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Harmonic oscillations of NACA 0012 airfoils in water are numerically simulated to assess the corresponding structural loads due to the generated forces. An appropriately devised procedure estimates the unsteady effect caused by the foil acceleration, i.e. the added mass effect. This is found to play a very important role as the resulting inertia forces are largely enhanced in the range of analysed parameters. The influence of the wing mass is investigated and it is found that light wings generate forces larger than those generated by heavy wings, as light wings accelerate more than heavy wings. The resulting bending stresses and unsteady deflections are calculated by modelling the wings as elastic cantilevers with uniform distributed loads. The maximum unsteady deflection is found to be about 1% of the wing span, that is, the fluid–structure interaction problem can be considered decoupled in the present analysis. It is also shown that heavy, rigid wings appear to be more suitable for the swimming mode corresponding to steady cruise, as the applied stresses result smaller than those obtained for light, flexible wings. The added mass effect could instead be exploited when required, by using lighter propulsors, which generate larger forces.

Unsteady effects caused by accelerating bodies in water play a very important role in biological propulsion. However, such propulsion mechanisms are challenging for simulation as both body geometry and locomotion patterns are quite complex and a natural first step is to model the motion of a standard man-made airfoil. The work presents simulations of harmonic oscillations of a NACA 0012 foil in water and the hydrodynamic forces generated were obtained by a Boundary Element Method (panel method) code. The focus is placed on one of the most important unsteady effects, the added mass effect, which has not been sufficiently addressed in the literature. The corresponding unsteady forces were obtained through appropriately devised two-dimensional added mass tensor. The computational results were compared to existing analytical ones and a maximum error of 10−6 was obtained for the added mass coefficients of the circle of unit diameter. The development of a dedicated numerical approach for the calculation of the added mass tensor is necessitated by the lack of analytical solution for a variety of wing shapes such as NACA foils. The simulations showed that for the range of investigated parameters the inertia thrust and lift generated by the flapping foil increase sharply when the added mass contribution is considered. For example, if the Strouhal number is set to 0.3 and the ratio between the wing and fluid densities to 0.3, the time average of the inertia thrust increases by 23 times and the maximum of the inertia lift is ca. 37 times larger when the added mass effect is considered. Generally, a densities' ratio of order 1 results in an increase of the time-average inertia thrust of order 10. It was confirmed that, as the densities' ratio becomes larger, the contribution of the added mass to the generated inertia forces decreased. As the Strouhal number increases, the added mass effect was found to be more dominant due to the imposed motion kinematics, i.e. the pitch amplitude. The obtained results show clearly that for the specific case of flapping flight in dense fluids the unsteady effects caused by the object acceleration are of prime importance for two reasons: (i) accurate estimate of the generated thrust and (ii) realistic assessment of the resulting structural loads.

Computational fluid mechanics (CFD) has made substantial progress on modelling a variety of important problems in industry. However, there is still lack of reliable methods to model the motion of the body in water. This is a central issue in understanding animal and human propulsion in water not only to advance science but to explore the possibility of utilising such propulsion modes for man made vehicles. The presented work identified the added mass effect as the prime contributor to propulsive force generation. The use of boundary element method (BEM) proved very successful as it allowed reducing this dynamic problem to a quasi-static one without sacrificing accuracy in the model. The comparison between the experimental data and the simulation result was in the range of 95% (average accuracy) suggesting that the added mass effect and dynamic lift and drag are the most significant physical phenomena in propulsive force generation despite the fact that there is undoubtedly and the presence of turbulent effects that were not considered.

Simulations of harmonically oscillating wings were performed using two-dimensional and three-dimensional boundary element method computer programs: the corresponding hydrodynamic forces were obtained by assuming potential flow. The maximum thickness of symmetric 4-digit NACA airfoils was varied in order to assess the effect of changing the foil shape on the generated thrust. It was found that the thrust coefficient per unit of wing mass decreases in magnitude when the thickness increases. The result indicates that, if the wing mass is fixed, its thickness has to be minimised in order to maximise the generated thrust. Another important finding is the dependence on the motion frequency, i.e. for a fixed foil thickness the thrust coefficient per unit of wing mass increases with the motion frequency. However, when the foil thickness becomes larger, the motion frequency effect on the generated thrust becomes less pertinent, i.e. the thrust range for a slender foil is larger than that of a thicker one over the same motion frequency range. The three-dimensional effect due to the wing spanwise shape was also investigated by changing the wing sweep angle and the influence on the generated thrust was insignificant within the range of investigated parameters. The outcome reinforces the idea that the function of swept wings for low-speed flyers, such as birds, is mainly structural as the sweep angle can be related to a desired aeroelastic response of the oscillating wing.

