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.

Pressure projection is the single most computationally expensive step in an unsteady incompressible fluid simulation. This work demonstrates the ability of data-driven methods to accelerate the approximate solution of the Poisson equation at the heart of pressure projection. Geometric Multi-Grid methods are identified as linear convolutional encoder–decoder networks and a data-driven smoother is developed using automatic differentiation to optimize the velocity-divergence projection. The new method is found to accelerate classic Multi-Grid methods by a factor of two to three with no loss of accuracy on eleven 2D and 3D flow cases including cases with dynamic immersed solid boundaries. The optimal parameters are found to transfer nearly 100% effectiveness as the resolution is increased, providing a robust approach for accelerated pressure projection of unsteady flows.

The concept of added (virtual) mass is applied to a vast array of unsteady fluid-flow problems; however, its origins in potential-flow theory may limit its usefulness in separated flows. A robust framework for modeling instantaneous fluid forces is proposed, named Energized Mass. The energized-mass approach is tested experimentally by acquiring the fluid kinetic-energy history around an accelerating sphere at both subcritical and supercritical terminal velocities. By tracking the energized-mass volume, the force response is shown to be related to changes in shear-layer growth as a function of acceleration moduli and Reynolds number. The energized-mass framework is then used to develop a low-order force model, requiring only body geometry and kinematics as input. An analytical expression for the instantaneous force on a sphere due to energized-mass growth is derived based on shear-layer mass flux arguments. Instantaneous forces determined experimentally, and modeled using the energized-mass approach, show strong agreement with direct force measurements. The results of this investigation thus demonstrate that the energized-mass framework provides a viable low-order modeling approach, and in tandem, can provide new insights into the origin of forces on accelerating bodies.

Simulations of turbulent fluid flow around long cylindrical structures are computationally expensive because of the vast range of length scales, requiring simplifications such as dimensional reduction. Current dimensionality reduction techniques such as strip-theory and depth-averaged methods do not take into account the natural flow dissipation mechanism inherent in the small-scale three-dimensional (3-D) vortical structures. We propose a novel flow decomposition based on a local spanwise average of the flow, yielding the spanwise-averaged Navier–Stokes (SANS) equations. The SANS equations include closure terms accounting for the 3-D effects otherwise not considered in 2-D formulations. A supervised machine-learning (ML) model based on a deep convolutional neural network provides closure to the SANS system. A-priori results show up to 92% correlation between target and predicted closure terms; more than an order of magnitude better than the eddy viscosity model correlation. The trained ML model is also assessed for different Reynolds regimes and body shapes to the training case where, despite some discrepancies in the shear-layer region, high correlation values are still observed. The new SANS equations and ML closure model are also used for a-posteriori prediction. While we find evidence of known stability issues with long time ML predictions for dynamical systems, the closed SANS simulations are still capable of predicting wake metrics and induced forces with errors from 1-10%. This results in approximately an order of magnitude improvement over standard 2-D simulations while reducing the computational cost of 3-D simulations by 99.5%.

This technical note presents a simplified method for quantifying the added mass of the soil that is mobilised as part of the failure mechanism around a foundation during rapid loading, and the resulting additional soil resistance. This note focuses on the solutions for an embedded plate anchor, which is a potential foundation system for offshore floating facilities. In current practice, only the shear strength of the soil surrounding the foundation is considered in calculations of the ultimate bearing capacity. However, the solutions presented in this technical note show that the added mass of the soil involved in the failure mechanism around the foundation can result in a significant increase in ultimate bearing capacity during extreme dynamic wave loading events. These lead to snatch loads transmitted to the anchoring and mooring system, which are high but brief. The technical note provides a general approach applicable to all foundation types, and illustrates the effect of the added mass term and the additional capacity for an embedded plate anchor with typical input conditions.

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.

This paper introduces a virtual boundary method for compressible viscous fluid flow that is capable of accurately representing moving bodies in flow and aeroacoustic simulations. The method is the compressible extension of the boundary data immersion method (BDIM, Maertens & Weymouth (2015), [18]). The BDIM equations for the compressible Navier–Stokes equations are derived and the accuracy of the method for the hydrodynamic representation of solid bodies is demonstrated with challenging test cases, including a fully turbulent boundary layer flow and a supersonic instability wave. In addition we show that the compressible BDIM is able to accurately represent noise radiation from moving bodies and flow induced noise generation without any penalty in allowable time step.

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.

Dynamic shape change of the octopus mantle during fast jet escape manoeuvres results in added mass energy recovery to the energetic advantage of the octopus, giving escape thrust and speed additional to that due to jetting alone. We show through numerical simulations and experimental validation of overall wake behaviour, that the success of the energy recovery is highly dependent on shrinking speed and Reynolds number, with secondary dependence on shape considerations and shrinking amplitude. The added mass energy recovery ratio η_ma, which measures momentum recovery in relation to the maximum momentum recovery possible in an ideal flow, increases with increasing the non-dimensional shrinking parameter σ^∗ = ȧ_max/URe₀, where ȧ_max is the maximum shrinking speed, U is the characteristic flow velocity and Re₀ is the Reynolds number at the beginning of the shrinking motion. An estimated threshold σ^∗∼10 determines whether or not enough energy is recovered to the body to produce net thrust. Since there is a region of high transition for 10 < σ^∗ < 30 where the recovery performance varies widely and for σ^∗ > 100 added mass energy is recovered at diminishing returns, we propose a design criterion for shrinking bodies to be in the range of 50 < σ^∗ < 100, resulting in 61-82% energy recovery.

