This article concerns the turbulent flow of Herschel–Bulkley slurries through circular horizontal pipes; in particular, that of concentrated domestic slurry obtained upon separation of domestic waste water and reduction in the use of water for domestic purposes. Experiments with a rheologically equivalent clay (kaolin) slurry indicated a non-Newtonian behaviour of the Herschel–Bulkley type. A modified wall function was developed to enable the Reynolds-averaged Navier–Stokes simulation of Herschel–Bulkley slurries to estimate the wall shear stress. Despite the accuracy achieved, the use of Reynolds-averaged Navier–Stokes models for an entire waste water system is impractical. Therefore, this article assesses the accuracy of semi-empirical models in estimating frictional losses. It also discusses possible modifications of existing models to encompass Herschel–Bulkley behaviour. An evaluation suggests that most existing models deliver estimates of comparable accuracy; however, the probability of these estimates being reliable, while accounting for experimental errors in quantifying the actual frictional losses, is rather low.

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Transition from laminar to turbulent flow of non-Newtonian fluids is investigated using velocimetry data. These data are obtained by applying particle image velocimetry to images obtained through ultrasound imaging (echography). This yielded the observation of intermittent structures (puffs and slugs) that are formed during transition. Post its observation, transition is characterized using the friction factor curves and turbulence intensity. Further, a number of models used to predict transition are assessed. This showed the Reynolds number based model by Slatter and the stability parameter based model by Hanks to be most suitable for non-Newtonian fluids with yield stress and low behaviour index.

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Domestic wastewater streams from households implemented with source separation, vacuum toilets, and food waste disposers are highly concentrated with respect to the total suspended solids. The concentrated domestic slurries (CDS), which generally consist of faecal matter, urine, ground kitchen waste (GKW) and water, need to be transported from the point of collection to its treatment. In order to design a transportation systems to convey CDS, its flow characteristics must be known. The objective of this thesis is to establish the flow characteristics of CDS that supports the design of its transportation system with pressurised pipelines. CDS is characterised as a non-Newtonian fluid with respect to its rheology. It has a shear-thinning property with a yield stress. However, at low concentrations it behaves as a Newtonian fluid, its non-Newtonian properties are only physically meaningful above a concentration of 2.0 % TSS (wt./wt.). The rheology of CDS is represented using a Herschel-Bulkley model, the parameters of which are a function of TSS concentration which describes the influence of concentration changes. The yield-stress follows a power law function with concentration and is significant only above a concentration of 2.0 % TSS (wt./wt.). The consistency index follows an exponential behaviour with the concentration, which tends towards the viscosity of water at low TSS concentration. The behaviour index follows an inverse logarithmic function decreasing from 1, and this change is significant only above a TSS concentration of 2.6 % (wt./wt.). The temperature of the slurry also influence the rheology of CDS. The influence of temperature is represented using an Arrhenius type equation with respect to the apparent viscosity. On the other hand, the influence of installing food waste disposers is reflected on the change in the overall particle size distribution (PSD) of the slurry, where an increase in the effective diameter of the particle shows an increase in the viscosity of the slurry. The pressure losses incurred in the transport of non-Newtonian slurries, including CDS, in pressurised pipelines are well represented using the Slatter transport model. The pressure loses are very much impacted by the rheological characteristics of the fluid. The pressure losses incurred increase with the increase in TSS concentration, but with the onset of non-Newtonian behaviour, the yield-stress and shear-thinning behaviour, provide some damping to the pressure losses particularly in the turbulent flow regime. The transition from laminar to turbulent flow occurs as a multi-stage process starting with the occurrence of puffs, and then to slugs and both together. The Slatter Reynolds number, provides good prediction of the transition to turbulence compared to the other available models. To conclude, a functional design of a pressurised pipeline transport system for CDS would have to meet the pressure losses estimated using the rheology of CDS at a certain concentration of TSS and temperature of the slurry. @en

This article follows from a previous study by the authors on the computational fluid dynamics-based analysis of Herschel-Bulkley fluids in a pipe-bounded turbulent flow. The study aims to propose a numerical method that could support engineering processes involving the design and implementation of a waste water transport system, for concentrated domestic slurry. Concentrated domestic slurry results from the reduction in the amount of water used in domestic activities (and also the separation of black and grey water). This primarily saves water and also increases the concentration of nutrients and biomass in the slurry, facilitating efficient recovery. Experiments revealed that upon concentration, domestic slurry flows as a non-Newtonian fluid of the Herschel-Bulkley type. An analytical solution for the laminar transport of such a fluid is available in literature. However, a similar solution for the turbulent transport of a Herschel-Bulkley fluid is unavailable, which prompted the development of an appropriate wall function to aid the analysis of such flows. The wall function (called ψ₁ hereafter) was developed using Launder and Spalding's standard wall function as a guide and was validated against a range of experimental test-cases, with positive results.ψ₁ is assessed for its sensitivity to rheological parameters, namely the yield stress, the fluid consistency index and the behaviour index and their impact on the accuracy with which ψ₁ can correctly quantify the pressure loss through a pipe. This is done while simulating the flow of concentrated domestic slurry using the Reynolds-Averaged Navier-Stokes (RANS) approach for turbulent flows. This serves to establish an operational envelope in terms of the rheological parameters and the average flow velocity within which ψ₁ is a must for accuracy. One observes that, regardless of the fluid behaviour index, ψ₁ is necessary to ensure accuracy with RANS models only in flow regimes where the wall shear stress is comparable to the yield stress within an order of magnitude. This is also the regime within which the concentrated slurry analysed as part of this research flows, making ψ₁ a requirement. In addition, when the wall shear stress exceeds the yield stress by more than one order (either due to an inherent lower yield stress or a high flow velocity), the regular Newtonian wall function proposed by Launder and Spalding is sufficient for an accurate estimate of the pressure loss, owing to the relative reduction in non-Newtonian viscosity as compared to the turbulent viscosity.

