An Improved Penalty Immersed Boundary Method for Fluid-Flexible Body Interaction

2011 ◽  
Author(s):  
Wei-Xi Huang ◽  
Cheong Bong Chang ◽  
Hyung Jin Sung
Keyword(s):  
Fluid Velocity ◽  
Fluid Motion ◽  
Immersed Boundary ◽  
Flexible Body ◽  
Fractional Step Method ◽  
Body Interaction ◽  
Lagrangian Variables ◽  
Material Points ◽  
Stiff Spring ◽  
Solid Motion

An improved penalty immersed boundary (pIB) method has been proposed for simulation of fluid-flexible body interaction problems. In the proposed method, the fluid motion is defined on the Eulerian domain, while the solid motion is described by the Lagrangian variables. To account for the interaction, the flexible body is assumed to be composed of two parts: massive material points and massless material points, which are assumed to be linked closely by a stiff spring with damping. The massive material points are subjected to the elastic force of solid deformation but do not interact with the fluid directly, while the massless material points interact with the fluid by moving with the local fluid velocity. The flow solver and the solid solver are coupled in this framework and are developed separately by different methods. The fractional step method is adopted to solve the incompressible fluid motion on a staggered Cartesian grid, while the finite element method is developed to simulate the solid motion using an unstructured triangular mesh. The interaction force is just the restoring force of the stiff spring with damping, and is spread from the Lagrangian coordinates to the Eulerian grids by a smoothed approximation of the Dirac delta function. In the numerical simulations, three-dimensional simulations of fluid-flexible body interaction are carried out, including deformation of a spherical capsule in a linear shear flow. A comparison between the numerical results and the theoretical solutions is presented.

scholarly journals An Unstructured Finite Volume Method for Incompressible Flows With Complex Immersed Boundaries

2009 ◽  
Author(s):  
Lin Sun ◽  
Sanjay R. Mathur ◽  
Jayathi Y. Murthy
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Incompressible Flows ◽  
Simple Algorithm ◽  
Flow Region ◽  
Solid Material ◽  
The Body ◽  
Immersed Boundary ◽  
Material Points ◽  
Volume Method

A numerical method is developed for solving the 3D, unsteady, incompressible flows with immersed moving solids of arbitrary geometrical complexity. A co-located (non-staggered) finite volume method is employed to solve the Navier-Stokes governing equations for flow region using arbitrary convex polyhedral meshes. The solid region is represented by a set of material points with known position and velocity. Faces in the flow region located in the immediate vicinity of the solid body are marked as immersed boundary (IB) faces. At every instant in time, the influence of the body on the flow is accounted for by reconstructing implicitly the velocity the IB faces from a stencil of fluid cells and solid material points. Specific numerical issues related to the non-staggered formulation are addressed, including the specification of face mass fluxes, and corrections to the continuity equation to ensure overall mass balance. Incorporation of this immersed boundary technique within the framework of the SIMPLE algorithm is described. Canonical test cases of laminar flow around stationary and moving spheres and cylinders are used to verify the implementation. Mesh convergence tests are carried out. The simulation results are shown to agree well with experiments for the case of micro-cantilevers vibrating in a viscous fluid.

scholarly journals Heat Induction by Viscous Dissipation Subjected to Symmetric and Asymmetric Boundary Conditions on a Small Oscillating Flow in a Microchannel

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 499 ◽  
Author(s):  
Chih Tso ◽  
Chee Hor ◽  
Gooi Chen ◽  
Chee Kok
Keyword(s):  
Temperature Field ◽  
Prandtl Number ◽  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Lower Plate ◽  
Brinkman Number ◽  
Energy Equations ◽  
Oscillation Rate

The heat induced by viscous dissipation in a microchannel fluid, due to a small oscillating motion of the lower plate, is investigated for the first time. The methodology is by applying the momentum and energy equations and solving them for three cases of standard thermal boundary conditions. The first two cases involve symmetric boundary conditions of constant surface temperature on both plates and both plates insulated, respectively. The third case has the asymmetric conditions that the lower plate is insulated while the upper plate is maintained at constant temperature. Results reveal that, although the fluid velocity is only depending on the oscillation rate of the plate, the temperature field for all three cases show that the induced heating is dependent on the oscillation rate of the plate, but strongly dependent on the parameters Brinkman number and Prandtl number. All three cases prove that the increasing oscillation rate or Brinkman number and decreasing Prandtl number, when it is less than unity, will significantly increase the temperature field. The present model is applied to the synovial fluid motion in artificial hip implant and results in heat induced by viscous dissipation for the second case shows remarkably close agreement with the experimental literature.

