Mohsen Daghooghi

The fish tail motion forms an attached leading edge vortex

The tail (caudal fin) is one of the most prominent characteristics of fishes, and the analysis of the flow pattern it creates is fundamental to understanding how its motion generates locomotor forces. A mechanism that is known to greatly enhance locomotor forces in insect and bird flight is the leading edge vortex (LEV) reattachment, i.e. a vortex (separation bubble) that stays attached at the leading edge of a wing. However, this mechanism has not been reported in fish-like swimming probably owing to the overemphasis on the trailing wake, and the fact that the flow does not separate along the body of undulating swimmers. We provide, to our knowledge, the first evidence of the vortex reattachment at the leading edge of the fish tail using three-dimensional high-resolution numerical simulations of self-propelled virtual swimmers with different tail shapes. We show that at Strouhal numbers (a measure of lateral velocity to the axial velocity) at which most fish swim in nature (approx. 0.25) an attached LEV is formed, whereas at a higher Strouhal number of approximately 0.6 the LEV does not reattach. We show that the evolution of the LEV drastically alters the pressure distribution on the tail and the force it generates. We also show that the tails delta shape is not necessary for the LEV reattachment and fish-like kinematics is capable of stabilising the LEV. Our results suggest the need for a paradigm shift in fish-like swimming research to turn the focus from the trailing edge to the leading edge of the tail.

The hydrodynamic advantages of synchronized swimming in a rectangular pattern

Fish schooling is a remarkable biological behavior that is thought to provide hydrodynamic advantages. Theoretical models have predicted significant reduction in swimming cost due to two physical mechanisms: vortex hypothesis, which reduces the relative velocity between fish and the flow through the induced velocity of the organized vortex structure of the incoming wake; and the channeling effect, which reduces the relative velocity by enhancing the flow between the swimmers in the direction of swimming. Although experimental observations confirm hydrodynamic advantages, there is still debate regarding the two mechanisms. We provide, to our knowledge, the first three-dimensional simulations at realistic Reynolds numbers to investigate these physical mechanisms. Using large-eddy simulations of self-propelled synchronized swimmers in various rectangular patterns, we find evidence in support of the channeling effect, which enhances the flow velocity between swimmers in the direction of swimming as the lateral distance between swimmers decreases. Our simulations show that the coherent structures, in contrast to the wake of a single swimmer, break down into small, disorganized vortical structures, which have a low chance for constructive vortex interaction. Therefore, the vortex hypothesis, which is relevant for diamond patterns, was not found for rectangular patterns, but needs to be further studied for diamond patterns in the future. Exploiting the channeling mechanism, a fish in a rectangular school swims faster as the lateral distance decreases, while consuming similar amounts of energy. The fish in the rectangular school with the smallest lateral distance (0.3 fish lengths) swims 20% faster than a solitary swimmer while consuming similar amount of energy.

Self-propelled swimming simulations of bio-inspired smart structures.

This paper presents self-propelled swimming simulations of a foldable structure, whose folded configuration is a box. For self-locomotion through water the structure unfolds and undulates. To guide the design of the structure and understand how it should undulate to achieve either highest speed or maximize efficiency during locomotion, several kinematic parameters were systematically varied in the simulations: the wave type (standing wave versus traveling wave), the smoothness of undulations (smooth undulations versus undulations of rigid links), the mode of undulations (carangiform: mackerel-like versus anguilliform: eel-like undulations), and the maximum amplitude of undulations. We show that the swimmers with standing wave are slow and inefficient because they are not able to produce thrust using the added-mass mechanism. Among the tested types of undulation at low Reynolds number (Re) regime of [Formula: see text] (Strouhal number of about 1.0), structures that employ carangiform undulations can swim faster, whereas anguilliform swimmers are more economic, i.e., using less power they can swim a longer distance. Another finding of our simulations is that structures which are made of rigid links are typically less efficient (lower propulsive and power efficiencies and also lower swimming speed) compared with smoothly undulating ones because a higher added-mass force is generated by smooth undulations. The wake of all the swimmers bifurcated at the low Re regime because of the higher lateral relative to the axial velocity (high Strouhal number) that advects the vortices laterally creating a double row of vortices in the wake. In addition, we show that the wake cannot be used to predict the performance of the swimmers because the net force in each cycle is zero for self-propelled bodies and the pressure term is not negligible compared to the other terms.