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The concentration of domestic slurry has two advantages, it promotes resource recovery (nutrients and biomass) and saves water. But the design of a relevant sewerage requires a clear understanding of the frictional losses incurred during the transport of the slurry. This abstracts describes numerical & CFD-based methods to estimate losses while the concentrated slurry flows through circular pipes in a fully-turbulent flow. To model turbulent flows through circular pipes, one can rely on either the Newtonian Moody Charts appropriate for engineering applications or a computational fluid dynamics (CFD)-based analysis, made possible through the Newtonian universal law of the wall. However, our studies reveal that concentrated domestic slurry behaves like a non-Newtonian fluid, of the Herschel-Bulkley type. Therefore, the analysis of such a slurry would require modifications to both, existing engineering models and CFD methods. This abstract summarises a modified law of the wall suitable for Herschel-Bulkley fluids, which has been validated against experiments on concentrated domestic slurry. It further details possible non-Newtonian numerical engineering models that could be modified to assess frictional losses incurred by Herschel-Bulkley fluids. The latter will be a quicker and perhaps reliable alternative to computationally expensive CFD-analyses.

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Information on the rheology of domestic slurries is essential in designing pipeline transportation in novel sanitation systems. As concentrated slurries in their original collected state have wide particle size distribution, with particles up to 2 mm, a wide gap rheometer is used to acquire the rheograms. Rheograms obtained from a wide gap rheometer require a method to convert the rotational velocity to the shear rate, and this method must be robust to noisy data and yield stress in the slurry. For this purpose, a Tikhonov regularisation method is chosen as it suits the criteria the best. Using this, the rheograms are obtained for various total suspended solids (TSS) concentrations of slurries. A Herschel-Bulkley rheological model is used to represent the rheology of the slurries. The influence of the change in concentration of the slurries is represented through its influence on the Herschel-Bulkley parameters. The consistency index K exponentially increases with the concentration. The yield stress τy , is 0 at low concentrations, and above 2.0% TSS (wt./wt.) exponentially increases with the concentration. The behaviour index n , is 1 at low concentrations, and above 2.6% TSS (wt./wt.) it decreases in an inverse power law with the concentration to reach a sort of plateau.@en

The much over-looked element in new sanitation, the transport systems which bridge the source and treatment facilities, is the focus of this study. The knowledge of rheological properties of concentrated domestic slurry is essential for the design of the waste collection and transport systems. To investigate these properties, samples were collected from a pilot sanitation system in the Netherlands. Two types of slurries were examined: black water (consisting of human faecal waste, urine, and flushed water from vacuum toilets) and black water with ground kitchen waste. Rheograms of these slurries were obtained using a narrow gap rotating rheometer and modelled using a Herschel-Bulkley model. The effect of concentration on the slurry are described through the changes in the parameters of the Herschel-Bulkley model. A detailed method is proposed on estimating the parameters for the rheological models. For the black water, yield stress and consistency index follow an increasing power law with the concentration and the behaviour index follows a decreasing power law. The influence of temperature on the viscosity of the slurry is described using an Arrhenius type relation. The viscosity of black water decreases with temperature. As for the black water mixed with ground kitchen waste, it is found that the viscosity increases with concentration and decreases with temperature. The viscosity of black-water with ground kitchen waste is found to be higher than that of black water, which can be attributed to the presence of larger particles in the slurry.

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The concentration (using a lesser amount of water) of domestic slurry promotes resource recovery (nutrients and biomass) while saving water. This article is aimed at developing numerical methods to support engineering processes such as the design and implementation of sewerage for concentrated domestic slurry. The current industrial standard for computational fluid dynamics-based analyses of turbulent flows is Reynolds-averaged Navier-Stokes (RANS) modelling. This is assisted by the wall function approach proposed by Launder and Spalding, which permits the use of under-refined grids near wall boundaries while simulating a wall-bounded flow. Most RANS models combined with wall functions have been successfully validated for turbulent flows of Newtonian fluids. However, our experiments suggest that concentrated domestic slurry shows a Herschel-Bulkley-type non-Newtonian behaviour. Attempts have been made to derive wall functions and turbulence closures for non-Newtonian fluids; however, the resulting laws or equations are either inconsistent across experiments or lack relevant experimental support. Pertinent to this study, laws or equations reported in literature are restricted to a class of non-Newtonian fluids called power law fluids, which, as compared to Herschel-Bulkley fluids, yield at any amount of applied stress. An equivalent law for Herschel-Bulkley fluids that require a minimum-yield stress to flow is yet to be reported in literature. This article presents a theoretically derived (with necessary approximations) law of the wall for Herschel-Bulkley fluids and implements it in a RANS solver using a specified shear approach. This results in a more accurate prediction of the wall shear stress experienced by a circular pipe with a turbulent Herschel-Bulkley fluid flowing through it. The numerical results are compared against data from our experiments and those reported in literature for a range of Reynolds numbers and rheological parameters that are relevant to the prediction of pressure losses in a sewerage transporting non-Newtonian domestic slurry. Nonetheless, the application of this boundary condition could be extended to areas such as chemical and food engineering, wherein turbulent non-Newtonian flows can be found.

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