The fluid mechanics employed by aquatic animals in their escape or attack maneuvers, what we call survival hydrodynamics, are fascinating because the recorded performance in animals is truly impressive. Such performance forces us to pose some basic questions on the underlying flow mechanisms that are not yet in use in engineered vehicles. A closely related issue is the ability of animals to sense the flow velocity and pressure field around them in order to detect and discriminate threats in environments where vision or other sensing is of limited or no use. We review work on animal flow sensing and actuation as a source of inspiration and as a way to formulate a number of basic problems and investigate the flow mechanisms that enable animals to perform these remarkable maneuvers. We also describe some intriguing mechanisms of actuation and sensing.

An accurate Cartesian-grid treatment for intermediate Reynolds number fluid-solid interaction problems is described. We first identify the inability of existing immersed boundary methods to handle intermediate Reynolds number flows to be the discontinuity of the velocity gradient at the interface. We address this issue by generalizing the Boundary Data Immersion Method (BDIM, Weymouth and Yue (2011)), in which the field equations of each domain are combined analytically, through the addition of a higher order term to the integral formulation. The new method retains the desirable simplicity of direct forcing methods and smoothes the velocity field at the fluid-solid interface while removing its bias. Based on a second-order convolution, it achieves second-order convergence in the L₂ norm, regardless of the Reynolds number. This results in accurate flow predictions and pressure fields without spurious fluctuations, even at high Reynolds number. A treatment for sharp corners is also derived that significantly improves the flow predictions near the trailing edge of thin airfoils. The second-order BDIM is applied to unsteady problems relevant to ocean energy extraction as well as animal and vehicle locomotion for Reynolds numbers up to 10⁵.

A perching bird is able to rapidly decelerate while maintaining lift and control, but the underlying aerodynamic mechanism is poorly understood. In this work we perform a study on a simultaneously decelerating and pitching aerofoil section to increase our understanding of the unsteady aerodynamics of perching. We first explore the problem analytically, developing expressions for the added-mass and circulatory forces arising from boundary-layer separation on a flat-plate aerofoil. Next, we study the model problem through a detailed series of experiments at \mathit{Re}=22\,000 and two-dimensional simulations at \mathit{Re}=2000. Simulated vorticity fields agree with particle image velocimetry measurements, showing the same wake features and vorticity magnitudes. Peak lift and drag forces during rapid perching are measured to be more than 10 times the quasi-steady values. The majority of these forces can be attributed to added-mass energy transfer between the fluid and aerofoil, and to energy lost to the fluid by flow separation at the leading and trailing edges. Thus, despite the large angles of attack and decreasing flow velocity, this simple pitch-up manoeuvre provides a means through which a perching bird can maintain high lift and drag simultaneously while slowing to a controlled stop.

We present the concepts of physics-based learning models (PBLM) and their relevance and application to the field of ship hydrodynamics. The utility of physics-based learning is motivated by contrasting generic learning models for regression predictions, which do not presume any knowledge of the system other than the training data provided with methods such as semi-empirical models, which incorporate physical insights along with data-fitting. PBLM provides a framework wherein intermediate models, which capture (some) physical aspects of the problem, are incorporated into modern generic learning tools to substantially improve the predictions of the latter, minimizing the reliance on costly experimental measurements or high-resolution highfidelity numerical solutions. To illustrate the versatility and efficacy of PBLM, we present three wave-ship interaction problems: 1) at speed waterline profiles; 2) ship motions in head seas; and 3) three-dimensional breaking bow waves. PBLM is shown to be robust and produce error rates at or below the uncertainty in the generated data at a small fraction of the expense of high-resolution numerical predictions.

A new robust and accurate Cartesian-grid treatment for the immersion of solid bodies within a fluid with general boundary conditions is described. The new approach, the Boundary Data Immersion Method (BDIM), is derived based on a general integration kernel formulation which allows the field equations of each domain and the interfacial conditions to be combined analytically. The resulting governing equation for the complete domain preserves the behavior of the original system in an efficient Cartesian-grid method, including stable and accurate pressure values on the solid boundary. The kernel formulation allows a detailed analysis of the method, and it is demonstrated that BDIM is consistent, obtains second-order convergence relative to the kernel width, and is robust with respect to the grid and boundary alignment. Formulation for no-slip and free slip boundary conditions are derived and numerical results are obtained for the flow past a cylinder and the impact of blunt bodies through a free surface. The BDIM predictions are compared to analytic, experimental and previous numerical results confirming the properties, efficiency and efficacy of this new boundary treatment for Cartesian grid methods.

This paper contributes to the state of the art in Cartesian-grid methods through development of new advection and reconstruction Volume-of-Fluid (VOF) algorithms which are applicable to two and three-dimensional flows. A computationally efficient and secondorder VOF reconstruction method is presented which uses no inversions to determine the interface normal direction. Next, the lack of conservation of fluid volume in previous VOF advection methods are shown to be due to improper treatment of one-dimensional stretching in the velocity field. This paper uses simple explicit time stepping and a cell-center estimate of the volume fraction in the dilatation term to achieve a completely conservative advection method. The new methods are simple, robust and shown to out perform existing approaches for canonical test problems relevant to breaking wave flows.