Fei He

Extracting energy from a flow is a fundamental problem in fluid mechanics of significant practical engineering importance. To generate power from a flow, a resistance must be applied. Open questions remain on how to optimise this resistance, particularly for non-uniform flows. In this paper, we extend the multi-streamtube theory to address this gap. The extended theory allows for an arbitrary resistance distribution across an actuator strip (representing either a single turbine or an array of turbines) and is formulated as a power-coefficient maximisation problem to determine the optimal resistance distribution for both uniform and non-uniform flows. When the undisturbed kinetic energy flux projected onto the strip’s frontal area is used to normalise the extracted power, a uniform resistance maximises the resulting power coefficient for both uniform and non-uniform incoming flows. When the upstream kinetic energy flux of the flow through the strip is used for normalisation, the same optimisation result is obtained for uniform incoming flow, regardless of the assumed resistance distribution. However, for a non-uniform incoming flow, the optimal resistance distribution is non-uniform, with greater resistance applied in regions of higher velocity within the shear flow. This different optimisation result for non-uniform flow arises physically because the kinetic energy flux used in the second power-coefficient definition depends on the resistance applied across the strip, whereas the first does not. Two-dimensional direct numerical simulations are employed to examine the applicability and limitations of the multi-streamtube theory. The numerical and optimisation results together demonstrate that optimising the resistance distribution requires accounting not only for the non-uniformity of the incoming flow but also for the local flow variability around the strip.

Using direct numerical simulations, this paper presents the first comprehensive investigation of the three-dimensional flow characteristics for a large array of cylinders in steady current, by systematically varying the array arrangement through the number of cylinders in the range N = 1–109, gap ratio G/d (1.2–14.7, G is the center-to-center distance between two adjacent cylinders, d is the cylinder diameter), array-to-element diameter ratio D/d (7.3–48.6, D is the array diameter), incident flow angle θ (0°, 90°), and the uniformity of the array. The three-dimensional flow field both within and behind the array is shown varying widely with gap ratio, array-to-element diameter ratio, incident flow angle, and the uniformity of the array, which demonstrates the influence of array arrangement. Physical mechanisms for the effects of G/d, D/d, θ and non-uniformity are interpreted. The arrangement effects become most critical in the intermediate range of flow blockage parameter ΓD= 0.8–3 (ΓD=aD/1−ϕ, where a is the frontal area per unit volume, and ϕ is the solid volume fraction). The flow three-dimensionality arises from the wakes of individual cylinders (element wake) and the array wake behind the array at low and high values of ΓD, respectively, and from both wakes at the intermediate range of ΓD. A transition from element-wake into array-wake three-dimensionality occurs as array shear layers are susceptible to shear layer instability while quasi-two-dimensional spanwise vortices form within the array. Across arrangements modeled, it is confirmed that the extent of flow three-dimensionality is, to first order, controlled by flow blockage parameter as this parameter controls the bleeding velocity that largely determines the extent of three-dimensionality.

Although previous studies have demonstrated the influence of spanwise length on the flow past an isolated cylinder, the effect of spanwise length on the flow past multiple cylinders has not been investigated, and no guidance exists on the appropriate choice of spanwise length for such configurations in numerical simulations. This gap motivates the present study, which employs three-dimensional direct numerical simulations, for the first time, to examine the influence of spanwise length on the flow past a line of 2–11 cylinders at a Reynolds number of 200 (Red=U∞d/υ, where U∞ is the velocity upstream of the cylinder, d is the cylinder diameter, and υ is the fluid viscosity). The spanwise length Lz is varied in the range of 1–48d. Significant variations in flow and force characteristics are observed as the spanwise length changes within the range. Varying the spanwise length can significantly alter wake transitions along the line of cylinders. While three-dimensionality in the system is entirely suppressed for Lz≤ 2d, fully developed three-dimensional flow features, including mode A and vortex dislocations, are captured for Lz≥ 16d. This critical length of 16d is found to be independent of the number of cylinders. Furthermore, applying periodic boundary conditions in the spanwise direction with a spanwise length that is not an integer multiple of the characteristic length scale of mode A structures (4d for an isolated cylinder) can introduce artificial disturbances into the system, leading to unphysical flow irregularities for a shorter spanwise domain (Lz< 16d) where natural vortex dislocations are suppressed. Based on numerical convergence and computational cost considerations, a spanwise length of at least 16d is recommended for accurately studying the flow past a line of cylinders at Red≈ 200.

Predicting hydrodynamic forces on an obliquely oscillating riser in current poses challenges, especially as existing practices rely on a linear summation of forces induced by the current and riser motion, which overlooks crucial nonlinear interactions. The present study, using three-dimensional numerical simulations at a fixed Reynolds number of 500 and a small oscillation amplitude of 0.4 cylinder diameters, evaluates these nonlinear effects over a range of oscillation wavelengths (λ* from 1.0 to 25.0) and orientation angles (θ from 0° to 90°). The results reveal significant nonlinear interactions at intermediate λ*=1.5–10, forming multiple resonant wake states that either amplify or reduce the hydrodynamic forces. For instance, time-averaged force coefficients in inline and transverse directions increase by more than 2.5 times compared to the no-oscillation case, while the root-mean-squared force coefficient in the motion direction can drop to a minimum (0.1–0.3) at λ*=4–10. Physical explanations on the influences of inclination angle on the wake dynamics and hydrodynamic force coefficients are provided. These findings indicate the inadequacy of linear summation method and propose a new framework incorporating data at 0°, 45°, and 90°, offering improved predictive capability for oblique angles.

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.