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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS

Int.J.Numer.Meth.Fluids2002;40:467–478(DOI:10.1002/ d.306)

Implicit uid–structure coupling for simulation

of cardiovascular problems

J.M.T.Penrose1;?and C.J.Staples2

1Department of Medical Physics and Clinical Engineering;University of She eld;Royal Hallamshire Hospital;

Glossop Road;She eld S102JF;U.K.

2AEA Technology Engineering Software;Building8.19Harwell;Didcot;Oxon.OX11OQJ,U.K.

SUMMARY

A three-dimensional(3-D)transient solid– uid coupling system has been developed in order to study cardiovascular systems and devices.The system utilized two commercial implicit solvers,which ex-changed boundary parameters from separate meshes over a common interface.Facility was made for the spatial interpolation of these exchange parameters so that the solid and uid domain meshes need not have similar density or topology.Stability algorithms were added to the iterative coupling process, as were algorithms to smooth or entirely remesh the uid domain interior subject to the deformations imposed at the solid– uid interface.Several application scenarios were undertaken,whereby simulation results could be compared to either analytical or detailed experimental data.It was hoped they would also o er further insight into the operation of a number of clinical devices.The results of these com-parisons show that the simulation of complex cardiac systems,with non-linear solid– uid interactions, can now be achieved with su cient accuracy to be of signi?cant bene?t to manufacturers.Copyright ?2002John Wiley&Sons,Ltd.

KEY WORDS:FEA;CFD; uid–structure coupling;cardiovascular

1.INTRODUCTION

Over the years,implantable and extra-corporeal devices have signi?cantly improved the life-expectancy and quality of life of patients su ering from cardiovascular disease.However, there are also signi?cant problems and complications associated with many of these devices. These could be partially addressed by better design work arising from a better understanding of the function of these devices,and their interaction with their physiological surroundings[1]. Simulation of these systems can provide valuable information that can be fed back into the design process.Thus,di erent materials and geometries can be evaluated relatively quickly and cheaply,hopefully leading to better clinical results.

?Correspondence to:J.M.T.Penrose,AEA Technology Engineering Software,The Gemini Building,Fermi Avenue, Harwell International Business Centre,Didcot,Oxfordshire OX11OQR,U.K.

Contract=grant sponsor:European Commission’s IST programme;contract=grant number:BloodSim EP28350

Received May2001 Copyright?2002John Wiley&Sons,Ltd.Revised October2001

468J.M.T.PENROSE AND C.J.STAPLES

It has long been recognized that the interactions between a uid phase and a deformable solid phase are of primary importance in a variety of systems,not least in physiological simulation.This is doubly true for cardiovascular simulation where the solid and uid materials may have complex,non-linear properties;where complex geometries are common,and where even small structural deviations may cause large changes in uid behaviour(and vice versa). However,high-performance computing power and numerical methods have progressed over the last decade to the point where such three-dimensional(3-D)transient coupled simulations can be achieved within realistic time-scales.

This paper describes the development of a transient coupled3-D?nite-element system aimed at the simulation of such cardiovascular problems,backed by a consortium of cardiac device manufacturers.

2.IMPLEMENTATION

Several commercial and research codes exist for the coupling of solid and uid mechanics. However,the vast majority of these codes have become available only over the last few years, and so algorithmic details,case studies and examples,particularly in physiological areas,are often hard to?nd.Perhaps,the most well-known cardiovascular research is that of Peskin and McQueen at NYU[2].They have managed to produce both2-D and3-D models of the heart,complete with functioning valves,within which the blood is pumped purely by the constrictive action of the ventricle walls.They use a?nite volume code which simultaneously solves for the solid– uid interaction based on the so-called‘immersed boundary’method. Here,the solid domain is not explicitly represented within the uid domain,but rather exists only by the additional force‘?eld’that the solid exerts on the uid where the two domains would overlap.Such a method can be straightforward to apply,but the researchers’models are very detailed and computationally costly.The method may also be only applicable to ‘thin’structures.

An alternative coupling scheme to the simultaneous solution is that whereby two separate solvers are used to solve the two distinct solid and uid phases.The separate phases are solved sequentially at a given time,with the boundary solution from one used as a boundary constraint for the other.Such a coupling has been exploited by Perktold and colleagues at the University of Graz[3–5].They have coupled the commercial solid code Abaqus to their own uid code(an arbitrary Lagrangian=Eularian FE code using the Galerkin method)exploiting the iterative coupling scheme.They have used it to study artery dynamics and anastemoses in3-D.A similar hybrid iterative scheme,coupling the uid code CFX and the solids code Abaqus,has been developed by Prof.Collins and his team at City University and Imperial College in London[6–8].They have produced some impressive3-D simulations of blood ow through the carotid bifurcation,using initially a coupling over a single cardiac cycle,as oppose to a single timestep of that cycle.

More recent developments have shown coupled simulations performed within a single soft-ware package.Kunzelman et al.[9]have modi?ed the explicit LS-Dyna package,which now boasts an incompressible ow solver in addition to their well established structures solver, and produced some impressive3-D simulations of cardiac valves.

It was decided that for the purposes of this research two existing commercial codes,Ansys and CFX,would be coupled,thereby exploiting the particular strengths of each in simulating Copyright?2002John Wiley&Sons,Ltd.Int.J.Numer.Meth.Fluids2002;40:467–478

IMPLICIT FLUID–STRUCTURE COUPLING469

Figure1.Solution variable exchange between the two solvers.

their particular phase physics.Both codes also o er parallel processing solvers,thus enabling signi?cant reductions in simulation time on multi-processor architectures.

2.1.CFX-5

CFX-5is a commercial CFD package that uses an implicit?nite-element control volume formulation to construct the discrete equations representing the Navier–Stokes equations for the uid ow.The mixed-element mesh can be unstructured and composed of hexahedra, tetrahedra,wedges and pyramids.A coupled algebraic multi-grid solver is used to give robust solutions for the governing discrete equations.

2.2.ANSYS

ANSYS[10]is a world-leading implicit?nite-element software product,for linear and non-linear stress analysis.It has the facility for a wide range of structural elements and formula-tions,and again meshes can be mixed and unstructured.It is used for calculating the response of any deformable regions within the coupled simulation,based on appropriate loading from the uid.

2.3.Overview of basic coupling approach

The basic coupling approach was to use each solver to sequentially solve the separate phases, on separate domain meshes that overlap only over a‘wet’boundary interface.Ideally,the full- uid stress tensor is passed from the uid solution as a boundary load to the solid domain,with the resultant deformation of that boundary returned as a uid constraint.This procedure is repeated at a given timestep until both solutions consistently produce the same result.Simulation then proceeds to the next timestep.However,it is quite usual for such a system to be unstable due to its inherent non-linearity;small structural deformations can cause quite large changes in the ow and pressure distributions within the uid,which in turn can have a signi?cantly di erent e ect on the solid deformations.Hence a simple under-relaxation scheme was employed to stabilize the exchange parameters,in both directions:

n=r calc+(1?r) n?1(1) Also,to simplify the exchange it was decided that only the dominant static pressure term would be passed from the uid phase to the solid.Figure1is a simpli?ed diagram of the approach taken.x–x represents the uid–structure interface.P F is the nodal uid pressure?eld,

470J.M.T.PENROSE AND C.J.STAPLES

Figure2.Unmatched solid and uid meshes.

Figure3.The parametric quadrilateral face interpolation.

Figure4.The parametric triangular face interpolation.

P S the nodal solid pressure?eld,S S represents the nodal solid displacement vector?eld and S F the nodal uid displacement?eld.A coupling cycle comprises a single coupled run of the uid and solid solvers.

2.4.Surface interpolation

The uid–structure interface is a surface where the uid and structural meshes conjoin and is de?ned by a set of element faces and nodes on each mesh.(Figure2).In many cases, the density or element type of the meshes will di er and the nodes of the two meshes will not coincide spatially.In order to pass solution-variable data across such an interface,surface interpolation must be carried out.A simpli?ed description of this process is as follows: Consider the uid mesh only.A mapping is generated for all nodes on the interface surface, as illustrated in Figures3(quadrilateral face)and4(triangular face).For a given node this

IMPLICIT FLUID–STRUCTURE COUPLING471

mapping comprises:

?The associated face in the structural mesh de?ned by nodes1–4.

