Turbulent mixing with multiple second‐order chemical reactions

Heeb, Thomas; Brodkey, Robert S.

doi:10.1002/aic.690361002

Cited by 29 publications

(12 citation statements)

References 19 publications

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“…The data from these experiments was compared with predictions of mechanistic models such as the slab diffusion model (Mao and Toor, 1971). Heeb (1986) carried out experiments with a polymerization reaction. The work was rather inconclusive, however, but led to suggestions of potentially better systems.…”

Section: Aiche Journalmentioning

confidence: 99%

Direct numerical simulation of chemical selectivity in homogenous turbulence

Chakrabarti¹,

Kerr²,

Hill³

1995

AIChE Journal

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(Nauman, 1975), and the nitration of aromatic hydrocarbons with nitronium salts (Pfister et al., 1975) are some examples of reaction schemes exhibiting seriesparallel behavior. The results of manufacturing the wrong distribution of products are a waste of raw materials and also an increased load on the separation stages to extract the desired product in pure form. Such considerations are also important in air-pollution, propulsion, and combustion problems, which involve a wide range of complex multiple reactions.Except for combustion studies, the principal fundamental experimental work on turbulent reacting flows with complex chemistry has been carried out by Bourne (1981) who studied a particular series-parallel reaction system-the diazo-coupling reaction, now referred to as Bourne's reaction. Several 2356November 1995 subsequent experimental studies (Li and Toor, 1986;Mehta and Tarbell, 1987) have made use of Bourne's reaction. It should be noted that in Bourne's reaction, the first reaction is very fast compared to the second. Since most experimental studies were limited to just this particular reaction system, knowledge about turbulent flow with multiple reactions has been extremely limited. Advances in the power and speed of computers have now made it possible to directly solve the equations for turbulent reacting flows at low to moderate Reynolds numbers. In direct numerical simulations (DNS), the nonlinear dynamical equations are solved with no turbulence modeling and with all time and length scales well-resolved. Direct numerical simulations of three-dimensional chemically reacting homogenous turbulent flow for unmixed reactants in a single step, finite rate reaction have been made by Givi and McMurtry (1988), Leonard and Hill (1988, 1989, 1991 and Me11 et al. (1993). Some preliminary investigations on the effect of various physical and chemical parameters for the seriesparallel reaction case have been made by Chakrabarti and Hill (1990) for decaying homogenous turbulence and by Gao and O'Brien (1991) for a forced turbulent flow.In the present study, described in more detail by Chakrabarti (19911, DNS of a series-parallel reaction pair in a decaying, homogenous turbulent flow was used to predict the product distribution in the problem of chemical selectivity and to help explain the interaction of turbulence, mixing, Vol. 41, No. 11AIChE Journal and complex chemistry in this problem. The effect of turbulence, compared to the case with no motion, was studied by examining the variations of product distributions with turbulence intensity and viscosity, that is, by varying the turbulence Reynolds number. The effects of other physical parameters such as Schmidt numbers, diffusivities, reaction rate constants, -initial stoichiometric ratios, and initial scalar field conditions were also studied. Comparisons between the single reaction and the series-parallel reaction systems were made to better understand the complexity introduced by a two-step chemical reaction. These results are used in a forthcoming arti...

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Section: Aiche Journalmentioning

confidence: 99%

Direct numerical simulation of chemical selectivity in homogenous turbulence

Chakrabarti¹,

Kerr²,

Hill³

1995

AIChE Journal

View full text Add to dashboard Cite

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“…When chemical reactions are involved, modeling the higher-order moments of scalar fields can be extremely difficult. The arbitrariness of such modeling is illustrated in several papers (e.g., Heeb and Brodkey, 1990;Leonard et al, 1995). The presumed PDF method (Bilger, 1980;Jones and Whitelaw, 1982;Girimaji, 1991;Fox, 1996) presents a major step towards overcoming the moment closure problem.…”

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confidence: 99%

“…Unfortunately, nor is there any other simple relation that is valid in general. For example, the predictions of even the most sophisticated moment closure (Heeb and Brodkey, 1990) for the 'relatively simple two-step consecutive (or competitive) reaction are unsatisfactory. Thus, given the complexity of the LDPE polymerization, moment closure approaches are likely to be inadequate.…”