Trust generation by flapping wing is a complex fluid phenomenon involving unsteady effects. The work discusses a Boundary Element Method (BEM) based computer model for the analysis of hydrodynamic forces on flapping foil. The specific focus is on the wake model and its effects on the generated thrust. An unsteady formulation of the Kutta condition, assuming finite pressure difference at the trailing edge of the moving foil, was implemented in the numerical procedure to account for the shedding of trailing-edge vortical structures. It is shown that the numerical results depend strongly on the choice of the wake model, especially at large oscillation frequencies. However, the model of the thrust-producing jet (due to the trailing-edge pressure differences) predicts accurately the thrust trend as a function of the oscillation frequency. In other words, the numerical results show the need of experimental data in order to choose the appropriate wake model. An experimental validation of the numerical method is proposed on the basis of recent experimental results that clearly show the time lag between the foil vertical acceleration and generated thrust as predicted by the model. This proves the point that the unsteady BEM approach to these problems is physically sound.

A computer program based on a potential-flow panel method was developed to evaluate the hydrodynamic forces acting on a harmonically heaving and pitching two-dimensional rigid foil. A new formulation of the unsteady Kutta condition, postulating a finite pressure difference at the trailing edge of the oscillating foil, is proposed and implemented in the numerical procedure. A comparison with published experimental data [Anderson JM, Streitlien K, Barrett DS, Triantafyllou MS. Oscillating foils of high propulsive efficiency. J Fluid Mech 1998;360(1):41–72; Read DA, Hover FS, Triantafyllou MS. Forces on oscillating foils for propulsion and maneuvering. J Fluids Struct 2003;17(1):163–83; Schouveiler L, Hover FS, Triantafyllou MS. Performance of flapping foil propulsion. J Fluids Struct 2005;20(7):949–59] showed good agreement with the computational results. The analysis of the experimental results indicates clearly that robust computational procedures are necessary for reliable data processing in terms of calibration, noise removal, correction factors, etc. The proposed two-dimensional approach to the problem is currently being developed as a three-dimensional procedure that will address the unsteady flow effects such as inertia-related ones that are currently omitted.

The work presents results on drag and lift measurement conducted in a low speed wind tunnel on a replica of the entire human arm. The selected model positions were identical to those during purely rotational front crawl stroke in quasi-static conditions. A computational fluid dynamics model using Fluent showed close correspondence with the experimental results and confirmed the suitability of low speed wind tunnel for the drag and lift measurement in quasi-static conditions. The obtained profiles of the hydrodynamic forces were similar to the dynamic data presented in an earlier study suggesting that shape drag is a major contributing factor in propulsive force generation. The aim of this study was to underline the importance of the entire arm analysis, the elbow angle and a newly defined angle of attack representing the angle of shoulder rotation. It was found that both the maximum value of the drag force at 160 degrees elbow flexion angle and the momentum generated by it exceed the respective magnitudes for the fully extended arm. The latter is underlined by a prolonged plateau of near maximum drag that was obtained at shoulder angle range of 50-140 degrees suggesting that optimal arm configuration in terms of propulsive force generation requires elbow flexion. Furthermore it was found that drag trend is not consistent with the widely assumed and used sinus wave profile. A gap in the existing experimental research was filled as for the first time the entire arm lift and drag was measured across the entire stroke range.

The purpose of this study was to investigate the validity of hydrodynamic force estimation in swimming as calculated by the quasi-static approach. To achieve this a full-scale mechanical arm was developed, built and tested. The mechanical arm, covered with a prosthetic shell and driven at the shoulder was used to simulate a single plane underwater rotation at four elbow configurations. A computer program controlled the shoulder movement to achieve a replicable angular velocity profile for each arm movement. A strain gauge system was used to directly measure the generated arm torque. Repeated trials were conducted at fixed elbow angles of 110 degrees, 135 degrees, 160 degrees and 180 degrees. All trials were filmed using a three-dimensional underwater set-up. Each trial was digitised at 25 Hz and the hydrodynamic drag force profile of the hand calculated using the quasi-static procedure. From these data, the estimated shoulder torque was calculated and compared to the direct measurement of shoulder torque from the mechanical arm. The results showed that the arm produced a repeatable movement through the water. The shoulder torque profiles using the direct measure (the arm) and the indirect measures (quasi-static approach) differed considerably. The quasi-static approach appears not to accurately reflect the hydrodynamic force profile generated by the arm movement in swimming. Furthermore, it seems that the swimmer's hand contribution is overstated in up to date studies. It is essential that the propulsive mechanisms in swimming be further investigated if factors underpinning an optimal technique are to be established.