?The parametric position de?ned by and of the projection of the uid node(5)onto the above face.

Where the associated face is a triangle, + =1.

Similar mappings are generated for all interface nodes in the structural mesh.Clearly, some faces may be associated with several nodes;conversely others may be associated with no nodes.If the topology of the surface mesh is to be maintained throughout the simulation, these mapping procedures need only to be carried out once,at the start of the simulation. The surface interpolation,carried out at each coupling cycle is given in Equation(2)(quad face)and3(triangle face)

5= ( 1? 2+ 3? 4)+ ( 4? 1)+ ( 2? 1)+ 1(2)

4= ( 3? 2)+ ( 2? 1)+ 1(3) where is the interpolated variable.Such an interpolation scheme is deemed valid provided that the uid and structural meshes are of similar density and that the variation of the inter-polated variable over a given element face is small[11].

2.5.Propagation of mesh displacement

Displacement of the uid domain is de?ned by the nodal displacement?eld at the uid–structure interface,as calculated by the structural code.In order to maintain a valid uid mesh,the remaining internal nodes must have their positions adjusted,whilst preserving the mesh topology.The method chosen was based on a simple Laplacian smoothing operation [12].The mesh is modelled as a spring system where the displacement of each internal node is calculated based on the displacements of its nearest neighbours using a simple iterative procedure

S0=S m;S(k)= n

p=1

S(k?1)

;k=1;2;:::;q;S(m+1)=S q(4)

where S is the displacement vector,m is the time-step,q is the number of smoothing iterations and n is the number of neighbouring nodes.

A simple weighting procedure was then added to this scheme based on the distance to each near neighbour,thus better preserving the original mesh topology.In addition,rather that repeating the smoothing procedure for a given number of iterations,a control was introduced whereby the iterations proceeded until the incremental displacement of the internal nodes was small in comparison to the smallest element size.

2.6.Mesh movement terms

In order to account for the arbitrary movement of the mesh,it is necessary to modify the governing discrete equations to include the motion of the mesh as well as the uid in the transient convection terms.If this is not done,a number of artefacts can result,including mesh-generated ows,when a mesh is moved through a stationary ow[13].

472J.M.T.PENROSE AND C.J.STAPLES

The CFX-4implementation is described approximately in Reference[14].The implemen-tation presented here follows their approach,although it has been extended to the cell-vertex treatment implemented in CFX-5.

The standard transient and convective terms in the Navier–Stokes equations can be written in the form

@ @t+@ u j

@x j(5)

where is the conserved quantity and u j are the cartesian velocity components.On transfor-mation to a moving co-ordinate system,this becomes

1√g @(√g )

@t+

@( (u j?v j))

@x j=

@t+

√g

@√g

@t+

@( (u j?v j))

@x j(6)

In these equations g is the determinant of the metric tensor of the transformation and

√g therefore represents the volume in physical space corresponding to a unit volume in compu-tational space.v j is the mesh velocity component.The changes that are required therefore are to add an extra transient term as a volumetric source and to modify the convective velocity subtracting the mesh velocity.However,this must be done in a consistent fashion,so as not to create spurious sources and sinks within the equations.

In a cell-vertex formulation,the control volumes are formed from mesh sectors that surround the nodal points.The convective velocities u j are required at‘integration’points,in the centre of the sector faces,in order to calculate the convective uxes across the sector boundaries. See Reference[15]for details.With a moving mesh,the mesh velocity is interpolated from the nodes to the integration points and added to the conservative velocity at these points.The conservation of volume constraint arises from Equation(6),by replacing the variable with unity.

The equation becomes

1√g @√g

@v j

@x j=0(7)

so that

1√g @√g

@t=

@v j

@x j(8)

Integrating this over the control volume,we obtain

1√g @√g

d V=

@x j

d V=

(v j n j)d S(9)

Equation(9)is used to de?ne the volumetric source term in Equation(6),from the mesh velocities,rather than from direct integration of the volume changes.It only requires a knowl-edge of the mesh velocity,obtained from the movement of the nodal mesh points only and gives a consistent treatment,which eliminates many potential artefacts of the approach.For incompressible,isothermal ows,the only terms requiring modi?cations are the above con-vective and transient terms,as the systems considered do not have an enthalpy equation. Copyright?2002John Wiley&Sons,Ltd.Int.J.Numer.Meth.Fluids2002;40:467–478

IMPLICIT FLUID–STRUCTURE COUPLING473 This implementation has been tested on a number of di erent cases;for example,moving meshes through stationary uid,rigid body uid motion,to demonstrate that the correct results are obtained.

2.7.Re-meshing

Despite the smoothing procedures performed on the internal uid nodes,if the solid displace-ments are large there is likely to be a time when one or more uid elements become so distorted that their volume becomes zero or negative and the mesh no longer remains valid. At such a point,there are two approaches to enable the simulation to continue:First,if the invalid displacement con?guration can be guessed a priori,then an alternative uid mesh can be prepared in advance.When the simulation displacement reaches this point,the?eld variables can be interpolated onto the alternative valid mesh,and the simulation can proceed. Several alternative meshes can be prepared for various displacement con?gurations.However, there is a signi?cant drawback to this semi-automatic method;unless the solid deformations can be approximated to a single-degree-of-freedom system,it is very di cult to predict when the uid mesh will become invalid,and also to produce an alternative uid mesh that will be close enough to the topology of the actual simulation mesh.

The second approach is to actually remesh a section or the entire uid domain,thus correct-ing the invalid elements.An automatic scheme such as this was developed,and invoked when a negative volume element was detected after the mesh smoothing procedure.The surface of the uid domain was retained while the CFX tetrahedral Delaunay mesher‘Meshgen’was invoked to remesh the interior.The?eld parameters from the last converged timestep were then interpolated onto this new mesh and the simulation could proceed as before.An addi-tional bene?t was that since the surface topology was conserved,the interpolation parameters for the exchange parameters at the solid– uid interface were maintained and did not require re-calculation.

2.8.Volume interpolation

As previously described,the uid mesh may be regenerated,the new mesh having a di erent topology to the previous.In order that the simulation may proceed,the solution variables, stored on nodes,must be interpolated from the previous mesh to the new mesh.This is accomplished using a second-order tri-linear interpolation procedure.The CFD simulation may then be re-started at the next timestep on the new mesh,using the interpolated solution variables as the initial conditions.However,in using the interpolation with the remeshing schemes it was noticeable that whilst the displacement results were continuous from one timestep to the next,the pressure results often showed an artefact for the single timestep where interpolation took place.Even though there are no constraints on the pressure being continuous,there is no clear reason for this e ect.

2.9.Rigid body simulation

In some simulation scenarios,a body in contact with,or immersed in,the uid ow undergoes so little structural deformation that it can be considered rigid.In these situations it was considered computationally ine cient to use the ANSYS solver,and so a separate rigid body solver was developed to compute the response of these bodies to the ow.The familiar Copyright?2002John Wiley&Sons,Ltd.Int.J.Numer.Meth.Fluids2002;40:467–478

474J.M.T.PENROSE AND C.J.STAPLES

equations of motion that are required to be solved,de?ned in the ?xed global axis system,are

m U

+C ˙U +KU =F (t )(10)I ˙! +! ×(I:! )=M (t )where I = J T and ! = !(11)

Here,F (t )and M (t )are the externally applied force and moment functions derived from the uid ow,m is the body mass,C and K are damping and sti ness matrices,!is the angular velocity vector,J is the constant inertia tensor of the body and is a tensor transformation matrix from the body’s own axis system to the global axis.The rotational motions can be sep-arated from the translational motion of the centre of mass and so di erent solution approaches can be separately adopted for each,according to suitability.For the translational motion,the Houbolt implicit time-integration scheme [16]was chosen to discretize Equation (10).For the rotations,an implicit algorithm proposed by Simo and Wong [17]has beenemployed to solve the momentum balance equation in conservation form using a variation on the implicit Newmark integration scheme [16].Here,a rotation increment is iteratively calculated ensuring that energy and angular momentum are conserved correctly.

