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Register a new userGlobal stability of rigid-body-motion fluid-structure-interaction problems
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A rigorous derivation and validation for linear fluid-structure-interaction (FSI) equations for a rigid-body-motion problem is performed in an Eulerian framework. We show that the added-stiffness terms arising in the formulation of Fanion et al. (2000) vanish at the FSI interface in a first-order approximation. Several numerical tests with rigid-body motion are performed to show the validity of the derived formulation by comparing the time evolution between the linear and non-linear equations when the base flow is perturbed by identical small-amplitude perturbations. In all cases both the growth rate and angular frequency of the instability matches within $0.1%$ accuracy. The derived formulation is used to investigate the phenomenon of symmetry breaking for a rotating cylinder with an attached splitter-plate. The results show that the onset of symmetry breaking can be explained by the existence of a zero-frequency linearly unstable mode of the coupled fluid-structure-interaction system. Finally, the structural sensitivity of the least stable eigenvalue is studied for an oscillating cylinder, which is found to change significantly when the fluid and structural frequencies are close to resonance.
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The secret to the spectacular flight capabilities of flapping insects lies in their wings, which are often approximated as flat, rigid plates. Real wings are however delicate structures, composed of veins and membranes, and can undergo significant deformation. In the present work, we present detailed numerical simulations of such deformable wings. Our results are obtained with a fluid-structure interaction solver, coupling a mass-spring model for the flexible wing with a pseudo-spectral code solving the incompressible Navier-Stokes equations. We impose the no-slip boundary condition through the volume penalization method; the time-dependent complex geometry is then completely described by a mask function. This allows solving the governing equations of the fluid on a regular Cartesian grid. Our implementation for massively parallel computers allows us to perform high resolution computations with up to 500 million grid points. The mass-spring model uses a functional approach, thus modeling the different mechanical behaviors of the veins and the membranes of the wing. We perform a series of numerical simulations of a flexible revolving bumblebee wing at a Reynolds number Re = 1800. In order to assess the influence of wing flexibility on the aerodynamics, we vary the elasticity parameters and study rigid, flexible and highly flexible wing models. Code validation is carried out by computing classical benchmarks.
The reliability of cardiovascular computational models depends on the accurate solution of the hemodynamics, the realistic characterization of the hyperelastic and electric properties of the tissues along with the correct description of their interaction. The resulting fluid-structure-electrophysiology interaction (FSEI) thus requires an immense computational power, usually available in large supercomputing centers, and requires long time to obtain results even if multi-CPU processors are used (MPI acceleration). In recent years, graphics processing units (GPUs) have emerged as a convenient platform for high performance computing, as they allow for considerable reductions of the time-to-solution. This approach is particularly appealing if the tool has to support medical decisions that require solutions within reduced times and possibly obtained by local computational resources. Accordingly, our multi-physics solver has been ported to GPU architectures using CUDA Fortran to tackle fast and accurate hemodynamics simulations of the human heart without resorting to large-scale supercomputers. This work describes the use of CUDA to accelerate the FSEI on heterogeneous clusters, where both the CPUs and GPUs are used in synergistically with minor modifications of the original source code. The resulting GPU accelerated code solves a single heartbeat within a few hours (from three to ten depending on the grid resolution) running on premises computing facility made of few GPU cards, which can be easily installed in a medical laboratory or in a hospital, thus opening towards a systematic computational fluid dynamics (CFD) aided diagnostic.
We are modelling multi-scale, multi-physics uncertainty in wave-current interaction (WCI). To model uncertainty in WCI, we introduce stochasticity into the wave dynamics of two classic models of WCI; namely, the Generalised Lagrangian Mean (GLM) model and the Craik--Leibovich (CL) model. The key idea for the GLM approach is the separation of the Lagrangian (fluid) and Eulerian (wave) degrees of freedom in Hamiltons principle. This is done by coupling an Euler--Poincare {it reduced Lagrangian} for the current flow and a {it phase-space Lagrangian} for the wave field. WCI in the GLM model involves the nonlinear Doppler shift in frequency of the Hamiltonian wave subsystem, which arises because the waves propagate in the frame of motion of the Lagrangian-mean velocity of the current. In contrast, WCI in the CL model arises because the fluid velocity is defined relative to the frame of motion of the Stokes mean drift velocity, which is usually taken to be prescribed, time independent and driven externally. We compare the GLM and CL theories by placing them both into the general framework of a stochastic Hamiltons principle for a 3D Euler--Boussinesq (EB) fluid in a rotating frame. In other examples, we also apply the GLM and CL methods to add wave physics and stochasticity to the familiar 1D and 2D shallow water flow models. The differences in the types of stochasticity which arise for GLM and CL models can be seen by comparing the Kelvin circulation theorems for the two models. The GLM model acquires stochasticity in its Lagrangian transport velocity for the currents and also in its group velocity for the waves. The Kelvin circulation theorem stochastic CL model can accept stochasticity in its both its integrand and in the Lagrangian transport velocity of its circulation loop.
The use of microscopic discrete fluid volumes (i.e., droplets) as microreactors for digital microfluidic applications often requires mixing enhancement and control within droplets. In this work, we consider a translating spherical liquid droplet to which we impose a time periodic rigid-body rotation which we model using the superposition of a Hill vortex and an unsteady rigid body rotation. This perturbation in the form of a rotation not only creates a three-dimensional chaotic mixing region, which operates through the stretching and folding of material lines, but also offers the possibility of controlling both the size and the location of the mixing. Such a control is achieved by judiciously adjusting the three parameters that characterize the rotation, i.e., the rotation amplitude, frequency and orientation of the rotation. As the size of the mixing region is increased, complete mixing within the drop is obtained.
We investigate the role of linear mechanisms in the emergence of nonlinear horizontal self-propelled states of a heaving foil in a quiescent fluid. Two states are analyzed: a periodic state of unidirectional motion and a quasi-periodic state of slow back & forth motion around a mean horizontal position. The states emergence is explained through a fluid-solid Floquet stability analysis of the non-propulsive symmetric base solution. Unlike a purely-hydrodynamic analysis, our analysis accurately determine the locomotion states onset. An unstable synchronous mode is found when the unidirectional propulsive solution is observed. The obtained mode has a propulsive character, featuring a mean horizontal velocity and an asymmetric flow that generates a horizontal force accelerating the foil. An unstable asynchronous mode, also featuring flow asymmetry and a non-zero velocity, is found when the back & forth state is observed. Its associated complex multiplier introduces a slow modulation of the flapping period, agreeing with the quasi-periodic nature of the back & forth regime. The temporal evolution of this perturbation shows how the horizontal force exerted by the flow is alternatively propulsive or resistive over a slow period. For both modes, an analysis of the velocity and force perturbation time-averaged over the flapping period is used to establish physical instability criteria. The behaviour for large solid-to-fluid density ratio of the modes is thus analyzed. The asynchronous fluid-solid mode converges towards the purely-hydrodynamic one, whereas the synchronous mode becomes marginally unstable in our analysis not converging to the purely-hydrodynamic analysis where it is never destabilised.
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