Bilal Khan Yusufi

Summary Not All Fluids Are Equal... This thesis concerns the turbulent flow of concentrated domestic slurry (CDS) in pipes, in the context of decentralised sanitation systems (DSS). Experimental studies have shown that CDS exhibits non-Newtonian behaviour, typically characterised by shear-thinning viscosity and a finite yield stress, which can be rheologically described by the Herschel–Bulkley (HB) model. To prevent particle settling and clogging, DSS pipelines typically employ pipe diameters of approximately 100 mm and operate at flow velocities exceeding 1 m/s, corresponding to Reynolds numbers of the order of 105. Modelling such flows remains a challenge, as it involves coupling two sub-models: one describing the non-Newtonian rheology and the other capturing near-wall turbulence. The objective of this thesis is therefore to develop a physically consistent and computationally efficient modelling framework for predicting turbulent pipe flow of HB fluids. A combined approach is adopted, integrating CFD simulations, experimental measurements, and physics-informed data-driven analysis. This enables accurate estimation of velocity profiles and wall shear stress, which are essential for hydraulic analysis, pressure-loss prediction, and pump selection. Existing approaches can be broadly categorised into semi-empirical, theoretical, and computational methods. While semi-empirical correlations remain widely used for their simplicity, their validity is often restricted to the fluid and flow conditions for which they were developed. High-fidelity approaches such as direct numerical simulation (DNS) and large-eddy simulation (LES) provide detailed physical insight but are computationally expensive at the Reynolds numbers relevant to DSS. Reynolds-averaged Navier–Stokes (RANS) models, therefore, offer a pragmatic alternative; however, most existing formulations either rely on modified damping functions that require near-wall fine-grid resolution or on assumptions that remain insufficiently validated. Consequently, this thesis adopts a rheology-based wall-function (ψ) approach, implemented as a specified shear boundary condition within a CFD framework. This formulation incorporates non-Newtonian rheology directly into the near-wall treatment without resolving the viscous sublayer, thereby reducing computational cost. Further, unlike conventional wall functions, ψ imposes a theoretical constraint on the iterated velocity field at the first cell centroid, such that the effective near-wall viscosity is adjusted according to the fluid’s rheological parameters. Results from numerical simulations demonstrate that this approach substantially improves predictions of wall shear stress and mean velocity profiles compared to existing numerical models, with deviations typically within 5–10% of experimental measurements. As the accuracy of ψ depends strongly on the rheological inputs, the thesis further investigates the rheological characterisation required under relevant conditions. Since ψ is intended for highly turbulent pipe-flow, the shear rates near the pipe wall are orders of magnitude higher than those typically accessible with standard rheometers. When rheological parameters are identified solely from conventional low-shear rheometric data, extrapolation to turbulent conditions can yield unrealistically low effective viscosities, in some cases even below those of the carrier fluid, leading to substantial modelling errors. To address this, finite-viscosity rheological models, such as the Sisko and combined HB formulations, are evaluated as a practical means of constraining the high-shear behaviour. Incorporating these models is found to improve the robustness and reliability of CFD predictions for high-shear turbulent HB flows. To further investigate the turbulence and near-wall behaviour, the next part of the thesis presents an experimental investigation using Ultrasound Velocity Profiling (UVP). Clay–water slurries with concentrations up to 19% w/w are used as analogues of CDS, and the resulting measurements are used to obtain mean velocity profiles and wall shear stress. The experimental observations reveal rheology-dependent shifts in the logarithmic region compared to Newtonian behaviour. For shear-thinning HB fluids, a consistent upward shift in the log-law intercept is observed, though the slope of the log-law, governed by the von Kármán constant, remains largely unchanged. This indicates that the conventional use of Newtonian constants in the formulation of ψ leads to systematic biases in predicted wall shear stress, and that tuning these constants offers potential to improve predictions. This motivates the final part of the thesis, in which a physics-informed, data-driven approach is employed to refine the wall-function constant. Using symbolic regression trained on experimental and literature datasets, a simplified analytical expression is derived that links the log-law intercept to rheological and flow parameters. The resulting formulation satisfies essential physical constraints while preserving Newtonian consistency. When implemented within the wall-function ψ, the new model predicts wall shear stress within the 95% confidence interval of the experimental data for approximately 76% of the cases, representing an improvement of about 25% over ψ and a threefold improvement over commonly used semi-empirical correlations. Overall, this thesis establishes a computationally efficient and physically consistent approach for predicting turbulent HB pipe flow in decentralised sanitation systems. It shows that accurate prediction of wall shear stress and velocity profiles requires not only rheology-informed near-wall modelling, but also rheological characterisation that remains valid at turbulent shear rates. The results further demonstrate that selected wall-function parameters should be treated as rheology-dependent rather than fixed Newtonian constants. More broadly, the methodology and insights developed here are applicable to a wide range of industrial slurry-transport systems, including mining, dredging, petroleum, and chemical processing.