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  • 1
    Electronic Resource
    Electronic Resource
    On the liquid flow distribution in trickle-bed reactors (1987)
    s.l. : American Chemical Society
    Industrial & engineering chemistry research 26 (1987), S. 2413-2419 
    Details
    ISSN: 1520-5045
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ie00072a004
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  • 2
    Electronic Resource
    Electronic Resource
    The spectral relaxation model of the scalar dissipation rate in homogeneous turbulence (1995)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 7 (1995), S. 1082-1094 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A model for the effect of scalar spectral relaxation on the scalar dissipation rate of an inert, passive scalar (Sc≥1) in fully developed homogeneous turbulence is presented. In the model, wave-number space is divided into a finite number [the total number depending on the turbulence Reynolds number Reλ and the Schmidt number (Sc)] of intermediate stages whose time constants are determined from the velocity spectrum. The model accounts for the evolution of the scalar spectrum from an arbitrary initial shape to its fully developed form and its effect on the scalar dissipation rate for finite Reλ and Sc≥1. Corrsin's result [AIChE J. 10, 870 (1964)] for the scalar mixing time is attained for large Reλ in the presence of a constant mean scalar gradient and a stationary, isotropic turbulence field. Comparisons with DNS results for stationary, isotropic turbulence and experimental data for decaying, homogeneous grid turbulence demonstrate the satisfactory performance of the model. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868550
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  • 3
    Electronic Resource
    Electronic Resource
    The Lagrangian spectral relaxation model of the scalar dissipation in homogeneous turbulence (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 2364-2386 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Lagrangian pdf methods are employed to extend the spectral relaxation (SR) model of the scalar dissipation of an inert, passive scalar (1≤Sc) in homogeneous turbulence. The Lagrangian spectral relaxation (LSR) model divides wavenumber space into a finite number (the total number depending on the Taylor-scale Reynolds number Rλ and the Schmidt number Sc) of wavenumber bands whose time constants are determined from the mean turbulent kinetic energy and instantaneous turbulent energy dissipation rate. The LSR model accounts for the evolution of the scalar spectrum (viz., pdf) from an arbitrary initial shape to its fully developed form. The effect of turbulent-frequency fluctuations on the instantaneous scalar dissipation rate following a Kolmogorov-scale fluid particle is incorporated into the LSR model through a Lagrangian pdf model for the turbulent frequency. Model results are compared with DNS data for passive scalar mixing in stationary, isotropic turbulence. Two distinct causes of non-Gaussian scalar statistics are investigated: small-scale intermittency due to scalar-dissipation fluctuations at scales near the Kolmogorov scale, and transient large-scale inhomogeneities due to the form of the initial scalar spectrum at scales near the integral scale. Despite the absence of fitting parameters, the LSR model shows satisfactory agreement with available DNS data for both types of flows. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869357
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  • 4
    Electronic Resource
    Electronic Resource
    On velocity-conditioned scalar mixing in homogeneous turbulence (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 2678-2691 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Scalar mixing models are required to model turbulent molecular mixing in full probability density function (pdf) simulations of turbulent reacting flows. Despite the existence of direct numerical simulation (DNS) data suggesting the contrary, most scalar mixing models assume that molecular mixing is independent of the instantaneous velocity, i.e., 〈D∇2φ|V,ψ〉=〈D∇2φ|ψ〉. Since in a joint velocity, composition pdf calculation the velocity is known, this assumption is unnecessary and leads to a lack of local isotropy in the scalar field. Moreover, since velocity conditioning offers a numerically tractable approach for including the effects of local anisotropy and mean velocity gradients on scalar mixing, it should be of considerable interest for the numerical simulation of scalar mixing in inhomogeneous turbulent flows. An efficient numerical implementation of velocity-conditioned scalar mixing for full pdf simulations is proposed and verified against DNS data for homogeneous turbulence (isotropic and shear flow) with a uniform mean scalar gradient. A second-moment closure relating the velocity-conditioned scalar dissipation to the scalar fluxes and Reynolds stresses that is exact in the limit of a joint Gaussian pdf is also derived for use with moment closure models. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869054
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  • 5
    Electronic Resource
    Electronic Resource
