Universal scaling law in drag-to-thrust wake transition of flapping foils

Reversed von K\'arm\'an streets are responsible for a velocity surplus in the wake of flapping foils, indicating the onset of thrust generation. However, the wake pattern cannot be predicted based solely on the flapping peak-to-peak amplitude $A$ and frequency $f$ because the transition also depends sensitively on other details of the kinematics. In this work we replace $A$ with the cycle-averaged swept trajectory $\mathcal{T}$ of the foil chord-line. Two dimensional simulations are performed for pure heave, pure pitch and a variety of heave-to-pitch coupling. In a phase space of dimensionless $\mathcal{T}-f$ we show that the drag-to-thrust wake transition of all tested modes occurs for a modified Strouhal $St_{\mathcal{T}}\sim 1$. Physically the product $\mathcal{T}\cdot f$ expresses the induced velocity of the foil and indicates that propulsive jets occur when this velocity exceeds $U_{\infty}$. The new metric offers a unique insight into the thrust producing strategies of biological swimmers and flyers alike as it directly connects the wake development to the chosen kinematics enabling a self similar characterisation of flapping foil propulsion.Comment: Rev

Development of turbulent boundary layers past a step change in wall roughness

In this study, the development of a boundary layer past a change in surface roughness (from rough to smooth, R -> S) is examined. Measurements of the flow were made by hot wires, whereas the friction velocity was estimated by Preston tube measurements. By means of a diagnostic plot of the turbulence intensity, it is shown that above the internal layer the flow exhibits characteristics of a rough, wall-bounded flow, whereas near the wall the turbulence intensity is similar to that of an isolated smooth wall. Similarly, viscous scaling of the mean streamwise velocity shows an excessive wake region downstream of the R -> S wall surface change that diminishes with the fetch from the surface change. Above the internal layer a second peak in the streamwise Reynolds stress was associated with the upstream rough-wall flow. Examination of the turbulent spectra revealed the presence of large-scale motions within this region that gradually diminish in strength with increasing distance from the change in surface roughness. The magnitude of the near-wall peak failed to collapse to that of a comparable smooth-wall boundary layer under viscous scaling, however, the wall-normal location of the peak appears to be at y+?15 at all downstream distances. A new mixed scaling is proposed for the near-wall peak based on the corrected wake deficit and the friction velocity. This shows the importance of outer region to the growth of near-wall peak in this non-equilibrium boundary layer

Wind resource assessment in heterogeneous terrain

High-resolution particle image velocimetry data obtained in rough-wall boundary layer experiments are re-analysed to examine the influence of surface roughness heterogeneities on wind resource. Two different types of heterogeneities are examined: (i) surfaces with repeating roughness units of the order of the boundary layer thickness (Placidi & Ganapathisubramani. 2015 J. Fluid Mech.782, 541-566. (doi:10.1017/jfm.2015.552)) and (ii) surfaces with streamwise-aligned elevated strips that mimic adjacent hills and valleys (Vanderwel & Ganapathisubramani. 2015 J. Fluid Mech.774, 1-12. (doi:10.1017/jfm.2015.228)). For the first case, the data show that the power extraction potential is highly dependent on the surface morphology with a variation of up to 20% in the available wind resource across the different surfaces examined. A strong correlation is shown to exist between the frontal and plan solidities of the rough surfaces and the equivalent wind speed, and hence the wind resource potential. These differences are also found in profiles of [Formula: see text] and [Formula: see text] (where U is the streamwise velocity), which act as proxies for thrust and power output. For the second case, the secondary flows that cause low- and high-momentum pathways when the spacing between adjacent hills is beyond a critical value result in significant variations in wind resource availability. Contour maps of [Formula: see text] and [Formula: see text] show a large difference in thrust and power potential (over 50%) between hills and valleys (at a fixed vertical height). These variations do not seem to be present when adjacent hills are close to each other (i.e. when the spacing is much less than the boundary layer thickness). The variance in thrust and power also appears to be significant in the presence of secondary flows. Finally, there are substantial differences in the dispersive and turbulent stresses across the terrain, which could lead to variable fatigue life depending on the placement of the turbines within such heterogeneous terrain. Overall, these results indicate the importance of accounting for heterogeneous terrain when siting individual turbines and wind farms.This article is part of the themed issue 'Wind energy in complex terrains'

Towards decoupling the effects of permeability and roughness on turbulent boundary layers