Additional facilities were added to this scheme to allow for rigid body degree-of-freedom constraints,initial velocities and rotations,as well as simple linear and torsion springs.This allowed for the simulation of moderately complex rigid body systems such as valves.

3.APPLICATIONS

The consortium were interested in a wide range of cardiovascular devices,employed in both simulated in vivo and in vitro situations.Thus to ensure that the coupled simulations were providing valid results,a series of test application cases were devised,whereby the results could be directly compared to either analytical solutions or well established experimental data.Some examples of these application cases are presented here.

3.1.Flow in an elastic vessel

The transient progression of a pressure pulse down a tube has been studied by many investi-gators over the years,and a good review of these can be found in Reference [18].The initial work on wave propagation in an elastic tube has been attributed to Moens and Korteweg in the latter part of the 19th century,based on Newton’s work on the speed of sound in air.Taking t as the thickness of the wall and E as the circumferential Young’s Modulus of the wall,and relating the change in radius to the applied pressure,the following can be written:c 0= Et (12)This is known as the Moens–Korteweg equation and is based upon several important as-sumptions:(1)the uid is ‘ideal’incompressible and inviscid,(2)the solid wall is thin and there are no changes in its thickness.The e ect of viscosity in the uid was studied by Womersley [19]in the 1950s,who assumed a sinusoidally variant input pressure,at fre-quency !.He showed that in the limiting condition of complete longitudinal constraint Copyright ?2002John Wiley &Sons,Ltd.Int.J.Numer.Meth.Fluids 2002;40:467–478

IMPLICIT FLUID–STRUCTURE COUPLING

475

Figure 5.The exaggerated deformation of the vessel wall (left),and the simulation =analytical comparison of wave propagation speed (right).Here,the dotted line is the Moens–Kortweg solution,and the dashed line is the Womersley solution.

(no axial movement of the wall),the following equation for the complex wave speed through an elastic vessel could be written c =c 0 1F 10where 1?2J 1( i ?3=2) i ?3=2J 0?3=2 =[1?F 10]=M 10e i ”10(13)Here,c 0is the wave speed for an inviscid uid (the Moens–Korteweg equation),and the real part gives the actual wave speed.R is the vessel radius, the uid density, is the dimensionless Womersley parameter where 2=R 2! = ( is the uid viscosity),and J 0;J 1are Bessel functions of order zero and one,respectively.

Using a simple quarter-cylinder symmetric model for the elastic vessel,it was possible to compare the coupled simulation results with these analytical solutions.A ramped pressure inlet condition was used,together with a timestep of 1ms,and simulations were conducted over a range of wall sti ness values.In the results,the dilation of the vessel wall could clearly be seen propagating along the vessel at a constant speed (Figure 5)and this speed was plotted alongside the analytical solutions (see Figure 5).

It can be seen that the simulation results are in good agreement with the analytical solutions,particularly considering the assumptions made in the analyses about the wall thickness and uid behaviour.

3.2.St Jude replacement heart valve

Rigid bi-lea et mechanical valves,like the St Jude valve,represent over 60%of the annual implants world wide.This particular valve features two symmetrical hinged lea ets made of pyrolytic carbon (see Figure 6),which can be considered rigid under typical physiological loading conditions.Therefore,for this simulation the rigid body solver was used to couple with the uid solutions,rather than Ansys.The simulation domain and parameters were designed to closely mimic an in vitro experimental set-up,data from which provided a validation of the simulation as a whole.A physiological ow rate waveform was applied at the inlet,a quarter-symmetry mesh model was used,and no constraints were placed on the lea et motion Copyright ?2002John Wiley &Sons,Ltd.Int.J.Numer.Meth.Fluids 2002;40:467–478

476J.M.T.PENROSE AND C.J.STAPLES

Figure https://www.wendangku.net/doc/ca2634327.html,parison of the simulated valve opening angle with that measured

from high-speed video in vitro.

other than the simple hinge.The semi and fully automatic remeshing methods were employed to cope with the large rotational deformation of the lea ets.As the modelling of narrow uid gaps is di cult,the valve was initially meshed slightly open by5?,and no e ort was made to simulate complete closure.

Solutions were obtained for the entire of systole using timesteps of1ms(see Plate1 for example),and took the order of several days to compute on a multi-processor IBM-SP3 https://www.wendangku.net/doc/ca2634327.html,parisons of these results were made to data obtained from the experimental set-up.In order to compare the opening and closing characteristics of the valve,a high-speed video camera(with frame rates of up to600fps)was employed to record the valve from various positions.From direct measurement on the screen of the recordings,together with the known fully open=closed angles,it was possible to estimate the opening and closing times of the valve,as well as its opening angle during opening=closure with respect to time.Errors were calculated based on an error of±2mm on the measurements.

The graph of the simulated opening angle can be seen in Figure6,with a90?opening representing the leaf parallel to the long axis of the valve.It shows that whilst the opening time of the simulated valve is somewhat slower than the experiments indicate(40–50ms compared to30–35ms),the overall behaviour of the simulated valve is remarkably similar to the experimental valve.Part of the di erence might also be attributable to the simulated valve starting at a slightly open position.

3.3.Berlin Heart cardiac assist device

The Berlin Heart is an extra-corporeal cardiac assist device,of which there are several varying designs based around the same principle;the predominantly rigid central chamber contains the blood,has an inlet and an outlet,and is bounded by two opposing exible roll membranes. The pump inlet would normally be connected directly to the ventricle via a cannula,with

IMPLICIT FLUID–STRUCTURE COUPLING477

Figure7.The symmetrical pump uid mesh(left),and velocity vectors along the symmetry

plane during the‘pump’phase(right).

another connecting the outlet to the aorta.Valves are built onto the blood chamber inlet and outlet to ensure the direction of ow,and these valves are usually rigid tilting disc valves (although they were not directly modelled)or a polyeurythane tri-lea et design.During the pump phase,symmetrically opposing pistons contact the membranes and push them towards each other,thus increasing the pressure in the chamber and forcing the blood through the outlet.During the?ll phase,the pistons retreat and contact with the membranes is broken. The movement of the membranes is then constrained only by the action of the blood entering via the inlet,and the pressure within the chamber becomes low thus retarding the movement of the membranes.

Simulation results were obtained over an entire‘cardiac’cycle using timesteps of10–20ms (see Figure7).These were compared to experimental ow?eld results obtained from laser light sheet and laser Doppler experiments.The simulated ow was clearly seen to pulsate from inlet to outlet and several important features,such as ow separation regions and particular membrane deformations,were identi?able in both the simulation and experiment.

4.CONCLUSIONS

Studies with this coupling system have demonstrated that accurate simulation of cardiovascular systems is now within reach.Indeed,the application of the system could equally extend into any?eld where uid–structure interactions are of primary concern.The data from such simulation will provide invaluable bene?t to device manufacturers that will optimize the design and prototyping process,reducing cost and ensuring that safer and better understood products reach the market.

ACKNOWLEDGEMENTS

The authors acknowledge the partial support provided for this work by the European Commission’s IST programme,under project BloodSim EP28350and the contribution of all the project partners.All trademarks are acknowledged.

478J.M.T.PENROSE AND C.J.STAPLES

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Plate1.The St Jude valve(left),and the simulation results midway through valve opening(right).

Velocity vectors are shown on a horizontal plane through the model.

