Modeling Reciprocating Compressors Using A Cartesian Cut-Cell Method With Automatic Mesh Generation

Computational Fluid Dynamics (CFD) models can offer great insight into flow phenomena and complex fluid-structure interactions present in reciprocating compressors. This is often achieved, however, at large computational cost and considerable user setup time. In this study, a Cartesian cut-cell finite-volume method is applied to model a small displacement refrigeration compressor. The cut-cell method has the key feature of representing discrete cell volumes exactly without requiring the computational grid to coincide with the bounding geometry. Additionally, the grid is dynamically generated at each time step based on the instantaneous boundary positions and is automatically refined based on gradients of local flow variables. These two features make this method ideal for modeling the deformation of the valves, the motion of the piston, and the complex geometries of the suction and discharge mufflers. The model is validated against experimental data. The sources of numerical error in the model are assessed, including the spatial and temporal discretization error and the model treatment for valve opening, closure, and contact. Lastly, several automated grid generation strategies are presented to establish guidelines for balancing cost and accuracy. The model formulation highlights the ease of incorporating complex and moving geometries characteristic of reciprocating compressors into a CFD model at a reasonable cost

A full Eulerian finite difference approach for solving fluid-structure coupling problems

A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation (Hirt and Nichols (1981, J. Comput. Phys., 39, 201)), which has been widely used for multiphase flow simulations, is applied to describing the multi-component geometry. The temporal change in the solid deformation is described in the Eulerian frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for nonlinear Mooney-Rivlin materials. In this paper, various verifications and validations of the present full Eulerian method, which solves the fluid and solid motions on a fixed grid, are demonstrated, and the numerical accuracy involved in the fluid-structure coupling problems is examined.Comment: 38 pages, 27 figures, accepted for publication in J. Comput. Phy

A fast and robust patient specific Finite Element mesh registration technique: application to 60 clinical cases

Finite Element mesh generation remains an important issue for patient specific biomechanical modeling. While some techniques make automatic mesh generation possible, in most cases, manual mesh generation is preferred for better control over the sub-domain representation, element type, layout and refinement that it provides. Yet, this option is time consuming and not suited for intraoperative situations where model generation and computation time is critical. To overcome this problem we propose a fast and automatic mesh generation technique based on the elastic registration of a generic mesh to the specific target organ in conjunction with element regularity and quality correction. This Mesh-Match-and-Repair (MMRep) approach combines control over the mesh structure along with fast and robust meshing capabilities, even in situations where only partial organ geometry is available. The technique was successfully tested on a database of 5 pre-operatively acquired complete femora CT scans, 5 femoral heads partially digitized at intraoperative stage, and 50 CT volumes of patients' heads. The MMRep algorithm succeeded in all 60 cases, yielding for each patient a hex-dominant, Atlas based, Finite Element mesh with submillimetric surface representation accuracy, directly exploitable within a commercial FE software

A Nitsche-based cut finite element method for a fluid--structure interaction problem

We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The embedding allows for an arbitrary overlap of the fluid meshes. The coupling between the embedded and background fluid meshes is enforced using a stabilized Nitsche formulation which allows us to establish stability and optimal order \emph{a priori} error estimates, see~\cite{MassingLarsonLoggEtAl2013}. We consider here a steady state fluid--structure interaction problem where a hyperelastic structure interacts with a viscous fluid modeled by the Stokes equations. We evaluate an iterative solution procedure based on splitting and present three-dimensional numerical examples.Comment: Revised version, 18 pages, 7 figures. Accepted for publication in CAMCo

Material flow during the extrusion of simple and complex cross-sections using FEM

This paper deals with the extrusion of rod and shape sections and uses a 3D finite element model analysis (FEM) to predict the effect of die geometry on maximum extrusion load. A description of material flow in the container is considered in more detail for rod and shape sections in order to fully comprehend the transient conditions occurring during the process cycle. A comparison with experiments is made to assess the relative importance of some extrusion parameters in the extrusion process and to ensure that the numerical discretisation yields a realistic simulation of the process. The usefulness and the limitation of FEM are discussed when modelling complex shapes. Results are presented for velocity contours and shear stress distribution during the extrusion process. It is shown that for most of the shapes investigated, the material making up the extrudate cross-sections originates from differing regions of virgin material within the billet. The outside surface of the extrudate originates from the material moving along the dead metal zone (DMZ) and the core of the extrudate from the central deformation zone. The FE program appears to predict all the major characteristics of the flow observed macroscopically