Numerical benchmarking of fluid-rigid body interactions

We propose a fluid-rigid body interaction benchmark problem, consisting of a solid spherical obstacle in a Newtonian fluid, whose centre of mass is fixed but is free to rotate. A number of different problems are defined for both two and three spatial dimensions. The geometry is chosen specifically, such that the fluid-solid partition does not change over time and classical fluid solvers are able to solve the fluid-structure interaction problem. We summarise the different approaches used to handle the fluid-solid coupling and numerical methods used to solve the arising problems. The results obtained by the described methods are presented and we give reference intervals for the relevant quantities of interest

Hybrid finite difference/finite element immersed boundary method

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach employs a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach

Benchmarking in a rotating annulus: a comparative experimental and numerical study of baroclinic wave dynamics

The differentially heated rotating annulus is a widely studied tabletop-size laboratory model of the general mid-latitude atmospheric circulation. The two most relevant factors of cyclogenesis, namely rotation and meridional temperature gradient are quite well captured in this simple arrangement. The radial temperature difference in the cylindrical tank and its rotation rate can be set so that the isothermal surfaces in the bulk tilt, leading to the formation of baroclinic waves. The signatures of these waves at the free water surface have been analyzed via infrared thermography in a wide range of rotation rates (keeping the radial temperature difference constant) and under different initial conditions. In parallel to the laboratory experiments, five groups of the MetStr\"om collaboration have conducted numerical simulations in the same parameter regime using different approaches and solvers, and applying different initial conditions and perturbations. The experimentally and numerically obtained baroclinic wave patterns have been evaluated and compared in terms of their dominant wave modes, spatio-temporal variance properties and drift rates. Thus certain ``benchmarks'' have been created that can later be used as test cases for atmospheric numerical model validation

Near-wall velocity of suspended particles in microchannel flow

This contribution investigates the characteristic reduction of the particle velocity with respect to the velocity profile of a pure liquid (water) in a pressure driven flow (PDF). It is shown by simulations and experiments that particles are slowed down once their local perturbation "cloud" of the velocity field hits the wall. We show that this effect scales with the ratio of the distance of sphere's surface from the wall, a, and the radius, a, of the sphere, i.e. delta/a

Nonlinear multi-mode interactions in subsea risers undergoing vortex-induced vibrations

This paper investigates nonlinear multi-mode interactions in subsea risers undergoing vortex-induced vibrations based on a computationally efficient reduced-order fluid-structure interaction model. Cross-flow responses as a result of a steady uniform current are considered. The geometrically nonlinear equations of riser motion are coupled with nonlinear wake oscillators which have been modified to capture the effect of initial curvatures of curved cylinder and to approximate the space-time varying hydrodynamic lift forces. The main objectives are to provide new insights into the vortex-induced vibration characteristics of risers under external and internal resonances and to distinguish nonlinear dynamic behaviors between curved catenary and straight toptensioned risers. The analyses of multi-mode contributions, lock-in regimes, response amplitudes, resonant nonlinear modes and curvatures are carried out and several interesting aspects are highlighted

ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics

Physical simulators have been widely used in robot planning and control. Among them, differentiable simulators are particularly favored, as they can be incorporated into gradient-based optimization algorithms that are efficient in solving inverse problems such as optimal control and motion planning. Simulating deformable objects is, however, more challenging compared to rigid body dynamics. The underlying physical laws of deformable objects are more complex, and the resulting systems have orders of magnitude more degrees of freedom and therefore they are significantly more computationally expensive to simulate. Computing gradients with respect to physical design or controller parameters is typically even more computationally challenging. In this paper, we propose a real-time, differentiable hybrid Lagrangian-Eulerian physical simulator for deformable objects, ChainQueen, based on the Moving Least Squares Material Point Method (MLS-MPM). MLS-MPM can simulate deformable objects including contact and can be seamlessly incorporated into inference, control and co-design systems. We demonstrate that our simulator achieves high precision in both forward simulation and backward gradient computation. We have successfully employed it in a diverse set of control tasks for soft robots, including problems with nearly 3,000 decision variables.Comment: In submission to ICRA 2019. Supplemental Video: https://www.youtube.com/watch?v=4IWD4iGIsB4 Project Page: https://github.com/yuanming-hu/ChainQuee

Numerical Study of Body Shape and Wing Flexibility in Fluid Structure Interaction

We discuss the equilibrium configurations of fibers clamped to an ellipsoidal body and immersed in a flow ranging between 0-50 cm/s. Experimental and numerical results are presented and the effects of flow speed, body shape, and orientation of the fibers upon the equilibrium configuration are investigated. Our investigations reveal that the orientation of the fibers, the length of the length fibers, as well as, the shape of the body has a significant impact upon the bending and drag experienced by the ellipsoid-fiber system. We note that (i) less eccentric bodies experience greater drag forces and increased bending of the attached fibers, (ii) the fibers oriented with the flow experienced less drag and bending than the fibers oriented perpendicular to the flow, (iii) the longer fibers bend significantly more than the shorter ones, and (iv) the longer fibers display oscillatory or flapping motion at much lower flow speeds than their shorter counterparts. The simulations also reveal that the drag on the fiber is noticeably affected by the size of the basal body. Drag exponents (or Vogel exponents) are also computed and seen to deviate slightly from previous results

Prediction of Ship Unsteady Maneuvering in Calm Water by a Fully Nonlinear Ship Motion Model

This is the continuation of our research on development of a fully nonlinear, dynamically consistent, numerical ship motion model (DiSSEL). In this study we will report our results in predicting ship motions in unsteady maneuvering in calm water. During the unsteady maneuvering, both the rudder angle, and ship forward speed vary with time. Therefore, not only surge, sway, and yaw motions occur, but roll, pitch and heave motions will also occur even in calm water as heel, trim, and sinkage, respectively. When the rudder angles and ship forward speed vary rapidly with time, the six degrees-of-freedom ship motions and their interactions become strong. To accurately predict the six degrees-of-freedom ship motions in unsteady maneuvering, a universal method for arbitrary ship hull requires physics-based fully-nonlinear models for ship motion and for rudder forces and moments. The numerical simulations will be benchmarked by experimental data of the Pre-Contract DDG51 design and an Experimental Hull Form. The benchmarking shows a good agreement between numerical simulations by the enhancement DiSSEL and experimental data. No empirical parameterization is used, except for the influence of the propeller slipstream on the rudder, which is included using a flow acceleration factor