A finite volume unstructured mesh approach to dynamic fluid-structure interaction: an assessment of the challenge of flutter analysis

Computational modelling of dynamic fluid-structure interaction (DFSI) is problematical since conventionally computational fluid dynamics (CFD) is solved using finite volume (FV) methods and computational structural mechanics (CSM) is based entirely on finite element (FE) methods. Hence, progress in modelling the emerging multi-physics problem of dynamic fluid-structure interaction in a consistent manner is frustrated and significant problems in computation convergence may be encountered in transferring and filtering data from one mesh and solution procedure to another, unless the fluid-structure coupling is either one way, very weak or both. This paper sets out the solution procedure for modelling the multi-physics dynamic fluid-structure interaction problem within a single software framework PHYSICA, using finite volume, unstructured mesh (FV-UM) procedures and will focus upon some of the problems and issues that have to be resolved for time accurate closely coupled dynamic fluid-structure flutter analysis.

Dynamic fluid-structure interactions using finite volume unstructured mesh procedures

A three-dimensional finite volume, unstructured mesh (FV-UM) method for dynamic fluid–structure interaction (DFSI) is described. Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, wind response of buildings, flows in elastic pipes and blood vessels. It involves the coupling of fluid flow and structural mechanics, two fields that are conventionally modelled using two dissimilar methods, thus a single comprehensive computational model of both phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply. More recently, strategies for solving the full coupling between the fluid and solid mechanics behaviour have been developed. A key contribution has been made by Farhat et al. [Int. J. Numer. Meth. Fluids 21 (1995) 807] employing FV-UM methods for solving the Euler flow equations and a conventional finite element method for the elastic solid mechanics and the spring based mesh procedure of Batina [AIAA paper 0115, 1989] for mesh movement. In this paper, we describe an approach which broadly exploits the three field strategy described by Farhat for fluid flow, structural dynamics and mesh movement but, in the context of DFSI, contains a number of novel features: a single mesh covering the entire domain, a Navier–Stokes flow, a single FV-UM discretisation approach for both the flow and solid mechanics procedures, an implicit predictor–corrector version of the Newmark algorithm, a single code embedding the whole strategy.

Dynamic fluid-structure interaction using finite volume unstructured mesh procedures

A three dimensional finite volume, unstructured mesh method for dynamic fluid-structure interation is described. The broad approach is conventional in that the fluid and structure are solved sequentially. The pressure and viscous stresses from the flow algorithm provide load conditions for the solid algorithm, whilst at the fluid structure interface the deformed structure provides boundary condition from the structure to the fluid. The structure algorithm also provides the necessary mesh adaptation for the flow field, the effect of which is accounted for in the flow algorithm. The procedures described in this work have several novel features, namely: * a single mesh covering the entire domain. * a Navier Stokes flow. * a single FV-UM discretisation approach for both the flow and solid mechanics procedures. * an implicit predictor-corrector version of the Newmark algorithm. * a single code embedding the whole strategy. The procedure is illustrated for a three dimensional loaded cantilever in fluid flow.

Dynamic fluid-structure interactions using finite volume unstructured mesh procedures

A three-dimensional finite volume, unstructured mesh (FV-UM) method for dynamic fluid–structure interaction (DFSI) is described. Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, wind response of buildings, flows in elastic pipes and blood vessels. It involves the coupling of fluid flow and structural mechanics, two fields that are conventionally modelled using two dissimilar methods, thus a single comprehensive computational model of both phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply. More recently, strategies for solving the full coupling between the fluid and solid mechanics behaviour have been developed. A key contribution has been made by Farhat et al. [Int. J. Numer. Meth. Fluids 21 (1995) 807] employing FV-UM methods for solving the Euler flow equations and a conventional finite element method for the elastic solid mechanics and the spring based mesh procedure of Batina [AIAA paper 0115, 1989] for mesh movement. In this paper, we describe an approach which broadly exploits the three field strategy described by Farhat for fluid flow, structural dynamics and mesh movement but, in the context of DFSI, contains a number of novel features: a single mesh covering the entire domain, a Navier–Stokes flow, a single FV-UM discretisation approach for both the flow and solid mechanics procedures, an implicit predictor–corrector version of the Newmark algorithm, a single code embedding the whole strategy.

