(338f) A Novel Method Of Grid Generation For Finite Elements With Application To Gasifier Dynamics

Finite element analysis (FEA) has become an irreplaceable tool in engineering analysis. A common use of FEA is for the determination of stresses and displacements in mechanical objects and systems. However, it is also routinely used in the analysis of many other types of problems, including those in heat transfer, solid state diffusion and reactions with moving boundaries, fluid mechanics and electromagentism. It uses a numerical technique called the Finite Element Method (FEM). There are generally two types of analysis that are used in industry: 2-D modeling, and 3-D modeling. While 2-D modeling conserves simplicity and allows the analysis to be run on a relatively normal computer, it tends to yield less accurate results. 3-D modeling, however, produces more accurate results while sacrificing the ability to run on all but the fastest computers effectively. FEA uses a complex system of points called nodes which make a grid called a mesh. This mesh is programmed to contain the material and structural properties which define how the structure will react to certain loading conditions.

Distribution of nodes (i.e. grid generation) constitutes an important aspect of the method. Although FEA is an approximate technique, the accuracy of the method can be improved by using more number of nodes, and hence a finer grid. This, however, leads to severe computational demands. Another option to improve the accuracy of this technique is to refine node placement so that the generated grid is a more reliable representation of the given structure. In such a scenario, smaller number of nodes is expected to give accurate results.

This work proposes to explore the idea of refining grid generation by using an efficient sampling technique, known as the Hammersley Sequence Sampling (HSS) that is based on quasi random number generator [1]. It uses an optimal design scheme for placing the n Hammersley points on a k-dimensional hypercube. This scheme ensures that the sample set is more representative of the population, showing uniformity properties in multi-dimensions, unlike Monte Carlo, Latin Hypercube, and its variant, the Median Latin Hypercube sampling techniques [1,2,3]. The main reason for this is that the Hammersley points are an optimal design for placing n points on a k-dimensional hypercube. One of the main advantages of HSS is that the number of samples required to obtain a given accuracy of estimates does not scale exponentially with the number of dimensions. We capitalized on these properties of the Hammersley Sequence Sampling technique by utilizing it for grid generation in the control region for the partial differentiation solver in Fluent computational fluid dynamics (CFD) solver.

As an initial demonstration, the approach has been previously implemented for a small problem in which a 2-D 4X4 square surface is heated to different levels at the 4 edges and hence has different boundary temperatures on each side. The objective was to find the steady-state surface temperature distribution. The results demonstrated that the HSS method of grid generation is more efficient than the existing methods for simple surfaces.

This work proposes to extend this approach to more complicated problems, where the trade-off between accuracy and computational properties will become really critical. The work implements this approach on a gasifier model which is an important equipment in energy systems. The aim is to determine the distribution of the various physical parameters such as temperature, pressure and others. The case of gasifier is complicated due to its 3-dimensional cylindrical structure which complicates the task of grid generation. Efficient mapping techniques to generate grid points along the 3-dimensional gasifies surface will need to be utilized. Moreover, the gasifier is a reactor, and reactor kinetics will need to be accounted for. Fluent computational fluid dynamics (CFD) model for the gasifier will be used to model the gasifier performance. The results from this work are expected to highlight the advantages of using HSS technique for grid generation for complicated structures, leading to improved computations properties for the Finiate Element Analysis.

References:

1. Kalagnanam, J.R. and Diwekar, U.M., ?An efficient sampling technique for off- line quality control', Technometrics, 39:308, 1997

2. Diwekar, U. M., ?Introduction to applied optimization (2003)', Kluwer Academic Publishers, Netherlands.

3. Wang, R., Diwekar, U.M., and Gregoire-Padro, C., ?Latin Hypercube Hammersley Sampling for risk and uncertainty analysis', Environmental Progress, 23(2):141, 2004.