Characteristics and Stability Analyses of Transient One-Dimensional Two-Phase Flow Equations and Their Finite Difference Approximations

Lyczkowski, Robert W.; Gidaspow, Dimitri; Solbrig, C.W.; Hughes, E.D.

doi:10.13182/nse78-4

Cited by 161 publications

(76 citation statements)

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“…The variables to be computed are the volume fractions, e phases-1 , the liquid phase pressure P, and the phase horizontal velocity, x -direction, and vertical velocity, z -direction components, u phase and v phase. This leads to an unconditionally well-posed problem, as discussed in detail by Gidaspow(1994) and Lyczkowski, et al (1978).…”

Section: [ ] [ ]mentioning

confidence: 93%

University/Netl Student Partnership Program

Holder¹

2003

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Section: [ ] [ ]mentioning

confidence: 93%

University/Netl Student Partnership Program

Holder¹

2003

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“…The gradient of pressure is in the fluid (continuous) phase only. This leads to an unconditionally wellposed problem, as discussed in detail by and Lyczkowski, et al (1978). The details of this model can be found in Matonis (2000) and Matonis et al (2001).…”

Section: Hydrodynamic Modelmentioning

confidence: 95%

Computational and Experimental Modeling of Slurry Bubble Column Reactors

Lam¹,

Gamwo²,

Gidaspow³

2002

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The objective of this study was to develop a predictive experimentally verified computational fluid dynamics (CFD) model for gas-liquid-solid flow. A three dimensional transient computer code for the coupled Navier-Stokes equations for each phase was developed and is appended in this report. The principal input into the model is the viscosity of the particulate phase which was determined from a measurement of the random kinetic energy of the 800 micron glass beads and a Brookfield viscometer. The details are presented in the attached paper titled "CFD Simulation of Flow and Turbulence in a Slurry Bubble Column". This phase of the work is in press in a refereed journal (AIChE Journal, 2002) and was presented at the Fourth International Conference on Multiphase Flow (ICMF 2001) in New Orleans, May 27-June 1, 2001 (Paper No. 909).The computed time averaged particle velocities and concentrations agree with Particle Image Velocimetry (PIV) measurements of velocities and concentrations, obtained using a combination of gamma-ray and X-ray densitometers, in a slurry bubble column, operated in the bubbly-coalesced fluidization regime with continuos flow of water. Both the experiment and the simulation show a down-flow of particles in the center of the column and up-flow near the walls and nearly uniform particle concentration.Normal and shear Reynolds stresses were constructed from the computed instantaneous particle velocities. The PIV measurement and the simulation produced instantaneous particle velocities. The PIV measurement and the simulation produced similar nearly flat horizontal profiles of turbulent kinetic energy of particles. To better understand turbulence we studied fluidization in a liquid-solid bed. This work was also presented at the Fourth International Conference on Multiphase Flow (ICMF 2001, Paper No. 910).To understand turbulence in risers, measurements were done in the IIT riser with 530 micron glass beads using a PIV technique. This report summarizes the measurements and simulations completed so far. This work will continue under the sponsorship of the National Science Foundation and Dow Corning Corporation. This phase of the work is part of the DOE/Industry/University Multiphase Fluid Dynamics Research Consortium.Optimization of the LaPorte pilot plant reactor was attempted by rearranging the heat exchangers. The paper accepted for presentation at the Sixth World Congress of Chemical Engineering, Melbourne, Australia, September 23-27, 2001 is a part of this report.ii Disclaimer This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency therefor, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, pro...

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“…Moreover, performing the analysis of the eigenvalues of the partial differential system (9), it is found that wide ranges of the relevant physical parameters exist where these eigenvalues are complex, then revealing the nonhyperbolicity nature of the partial differential system (9). The loss of hyperbolicity causes instability during numerical integration (Garabedian, 1964;Bradford et al, 1997;Lyczkowski et al, 1978;Lee & Lyczkowski, 2000).…”

Section: The Case Of Two Immiscible Liquids With Constant Densitymentioning

confidence: 99%