Predicting Mean Flow Through an Array of Cylinders

The present paper develops a new framework to predict the mean flow through an array of cylinders in which the flow around the array (array-scale) and the flow around individual cylinders (element-scale) are modeled separately using actuator disc theory and empirical drag models respectively, and then coupled through the net drag force. Applying this framework only requires knowledge of the array geometry and incident flow. The framework is validated using high-fidelity direct numerical simulations for arrays of between 7 and 109 cylinders having different arrangements (staggered, concentric, random) and bounding shapes (circular, square) in both two- and three-dimensional flows. In general, the framework outperforms existing models which require calibration and are only valid for part of the practical parameter space. The demonstrated scale separation suggests different combinations of element-scale and array-scale models/theories may be used for other arrangements of bluff bodies. The temporally and spatially averaged velocity, or mean flow, within an array of cylinders is important for many practical applications including, for example, estimating the rates of sediment transport and nutrient uptake within a patch of aquatic vegetation, the hydrodynamic forces on offshore structures, and the efficiency of power generation with a turbine farm. However, a general predictive tool for mean flow is currently lacking. To develop this predictive capacity, this study uses the idea of scale separation to integrate models from different research fields, including the actuator disc theory originally developed for design of turbines and propellers, and element-scale drag models initially proposed for aquatic vegetated flows, to develop a unifying, predictive, analytical framework to estimate the mean flow. The framework is validated using high-fidelity direct numerical simulations of arrays of cylinders with different arrangements (staggered, concentric, random) and array shapes (square, circular). With only knowledge of the array geometry and incident flow, the framework predicts the mean flow exceptionally well across a wide range of practical flow conditions. This leads to a step-change in our ability to predict the fraction of incoming flow passing through a porous array, hydrodynamic load on offshore structures, and sediment flux within aquatic vegetation systems when combined with bed load transport models. The framework could be an important guide for coastal and riverine restoration projects using aquatic vegetation and the design of offshore structures and turbine farms. A predictive framework based on an idea of scale separation is proposed for the mean velocity of the flow passing through an array of cylinders The framework is versatile, being applicable for a wide range of practically meaningful cylinder arrangements, array shapes and array flow blockages High-fidelity, three-dimensional direct numerical simulations are employed to investigate flow through the array of cylinders and validate the new predictive framework