Boundary layer flow over a realistic porous wall might contain both the effects of wall-permeability and wall-roughness. These two effects are typically examined in the context of a rough-wall flow, i.e., by defining a ``roughness'' length or equivalent to capture the effect of the surface on momentum deficit/drag. In this work, we examine the hypothesis of Esteban et al. (2022), that a turbulent boundary layer over a porous wall could be modelled as a superposition of the roughness effects on the permeability effects by using independently obtained information on permeability and roughness. We carry out wind tunnel experiments at high Reynolds number ($14400 \leq Re_{\tau} \leq 33100$) on various combinations of porous walls where different roughnesses are overlaid over a given permeable wall. Measurements are also conducted on the permeable wall as well as the rough walls independently to obtain the corresponding lengthscales. Analysis of mean flow data across all these measurements suggests that an empirical formulation can be obtained where the momentum deficit ($\Delta U^+$) is modelled as a combination of independently obtained roughness and permeability lengthscales. This formulation assumes the presence of outer-layer similarity across these different surfaces, which is shown to be valid at high Reynolds numbers. Finally, this decoupling approach is equivalent to the area-weighted power-mean of the respective permeability and roughness lengthscales, consistent with the approach recently suggested by Hutchins et al. (2023) to capture the effects of heterogeneous rough surfaces.Comment: Under review for publication in JFM Rapid

Turbulent separation upstream of a forward-facing step

The turbulent flow over a forward-facing step is studied using two-dimensional time-resolved particle image velocimetry. The structure and behaviour of the separation region in front of the step is investigated using conditional averages based on the area of reverse flow present. The relation between the position of the upstream separation and the two-dimensional shape of the separation region is presented. It is shown that when of ‘closed' form, the separation region can become unstable resulting in the ejection of fluid over the corner of the step. The separation region is shown to grow simultaneously in both the wall-normal and streamwise directions, to a point where the maximum extent of the upstream position of separation is limited by the accompanying transfer of mass over the step corner. The conditional averages are traced backwards in time to identify the average behaviour of the boundary-layer displacement thickness leading up to such events. It is shown that these ejections are preceded by the convection of low-velocity regions from upstream, resulting in a three-dimensional interaction within the separation region. The size of the low-velocity regions, and the time scale at which the separation region fluctuates, is shown to be consistent with the large boundary layer structures observed in the literature. Instances of a highly suppressed separation region are accompanied by a steady increase in velocity in the upstream boundary laye

Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers

Experiments were conducted in the fully rough regime on surfaces with large relative roughness height (h/δ ≈ 0.1, where h is the roughness height and δ is the boundary layer thickness). The surfaces were generated by distributed LEGO® bricks of uniform height, arranged in different configurations. Measurements were made with both floating-element drag balance and high-resolution particle image velocimetry on six configurations with different frontal solidities, λF, at fixed plan solidity, λP, and vice versa, for a total of twelve rough-wall cases. The results indicated that the drag reaches a peak value λF ≈ 0.21 for a constant λP 0.27, while it monotonically decreases for increasing values of λP for a fixed λF = 0.15. This is in contrast to previous studies in the literature based on cube roughness which show a peak in drag for both λF and λP variations. The influence of surface morphology on the depth of the roughness sublayer (RSL) was also investigated. Its depth was found to be inversely proportional to the roughness length, y0. A decrease in y0 was usually accompanied by a thickening of the RSL and vice versa. Proper orthogonal decomposition (POD) analysis was also employed. The shapes of the most energetic modes calculated using the data across the entire boundary layer were found to be self-similar across the twelve rough-wall cases. However, when the analysis was restricted to the roughness sublayer, differences that depended on the wall morphology were apparent. Moreover, the energy content of the POD modes within the RSL suggested that the effect of increased frontal solidity was to redistribute the energy towards the larger scales (i.e. a larger portion of the energy was within the first few modes), while the opposite was found for variation of plan solidity

Optimal mode decomposition for unsteady flows

A new method, herein referred to as optimal mode decomposition (OMD), of finding a linear model to describe the evolution of a fluid flow is presented. The method estimates the linear dynamics of a high-dimensional system which is first projected onto a subspace of a user-defined fixed rank. An iterative procedure is used to find the optimal combination of linear model and subspace that minimizes the system residual error. The OMD method is shown to be a generalization of dynamic mode decomposition (DMD), in which the subspace is not optimized but rather fixed to be the proper orthogonal decomposition (POD) modes. Furthermore, OMD is shown to provide an approximation to the Koopman modes and eigenvalues of the underlying system. A comparison between OMD and DMD is made using both a synthetic waveform and an experimental data set. The OMD technique is shown to have lower residual errors than DMD and is shown on a synthetic waveform to provide more accurate estimates of the system eigenvalues. This new method can be used with experimental and numerical data to calculate the ‘optimal' low-order model with a user-defined rank that best captures the system dynamics of unsteady and turbulent flow

Mechanisms of airfoil noise near stall conditions

The focus of this paper is on investigating the noise produced by an airfoil at high angles of attack over a range of Reynolds number Re≈2×10⁵–4×10⁵. The objective is not modeling this source of noise but rather understanding the mechanisms of generation for surface pressure fluctuations, due to a separated boundary layer, that are then scattered by the trailing edge. To this aim, we use simultaneous noise and surface pressure measurement in addition to velocimetric measurements by means of hot wire anemometry and time-resolved particle image velocimetry. Three possible mechanisms for the so-called “separation-stall noise” have been identified in addition to a clear link between far-field noise, surface pressure, and velocity fields in the noise generation