In this paper we show and discuss the use of a versatile interaction potential approach coupled with an immersed boundary method to simulate a variety of flows involving deformable bodies. In particular, we focus on two kinds of problems, namely (i) deformation of liquid-liquid interfaces and (ii) flow in the left ventricle of the heart with either a mechanical or a natural valve. Both examples have in common the two-way interaction of the flow with a deformable interface or a membrane. The interaction potential approach (de Tullio & Pascazio, Jou. Comp. Phys., 2016; Tanaka, Wada and Nakamura, Computational Biomechanics, 2016) with minor modifications can be used to capture the deformation dynamics in both classes of problems. We show that the approach can be used to replicate the deformation dynamics of liquid-liquid interfaces through the use of ad-hoc elastic constants. The results from our simulations agree very well with previous studies on the deformation of drops in standard flow configurations such as deforming drop in a shear flow or a cross flow. We show that the same potential approach can also be used to study the flow in the left ventricle of the heart. The flow imposed into the ventricle interacts dynamically with the mitral valve (mechanical or natural) and the ventricle which are simulated using the same model. Results from these simulations are compared with adhoc in-house experimental measurements. Finally, a parallelisation scheme is presented, as parallelisation is unavoidable when studying large scale problems involving several thousands of simultaneously deforming bodies on hundreds of distributed memory computing processors.

The AFiD code, an open source solver for the incompressible Navier-Stokes equations (http://www.afid.eu), has been ported to GPU clusters to tackle large-scale wall-bounded turbulent flow simulations. The GPU porting has been carried out in CUDA Fortran with the extensive use of kernel loop directives (CUF kernels) in order to have a source code as close as possible to the original CPU version; just a few routines have been manually rewritten. A new transpose scheme, which is not limited to the GPU version only and can be generally applied to any CFD code that uses pencil distributed parallelization, has been devised to improve the scaling of the Poisson solver, the main bottleneck of incompressible solvers. The GPU version can reduce the wall clock time by an order of magnitude compared to the CPU version for large meshes. Due to the increased performance and efficient use of memory, the GPU version of AFiD can perform simulations in parameter ranges that are unprecedented in thermally-driven wall-bounded turbulence. To verify the accuracy of the code, turbulent Rayleigh-Bénard convection and plane Couette flow are simulated and the results are in good agreement with the experimental and computational data that published in previous literatures. PROGRAM SUMMARYProgram Title: AFiD-GPU Licensing provisions(please choose one): GPLv3 Programming language: Fortan 90, CUDA Fortan, MPI External routines: PGI, CUDA Toolkit, FFTW3, HDF5 Nature of problem(approx. 50-250 words): Solving the three-dimensional Navier-Stokes equations coupled with a scalar field in a cubic box bounded between two walls and other four periodic boundaries. Solution method(approx. 50-250 words): Second order finite difference method for spatial discretization, third order Runge-Kutta scheme and Crank-Nicolson method for time advancement, two dimensional pencil distributed MPI parallelization, GPU accelerated routines. Additional comments including Restrictions and Unusual features (approx. 50-250 words): The open-source code is supported and updated on http://www.afid.eu.

The phenomenon of drag reduction induced by injection of bubbles into a turbulent carrier fluid has been known for a long time; the governing control parameters and underlying physics is however not well understood. In this paper, we use three dimensional numerical simulations to uncover the effect of deformability of bubbles injected in a turbulent Taylor-Couette flow on the overall drag experienced by the system. We consider two different Reynolds numbers for the carrier flow, i.e. Re i = 5 × 10 3 and Re i = 2 × 10 4 ; the deformability of the bubbles is controlled through the Weber number which is varied in the range W e = 0.01 − 2.0. Our numerical simulations show that increasing the deformability of bubbles i.e., W e leads to an increase in drag reduction. We look at the different physical effects contributing to drag reduction and analyse their individual contributions with increasing bubble deformability. Profiles of local angular velocity flux show that in the presence of bubbles, turbulence is enhanced near the inner cylinder while attenuated in the bulk and near the outer cylinder. We connect the increase in drag reduction to the decrease in dissipation in the wake of highly deformed bubbles near the inner cylinder.

