Wake and aeroelasticity of a flexible pitching foil

The wake of a flapping foil is the basic model representing the propulsive mechanism of swimming and flying animals that use wings, fins, and body oscillations to drive their locomotion. The reverse Bénard-von Kármán vortex street is one of the landmark features of such wakes, since it is associated to the onset of thrust generation. The vortex shedding frequency is clocked by the flapping motion but, in a realistic model the force production dynamics is intimately linked to the elastic response of the flapping structure and the resonance between the different frequencies involved has been invoked in the literature to explain efficient flapping regimes. Here we show, using a wind tunnel experiment and hydrodynamic stability analysis, that thrust peaks occur when the wake resonant frequency is tuned with the foil elastic dynamics.

Wake and aeroelasticity of a flexible pitching foil
J. D’Adamo, M. Collaud, R. Sosa & R. Godoy-Diana
Bioinspiration & Biomimetics 17, 045002 (2022)
doi: 10.1088/1748-3190/ac6d96
[pdf file]

Synchronized Side-by-Side Swimmers

On the fluid dynamical effects of synchronization in side-by-side swimmers
R. Godoy-Diana, J. Vacher, V. Raspa & B. Thiria
Biomimetics 4(4), 77 (2019)
(in the Special issue “Fluid Dynamic Interactions in Biological and Bioinspired Propulsion”, Editors K. W. Moored and G. V. Lauder)


We examined experimentally the in-phase and anti-phase synchronized swimming of two self-propelled independent flexible foils swimming side-by-side in a water tank. The foils are actuated by pitching oscillations at one extremity—the head of the swimmers—and the flow engendered by their undulations is analyzed using two-dimensional particle image velocimetry in their frontal symmetry plane. Following recent observations on the behavior of real fish, we focus on the comparison between in-phase and anti-phase actuation by fixing all other geometric and kinematic parameters. We show that swimming with a neighbor is beneficial for both synchronizations tested, as compared to swimming alone, with an advantage for the anti-phase synchronization. We show that the advantage of anti-phase synchronization in terms of swimming performance for the two-foil “school” results from the emergence of a periodic coherent jet between the two swimmers.

Review paper: Insect and insect-inspired aerodynamics

Image credit: T. Engels (see also Engels et al. Physical Review Fluids 4, 013103, 2019)


Insect and insect-inspired aerodynamics: unsteadiness, structural mechanics and flight control
R. Bomphrey & R. Godoy-Diana
Current Opinion in Insect Science 30, 26–32 (2018)

Flying insects impress by their versatility and have been a recurrent source of inspiration for engineering devices. A large body of literature has focused on various aspects of insect flight, with an essential part dedicated to the dynamics of flapping wings and their intrinsically unsteady aerodynamic mechanisms. Insect wings flex during flight and a better understanding of structural mechanics and aeroelasticity is emerging. Most recently, insights from solid and fluid mechanics have been integrated with physiological measurements from visual and mechanosensors in the context of flight control in steady airs and through turbulent conditions. We review the key recent advances concerning flight in unsteady environments and how the multi-body mechanics of the insect structure — wings and body — are at the core of the flight control question. The issues herein should be considered when applying bio-informed design principles to robotic flapping wings.

Centrifugal instability of Stokes layers in crossflow

centrifugal_instability_cylinderCentrifugal instability of Stokes layers in crossflow: the case of a forced cylinder wake
J. D’Adamo, R. Godoy-Diana & J. E. Wesfreid
Proceedings of the Royal Society A 471: 20150011 (2015).

A circular cylinder oscillating in a viscous fluid produces an axisymmetric Stokes layer, a fundamental flow susceptible to centrifugal instabilities [see e.g. Seminara & Hall, Proc. Roy. Soc. London A 350, 299 (1976)]. In the present work we study such problem in the wake flow around a circular cylinder at Re = 100 performing rotary oscillations. Continue reading “Centrifugal instability of Stokes layers in crossflow”

Undulatory swimming near a wall

wall_effect_visuLarge-amplitude undulatory swimming near a wall
R. Fernández-Prast, V. Raspa, B. Thiria, F. Huera-Huarte & R. Godoy-Diana. Bioinspiration and Biomimetics 10 016003 (2015).


[PDF file]

We study experimentally the propulsive dynamics of flexible undulating foils in a self-propelled swimming configuration near a wall. Measurements of swimming speed and propulsive force are performed, together with full recordings of the elastic wave kinematics and particle image velocimetry. Continue reading “Undulatory swimming near a wall”

Habilitation à diriger des recherches (HDR)

Bio-inspired swimming and flying – Vortex dynamics and fluid/structure interaction

Ramiro Godoy-Diana
Habilitation à diriger des recherches, Université Pierre et Marie Curie, 2014.

PDF file here (19.4 MB)

The present document, prepared in view of obtaining the Habilitation à diriger des recherches, reviews my main research subject at PMMH since 2006, which concerns the study of swimming and flying inspired by nature. Canonical examples of flapping flight and undulatory swimming are explored using simplified experimental models as a starting point. This allows for the discussion of some fundamental questions related to the physics of bio-inspired locomotion at “intermediate” Reynolds numbers. In particular, we address the strong fluid-structure interactions that arise in these problems, where we have focused on: simplified models of flapping foils in hydrodynamic tunnel experiments, especially in the dynamics of vorticity in the wake of an oscillating foil ; mechanical models of flapping flyers with flexible wings in a self-propelled configuration (in the spirit of the pioneer experiments of Etienne-Jules Marey), as well as novel experimental models of undulatory swimming.
Continue reading “Habilitation à diriger des recherches (HDR)”

Drag in undulatory swimmers

vortices_foilsVortex-induced drag and the role of aspect ratio in undulatory swimmers
V. Raspa, S. Ramananarivo, B. Thiria & R. Godoy-Diana. Physics of Fluids, 26 : 041701 (2014).

