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An immersed boundary approach for shape and topology optimization of stationary fluid-structure interaction problems

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2016年第5期54卷 1191-1208页

作者： Jenkins, Nicholas Maute, Kurt Univ Colorado Dept Aerosp Engn Sci 429 UCB Boulder CO 80309 USA

This paper presents an approach to shape and topology optimization of fluid-structure interaction (FSI) problems at steady state. The overall approach builds on an immersed boundary method that couples a Lagrangian formulation of the structure to an Eulerian fluid model, discretized on a deforming mesh. The geometry of the fluid-structure boundary is manipulated by varying the nodal parameters of a discretized level set field. This approach allows for topological changes of the fluid-structure interface, but free-floating volumes of solid material can emerge in the course of the optimization process. The free-floating volumes are tracked and modeled as fluid in the FSI analysis. To sense the isolated solid volumes, an indicator field described by linear, isotropic diffusion is computed prior to analyzing the FSI response of a design. The fluid is modeled with the incompressible Navier-Stokes equations, and the structure is assumed linear elastic. The FSI model is discretized by an extended finite element method, and the fluid-structure coupling conditions are enforced weakly. The resulting nonlinear system of equations is solved monolithically with Newton's method. The design sensitivities are computed by the adjoint method and the optimization problem is solved by a gradient-based algorithm. The characteristics of this optimization framework are studied with two-dimensional problems at steady state. Numerical results indicate that the proposed treatment of free-floating volumes introduces a discontinuity in the design evolution, yet the method is still successful in converging to meaningful designs.

关键词： Topology optimization Nitsche Extended finite element method Level set method fluid-structure interaction Heart valve

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Immersed boundary-finite element model of fluid-structure interaction in the aortic root

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THEORETICAL AND COMPUTATIONAL fluid DYNAMICS 2016年第1-2期30卷 139-164页

作者： Flamini, Vittoria DeAnda, Abe Griffith, Boyce E. NYU Dept Mech & Aerosp Engn Tandon Sch Engn Brooklyn NY USA Univ Texas Med Branch Dept Surg Div Cardiothorac Surg Galveston TX 77555 USA Univ N Carolina Dept Math Phillips HallCampus Box 3250 Chapel Hill NC USA Univ N Carolina Dept Biomed Engn Phillips HallCampus Box 3250 Chapel Hill NC USA Univ N Carolina McAllister Heart Inst Phillips HallCampus Box 3250 Chapel Hill NC USA

It has long been recognized that aortic root elasticity helps to ensure efficient aortic valve closure, but our understanding of the functional importance of the elasticity and geometry of the aortic root continues to evolve as increasingly detailed in vivo imaging data become available. Herein, we describe a fluid-structure interaction model of the aortic root, including the aortic valve leaflets, the sinuses of Valsalva, the aortic annulus, and the sinotubular junction, that employs a version of Peskin's immersed boundary (IB) method with a finite element description of the structural elasticity. As in earlier work, we use a fiber-based model of the valve leaflets, but this study extends earlier IB models of the aortic root by employing an incompressible hyperelastic model of the mechanics of the sinuses and ascending aorta using a constitutive law fit to experimental data from human aortic root tissue. In vivo pressure loading is accounted for by a backward displacement method that determines the unloaded configuration of the root model. Our model yields realistic cardiac output at physiological pressures, with low transvalvular pressure differences during forward flow, minimal regurgitation during valve closure, and realistic pressure loads when the valve is closed during diastole. Further, results from high-resolution computations indicate that although the detailed leaflet and root kinematics show some grid sensitivity, our IB model of the aortic root nonetheless produces essentially grid-converged flow rates and pressures at practical grid spacings for the high Reynolds number flows of the aortic root. These results thereby clarify minimum grid resolutions required by such models when used as stand-alone models of the aortic valve as well as when used to provide models of the outflow valves in models of left-ventricular fluid dynamics.

