Frequency and Magnitude Analysis of the Macro-instability Related Component of the Tangential Force Affecting Radial Baffles in a Stirred Vessel

Experimental data obtained by measuring the tangential component of force affecting radial baffles in a flat-bottomed cylindrical mixing vessel stirred with pitched blade impellers is analysed. The maximum mean tangential force is detected at the vessel bottom. The mean force value increases somewhat with decreasing impeller off-bottom clearance and is noticeably affected by the number of impeller blades. Spectral analysis of the experimental data clearly demonstrated the presence of its macro-instability (MI) related low-frequency component embedded in the total force at all values of impeller Reynolds number. The dimensionless frequency of the occurrence of the MI force component is independent of stirring speed, position along the baffle, number of impeller blades and liquid viscosity. Its mean value is about 0.074. The relative magnitude (QMI) of the MI-related component of the total force is evaluated by a combination of proper orthogonal decomposition (POD) and spectral analysis. Relative magnitude QMI was analysed in dependence on the frequency of the impeller revolution, the axial position of the measuring point in the vessel, the number of impeller blades, the impeller off-bottom clearance, and liquid viscosity. Higher values of QMI are observed at higher impeller off-bottom clearance height and (generally) QMI decreases slightly with increasing impeller speed. The QMI value decreases in the direction from vessel bottom to liquid level. No evident difference was observed between 4 blade and 6 blade impellers. Liquid viscosity has only a marginal impact on the QMI value

The Tangential Force Affecting the Radial Baffles in a Stirred Vessel: Analysis of the Macro-instability Related Component

Experimental data obtained by measuring the tangential component of the force affecting radial baffles in a flat-bottomed cylindrical mixing vessel stirred with a Rushton turbine impeller is analysed. Spectral analysis of the experimental data demonstrated the presence of its macro-instability (MI) related low-frequency component embedded in the total force. Two distinct dimensionless frequencies (both directly proportional to the impeller speed of rotation N) of the occurence of the MI component were detected: a lower frequency of approximately 0.025N and a higher frequency of about 0.085N. The relative magnitude QMI of the MI-related component of the total tangential force was evaluated by a combination of proper orthogonal decomposition (POD) and spectral analysis. The values of magnitude QMI varied in the interval [rom approximately 0.05 to 0.30. The magnitude QMI takes maximum values at low Reynolds number values (in laminar and transitional regions). In the turbulent region (ReM >20000) the QMI value is low and practically constant. The dependence oj the QMI values on vertical position in the vessel is only marginal. The results suggest that the magnitude of the MI component of the force is significantly influenced by the liquid viscosity and density

Axial Force at the Vessel Bottom Induced by Axial Impellers

This paper deals with the axial force affecting the flat bottom of a cylindrical stirred vessel. The vessel is equipped with four radial baffles and is stirred with a four 45° pitched blade impeller pumping downwards. The set of pressure transducers is located along the whole radius of the flat bottom between two radial baffles. The radial distribution of the dynamic pressures indicated by the transducers is measured in dependence on the impeller off-bottom clearance and impeller speed.It follows from the results of the experiments that under a turbulent regime of flow of an agitated liquid the mean time values of the dynamic pressures affecting the bottom depend not on the impeller speed but on the impeller off-bottom clearance. According to the model of the flow pattern of an agitated liquid along the flat bottom of a mixing vessel with a pitched blade impeller, three subregions can be considered in this region: the liquid jet streaming downwards from the impeller deviates from its vertical (axial) direction to the horizontal direction,  the subregion of the liquid flowing horizontally along the bottom and, finally, the subregion of the liquid changing direction from the bottom upwards (vertically) along the wall of the cylindrical vessel, when the volumetric flow rates of the liquid taking place in the downward and upward flows are the same.

