Fluid flow in a thick torus driven by distributed forces
DOI:
https://doi.org/10.7242/1999-6691/2025.18.4.30Keywords:
curved pipe flow, curved boundary, Navier-Stokes equations, nonlinear dynamics, Dean number, DNS (direct numerical simulation), artificial compressibilityAbstract
In this article, a laminar, steady-state flow of incompressible fluid in a curvilinear channel with a circular cross-section is studied numerically. The influence of the bulk force on the stationary flow is analyzed through the consideration of its three main natural causes: a pressure gradient in the channel, a uniform action of external forces, and an analog of the force generated by the uniform deceleration of a rotating channel (inertia force). The key parameter used to describe flows in a toroidal channel is the Dean number, which takes into account the influence of the channel curvature and flow intensity. Direct numerical simulations at all possible channel curvatures and Reynolds numbers up to 300 showed that to describe all features of flow in thick toroidal channels, it is insufficient to use the Dean number alone. It has been found that the position of the longitudinal velocity maximum depends on the Reynolds number and curvature, and the type of force. At low values of the Reynolds number, that is, less than 40, the maximum may shift towards the outer axis of the torus, whereas at high values, it shifts only away from it. The simulation revealed the splitting of the velocity maximum , as well as the occurrence of a third local maximum ; these effects arise only under a gradient force and at relatively high curvatures. It has been shown that the Dean number is insufficient to fully describe the flow at high curvatures. For the inertial force, the Dean number unambiguously determines the position of the velocity maximum but fails to describe the intensity of the secondary flow at the Reynolds numbers of 50 and higher. At a constant force, the Dean number is applicable only up to certain values of the Reynolds number, while for a pressure gradient, the use of the Dean number is absolutely meaningless. It has been established that the intensity of the secondary flow reaches a maximum at the Reynolds numbers from 50 to 100 (with nondimensionalization performed in this study). In this case the curvature responsible for the occurrence of this maximum depends on the type of force. The obtained results are important for designing systems involving curved channels (e.g., heat exchangers, chemical reactors).
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