Stresses in egg-shaped sludge digesters in the form of ellipsoidal shells of revolution

Naidoo, Pranava

Stresses in egg-shaped sludge digesters in the form of ellipsoidal shells of revolution

Master Thesis

2019

Abstract

Anaerobic sludge digesters of the squat cylindrical shape have inherent flaws which drive up maintenance costs, limits its ability to maintain optimum environmental conditions and is not shaped for efficient mixing. The egg-shaped sludge digester is an effective solution to these flaws. However, the analysis of these structures are complex and design guides are not readily available to designers of anaerobic sludge digesters. In previous studies, various shells of revolution were considered as egg-shaped sludge digester geometries. In terms of stress behaviour, these studies found the geometries to be suitable to act as egg-shaped sludge digesters. This thesis extends the list of geometries explored and considers the stress behaviour in an ellipsoid of revolution. First, only the membrane stress distributions were considered by varying a parameter e (the major axis radius over the minor axis radius) of the ellipsoidal shell. To conduct the study, closed form solutions for the meridional and hoop stresses were derived. The stress distributions of the varying ellipsoidal geometries were then compared and analysed. Additionally, the parametric study considered structural efficiency of the shell. Following this, in order to judge the effectiveness of the geometry, it was compared to findings of previous studies on different geometries. The study compared the geometries on the bases of volume, smoothness and maximum hoop stresses. It was found that the ellipsoidal geometry faired extremely well against the other geometries in the volume and maximum hoop stress criteria. Due to the limitations of the membrane theory of shells to predict bending stresses at supports and other discontinuities, a finite element study was conducted to achieve a complete shell stress distribution. Special attention was paid to bending at the support region where large meridional stress peaks occur as well as bending stresses seen at the apexes. Following this, various support conditions were tested to gather a full understanding of how this affects the total stress distribution in the shell. Finally based on findings of the study a design guide for egg-shaped digesters of ellipsoidal geometry was given.

Keywords

Engineering

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