流固耦合应用研究进展

文章编号:1671-3559(2004)02-0123-04 收稿日期:2003-12-03 基金项目:山东省科学技术发展计划资助项目(012050107);山东省自然科学基金资助项目(Y 2002F19) 作者简介:郭术义(1971-),男,山东济南人,山东大学机械工程学院博士研究生。流固耦合应用研究进展郭术义,陈举华 (山东大学机械工程学院,山东济南250061) 摘　要:流固耦合力学是一门新兴学科。本文简要介绍了该学科的典型应用进展情况,总结了各种研究中的典型方程、数值解法,展望了进一步发展的趋势。关键词:流固耦合;数值模拟;展望中图分类号:O35112;O34717 文献标识码:A 流固耦合力学是一门比较新的力学边缘分支, 是流体力学与固体力学二者相互交叉而生成的。它的研究对象是固体在流场作用下的各种行为以及固体变形或运动对流场的影响。流固耦合力学的重要特征是两相介质之间的相互作用:固体在流体动载荷作用下产生变形或运动,而固体的变形或运动又反过来影响到流场,从而改变流体载荷的分布和大小。总体上,流固耦合问题按耦合机理可分为两大类:一类的特征是流固耦合作用仅仅发生在流、固两相交界面上,在方程上耦合是由两相耦合面的平衡及协调关系引入的;另一类的特征是流、固两相部分或全部重叠在一起,耦合效用通过描述问题的微分方程来实现。本文就流固耦合问题的两大分类中三种基本情况进行了讨论。 1　流固耦合典型应用流固耦合作用的研究在航空、航天、水利、建筑、石油、化工、海洋以及生物领域都有着十分重要的意义。如液体晃动对火箭飞行稳定性的影响,大型贮液管在地震激励作用下产生的流固耦合作用,液体湍振对输液管道的影响。本文就如下三个大方面进行了总结。1.1　输流管道流固耦合流体引起输流管道振动的研究最初来源于横跨阿拉伯输油管道振动的分析[1]。管道在众多的工业领域中应用十分广泛,作用极其重要。但是,在管道内流体流动状态的微弱变化往往引起在工作过程中的湍振现象,诱发流体、管道之间的耦合振动,动力学行为相当复杂。这使得人们很早就开始了这方面的研究,Paidoussis M P [2]是其中最具有代表性的。输流管道的振动问题之所以能引起学者的兴趣,除因为该问题的广泛工业背景和现实意义之外,还因为输流管道虽然是最简单的流固耦合系统,但它却涉及了流固耦合的大多数问题,并且它的物理模型简单,系统比较容易实现,因而便于理论与试验的相互协同。考虑因素侧重面的不同,输液管道非线性运动方程有几种类型[3-5],它们之间有一定的差别。它们的基本假设都是:流体无粘且不可压;管道作为梁模型来处理;管道只是在平面内振动。尽管输流管道的非线性动力问题受到50多年极为广泛的研究,但至今尚没有一个公认的模型。文[6]建立的4个独立变量(轴向位移、横向位移、流速和压力)的全耦合模型(耦合形式包含摩擦耦合、P oiss on 耦合、结合部耦合以及管道轴向和横向运动的耦合)在众多的非线性分析模型中是一个较为完整的模型。 m ¨u +m f [ υf (1+u ′)+2υf u ′+υ2 f u ″+ ωυ′f ]+ P (υf + u )/c 2F -[(1-2υ)P (1+u ′)]′+4f ρf ρ′?υ2f /DK -gm f (1-2υ)(1+u ′)ω′-EI (7ω″ω +ω′ ω )-E A p (2u ″+6u ′u ″+2ω′ω″ )/2=0(1)m ¨ω+m f [ υf (1+ω′)+2υf ω′+υ2f u ″+ω″υ2 f ]+ P (υf + ω)/c 2F -[(1-2υ)P ω′]′-gm +EI ω″″-EI (u ′ω′+6u ″ω +4u ′ω ′)-E A p (u ″ω′+u ′ω″ )=0(2) P /c 2F +m f [(1-2υ)( u +υf )u ″- u ′+υ′f ]-m f (1-2υ)( u ′+u ′ u ′+ω′ ω′ )=0(3)P ′+m f (¨u + υf )+m f ¨ωω′+gm f ω′+Df ρf υ2 f /2=0 (4)随着对输流管道问题研究的深入,各种不同的分析计算方法也相继被提出。其中有限元法(FE M ) 第18卷第2期2004年6月济南大学学报(自然科学版) JOURNA L OF J I NAN UNI VERSITY (Sci.&T ech 1) V ol.18　N o.2 Jun.2004

ansys流固耦合模态分析

有问题可以发邮件给我一起讨论xw4996@https://www.wendangku.net/doc/ca2634327.html, FSI流固耦合命令求解流固耦合问题使用ANSYS计算结构在水中的模态时, FLUID29,FLUID30单元分别用来模拟二维和三维流体部分,相应的结构模型则利用PLANE42单元和SOL ID45等单元来构造，其中，PLANE42和SOL ID45分别是用来构造二维和三维结构模型的单元。FLUID30是流体声单元,主要用于模拟流体介质及流固耦合问题。该单元有8 个节点,每个节点上有4 个自由度,分别是XYZ上3个方向位移自由度和1个压力自由度,为各向同性材料。输入材料属性时,需要输入流体的材料密度(作为DENS 输入)及流体声速(作为SONC输入),流体粘性产生的损耗效应忽略不计。FLUID29是FLUID30单元在二维上的简化，少了一个Z向的位移。SOLID45单元用于构造三维实体结构。单元通过8 个节点来定义,每个节点有 3 个沿着XYZ方向平移的自由度。PLANE42是SOLID45单元在二维上的简化。在利用ANSYS建模分析时,流场域单元属性分为2种,由KEYOPT(2)(指定流体和结构分界面处结构是否存在) 控制,在流固耦合交界面上的单元KEYOPT(2) = 0 ,表示分界面处有结构,其他流体单元KEYOPT(2)=1,表示分界面处无结构。流体-结构分界面通过面载荷标志出来,指定FSI label可以把分界面处的结构运动和流体压力耦合起来,分界面标志在分界面处的流体单元标出。数值分析的步骤 1) 建立流体单元的实体模型。建立流体模型,需要确定流体域的范围,可以把无限边界流体简化成流体区域的半径为固体结构半径的10倍。 2) 标记流固耦合界面。选取流体单元中流固交界面上的节点,执行FSI 命令,流固耦合交界面的处理:流体与固体是两个独立的实体,在划分单元时在两者交界面上的单元网格要划分一致,这样在交界面上的同一位置一般就有两个重合的节点,一个节点属于流体单元,一个节点属于固体单元,这两个重合节点在交界面的位移强制保持一致。 3) 建立固体结构实体模型。建立固体结构模型，定义单元属性，采用映射方式进行网格的划分。 4) 施加约束条件。由于流体区域的尺寸远大于固体结构尺寸，故可以不考虑流体液面的重力的影响，将流体边界处的单元节点上施加压力(PRES) 为零的约束。因为选择的算例为悬臂结构，在固体结构底部加全约束。 5) 选择求解算法，进行求解。定义分析类型为模态分析，设定提取频率阶数和提取模态的方法。因为耦合问题的刚度矩阵，质量矩阵都不对称，需要采用非对称矩阵法(UNSYMMETRIC)求解。 6) 查看结果。进入后处理模块，查看结构模型的频率及振型。以半浸没与水中的桥墩模态问题为背景，并假设： 1. 桥墩为实心等截面的实体，实际桥墩模型应该是空心壳体，截面尺寸也非常复杂，因而需要分块划分单元。

ANSYS流固耦合计算实例

ANSYS流固耦合计算实例 Oscillating Plate with Two-Way Fluid-Structure Interaction Introduction This tutorial includes: , Features , Overview of the Problem to Solve , Setting up the Solid Physics in Simulation (ANSYS Workbench) , Setting up the Fluid Physics and ANSYS Multi-field Settings in ANSYS CFX-Pre , Obtaining a Solution using ANSYS CFX-Solver Manager , Viewing Results in ANSYS CFX-Post If this is the first tutorial you are working with, it is important to review the following topics before beginning: , Setting the Working Directory , Changing the Display Colors Unless you plan on running a session file, you should copy the sample files used in this tutorial from the installation folder for your software (/examples/) to your working directory. This prevents you from overwriting source files provided with your installation. If you plan to use a session file, please refer to Playing a Session File. Sample files referenced by this tutorial include:

ansys workbench 流固耦合计算实例

Oscillating Plate with Two-Way Fluid-Structure Interaction Introduction This tutorial includes: ?Features ?Overview of the Problem to Solve ?Setting up the Solid Physics in Simulation (ANSYS Workbench) ?Setting up the Fluid Physics and ANSYS Multi-field Settings in ANSYS CFX-Pre ?Obtaining a Solution using ANSYS CFX-Solver Manager ?Viewing Results in ANSYS CFX-Post If this is the first tutorial you are working with, it is important to review the following topics before beginning: ?Setting the Working Directory ?Changing the Display Colors Unless you plan on running a session file, you should copy the sample files used in this tutorial from the installation folder for your software (/examples/) to your working directory. This prevents you from overwriting source files provided with your installation. If you plan to use a session file, please refer to Playing a Session File. Sample files referenced by this tutorial include: ?OscillatingPlate.pre ?OscillatingPlate.agdb ?OscillatingPlate.gtm ?OscillatingPlate.inp 1.Features This tutorial addresses the following features of ANSYS CFX.

