Rotational viscometers with coaxial cylinders are often used for measuring rheological behaviour. If the inner to outer cylinder diameter ratio does not differ significantly from 1, the curvature can be neglected and the flow reduces to the flow between moving and stationary plates. The power-law and Bingham models are often used for describing rheological behaviour. This paper deals with the temperature distribution obtained by solving the Fourier-Kirchhoff equation and in the case of negligible inner heat resistance it also covers temperature time dependence. The solution is illustrated by a numerical example.
Knowledge about rheological behavior is necessary in engineering calculations for equipment used for processing concentrated suspensions and polymers. Power-law and Bingham models are often used for evaluating the experimental data. This paper proposes the reference radius to which experimental results obtained by measurements on a rotational viscometer with coaxial cylinders should be related.
The paper deals with measurements of non-Newtonian fluids on a viscometer with coaxial cylinders. The procedure for determining the rheological model parameters is recommended for power-law fluids and Bingham plastics.
Most information on pumping efficiency that is available in the literature is limited to the turbulent region (centrifugal pumps). The aim of this paper is to show the effect of the Reynolds number on the pumping efficiency of screw agitators for a wide range of Reynolds number values from creeping to the turbulent flow region. The dependence of pumping efficiency on Reynolds number extends our knowledge about the efficiency of classical impeller pumps restricted usually to the turbulent region.
Screw agitators rotating in tubes are very efficient tools for mixing and pumping viscous liquids. The power characteristic of the agitator-tube assembly must be known to enable its power consumption in a given configuration to be calculated. The dimensionless power characteristic is described by Eq. (6). An estimate of power consumption from the power characteristic is schematically shown in Fig. 1. The dependence of the coefficients in Eq. (6) on the Reynolds number is shown in Fig. 5. The power characteristics for selected Reynolds number values are shown in Figs. 6- 9.
A tall vessel with a telescopic draught tube is proposed for mixing suspensions. The paper presents the relations for calculating the agitator power consumption and the speed necessary to keep a particle in suspension.
Industrial suspension mixing processes are carried out both in standard tanks (H/D =1) and in the tanks with height H/D > 1. When only one impeller is used in such slender tanks, it may be difficult to produce a suspension of desired homogeneity. Hence it may be necessary to install a larger number of impellers on the shaft.The aim of this study was to explain the mechanism of suspension formation in slender tanks (H/D = 2) with an increased number of impellers. On the basis of the solid bed height on the tank bottom, the position of the suspension - water interface and the concentration profile of solid particles in the suspension (standard deviation of solid body concentration) the operation of the impellers was estimated and conclusions were drawn on how and at what distance from each other to install them were presented.The location of the upper, highest impeller appeared to be specially significant. On the basis of this study it is recommended to locate the upper impeller so that its distance from the free liquid surface is less than 0.8 D. It was found that such a position of the highest impeller was also advantageous from the energy point of view.
Mixing suspensions is a very important hydraulic operation. The pitched six-blade turbine is a widely-used axial-flow impeller. This paper deals with effect relative impeller size and particle content on theefficiency of a pitched six-blade turbine at particle suspension. Two pitched six-blade turbines were used in model measurements of just suspension impeller speed. The ratios of the vessel to agitator diameter D/d were 3 and 4.5. The measurements were carried out in a dish-bottomed vessel 300 mm in diameter. The just suspension impeller speeds were measured using an electrochemical method, and were checked visually. A 2.5 % NaCl water solution was used as the liquid phase, and glass particles with four equivalent diameters between 0.18 and 0.89 mmand volumetric concentration from 2.5 % to 40% were usedasthesolid phase. The criterion values πs=Po√Fr'3(d/D)7 were calculated from the particle suspension and power consumption measurements. The dependencies of πs on particle content cv show that larger agitators are more efficient for higher particle content.
