Fluid Grid Research Articles

An embedded mesh method in a multiple material ALE

A new approach for treating the mechanical interactions of overlapping finite element meshes is presented. Referred to as embedded mesh methods here, these overlapping mesh methods typically include a foreground solid mesh and a background Euler fluid grid or solid mesh. A number of different approaches have been used in previous work to characterize the interactions of the background and foreground meshes at the interface. Lagrange multipliers are well suited to enforce the continuity constraints but care must be taken such that the resulting formulation is stable. Several Lagrange multiplier techniques are examined in this work and applied to coupling solid meshes and fluid-structure interaction type problems. In addition, details regarding implementation in a two-step, multi-material, Arbitrary Lagrangian Eulerian (ALE) code are presented. Example problems demonstrate convergence and applicability to a range of problems. In particular, the fluid-structure interaction examples focus on blast applications.

An embedded mesh method for treating overlapping finite element meshes

SUMMARYA new technique for treating the mechanical interactions of overlapping finite element meshes is presented. Such methods can be useful for numerous applications, for example, fluid–solid interaction with a superposed meshed solid on an Eulerian background fluid grid. In this work, we consider the interaction of two elastic domains: one mesh is the foreground and defines the surface of interaction, the other is a background mesh and is often a structured grid. Many of the previously proposed methods employ surface defined Lagrange multipliers or penalties to enforce the boundary constraints. It has become apparent that these methods will cause mesh locking under certain conditions. Appropriately applied, the Nitsche method can overcome this locking, but, in its canonical form, is generally not applicable to non‐linear materials such as hyperelastics. The relationship between interior point penalty, discontinuous Galerkin and Nitsche's method is well known. Based on this relationship, a nonlinear theory analogous to the Nitsche method is proposed to treat nonlinear materials in an embedded mesh. Here, a discontinuous Galerkin derivative based on a lifting of the interface surface integrals provides a consistent treatment for non‐linear materials and demonstrates good behavior in example problems. Published 2012. This article is a US Government work and is in the public domain in the USA.

Computational Aeroelasticity of Rotating Wings with Deformable Airfoils

This paper presents a simulation for high-fidelity aeroelastic analysis of rotating wings with camber-wise structural flexibility and embedded actuators. An unstructured Reynolds-Averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) solver is coupled with a non-linear structural dynamics analysis. The CFD solution uses overset grids to combine the stationary and moving frames of reference. The structural formulation expands the conventional one-dimensional beam representation with additional degrees-of-freedom to capture plate-like cross-sectional deformations while allowing an arbitrary distribution of active and passive materials in the cross section. Motion and forces on the non-coincident fluid and structural grids are transferred using a finite-element-based interpolation, along with a least-squares fit for extrapolations. Trim and convergence to periodic response are assisted by a low-order analysis that is also discussed. Finally, as an initial verification of the implementations, results from the low-order and CFD-based solutions are compared for a rigid-airfoil rotor in forward flight.

Fluid–structure analysis of a flexible flapping airfoil at low Reynolds number flow

In this paper, a coupling simulation methodology is applied to investigate the fluid flow around a light and flexible airfoil based on a handfoil of a seagull. A finite element model of the flexible airfoil is fully coupled to the flow solver by using a load and displacement transfer as well as a fluid grid deformation algorithm. The flow field is characterized by a laminar-turbulent transition at a Reynolds number of Re=100 000, which takes place along a laminar separation bubble. An unsteady Reynolds-averaged Navier–Stokes flow solver is used to take this transition process into account by comparison of a critical N-factor with the N-factor computed by the e N -method. Results of computations have shown that the flexibility of the airfoil has a major influence on the thrust efficiency, the mean drag and lift, and the location of laminar-turbulent transition. The thrust efficiency can be considerably improved by increasing the plunging amplitude and by using a time dependent airfoil stiffness, inspired by the muscle contraction of birds.

A Nitsche embedded mesh method

A new technique for treating the mechanical interactions of overlapping finite element meshes is proposed. Numerous names have been applied to related approaches, here we refer to such techniques as embedded mesh methods. Such methods are useful for numerous applications e.g., fluid-solid interaction with a superposed meshed solid on an Eulerian background fluid grid or solid-solid interaction with a superposed meshed particle on a matrix background mesh etc. In this work we consider the interaction of two elastic domains: one mesh is the foreground and defines the surface of interaction, the other is a background mesh and is often a grid. We first employ a classical mortar type approach [see Baaijens (Int J Numer Methods Eng 35:743–761, 2001)] to impose constraints on the interface. It turns out that this approach will work well except in special cases. In fact, many related approaches can exhibit mesh locking under certain conditions. This motivates the proposed version of Nitsche’s method which is shown to eliminate the locking phenomenon in example problems.