(完整版)流固耦合教学

1、打开ANSYS Workbench, 拖动各模块到空白区，并照此连接各模块。 2 2、打开第一个模块当中的Geometry，建立几何模型：（1）在XY Plane内建立Ship Shell 船长：0.4、船宽：0.14、型深0.11 将第一个Solid重命名为Ship Solid 在Concept中选择Surfaces From Faces，选中模型的六个面，然后Apply、Generate。重命名第二个Ship Solid为Ship Shell 右击Ship Solid, 选择Hide Body，显示Ship Shell, 然后对Ship Shell执行同样操作（即隐去）

（2）在YZ Plane内建立液舱单击（New Plane），选择YZ plane，，Apply一下将YZ Plane 向X正方（图中为法向，即Z）向偏移0.02m Generate一下，然后Show body 一下Ship Solid 与Ship Shell 可以看到YZ Plane已平移到Body内了再将Ship Solid 与Ship Shell 都Hide，选择Plane 4，调为正视，Generate一下新建一个Sketch：单击，显示，在此Sketch中建立液舱模型草图

单击约束（Constrains），将草图中的“水平线”调整为水平，“垂直线”调整为垂直：事实上仅用Horizontal（水平）和Vertical（垂直）就OK了。以水平约束为例，先单击Horizontal，再依次单击草图中的水平线段。调整后如下图所示：定义尺寸：左下角空缺的部分是预留贴“应变片”的部分，需要单独建模单击Extrude（拉伸），设置Operation（下拉列表中改选为Add Frozen）与拉伸尺寸（0.1m）：然后Generate一下

流固耦合概述及应用研究进展

流固耦合概述及应用研究进展摘要流固耦合力学是流体力学与固体力学交叉而生成的一门力学分支。顾名思义，它是研究变形固体在流场作用下的各种行为以及固体位形对流场影响这二者交互作用的一门科学。流固耦合力学的重要特征是两相介质之间的交互作用(fluid．solid interaction)：变形固体在流体载荷作用下会产生变形或运动，而变形或运动又反过来影响流场，从而改变流体载荷的分布和大小。总体上 , 流固耦合问题按耦合机理可分为两大类:一类的特征是流固耦合作用仅仅发生在流、固两相交界面上 ,在方程上耦合是由两相耦合面的平衡及协调关系引入的;另一类的特征是流、固两相部分或全部重叠在一起 ,耦合效用通过描述问题的微分方程来实现。 1 流固耦合概述 1．1引言历史上，人们对流固耦合现象的早期认识源于飞机工程中的气动弹性问题。Wright兄弟和其它航空先驱者都曾遇到过气动弹性问题。直到1939年二战前夕，由于飞机工业的迅猛发展，大量出现的飞机气动弹性问题的需要，有一大批科学家和工程师投入这一问题的研究。从而，气动弹性力学开始发展成为一门独立的力学分支。如果将与飞机颤振密切相关的气动弹性研究作为流固耦合的第一次高潮的话，则与风激振动及化工容器密切相关的研究可作为流固耦合研究的第二次高潮。事实上，从美国ASME应用力学部召开的历次流固耦合研讨会上可以看出，流固耦合问题涉及到很多方面。比如：空中爆炸及响应，噪声相互作用问题，气动弹性，水弹性问题，充液结构内的爆炸分析，管道中的水锤效应，充液容器的晃动及毛细流中血细胞的变形，沉浸结构的瞬态运动，流固相互冲击，板的颤振及流体引起的振动，圆柱由于热交换引起支持附件松动的非线性流固耦合系统，声音与结构的相互作用，涡流与结构的相互作用，机械工程中的机械气动弹性问题等等。 1.2流固耦合力学定义和特点流固耦合力学是流体力学与固体力学交叉而生成的--I'l力学分支。顾名思义，它是研究变形固体在流场作用下的各种行为以及固体位形对流场影响这二者交互作用的一门科学。流固耦合力学的重要特征是两相介质之间的交互作用（fluid-solid interaction)．变形固体在流体载荷作用下会产生变形或运动，而变形或运动又反过来影响流场，从而改变流体载荷的分布和大小。正是这种相互作用将在不同条件下产生形形色色的流固耦合现象。流固耦合问题可由其耦合方程来定义，这组方程的定义域同时有流体域与固体域，而未知变量含有描述流体现象的变量及描述固体现象的变量，一般而言，具有以下两点特征： a)流体域或固体域均不可能单独地求解； b)无法显式地消去描述流体运动的独立变量或描述固体运动的独立变量。 1．3流固耦合力学涉及领域及分类流固耦合问题涉及到很多方面。比如：工程实际中所涉及到的流固耦合问题，

基于MpCCI的Abaqus和Fluent流固耦合案例1

CAE联盟论坛精品讲座系列基于MpCCI的Abaqus和Fluent流固耦合案例主讲人：mafuyin CAE联盟论坛总监摘要：通过MpCCI流固耦合接口程序，对某薄壁管道流动中的传热过程进行了Abaqus和Fluent相结合的流固耦合仿真分析。信息介绍了从建模、设置到求解计算和后处理的全过程，对相关研究人员具有参考意义。 1 分析模型用三维建模软件solidworks建立了一个管径为1m的弯管，结构尺寸如图1a所示，管的结构如图1b所示，流体的模型如图1c所示。值得注意的是，由于拓扑特征的原因，这样的管壁模型无法通过对圆环扫略直接生成，而需先通过对大圆的扫略生成实心的模型(类似于流体模型)，然后进行抽壳得到管壁的模型。用同样的方法对大圆半径减去管壁厚度的圆进行扫略得到流体模型。 a. 尺寸关系 b. 管壁结构 c. 流体模型图1. 几何模型示意图图2. 流固耦合传热分析模型示意图内壁面(耦合面) 速度入口 v=6m/s; T in=600K 外壁面压力出口 P=0Pa；T out=300K

由于管壁结构和流体的热学行为不同，传热系数等都不一样，所以属于典型的流固耦合传热问题，热学模型如图2所示。即管的一端为流体速度入口，一端为压力出口，给定流体外壁面一个初始温度600K，流体入口速度为6m/s，温度为600K，出口相对大气压力为0Pa，出口温度为300K。需要求解流体和管壁的温度场分布情况。 2 流体模型将图1c的流体模型以Step格式导入Fluent软件通常使用的前处理器Gambit中，如图3a所示。设置求解器为，然后划分体网格，网格尺寸为100mm，类型为六面体单元，一共生成4895个体单元，网格如图3b所示。 a. 导入Gambit软件中的流体模型 b. 流场的网格模型图3. 流体模型及网格示意图进行网格划分后，需定义边界条件，在Gambit软件中先分别定义速度入口(VELOCITY_INLET)、压力出口(PRESSURE_OUTLET)和壁面(Wall)三组边界条件，具体参数设置在Fluent软件中进行。然后定义流体属性，名称定义为air，类型为Fluid。这些定义的目的是能够在Fluent软件中识别出这些特征，具体类型和参数都可以在Fluent软件中进行设置和修改。定义完后点击【Export】，选择【Mesh】，选择路径和文件名称并进行输出。打开Fluent6.3.26或以上的版本，选择3D求解器，点击【File】→【Read】→【Case】，然后选择Gambit中输出的msh文件，即可将网格文件读入Fluent 软件中。读入模型后，进行求解参数和条件的设置。

