## Electronic Theses and Dissertations

1997

Dissertation

Ph.D.

#### Department

Civil and Environmental Engineering

McCorquodale, J. A.,

#### Keywords

Engineering, Civil.

CC BY-NC-ND 4.0

#### Abstract

A new high accuracy numerical technique has been developed. This technique is based on a Skew Third Order Upwinding Scheme (STOUS) which eliminates numerical diffusion. This scheme introduces cross-difference terms to overcome the instability problems of the component-wise one-dimensional formulas for simulating multi-dimensional flows. Small physically unrealistic overshooting and undershooting have been avoided by using a well established technique known as the Universal Limiter. STOUS is also compared with another third order upwinding technique which is referred to as Uniformly Third Order Interpolation Algorithm (UTOPIA). A complete von Neumann stability analysis is conducted on both schemes to show the stability range of each scheme. STOUS is found to have a wider stability range than UTOPIA. A well-known rotating velocity field test is used to show the capability of the STOUS in eliminating numerical diffusion. The STOUS results are compared with UTOPIA and HYBRID. Both STOUS and UTOPIA also have been compared with other finite element techniques in modelling different ideal flows. STOUS has been used to develop a numerical model to simulate the flow pattern and transport of dye in primary rectangular settling tanks operating under neutral density conditions. The computational domain includes the settling zone and withdrawal zones. The velocity field is obtained by solving the equations of motion in the vorticity and streamfunction formulation. A k-$\varepsilon$ model is used to simulate the turbulence phenomena. The velocity field compares favourably with previous measurements and with UTOPIA results. An additional differential equation governing the unsteady transport of dye in a steady flow field is solved to calculate the dye concentration and to produce the Flow-Through-Curves (FTCs) which are used in evaluating the hydraulic efficiency of settling tanks. The resulting FTC is compared with both measurements and numerical results predicted by different discretization schemes. The computational domain of the numerical model has been extended to include the inlet zone and settling zone, withdrawal zone and sludge zone. Density stratification effect has been incorporated in the model. Thus, the final model can be used to simulate the density waterfall phenomenon at the settling tank entrance. A double exponential relationship to describe the settling process is used. The final model has been calibrated and verified using the field data obtained through the application of the Clarifier Research Technical Committee (CRTC) protocol. Model predictions compare favourably with flow fields, suspended solids distributions, Flow- Through-Curves (FTCs) and dye profiles in the settling tank for different hydraulic and solids loading.Dept. of Civil and Environmental Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1997 .G47. Source: Dissertation Abstracts International, Volume: 59-08, Section: B, page: 4299. Adviser: J. A. McCorquodale. Thesis (Ph.D.)--University of Windsor (Canada), 1997.

COinS