Modelling of Quadratic-Surface Sludge Digesters by Smoothed Particle Hydrodynamics (SPH) – Finite Element (FE) Methods

Kiran Tota-Maharaj, Ghassan Nounu, Navin Ramroop

Research output: Contribution to journalArticlepeer-review


The quadric-surfaced sludge digester (QSD), also known as the egg-shaped sludge digester, has proven its advantages over traditional cylindrical digesters recently. A reduction in operational cost is the dominant factor. Its shell can be described as a revolution of a parabola with the apex and base being either tapered or spherical. This shape provides a surface free of discontinuities, which is advantageous regarding the efficiency during mixing. Since the shape does not produce areas of inactive fluid motion within the tank, sludge settlement and an eventual grit build-up are avoided. The stresses developed in the shell of the sludge digester, vary along the meridian and equatorial diameters. A non-dimensional parameter, ξ, defines the height-to-diameter aspect ratio which is used to delineate the parametric boundary conditions of the shell’s surface. Three groups of analyses were conducted to determine the orthogonal stresses in the shell of the QSD. The first-principles numerical models ran reasonably quickly, and many simulations were made during the study. The results showed that they were in within the range 5.34% to 7.2% to 2D FEA results. The 3D FEA simulation results were within the range of 8.3% to 9.2% to those from the MATLAB time-history models. This is a good indicator that the first principles numerical models are an excellent time-saving method to predict the behaviour of the QSD under seismic excitation. Upon examining the criteria for the design, analysing the results for the 2D FEA simulations showed that the fill height is not a significant variable with sloshing however the 3D FEA showed that the hydrostatic pressure is a significant variable. With the maximum tensile stress of the 3D-printed Acrylonitrile Butadiene Styrene (ABS)-a common thermoplastic polymer typically used for injection molding applications, being 24.4 MPa, the overall maximum stress of 5.45 MPa, the material can be a viable option for the use of QSD construction in small island developing states (SIDS).

Original languageEnglish
Pages (from-to)35-53
Number of pages19
JournalArchives of Hydro-Engineering and Environmental Mechanics
Issue number1-4
Publication statusPublished - 29 Jan 2021

Bibliographical note

©2020 Institute of Hydro-Engineering of the Polish Academy of Sciences. This is an open access article licensed under the
Creative Commons Attribution-NonCommercial-NoDerivs License (


  • Egg-shaped reactors
  • Hydraulic infrastructure
  • Quadric-surfaced sludge digesters
  • Shell structures
  • Small Island Developing States (SIDS)


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