What Is Fluid-Structure Interaction?

Classifications of FSI Coupling

This section describes the various types of fluid-structure interactions.

FSI problems can also be grouped by the kind of coupling used:

• Weak coupling
• Strong coupling
• Other coupling algorithms

Each type of interaction is discussed below.

One-Way Interactions

In “one-way” interactions, the fluid can impart some action on the structure but the response of the structure to the fluid loading does little to affect the fluid motion. For example, a fluid can heat or cool a stiff, supported structure, which produces thermal stress loads and deformations in the solid material. However, these thermal deformations do not necessarily lead to any significant change in the flow patterns of the fluid. Such a problem involves a two-way exchange of heat, which is referred to as Conjugate Heat Transfer. Nonetheless, the mechanical exchange is only one way, so it is sufficient to compute the temperature in the fluid and solid domains in separate simulations. Then you can compute the stresses in another simulation using the results of the temperature that is computed in the previous simulation.

The one-way interaction can also be the other way. For example, the motion of a piston and valves in an internal combustion engine certainly affects the fluid flow patterns in the combustion chamber. However, the motion of the fluid has little effect on the deformation of the piston and valves (other than, or course, the thermal effects).

Two-Way Interactions

In “two-way” interactions, the fluid motion and pressure affect the displacement and deformation in the structure. The response of the structure has a significant effect on the fluid flow. A prime example is the Dynamic Fluid Body Interaction capability of 6DoF to model the coupled interaction between a rigid body and the fluid.

Traditionally, FSI implies two-way coupling of a fluid and a deformable structure, such that the deformation and rigid body DOF are coupled with the fluid. Even under this definition, there are classifications of the degrees of coupling, ranging from “weak” or “loose” coupling to “strong” coupling.

In two-way interactions, it is clear that the solid structure responds to the pressure or viscous shear traction in the fluid. On the other hand, the fluid responds to the structure in various ways. The shape of the structure obviously affects the flow field, but it is the velocity of the structure (or change in displacement) that has the greatest effect. In fact, it can be shown that the acceleration of the structure causes proportional pressure responses much like how the acceleration of the fluid leads to a hydrostatic pressure gradient. For example, striking a hammer on a constrained pipe. In the fluid, the response would be a pressure wave that could be heard but not seen, and the small deformations in the pipe would be visually imperceptible. In this case, the response is determined by how fast the structure moved, or more accurately, how the structure accelerated. It is not determined by how much the structure moved.

Aero (Hydro) Elastic Equilibrium

In most cases, FSI implies “dynamic” simulations, or what would be referred to in CFD as “transient” simulations. However, in some situations, “static” solutions can be important. For example, the static deformation of a wing structure due to a “steady-state” airflow around the deformed wing. In such cases, a transient analysis in the fluid and structure can still be used to reach the static steady-state solution. However, the time-step can be thought of as a pseudo time-step, since the simulation does not need to be “time accurate” in its search for the steady solution. The fluid and solid time integration can be reduced to first order. Also, by definition, “static” implies that the velocity of the structure is zero. Therefore in the static solution you can ignore the grid flux terms in the fluid, since the grid flux terms are zero. On the structural side, you can increase the material damping or Rayleigh damping for the same reason. That is, when the velocity of the structure goes to zero, the damping forces are zero. More precisely, setting the damping to “critical” damping is the quickest way to drive the structure to the steady-state. Thus, ignoring the grid flux and adding structural damping promotes stability.

Weak Coupling

In some two-way FSI problems, you can regard the coupling to be “weak”, and so employ a “loose” coupling algorithm to find the solution.

Consider a structure that bends in steady-state flow. This bending can significantly alter the flow patterns around the structure, which, in turn, affect the bending. When searching for a steady-state condition, one is interested in the shape the structure takes under the steady condition. As the structure and fluid reach the steady-state, the structure material point velocities approach zero. In this situation, the coupling is “weak” since in the steady state the structure imparts no motion on the fluid. In fact, it is almost “one-way”, since the primary influence of the structure on the fluid is from its velocity, which in steady state is zero. In this situation, a “loose” coupling algorithm between the solid and fluid is sufficient to determine the end steady condition.

For example, the fluid can initially assume the structure is rigid and constrained, and a flow field can be computed independently. The pressure that is generated can be passed to a separate structural solver and the deformations in the structure can be computed from this initial guess of the fluid loading. Once the deformations in the structure are known, they can be provided to the CFD analysis to compute the steady flow with the new deformed geometry. This iteration can be repeated until a steady-condition is met. The important thing to notice is that this analysis has no consideration for the time scales. Since the point of interest is not how it reaches the steady-state solution, but simply what steady-state solution the fluid/structure reaches. The fluid solver only requires to know where the fluid/structure interface lies, not how fast it is moving or accelerating.

In a general sense, weak coupling implies that the response times of the structure to a disturbance in the fluid are slow, compared to the fluid. The opposite is also true, the response times in the fluid to a disturbance in the solid are slow, compared to the solid.

