Fluid Mesh Research Articles

A Non-Linear Aeroelasticity Analysis of a Fan Blade Using Unstructured Dynamic Meshes

The main objective of this paper is to present a methodology for the three-dimensional aeroelasticity analysis of turbomachinery blades using an unstructured compressible Navier-Stokes solver for the fluid and a modal model for the structure. The basic fluid solver is constructed in the form of a central difference scheme with explicitly added artificial dissipation which is based upon the fourth- and second-order differences of the solution. The temporal discretization uses an implicit time integration scheme based on a Jacobi relaxation procedure. The structural modes of vibration are determined via a finite element model and the mode shapes are interpolated on to the fluid mesh in a manner that is consistent with general unstructured tetrahedral grids. A spring analogy algorithm that can move the mesh according to the instantaneous shape of a deforming blade has been developed for the accurate tracking of the solid boundaries without creating excessive grid distortions. The performance of the resulting system was examined by considering the aeroelastic behaviour of NASA Rotor 67 fan blade and predictions were compared to experimental results wherever possible. Using a three-dimensional cyclic symmetry model, the tip leading edge time histories were predicted under peak-efficiency and near-stall conditions, and the corresponding aeroelastic natural frequencies and aerodynamic damping values were determined. The blade was found to be stable in all cases considered.

Geometric conservation laws for flow problems with moving boundaries and deformable meshes, and their impact on aeroelastic computations

Numerical simulations of flow problems with moving boundaries commonly require the solution of the fluid equations on unstructured and deformable dynamic meshes. In this paper, we present a unified theory for deriving Geometric Conservation Laws (GCLs) for such problems. We consider several popular discretization methods for the spatial approximation of the flow equations including the Arbitrary Lagrangian-Eulerian (ALE) finite volume and finite element schemes, and space-time stabilized finite element formulations. We show that, except for the case of the space-time discretization method, the GCLs impose important constraints on the algorithms employed for time-integrating the semi-discrete equations governing the fluid and dynamic mesh motions. We address the impact of these constraints on the solution of coupled aeroelastic problems, and highlight the importance of the GCLs with an illustration of their effect on the computation of the transient aeroelastic response of a flat panel in transonic flow.

Matching fluid and structure meshes for aeroelastic computations: A parallel approach

Matcher is a program that generates the data structures needed for handling arbitrary and non-conforming fluid/structure interfaces in aeroelastic computations. In this paper, we describe the key issues addressed by Matcher and overview the underlying parallel algorithm. We highlight its parallel performance on the iPSC860/32 for a complete aircraft configuration where the fluid mesh contains 439,272 tetrahedra and 77,279 vertices and the structural model contains 7520 triangular shell elements and 3841 nodes.

The Vibration of Ring-Stiffened Cones Under External Water Pressure

This paper describes a theoretical and an experimental investigation into the vibration of three ring-stiffened thin-walled conical shells, under external water pressure. The theoretical investigation was via the finite element method for both the shell structure and the surrounding water. Various fluid meshes were chosen, and a relatively simple one showed good agreement between experiment and theory.

Mesh Rezoning Technique for Fluid-Structure Interaction Problem.

The Space-Time Galerkin method provides a framework for solving fluid-structure interaction problems #(FSI). These formulations allow us to use different fluid meshes for each time-slab. The space-time elements can be oriented in time, thus accommodating spatial deformation. The mesh generator between time slabs and adaptive mesh rezoning techniques within each time-slab play important roles in FSI problems. We have developed an adaptive mesh rezoning technique with the least-square constrained conditions, which prevents the element located close to the moving boundary from breakdown trouble and maintains its well-conditioned shape. The technique is entirely general in that it can be effectively applied to structured and unstructured meshes.

Coupled shell-fluid interaction problems with degenerate shell and three-dimensional fluid elements

Discrete methods for practical coupled three-dimensional fluid-structure interaction problems are developed. A C° explicitly integrated two-dimensional degenerate shell element and a three-dimensional fluid element are coupled to study shell dynamics, fluid transient and coupled shell-fluid interaction problems. The method of partitioning is used to integrate the fluid and shell meshes in a staggered fashion in an optimum manner. Effective explicit-implicit partitioning is shown to achieve high computational efficiency for this type of problem.

Coupled finite element/boundary element approach for fluid–structure interaction

A new computational capability is described for calculating the sound-pressure field radiated or scattered by a harmonically excited, submerged, arbitrary, three-dimensional elastic structure. This approach, called nashua, couples a nastran finite element model of the structure with a boundary element model of the surrounding fluid. The surface fluid pressures and normal velocities are first calculated by coupling the finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior fluid. After generation of the fluid matrices, most of the required matrix operations are performed using the general matrix manipulation package available in nastran. Farfield radiated pressures are then calculated from the surface solution using the Helmholtz exterior integral equation. The overall capability is very general, highly automated, and requires no independent specification of the fluid mesh. An efficient, new, out-of-core block equation solver was written so that very large problems could be solved. The use of nastran as the structural analyzer permits a variety of graphical displays of results, including computer animation of the dynamic response. The overall approach is illustrated and validated using known analytic solutions for submerged spherical shells subjected to both incident pressure and uniform and nonuniform applied mechanical loads.

Coupled finite element/boundary element approach for acoustic radiation and scattering

A new computational capability is described for calculating the sound‐pressure field radiated or scattered by a harmonically excited, submerged, arbitrary, 3‐D elastic structure. This approach, called NASHUA, first calculates the fluid pressures and velocities on the structural surface by coupling a NASTRAN finite element model of the structure with a boundary element model (based on a discretized form of the Helmholtz surface integral equation) of the surrounding fluid. Farfield radiated pressures are then calculated from the surface solution using the Helmholtz exterior integral equation. The overall capability is very general, highly automated, and requires no independent specification of the fluid mesh. A new out‐of‐core block equation solver was written so that very large problems could be solved. The use of NASTRAN as the structural analyzer permits a variety of graphical displays of results, including computer animation of the dynamic response. The overall approach is illustrated and validated using known analytic solutions for submerged spherical shells subjected to both incident pressure as well as uniform and nonuniform applied mechanical loads.

An algorithm for continuous rezoning of the hydrodynamic grid in Arbitrary Lagrangian-Eulerian computer codes

This paper describes a new efficient algorithm developed for the automatic and continuous rezoning of the fluid mesh in two-dimensional Arbitrary Lagrangian-Eulerian finite-element codes. The algorithm is easy to implement and requires modest computing time. Some problems involving significant distorsions of the fluid domain are illustrated. The extension of the rezone procedure to deal with three-dimensional grids is also described.

Response of fast-reactor core subassemblies to pressure transients

An Arbitrary Lagrangian-Eulerian (ALE) finite element method for analyzing the transient, nonlinear fluid-structure interaction in fast-reactor core subassemblies is presented. The method combines the basic attributes of the finite element technique — namely, ease in modeling complex geometries and in mixing fluid elements with structural elements — and the flexibility in moving the fluid mesh offered by the ALE description. The result of this combination is a very versatile modeling technique which permits accommodation of large fluid and structure displacements and logically simple, but accurate fluid-structure coupling. Numerical results are presented to illustrate the effectiveness of the proposed method. These include the response of a single hexagonal duct to internal, static or dynamic, pressure loading for which numerical predictions are compared to experimental data, and applications to clustered hexcans.