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43857-AC9
An Integrated Numerical and Experimental Study of Scaling Effects in Stirred Tank Reactors

David F. Hill, Pennsylvania State University

An Integrated Numerical and Experimental Study of Scaling Effects in Stirred Tank Reactors

Second Year Report

Overview

This project proposed to conduct an integrated numerical and experimental study of the turbulent flow in stirred tank reactors.  These flows are widely used in the chemical, petroleum, and environmental engineering industries.  Knowledge of the mean and turbulent velocity fields in these flows is important as the large and small scale flow structures help to control reaction and blending rates.  The work was motivated by the need to be able to scale up small laboratory-scale experimental results to full prototype scale.  Presently, the literature contains many experimental studies of these flows.  Aggregated together, the studies span a modest range of physical scale and operating conditions.  Individually, however, the studies are individually quite limited in terms of the range of parameter space covered.  As a result of differences in experimental configuration from one study to the next, which lead to differences in derived results, it is difficult to arrive at any substantive overall conclusions about the scaling of the flow field.  The funded project sought to conduct the most extensive set of scaling experiments to date.  In addition, computation simulations of the flow, using the experimental results, were performed.

Project Management

The funded project spans a period of two years, which ended in August 2008, with an unfunded extension presently ongoing.  The first year was conducted at the Pennsylvania State University, under the direction of Dr. D. Hill.  The second year was conducted at the University of Florida, under the direction of Dr. S. Balachandar.

Work Accomplished

1. We have completed our experimental work on the geometric and Reynolds number scaling.  Regarding the Reynolds number scaling, we have found that the mean velocity fields collapse well over a wide range of Re, as expected.  The turbulent velocity fields were found to approach Re invariance for values of Re > 100,000.  Regarding the geometric scaling, we found that the scaled results from the four differently sized experimental facilities did not collapse well, despite the extraordinary care taken to ensure exact geometric similarity in the facilities.  This relative lack of agreement was found both in the mean and in the turbulent velocity fields.

2. We performed extremely unique volumetric three-component (V3V) particle image velocimetry (PIV) measurements in our experimental facility.  This technique is able to measure the instantaneous velocity field over a finite three-dimensional volume, yielding an extremely dense grid of velocity data.  As Fig. 1 shows, these measurements allow, for the first time, the instantaneous visualization of the vortex pairs that are shed by the blade tips and that are responsible for the mixing in the tank.

Figure  SEQ Figure \* ARABIC 1: Isosurfaces (and slices) of vorticity, illustrating the vortices shed by the blade tips.

3. We have developed a versatile finite volume code that uses an immersed boundary (IB) technique.  This code has several attractive features that make it suitable for the investigation of complex geometries, such as the mixing tank, as in the present case.  We have conducted several direct numerical simulations to study the applicability of the code to present problem of a mixing tank with Rushton impellers.  During the ongoing unfunded extension of this project, we are actively working to make the code meet our final goal, which is to simulate a wide array of cases and find out the physical understanding for high Re turbulent flow in a mixing tank.  The improvements we are pursing include the use of Large Eddy Simulations (LES), fully parallelized MPI (message passing interface), scalar mixing, and the direct integration of the numerical and experimental results.

Figure  SEQ Figure \* ARABIC 2: Numerical simulation of the flow in a cylindrical tank stirred by a Rushton turbine.

Project Deliverables, Presentations, and Publications

1. Hill, D.F., Troolin, D., Walters, G., Lai, W., Sharp, K.V., 2008, “Volumetric three component velocimetry measurements of the turbulent flow in stirred tank reactors,” 14th International Symposium on Applications of Laser Techniques to Fluid Mechanics, July 7-10, Lisbon, Portugal.

2. Sharp, K.V., Hill, D.F., Troolin, D., Walters, G., Lai, W., 2008, "Volumetric 3-component velocimetry (V3V) measurements of the turbulent flow in stirred tank reactors," Experiments in Fluids, submitted.

3. Walters, G., 2008, “An investigation of geometric scaling of mean and turbulent flows in cylindrical stirred tank reactors,” The Pennsylvania State University, M.S. Thesis.
4. Vergara, A., Hill, D.F., 2008, “Destratification by mechanical mixers: mixing efficiency and flow scaling,” Penn State College of Engineering Research Symposium, April, University Park, PA.

5. Walters, G., Hill, D.F., 2008, “An investigation of geometric scaling of mean and turbulent flows in cylindrical stirred tank reactors,” Penn State College of Engineering Research Symposium, April, University Park, PA.

    

In addition to these, the PIs are presently drafting additional manuscripts for submission in 2009.

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