A distinction must be made between “loose coupling” and “loose coupling algorithms”. Loose coupling implies the physical strength of the coupling, whereas loose coupling algorithms imply the degree to which the fluid and structure codes are coupled. The loose coupling algorithm can mean simply passing data back and forth between different codes using files on the disk. It can also mean the fluid and structure solvers are not necessarily in the processor memory at the same time. Also, most certainly it means a superficial coupling strategy that does not go deep into the solution algorithms of either code. In particular, loose coupling algorithms are often explicit, in that the response of the solid depends on the conditions of the fluid at the previous time step. The opposite can also be said. This coupling strategy is often referred to as “staggered” coupling.

Strong Coupling

In “strong” coupling, the physical coupling is two way and the coupling between the codes is pronounced.

Often “strong” coupling is associated with “dynamic” problems where the hydrodynamic loads and the structural velocities change dramatically. In strong coupling algorithms, the fluid and structure solvers can be resident in processor memory at the same time. Data is passed at regular intervals (often referred to as coupling time or coupling step) from the memory that the structure solver uses to/from the memory that the fluid solver uses. Depending on the actual strength of the coupling it can be necessary to exchange data between the solvers more than once per time step for the simulation to remain stable. This type of coupling implies a deeper communication between the structure and fluid codes and is known as: “implicit”, “iterative staggered”, “iterative successive substitution”, or “multiple iterative coupling”.

Implicit coupling is necessary when a relatively light or compliant structure interacts with a relatively heavy, almost incompressible fluid. For example, a steel structure interacting with air is not coupled strongly in the physical sense. However, a steel structure in water can be coupled strongly as long as the structure is relatively light compared to the fluid it displaces or moves. This phenomenon is true even although the structure is relatively stiff compared to the bulk modulus of the water. A ship only floats because it is lighter than the water it displaces, and thus the interaction is coupled strongly. Indeed the Dynamic Fluid Body Interaction (DFBI) capabilities in Simcenter STAR-CCM+ couple the rigid body dynamics of a structure with the fluid flow in an implicit manner.

Strong coupling can occur in situations that are not immediately evident. For example, flow of water through a stiff, vibrating pipe. In this case, the mass of the pipe can be smaller than the mass of the water that is contained within the pipe. Unless the coupling time step is small, explicit coupling is not stable in this situation. Such cases can be dealt with in Simcenter STAR-CCM+ by taking advantage of the implicit coupling between the CFD and FV Stress solvers. This coupling algorithm is strong and deep, and the exchange of data occurs at each iteration within a time step. This coupling also considers the load balancing and the partitioning, and minimizes the cross-talk among different processors between the fluid and the solid.

Other Categories of Coupling Algorithms

As mentioned in the previous section, the DFBI capability in Simcenter STAR-CCM+ is implicitly coupled. You can take advantage of this stable implicit coupling even when you are interested in the deformations and resulting stresses in the ship. If actual deformations about the rigid body modes are relatively small, then the fluid motion is not sensitive to the deformations, only the rigid body motions. Thus, for example, the CFD and rigid body modes can be solved together in this implicit fashion. Then the transient loads can then be applied to the structural solver, which accounts for deformations and stresses. This process, in effect, is a one-way coupling, since the deformations computed in the structure code are not passed back to the CFD solver. Simcenter STAR-CCM+ can be controlled using Java macros to map and export fluid dynamic loads for use in a structural solver such as Abaqus.

Dynamic Mesh Evolution

The motion of a structure in a fluid requires the CFD solver to account for changes in the shape and position of the solid structure. In Simcenter STAR-CCM+, various strategies are used for this problem. The strategies are discussed in the following sections:

Mesh Rotation and Translation in FSI

The simplest type of mesh motion strategy is to displace the fluid mesh as if it were a rigid body. In this case, all the cells maintain their shape and the description of the mesh motion is from a displacement vector and Euler angles.

In DFBI, the position of the grid is determined by solving the equations of the assumed rigid structure, and the fluid transport equations automatically account for motion of the grid. This type of mesh motion is suitable when the rigid structure does not approach other solid structures. For example, this technique could be used for a ship that is in relatively deep water with no other structures or ships nearby. If other structures were nearby, the mesh is sometimes required to morph to account for the relative motion between the structure and other structures.

Simcenter STAR-CCM+ also allows the fluid mesh to rotate with a rigid structure, and the rotating mesh to be embedded within another stationary mesh in a different region. The two mesh regions can then slide with respect to each other at an interface. The solver automatically calculates this interface projection and imprinting at each time step.

Morphing in FSI

Morphing, in this context, is the deformation of the fluid grid. Morphing occurs by moving the fluid vertices in such a manner as to conform to the solid structure and maintain a reasonable quality fluid grid.

This process is often referred to as a “topologically constant” operation since all the cells maintain the same neighbors but the shapes of the cells can change over time. The fluid transport equations are solved to account for this arbitrary motion of the mesh. This technique is sometimes referred to as the Arbitrary Lagrangian Eulerian (ALE) technique, but often ALE is associated with FEA, rather than FVA. Simcenter STAR-CCM+ uses a “space conservation law” to conservatively and accurately express the transport motion. The key word in ALE is arbitrary, since the motion of the vertices is arbitrary except that it must conform to the moving boundaries and it must provide a reasonable quality mesh.