关键词： Aortic valve fluid-structure interaction Immersed boundary method Incompressible flow Hyperelasticity Finite element method Finite difference method

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ASSESSMENT RESULTS OF fluid-structure interaction NUMERICAL SIMULATION USING FUZZY LOGIC

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THERMAL SCIENCE 2016年第Sup1期20卷 S235-S250页

作者： Markovic, Zoran J. Stupar, Slobodan N. Dinulovic, Mirko R. Pekovic, Ognjen M. Stefanovic, Predrag Lj. Cvetinovic, Dejan B. Univ Belgrade Vinca Inst Nucl Sci Lab Thermal Engn & Energy Belgrade Serbia Univ Belgrade Dept Aerosp Engn Fac Mech Engn Belgrade Serbia

A fuzzy approximation concept is applied in order to predict results of coupled computational structure mechanics and computational fluid dynamics while solving a problem of steady incompressible gas flow through thermally loaded rectangular thin-walled channel. Channel wall deforms into wave-type shapes depending on thermal load and fluid inlet velocity inducing the changes of fluid flow accordingly. A set of fluid-structure interaction numerical tests have been defined by varying the values of fluid inlet velocity, temperature of inner and outer surface of the channel wall, and numerical grid density. The unsteady Navier-Stokes equations are numerically solved using an element-based finite volume method and second order backward Euler discretization scheme. The structural model is solved by finite element method including geometric and material non-linearities. The implicit two-way iterative code coupling, partitioned solution approach, were used while solving these numerical tests. Results of numerical analysis indicate that gravity and pressure distribution inside the channel contributes to triggering the shape of deformation. In the inverse problem, the results of fluid-structure interaction numerical simulations formed a database of input variables for development fuzzy logic based models considering downstream pressure drop and maximum stresses as the objective functions. Developed fuzzy models predicted targeting results within a reasonable accuracy limit at lower computation cost compared to series of fluid-structure interaction numerical calculations. Smaller relative difference were obtained when calculating the values of pressure drop then maximal stresses indicating that transfer function influence on output values have to be additionally investigated.

关键词： thin-walled structure fluid-structure interaction fuzzy inference model

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A hybridizable discontinuous Galerkin method for modeling fluid-structure interaction

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JOURNAL OF COMPUTATIONAL PHYSICS 2016年第0期326卷 91-114页

作者： Sheldona, Jason P. Miller, Scott T. Pitt, Jonathan S. Penn State Univ Appl Res Lab University Pk PA 16802 USA Sandia Natl Labs POB 5800 Albuquerque NM 87185 USA

This work presents a novel application of the hybridizable discontinuous Galerkin (HDG) finite element method to the multi-physics simulation of coupled fluid-structure interaction (FSI) problems. Recent applications of the HDG method have primarily been for single-physics problems including both solids and fluids, which are necessary building blocks for FSI modeling. Utilizing these established models, HDG formulations for linear elastostatics, a nonlinear elastodynamic model, and arbitrary Lagrangian-Eulerian Navier-Stokes are derived. The elasticity formulations are written in a Lagrangian reference frame, with the nonlinear formulation restricted to hyperelastic materials. With these individual solid and fluid formulations, the remaining challenge in FSI modeling is coupling together their disparate mathematics on the fluid-solid interface. This coupling is presented, along with the resultant HDG FSI formulation. Verification of the component models, through the method of manufactured solutions, is performed and each model is shown to converge at the expected rate. The individual components, along with the complete FSI model, are then compared to the benchmark problems proposed by Turek and Hron [1]. The solutions from the HDG formulation presented in this work trend towards the benchmark as the spatial polynomial order and the temporal order of integration are increased. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Hybridizable discontinuous Galerkin fluid-structure interaction HDG FSI Monolithic coupling Arbitrary Lagrangian-Eulerian Navier-Stokes Elastodynamics

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Numerical modeling of current loads on a net cage considering fluid-structure interaction

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JOURNAL OF fluidS AND structureS 2016年第0期62卷 350-366页

作者： Yao, Yeming Chen, Yinglong Zhou, Hua Yang, Huayong Zhejiang Univ State Key Lab Fluid Power Transmiss & Control Zheda Rd 38 Hangzhou 310027 Zhejiang Peoples R China

In this paper we propose and discuss a numerical method to model the current loads on a net cage. In our numerical model, the fluid-structure interaction is taken into consideration. The net cage is modeled on the mass-spring model;the flow field is modeled by the finite volume method (FVM). A novel hybrid volume approach is used to add the resistance force of the net cage into the flow field for coupling the fluid and net. The net resistance to the flow is calculated directly by the net's current load using Newton's Third Law. The resistance force is discretized in the hybrid volume and represented in the source term of the Navier-Stokes equation. By using the hybrid volume method, the mesh grid is separated from the net shape, and sparse grid (0.1 m) can be used to calculate the flow field for computational efficiency. Based on the detailed flow field, we can predict the net's current load more accurately. The final results are derived by the segregated iterative calculation of net shape and flow field. Current forces acting on both rigid and flexible net cages are simulated at water velocity from 0 to 1 m/s;the simulation results of proposed numerical method are compared with the existing experiments, good agreements are shown in both flow field and current force, the mean normalized absolute error of the current force between simulations and measurements is about 5%. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Net cage Numerical simulation Current loads fluid-structure interaction Finite volume method Hybrid volume

