Accurate predictions of the drag penalty in rough-wall flows require careful characterisation of surface roughness to determine the equivalent sand-grain roughness height (k_s). The procedure involves measuring wall-shear stress (τ_w) using direct or indirect methods and analyzing velocity profiles. However, indirect methods often rely on assumptions whose validity cannot always be guaranteed. In this paper (partly based on the study [1]), wind tunnel measurements on a realistic rough surface scanned from a fouled ship hull are carried out to evaluate drag penalty predictions. Current data enabled the evaluation of k_s and associated wake parameters using several methods, which were then used for full-scale drag penalty predictions at high Reynolds numbers, with results showing the drag penalty could vary by nearly 15% among methods, highlighting the importance of exercising caution when employing such methods.

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The floating-element (FE) principle, introduced nearly a century ago, remains one of the most versatile direct wall shear stress measurement methods. Yet, its intrinsic sources of systematic error, associated with the flow-exposed gap, off-axis load sensitivity, and calibration, have thus far limited its widespread application. In combination with the lack of standard designs and testing procedures, measurement reliability still hinges heavily on individual judgement and expertise. This paper presents a framework to curb these limitations, whereby the design and operation of a FE balance are leveraged by an analytical model that attempts to capture the behaviour and predict the relative contribution of the systematic sources of error. The design is based on a parallel-shift linkage and a zero-displacement force-feedback system. The FE has a surface area of 200×200 mm, and measurement sensitivity is adjustable depending on the surface condition and the Reynolds number. It is thus suitable for application in a wide range of low-speed, boundary-layer wind tunnels, small or large scale. Measurements of the skin friction coefficient over a smooth wall show a remarkable agreement with oil-film interferometry, especially for Re_θ>1.3×10⁴. The discrepancy relative to the empirical Coles–Fernholz relation (κ=0.39 and C=4.352) is within 0.5%, and the level of uncertainty is below 1% for a confidence interval of 95%.

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The hydrodynamic influence of surface texture on static surfaces ranges from large drag penalties (roughness) to potential performance benefits (shark-like skin). Although it is of wide-ranging research interest, the impact of roughness on flapping systems has received limited attention. In this work, we explore the effect of roughness on the unsteady performance of a harmonically pitching foil through experiments using foils with different surface roughness, at a fixed Strouhal number and within the Reynolds number range of. The foils' surface roughness is altered by changing the distribution of spherical-cap-shaped elements over the propulsor area. We find that the addition of surface roughness does not improve the performance compared with a smooth surface over the range considered. The analysis of the flow fields shows near-identical wakes regardless of the foil's surface roughness. The performance reduction mainly occurs due to an increase in profile drag. However, we find that the drag penalty due to roughness is reduced from for a static foil to for a flapping foil at the same mean angle of attack, with the strongest decrease measured at the highest. Our findings highlight that the effect of roughness on dynamic systems is very different than that on static systems; thereby, it cannot be estimated by only using information obtained from static cases. This also indicates that the performance of unsteady, flapping systems is more robust to the changes in surface roughness.

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In this work, we describe the impact of aspect ratio on the performance of optimally phased, identical flapping flippers in a tandem configuration. Three-dimensional simulations are performed for seven sets of single and tandem finite foils at a moderate Reynolds number, with thrust producing, heave-to-pitch coupled kinematics. Increasing slenderness (or) is found to improve thrust coefficients and thrust augmentation but the benefits level off towards higher values of. However, the propulsive efficiency shows no significant change with increasing, while the hind foil outperforms the single by a small margin. Further analysis of the spanwise development and propagation of vortical structures allows us to gain some insights into the mechanisms of these wake interactions and provide valuable information for the design of novel biomimetic propulsion systems.

