4468
Ind. Eng. Chem. Res. 2010, 49, 4468–4470
Comments on “Dynamics of Flow Structures and Transport PhenomenasPart 1. Experimental and Numerical Techniques for Identification and Energy Control of Flow Structures” Ivan Forˇt* Department of Process Engineering, Czech Technical UniVersity in Prague, Technicka 4, 16607 Prague 6, Czech Republic Sir: I read, with great interest, the paper “Dynamics of Flow Structures and Transport PhenomenasPart 1. Experimental and Numerical Techniques for Identification and Energy Content of Flow Structures”, which was written by Joshi et al.1 This paper provides a valuable review of up-to-date experimental and numerical procedures for detecting and evaluating the flow structure in various types of equipment used in the chemical industry under a turbulent regime of flow. These experimental and numerical methods confirm the great development of research hardware and software in recent decades, with sophistical applications. The developments are based on physical and mathematical procedures originally developed in basic research in these scientific disciplines. My comments describe additional techniques for investigating the flow structure in an agitated charge under a turbulent flow regime. The first comment is based on visual observation of the circulation of a small indicating particle in an agitated liquid. The simple model that was proposed by Porcelli and Marr2 represents the flow lines of the primary and induced flow of an agitated liquid. The primary flow (Qp) concerns the fraction of the charge that passes directly through the rotational area around the rotating impeller, which according to the definition is the impeller pumping capacity. The flow lines for this stream are closed curves that intersect the above-mentioned region. The induced flow (Qe) is provoked by momentum transfer between the mass entrained by the primary flow and the medium that surrounds it. The entire volume of the charge under a fully turbulent flow regime can then be divided in two parts only: a volume Vp, which contains the primary flow, and a volume Ve, which contains the induced flow. A concept corresponding to actual conditions, however, would have to take into account the mass exchange between the two regions, which means that liquid will flow from one volume to the other. Porcelli and Marr2 assumed that the probability (P) of the occurrence of an arbitrary particle p in the primary or induced flow is given by the ratio of the volumetric flow rate corresponding to the appropriate partial flow and the sum of the flow rates of the two types of flow; this is expressed by the relation Qp P(p ∈ Qp) ) Qp + Qe
(1)
and by an analogous expression for the probability of occurrence of a particle in the induced flow (Qe). Porcelli and Marr2 also adopted Danckwert’s3 concept: that is, the mean residence time of a particle entrained by a stream of a volumetric flow rate Q in volume Vi is expressed by the ratio * E-mail:
[email protected].
τVi¯ )
Vi Q
(2)
irrespective of the distribution of residence times about this mean value. Assuming that the induced and primary flows fill the entire volume of the charge, the authors2 derived, by means of these equations, a relation for the mean primary circulation time, i.e., the mean time between two successive passages of the indicating particle through the body created by the rotating impeller, the so-called impeller rotor region, V Qp
τp )
(3)
and, finally, for the impeller pumping capacity, it holds: Qp )
V τp
(4)
The impeller pumping capacity was measured visually both for axial flow impellers4,5 and radial flow impellers6,7 in baffled tanks under a turbulent regime of flow of an agitated liquid in transparent pilot-plant systems. Steidl8 described the indicating particle (“flow follower”) made from three mutually perpendicular plates comprised of Silon 0.2 mm thick and 6 mm in diameter. A particle with such a geometry will move along with the liquid volume in the space it occupies. When choosing the number of passages of the indicating particle through the impeller rotor region that is needed to calculate the mean time of primary circulation, it is necessary to take into consideration the distribution function of the quantity jτp, which was found to be of the form9 f(τp) ) 0 (τp e τpmin)
(5a)
f(τp) ) m exp[-m(τp - τpmin)] (τp g τpmin)
(5b)
so that the first moment of this function equals τp )
∫
∞ τ f(τp) τpmin p
dτp )
1 + τpmin m
(6)