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confidence: 99%

PDF modeling of turbulent‐mixing effects on initiator efficiency in a tubular LDPE reactor

Tsai

Fox

1996

AIChE Journal

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“…Ever since Toor and coworkers (Vassilatos and Toor, 1965;Toor, 1969;Mao and Toor, 197 1 ;Li and Toor, 1986) 6% defined methods for relating reaction conversion for nonpremixed reactants to their degree of mixing, workers in the field of mixed chemical reactors have attempted to build upon and refine their analysis, which was based on the use of an assumed probability density function (PDF) for reactant concentration (see Kosaly, 198 1;Brodkey and Lewalle, 1985;Baldyga, 1994;Baldyga and Henczka, 1995), or develop alternatives to improve on the approach (Heeb and Brodkey, 1990). Pope (1985) presented an extensive review of PDF methods for mixed reaction closure.…”

Section: Numerical Simulation Of Turbulent Mixing With Reactionmentioning

confidence: 99%

Experimental measurements and simulation of mixing and chemical reaction in a stirred tank

Zipp

Patterson

1998

Can J Chem Eng

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Effects of mixing on the rate of second-order chemical reactions have been studied by measuring the time-average degree of conversion at enough points in a steady-state, continuous-flow stirred reactor to provide comparisons with numerical simulations of the same reactions using a standard Reynolds-averaged turbulence simulation code with an added closure. The reactants were introduced in widely separated feed streams in order to provide a difficult test for the measurements and simulations. Concentration and segregation measurements were made with two fluorescence based methods -one remote and one using a fiber optic probe. The rates of mixing and reaction were simulated using the Corrsin mixing term and the Spalding segregation production term with the Paired-Interaction reaction closure term.On a CtudiC les effets du mClange sur la cinttique des rkactions chimiques de deuxikme ordre en mesurant le degrC de conversion moyennC dans le temps pour un nombre impotant de points dans un rCacteur agitC ti Ccoulement continu en rCgime permanent. Ces effets mesurts ont Ct C cornparks B des simulations numCriques effectuCs avec un code de simulation de la turbulence de Reynolds moyenne classique muni d'une condition de cl8ture. Les rkactifs ont Ct C introduits dans des courants d'alimentation largement sCparCs afin de fournir un test difficile pour les mesures et simulations. he importance of turbulent mixing in chemical process-T ing cannot be overstated. Advantage is taken of this process in many diverse areas, such as fermentation, separation, dispersion, combustion, and other chemical reactions.In chemical reactors the turbulent motion is responsible for bringing reactants together rapidly so that reaction can occur and is responsible for dispersing the products of the reaction. For fast reactions the mixing rate frequently controls the reaction rate, and for multiple reactions the mixing rate and its spatial variation relative to reactive feed points controls the product yield.The turbulent mixing process generally can be viewed as taking place in three stages. The first stage is convective transport caused by the flow which leads to large scale blending. In the second stage of mixing, dispersion, the turbulence -primarily in the form of vortices of various scales -spreads and stretches the fluid, reducing large unmixed (segregated) regions of fluid to smaller, thinner unmixed regions of fluid. Bakker and van den Akker( 1994a and 1994b) have discussed in depth the importance of the vortices in the mixing process and, in particular, the effects of the small high energy vortices in mixed reactors. The effect of the vortex stretching is to reduce the scale of segregation, to increase the relative concentration gradients between regions of unmixed fluids, and to increase the surface area defined by surfaces of constant concentration of one of the mixing components. In the third stage molecular diffusion causes the final homogenization of fluids on a molecular scale. This reduces the magnitude of the concentration variat...

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Turbulent mixing with multiple second‐order chemical reactions

Cited by 29 publications

References 19 publications

Direct numerical simulation of chemical selectivity in homogenous turbulence

Direct numerical simulation of chemical selectivity in homogenous turbulence

PDF modeling of turbulent‐mixing effects on initiator efficiency in a tubular LDPE reactor

Experimental measurements and simulation of mixing and chemical reaction in a stirred tank

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