Two-fluid modeling of cratering in a particle bed by a subsonic turbulent jet

Abstract

The Two-Fluid Method is capable of modeling large-scale (i.e., lab scale or larger) multiphase (particle-fluid) flows by treating both the fluid and particle phase as interpenetrating continua and solving mass and momentum balances for each phase. To solve for the flow of the solids phase the momentum balance requires constitutive relations in the form of normal and shear stresses ± i.e., pressures and viscosities. However, the stresses that account for frictional contacts in dense particle systems, and are relevant to this work, are empirically based. A study of the effects of adjusting the frictional model formulation (the empirical parameters of the model), by changing the overall frictional stress magnitude and the relative magnitude of the frictional viscosity to the frictional pressure, on the behavior of the bed is presented here. It was found that the magnitude of the frictional viscosity relative to the frictional pressure affects the crater growth prediction almost as much as the magnitude of the overall frictional stress. Additionally, a frictional model formulation is validated for sand particles, and predictions are compared with existing experimental data for the crater formation of a sand bed under a vertical, impinging jet of gas (Metzger et al. J Areo Eng (2008) v22, p24-32). In the low jet velocity regime (subsonic, turbulent jet), the model predicts the salient features previously measured for the growth rate of the crater of time, the profile of the crater, and the response of the crater to turning the jet off. In the high jet velocity regime (compressible, near sonic jet flow) the prediction agrees qualitatively with prior experimental observations.

How to generate valid local quantities of particle–fluid flows for establishing constitutive relations

“…P s increases consistently with increasing ε s . The present study did not observe the fast diverging trend with the frictional solid pressure relation 38 and this might be due to the particle properties and dynamic characteristic of the moving bed or the formulation of the relation. In the other branch (referred as B2 hereafter) P s decreases with increasing ε s when ε s > ~ 0.58 around the transition from the quasistatic to the intermediate regime, which is system dependent.…”

“…By the second one it is determined through the KTGG relation by using the average ε s , the radial distribution function g 0 , and the corresponding local granular temperature θ, or the critical state theory. 38 It is noted that the quantity corresponding to θ, obtained from the averaging method, is actually the fluctuating kinetic energy (k p ) which can be comparable to θ only in some special cases (e.g., average over the sample and no spatial resolution inside the sample). 39,40 In the following discussion θ is still used but the value is converted from k p by θ=2k p /3 for a simple comparison.…”

Fluid density effects in supersonic jet-induced cratering in a granular bed on a planetary body having an atmosphere in the continuum regime

“…the model of LaMarche et al. 2017) will not capture the true nature of the turbulent structures in the jet (see § 4.5 ) and thus the phenomenon of mini-crater formation may not be predicted.

Figure 15.Plots of plane views of for cases C1 ( a , d , g ), C4 ( b , e , h ) and C5 ( c , f , i ) at ( a – c ), 74 ( d – f ) and 124 ( g – i ).

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“…2012, 2015; LaMarche et al. 2017), albeit they have lower physical fidelity than those of Balakrishnan & Bellan (2018, 2019) in that they are either two-dimensional or do not account for all the underlying phenomena of relevance to the problem. A detailed discussion of these past studies can be found in Balakrishnan & Bellan (2018, 2019) and is not reproduced here, for brevity.…”

Improving Solid-Phase Fluidization Prediction in Circulating Fluidized Bed Risers: Drag Model Sensitivity and Turbulence Modeling

“…This methodology is best suited for situations where there is high particle concentration such as in industrial scale equipment [9]. Rather than dealing with particles individually, this framework averages out their motion while treating both solid and gas phases as interpenetrating continuums-also known as Eulerian-Eulerian or two-fluid model [10][11][12][13]. The E-E model has significantly lower computational demands compared to tracking a large number of individual particles using the Lagrangian methodology and monitoring each one's movement separately.…”