An XFEM‐based embedding mesh technique for incompressible viscous flows

AbstractThis paper presents a finite element (FE) embedding mesh technique to efficiently embed arbitrary fluid mesh patches into Cartesian or unstructured background fluid grids. Our motivating application for such a technique is to efficiently resolve flow features like boundary layers around structures, which is achieved by attaching fluid boundary layer meshes around these structure surfaces. The proposed technique can be classified as a non‐overlapping domain decomposition method. The particular feature is that the embedded patch cuts a void region into the background grid independently of background element edges. Since the embedded fluid domain ends in the middle of background elements, extended FE techniques are used to model a sharp separation between active and inactive regions on the background grid. The active background region is coupled to the boundary layer mesh using a mixed/hybrid Lagrange multiplier technique as proposed in Gerstenberger and Wall (textitInt. J. Numer. Meth. Engng. 2010; 82:537–563). The coupling formulation works without stabilization for the Lagrange multiplier unknowns and the Lagrange multiplier can be completely condensed on the element level. Within this paper, the approach is derived for incompressible, viscous flows. Three‐dimensional examples using linear and quadratic shape functions demonstrate the correctness and the versatility of the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.

Coupled fluid-solid interaction under shock wave loading

This paper considers the treatment of fluid–solid interaction problems under shock wave loading, where the solid experiences large bulk Lagrangian displacements. This work addresses the issues associated with using a level set as a generalized interface for fluid–solid coupling where the fluid–solid interface is embedded in an unstructured fluid grid. We outline the formulation used for the edge-based unstructured-grid Euler solver. The identification of the fluid–solid interface on the unstructured fluid mesh uses a super-sampled ℒ2 projection technique, which in conjunction with a Lagrangian interface position, permits fast identification of the interface and the concomitant imposition of boundary conditions. The use of a narrow-band approach for the identification of the wetted interface is presented with the details of the construction of interface conditions. A series of two and three-dimensional shock-body computations are presented to demonstrate the validity of the current approach on problems with static and dynamic interfaces, including projectile/shock interaction simulations. Copyright © 2010 John Wiley & Sons, Ltd.

A novel algorithm for incompressible flow using only a coarse grid projection

Large scale fluid simulation can be difficult using existing techniques due to the high computational cost of using large grids. We present a novel technique for simulating detailed fluids quickly. Our technique coarsens the Eulerian fluid grid during the pressure solve, allowing for a fast implicit update but still maintaining the resolution obtained with a large grid. This allows our simulations to run at a fraction of the cost of existing techniques while still providing the fine scale structure and details obtained with a full projection. Our algorithm scales well to very large grids and large numbers of processors, allowing for high fidelity simulations that would otherwise be intractable.

Numerical Investigation on the Aerodynamics of Oscillating Airfoils with Deployable Gurney Flaps

To assess their application to rotorcraft, the two-dimensional aerodynamics of deployable Gurney flaps, referred to as miniature trailing-edge effectors, are explored using computational fluid dynamics. These deployable devices have a height of only a few percent of the airfoil chord and deploy normal to the airfoil surface near the trailing edge. Their small size, low inertia, and small added mass make them well suited for deployment in high-frequency applications such as those needed for rotorcraft. A combination of wind-tunnel measurements using airfoils fitted with Gurney flaps and unsteady circulatory theory are used to validate the computational fluid dynamics, and grid and time-resolution studies are used for code verification. Qualitative and quantitative agreement of the effects of a Gurney flap with experiments and theory suggest that the computational fluid dynamics results are valid. These investigations examine the effects of the chordwise positioning and deployment frequency of the miniature trailing-edge effectors. In doing so, their operation on both static and dynamically pitching airfoils is considered. Through these studies, a number of physical insights into miniature trailing-edge effectors and Gurney flap aerodynamics have been obtained. These insights have led to the introduction of a scaling parameter that easily accounts for compressibility effects, an understanding of the aerodynamic consequences due to positioning miniature trailing-edge effectors upstream of the trailing edge, and an assessment on the benefits of using of miniature trailing-edge effectors for active stall alleviation on an airfoil oscillating in pitch.

A front-tracking method with projected interface conditions for compressible multi-fluid flows

A front-tracking method for compressible multi-fluid flows is presented, where marker points are used both for tracking fluid interfaces and also for constructing the Riemann problem on the interfaces. The Riemann problem between the two fluid phases (defined in the interface normal direction) is solved using the exact Riemann solver on the marker points. The solutions are projected onto fixed grid points and then extrapolated into the corresponding ghost-fluid regions, to be used as boundary conditions. Each fluid phase is solved separately as in the ghost-fluid method. The proposed procedures, especially the projection of the exact Riemann solutions onto the fluid grids, are designed to be simple and consistent in any spatial dimensions. Several multi-fluid problems, including the breakup of a water cylinder induced by the passage of a shock wave were computed in order to demonstrate the capability of the proposed method.