A Method for Tracking a Solid Body in a Fluid Field in Immersed Boundary Methods

2018 ◽  
Author(s):  
Guangfa Yao
Keyword(s):  
Level Set ◽  
Solid Body ◽  
Volume Fraction ◽  
Transformation Matrix ◽  
The Body ◽  
New Method ◽  
Immersed Boundary ◽  
Body Interaction ◽  
Level Set Function ◽  
Set Function

Immersed boundary method has got increasing attention in modeling fluid-solid body interaction using computational fluid dynamics due to its robustness and simplicity. It usually simulates fluid-solid body interaction by adding a body force in the momentum equation. This eliminates the body conforming mesh generation that frequently requires a very labor-intensive and challenging task. But accurately tracking an arbitrary solid body is required to simulate most real world problems. In this paper, a few methods that are used to track a rigid solid body in a fluid domain are briefly reviewed. A new method is presented to track an arbitrary rigid solid body by solving a transformation matrix and identifying it using a level set function. Knowing level set function, the solid volume fraction can be derived if needed. A three-dimensional example is used to study a few methods used to represent and solve the transformation matrix, and demonstrate the presented new method.

scholarly journals Closed-Form Non-Stationary Solutionsfor Thermo and Chemovibrational Viscous Flows

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 175 ◽  
Author(s):  
Dmitry Bratsun ◽  
Vladimir Vyatkin
Keyword(s):  
Viscous Flow ◽  
Closed Form ◽  
General Procedure ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Chemical Transformations ◽  
Navier Stokes Equation ◽  
Harmonic Vibrations

A class of closed-form exact solutions for the Navier–Stokes equation written in the Boussinesq approximation is discussed. Solutions describe the motion of a non-homogeneous reacting fluid subjected to harmonic vibrations of low or finite frequency. Inhomogeneity of the medium arises due to the transversal density gradient which appears as a result of the exothermicity and chemical transformations due to a reaction. Ultimately, the physical mechanism of fluid motion is the unequal effect of a variable inertial field on laminar sublayers of different densities. We derive the solutions for several problems for thermo- and chemovibrational convections including the viscous flow of heat-generating fluid either in a plain layer or in a closed pipe and the viscous flow of fluid reacting according to a first-order chemical scheme under harmonic vibrations. Closed-form analytical expressions for fluid velocity, pressure, temperature, and reagent concentration are derived for each case. A general procedure to derive the exact solution is discussed.

Vortex dynamics and new lift enhancement mechanism of wing–body interaction in insect forward flight

2016 ◽  
Vol 795 ◽  
pp. 634-651 ◽  
Author(s):  
Geng Liu ◽  
Haibo Dong ◽  
Chengyu Li
Keyword(s):  
Vortex Dynamics ◽  
High Speed ◽  
Stokes Equations ◽  
The Body ◽  
Immersed Boundary ◽  
Dramatic Improvement ◽  
Forward Flight ◽  
Body Interaction ◽  
Enhancement Mechanism ◽  
Lift Enhancement

The effects of wing–body interaction (WBI) on aerodynamic performance and vortex dynamics have been numerically investigated in the forward flight of cicadas. Flapping wing kinematics was reconstructed based on the output of a high-speed camera system. Following the reconstruction of cicada flight, three models, wing–body (WB), body-only (BD) and wings-only (WN), were then developed and evaluated using an immersed-boundary-method-based incompressible Navier–Stokes equations solver. Results have shown that due to WBIs, the WB model had a 18.7 % increase in total lift production compared with the lift generated in both the BD and WN models, and about 65 % of this enhancement was attributed to the body. This resulted from a dramatic improvement of body lift production from 2 % to 11.6 % of the total lift produced by the wing–body system. Further analysis of the associated near-field and far-field vortex structures has shown that this lift enhancement was attributed to the formation of two distinct vortices shed from the thorax and the posterior of the insect, respectively, and their interactions with the flapping wings. Simulations are also used to examine the new lift enhancement mechanism over a range of minimum wing–body distances, reduced frequencies and body inclination angles. This work provides a new physical insight into the understanding of the body-involved lift-enhancement mechanism in insect forward flight.