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Three-dimensional fluid-structure interaction simulation with a hybrid RANS-LES turbulence model for applications in transonic flow domain

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AEROSPACE SCIENCE AND TECHNOLOGY 2016年 49卷 1-16页

作者： Sekutkovski, Bojan Kostic, Ivan Simonovic, Aleksandar Cardiff, Philip Jazarevic, Vladimir Univ Belgrade Fac Mech Engn Kraljice Marife 16 Belgrade Serbia Univ Coll Dublin Sch Mech & Mat Engn Belfield D4 Dublin 2 Ireland

Current industrial practice for the fluid-structure interaction (FSI) analyses and prediction of aeroelastic phenomena, such as flutter, is heavily based on linear methods. These methods involve many of design limitations and envelope restrictions for aircraft. In this paper novel hybrid Reynolds-Averaged Navier-Stokes - Large Eddy Simulation (RANS-LES) turbulence model, i.e. k-Omega Shear Stress Transport Scale-Adaptive Improved Delayed Detached Eddy Simulation (k-Omega SST SA IDDES) is tested and implemented in the FSI procedure and is applied in transonic flow. This model is also compared with the lower fidelity RANS models, i.e. k-omega SST and Spalart-Allmaras. More precisely, a strongly coupled three-dimensional (3D) PSI solver is combined with the turbulence model and large deformation updated Lagrangian finite volume structural solver in order to resolve standard computational fluid dynamics (CFD) and aeroelastic benchmark cases of transonic flow. The turbulence model combines the advanced capabilities of the existing SST, SAS and IDDES turbulence models. Unsteadiness detection deficiency of SAS is automatically supplemented by the IDDES term included in kinetic energy equation. The numerical results of Onera M6 and AGARD 445.6 validation cases are presented and compared with the existing experimental results. Discretization of the governing equations is performed by cell-centered finite volume method (FVM) on unstructured meshes. Further application of the FSI procedure for the FSI analyzes of the whole aircraft structures is one of the aims. The emphasis is made on turbulence modeling which appears to have a major impact to the prediction of FSI behavior in transonic flow domain. In this work the aeroelasticity is treated as one of the many FSI branches. Described FSI solver is custom written and implemented in OpenFOAM. (C) 2015 Elsevier Masson SAS. All rights reserved.

关键词： fluid-structure interaction Aeroelasticity Finite volume method RANS-LES Transonic turbulent flow OpenFOAM

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Simulation of 2D fluid structure interaction in inviscid compressible flows using a cell-vertex central difference finite volume method

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JOURNAL OF fluidS AND structureS 2016年 67卷 190-218页

作者： Hejranfar, K. Azampour, M. H. Sharif Univ Technol Dept Aerosp Engn Tehran Iran

In the present study, the applicability and accuracy of a cell-vertex finite volume method developed are assessed in simulating 2D fluid structure interaction in inviscid compressible flows where the nonlinear phenomena exist in both the unsteady transonic fluid flows and the large nonlinear deformation of solid structures. The unsteady Euler equations are considered as the governing equations of the fluid flow in the arbitrary Lagrangian-Eulerian form and the large nonlinear deformation of the solid structure is considered to be governed by the Cauchy equations in the total Lagrangian form. Both the domains are discretized by a second-order central-difference cell-vertex finite volume method in space on arbitrary quadrilateral grids and a second-order implicit method in time. For each time step, the resulting set of coupled implicit nonlinear equations in either domains is solved iteratively in the pseudo-time. The fluidic and structural parts are coupled in a partitioned manner for the simulation of fluid structure interaction problems where at the interface the grids of the two domains are coincident. The formulation for the structural dynamics applied here can accurately simulate different types of boundary conditions. It can also properly model the panel thickness and therefore the stress distribution within the structure can be reasonably obtained. Some benchmark test cases are studied and the results obtained are compared with the available experimental/numerical results. Simplicity of the implementation, similarity of the discretization and accuracy of the solution demonstrate the capability and robustness of the solution methodology proposed in simulating fluid structure interaction problems in compressible flows.

