Correlation of data concerning resistance to flow of generalized Newtonian fluids through granular beds

Summary The paper is concerned with the pressure drop during the flow of rheologically complex fluids through granular beds. An approach is proposed which enables the correlation of the data for any generalized Newtonian fluid. As an example, a detailed derivation of a correlation equation is presented for Carreau fluids. The applicability of the derived equation was proved experimentally in the case of flow of molten poly(ethylene terephthalate) through granular beds.

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Zusammenfassung Die Arbeit betrifft den Druckverlust bei der Strömung von Flüssigkeiten mit komplexen rheologischen Eigenschaften durch Kornschüttungen. Es wird ein Verfahren vorgeschlagen, das eine Korrelation der Daten für beliebige verallgemeinerte newtonsche Flüssigkeiten ermöglicht. Als Beispiel wird die Ableitung der Korrelationsgleichung für Carreau-Flüssigkeiten ausführlich dargestellt. Die Anwendbarkeit der abgeleiteten Gleichung wird für die Strömung von geschmolzenem Polyäthylenterephthalat durch Kornschüttungen experimentell bestätigt.

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a_T temperature shift factor - A constant in eq. [1] - b_M molecular weight shift factor - d_p effective particle diameter, m - D capillary diameter, m - f_BK friction factor, defined by eq. [4] - K constant in eq. [22] - K₀ constant depending on the shape of a conduit cross-section - K₁ constant in eq. [11] - l bed height, m - l_e average length of the bed channels, m - L length of a conduit, m - M_n number-average molecular weight - M_w weight-average molecular weight - N constant in Carreau model - p pressure drop due to friction, Pa - r_h hydraulic radius, m - T absolute temperature, K - v mean linear velocity, m/s - v_e mean linear velocity in the bed channels, m/s - v₀ superficial velocity, related to an empty cross-section of the column, m/s - dimensionless factor, defined by eq. [21] - shear rate, s^–1 - nominal shear rate at the wall of a circular pipe, s^–1 - average shear rate at the wall of a noncircular channel, s^–1 - bed porosity - shear dependent viscosity, Pa s - ₀ zero-shear rate viscosity, Pa s - infinite-shear rate viscosity, Pa s - [] intrinsic viscosity - time constant in Carreau model, s - µ Newtonian viscosity, Pa s - fluid density, kg/m³ - _w shear stress at the wall of a circular pipe, Pa - average shear stress at the wall of a noncircular channel, Pa - {Re} general form of Reynolds number in eq. [1] - Re_BK modified Reynolds number for Newtonian fluids, defined by eq. [25] - Re_BK^* generalized Reynolds number for Carreau fluids, defined by eq. [24]With 5 figures and 2 tables