Computation of Turbulent Flows in Complex and Moving Geometries Using Immersed Boundary Method

2003 ◽  
Author(s):  
Mayank Tyagi ◽  
Sumanta Acharya
Keyword(s):  
Turbulent Flows ◽  
Immersed Boundary Method ◽  
Complex Geometry ◽  
Fluid Motion ◽  
The Body ◽  
Immersed Boundary ◽  
Full Potential ◽  
Heated Cylinder ◽  
Boundary Method ◽  
Trapped Vortex

A solution methodology for complex turbulent flows of industrial interests is developed using Immersed Boundary Method (IBM). IBM combines the efficiency inherent in using a fixed Cartesian grid to compute the fluid motion, along with the ease of tracking the immersed boundary at a set of moving Lagrangian points. IBM relies upon the body force terms added in the momentum equations to represents the complex geometry on a fixed Cartesian mesh. Resolution issues for turbulent flows can be addressed by Large Eddy Simulation (LES) technique provided an accurate and robust Subgrid Stress (SGS) model is available. Higher order of numerical accuracy schemes for turbulent flows can be maintained as well as the geometrical complexities can be rendered physically by combining LES with IBM. The proposed methodology is simple and ideally suited for the moving geometries involving no-slip walls with prescribed trajectories and locations. IBM is validated for the laminar flow past a heated cylinder in a channel and LES is validated for the turbulent lid-driven cavity flow. LES-IBM is then is used to render complex geometry of trapped vortex combustor to study fluid mixing inside trapped vortex cavity. To demonstrate the full potential of LES-IBM, a complex moving geometry problem of stator-rotor interaction is solved.

Two-Color Micro PIV Measurements of Particle and Fluid Motion in AC Electrokinetics

Materials ◽  
2003 ◽  
Author(s):  
Dazhi Wang ◽  
Carl Meinhart ◽  
Marin Sigurdson
Keyword(s):  
Electric Fields ◽  
Fluorescent Dyes ◽  
Fluid Velocity ◽  
A Priori ◽  
Fluid Motion ◽  
Ac Electroosmosis ◽  
Ac Electrokinetics ◽  
Piv Measurements ◽  
Drag Forces ◽  
Micro Piv

Two-Color μ-PIV is developed and used to uniquely determine the fluid velocity based on the micron-resolution Particle Image Velocimetry (μ-PIV) technique [1–3]. The fluid velocity field was obtained by measuring the motion of two different sizes particles, 0.7 and 1.0 μm. The different sizes of particles contain different fluorescent dyes, allowing them to be distinguished using fluorescent filter cubes. By comparing the velocity fields from the two different size particles, the underlying fluid motion can be uniquely determined, without a priori knowledge of the electrical properties of the particles, or the electrical field. The test section is formed by two wedge-shaped electrodes sandwiched between two glass wafers. In the presence of nonuniform ac electric fields, the particles experience dielectrophoretic (DEP) forces due to polarization and drag forces due to viscous interaction with the suspending medium, and the fluid motion is induced by the electrothermal effect and/or ac electroosmosis. The micro-PIV measurements are used to determine quantitatively the physical characteristics of the AC electrokinetic effects.

scholarly journals Immersed Boundary Method Application as a Way to Deal with the Three-Dimensional Sudden Contraction

Computation ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 50
Author(s):  
Jonatas Borges ◽  
Marcos Lourenço ◽  
Elie Padilla ◽  
Christopher Micallef
Keyword(s):  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Immersed Boundary ◽  
Fractional Step Method ◽  
Central Difference ◽  
Boundary Method ◽  
Contraction Ratio ◽  
Sudden Contraction

The immersed boundary method has attracted considerable interest in the last few years. The method is a computational cheap alternative to represent the boundaries of a geometrically complex body, while using a cartesian mesh, by adding a force term in the momentum equation. The advantage of this is that bodies of any arbitrary shape can be added without grid restructuring, a procedure which is often time-consuming. Furthermore, multiple bodies may be simulated, and relative motion of those bodies may be accomplished at reasonable computational cost. The numerical platform in development has a parallel distributed-memory implementation to solve the Navier-Stokes equations. The Finite Volume Method is used in the spatial discretization where the diffusive terms are approximated by the central difference method. The temporal discretization is accomplished using the Adams-Bashforth method. Both temporal and spatial discretizations are second-order accurate. The Velocity-pressure coupling is done using the fractional-step method of two steps. The present work applies the immersed boundary method to simulate a Newtonian laminar flow through a three-dimensional sudden contraction. Results are compared to published literature. Flow patterns upstream and downstream of the contraction region are analysed at various Reynolds number in the range 44 ≤ R e D ≤ 993 for the large tube and 87 ≤ R e D ≤ 1956 for the small tube, considerating a contraction ratio of β = 1 . 97 . Comparison between numerical and experimental velocity profiles has shown good agreement.

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