The dissolution of liquid nanodroplets is a crucial step in many applied processes, such as separation and dispersion in the food industry, crystal formation of pharmaceutical products, concentrating and analysis in medical diagnosis, and drug delivery in aerosols. In this work, using both experiments and numerical simulations, we quantitatively study the dissolution dynamics of femtoliter surface droplets in a highly ordered array under a uniform flow. Our results show that the dissolution of femtoliter droplets strongly depends on their spatial positions relative to the flow direction, drop-to-drop spacing in the array, and the imposed flow rate. In some particular cases, the droplet at the edge of the array can dissolve about 30% faster than the ones located near the centre. The dissolution rate of the droplet increases by 60% as the inter-droplet spacing is increased from 2.5 μm to 20 μm. Moreover, the droplets close to the front of the flow commence to shrink earlier than those droplets in the center of the array. The average dissolution rate is faster for the faster flow. As a result, the dissolution time (Ti) decreases with the Reynolds number (Re) of the flow as Ti ∝ Re-3/4. The experimental results are in good agreement with the numerical simulations where the advection-diffusion equation for the concentration field is solved and the concentration gradient on the surface of the drop is computed. The findings suggest potential approaches to manipulate nanodroplet sizes in droplet arrays simply by dissolution controlled by an external flow. The obtained droplets with varying curvatures may serve as templates for generating multifocal microlenses in one array.

In this paper we propose and test the validity of simple and easy-to-implement algorithms within the immersed boundary framework geared towards large scale simulations involving thousands of deformable bodies in highly turbulent flows. First, we introduce a fast moving least squares (fast-MLS) approximation technique with which we speed up the process of building transfer functions during the simulations which leads to considerable reductions in computational time. We compare the accuracy of the fast-MLS against the exact moving least squares (MLS) for the standard problem of uniform flow over a sphere. In order to overcome the restrictions set by the resolution coupling of the Lagrangian and Eulerian meshes in this particular immersed boundary method, we present an adaptive Lagrangian mesh refinement procedure that is capable of drastically reducing the number of required nodes of the basic Lagrangian mesh when the immersed boundaries can move and deform. Finally, a coarse-grained collision detection algorithm is presented which can detect collision events between several Lagrangian markers residing on separate complex geometries with minimal computational overhead.

Two-phase turbulent Taylor-Couette (TC) flow is simulated using an Euler-Lagrange approach to study the effects of a secondary phase dispersed into a turbulent carrier phase (here bubbles dispersed into water). The dynamics of the carrier phase is computed using Direct Numerical Simulations (DNS) in an Eulerian framework, while the bubbles are tracked in a Lagrangian manner by modelling the effective drag, lift, added mass and buoyancy force acting on them. Two-way coupling is implemented between the dispersed phase and the carrier phase which allows for momentum exchange among both phases and to study the effect of the dispersed phase on the carrier phase dynamics. The radius ratio of the TC setup is fixed to η=0.833, and a maximum inner cylinder Reynolds number of Re i =8000 is reached. We vary the Froude number (F r), which is the ratio of the centripetal to the gravitational acceleration of the dispersed phase and study its effect on the net torque required to drive the TC system.For the two-phase TC system, we observe drag reduction, i.e., the torque required to drive the inner cylinder is less compared to that of the single phase system. The net drag reduction decreases with increasing Reynolds number Re i , which is consistent with previous experimental findings ( Murai et al. 2005Murai et al. , 2008. The drag reduction is strongly related to the Froude number: for fixed Reynolds number we observe higher drag reduction when F r < 1 than for with F r > 1. This buoyancy effect is more prominent in low Re i systems and decreases with increasing Reynolds number Re i . We trace the drag reduction back to the weakening of the angular momentum carrying Taylor rolls by the rising bubbles. We also investigate how the motion of the dispersed phase depends on Re i and F r, by studying the individual trajectories and mean dispersion of bubbles in the radial and axial directions. Indeed, the less buoyant bubbles (large F r) tend to get trapped by the Taylor rolls, while the more buoyant bubbles (small Fr) rise through and weaken them.

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The influence of the underlying flow topology on the shape and size of sub-Kolmogorov droplets dispersed in a turbulent flow is of considerable interest in many industrial and scientific applications. In this work we study the deformation and orientation statistics of sub-Kolmogorov droplets dispersed into a turbulent Taylor-Couette flow. Along with Direct Numerical Simulations (DNS) of the carrier phase and Lagrangian tracking of the dispersed droplets, we solve a phenomenological equation proposed by Maffettone and Minale (J. Fluid Mech. 78, 227-241 (1998)) to track the shape evolution and orientation of approximately 10 5 ellipsoidal droplets. By varying the capillary number Ca and viscosity ratioμ of the droplets we find that the droplets deform more with increasing capillary number Ca and this effect is more pronounced in the boundary layer regions. This indicates that along with a capillary number effect there is also a strong correlation between spatial position and degree of deformation of the droplet. Regardless of the capillary number Ca, the major-axis of the ellipsoids tends to align with the stream-wise direction and the extensional strain rate eigen direction in the boundary layer region while the distribution is highly isotropic in the bulk. When the viscosity ratio between the droplet and the carrier fluid is increased we find that there is no preferential stretched axis which is due to the increased influence of rotation over stretching and relaxation. Droplets in high viscosity ratio systems are thus less deformed and oblate (disk-like) as compared to highly deformed prolate (cigar-like) droplets in low viscosity ratio systems.