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. ... Read more

This review explores recent advancements in modeling the flow behavior of Herschel-Bulkley (HB) fluids in pipes, discussing theoretical, semi-empirical, computational, and experimental methods. While the laminar flow of non-Newtonian HB fluids can be effectively modeled using first-principle physics, significant challenges remain in turbulent and transitional flow regimes. Existing turbulence models, though widely used, may not always fully align with experimental data, often requiring further validation or complex mathematical tuning, leading to higher computational costs. Further, the transition to turbulence in HB fluids is influenced by shear-thinning and yield stress, yet current models often fail to account for this delayed transition. Consequently, stability and Reynolds number-based transition models can exhibit inconsistencies, limiting their broader applicability. Progress is further hindered by limited experimental studies, constrained by resolution, attenuation, cost, and material combinations. Inaccuracies in rheological modeling—due to inappropriate shear rate ranges, curve-fitting techniques, or simplifying assumptions such as homogeneity and non-elasticity—further complicate flow predictions. Through this review, we delve deeper into the state-of-the-art modeling of HB fluids, highlighting progress and these challenges. Addressing these limitations requires advanced experimental and numerical studies, particularly for near-wall measurements, to better capture flow complexities and improve model predictions. This could also facilitate the development of data-driven approaches and operational envelopes that define their validity thresholds. Future research should also prioritize the independent effects of yield stress and shear-thinning properties while considering material attributes and settling phenomena in non-Newtonian suspensions. Ultimately, these advancements will enable more accurate flow predictions and practical solutions for industrial applications. ... Read more

Transportation of non-Newtonian fluids (NNFs) through pipelines is a cornerstone of modern infrastructure. While the laminar and transitional flows have been extensively studied, the turbulent behavior of NNFs remains poorly understood. This study investigates large-scale pipe-loop experiments on clay–water slurries, spanning Reynolds numbers (Formula presented) in a 100-mm diameter facility. Using non-invasive ultrasound velocity profiling (UVP) together with wall shear stress measurements, we characterize flows ranging from weakly to highly non-Newtonian conditions with concentrations up to 19%(w/w). The experiments show that the transition to the log-law region is delayed and the log-law intercept shifts upward with increasing concentration, reflecting the redistribution of stresses as shear-thinning and yield effects become more pronounced. To further interpret these findings, the experimental observations were compared with established modeling approaches. Semi-empirical correlations exhibited intermediate performance (mean absolute error, MAE, up to 0.55 Pa for wall shear stress and 0.15 m/s for velocity), while the Launder–Spalding wall function performed worst due to its assumption of constant viscosity (MAE ≈ 1.48 Pa and 0.08 m/s). In contrast, the rheology-based wall function achieved the most reliable predictions, with minimal deviations from experiments (MAE ≈ 0.20 Pa for wall shear stress and 0.06 m/s for velocity). Overall, this work provides a comprehensive experimental and modeling assessment of turbulent non-Newtonian pipe flow at an industrial scale, yielding new insights into flow physics and establishing a valuable reference for future experimental and computational studies. ... Read more

Modeling fully developed turbulent flow for Herschel–Bulkley (HB) fluids in pipes is a long-standing challenge. Existing semi-empirical, theoretical, and numerical methods are either inconsistent with experimental data or are validated for low Reynolds numbers. This study focuses on validating a novel approach using rheology-based wall functions within Reynolds-averaged Navier–Stokes solvers. Simulations of wall shear stress and velocity profiles were conducted across a wide range of Reynolds numbers using a single-phase HB fluid, with measurements taken both upstream and downstream of a 90 pipe bend. Two turbulence closure models, the k–e model and the Reynolds stress model, were employed with the wall function implemented as a specified shear boundary condition. Results demonstrate significant improvements over the Newtonian-based models, such as standard wall function by Launder–Spalding or with available semi-empirical models, achieving strong statistical correlations and minimal deviation (from the experimental findings) at high Reynolds numbers. The study also examines the utility of the wall viscosity Reynolds number and assesses the reliability of semi-empirical models for HB fluids. These findings offer valuable insights for enhancing modeling accuracy in complex fluid flow scenarios, with potential applications spanning industries like mining, chemical processing, petroleum transportation, and sanitation systems, providing practical alternatives to costly experimental procedures in pipe systems. ... Read more