关键词： fluid-structure interaction Inviscid compressible flows Structural analysis Cell-vertex finite volume method Arbitrary quadrilateral unstructured grids

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The influence of anesthesia and fluid-structure interaction on simulated shear stress patterns in the carotid bifurcation of mice

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JOURNAL OF BIOMECHANICS 2016年第13期49卷 2741-2747页

作者： De Wilde, David Trachet, Bram De Meyer, Guido Segers, Patrick Ghent Univ IMinds Med IT IBiTech bioMMeda Ghent Belgium Ecole Polytech Fed Lausanne Inst Bioengn Lausanne Switzerland Univ Antwerp Div Physiopharmacol Antwerp Belgium

Background: Low and oscillatory wall shear stresses (WSS) near aortic bifurcations have been linked to the onset of atherosclerosis. In previous work, we calculated detailed WSS patterns in the carotid bifurcation of mice using a fluid-structure interaction (FSI) approach. We subsequently fed the animals a high-fat diet and linked the results of the FSI simulations to those of atherosclerotic plaque location on a within-subject basis. However, these simulations were based on boundary conditions measured under anesthesia, while active mice might experience different hemodynamics. Moreover, the FSI technique for mouse-specific simulations is both time- and labor-intensive, and might be replaced by simpler and easier Computational fluid Dynamics (CFD) simulations. The goal of the current work was (i) to compare WSS patterns based on anesthesia conditions to those representing active resting and exercising conditions;and (ii) to compare WSS patterns based on FSI simulations to those based on steady-state and transient CFD simulations. Methods: For each of the 3 computational techniques (steady state CFD, transient CFD, FSI) we performed 5 simulations: 1 for anesthesia, 2 for conscious resting conditions and 2 more for conscious active conditions. The inflow, pressure and heart rate were scaled according to representative in vivo measurements obtained from literature. Results: When normalized by the maximal shear stress value, shear stress patterns were similar for the 3 computational techniques. For all activity levels, steady state CFD led to an overestimation of WSS values, while FSI simulations yielded a clear increase in WSS reversal at the outer side of the sinus of the external carotid artery that was not visible in transient CFD-simulations. Furthermore, the FSI simulations in the highest locomotor activity state showed a flow recirculation zone in the external carotid artery that was not present under anesthesia. This recirculation went hand in hand with locally

关键词： Carotid bifurcation Mice Wall shear stress Computational fluid dynamics fluid-structure interaction

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Finite element error estimation for quasi-Newtonian fluid-structure interaction problems

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APPLIED MATHEMATICS AND COMPUTATION 2016年 274卷 93-105页

作者： Lee, Hyesuk Xu, Shuhan Clemson Univ Dept Math Sci Clemson SC 29634 USA

We consider a monolithic scheme for fluid-structure interaction problems involving an incompressible quasi-Newtonian fluid. The monolithic formulation is obtained using the Arbitrary Lagrangian Eulerian (ALE) method with matching conditions at the fluid-structure interface. The stability and error analysis are performed for the finite element approximation. Finally, some numerical experiments that confirm the theoretical analysis are presented. (C) 2015 Elsevier Inc. All rights reserved.

关键词： fluid-structure interaction Monolithic approach Finite element error estimate

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HYDRODYNAMIC CHARACTERISTICS AND STRUCTURAL IMPROVEMENT OF A FIXED MOUNT IN A HEAT EXCHANGER WITH ONE-WAY fluid-structure interaction

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JOURNAL OF ENHANCED HEAT TRANSFER 2016年第6期23卷 431-447页

作者： He, Lichen Yang, Weimin Guan, Changfeng Yan, Hua Beijing Univ Chem Technol Coll Mech & Elect Engn Mail Box 268North Third Ring Rd 15 Beijing 100029 Peoples R China

A rotor-assembled strand works as a typical tube insert to achieve heat transfer augmentation and scale prevention in a heat exchanger. In this paper, a fixed mount (FM), which is an essential part of the rotor-assembled strand, was simulated using the one-way fluid-structure interaction (FSI) method in order to improve its structure by analyzing its hydraulic performance and structural stress. Prior to the simulation, the accuracy of the FSI method was verified using an example of a conical tube. The results showed that the fluid deviated remarkably from the axis at the inlet of the central tube with original FM, which helps the heat transfer in the fluid;the pressure drop between the inlet and the outlet in the tube with the original FM increased by 23.89% compared with that in a plain tube;the stress at the shoulders and the joints of different parts was high;and the maximum stress point occurred at the joint of the central axis and the shoulder. To reduce the pressure drop, the structure of the original FM was improved. After modification, the pressure drop decreased, while the maximum stress magnitude was raised, and the modified FM was still safe enough when it worked under the worst conditions. The results indicate that the stress distribution and pressure drop should be considered when designing FMs.

关键词： fluid-structure interaction pressure drop equivalent stress fixed mount

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