Modelling of flow past long cylindrical structures

Abstract

Turbulent flows are fundamental in engineering and the environment, but their chaotic and three-dimensional (3-D) nature makes them computationally expensive to simulate. In this work, a dimensionality reduction technique is investigated to exploit flows presenting an homogeneous direction, such as wake flows of extruded two-dimensional (2-D) geometries. First, we examine the effect of the homogeneous direction span on the wake turbulence dynamics of incompressible flow past a circular cylinder at Re = 104 . It is found that the presence of a solid wall induces 3-D structures even in highly constricted domains. The 3-D structures are rapidly two-dimensionalised by the large-scale K´arm´an vortices if the cylinder span is 50% of the diameter or less, as a result of the span being shorter than the natural wake Mode B instability wavelength. It is also observed that 2-D and 3-D turbulence dynamics can coexist at certain points in the wake depending on the domain geometric anisotropy. With this physical understanding, a 2-D data-driven model that incorporates 3-D effects, as found in the 3-D wake flow, is presented. The 2-D model is derived from a novel flow decomposition based on a local spanwise average of the flow, yielding the spanwise-averaged Navier–Stokes (SANS) equations. The 3-D effects included in the SANS equations are in the form of spanwise-stress residual (SSR) terms. The inclusion of the SSR terms in 2-D systems modifies the flow dynamics from standard 2-D Navier–Stokes to spanwise-averaged dynamics. A machine-learning (ML) model is employed to provide closure to the SANS equations. In the a-priori framework, the ML model yields accurate predictions of the SSR terms, in contrast to a standard eddy-viscosity model which completely fails to capture the closure term structures. The trained ML model is also assessed for different Reynolds regimes and body shapes to the training case where, despite some discrepancies in the shear-layer region, high correlation values are still observed. In the a-posteriori analysis, while we find evidence of known stability issues with long-time ML predictions for dynamical systems, the closed SANS equations are still capable of predicting wake metrics and induced forces with errors from 1-10%. This results in approximately an order of magnitude improvement over standard 2-D simulations while reducing the computational cost of 3-D simulations by 99.5%.

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ORCID for Bernat Font: orcid.org/0000-0002-2136-3068

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