Heating and Cooling Anomaly of a Rotating Body

This paper deals with an effect which appears when heating or cooling a rotating body. No external forces acting on the body are supposed. Due to thermal expansion, the moment of inertia of the body varies together with the temperature changes. In agreement with the principle of conservation of angular momentum [1], the angular momentum is constant. This results in angular velocity changes and subsequently in kinetic energy changes. Also the stress energy varies together with the changes in thermal dimension. To satisfy the principle of energy conservation we have to suppose that the changes in kinetic and stress energy are compensated by the changes in internal energy, which is correlated with temperature changes of the body. This means that the rules for the heating or cooling process of a rotating body are not the same as those for a body at rest. This idea, applied to a cylinder rotating around its geometric axis under specific parameters, has been mathematically treated. As a result, the difference between the final temperature of the rotating cylinder and the temperature of the cylinder at rest has been found.

Dynamics of the Flow Pattern in a Baffled Mixing Vessel with an Axial Impeller

This paper deals with the primary circulation of an agitated liquid in a flat-bottomed cylindrical stirred tank. The study is based on experiments, and the results of the experiments are followed by a theoretical evaluation. The vessel was equipped with four radial baffles and was stirred with a six pitched blade impeller pumping downwards. The experiments were concentrated on the lower part of the vessel, where the space pulsations of the primary loop, originated due to the pumping action of the impeller. This area is considered to be the birthplace of the flow macroinstabilities in the system – a phenomenon which has been studied and described by several authors. The flow was observed in a vertical plane passing through the axis of the vessel. The flow patterns of the agitated liquid were visualized by means of Al micro particles illuminated by a vertical light knife and scanned by a digital camera. The experimental conditions corresponded to the turbulent regime of agitated liquid flow.It was found that the primary circulation loop is elliptical in shape. The main diameter of the primary loop is not constant. It increases in time and after reaching a certain value the loop disintegrates and collapses. This process is characterized by a certain periodicity and its period proved to be correlated to the occurrence of flow macroinstability. The instability of the loop can be explained by a dissipated energy balance.  When the primary loop reaches the level of disintegration, the whole impeller power output is dissipated and under this condition any flow alteration requiring additional energy, even a very small vortex separation, causes the loop to collapse.

Dynamic Effect of Discharge Flow of a Rushton Turbine Impeller on a Radial Baffle

This paper presents an analysis of the mutual dynamic relation between the impeller discharge flow of a standard Rushton turbine impeller and a standard radial baffle at the wall of a cylindrical mixing vessel under turbulent regime of flow of an agitated liquid. A portion of the torsional moment of the baffle corresponding to the region of the force interaction of the impeller discharge stream and the baffle is calculated under the assumption of constant angular momentum in the flow region between the impeller and the baffles. This theoretically obtained quantity is compared with the torsional moment of the baffles calculated from the experimentally determined distribution of the peripheral (tangential) component of dynamic pressure along the height of the radial baffle in pilot plant mixing equipment. It follows from the results of our calculations that for both investigated impeller off-bottom clearances the theoretically determined transferred torsional moment of the baffles in the area of interference between the impeller discharge flow and the baffles agrees fairly well with experimentally determined data and, moreover, that more than 2/3 of the transferred torsional moment of the baffles as a whole is located in the above mentioned interference area

Power Input of High-Speed Rotary Impellers

This paper presents the results of an experimental investigation of the power input of pitched blade impellers and standard Rushton turbine impellers in a cylindrical vessel provided with four radial baffles at its wall under a turbulent regime of flow of an agitated liquid. The influence of the geometry of the pitched blade impellers (pitch angle, number of blades) and the off-bottom impeller clearance of both high-speed impellers tested on the impeller power input is determined in two sizes of the cylindrical vessel (0.3 m and 0.8 m diameter of vessel). A strain gauge torquemeter is used in the small vessel and a phase shift mechanical torquemeter is used in the large vessel. All results of the experiments correspond to the condition that the Reynolds number modified for the impeller exceeds ten thousand. The results of this study show that the significant influence of the separating disk thickness of the turbine impeller corresponds fairly well to the empirical equations presented in the literature. Both the influence of the number of impeller blades and the blade pitch angle of the pitched blade impeller were expressed quantitatively by means of the power dependence of the recently published correlations: the higher the pitch angle and the number of blades, the higher the values of the impeller power input. Finally, it follows from results of this study that the impeller off-bottom clearance has a weak influence on the power input of the Rushton turbine impeller, but with decreasing impeller off-bottom clearance the power input of the pitched blade impeller increases significantly

Dynamics of the Flow Pattern in a Baffled Mixing Vessel with an Axial Impeller

This paper deals with the primary circulation of an agitated liquid in a flat-bottomed cylindrical stirred tank. The study is based on experiments, and the results of the experiments are followed by a theoretical evaluation. The vessel was equipped with four radial baffles and was stirred with a six pitched blade impeller pumping downwards. The experiments were concentrated on the lower part of the vessel, where the space pulsations of the primary loop, originated due to the pumping action of the impeller. This area is considered to be the birthplace of the flow macroinstabilities in the system – a phenomenon which has been studied and described by several authors. The flow was observed in a vertical plane passing through the axis of the vessel. The flow patterns of the agitated liquid were visualized by means of Al micro particles illuminated by a vertical light knife and scanned by a digital camera. The experimental conditions corresponded to the turbulent regime of agitated liquid flow.It was found that the primary circulation loop is elliptical in shape. The main diameter of the primary loop is not constant. It increases in time and after reaching a certain value the loop disintegrates and collapses. This process is characterized by a certain periodicity and its period proved to be correlated to the occurrence of flow macroinstability. The instability of the loop can be explained by a dissipated energy balance.  When the primary loop reaches the level of disintegration, the whole impeller power output is dissipated and under this condition any flow alteration requiring additional energy, even a very small vortex separation, causes the loop to collapse.

Dynamic Stress Affecting the Radial Baffle on an Industrial Mixing Unit with a Pitched Blade Impeller

This paper presents a study of dimensioning under fatigue stress of a standard radial baffle in an industrial mixing unit (T = 5 m) with a pitched blade impeller under a turbulent regime of flow of an agitated liquid. The fatigue stress of the radial baffle is calculated from the known experimentally determined distribution of the dynamic pressure affecting the standard radial baffle in a pilot plant agitated system. Asymmetrical distribution of the dynamic pressure along the height of the baffle significantly affects the thickness of the baffle as well as the dimensions of the doublefillet weld fixing the baffle to the vessel wall. Our results are valid for standard pitched blade impellers with four or six inclined blades (D/T = 1/3, a = 45°) and off-bottom clearances h/T = 0.2, 0.35 and 0.5 pumping liquid downwards in a cylindrical mixing vessel with a flat bottom and four baffles (b/T = 0.1) when the Reynolds number exceeds ten thousand