(完整版)5流固耦合

第五章轴流泵的流固耦合 5-1 流固耦合概论流固耦合问题一般分为两类，一类是流‐固单向耦合，一类是流‐固双向耦合。单向耦合应用于流场对固体作用后，固体变形不大，即流场的边界形貌改变很小，不影响流场分布的，可以使用流固单向耦合。先计算出流场分布，然后将其中的关键参数作为载荷加载到固体结构上。典型应用比如小型飞机按刚性体设计的机翼，机翼有明显的应力受载，但是形变很小，对绕流不产生影响。当固体结构变形比较大，导致流场的边界形貌发生改变后，流场分布会有明显变化时，单向耦合显然是不合适的，因此需要考虑固体变形对流场的影响，即双向耦合。比如大型客机的机翼，上下跳动量可以达到5 米，以及一切机翼的气动弹性问题，都是因为两者相互影响产生的。因此在解决这类问题时，需要进行流固双向耦合计算。下面简单介绍其理论基础。连续流体介质运动是由经典力学和动力学控制的，在固定产考坐标系下，它们可以被表达为质量、动量守恒形式: ()0v t ρρ?+??=? (1) ()B v vv f t ρρτ?+??-=? (2) 式中，ρ为流体密度；v 为速度向量；B f 流体介质的体力向量；τ为应力张量；在旋转的参考坐标系下，控制方程变为： ()0r v v t ρρ?+??=? （3） (-)+B r r c v v v f f t ρρτ?+??=? （4）形式和固定坐标系下基本相同，只是速度变成了相对速度，另外就是增加了附加力项 c f 。固体有限元动力控制方程为： []{}[]{}{}...[]{}M u C u K u F ++= （5）式中，[]M ，[]C ，[]K 分别是质量矩阵，阻尼矩阵以及刚度矩阵，{}F 为载荷矩阵。流固耦合遵循最基本的守恒原则，所以在流固耦合交界面处，应满足流体与固体应力、位移、热流量、温度等变量的相等或守恒，即满足如下四方程： f f s s n n ττ?=? (6) f s d d = (7) f s q q = (8) f s T T = (9) 5-2 单向流固耦合

基于LSDYNA及FLUENT的板壳结构流固耦合分析

基于 LS-DYNA 及 FLUENT 的板壳结构流-固耦合分析
汪丽军北京航空航天大学，交通科学与工程学院 100191
[摘要]：本文采用 ANSYS 显示动力分析模块 LS-DYNA 及流场分析模块 FLUENT，对水下的板壳结构运动及其界面的流-固耦合现象进行了仿真分析。流场计算得到的界面压强数据以外载荷的形式施加于结构表面，使其产生位移及变形；同时，结构的变化又进一步影响了流场的分布。通过往复的双向耦合迭代，得到了板壳结构的动力学响应以及流场的分布情况。仿真结果与试验结果的对比表明，此方法适用于解决兼有大位移及较大变形特征的流-固耦合问题。 [关键词]：板壳结构流-固耦合有限元方法 ANSYS
Analysis of Fluid-Structure Interaction for Plate/Shell Structure Based on LS-DYNA and FLUENT
Wang Lijun School of Transportation Science & Engineering, Beihang University 100191
Abstract: In this paper，the movement of plate under water and the fluid-structure interaction(FSI) is simulated numerically by combining explicit dynamic solver LS-DYNA and computational fluid dynamics solver FLUENT in ANSYS. The pressure obtained from the calculation of flow field are applied as external loads on the surface of the plate, then the structural deformation and displacement can be calculated as well, which will affect the shape and pressure distribution of the flow field reversely. After sequential coupling iterations the dynamic response of the structure and flow field distribution are obtained consequently. By comparing numerical and experimental results it is proved that this proposed coupling method is suitable for solving such a kind of FSI problems considering both large displacement and comparatively large deformation. Keyword: Plate/shell structure, Fluid-Structure Interaction, Finite element method，ANSYS
1
前言
在自然界中，流-固耦合现象广泛存在于航空、航天、汽车、水利、石油、化工、海洋以及生物等领域。很多实际问题中流体载荷对于结构的影响不可忽略；同时，结构的位移和变形也会对流场的分布产生重要影响。例如各种水下运动机构都需要考虑这种现象。

几个耦合的例子

一般说来，ANSYS的流固耦合主要有4种方式： 1，sequential 这需要用户进行APDL编程进行流固耦合 sequentia指的是顺序耦合以采用MpCCI为例,你可以利用ANSYS和一个第三方CFD产品执行流固耦合分析。在这个方法中，基于网格的平行代码耦合界面(MpCCI) 将ANSYS和CFD程序耦合起来。即使网格上存在差别，MpCCI也能够实现流固界面的数据转换。ANSYS CD中包含有MpCCI库和一个相关实例。关于该方法的详细信息，参见ANSYS Coupled-Field Analysis Guide中的Sequential Couplin 2，FSI solver 流固耦合的设置过程非常简单，推荐你使用这种方式 3，multi-field solver 这是FSI solver的扩展，你可以使用它实现流体，结构，热，电磁等的耦合 4，直接采用特殊的单元进行直接耦合，耦合计算直接发生在单元刚度矩阵一个流固耦合的例子 length=2 width=3 height=2 /prep7 et,1,63 et,2,30 !选用FLUID30单元，用于流固耦合问题 r,1,0.01 mp,ex,1,2e11 mp,nuxy,1,0.3 mp,dens,1,7800 mp,dens,2,1000 !定义Acoustics材料来描述流体材料-水 mp,sonc,2,1400 mp,mu,0, ! block,,length,,width,,height esize,0.5 mshkey,1 ! type,1 mat,1 real,1 asel,u,loc,y,width amesh,all alls ! type,2 mat,2 vmesh,all

ansys14workbench血管流固耦合分析实例

Ansys14 workbench血管流固耦合实例根据收集得一些资料,进行学习后,试着做了这个ansys14workbench得血管流固耦合模拟,感觉能够耦合上,仅就是熟悉流固耦合分析过程,不一定正确,仅供参考,希望大家多讨论。谢谢！ 1、先在proe5中建立血管与血液流体区得模型(两者装配起来),或者直接在workbench中建模。图1 模型图 2、新建工程。在workbench中toolbox中选custom system,双击FSI: FluidFlow(fluent)->static structure、图2 计算工程 3、修改engineering data,因为系统缺省材料就是钢,需要构建血管材料,如图3所示。先复制steel,而后修改密度1150kg/m3,杨氏模量 4、5e8Pa,泊松比0、3,重新命名,最后在主菜单中点击“update project”保存、

图3 修改工程材料 4、模型导入,进入gemetry模块,import外部模型文件。图4 模型导入图 5、进入FLUENT网格划分。在workbench工程视图中得Mesh上点击右键,选择Edit…,如图5所示,进入网格划分meshing界面,如图6所示。我们这里需要去掉血管部分,只保留血液几何。

图5 进入网格划分

图6 禁用血管模型 6、设置网格方法。默认就是采用ICEM CFD进行网格划分,设置方式如图7所示,截面圆弧边分为12份,纵截面得边均分为10份,网格结果如图8所示。另外在这个界面中要设置边界得几何面,如inlet、outlet、symmetry 图7 设置网格划分方式图8 最终出网格