Dynamic fluid–structure interaction using finite volume unstructured mesh procedures

A three-dimensional finite volume, unstructured mesh (FV-UM) method for dynamic fluid–structure interaction (DFSI) is described. Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, wind response of buildings, flows in elastic pipes and blood vessels. It involves the coupling of fluid flow and structural mechanics, two fields that are conventionally modelled using two dissimilar methods, thus a single comprehensive computational model of both phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply. More recently, strategies for solving the full coupling between the fluid and solid mechanics behaviour have been developed. A key contribution has been made by Farhat et al. [Int. J. Numer. Meth. Fluids 21 (1995) 807] employing FV-UM methods for solving the Euler flow equations and a conventional finite element method for the elastic solid mechanics and the spring based mesh procedure of Batina [AIAA paper 0115, 1989] for mesh movement. In this paper, we describe an approach which broadly exploits the three field strategy described by Farhat for fluid flow, structural dynamics and mesh movement but, in the context of DFSI, contains a number of novel features: • a single mesh covering the entire domain, • a Navier–Stokes flow, • a single FV-UM discretisation approach for both the flow and solid mechanics procedures, • an implicit predictor–corrector version of the Newmark algorithm, • a single code embedding the whole strategy.

Details of an integrated approach to three-dimensional dynamic fluid structure interaction

Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, wind response of buildings, flows in elastic pipes and blood vessels. Numerical modelling of dynamic fluid-structure interaction (DFSI) involves the coupling of fluid flow and structural mechanics, two fields that are conventionally modelled using two dissimilar methods, thus a single comprehensive computational model of both phenomena is a considerable challenge and until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply. A single, finite volume unstructured mesh (FV-UM) spatial discretisation method has been employed on a single mesh for the entire domain. The Navier Stokes equations for fluid flow are solved using a SIMPLE type procedure and the Newmark b algorithm is employed for solving the dynamic equilibrium equations for linear elastic solid mechanics and mesh movement is achieved using a spring based mesh procedure for dynamic mesh movement. In the paper we describe a number of additional computation issues for the efficient and accurate modelling of three-dimensional, dynamic fluid-structure interaction problems.

A finite volume unstructured mesh approach to dynamic fluid–structure interaction: an assessment of the challenge of predicting the onset of flutter

Computational modelling of dynamic fluid–structure interaction (DFSI) is a considerable challenge. Our approach to this class of problems involves the use of a single software framework for all the phenomena involved, employing finite volume methods on unstructured meshes in three dimensions. This method enables time and space accurate calculations in a consistent manner. One key application of DFSI simulation is the analysis of the onset of flutter in aircraft wings, where the work of Yates et al. [Measured and Calculated Subsonic and Transonic Flutter Characteristics of a 45° degree Sweptback Wing Planform in Air and Freon-12 in the Langley Transonic Dynamic Tunnel. NASA Technical Note D-1616, 1963] on the AGARD 445.6 wing planform still provides the most comprehensive benchmark data available. This paper presents the results of a significant effort to model the onset of flutter for the AGARD 445.6 wing planform geometry. A series of key issues needs to be addressed for this computational approach. • The advantage of using a single mesh, in order to eliminate numerical problems when applying boundary conditions at the fluid-structure interface, is counteracted by the challenge of generating a suitably high quality mesh in both the fluid and structural domains. • The computational effort for this DFSI procedure, in terms of run time and memory requirements, is very significant. Practical simulations require even finer meshes and shorter time steps, requiring parallel implementation for operation on large, high performance parallel systems. • The consistency and completeness of the AGARD data in the public domain is inadequate for use in the validation of DFSI codes when predicting the onset of flutter.

