A singular perturbation model of fluid dynamics in the vestibular semicircular canal and ampulla

1996 ◽  
Vol 307 ◽  
pp. 333-372 ◽  
Author(s):  
E. R. Damiano ◽  
R. D. Rabbitt
Keyword(s):  
Fluid Dynamics ◽  
Boundary Condition ◽  
Angular Velocity ◽  
Semicircular Canal ◽  
Fluid Structure Interaction ◽  
Three Dimensional ◽  
Shear Angle ◽  
Horizontal Semicircular Canal ◽  
Fluid Structure ◽  
Structure Interaction

A matched asymptotic analysis is presented that describes the mechanical response of the vestibular semicircular canals to rotation of the head and includes the fluid–structure interaction which takes place within the enlarged ampullary region of the duct. New theoretical results detail the velocity field in a fluid boundary layer surrounding the cupula. The governing equations were linearized for small perturbations in fluid displacement from the prescribed motion of the head and reduced asymptotically by exploiting the slender geometry of the duct. The results include the pressure drop around the three-dimensional endolymphatic duct and through the transitional boundary layers within the ampulla. Results implicitly include the deflected shape of the cupular partition and provide an expression for the dynamic boundary condition acting on the two surfaces of the cupula. In this sense, the analysis reduces the three-dimensional fluid dynamics of the endolymph to a relatively simple boundary condition acting on the surfaces of the cupula. For illustrative purposes we present specific results modelling the cupula as a simple viscoelastic membrane. New results show that the multi-dimensional fluid dynamics within the enlarged ampulla has a significant influence on the pointwise deflection of the cupula near the crista. The spatially averaged displacement of the cupula is shown to agree with previous macromechanical descriptions of endolymph flow and pressure that ignore the fluid–structure interaction at the cupula. As an example, the model is applied to the geometry of the horizontal semicircular canal of the toadfish, Opsanus tau, and results for the deflection of the cupula are compared to individual semicircular canal afferent responses previously reported by Boyle & Highstein (1990). The cupular-shear-angle gain, defined by the angular slope of the cupula at the crista divided by the angular velocity of the head, is relatively constant at frequencies from 0.01 Hz up to 1 Hz. Over this same range, the phase of the cupular shear angle aligns with the angular velocity of the head. Near 10 Hz, the shear-angle gain increases slightly and the phase shows a lead of as much a 30°. Results are sensitive to the cupular stiffness and viscosity. Comparing results to the afferent responses represented within the VIIIth nerve provides additional theoretical evidence that the macromechanical displacement of the cupula accounts for the behaviour of only a subset of afferent fibres.

Modeling of aortic valve stenosis using fluid-structure interaction method

Perfusion ◽  
2021 ◽  
pp. 026765912199854
Author(s):  
Mohammad Javad Ghasemi Pour ◽  
Kamran Hassani ◽  
Morteza Khayat ◽  
Shahram Etemadi Haghighi
Keyword(s):  
Blood Flow ◽  
Aortic Valve ◽  
Fluid Structure Interaction ◽  
Three Dimensional ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Relaxation Phase ◽  
Exercise Condition ◽  
Time Dependent Domain ◽  
Comparison Of The Results

Background and objectives: Fluid structure interaction (FSI) is defined as interaction of the structures with contacting fluids. The aortic valve experiences the interaction with blood flow in systolic phase. In this study, we have tried to predict the hemodynamics of blood flow through a normal and stenotic aortic valve in two relaxation and exercise conditions using a three-dimensional FSI method. Methods: The aorta valve was modeled as a three-dimensional geometry including a normal model and two others with 25% and 50% stenosis. The geometry of the aortic valve was extracted from CT images and the models were generated by MMIMCS software and then they were implemented in ANSYS software. The pulsatile flow rate was used for all cases and the numerical simulations were conducted based on a time-dependent domain. Results: The obtained results including the velocity, pressure, and shear stress contours in different systolic time sequences were explained and discussed. The maximum blood flow velocity in relaxation phase was obtained 1.62 m/s (normal valve), 3.78 m/s (25% stenosed valve), and 4.73 m/s (50% stenosed valve). In exercise condition, the maximum velocities are 2.86, 4.32, and 5.42 m/s respectively. The maximum blood pressure in relaxation phase was calculated 111.45 mmHg (normal), 148.66 mmHg (25% stenosed), and 164.21 mmHg (50% stenosed). However, the calculated values in exercise situation were 129.57, 163.58, and 191.26 mmHg. The validation of the predicted results was also conducted using existing literature. Conclusions: We believe that such model are useful tools for biomechanical experts. The further studies should be done using experimental data and the data are implemented on the boundary conditions for better comparison of the results.