The model of the frequency function of the time of primary circulation corresponds to a combination of an ideal mixer in the space outside the impeller rotor region connected in series with a section of the piston flow (inside the rotor region). This experimental technique for visual observation of the indicating particle in an agitated charge was improved for a slender vessel with two impellers on the same shaft under a turbulent regime of flow of an agitated liquid.10 Four types of particle circulation were examined: circulation in the lower part of the system (pumping effect of the lower impeller), circulation in the upper part of the system (pumping effect of the upper impeller), and exchangeable circulation between the upper and
10.1021/ie9017447 2010 American Chemical Society Published on Web 04/13/2010
Ind. Eng. Chem. Res., Vol. 49, No. 9, 2010
lower parts of the system, and vice versa. Two standard Ruston impellers or a lower standard Rushton turbine impeller and an upper six-blade pitched-blade (at 45°) impeller were investigated in an transparent pilot-plant vessel. The principle of the experimental technique consisted of making a visual observation of the motion of the indicating particle (flow follower) in charge and storing its passages through the rotor regions of single impellers by means of a joystick into the store of a computer. The joystick has an operating handle that is movable only along one axis. It can be set to three positions: neutral, up, and down. If the flow follower moves outside the rotor region of the impellers, the handle is in the neutral position. If it passes through the rotor region of the lower impeller, the handle is deflected downward, and if it passes through the rotor region of the upper impeller, the handle is deflected upward. In the sensing phase, the time course of the circulations of the indicating particle, the computer continuously registers the position of the joystick handle on the basis of a computer program. As soon as the handle is deflected from neutral, the program begins to store the time at which the deflection occurs and also the position of the handle. In the processing phase, the current time values are converted to time intervals between single changes of the joystick position. These intervals are further classified into four groups, according to the handle position at the beginning and at the end of the interval: “down-down”, “from down-upward”, “up-up”, and “from up-downward”, which correspond to the above-defined transitions (circulations). It follows from the average data of these circulations that homogeneous circulation of the charge in the entire system is achieved if the vertical distance of the high-speed impellers is equal to at least twice their diameter, then pumping capacities being approximately double, compared to those achieved in the system with one impeller, where the off-bottom liquid level is equal to the vessel diameter. It follows from a comparison of the two arrangements, when the upper pitched-blade impeller pumps the liquid either upward or downward, that homogeneous circulation of the entire charge is attained in the first of the two cases compared here. The second comment on the paper by Joshi et al.1 deals with indirect experimental techniques for investigating the flow structure in an agitated charge. These techniques are based on the interference of the boundaries of the agitated tank (bottom, radial baffles) with the turbulent flow of an agitated charge. The responses of the boundaries can be interpreted by means of general ideas of fluid dynamics and, then, they can provide valuable information about the mean flow and turbulence inside the opaque system without any direct disturbance of the experimental device with an agitated batch. Axial high-speed rotary impellers (propeller impellers, pitchedblade impellers, axial hydrofoil impellers) create a significant axial force (thrust).4 The rotation of the impeller causes a field of axial forces by which the flowing liquid or suspension acts on the impeller and the vessel. It is relatively easy to determine such forces and their components without interfering with the velocity field.4,11 It follows from these investigations that the distribution of the axial force affecting the flat bottom of the baffled cylindrical tank with downward pumping axial high speed impeller (preferred for mixing suspensions of solid particles12) is unambiguously joined with the flow pattern along the bottom. Force fax1 originates when the liquid jet streaming downward from the impeller rotor region deviates from its vertical (axial) direction and flows along the bottom of the vessel, and force fax2 appears in the region where the liquid