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Full-scale drag penalty predictions of flows over rough walls require surface roughness characterisation from laboratory experiments or numerical simulations. In either approach, it is necessary to determine the so-called equivalent sand-grain roughness height (k_s ). There are several steps involved in determining this aerodynamic roughness lengthscale, but its procedure typically includes a combination of measurement of wall-shear stress (τ_w ) using direct or indirect methods as well as analysis of velocity profiles. Indirect methods usually rely on assumptions made about flow and its scaling including the validity of universal outer-layer similarity. However, the implications of the underlying assumptions involved in full-scale drag prediction are unclear. In this work, we carry out wind tunnel measurements over a realistic rough surface (from a fouled ship-hull) to evaluate the impact of different methods with an emphasis on using the outer-layer similarity hypothesis for full-scale drag predictions. Wall-shear stress is measured using an in-house floating-element drag balance (DB), and velocity profiles are obtained using particle image velocimetry (PIV), allowing the evaluation of k_s , and the associated wake parameters through several methods. The aerodynamic roughness parameters hence obtained are used for full-scale drag penalty calculations. It is observed that the predicted drag penalty can vary by over 15 % among the different methods highlighting the care that should be taken when employing such methods.

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The importance of the leading-edge sweep angle of propulsive surfaces used by unsteady swimming and flying animals has been an issue of debate for many years, spurring studies in biology, engineering, and robotics with mixed conclusions. In this work, we provide results from three-dimensional simulations on single-planform finite foils undergoing tail-like (pitch-heave) and flipper-like (twist-roll) kinematics for a range of sweep angles covering a substantial portion of animals while carefully controlling all other parameters. Our primary finding is the negligible 0.043 maximum correlation between the sweep angle and the propulsive force and power for both tail-like and flipper-like motions. This indicates that fish tails and mammal flukes with similar range and size can have a large range of potential sweep angles without significant negative propulsive impact. Although there is a slight benefit to avoiding large sweep angles, this is easily compensated by adjusting the fin's motion parameters such as flapping frequency, amplitude and maximum angle of attack to gain higher thrust and efficiency.

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Flapping flight and swimming are increasingly studied due to both their intrinsic scientific richness and their applicability to novel robotic systems. Strip theory is often applied to flapping wings, but such modeling is only rigorously applicable in the limit of infinite aspect ratio (AR) where the geometry and kinematics are effectively uniform. This work compares the flow features and forces of strip theory and three-dimensional flapping foils, maintaining similitude in the rolling and twisting kinematics while varying the foil AR. We find the key influence of finite AR and spanwise varying kinematics is the generation of a time-periodic spanwise flow which stabilizes the vortex structures and enhances the dynamics at the foil root. An aspect-ratio correction for flapping foils is developed analogous to Prandtl finite wing theory, enabling future use of strip theory in analysis and design of finite aspect ratio flapping foils.

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Symmetric flapping foils are known to produce deflected jets at high frequency-amplitude combinations even at a zero mean angle of attack. This reduces the frequency range of useful propulsive configurations without side force. In this study, we numerically analyse the interaction of these deflected jets for tandem flapping foils undergoing coupled heave-to-pitch motion in a two-dimensional domain. The impact of the flapping Strouhal number, foil spacing and phasing on wake interaction is investigated. Our primary finding is that the back foil is capable of cancelling the wake deflection and mean side force of the front foil, even when located up to five chord lengths downstream. This is achieved by attracting the incoming dipoles and disturbing their cohesion within the limits of the back foil's range of flapping motion. We also show that the impact on cycle-averaged thrust varies from high augmentation to drag generation depending on the wake patterns downstream of the back foil. These findings provide new insights towards the design of biomimetic tandem propulsors, as they expand their working envelope and ability to rapidly increase or decrease the forward speed by manipulating the size of the shed vortices.