Scalability study of an implicit solver for coupled fluid-structure interaction problems on unstructured meshes in 3D

2016 ◽  
Vol 32 (2) ◽  
pp. 207-219 ◽  
Author(s):  
Fande Kong ◽  
Xiao-Chuan Cai
Keyword(s):  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Three Dimensional ◽  
Coupled System ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Krylov Method ◽  
Fine Mesh ◽  
Processor Cores ◽  
Fully Coupled

Fluid-structure interaction (FSI) problems are computationally very challenging. In this paper we consider the monolithic approach for solving the fully coupled FSI problem. Most existing techniques, such as multigrid methods, do not work well for the coupled system since the system consists of elliptic, parabolic and hyperbolic components all together. Other approaches based on direct solvers do not scale to large numbers of processors. In this paper, we introduce a multilevel unstructured mesh Schwarz preconditioned Newton–Krylov method for the implicitly discretized, fully coupled system of partial differential equations consisting of incompressible Navier–Stokes equations for the fluid flows and the linear elasticity equation for the structure. Several meshes are required to make the solution algorithm scalable. This includes a fine mesh to guarantee the solution accuracy, and a few isogeometric coarse meshes to speed up the convergence. Special attention is paid when constructing and partitioning the preconditioning meshes so that the communication cost is minimized when the number of processor cores is large. We show numerically that the proposed algorithm is highly scalable in terms of the number of iterations and the total compute time on a supercomputer with more than 10,000 processor cores for monolithically coupled three-dimensional FSI problems with hundreds of millions of unknowns.

Numerical Investigation of Hydroelastic Response of a Three-Dimensional Deformable Hydrofoil

2020 ◽  
Author(s):  
Saeed Hosseinzadeh ◽  
Kristjan Tabri
Keyword(s):  
Pressure Coefficient ◽  
Fluid Structure Interaction ◽  
Three Dimensional ◽  
Leading Edge ◽  
Elastic Response ◽  
Fluid Structure ◽  
Strongly Coupled ◽  
Structure Interaction ◽  
Lift And Drag ◽  
Hydroelastic Response

The present study is concerned with the numerical simulation of Fluid-Structure Interaction (FSI) on a deformable three-dimensional hydrofoil in a turbulent flow. The aim of this work is to develop a strongly coupled two-way fluid-structure interaction methodology with a sufficiently high spatial accuracy to examine the effect of turbulent and cavitating flow on the hydroelastic response of a flexible hydrofoil. A 3-D cantilevered hydrofoil with two degrees-of-freedom is considered to simulate the plunging and pitching motion at the foil tip due to bending and twisting deformation. The defined problem is numerically investigated by coupled Finite Volume Method (FVM) and Finite Element Method (FEM) under a two-way coupling method. In order to find a better understanding of the dynamic FSI response and stability of flexible lifting bodies, the fluid flow is modeled in the different turbulence models and cavitation conditions. The flow-induced deformation and elastic response of both rigid and flexible hydrofoils at various angles of attack are studied. The effect of three-dimension body, pressure coefficient at different locations of the hydrofoil, leading-edge and trailing-edge deformation are presented and the results show that because of elastic deformation, the angle of attack increases and it lead to higher lift and drag coefficients. In addition, the deformations are generally limited by stall condition and because of unsteady vortex shedding, the post-stall condition should be considered in FSI simulation of deformable hydrofoil. To evaluate the accuracy of the numerical model, the present results are compared and validated against published experimental data and showed good agreement.

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