During cruising, the thrust produced by a self-propelled swimmer is balanced by a global drag force. For a given object shape, this drag can involve skin friction or form drag, both being well-documented mechanisms. However, for swimmers whose shape is changing in time, the question of drag is not yet clearly established. Continue reading “Drag in undulatory swimmers”

Transitions in the wake of a flapping foil

transitions_wakeTransitions in the wake of a flapping foil
R. Godoy-Diana; J. L. Aider & J. E. Wesfreid.
Physical Review E, 77 : 016308 (2008).

Abstract: We study experimentally the vortex streets produced by a flapping foil in a hydrodynamic tunnel, using two-dimensional particle image velocimetry. An analysis in terms of a flapping frequency-amplitude phase space allows the identification of (i) the transition from the well-known Bénard-von Kármán (BvK) wake to the reverse BvK vortex street that characterizes propulsive wakes, and (ii) the symmetry breaking of this reverse BvK pattern giving rise to an asymmetric wake. Continue reading “Transitions in the wake of a flapping foil”

Vertical length scale selection for pancake vortices in strongly stratified viscous fluids


Vertical length scale selection for pancake vortices in strongly stratified viscous fluids
R. Godoy-Diana; J. M. Chomaz & P. Billant.
Journal of Fluid Mechanics, 504 : 229-238 (2004).

Abstract: The evolution of pancake dipoles of different aspect ratio is studied in a stratified tank experiment. Two cases are reported here for values of the dipole initial aspect ratio $\alpha_0 = L_v/L_h$ (where $L_v$ and $L_h$ are vertical and horizontal length scales, respectively) of $\alpha_0 = 0.4$ (case I) and $\alpha_0 = 1.2$ (case II). Continue reading “Vertical length scale selection for pancake vortices in strongly stratified viscous fluids”

The dynamics of pancake vortices in strongly stratified fluids

schmidt I did my PhD at LadHyX during 2000-2004 supervised by Jean-Marc Chomaz. My dissertation was an experimental and theoretical study of the dynamics of pancake vortices and their interaction with internal gravity waves in a strongly stratified fluid.

Abstract. Stably stratified fluids give rise to distinct internal wave modes and potential vorticity modes (PV). The timescales relevant to these two types of motion separate when the stratification is strong: Internal waves propagate on a fast timescale based on the buoyancy frequency (TN = N-1) while a slower timescale in terms of the horizontal advection —TA = Lh/U, where Lh and U are the horizontal length scale and mean velocity of the horizontal motions— characterizes the evolution of vortices. An illustration of the difference between these two modes can be observed in turbulent regions decaying in presence of background stable stratification : As vertical motions are suppressed, energy is either radiated as internal waves, which propagate away from the initially turbulent region, or transferred to horizontal advective motions which are finally organized as patches of potential vorticity. This thesis presents a theoretical and experimental study of the interaction between pancake vortices (representing the PV mode) and internal gravity waves in a strongly stratified fluid, and of the diffusive mechanisms of pancake vortices.

Document indexed at https://pastel.archives-ouvertes.fr/tel-00007046/

Continue reading “The dynamics of pancake vortices in strongly stratified fluids”

Diffusion of pancake-like vortices in cyclostrophic balance

conical_diffuserEffect of the Schmidt number on the diffusion of axisymmetric pancake vortices in a stratified fluid
R. Godoy-Diana & J. M. Chomaz.
Physics of Fluids, 15 : 1058-1064 (2003).

Abstract: An asymptotic analysis of the equations for quasi-two-dimensional flow in stratified fluids is conducted, leading to a model for the diffusion of pancake-like vortices in cyclostrophic balance. This analysis permits one to derive formally the model for the diffusion of an axisymmetric monopole proposed by Beckers et al. [J. Fluid Mech. 433, 1 (2001)], and to extend their results. The appropriate parameter for the perturbation analysis is identified as the square of the vertical Froude number Fv=U/(Lv N), where U is the horizontal velocity scale, N is the Brunt–Väisälä frequency, and Lv the vertical length scale. Continue reading “Diffusion of pancake-like vortices in cyclostrophic balance”

Vortex suppresion in an oscillating flow

conical_diffuserVortex suppresion in an oscillating flow
C. Stern; S. Czitrom; E. Prado & R. Godoy.
Revista Mexicana de Fisica, 46 : 409-410 (2000).

Abstract: The motivation for this work was the reduction of losses due to vortex formation at the entrance of a wave driven seawater pump. Measurements in a wave tank using a prototype had shown a 10% ¡ncrease in the pumping efficiency when a trumpet like shape was added to the intake. This lead us to search for an inlake that would reduce or completely suppress vortex formation. In this experiment a piston produces an oscil1ating flow inside a partly submerged duct. At the end of the duct four different shapes were tested. Continue reading “Vortex suppresion in an oscillating flow”

Oscillating Flow through a Funnel

vortex_owc_exitOscillating Flow through a Funnel
C. Stern; S. Czitrom & R. Godoy.
Physics of Fluids, 11 : S3 (Gallery of Fluids) (1999).

Abstract: Our interest in vortex suppression at the entrance of a wave-driven seawater pump leads us to study vortex formation at the exit of a diffuser due to an oscillating flow. In the present experiment, a piston produces an oscillating flow inside a partly submerged duct that ends in a diffuser. The diffuser is designed such that a constant relationship between centripetal and inertial forces is maintained along the profile. The flow in the near field of the mouth is visualized by injecting diluted fluorescent water paint just outside the diffuser. Continue reading “Oscillating Flow through a Funnel”