The Burns Fluid Grid. A Pre-Hospital Guide to Fluid Resuscitation in Burns

The Burns Fluid Grid. A Pre-Hospital Guide to Fluid Resuscitation in Burns

Evaluation of interfacial fluid dynamical stresses using the immersed boundary method

The goal of this paper is to examine the evaluation of interfacial stresses using a standard, finite difference based, immersed boundary method (IMBM). This calculation is not trivial for two fundamental reasons. First, the immersed boundary is represented by a localized boundary force which is distributed to the underlying fluid grid by a discretized delta function. Second, this discretized delta function is used to impose a spatially averaged no-slip condition at the immersed boundary. These approximations can cause errors in interpolating stresses near the immersed boundary.To identify suitable methods for evaluating stresses, we investigate three model flow problems at very low Reynolds numbers. We compare the results of the immersed boundary calculations to those achieved by the boundary element method (BEM). The stress on an immersed boundary may be calculated either by direct evaluation of the fluid stress (FS) tensor or, for the stress jump, by direct evaluation of the locally distributed boundary force (wall stress or WS). Our first model problem is Poiseuille channel flow. Using an analytical solution of the immersed boundary formulation in this simple case, we demonstrate that FS calculations should be evaluated at a distance of approximately one grid spacing inward from the immersed boundary. For a curved immersed boundary we present a procedure for selecting representative interfacial fluid stresses using the concepts from the Poiseuille flow test problem. For the final two model problems, steady state flow over a bump in a channel and unsteady peristaltic pumping, we present an 'exclusion filtering' technique for accurately measuring stresses. Using this technique, these studies show that the immersed boundary method can provide reliable approximations to interfacial stresses.

Fluid–structure interaction by the discontinuous‐Galerkin method for large deformations

AbstractA discontinuous‐Galerkin method for large deformation fluid–structure interaction problems is developed. The fluid–structure interface can be arbitrarily aligned relative to the fluid grid. An Eulerian description is used for the fluid with a Lagrangian description of the solid. Results are presented for several examples that show excellent agreement with immersed/fictitious element methods. Copyright © 2008 John Wiley & Sons, Ltd.

Imposing rigidity constraints on immersed objects in unsteady fluid flows

Imposing rigidity constraints of an immersed elastic body in a transient flow field is not trivial. It requires solution stability and accuracy. In this paper, we present an efficient and accurate algorithm implemented to enforce fluid–structure interface constraints used in the immersed finite element method (IFEM). This interface treatment is a constraint applied onto the rigid bodies based on the fluid structure interaction force evaluated from the immersed solid object. It requires no ad hoc constants or adjustments, thus providing numerical stability and avoiding unnecessary trial-and-error procedures in defining the stiffness of the elastic body. This force term can be evaluated for both uniform and nonuniform fluid grids based on the higher order interpolation function adopted in the IFEM. The ability in handling nonuniform interpolations offers the convenience in modeling arbitrary geometrical shapes and provides solution refinements around interfaces. The results we obtained from flow past a rigid cylinder demonstrate that this convenient way of constraining the interface is a reliable and robust numerical approach to solve unsteady fluid flow interacting with immersed rigid bodies.

Aeroacoustic study of a forward facing step using linearized Euler equations

We present a hybrid approach for computational aeroacoustics in the time domain. The flow field is computed using large eddy simulation and coupled to the acoustic propagation solver based on linearized Euler equations. Coupling in the time domain avoids storage of large flow field volume data, avoiding the slow hard disk access rate and hence speeding up the computation. Acoustic sources are calculated on the fine fluid grid and interpolated conservatively onto the coarse acoustic grid. The problem studied is flow-induced noise from flow over a forward facing step and the Reynolds number based on the height of the step ( H = 12 mm ) is Re H ≈ 8000 . The sound pressure levels obtained compare well with the published results.