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Propulsive flapping foils are widely studied in the development of swimming and flying animal-like autonomous systems. Numerical studies in this topic are mainly two-dimensional (2-D) studies, as they are quicker and cheaper, but this inhibits the three-dimensional (3-D) evolution of the shed vortices from leading and trailing edges. In this work, we examine the similarities and differences between 2-D and 3-D simulations through a case study in order to evaluate the efficacy and limitations of using 2-D simulations to describe a 3-D system. We simulate an infinite-span NACA0016 foil in both two and three dimensions at a Reynolds number of 5300 and an angle of attack of 10^°. The foil is subject to prescribed heaving and pitching kinematics with varying trailing-edge deflection amplitude. Our primary finding is that the flow and forces are effectively 2-D at intermediate amplitude-based Strouhal numbers (, where is the free-stream velocity and is the flapping frequency), for heaving, for pitching and for coupled motion, while 3-D effects dominate outside of these ranges. These 2-D regions begin when the fluid energy induced by the flapping motion overcomes the 3-D vortex shedding found on a stationary foil, and the flow reverts back to 3-D when the strength of the shed vortices overwhelms the stabilising influence of viscous dissipation. These results indicate that 3-D to 2-D transitions or vice versa are a balance between the strength and stability of leading/trailing-edge vortices and the flapping energy. However, 2-D simulations can still be used for flapping flight/swimming studies provided that the flapping amplitude/frequency is within a given range.

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Reversed von Kármán 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 and frequency because the transition also depends sensitively on other details of the kinematics. In this work we replace with the cycle-averaged swept trajectory of the foil chordline. Two-dimensional simulations are performed for pure heave, pure pitch and a variety of heave-to-pitch coupling. In a phase space of dimensionless we show that the drag-to-thrust wake transition of all tested modes occurs for a modified Strouhal. Physically, the product expresses the induced velocity of the foil and indicates that propulsive jets occur when this velocity exceeds. 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.@en

The propulsive performance of a pair of tandem flapping foils is sensitively dependent on the spacing and phasing between them. Large increases in thrust and efficiency of the hind foil are possible, but the mechanisms governing these enhancements remain largely unresolved. Two-dimensional numerical simulations of tandem and single foils oscillating in heave and pitch at a Reynolds number of 7000 are performed over a broad and dense parameter space, allowing the effects of inter-foil spacing and phasing to be investigated over a range of non-dimensional frequencies (or Strouhal number, ). Results indicate that the hind foil can produce from no thrust to twice the thrust of a single foil depending on its spacing and phasing with respect to the fore foil, which is consistent with previous studies that were carried out over a limited parameter space. Examination of instantaneous flow fields indicates that high thrust occurs when the hind foil weaves between the vortices that have been shed by the fore foil, and low thrust occurs when the hind foil intercepts these vortices. Contours of high thrust and minimal thrust appear as inclined bands in the parameter space and this behaviour is apparent over the entire range of Strouhal numbers considered . A novel quasi-steady model that utilises kinematics of a virtual hind foil together with data obtained from simulations of a single flapping foil shows that performance augmentation is primarily determined through modification of the instantaneous angle of attack of the hind foil by the vortex street established by the fore foil. This simple model provides estimates of thrust and efficiency for the hind foil, which is consistent with data obtained through full simulations. The limitations of the virtual hind foil method and its physical significance is also discussed.

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The extinct ocean-going plesiosaurs were unique within vertebrates because they used two flipper pairs identical in morphology for propulsion. Although fossils of these Mesozoic marine reptiles have been known for more than two centuries, the function and dynamics of their tandem-flipper propulsion system has always been unclear and controversial. We address this question quantitatively for the first time in this study, reporting a series of precisely controlled water tank experiments that use reconstructed plesiosaur flippers scaled from well-preserved fossils. Our aim was to determine which limb movements would have resulted in the most efficient and effective propulsion. We show that plesiosaur hind flippers generated up to 60% more thrust and 40% higher efficiency when operating in harmony with their forward counterparts, when compared with operating alone, and the spacing and relative motion between the flippers was critical in governing these increases. The results of our analyses show that this phenomenon was probably present across the whole range of plesiosaur flipper motion and resolves the centuries-old debate about the propulsion style of these marine reptiles, as well as indicating why they retained two pairs of flippers for more than 100 million years.

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The aim of this article is to provide a theoretical basis upon which to advance and deploy novel tandem flapping foil systems for efficient marine propulsion. We put forth three key insights into tandem flapping foil hydrodynamics related to their choreography, propulsive efficiency, and unsteady loading. in particular, we propose that the performance of the aft foil depends on a new nondimensional number, s/Uτ, which is the interfoil separation s normalized by the distance that the freestream U advects in one flapping period, τ. Additionally, we show how unsteady loading can be mitigated through choice of phase lag.

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