A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies

We present a moving control volume (CV) approach to computing hydrodynamic forces and torques on complex geometries. The method requires surface and volumetric integrals over a simple and regular Cartesian box that moves with an arbitrary velocity to enclose the body at all times. The moving box is aligned with Cartesian grid faces, which makes the integral evaluation straightforward in an immersed boundary (IB) framework. Discontinuous and noisy derivatives of velocity and pressure at the fluid-structure interface are avoided and far-field (smooth) velocity and pressure information is used. We re-visit the approach to compute hydrodynamic forces and torques through force/torque balance equation in a Lagrangian frame that some of us took in a prior work (Bhalla et al., J Comp Phys, 2013). We prove the equivalence of the two approaches for IB methods, thanks to the use of Peskin's delta functions. Both approaches are able to suppress spurious force oscillations and are in excellent agreement, as expected theoretically. Test cases ranging from Stokes to high Reynolds number regimes are considered. We discuss regridding issues for the moving CV method in an adaptive mesh refinement (AMR) context. The proposed moving CV method is not limited to a specific IB method and can also be used, for example, with embedded boundary methods

Coupling the fictitious domain and sharp interface methods for the simulation of convective mass transfer around reactive particles: towards a reactive Sherwood number correlation for dilute systems

We suggest a reactive Sherwood number model for convective mass transfer around reactive particles in a dilute regime. The model is constructed with a simple external-internal coupling and is validated with Particle-Resolved Simulation (PRS). The PRS of reactive particle-fluid systems requires numerical methods able to handle efficiently sharp gradients of concentration and potential discontinuities of gradient concentrations at the fluid-particle interface. To simulate mass transfer from reactive catalyst beads immersed in a fluid flow, we coupled the Sharp Interface Method (SIM) to a Distributed Lagrange Multiplier/Fictious Domain (DLM/FD) two-phase flow solver. We evaluate the accuracy of our numerical method by comparison to analytic solutions and to generic test cases fully resolved by boundary fitted simulations. A previous theoretical model that couples the internal diffusion-reaction problem with the external advection-diffusion mass transfer in the fluid phase is extended to the configuration of three aligned spherical particles representative of a dilute particle-laden flow. Predictions of surface concentration, mass transfer coefficient and chemical effectiveness factor of catalyst particles are validated by DLM-FD/SIM simulations. We show that the model captures properly the effect of an internal first order chemical reaction on the overall respective reactive Sherwood number of each sphere depending on their relative positions. The proposed correlation for the reactive Sherwood number is based on an existing non-reactive Sherwood number correlation. The model can be later used in Euler/Lagrange or Euler/ Euler modelling of dilute reactive particle-laden flows

A unified constraint formulation of immersed body techniques for coupled fluid-solid motion: continuous equations and numerical algorithms

Numerical simulation of moving immersed solid bodies in fluids is now practiced routinely following pioneering work of Peskin and co-workers on immersed boundary method (IBM), Glowinski and co-workers on fictitious domain method (FDM), and others on related methods. A variety of variants of IBM and FDM approaches have been published, most of which rely on using a background mesh for the fluid equations and tracking the solid body using Lagrangian points. The key idea that is common to these methods is to assume that the entire fluid-solid domain is a fluid and then to constrain the fluid within the solid domain to move in accordance with the solid governing equations. The immersed solid body can be rigid or deforming. Thus, in all these methods the fluid domain is extended into the solid domain. In this review, we provide a mathemarical perspective of various immersed methods by recasting the governing equations in an extended domain form for the fluid. The solid equations are used to impose appropriate constraints on the fluid that is extended into the solid domain. This leads to extended domain constrained fluid-solid governing equations that provide a unified framework for various immersed body techniques. The unified constrained governing equations in the strong form are independent of the temporal or spatial discretization schemes. We show that particular choices of time stepping and spatial discretization lead to different techniques reported in literature ranging from freely moving rigid to elastic self-propelling bodies. These techniques have wide ranging applications including aquatic locomotion, underwater vehicles, car aerodynamics, and organ physiology (e.g. cardiac flow, esophageal transport, respiratory flows), wave energy convertors, among others. We conclude with comments on outstanding challenges and future directions

A Review on Contact and Collision Methods for Multi-body Hydrodynamic problems in Complex Flows

Modeling and direct numerical simulation of particle-laden flows have a tremendous variety of applications in science and engineering across a vast spectrum of scales from pollution dispersion in the atmosphere, to fluidization in the combustion process, to aerosol deposition in spray medication, along with many others. Due to their strongly nonlinear and multiscale nature, the above complex phenomena still raise a very steep challenge to the most computational methods. In this review, we provide comprehensive coverage of multibody hydrodynamic (MBH) problems focusing on particulate suspensions in complex fluidic systems that have been simulated using hybrid Eulerian-Lagrangian particulate flow models. Among these hybrid models, the Immersed Boundary-Lattice Boltzmann Method (IB-LBM) provides mathematically simple and computationally-efficient algorithms for solid-fluid hydrodynamic interactions in MBH simulations. This paper elaborates on the mathematical framework, applicability, and limitations of various 'simple to complex' representations of close-contact interparticle interactions and collision methods, including short-range inter-particle and particle-wall steric interactions, spring and lubrication forces, normal and oblique collisions, and mesoscale molecular models for deformable particle collisions based on hard-sphere and soft-sphere models in MBH models to simulate settling or flow of nonuniform particles of different geometric shapes and sizes in diverse fluidic systems.Comment: 37 pages, 12 Figure

Computer Simulation of Three Particles Sedimentation in a Narrow Channel

The settling of three particles in a narrow channel is simulated via the lattice Boltzmann direct-forcing/fictitious domain (LB-DF/FD) method for the Reynolds number ranging from 5 to 200. The effects of the wall and the Reynolds number are studied. It is interesting to find that at certain Reynolds numbers the left (right) particle is settling at 0.175 (0.825) of the channel width irrespective of its initial position or the channel width. Moreover, numerical results have shown that the lateral particles lead at small Reynolds numbers, while the central particle leads at large Reynolds numbers due to the combined effects of particle-particle and particle-wall interactions. The central particle will leave the lateral ones behind when the Reynolds number is large enough. Finally the effect of the Reynolds number on the trajectory of the lateral particles is presented