A Simulation Study on von Karman Vortex Shedding with Navier-Stokes and Shallow-Water Models

Shin-Jye Liang; Shih-Huang Wu; Wei-Ting Chao

doi:10.46604/emsi.2023.11974

Authors

Shin-Jye Liang Department of Marine Environmental Informatics, National Taiwan Ocean University, Keelung, Taiwan
Shih-Huang Wu Department of Marine Environmental Informatics, National Taiwan Ocean University, Keelung, Taiwan
Wei-Ting Chao Center of Excellence for Ocean Engineering, National Taiwan Ocean University; Keelung, Taiwan

DOI:

https://doi.org/10.46604/emsi.2023.11974

Keywords:

Navier-Stokes equations, Reynolds number, Shallow-Water equations, Strouhal number, von Karman vortex street

Abstract

This study aims to investigate the advantages of employing numerical models based on Shallow-water equations for simulating von Karman vortex shedding. Furthermore, a comparative analysis with Navier-Stokes equations will be conducted to assess their effectiveness. In addition to Reynolds number (Re), Froude number (Fr), relevant to water depth, plays an important role in the Shallow-Water modeling of the von Karman vortex. In this study, simulations of 2D von Karman vortex shedding are performed using the Navier-Stokes model and Shallow-Water model, employing the least-squares finite-element method for space discretization and θ-method for time integration. The computed vortices characteristics, including the recirculation zone behind the cylinder, vortices size, and frequency, are presented. In the Navier-Stokes modeling, the computed results indicate that the size of vortices in space decreases and the Strouhal number increases as Re increases. In the Shallow-Water modeling for the same Re condition, the size of vortices increases and the Strouhal number decreases as Fr increases.

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