Technical Development of a New Semispherical Radiofrequency Bipolar Device (RONJA): Ex Vivo and In Vivo Studies

The aim of this study is to inform about the development of a new semispherical surgical instrument for the bipolar multielectrode radiofrequency liver ablation. Present tools are universal; however they have several disadvantages such as ablation of healthy tissue, numerous needle punctures, and, therefore, longer operating procedure. Our newly designed and tested semispherical surgical tool can solve some of these disadvantages. By conducting an in vivo study on a set of 12 pigs, randomly divided into two groups, we have compared efficiency of the newly developed instrument with the commonly used device. Statistical analysis showed that there were no significant differences between the groups. On average, the tested instrument RONJA had shorter ablation time in both liver lobes and reduced the total operating time. The depth of the thermal alteration was on average 4 mm larger using the newly tested instrument. The new radiofrequency method described in this study could be used in open liver surgery for the treatment of small liver malignancies (up to 2 cm) in a single application with the aim of saving healthy liver parenchyma. Further experimental studies are needed to confirm these results before clinical application of the method in the treatment of human liver malignancies

Macro-instabilities of the Flow Pattern in a Stirred Vessel: Detection and Characterization Using Local Velocity Data

Velocity data obtained by laser Doppler velocimetry (LDV) in a flat-bottomed cylindrical stirred vessel (diameter: 300 mm, filling height: 300 mm, working liquids: water and aqueous glycerine, impeller Reynolds number values (ReM): 750, 1200 and 75000) equipped with four radial baffles and stirred with a pitched blade impeller are analyzed by methods of non-linear analysis. The macro-instability of the flow pattern (MI) was extracted from the experimental data by a combination of the proper orthogonal decomposition (POD) technique and spectral analysis. The relative magnitude of the MI (the fraction of flow total kinetic energy captured by MI) was evaluated and its spatial distribution was determined. The temporal evolution of the MI was constructed from the POD eigenmodes. The chaotic attractors of the macro-instabilities were reconstructed by the method of delays. The embedding dimension was determined by the false nearest neighbor analysis (FNN) method, and the time delay from the first min imum of mutual information. Correlation dimension de and the largest Lyapunov exponents λmax of the reconstructed attractorswere evaluated. The correlation dimension slightly increases with the increasing ReM value. The spatial distribution of dc is quite uniform at all ReM values. The maximum Lyapunov exponent is clearly positive for all analyzed at tractors. Spatial distribution of λmax is markedly non-uniform and exhibits irregular variations. Possible applications of nonlinear analysis of local velocity data in mixing processes are mentioned

Axial Force at the Vessel Bottom Induced by Axial Impellers

This paper deals with the axial force affecting the flat bottom of a cylindrical stirred vessel. The vessel is equipped with four radial baffles and is stirred with a four 45° pitched blade impeller pumping downwards. The set of pressure transducers is located along the whole radius of the flat bottom between two radial baffles. The radial distribution of the dynamic pressures indicated by the transducers is measured in dependence on the impeller off-bottom clearance and impeller speed.It follows from the results of the experiments that under a turbulent regime of flow of an agitated liquid the mean time values of the dynamic pressures affecting the bottom depend not on the impeller speed but on the impeller off-bottom clearance. According to the model of the flow pattern of an agitated liquid along the flat bottom of a mixing vessel with a pitched blade impeller, three subregions can be considered in this region: the liquid jet streaming downwards from the impeller deviates from its vertical (axial) direction to the horizontal direction,  the subregion of the liquid flowing horizontally along the bottom and, finally, the subregion of the liquid changing direction from the bottom upwards (vertically) along the wall of the cylindrical vessel, when the volumetric flow rates of the liquid taking place in the downward and upward flows are the same.

Axial force at the vessel bottom induced by axial impellers

This paper deals with the axial force affecting the flat bottom of a cylindrical stirred vessel. The vessel is equipped with four radial baffles and is stirred with a four 45o pitched blade impeller pumping downwards. The set of pressure transducers is located along the whole radius of the flat bottom between two radial baffles. The radial distribution of the dynamic pressures indicated by the transducers is measured in dependence on the impeller off-bottom clearance and impeller speed. It follows from the results of the experiments that under a turbulent regime of flow of an agitated liquid the mean time values of the dynamic pressure affecting the bottom depend not on the impeller speed but on the impeller off-bottom clearance. According to the model of the flow pattern of an agitated liquid along the flat bottom of a mixing vessel with a pitched blade impeller, three subregions can be considered in this region: the liquid jet streaming downwards from the impeller deviates from its vertical (axial) direction to the horizontal direction, the subregion of the liquid flowing horizontally along the bottom and, finally, the subregion of the liquid changing direction from the bottom upwards (vertically) along the wall of the cylindrical vessel, when the volumetric flow rates of the liquid taking place in the downward and upward flows are the same