Turbulent Pipe Flow of Non-Newtonian Fluids

<p dir="ltr">The turbulent pipe flow of complex fluids is central to many critical industries, including mineral, chemical, polymer, food, and pharmaceutical processing, as well as wastewater treatment and the oil and gas industry. Despite its critical role, significant knowledge gaps remain regarding the fundamental physics of non-Newtonian turbulence and its impacts on large-scale industrial processes. </p><p dir="ltr">These complex fluids, which include suspensions, emulsions, polymer melts and solutions, all possess a microstructure that imparts non-Newtonian rheology, including nonlinear viscosity, elasticity, plasticity, and thixotropy. The interactions between the microstructural state, material rheology, and the turbulence structure remain poorly understood, making the prediction and optimisation of industrial processes an outstanding challenge. </p><p dir="ltr">Although much recent work has focused on the turbulent flow of viscoelastic fluids, much less attention has been paid to inelastic non-Newtonian turbulence. This is even though many industrially relevant complex fluids, such as multiphase suspensions, can behave as inelastic materials under fully developed turbulent pipe flow. Of this important class of inelastic fluids, several key knowledge gaps remain. </p><p dir="ltr">First, very little is known regarding the turbulent flow of thixotropic fluids, i.e. those whose viscosity depends upon shear history. Second, even for time-independent generalised Newtonian (GN) fluids with shear-dependent rheology, methods to accurately predict turbulent flow have only been validated on model fluids. Third, accurate correlations for the turbulent pipe flow of GN fluids have not been developed or validated. Finally, methods to utilise the turbulent pipe flow data to estimate the rheology of GN fluids do not exist. </p><p dir="ltr">To explore the relationship between rheology, microstructural state, and turbulence structure in thixotropic fluids, the thesis first performs the first direct numerical simulations (DNS) of thixotropic turbulent pipe flows. $\Lambda$ is defined as the thixoviscous number, which characterises the thixotropic effects relative to turbulence eddy turnover time. The study finds that for all ranges of thixotropic kinetics $\Lambda \in (0, \infty^+)$, the turbulent pipe flow of thixotropic fluids is analogous to that of time-independent GN fluids. This has practical implications for pipe flow design, as complex fluids in turbulent flow regimes can now be effectively treated as model fluids with shear-thinning rheology. </p><p dir="ltr">From this point forward, the thesis adopts the GN fluid assumption to model complex fluids. To extend the validation of the DNS method beyond model fluids, such as Carbopol, the thesis validates it for the case of wastewater sludge, which is a multiphase suspension, marking a significant advancement in the field. Under the assumptions of single-phase homogeneity and shear-thinning rheology (using the Herschel-Bulkley model), DNS simulations were conducted and compared against the turbulent pipe loop measurements of digested sludge. The study finds that the DNS method successfully validates this case, with velocity prediction errors of $\sim$15\%, compared to existing empirical correlations that exhibit errors of up to 70\%. These discrepancies are primarily attributed to limitations in characterising high-shear rheology data, which was explored in greater detail later on in the thesis. Overall, the results validate the broader applicability of the DNS method to non-Newtonian multiphase suspensions. </p><p dir="ltr">To address the challenges of predicting non-Newtonian turbulent pipe flows, the thesis also introduces accurate yet straightforward correlations for the turbulent pipe flow of GN fluids. These correlations were derived from direct DNS computations of GN fluids that assume single-phase homogeneity and shear-thinning rheology. The rheology models chosen were the Herschel-Bulkley and the Sisko models, as they effectively capture the key behaviours of a wide range of complex fluids, including yield stress, shear-thinning properties, and Newtonian viscosity at high shear rates. The correlations were validated against the turbulent pipe loop measurements of a model fluid, such as Carbopol, and multiphase suspensions, including wastewater sludge. The study finds that the correlations for the onset of sustained turbulence are consistent with the experimental results. At the same time, the predictions from the correlations for the friction factor showed an accuracy of $\sim$7\%, outperforming existing empirical correlations. Overall, these results demonstrate the capability of the correlations to optimise the pipeline transport handling of complex fluids. </p><p dir="ltr">Presently, conventional methods present practical limitations in characterising high-shear rheology data of non-Newtonian fluids. While these methods utilise benchtop rheometer or laminar pipe flow data for rheological characterisation, they cannot utilise turbulent pipe flow data due to the inadequacy of existing correlations. To address this, the thesis introduces a novel rheological characterisation method for GN fluids that incorporates turbulent pipe flow data with rheometer or laminar pipe flow data. The previously developed correlations enable the method to estimate rheological parameters from turbulent pipe loop data, allowing multiple datasets to be fitted simultaneously. The study reveals that the method yields precise high-shear rheological data for the Herschel-Bulkley and Sisko models, yielding predictive errors as low as 2\% for wastewater sludges. These findings have practical implications, as accurate rheological data ultimately enhances turbulent pipe flow predictions. </p><p dir="ltr">The study delivers several key findings. Time-dependent thixotropic turbulent flows can be treated as purely viscous GN flows, allowing for simplification of the non-Newtonian rheology. DNS methods have been successfully validated for the turbulent pipe flow of industrially relevant multiphase suspensions. Accurate and simple correlations for the onset of turbulence and pressure drop in GN fluids have been successfully developed, and a novel method for estimating the high-shear GN rheology from the turbulent pipe flow experiments is introduced. </p><p dir="ltr">Together, the thesis advances the scientific understanding of non-Newtonian turbulent pipe flows through rheology modelling, turbulence analysis and systematic validations. For application areas such as wastewater sludge transport, the work offers a rigorous and practical framework for accurate flow prediction, improved rheological characterisation, and more efficient and cost-effective pipeline systems for transporting complex fluids.</p>