fields greatly influence trimaran research. In this research, the unsteady wake flow field of a trimaran was obtained by Reynolds-Averaged Navier-Stokes (RANS) equations on the basis of the viscous flow principles with consideration of the heaving and pitching of the trimaran. Then, we designed an experimental method based on particle-image velocimetry (PIV) and obtained a detailed flow field between the main hull and demi-hull of the trimaran. A trimaran model with one demi-hull made of polycarbonate material with 90% light transmission rate and a refractive index 1.58 (close to that of water 1.33) was manufactured as the experiment sample. Using polycarbonate material, the laser-sheet light-source transmission and high-speed camera recording problems were effectively rectified. Moreover, a nonstandard calibration was added into the PIV flow field measurement system. Then, we established an inverse three-dimensional (3D) distortion coordinate system and obtained the corresponding coordinates by using optics calculations. Further, the PIV system spatial mapping was corrected, and the real flow field was obtained. The simulation results were highly consistent with the experimental data, which showed the methods established in this study provided a strong reference for obtaining the detailed flow field information between the main hull and demi-hull of trimarans.

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Application of a Vortex Method to Fluid Dynamics in Sports Science

Volume 1: Symposia, Parts A and B ◽

10.1115/fedsm2007-37066 ◽

2007 ◽

Cited By ~ 1

Author(s):

Kyoji Kamemoto ◽

Akira Ojima

Keyword(s):

Fluid Dynamics ◽

Three Dimensional ◽

Vortex Method ◽

Mathematical Treatment ◽

Sports Science ◽

Lagrangian Simulation ◽

Eddy Simulation ◽

Flow Features ◽

Vortex Element ◽

Basic Equations

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.

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Vortex Simulation for Behavior of Solid Particles Falling in Air

ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 1, Symposia – Parts A, B, C, and D ◽

10.1115/ajk2011-12019 ◽

2011 ◽

Author(s):

Hisanori Yagami ◽

Tomomi Uchiyama

Keyword(s):

Volume Fraction ◽

Particle Volume Fraction ◽

Air Flow ◽

Three Dimensional ◽

Particle Diameter ◽

Vortex Method ◽

Solid Particles ◽

Particle Volume ◽

Two Phase ◽

Spherical Region

The behavior of small solid particles falling in an unbounded air is simulated. The particles, initially arranged within a spherical region in a quiescent air, are made to fall, and their fall induces the air flow around them, resulting in the gas-particle two-phase flow. The particle diameter and density are 1 mm and 7.7 kg/m3 respectively. A three-dimensional vortex method proposed by one of the authors is applied. The simulation demonstrates that the particles are accelerated by the induced downward air flow just after the commencement of their fall. It also highlights that the particles are whirled up by a vortex ring produced around the downward air flow after the acceleration. The effect of the particle volume fraction at the commencement of the fall is also explored.

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Simulation of Artificial Turbulence by the Vortex Method

Computational Technologies for Fluid/Thermal/Structural/Chemical Systems With Industrial Applications, Volume 1 ◽

10.1115/pvp2002-1536 ◽

2002 ◽

Author(s):

Yoshifumi Ogami ◽

Kazuie Nishiwaki ◽

Yoshinobu Yoshihara

Keyword(s):

Turbulent Flows ◽

Three Dimensional ◽

Vortex Method ◽

Energy Spectra ◽

System Of Nonlinear Equations ◽

Vortex Methods ◽

Velocity Fluctuations ◽

Integral Scales ◽

Relative Errors ◽

Les Model

First, a simple and accurate numerical method is presented to produce velocity fluctuations that are determined by the prescribed physical quantities and qualities of turbulence such as longitudinal and lateral spectra, and integral scales. The fluctuations are obtained by solving a system of nonlinear equations that are derived from the equations of energy spectra and of root mean square of the fluctuations. This method requires as many computer memories and computations as one-dimensional case even for the three dimensional calculations. It is shown that there is a strong resemblance of the simulated velocity fluctuations and experimental data. The energy spectra of these velocity fluctuations are quite accurate with less than 0.01% relative errors to the prescribed spectra. Secondly, these solutions are used to examine the capability of the vortex methods to produce turbulent flows with the prescribed parameters. It is found that although the energy spectra by the vortex method scatter to some extent, they are distributed along the prescribed spectra. It can be said that the vortex methods are able to simulate the target turbulence fairly well. Also it is found that the solutions with the LES model increase and deviate from the target spectrum at the higher frequency regions. This may suggest the nonessentiality of the LES model for the vortex method.

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