Suzanne M. Kresta

Handbook of Industrial Mixing

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The flow field produced by a pitched blade turbine: Characterization of the turbulence and estimation of the dissipation rate

This paper compares various methods which have been used for the estimation of turbulent length scales, and/or the rate of dissipation of turbulence kinetic energy (e) in stirred tanks. The system examined was a four-blade, 45° pitched blade turbine rotating in a cylindrical, fully baffled tank with velocity measurement by laser Doppler anemometry. Four methods were chosen for experimental application. The methods used, and the principles upon which they rest, can be summarized as follows: the gradient hypothesis method uses the constitutive equation from the k-e model; Taylors hypothesis is used to convert time derivatives to spatial derivatives; dimensional arguments lead to the estimation of e from k using a constant length scale; finally, the autocorrelation coefficient function is used to calculate the Eulerian integral time scale, which is then combined with k to estimate e. Various corrections have been suggested for each of these methods, many of which were tested and compared in this work. Although all these methods have previously been applied in stirred tanks, the underlying assumptions and approximations have often been implicit. The impact of these assumptions on the final result, in particular, the importance of the trailing vortices, has been evaluated in a quantitative sense in this paper.

Correlation of mean drop size and minimum drop size with the turbulence energy dissipation and the flow in an agitated tank

Previous correlations have focused on the relationship between the mean drop size and the physical properties of the fluids (interfacial tension, density and viscosity), the volume fraction of the dispersed phase and the average power input per unit mass of fluids. This investigation relates the mean drop size to both the maximum turbulence energy dissipation rate and the turbulent flow in an agitated tank. Four impellers with varying diameters and clearances were used. The maximum turbulence energy dissipation rate was first estimated in the continuous phase (water) using a laser Doppler anemometer (LDA). Then the dispersed phase (silicone oil) was introduced. Drop sizes were measured using a phase Doppler particle analyzer (PDPA). Examination of the smallest drops showed that use of the Kolmogoroff length scale (η=(ν3e)14) to estimate the minimum drop size in liquid–liquid dispersions is not accurate. In some cases, more than 30% of the droplets have diameters smaller than the Kolmogoroff length. It was found that the mean drop size is better correlated to the maximum turbulence energy dissipation rate than to either the average power input per unit mass of fluids, or the tip speed of the impeller. Scale-up of liquid–liquid dispersions can be improved when both the energy dissipation and the flow are considered.

The Effect of Impeller and Tank Geometry on Power Number for a Pitched Blade Turbine

Previous studies of the Rushton turbine have shown that the power number is sensitive to the details of impeller geometry, and in particular to the blade thickness, but is independent of the impeller diameter to tank diameter ratio. In this paper, a similar study is reported for the pitched blade impeller. The results show that the power number is independent of blade thickness, but dependent on the impeller to tank diameter ratio. This is exactly the opposite result to that observed for the Rushton turbine. Physical explanations are given for the differences in behaviour between the two impellers. For the Rushton turbine, power consumption is dominated by form drag, so details of the blade geometry and flow separation have a significant impact (30%) on the power number. For the pitched blade impeller, form drag is not as important, but the flow at the impeller interacts strongly with the proximity of the tank walls, so changes in the position of the impeller in the tank can have a significant impact on the power number.

Active volume of mean circulation for stirred tanks agitated with axial impellers

Abstract The total volume of a stirred tank is currently treated as the active volume. In this work, laser doppler velocimetry (LDV) is used to show that for stirred tanks agitated with axial impellers the active volume of mean circulation for a stirred tank is not the whole tank, but a height equivalent to 2 3 of the tank diameter (T). The active volume was defined using the decay of the three-dimensional wall jet in front of the baffle. At the point where the dimensionless slope of the axial velocity approaches zero the jet stops being effective for gross circulation. The active volume in fully turbulent flow remains constant for three types of axial impellers (PBT, A-310, HE3) independent of speed, diameter or off-bottom clearance. The absolute value of the velocities, of course, is a function of impeller speed, size and off-bottom clearance. The direction of the impeller discharge stream affects the location of the active volume. The discharge from axial impellers (A-310 and HE3) is always directed at the bottom of the tank, but this is not the case for the PBT. For the PBT, a transition point exists, above which the discharge stream impinges on the tank wall. The factors affecting the maximum clearance or transition point are the angle of the impeller blade, and the direction of the r–θ component of the impeller discharge stream. If the impeller discharge stream reaches the bottom of the tank, the active volume is the bottom two-thirds of the tank. If, however, the jet impinges on the tank wall, the zone of least activity is distributed between the bottom and the top of the tank.

