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Compressibility or incompressibility for gas-phase Navier-Stokes equations in fluidised beds? Why?

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Old   May 18, 2000, 17:34
Default Compressibility or incompressibility for gas-phase Navier-Stokes equations in fluidised beds? Why?
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Alberto Di Renzo
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I am a student of chemical engineering involved in studying fluidisetion process by simulating dynamically the motion of the two phase gas-solid numerically. Actually my problem is the choice of the model for gas phase equations (in the Navier-Stokes form); in particular whether I shall consider the gas flow as compressible (as I would say at first) or incompressible (as many CFD text that I consulted suggest for Mach<0.3 flow fields) and especially why???

For anyone who may answer, please consider that the discretisation in time is rather tight (about 10^-6 s) due to the characteristics of solid-phase model (Distinct Element Model) whilst discretisation in space is larger because of the need of a cell to contain a sufficient number of particles (about 10^-2 m side ). Until now I decided to choose a central difference scheme for the spatial derivatives and a three step explicit scheme for time integration, because the very small time step is already accurate for this unsteady problem; I would appreciate any comment on this as well. The fluid velocity is approximately in the range 0.5 - 10 m/s.

Thanks a lot
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Old   May 19, 2000, 22:53
Default Re: Compressibility or incompressibility for gas-phase Navier-Stokes equations in fluidised beds? Why?
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Jin Wook LEE
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Dear Alberto Di Renzo

You should consider your system as incompressible flow.

Your operating fluid(combustion gas) is, of course, compressible fluid. But, for CFD analysis, flow of compressible fluid does not mean compressible flow. Compressibility effect is only significant when velocity is very large(e.g., M>0.3) and/or pressure gradient is very large(i.e., dP/P is not negligible). I am not expert of compressible flow, but I can say that dominant compressible effect is :

- viscous effect : energy change by velocity gradient - pressure effect : energy change by pressure gradient

I am sure that the effect of compressibility in the fluidized bed system is negligible.

Sincerely, Jinwook

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Old   May 22, 2000, 01:12
Default Re: Compressibility or incompressibility for gas-phase Navier-Stokes equations in fluidised beds? Why?
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Abhijit Tilak
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Hi,

I solved a similar problem of pulverized coal combustion for my masters thesis. As rightly pointed out by Jin wook, s such flow's are incompressible, HOWEVER are variable density flows.I used the Eulerian model by Zaichik for gas-particle flow although in quiet simplified form ( appeared in Experimental Thermal and Fluid Science 1997, vol and pg i don't remember.)There are two papers, one for isothermal and other for combusting flow. I used hybrid scheme for convection.I also required time step of 1e-6 , which came to 1e-3 for particle dia of 70micron, the larger the particle size smaller the time step. because the source terms increase with particle size as the drag increases. let me know if u need any info.
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