Abstract
The rheological behavior of non-Newtonian fluids in turbulent conditions is an important topic in several fields of engineering. Nevertheless, this topic was not deeply investigated in the past due to the complexity of the experimental tests for the assessment of the constitutive parameters. Pressure pipe tests on Herschel-Bulkley mixtures were proven to be suitable for exploring turbulent conditions, but discrepancies with the results of tests performed in laminar flow were detected. These contradictions could be attributed to the inconsistencies of the Herschel-Bulkley model (HB) for high shear rate flows, proven by Hallbom and Klein, who suggested a more general “yield plastic” model (HK). Hence, in this study, a procedure for the estimation of the rheological parameters of both HB and HK models in pressure pipe tests is defined and rated on a complete set of experiments. The HK model performed much better than HB model in the turbulent range and slightly better than the HB model in the laminar range, confirming the consistency of the “yield plastic” model. The rheological parameters obtained by the proposed procedure were used to numerically model a dam-break propagation of a non-Newtonian fluid, showing significant differences in terms of process evolution depending on the constitutive model.
Highlights
Non-Newtonian flows are present in many applications, such as mining, chemical engineering, environmental and civil engineering, etc
The non-Newtonian rheological behavior is generally well described by the Herschel-Bulkley equation [3]: τ = τy + kγ. n where τ (Pa) is the shear stress, γ. (s−1) is the shear rate, τy (Pa) is the yield stress, n (-) is the flow behavior index, and k (Pa sn) is the flow consistency index
Several theoretical, semiempirical, or empirical models described the influence of the rheology in turbulent conditions
Summary
Non-Newtonian flows are present in many applications, such as mining, chemical engineering, environmental and civil engineering, etc. The non-Newtonian rheological behavior is generally well described by the Herschel-. (s−1) is the shear rate, τy (Pa) is the yield stress, n (-) is the flow behavior index, and k (Pa sn) is the flow consistency index. The HB rheological model describes both shear thinning (n < 1) and dilatant (n > 1) behavior [2], and it is equivalent to the Bingham plastic model [4] for n = 1, the power-law model for τy = 0, and the Newtonian model [5] for n = 1 and τy = 0. The HB model has been generally employed for its simplicity and ability to quantify the presence of yield stress and has been applied to several fluids, including sediment mixtures and sewage sludge [6,7]
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