流固耦合文献总结

小论文拟采用DP模型，在应力较高的土体中，比Mohr-coulomb理想弹塑性模型的数值计算结果更精确。设定DP模型需要输入3个特殊参数，粘聚力，内摩擦角，膨胀角，其中的膨胀角是用来控制体积膨胀的大小的。在岩土工程中，一般密实的砂土和超强固结土在发生剪切的时候会出现体积膨胀，因为颗粒重新排列了；而一般的砂土或者正常固结的土体，只会发生剪缩。在使用DP模型的时候，对于一般的土，膨胀角设置为0度比较符合实际。渗流耦合分析拟采用的边界条件是全地基边界，即把要分析的模型所有的区域看成是一个封闭的整体。在计算渗流应力耦合分析时，考虑基坑空间效应，建立三维实体模型，不仅考虑施工降水耦合，也考虑施工间歇变形耦合。最终通过支护结构桩和锚杆的变形以及基坑的变形，得出以下两条结论：（1）采用渗流应力耦合理论计算的基坑工程变形形态符合实际情况，随着基坑开挖深度增加，基坑变形规律也符合实际情况。（2）渗流应力耦合情况下基坑变形与不考虑渗流耦合影响下基坑变形曲线相比，数值较大，可见，分析基坑变形时不考虑渗流耦合影响是偏不安全的，耦合分析对基坑变形的影响不能忽视。 1、基于渗流场-应力场耦合作用下的深基坑降水支护结构的位移研究工程勘察2012 本文采用大型通用岩土工程有限元软件PLAXIS对复合土钉支护进行分析,模型采用平面应变模型,土体采用Mohr-coulomb理想弹塑性模型且具有对称性，故取一半对其分析，模型底部为固定约束，侧面只限制水平位移，上表面为自由边界。本工程的数值模拟主要为比较在有降水作用下和未考虑地下水两种情况下的支护结构体系的位移，为此，首先进行了在未考虑地下水条件下的模拟，即不考虑孔隙水压，地下水位线默认为基坑底部。其次依据实际工程的地下水位线-7.24m，进行了数值模拟，以便找到降水作用对支护结构体系位移的影响。 2、考虑流-固耦合效应的基坑水土压力计算工程勘察2011 针对地下水绕过围护墙渗流情况，分析了传统的水土压力分算、合算及考虑土体渗流-固结变形方法计算土压力的区别，并利用实测数据进行对比。流过耦合分析，PLAXIS程序采用水土分算的方法，通过输入地下水水头执行地下水渗流程序进行计算，利用单元应力点上的压力水头求得孔隙水压力，将围护墙与土体接触界面上的有效压力与孔隙水压力值相加，得到基坑围护墙上总的水土压力分布。 3、考虑流固耦合作用的深基坑有限元分析地下空间与工程学报2012 利用FLAC流固耦合模型对复杂地质条件下深基坑降水开挖过程中深基坑的时间效应进行研究。建立考虑参数变化的弹塑性流固耦合数值模型，分析基坑开挖及降水作用下地表沉降、水压力、基底隆起随时间变化的规律。平面应变模型，土体采用修正的剑桥模型模拟，只是在理论上提出考虑基坑开挖过程中渗透系数随孔隙比变化的现象，未应用在模型模拟中。 4、考虑渗流-应力耦合基坑开挖降水数值分析广东工业大学学报2013 本文运用通用软件MIDAS/GTS考虑渗流应力耦合作用下模拟基坑开挖降水的详细过程，分析了不同阶段渗流情况,同时探讨了止水帷幕、渗透系数与不同降水深度对基坑支护特性的影响，以期为基坑降水和支护结构优化提供理论参考。采用的摩尔库伦土体模型，基坑较小，应力水平较低，平面应变模型，未考虑基坑的空间效应。 5、深基坑工程降水与地面沉降耦合数值模拟研究中国市政工程2012 采用基坑降水与地面沉降耦合模型分析，四周边界取为定水头边界，其中，求解地下水问题简化为求解地下水在多孔介质中流动的问题，建立相适应的地下水三维非稳定渗流数学模型为地面沉降模型为方程的求解条件为：利用建立的三维渗流沉降模型预测抽水减压期间对水位降深和区域沉降影响。计算结果

流固耦合问题研究进展及展望

流固耦合问题研究进展及展望摘要：天然岩体大多数为多相不连续介质，岩体内充满着诸如节理、裂隙、断层、接触带、剪切带等各种各样的不连续面，为地下水提供了储存和运动的场所。地下水的渗流以渗透应力作用于岩体，影响岩体中应力场的分布；同时岩体应力场的改变使裂隙产生变形，从而影响了裂隙的渗透性能，因此，流固耦合问题研究主要考虑流体在固体中的变化规律，尤其是流体渗流与和岩体应力之间的耦合作用,通过对国内外相关文献的分析与整理，从流固耦合的研究现状、特点、研究方法及展望这四个方面进行了论述。关键词：流固耦合；岩体；地下水；研究方法；渗流中图分类号：X523文献标识码：A 文章编号：天然岩石不只是单一固相介质，尚有固相、液相和气相并存的多孔介质组合，岩石经历了漫长的成岩和改造历史，其内部富含各种缺陷，包括微裂纹、孔隙以及节理裂隙等宏观非连续面，它们的存在为地下水提供了储存和运动的场所。地下水的渗流还以渗透应力作用于岩体，影响岩体中应力场的分布，同时岩体应力场的改变往往使裂隙产生变形，影响裂隙的渗透性能，所以渗流场随着裂隙渗透性的变化重新分布，因此，在许多情况下必须考虑流体,包括液体(油或水)、气体(天然气、煤矿瓦斯等)在多孔介质中的流动规律及其对岩体本身的变形或强度造成的影响，即应考虑岩体内应力场与渗流场之间的相互耦合作用。近年来，流固耦合问题越来越受到人们的重视，这方面的研究涉及许多领域，在采矿领域，涉及地热开发，石油开采中的流固耦合渗流，采矿围岩突水问题等。在建筑工程领域，包括地下水抽取引起的地面沉降问题，基坑渗流引起变形问题，坝基渗流及稳定性问题，隧道建设等。在环境工程领域涉及地下核废料存储，城市垃圾废弃物处理等以及生物医学工程等领域，这一问题的研究对促进科技进步和解决实际工程技术问题有着重要意义。 1 国内外研究现状关于岩体和流体相互作用研究最早见诸K.Terzaghi对有关地面沉降研究，其内容主要限于考虑一维弹性孔隙介质中饱和流体流动时的固结，提出了著名的有效应力公式，迄今该公式仍是研究岩体和流体相互作用的基础公式之一。二十世纪中期Biot(1941,1956)进一步研究了三向变形材料与孔隙压力的相互作用，并在一些假设，如材料为各向同性、线弹性小变形，孔隙流体是不可压缩的且充满固体骨架的孔隙空间，而流体通过孔隙骨架的流动满足达西定律的基础上，建立了比较完善的三维固结理论。在此基础上，进一步发展了多相饱和渗流与孔隙介质耦合作用的理论模型，并在连续介质力学的系统框架内建立了多相流体运移和变形空隙介质耦合问题的理论模型。 Lous等（1974）运用单裂隙试件进行单向水流的室内模型，综合研究了天

adina热-流-固耦合建模过程

基于adina热-流-固耦合建模过程热-流-固耦合作用是存在高度非线性的复杂耦合作用。有关这三场的耦合作用研究在地石油工程、热资源开发、地下核废料存储安全、采矿工程等很多领域有着非常重要的应用价值。由于研究对象的不同，热流固耦合模型的形式存在差异，建立符合实际问题的三场耦合模型十分困难，文中在国内外学者对三场耦合模型理论研究的进展状况的基础上，通过一个例子，介绍了用adina建立模型的过程。 1三场耦合理论模式介绍在三场耦合尤其是三场耦合机制的研究过程中，人们根据各自对三场耦合的认识提出了不同的三场耦合作用模式。1995年前有关三场耦合作用模式的研究在场与场之间的联系关系上主要是以速度等变量为桥梁，如HART、Jing提出的作用模式，其中Jing主要描述的核储存库三场耦合模式，后来作用模式发展为主体为物理现象，它们之间的相互联系是以场作用或物理作用为桥梁的，如Guvanasen、柴军瑞的作用模式，前者同样以核废料储库库围岩三场耦合作用研究为主，后者为一般模式。 Jing等描述了核废料贮库围岩裂隙岩体中的热-液-力耦合过程，如图1所示。H art等提出了如图2所示的三场耦合作用模式。柴军瑞从岩体渗流-应力-温度三者两两之间的相互关系出发，建立了如图3的作用模式。图中：口渗透水流对岩体固相的力学作用，一般应用有效应力原理来反映;a’为应力引起裂隙岩体空隙率和渗透特性变化，目前有经验关系式(如Lours负指数关系式)和理论关系式(包括各种概化情况下和各种概化模型下的理论关系式)两大类表示方法;b为温度引起热应变(力)及与温度有关的岩体固相力学特性变化;b’为岩体固相力学变形引起热力学特性变化及岩体固相内部热耗散;c为水流的热对流及与岩体固相的热交换;c’为温度势梯度引起水份运动及与温度有关的水特性变化。图1裂隙岩体中的热液力耦合过程(据Jing等。1995年)