4469
flowing along the bottom of the vessel changes direction and starts flowing vertically (axially) up around the walls and baffles of the cylindrical vessel. Between the areas of the bottom affected by forces fax1 and fax2, there is, under certain conditions (e.g., impeller off-bottom clearance), a subregion where this pressure force acts in the corresponding area, according to the flow parallel around the bottom. The values of the mean time components fax1 and fax2 are joined with the intensity of the convective flow along the bottom of the vessel bottom by means of the impulse theorem. The vertical (axial) component of the free liquid stream changes in both subregions where a π/2-radians turn occurs: ¯fax1 )
¯fax2 )
F(Qbt1)2 πr12 F(Qbt2)2
π[(T2 /4) - r22]
(7)
(8)
The volumetric flow rates along the bottom Qbt1 and Qbt2 act on the areas limited by the radii r1 and r2 or T/2 (the radius of the vessel), respectively, and create the mean axial forces jfax1 and jfax2. In experiments, most attention has been paid to the distribution of the axial pressures along the bottom. These distributions were determined directly: (1) By measuring the total pressures in holes situated in the bottom of the vessel.4 The dynamic pressures corresponding to them were calculated as the differences between the total pressure measured and the hydrostatic pressure under the conditions of the experiment. (2) By direct measurement of the dynamic pressures using a set of pressure transducers distributed along the bottom of the vessel.11 The transducer is based on an silica chip and a slim diaphragm with a surface area of 2.54 mm2, which is able to reveal small pressure variations. Both of the above-mentioned techniques enabled a radial profile of the mean values of the dynamic pressures along the flat vessel bottom to be determined as well as the main parts of the profile: radial coordinates r1 and r2. The latter techniques allowed not only the mean value of the local dynamic pressure to be determined, but also its statistics to be estimated (in the form of a standard deviation). Experimentally found radial profiles of the mean dynamic pressures at the bottom were integrated over corresponding parts of the bottom, to calculate the total axial thrust, the mean values jfax1 and jfax2 and the volumetric flow rates Qbt1 and Qbt2 (see eqs 7 and 8), in dependence on the impeller off-bottom clearance. For a fully turbulent regime of agitated charge, the two flow rates Qbt1 and Qbt2 can be considered the same (i.e., the flow direction changes below the impeller rotary region and at the vessel wall are the same). A radial baffle in a mechanically agitated tank prevents rotation of a liquid, resulting in the origination of a central vortex and increasing mixing efficiency. At the same time, it is loaded by forces causing fatigue stress. The distribution of the peripheral (tangential) components of dynamic pressure affecting a radial baffle at the wall of a cylindrical pilot-plant mixing tank with an axially located rotary impeller under a turbulent regime of flow of an agitated charge was determined experimentally and evaluated.13,14 One of the baffles was equipped with a trailing target, enabling it to be rotated parallel to the axis of the vessel with small eccentricity and balanced by
4470
Ind. Eng. Chem. Res., Vol. 49, No. 9, 2010
springs. Eleven positions of the target along the height of the baffle were examined. The circular displacement of the target is directly proportional to the peripheral force affecting the balancing springs. A small photoelectric device, composed of two photodiodes, scanned the angular displacement, and the output signal was treated, stored, and analyzed by a computer. The vertical profile of the mean dynamic pressures affecting the baffle corresponds to the flow pattern of the system, which is dependent on the high-speed impeller that is introduced. The pitched-blade impeller exhibits the main effect at the bottom, while the standard Rushton impeller affects mainly the area around the horizontal plane of its separating disksa subregion of the interference of the impeller discharge flow and the baffle. More than 75% of the turbine impeller torque is transferred via the agitated liquid by the baffles, and more than 2/3 of the baffle reaction moment is located