Cooling or heating an agitated liquid is a very common operation in many industrial processes. A classic approach is to transfer the necessary heat through the vessel jacket. Another option, frequently used in the chemical and biochemical industries is to use the heat transfer area of vertical tube baffles. In large equipment, e.g. fermentor, the jacket surface is often not sufficient for large heat transfer requirements and tube baffles can help in such cases. It is then important to know the values of the heat transfer coefficients between the baffles and the agitated liquid. This paper presents the results of heat transfer measurements using the transient method when the agitated liquid is periodically heated and cooled by hot and cold water running through tube baffles. Solving the unsteady enthalpy balance, it is possible to determine the heat transfer coefficient. Our results are summarized by the Nusselt number correlations, which describe the dependency on the Reynolds number, and they are compared with other measurements obtained by a steady-state method.
A study was made of the pumping capacity of pitched blade impellers in a cylindrical pilot plant vessel with four standard radial baffles at the wall under a turbulent regime of flow. The pumping capacity was calculated from the radial profile of the axial flow, under the assumption of axial symmetry of the discharge flow. The mean velocity was measured using laser Doppler anemometry in a transparent vessel of diameter T = 400 mm, provided with a standard dished bottom. Three and six blade pitched blade impellers (the pitch angle varied within the interval a Îá24°; 45°ń) of impeller/vessel diameter ratio D/T = 0.36, as well as a three blade pitched blade impeller with folded blades of the same diameter, were tested. The calculated results were compared with the results of experiments mentioned in the literature, above all in cylindrical vessels with a flat bottom. Both arrangements of the agitated system were described by the impeller energetic efficiency, i.e, a criterion including in dimensionless form both the impeller energy consumption (impeller power input) and the impeller pumping effect (impeller pumping capacity). It follows from the results obtained with various geometrical configurations that the energetic efficiency of pitched blade impellers is significantly lower for configurations suitable for mixing solid-liquid suspensions (low impeller off bottom clearances) than for blending miscible liquids in mixing (higher impeller off bottom clearances).
This paper presents an analysis of the blending efficiency of pitched blade impellers under a turbulent regime of flow of an agitated low viscous liquid. The conductivity method is used to determine of the blending (homogenization) time of miscible liquids in pilot plant mixing equipment with standard radial baffles. For the given homogeneity degree (98 %) a three-blade pitched blade impeller is tested with various off-bottom clearances, vessel/ impeller diameter ratios and various impeller pitch angles. The experimental results show in accordance with theoretical data from the literature, that the greatest effect on the dimensionless blending time is exhibited by the vessel/ impeller diameter ratio and the impeller pitch angle. The number of total circulations necessary for reaching the chosen homogeneity degree depends on the impeller pitch angle and amounts more than three. Finally, the energetic efficiency of the blending process is calculated. The results of this study show, that the highest energetic efficiency of the three-blade pitched blade impeller appears for the pitch angle a = 24°, the impeller/vessel diameter ratio T/D = 2 and the impeller off-bottom clearance h/D = 1.
