A stochastic method to account for the ambient turbulence in Lagrangian Vortex computations |
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| Institution: | 1. Normandie Univ, UNILEHAVRE, CNRS, LOMC, 76600 Le Havre, France;2. IFREMER, Institut Français pour la Recherche et l’Exploitation de la Mer Boulogne-Sur-Mer, France;3. Normandie Univ, INSA Rouen, LMN, 76000 Rouen, France;1. Department of Basic and Applied Sciences, Punjabi University, Patiala, Punjab, India;2. Kurukshetra University Kurukshetra, India;1. Department of Mathematics, College of Arts and Science in Wadi Addawasir, Prince Sattam Bin, Abdulaziz University, P.O. Box 54, Wadi Addawasir 11991, Saudi Arabia;2. Department of Basic Sciences, Modern Academy for Engineering and Technology,Egypt;3. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt;1. Industrial Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, PO Box: 91775-111, Mashhad, Iran;2. Department of Mechanics, Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia;1. Department of Astronautic Science and Mechanics, Harbin Institute of Technology, Harbin 150001, China;2. College of Mathematics, Sichuan University, Chengdu 610043, China;1. Center of Materials Science and Optoelectronics Engineering, College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China;2. Qiushi Honors College, Tianjin University, Tian jin 300350, China;3. McGill Metals Processing Centre, McGill University, Montreal, Quebec H3A 2B2 Canada |
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| Abstract: | This paper describes a detailed implementation of the Synthetic Eddy Method (SEM) initially presented in Jarrin et al. (2006) applied to the Lagrangian Vortex simulation. While the treatment of turbulent diffusion is already extensively covered in scientific literature, this is one of the first attempts to represent ambient turbulence in a fully Lagrangian framework. This implementation is well suited to the integration of PSE (Particle Strength Exchange) or DVM (Diffusion Velocity Method), often used to account for molecular and turbulent diffusion in Lagrangian simulations. The adaptation and implementation of the SEM into a Lagrangian method using the PSE diffusion model is presented, and the turbulent velocity fields produced by this method are then analysed. In this adaptation, SEM turbulent structures are simply advected, without stretching or diffusion of their own, over the flow domain. This implementation proves its ability to produce turbulent velocity fields in accordance with any desired turbulent flow parameters. As the SEM is a purely mathematical and stochastic model, turbulent spectra and turbulent length scales are also investigated. With the addition of variation in the turbulent structures sizes, a satisfying representation of turbulent spectra is recovered, and a linear relation is obtained between the turbulent structures sizes and the Taylor macroscale. Lastly, the model is applied to the computation of a tidal turbine wake for different ambient turbulence levels, demonstrating the ability of this new implementation to emulate experimentally observed tendencies. |
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