The morpher in Simcenter STAR-CCM+ currently uses a multi-quadric morphing model that is based on radial basis functions to define the motion of interior vertices. This model originates from the motion of the vertices on the structural surface. When the structure moves in relation to other solid structures, the fluid mesh is distorted to conform to the structures. However, when two structures come into contact or move nearby, a morphing strategy can lead to poor cells.

It is not possible to morph between topologies that are dramatically different. In this case, you can:

• use the overset mesh capability and morph the overset mesh around the deforming structure, or
• use the advanced automatic meshing capabilities in Simcenter STAR-CCM+ to remesh the model completely, using the most recent boundaries as a starting point.

Overset Mesh for FSI

When two structures approach each other, the fluid mesh between them must be squeezed in such a way as to retain the boundary shape that is formed by the structures. When two structures move apart, the fluid mesh must expand. In both cases, there is a threshold beyond which the morpher cannot avoid creating poor quality cells. For such situations, the overset mesh technology in Simcenter STAR-CCM+ provides an effective solution.

Overset meshes that wrap around deformable structures can still be morphed using the structural deformation for the control points. If structures drift apart, however, most of the distance between the structures is treated using the background mesh.

Overset interpolation requires that the overset mesh always overlaps the background mesh by at least 4–5 cells rows. For this reason, it is not possible to close a gap completely when using the overset technique. However, you can still satisfy the overall interpolation requirement for a small gap size by adding more prism cell layers on the walls of both approaching structures.

Gap Closure

To mimic gap closure in Simcenter STAR-CCM+, make the final gap sufficiently small that it gives a high resistance to fluid moving through it. If you intend to stop the flow (as in a stop valve), then drive the flow using pressure boundary conditions at both the outlet and inlet. In these circumstances, the maximum flow rate is proportional to the pressure difference across the gap, and inversely proportional to the viscous resistance of the flow within the gap. Ultimately the gap does leak fluid, but potentially at a small enough rate for the simulation to be an acceptable engineering approximation for the needs of FSI analysis.

Mapping Between Structure and Fluid Grids

Another challenge that must be overcome in FSI cases is the difference in the resolution between the fluid and structure grids. Often the grids are different due to the difference in physical processes in the fluid and the structure.

If the structural mesh and the fluid mesh are both constructed in Simcenter STAR-CCM+, the two meshes can be made conformal at the fluid-structure interface. That is, the vertex positions on the fluid surface match the vertex positions on the surface of the structure. In this case, the mapping of fluid loads and structural displacements is more or less trivial.

When the opposing meshes are not conformal, Simcenter STAR-CCM+ offers various strategies to map the data efficiently and accurately to and from meshes that are imported from other CAE products. This mapping is accurate, continuous, bounded, and as conservative as possible. When the opposing surface is an FEA mesh, Simcenter STAR-CCM+ uses the innate shape functions of the finite element topology to map between the structure and fluid meshes.

Reference Configuration

Mapping requires that fluid and solid meshes must be similar at some reference configuration. The meshes must be sufficiently similar that the neighbors of faces on one side are matched to faces on the opposite side. The reference configuration is usually the geometry at the initial time. The fluid and solid mesh are assumed to move together so that their neighbors remain the same. For this reason, the weights of the mapping are defined entirely by the geometry of the mesh at the reference configuration—the mapping does not depend on the current deformed geometry.

In the data mappers, you can choose whether the reference configuration is set by the original mesh or by the current mesh, which could be deformed as a result of morphing. When the reference configuration is set to use the current mesh, Simcenter STAR-CCM+ performs a neighbor search each time the mesh is moved or morphed. As this neighbor search is an expensive operation, you are recommended to set the reference configuration to the original mesh. Simcenter STAR-CCM+ generally uses the original mesh configuration when it automatically sets the data mapping schemes appropriate for the physics in co-simulation. It also uses this configuration for mapped fluid/solid interfaces within a single simulation.

The assumption that neighbors at the reference configuration will always be neighbors is violated if the fluid mesh slides with respect to the solid mesh. In this case, the reference configuration must always be the current deformed mesh and neighbors must be re-established at each new time step.

The reference configuration need not always be at the initial time or at a re-meshing event. For example a structure can be pre-loaded to deform the shape. The fluid mesh can be initially constructed to conform around the deformed shaped of the structure (for example, the deformed tire loaded by the weight of the car and contact with the pavement). The reference configuration is now the deformed shape at this point in time.

HPC and Grid Partitioning on Multiple Processors

Modeling FSI also presents challenges regarding the partition of the fluid and structural grids.

In Simcenter STAR-CCM+, when one employs the FV Stress solver for the structure, the grid is automatically partitioned for load balancing and to minimize processor-to-processor communications. In this case, the partition is not required to respect the boundaries between the structure and the fluid. In other words, any particular partition can have part of the fluid grid and part of the structural grid. It is this unique feature that makes Simcenter STAR-CCM+ efficient for FSI applications on multiple processors.