A study was made of the pumping capacity of pitched blade impellers (two, three, four, five and six blade pitched blade impellers with pitch angles α = 35° and 45°) coaxially located in a cylindrical pilot plant vessel with cylindrical draught tube provided with a standard dished bottom. The draught tube was equipped with four equally spaced radial baffles above the impeller pumping liquid upwards towards the liquid surface. In all investigated cases the liquid aspect ratio H/T = 1.2 - 1.5, the draught tube / vessel diameter ratios DT /T = 0.2 and 0.4 and the impeller / draught tube diameter ratio D/DT = 0.875. The pumping capacity of the impeller was calculated from the radial profile of the axial component of the mean velocity in the draught tube below the impeller at such an axial distance from the impeller that the rotor does not affect the vorticity of the flow. The mean velocity was measured using a laser Doppler anemometer with forward scatter mode in a transparent draught tube and a transparent vessel of diameter T = 400 mm. Two series of experiments were performed, both of them under a turbulent regime of flow of the agitated liquid. First, the optimum height of the dished bottom was sought, and then the dependences of the dimensionless flow rate criterion and the impeller power number on the number of impeller blades were determined for both pitch angles tested under conditions of optimum ratio HT /DT. It follows from the results of the experiments that the optimum ratio HT /DT = 0.25 when the cross sectional areas of the horizontal flow around the bottom and the vertical inflow to the draught tube are the same. For all the tested pitched blade impellers the impeller power number when α = 45° exceeds the value of this quantity when pitch angle α = 35°, while the flow rate number when α = 35° exceeds this quantity when α = 45°. On the other hand, the absolute values of the impeller power number when the draught tube was introduced correspond fairly well to the dimensionless impeller power input measured in a system without a draught tube. However, the absolute values of the flow rate number found in the former system are significantly lower than the dimensionless impeller pumping capacity determined in the latter system. The hydraulic efficiency of pitched blade impellers N3Qp/Po for the investigated geometry of the agitated systems does not depend on the number of impeller blades, but it is significantly lower than the quantity determined in an agitated system with a dished bottom but without the draught tube.
Recurrent novae are repeating thermonuclear explosions in the outer layers of white dwarfs, due to the accretion of fresh material from a binary companion. The shock generated when ejected material slams into the companion star's wind can accelerate particles. We report very-high-energy (VHE; ≳100 giga–electron volts≳100 giga–electron volts) gamma rays from the recurrent nova RS Ophiuchi, up to 1 month after its 2021 outburst, observed using the High Energy Stereoscopic System (H.E.S.S.). The temporal profile of VHE emission is similar to that of lower-energy giga–electron volt emission, indicating a common origin, with a 2-day delay in peak flux. These observations constrain models of time-dependent particle energization, favoring a hadronic emission scenario over the leptonic alternative. Shocks in dense winds provide favorable environments for efficient acceleration of cosmic rays to very high energies.
A search for dark matter linelike signals iss performed in the vicinity of the Galactic Center by the H.E.S.S. experiment on observational data taken in 2014. An unbinned likelihood analysis iss developed to improve the sensitivity to linelike signals. The upgraded analysis along with newer data extend the energy coverage of the previous measurement down to 100 GeV. The 18 h of data collected with the H.E.S.S. array allow one to rule out at 95% C.L. the presence of a 130 GeV line (at l=-1.5°, b=0° and for a dark matter profile centered at this location) previously reported in Fermi-LAT data. This new analysis overlaps significantly in energy with previous Fermi-LAT and H.E.S.S. RESULTS: No significant excess associated with dark matter annihilations was found in the energy range of 100 GeV to 2 TeV and upper limits on the gamma-ray flux and the velocity weighted annihilation cross section are derived adopting an Einasto dark matter halo profile. Expected limits for present and future large statistics H.E.S.S. observations are also given. ; The support of the Namibian authorities and of the University of Namibia in facilitating the construction and operation of H.E.S.S. is gratefully acknowledged, as is the support by the German Ministry for Education and Research (BMBF), the Max Planck Society, the German Research Foundation (DFG), the French Ministry for Research, the Centre National de la Recherche Scientifique-Institut National de Physique Nucléaire et de Physique des Particules and the Astroparticle Interdisciplinary Programme of the Centre National de la Recherche Scientifique, the United Kingdom Science and Technology Facilities Council (STFC), the Institute of Particle and Nuclear Physics of the Charles University, the Czech Science Foundation, the Polish Ministry of Science and Higher Education, the South African Department of Science and Technology and National Research Foundation, and the University of Namibia. We appreciate the excellent work of the technical support staff in Berlin, Durham, Hamburg, Heidelberg, Palaiseau, Paris, Saclay, and Namibia in the construction and operation of the equipment. R. C. G. Chaves Funded by European Union Seventh Framework Programme Marie Curie, Grant Agreement No. PIEF-GA-2012-332350. ; Peer-reviewed ; Publisher Version