Self-Assembling Swimming Smart Boxes

This paper presents vibration analysis and structural optimization of a self-assembled structure for swimming. The mode shapes of the structure resemble the body waveform of a swimming Mackerel fish. The lateral deformation waveform of the body of Mackerel is extracted from literature. At higher swimming speeds fish generate the waveform at a higher frequency. Their body waveform stays the same at almost all normal swimming speeds. At the final destination, the box self-assembles using shape memory alloys. The shape memory alloys used for configuration change of the box robot cannot be used for swimming since they fail to operate at high frequencies. MFCs are actuated at the fundamental natural frequency of the structure. This excites the primary mode of resonance. The primary mode of resonance involves rotations of the joints of the robot in the desired fashion. The MFCs are therefore used to indirectly generate the body waveform. We optimize the thickness of the panels and the stiffness of the joints to most efficiently generate the swimming waveforms. Unlike eel we change the speed of the robot by changing the amplitude of the body motions. This is because the frequency of the motion is fixed to the first natural frequency of the robot. The swimming box can swim over the surface and can also swim underwater. With slight modification the boxes can crawl or slither over the land.Copyright

Self-Propelled Swimming Simulations of Self-Assembling Smart Boxes

This paper presents self-propelled swimming simulations of a smart foldable structure capable of swimming and self-assembly for rescue or rapid construction missions, e.g., making temporary bridges. The open configuration of the robot is like a wide cross, which undulates like an eel to swim to a given location. Micro Fiber Composites (MFCs) attached to the surface of the foldable robot actuate the surfaces for swimming purpose. Once the robot arrives at the desired locations shape memory alloys will be activated to fold the robot to a box. To optimize the kinematics of the robot to achieve either highest speed or maximize efficiency during locomotion. self-propelled swimming simulations of the robot was carried out by varying two kinematic parameters: the body motion wavelength and the amplitude. The simulations shows that to achieve higher speed, higher wavelengths are more desirable, e.g., wavelength of 0.95L achieved 15% higher swimming speed relative to 0.65L (L is the swimmer’s length). In contrast, to achieve higher efficiency, lower wavelengths (0.65L) and higher undulation amplitude (0.15L) was 14% more efficient than the other swimmer with wavelength 0.95L and amplitude 0.1L.Copyright

An Immersed Boundary Method for Calculating the Relative Viscosity of a Suspension of Rigid Particles

In this paper, we provide a numerical framework to calculate the relative viscosity of a suspension of rigid particles. A high-resolution background grid is used to solve the flow around the particles. In order to generate infinite number of particles in the suspension, a particle is placed in the center of a cubic cell and periodic boundary conditions are imposed in two directions. The flow around the particle is solved using the second-order accurate curvilinear immersed boundary (CURVIB) method [1]. The particle is discretized with triangular elements, and is treated as a sharp interface immersed boundary by reconstructing the velocities on the fluid nodes adjacent to interface using a quadratic interpolation method. Hydrodynamic torque on the particle has been calculated, to solve the equation of motion for the particle and obtain its angular velocity. Finally, relative viscosity of the suspension has been calculated based on two different methods: (1) the rate of the energy consumption and (2) bulk stress-bulk strain method. The framework has been validated by simulating a suspension of spheres, and comparing the numerical results with the corresponding analytical ones. Very good agreement has been observed between the analytical and the calculated relative viscosities using both methods. This framework is then used to model a suspension with arbitrary complex particles, which demonstrates the effect of shape on the effective viscosity.Copyright

Parallel Implementation of Periodic Boundary Conditions for a Curvilinear Immersed Boundary Method