A generic time and space accurate numerical approach to closely coupled fluid-structure interaction problems

Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, flow in elastic pipes and blood vessels and extrusion of metals through dies. However a comprehensive computational model of these multi-physics phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply even to the extent in metal forming, for example, that the deformation of the die is totally ignored. More recently, strategies for solving the full coupling between the fluid and soild mechanics behaviour have developed. Conventionally, the computational modelling of fluid structure interaction is problematical since computational fluid dynamics (CFD) is solved using finite volume (FV) methods and computational structural mechanics (CSM) is based entirely on finite element (FE) methods. In the past the concurrent, but rather disparate, development paths for the finite element and finite volume methods have resulted in numerical software tools for CFD and CSM that are different in almost every respect. Hence, progress is frustrated in modelling the emerging multi-physics problem of fluid structure interaction in a consistent manner. Unless the fluid-structure coupling is either one way, very weak or both, transferring and filtering data from one mesh and solution procedure to another may lead to significant problems in computational convergence. Using a novel three phase technique the full interaction between the fluid and the dynamic structural response are represented. The procedure is demonstrated on some challenging applications in complex three dimensional geometries involving aircraft flutter, metal forming and blood flow in arteries.

Multi-physics modelling for microelectronics and microsystems - current capabilities and future challenges

At present the vast majority of Computer-Aided- Engineering (CAE) analysis calculations for microelectronic and microsystems technologies are undertaken using software tools that focus on single aspects of the physics taking place. For example, the design engineer may use one code to predict the airflow and thermal behavior of an electronic package, then another code to predict the stress in solder joints, and then yet another code to predict electromagnetic radiation throughout the system. The reason for this focus of mesh-based codes on separate parts of the governing physics is essentially due to the numerical technologies used to solve the partial differential equations, combined with the subsequent heritage structure in the software codes. Using different software tools, that each requires model build and meshing, leads to a large investment in time, and hence cost, to undertake each of the simulations. During the last ten years there has been significant developments in the modelling community around multi- physics analysis. These developments are being followed by many of the code vendors who are now providing multi-physics capabilities in their software tools. This paper illustrates current capabilities of multi-physics technology and highlights some of the future challenges

Uncertainty analysis to minimise risk in designing micro-electronics manufacturing processes

A design methodology based on numerical modelling, integrated with optimisation techniques and statistical methods, to aid the process control of micro and nano-electronics based manufacturing processes is presented in this paper. The design methodology is demonstrated for a micro-machining process called Focused Ion Beam (FIB). This process has been modelled to help understand how a pre-defined geometry of micro- and nano- structures can be achieved using this technology. The process performance is characterised on the basis of developed Reduced Order Models (ROM) and are generated using results from a mathematical model of the Focused Ion Beam and Design of Experiment (DoE) methods. Two ion beam sources, Argon and Gallium ions, have been used to compare and quantify the process variable uncertainties that can be observed during the milling process. The evaluations of the process performance takes into account the uncertainties and variations of the process variables and are used to identify their impact on the reliability and quality of the fabricated structure. An optimisation based design task is to identify the optimal process conditions, by varying the process variables, so that certain quality objectives and requirements are achieved and imposed constraints are satisfied. The software tools used and developed to demonstrate the design methodology are also presented.

Optimisation methodology for risk mitigation in advanced micro-system electronics manufacturing

This paper presents a design methodology based on numerical modelling, integrated with optimisation techniques and statistical methods, to aid the development of new advanced technologies in the area of micro and nano systems. The design methodology is demonstrated for a micro-machining process called Focused Ion Beam (FIB). This process has been modelled to provide knowledge of how a pre-defined geometry can be achieved through this direct milling. The geometry characterisation is obtained using a Reduced Order Models (ROM), generated from the results of a mathematical model of the Focused Ion Beam, and Design of Experiment (DoE) methods. In this work, the focus is on the design flow methodology which includes an approach on how to include process parameter uncertainties into the process optimisation modelling framework. A discussion on the impact of the process parameters, and their variations, on the quality and performance of the fabricated structure is also presented. The design task is to identify the optimal process conditions, by altering the process parameters, so that certain reliability and confidence of the application is achieved and the imposed constraints are satisfied. The software tools used and developed to demonstrate the design methodology are also presented.