in the impinging area of the turbine impeller discharge stream and the vessel wall. This experimental device enabled an analysis of the oscillating values of the peripheral force affecting the baffle in the agitated system investigated with a pitched-blade impeller or a standard Rushton turbine impeller.14 Special efforts were made to detect the low-frequency band of the oscillating force, because of its meaning for stress analysis of the baffle, above all in industrial plants provided with tested impellers. The presence of a macroinstability (MI)-related component of the force was detected by special analysis of the measured data. It follows from the results of experiments in the system with the standard Rushton impeller that two distinct frequencies exist, both directly proportional to the impeller speed N: a lower frequency of ∼0.025N and a higher frequency of ∼0.085N. The upper frequency of the MI-related component occurred only at low impeller Reynolds number (ReM) values, and the lowerfrequency component occurred over the entire range of ReM values. These results correspond fairly well with the results obtained from a direct determination of the velocity field in an investigated mechanically agitated system.14 Finally, proper orthogonal decomposition (POD), combined with spectral analysis of the oscillating force signal, was used to evaluate the relative magnitude of the MI-related component of the peripheral force affecting the baffle.14 It follows from the results of these experiments that the MI-related components constitute a highly significant contribution to the total dynamic force (up to 50%). Therefore, the dynamic low-frequency force
generated by the MI contributes very significantly to the fatigue of materials used in the manufacture of mixing vessel internals. Knowledge of the magnitude and frequency of the MI-related forces acting on solid bodies in an agitated charge may contribute significantly to the safety of mixing tank operation, because the risk of fatigue breaks can be diminished by proper design of the stirred tank parts. Literature Cited (1) Joshi, J. B.; Tabib, M. V.; Deshande, S., S.; Mathpati, Ch., S. Dynamics of Flow Structures and Transport PhenomenasPart 1. Experimental and Numerical Techniques for Identification and Energy Content of Flow Structures. Ind. Eng. Chem. Res. 2009, 48, 8244–8284. (2) Porcelli, J. V.; Marr, G. R. Propeller Pumping and Solids Fluidization in Stirred Tanks. Ind. Eng. Chem. Fundam. 1962, 1, 172–183. (3) Danckwerts, P. V. Continuous Flow Systems: Distribution of Residence Times. Chem. Eng. Sci. 1953, 2, 1–12. (4) Forˇt, I. Flow and Turbulence in Vessels with Axial Impellers. In Mixing, Theory and Practice; Uhl, V. W., Gray, J. B., Eds.; Academic Press: New York, 1986; Vol. III, pp 133-197. (5) Medek, J.; Forˇt, I. Contribution to the Analysis of Liquid Macroflow in a Cylindrical Vessel with a High-Speed Impeller. Collect. Czech. Chem. Commun. 1981, 46, 963–974. (6) Sato, K.; Inoue, I. Effect of Scale up on the Mixing Characteristics of a Stirred Vessel. Chem. Eng. Jpn. 1973, 37, 937–946. (7) Sato, T.; Taniyama, I. Discharge and Circulation Flow Rate in Agitated Vessel. Kagaku Kogaku 1965, 29, 153–173. (8) Steidl, H. Indikation von Stro¨mungsbahnen durch einen Schwebeko¨rper. Eine auf statistischer Grundlage beruhende Methode zur Untersuchung des Ru¨hrorganes in flu¨ssiger Phase. Collect. Czech. Chem. Commun. 1958, 23, 1664–1679. (9) Forˇt, I. Pumping Capacity of Propeller Mixer. Collect. Czech. Chem. Commun. 1967, 32, 3663–3678. (10) Forˇt, I.; Machonˇ, V.; Ha´jek, J.; Fialova´, E. Liquid Circulation in a Cylindrical Baffled Vessel of High Height/Diameter Ratio with Two Impellers on the Same Shaft. Collect. Czech. Chem. Commun. 1987, 52, 2640–2653. (11) Forˇt, I.; Hasal, P.; Paglianti, A.; Magelli, F. Axial Force at the Vessel Bottom Induced by Axial Impellers. Acta Polytech. 2008, 48 (4), 45–50. (12) Wu, J.; Zhu, Y.; Pullum, L. Impeller Geometry Effect on Velocity and Solids Suspension. Chem. Eng. Res. Des. 2001, 79/A, 989–997. (13) Krateˇna, J.; Forˇt, I.; Bru˚ha, O.; Pavel, J. Distribution of Dynamic Pressure along a Radial Baffle in an Agitated System with Standard Rushton Turbine Impeller. Chem. Eng. Res. Des. 2001, 79/A, 819–823. (14) Hasal, P.; Forˇt, I.; Krateˇna, J. Force Effects of the Macro-Instability of Flow Pattern on Radial Baffles in a Stirred Vessel with Pitched-Blade and Rushton Turbine Impellers. Chem. Eng. Res. Des. 2004, 82/A, 1268–1281.
IE9017447