Modeling Transport Phenomena of High Mass Loadings with Applications to Fire Suppression

Improvements to the existing Eulerian-Lagrangian two-phase dilute spray model, referred to as Vulcan, are required in order to handle high mass loadings or very small solid particles. Such flows are relevant to modern fire-suppression techniques among other applications. These improvements include developing a new treatment for efficiently integrating small particles, a new subcycling time-step selection algorithm for the time-splitting solution technique, and a new treatment for placement of the two-way coupling source terms on the fluid grid. Despite the added complexity of these modifications, performance tuning of the code was also performed so that the solution speed is either equivalent to or faster than the previous code, depending on particle size. The new algorithms are applied to predicting suppressant distribution from a Goodrich-244 fire-suppression system in a simulated aircraft cargo bay. Results using these new algorithms indicate that the larger particles found in the Goodrich-244 suppressant disperse more uniformly throughout the aircraft cargo bay, although a large fraction of these particles adhere to the side walls before being delivered to the fire. Buoyancy of the hot combustion products was found to inhibit particle dispersion, and to generate large unwanted convective heat fluxes to the roof of the cargo bay.

Transient fluid–structure coupling for simulation of a trileaflet heart valve using weak coupling

In this article, a three-dimensional transient numerical approach coupled with fluid-structure interaction for the modeling of an aortic trileaflet heart valve at the initial opening stage is presented. An arbitrary Lagrangian-Eulerian kinematical description together with an appropriate fluid grid was used for the coupling strategy with the structural domain. The fluid dynamics and the structure aspects of the problem were analyzed for various Reynolds numbers and times. The fluid flow predictions indicated that at the initial leaflet opening stage a circulation zone was formed immediately downstream of the leaflet tip and propagated outward as time increased. Moreover, the maximum wall shear stress in the vertical direction of the leaflet was found to be located near the bottom of the leaflet, and its value decreased sharply toward the tip. In the horizontal cross section of the leaflet, the maximum wall shear stresses were found to be located near the sides of the leaflet.

Penalty immersed boundary method for an elastic boundary with mass

The immersed boundary (IB) method has been widely applied to problems involving a moving elastic boundary that is immersed in fluid and interacting with it. Most of the previous applications of the IB method have involved a massless elastic boundary and used efficient Fourier transform methods for the numerical solutions. Extending the method to cover the case of a massive boundary has required spreading the boundary mass out onto the fluid grid and then solving the Navier-Stokes equations with a variable mass density. The variable mass density of this previous approach makes Fourier transform methods inapplicable, and requires a multigrid solver. Here we propose a new and simple way to give mass to the elastic boundary and show that the method can be applied to many problems for which the boundary mass is important. The method does not spread mass to the fluid grid, retains the use of Fourier transform methodology, and is easy to implement in the context of an existing IB method code for the massless case. Two verifications of the method are given. One is a numerical convergence study that shows that our numerical scheme is second-order accurate for a particular test problem. The other is direct comparison with experimental data of vortex-induced vibrations of a massive cylinder, which shows that the results obtained by the present method are quite comparable to the experimental data.

LTCC Microsystems and Microsystem Packaging and Integration Applications

Low Temperature Cofired Ceramic (LTCC) has proven to be an enabling medium for microsystem technologies, because of its desirable electrical, physical, and chemical properties coupled with its capability for rapid prototyping and scalable manufacturing of components. LTCC is viewed as an extension of hybrid microcircuits, and in that function it enables development, testing, and deployment of silicon microsystems. However, its versatility has allowed it to succeed as a microsystem medium in its own right, with applications in non-microelectronic meso-scale devices and in a range of sensor devices. Applications include silicon microfluidic ‘chip-and-wire’ systems and fluid grid array (FGA)/microfluidic multichip modules using embedded channels in LTCC, and cofired electro-mechanical systems with moving parts. Both the microfluidic and mechanical system applications are enabled by sacrificial volume materials (SVM), which serve to create and maintain cavities and separation gaps during the lamination and cofiring process. SVMs consisting of thermally fugitive or partially inert materials are easily incorporated. Screeding is an incorporation technique we describe that improves uniformity and eliminates processing steps. Recognizing the premium on devices that are cofired rather than assembled, we report on functional-as-released and functional-as-fired moving parts, including an impeller that has been exercised over thirty million cycles, and a cofired pressure sensor that requires only pressure source and electrical connections. Additional applications for cofired transparent windows, some as small as an optical fiber, are also described. The applications described help pave the way for widespread application of LTCC to biomedical, control, analysis, characterization, and radio frequency (RF) functions for macro-meso-microsystems.

Aeroelasticity of Nonlinear Structures Using the Corotational Method

A method to solve aeroelasticity of geometrically nonlinear structures in the time domain is presented. Large structural deformations are taken into account using the nonlinear corotational theory. Stable and accurate nonlinear solutions are obtained using the corotational theory in combination with an implicit energy-conserving algorithm. The fluid flow is modeled using Euler equations solved using a modified multiple moving-frames method. The application of the proposed methodology is illustrated on a study of nonlinear aeroelastic response of a NACA0012 airfoil in transonic flow. The proposed method is stable and results in accurate nonlinear solutions without the need to deform or regenerate the fluid grid.