AnsysCF流固耦合分析

A n s y s C F流固耦合分析文档编制序号：[KKIDT-LLE0828-LLETD298-POI08]

流固耦合FSI分析分析原理：流场采用CFX12，固体采用ANSYS12分别计算，通过界面耦合。流体网格：流体部分采用分网，按照流体分网步骤即可，没有特殊要求。网格导出：CFX可以很好的支持Fluent的.cas格式。直接导出这个格式即可。流体的其余设置都在CFX-PRE中设置。固体网格即设置：划分固体网格。设置边界条件，载荷选项，求解控制，导出.cdb文件。实例练习：以CFX12实例CFX tutorial 23作为练习。为节省时间，将计算时间缩短为2s。网格划分：提取CFX tutorial 23中的实体模型到hm中，分别划分流体，固体网格。分别导出为fluent的.cas格式和ansys的cdb格式。流体网格如下：网格文件见: 固体网格为：特别注意：做FSI分析时，ANSYS固体部分必须在BATCH下运行（即将.cdb文件导入ansys不需要任何操作就能直接计算出结果），所以导出的.CDB文件需要添加一个命令，在hm建立FSIN_1的set，以方便在.cdb中手动添加命令 SF,FSIN_1,FSIN,1，具体位置在定义了节点集合FSIN_1之后。另一个set：pressure用于施加压强。这里还设置了一些控制卡片用于分析，当然也可以直接修改.cdb文件

详细.cdb文件请参看将固体部分在ansys中计算一下，以确定没有问题。通过ansys计算检查最大位移：最上面的点x向变形曲线至此，固体部分的计算文件已经准备好，流体网格需要导入CFX以进一步设置求解选项和耦合选项。以下在CFX-PRE中进行设置由于固体模型已经生成，故不需要利用workbench，所以不必按照指南的做法。启动workbench，拖动fluid flow(CFX)到工作区直接双击setup进入CFX-PRE 导入流体网格然后设置分析选项：注意：mechanical input file即是固体部分网格。再新建一个流体，取名fluid。设置domain 添加边界条件取名为interface设置流固耦合界面，对应为abc。这就是流固耦合界面的设置过程。同理，建立sym1 Sym2 这个选项默认为no slip 的 wall，最普通的那种，不必特殊设置初始化：求解控制

双向流固耦合实例(Fluent与structure)

双向流固耦合实例（Fluent与structure）说明：本例只应用于FLUENT14.0以上版本。 ANSYS 14.0是2011年底新推出的版本，在该版本中，加入了一个新的模块System Coupling，目前只能用于fluent与ansys mechanical的双向流固耦合计算。官方文档中有介绍说以后会逐渐添加对其它求解器的支持，不过这不重要，重要的是现在FLUENT终于可以不用借助第三方软件进行双向流固耦合计算了，个人认为这是新版本一个不小的改进。模块及数据传递方式如下图所示。一、几何准备流固耦合计算的模型准备与单独的流体计算不同，它需要同时创建流体模型与固体模型。在geometry模块中同时创建流体模型与固体模型。到后面流体模型或固体模块中再进行模型禁用处理。模型中的尺寸：v1:32mm，h2:120mm，h5:60mm，h3:3mm，v4:15mm。由于流体计算中需要进行动网格设置，因此推荐使用四面体网格。当然如果挡板刚度很大网格变形很小时，可以使用六面体网格，划分六面体网格可以先将几何进行slice切割。这里对流体区域网格划分六面体网格，固体域同样划分六面体网格。二、流体部分设置 1、网格划分双击B3单元格，进入meshing模块进行网格划分。禁用固体部分几何。设定各相关部分的尺寸，由于固体区域几何较为整齐，因此在切割后只需设定一个全局尺寸即可划分全六面体网格。这里设定全局尺寸为1mm。划分网格后如下图所示。

2、进行边界命名，以方便在fluent中进行边界条件设置设置左侧面为速度进口velocity inlet，右侧面为自由出流outflow，上侧面为壁面边界wall_top，正对的两侧面为壁面边界wall_side1与wall_side2（这两个边界在动网格设定中为变形域），设定与固体交界面为壁面边界（该边界在动网格中设定为system coupling类型）。操作方式：选择对应的表面，点击右键，选择菜单create named selection，然后输入相应的边界名称。注意：FLUENT会自动检测输入的名称以使用对应的边界类型，当然用户也可以在fluent进行类型更改。完成后的树形菜单如下图所示。本部分操作完毕后，关闭meshing模块。返回工程面板。 3、进入fluent设置 FLUENT主要进行动网格设置。其它设置与单独进行FLUENT仿真完全一致。设置使用瞬态计算，使用K-Epsilon湍流模型。这里的动网格主要使用弹簧光顺处理（由于使用的是六面体网格且运动不规律），需要使用TUI命令打开光顺对六面体网格的支持。使用命令 /define/dynamic-mesh/controls/smoothing-parameters。动态层技术与网格重构方法在六面体网格中失效。因此，建议使用四面体网格。我们这里由于变形小，所以只使用光顺方法即可满足要求。点击Dynamic mesh进入动网格设置面板。如下图所示，激活动网格模型。

流固耦合的研究与发展综述

目录 1.引言............................................... - 1 - 2.流固耦合的分类与发展............................... - 1 - 3.流固耦合的研究方法................................. - 2 - 4.流固耦合计算法..................................... - 4 - 5.软件应用方法....................................... - 6 - 6.总结与展望........................................ - 14 - 参考文献............................................ - 15 -

流固耦合的研究与发展 1.引言近来，航空航天工业在世界上发展迅速，而作为“飞机心脏”的航空发动机是限制其发展的主要因素。目前，航空发动机日益向高负荷、高效率和高可靠性的趋势发展，高负荷导致的高你压力梯度容易引起流动分离，同时随着科技的发展，航空发动机的设计使得材料越来越轻，越来越薄，这就使得发动机内部的不稳定流动对叶片的影响大大增加，成为发动机气动及结构设计要考虑的关键问题之一。而以往单单考虑气动或结构因素不能满足实际的需求，必须将气动设计和结构设计相结合，考虑其相互作用的影响，因此流固耦合的研究应运而生。流固耦合是流体力学与固体力学交叉而生成的一门独立的力学分支,它的研究对象是固体在流场作用下的各种行为以及固体变形或运动对流场影响。流固耦合力学的重要特征是两相介质之间的交互作用,固体在流体动载荷作用下会产生变形或运动，而固体的变形或运动又反过来影响流场，从而改变流体载荷的分布和大小，正是这种相互作用将在不同条件下产生形形色色的流固耦合现象。 2.流固耦合的分类与发展总体上，从流固耦合的机理上可以分为两大类：第一类，耦合作用仅仅发生在两相交界面上，在方程上的耦合是由两相耦合面上的平衡及协调来引入的如气动弹性、水动弹性等；第二类，两相部分或全部重叠在一起，难以明显地分开，使描述物理现象的方程，特别是本