    The Fokker–Planck closure for turbulent molecular mixing: Passive scalars (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 1230-1244 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A turbulent-molecular-mixing closure for passive scalar mixing is derived based on the theory of diffusion in layerlike lamellar structures. The closure is formulated in terms of the Fokker–Planck (FP) equation (or an equivalent stochastic differential equation), and is to be employed in conjunction with the probability density function (pdf) balance equation appearing in the pdf methods for modeling turbulent reactive flows. Like the mapping closure, the FP closure predicts a limiting Gaussian pdf for the passive scalar concentration in isotropic turbulence. In addition, the FP closure models the joint pdf of the scalar concentration and the scalar gradient and thus predicts the scalar dissipation rate. The closure predictions for the scalar rms concentration, the marginal pdf, and the joint pdf as well as other relevant statistics have been studied by Monte Carlo simulation. The shape and temporal evolution of the marginal pdf for the scalar concentration compare favorably with published results found from direct numerical simulations and from the mapping closure. Finally, unlike the mapping closure, the FP closure is shown to easily extend to the case of multiple scalar mixing.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858241
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  • 6
    Electronic Resource
    Electronic Resource
    Improved Fokker–Planck model for the joint scalar, scalar gradient PDF (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 334-348 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The joint scalar, scalar gradient probability density function (PDF) of an inert nonpremixed scalar diffusing in a one-dimensional system of random-sized lamellas is investigated by numerical simulation. The form of the scalar PDF, at a given RMS value, is nearly identical to that predicted by direct numerical simulation (DNS) of scalar mixing in isotropic turbulence and the mapping closure, and the moments of both the scalar and the scalar gradient suggest that their limiting marginal PDF are Gaussian. The joint scalar, scalar gradient PDF is found to be restricted to a bounded region in the scalar–scalar gradient plane, whose form is independent of the initial mixing ratio. These results are incorporated into the Fokker–Planck (FP) model for the joint scalar, scalar gradient PDF, and the improved model shows good agreement with numerical simulation data. An extension of the FP model that includes random stretching of the scalar gradient in isotropic turbulence is formulated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868088
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  • 7
    Electronic Resource
    Electronic Resource
    The Lagrangian spectral relaxation model for differential diffusion in homogeneous turbulence (1999)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 11 (1999), S. 1550-1571 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The Lagrangian spectral relaxation (LSR) model is extended to treat turbulent mixing of two passive scalars (φα and φβ) with different molecular diffusivity coefficients (i.e., differential-diffusion effects). Because of the multiscale description employed in the LSR model, the scale dependence of differential-diffusion effects is described explicitly, including the generation of scalar decorrelation at small scales and its backscatter to large scales. The model is validated against DNS data for differential diffusion of Gaussian scalars in forced, isotropic turbulence at four values of the turbulence Reynolds number (Rλ=38, 90, 160, and 230) with and without uniform mean scalar gradients. The explicit Reynolds and Schmidt number dependencies of the model parameters allows for the determination of the Re (integral-scale Reynolds number) and Sc (Schmidt number) scaling of the scalar difference z=φα−φβ. For example, its variance is shown to scale like 〈z2〉∼Re−0.3. The rate of backscatter (βD) from the diffusive scales towards the large scales is found to be the key parameter in the model. In particular, it is shown that βD must be an increasing function of the Schmidt number for Sc≤1 in order to predict the correct scalar-to-mechanical time-scale ratios, and the correct long-time scalar decorrelation rate in the absence of uniform mean scalar gradients. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870018
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  • 8
    Electronic Resource
    Electronic Resource
    The charge density in polymorph II of 5,5-diethylbarbituric acid (barbital) at 198 K (1982)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 1942-1952 
    Details
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S056774088200764X
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  • 9
    Electronic Resource
    Electronic Resource
    The neutron crystal structure at –75°C of polymorph II of 5,5-diethylbarbituric acid (barbital) (1978)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 3719-3722 
    Details
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567740878011954
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  • 10
    Electronic Resource
    Electronic Resource
    Stochastic modeling of a fluidized-bed reactor (1985)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 31 (1985), S. 992-998 
    Details
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: In this work dispersive mixing and chemical reactions are treated simultaneously by resorting to the theory of stochastic processes. A fluidized-bed reactor is modeled by discretizing it into ideally stirred tanks of various sizes corresponding to bubble, cloud, and emulsion phases. All parameters in the model are correlated with known or experimentally obtainable quantities. Examples using a complex chemical reaction are given to demonstrate the applicability of the approach.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690310616
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