In this paper, a periodic boundary condition is implemented for 3D unsteady finite volume solver for incompressible Navier-Stokes equations on curvilinear structured grids containing moving immersed boundaries of arbitrary geometrical complexity. The governing equations are discretized with second-order accuracy on a hybrid staggered/non-staggered grid layout. The discrete equations are integrated in time via a second-order fractional step method. To resolve all the relevant scales in the flow accurately, a high-resolution curvilinear mesh is required, i.e., the simulations are computationally expensive. Therefore, high-performance parallel computing is essential to obtain results within reasonable time for practical applications. The main challenge with the implantation of the parallel periodic boundary condition is to update information at ghost nodes on different processors. An efficient parallel algorithm is implemented to update the ghost nodes for the periodic boundary condition. The parallel implementation is tested by comparing the results with analytical solutions, which are found to be in excellent agreement with each other. The parallel performance of the solver with the periodic boundary condition is also investigated for different cases.Copyright

The effect of undulations on the particle stress in dilute suspensions of rod-like particles

Abstract We compared a dilute suspension of undulating rod-like particles (active suspension) with a similar one consisting of rigid rods (passive suspension) under shear flow. For the active suspension, a synchronised group of swimmers propel themselves forward by passing a travelling wave through their bodies while at the same time rotate due to planar background shear flow. Using a high resolution immersed body numerical simulations, we have shown that an active particle can exhibit complex dynamics, which is fundamentally different from a similar passive one. The orientation of the active particle consists of two separate oscillations: a low-frequency oscillation similar to the passive particle (determined by shear rate) and a high-frequency oscillation due to the body undulations. Nevertheless, different dynamics did not result in a major difference in rheological behaviour of the suspension. We found that the effective viscosity of the active suspension is equal to that of a passive one, i.e. self-propulsion did not change the viscosity of the suspension probably because of the high shear rate and inertia of our simulations.

Visualizing the wake of aquatic swimmers

Fish-like swimming is fascinating not only for its fundamental scientific value but also for engineering biomimetically inspired vehicles. Discovering physical principles behind the evolution of different aquatic swimmers can drastically improve the design of such vehicles. We are interested in the evolution of different caudal fin profiles (shape) because it is hypothesized that most of the thrust force is generated by the caudal fin. In fact, the caudal fin shape varies from hemocercal in mackerel to almost trapezoidal in trout and heterocercal in sharks. We investigate if such shape differences have hydrodynamic implications using numerical simulations. The equations governing the fluid motion are solved in the non-inertial reference frame attached to the fish center of mass (COM) via the curvilinear/immersed boundary method (CURVIB), which is capable of carrying out direct numerical simulation of flows with complex moving boundaries. The motion of the fish body is prescribed based on carangiform kinematics while the motion of the COM is calculated based on the fluid forces on the fish body through the fluid-structure interaction algorithm of Borazjani et. al. (2008) [3]. The reader is referred to Borazjani & Sotiropoulos (2010) [4] for the details of the method. For self-propelled simulations, the virtual swimmers start to undulate in an initially stagnant fluid and the swimming speed is determined based on the forces on the fish body. Therefore, physical parameters based on the swimming velocity change as the swimmer accelerates until the quasi-steady state is reached. The computational domain and time step for the self-propelled fish body simulations in the free stream is a cuboid with dimensions 2LxLx7L, which is discretized with 5.5 million grid nodes. The domain width 2L and height L are more than ten times the mackerel width 0.2L and height 0.1L, respectively. The fish is placed 1.5L from the inlet plane in the axial direction and centered in the transverse and the vertical directions. The simulations are partly run on our in-house computing cluster, Nami, with a total of 448 computing cores distributed across 28 nodes, each node containing a 2x8 Magny-Cours core (AMD 2.0 GHz). The memory available is 2GB RAM/core, 896GB total and the nodes are connected through QDR Infiniband. Some of the simulations were run on the dual-quad core nodes in the u2 cluster at CCR; these are also connected through QDR Infiniband. The simulations generate velocity field data in VTK format [5], allowing one to apply ParaViews tetrahedralize algorithm [2] to the 5.5 million point data set. The result is shown in Figure 1 for a swimming mackerel, where volume rendered points are colored by the magnitude of the velocity field. The domain has been truncated in the vicinity of the fish and an appropriate colormap has been chosen to emphasis dynamics local to the fish. For each time-step and viewing angle, the tetrahedralize algorithm is applied. A single frame takes (at least) 10 minutes to render on an Intel dual-quad core node (w/ 24GB RAM). An animation of 95 frames was generated in a batch job using off-screen rendering. The animation can be downloaded at [1].