Philip E. Wood

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.

Experimental investigation of vinyl chloride polymerization at high conversion: mechanism, kinetics and modelling

Abstract The mechanism of vinyl chloride (VCM) polymerization is discussed in detail from both a chemical and a physical point of view. A comprehensive kinetic model for VCM bulk/suspension polymerization is developed based on all of the important elementary reactions for two-phase polymerization. A series of kinetic experiments covering an extensive temperature range with different initiator systems was carried out in an agitated 51 batch reactor. Kinetic parameters were estimated by using these experimental data. The present model is in excellent agreement with experimental rate data measured in different laboratories and can be used to predict polymerization rate, conversion history and other kinetic features over the entire monomer conversion range.

Experimental and computational studies of the fluid mechanics in an opposed jet mixing head

The flow field created by two impinging liquid jets in a cylindrical chamber is investigated using particle tracing, laser Doppler anemometry, and three‐dimensional numerical simulation. The jet Reynolds number (based on the mean jet velocity and diameter) range is from 50–300. Results show that there is a threshold value of the Reynolds number beyond which the flow exhibits oscillations. Computer simulations agree well with the experimental visualizations, for both the overall observed flow pattern and a quantitative measure of the oscillations.

Auto-Acceleration Effect in Free Radical Polymerization. A Comparison of the CCS and MH Models

ABSTRACTA comparison of the structure and performance behaviour of two popular models for modelling diffusion-controlled kinetics in free radical polymerization (the so called Chiu-Carratt-Soong, CCS, and Marten-Hamielec, MH, models) is presented. It is demonstrated that if some modifications on their structure are made, and some of the most recent findings in this area are incorporated into them, a new model is obtained. This new model has at most the same degree of complexity as the preceding models, but is capable of producing more accurate and reliable predictions, even for weight average molecular weight at high conversions. Bulk and solution styrene polymerization data are used to make the comparison analysis and test the predictive power of the new model.

Batch Reactor Modelling of the Free Radical Copolymerization Kinetics of Styrene/Divinylbenzene Up to High Conversions

ABSTRACTAn effective model for the bulk, solution and suspension copolymerization of styrene/divinylbenzene has been developed. Experimental data from different sources and model predictions are in very good agreement in most cases for pre and post-gelation periods. The effects of solvent, chain transfer agent, inhibitor, type and concentration of crosslinker (m-DVB, p-DVB or a mixture of both), type and concentration of initiator, and temperature are accounted for by the present model.

Experimental investigation of vinyl chloride polymerization at high conversion: molecular-weight development

Abstract A comprehensive model for molecular-weight development during the suspension polymerization of vinyl chloride has been developed. The poly(vinyl chloride) (PVC) was characterized by low-angle laser light scattering (LALLS) and gel permeation chromatography calibrated using the results of LALLS measurements. Kinetic parameters were estimated using accumulated molecular weights measured at different conversions and polymerization temperatures. The present model is in excellent agreement with the experimental accumulated number-, weight- and Z -average molecular weights and distribution data over the entire conversion range. The mechanisms of termination and chain transfer and the effect of conversion, monomer and initiator concentrations and polymerization temperature on molecular-weight development are discussed in some detail. The present model predicts instantaneous molecular weights and distributions in each phase, the total instantaneous and accumulated molecular-weight averages, and instantaneous and accumulated molecular-weight distributions as functions of the reactor operational conditions, and can satisfactorily explain the kinetic features of PVC molecular-weight development.

Kinetic model-based experimental design of the polymerization conditions in suspension copolymerization of styrene/divinylbenzene

The use of a mechanistic model-based experimental design technique to determine the polymerization conditions and polymer properties in suspension copolymerization of styrene and divinylbenzene is reported. The technique consists of using a mathematical model to design the polymerization conditions of a copolymer with characteristics specified beforehand. The properties (conversion, gel content, molecular weight averages, and copolymer composition) of the copolymer synthesized using this approach agree very well with the calculated properties for the pregelation period, but accurate prediction of properties during the postgelation period is still uncertain. It is demonstrated that the use of mechanistic modeling for experimental design purposes can be more adequate (when the model is sound, yet simple to solve) than other design techniques (e.g., factorial designs).

Experimental investigation of vinyl chloride polymerization at high conversion : effect of polymerization conditions on polymer properties

Abstract A series of poly(vinyl chloride) (PVC) samples was synthesized under various polymerization conditions. It was found that the thermal stability of PVC as measured by dehydrochlorination rate is independent of monomer conversion when the conversion is less than X f (the conversion at the pressure drop). However, the dehydrochlorination rate increases significantly with conversion for conversions greater than X f . The thermal stability of PVC decreases with increase in polymerization temperature. These phenomena can be satisfactorily explained by accepted reaction mechanisms and diffusion-controlled kinetics. The reactions forming defect structures are favoured at low monomer concentrations. Therefore, the most effective way to minimize the formation of defect structures is to maintain monomer concentration as high as possible during polymerization after the pressure drop.

Experimental investigation of vinyl chloride polymerization at high conversion: semi-batch reactor modelling

Abstract A comprehensive semi-batch reactor model for suspension polymerization of vinyl chloride at high conversions has been developed. A series of kinetic experiments covering different pressure levels was carried out in a semi-batch process. The present model is in excellent agreement with the experimental data including monomer consumption, conversion history and accumulated number- and weight-average molecular weights and molecular weight distribution. The present model combined with our previous batch reactor model can be used to predict monomer feed rate, accumulated monomer consumption, polymerization rate, conversion history, reactor pressure, instantaneous and accumulated molecular weight averages and distribution and other kinetic features. The advantages of a semi-batch process operated at the vapour pressure of vinyl chloride include increased productivity, narrower molecular weight distributions and increased thermal stability of poly(vinyl chloride) (PVC) compared with a batch process taken to high conversions.