Evolution of drop size distribution in liquid–liquid dispersions for various impellers

Abstract The drop size distribution is one of the most important characteristics of liquid–liquid dispersions. Several shapes of the distribution have been proposed by previous investigators. This work investigates the drop size distribution in very dilute (0.03% by volume) liquid–liquid dispersions over a wide range of rotational speeds, using different impellers with varying diameters and off-bottom clearances. Four impellers were used: one radial flow impeller (Rushton turbine); and three axial flow impellers [pitched blade turbine, HE3 turbine and fluidfoil (A310) turbine]. Drop sizes were measured using a phase Doppler particle analyzer (PDPA) in both the bulk and impeller regions in an agitated tank. It was found that the drop size distribution changes with an increase in the rotational speed. Typically, four types of drop size distribution evolve with increasing rotational speed: long tail, double peak, skew and skew-normal distribution. A new scaling parameter; the product of average power input per unit mass P ρV T and ND 2 is proposed to define the regions where the four types of drop size distribution occur.

Prediction of Cloud Height for Solid Suspensions in Stirred Tanks

For solids loadings greater than 10 weight percent in a stirred tank, a clear interface may form towards the top of the vessel at what is known as the cloud height. Under these conditions, mixing between the lower solids rich volume (the cloud) and the upper clear volume is very limited. This is of critical importance in slurry catalyst reactor design, as the poor mixing in the clear layer will lead to large amounts of unreacted fluid. This investigation concentrates on developing a model for the prediction of the solids cloud height. The model is based upon two essential features of the flow: the velocity decay in the three-dimensional wall jets which form along the baffles, and the impeller speed required to fully suspend the solids off the bottom of the tank ( N js ).

Study of Macro-instabilities in Stirred Tanks Using a Velocity Decomposition Technique

In this paper a quantitative measure of errors introduced in the turbulent velocity RMS signal due to the presence of macroinstabilities (MI) in the velocity field is presented. The velocity time series were measured for four commonly used impellers (PBT, A310, HE3 and RT) with a one component LDV. Two locations in the tank, the impeller stream I and upper corner U, were studied. Three aspects of the geometry were varied: impeller diameter ( D = T/2 and D = T/4 ); number of baffles (two and four); and off-bottom clearance ( C/D = 1.0 and C/D = 0.5). By resampling and smoothing the velocity records the RMS velocity due to MI, υ MI , was determined. Further velocity decomposition recovered the high frequency component of the signal, υ HF , due to the randomfluctuations and the blade passages. Inclusion of the non-stationary, non-equilibrium MI component in the calculation of the RMS velocity can result in an overestimation of up to 50%. Analysis of the time series records shows that the MI is present in all configurations tested. In some cases (PBT and RT) the MI dominates the signal while for others (HE3 and A310) the amplitude of the signal is low and the MI is much less pronounced. The MI is very sensitive to geometry: for the impeller stream of the RT, increasing the number of baffles from two to four completely changes the velocity time series. The MI can have as dramatic an impact on experiments and analysis of the flow as the trailing vortices observed behind impeller blades. An understanding of this phenomenon is important for accurate analysis of the velocity and turbulence fields, for measurement of blend time and solids distribution, and for improving understanding of mesomixing.

The effect of geometry on the stability of flow patterns in stirred tanks

Abstract The stability of circulation patterns in stirred tanks was examined using tuft flow visualization. Tufts were placed throughout the tank and their direction was recorded continuously for 20 min. A direction coefficient, which allowed comparison of the stability between various tank geometries, was defined and measured. Using a two-level factorial design, the influence of four different geometric variables (impeller type, impeller diameter, off-bottom clearance and number of baffles) was examined. The impeller diameter, the number of baffles, and the interactions of the type of impeller with the number of baffles, and the type of impeller with off-bottom clearance affected the directional stability of the flow. This study has confirmed our understanding of time-varying phenomena in stirred tanks, and clarified the more complex interactions between elements of the geometry.

Limits of Fully Turbulent Flow in a Stirred Tank

Publisher Summary This chapter illustrates a new method for scaling velocities in a stirred tank in which the velocity profiles in the bulk of the tank are scaled with the characteristic velocity and length scale in the wall jet that is formed along the baffle of the tank.. Here the limit of fully developed turbulence is defined using the Reynolds number (Re), or the ratio of inertial to viscous forces. Using this Reynolds number the chapter illustrates that fully turbulent flow in the top third of the tank does not exist for Re I = 2 x 10 4 . This is important for design of vessels that have greater height than vessel diameter because the lack of fully turbulent flow means that the velocity profiles will be affected both by the characteristic velocity scale and the fluid viscosity. The chapter also describes some conditions that are required for the characterization of turbulence and the application of computational fluid dynamics (CFD) to conditions in the bulk of the tank. The power number and friction factor are used to define the onset of fully turbulent flow for their respective systems; however, the onset of fully turbulent flow can be more accurately determined using dimensionless velocity profiles. In fully turbulent flow, the dimensionless velocity profiles will collapse to a single similarity profile if the proper characteristic velocity and length scales are used. In the transitional regime, both inertial and viscous forces influence the velocity profiles and similarity no longer holds. The objective of this chapter is to carefully examine the limits of fully developed turbulence in the bulk of a stirred tank.