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SUMMARY:The effect of clusters on the heat transfer in gas-particle flows 
 - Stefanie Rauchenzauner\, Johannes Kepler University in Linz\, Austria
DTSTART:20221111T130000Z
DTEND:20221111T140000Z
UID:TALK192518@talks.cam.ac.uk
CONTACT:Rajesh Kumar Bhagat
DESCRIPTION:Moderately dense gas-particle flows represent a large number o
 f processes\, not only in chemical engineering. Reliable simulation predic
 tions are crucial in conception and optimization of reactors. Due to the l
 arge difference in scales\, from tens of meters in reactor dimensions to a
  few micro-meters in particle diameters\, and the large number of particle
 s involved\, Particle-Resolved Direct Numerical Simulations (PR-DNS) are u
 nfeasible even on current supercomputers. An approach\, which is suitable 
 for a large number of particles in the moderately dense regime is the Two-
 Fluid Model (TFM). Thereby\, both phases are treated as continua and the c
 ollisions between the particles are represented by a granular temperature\
 , which yields a stress-tensor in the Navier-Stokes equations [1]. The int
 erphase forces are modelled by correlations\, which are determined empiric
 ally or based on PR-DNS data. The TFM with these exchange forces was shown
  to yield good predictions for the flow variables on sufficiently fine gri
 ds\, with grid-spacings of a few particle diameters [2]. Coarser numerical
  grids\, however\, do not resolve meso-scale heterogeneous structures\, su
 ch as particle clusters\, which form due to an instability if a mean body 
 force is acting on the gas-particle flow. Thus\, using the (homogeneous) i
 nterphase exchange correlations leads to significantly wrong predictions o
 f the macro-scale flow properties\, such as fluidized bed expansion [3]\, 
 volume fraction and temperature distribution [4\,5]\, and\, consequentiall
 y\, reaction rates. \nIn order to model the influence of the heterogeneous
  meso-scale structures\, we apply spatial averages to the TFM balance equa
 tions and described each variable by their mean and fluctuating component.
  Thereby\, we found that the filtered drag force can be approximated by th
 e resolved drag force corrected by a drift velocity [4]. The drift velocit
 y is the gas-phase velocity as seen by the particles\, a measure for the s
 ub-filter heterogeneity of the flow. It can be expressed as a covariance b
 etween the solid volume fraction and the gas-phase velocity. We choose to 
 model this covariance by the variances of the variables scaled by a (linea
 r) correlation coefficient. Based on the scale-similarity theory\, we prop
 ose to estimate the values of the correlation coefficients locally and dyn
 amically through the application of test-filters [6]. In addition\, transp
 ort equations are derived for the variance of the solid volume fraction an
 d the phase velocities\, where the unresolved terms were closed using mode
 ls known from single-phase Large-Eddy-Simulation approaches. Thereby\, an 
 additional sub-filter fluctuating kinetic energy production term involving
  the drift velocity arises naturally. This is referred to as cluster-induc
 ed turbulence [7]. \nIn the later part of this talk\, the main focus is la
 id upon the filtered thermal energy balance equation. Thereby\, we found t
 hat the resolved interphase heat transfer can also be corrected by a const
 ruct similar to the drift velocity\, which we call the drift temperature [
 4]. Finally\, we give some outlook on how this approach can be extended to
  include mass transfer. \n\n\n\n\nReferences \n\n\n[1] C. K. K. Lun\, S. B
 . Savage\, D. J. Jeffrey\, and N. Chepurniy. Kinetic theories for granular
 \n      flow: Inelastic particles in Couette flow and slightly inelastic p
 articles in a general\n      flowfield. J. Fluid Mech.\, 140:223–256\, 1
 984.\n\n[2] W. D. Fullmer and C. M. Hrenya. Quantitative assessment of fin
 e-grid kinetic-theory-\n      based predictions of mean-slip in unbounded 
 fluidization. AIChE J.\, 62(1):11–17\, 2016.\n\n[3] S. Schneiderbauer an
 d S. Pirker. Filtered and heterogeneity based subgrid modifications\n     
  for gas-solid drag and solids stresses in bubbling fluidized beds. AIChE 
 J.\, 60(3):839–854\,       \n      2014.\n\n[4] S. Rauchenzauner and S. 
 Schneiderbauer. A dynamic anisotropic Spatially-Averaged\n      Two-Fluid 
 Model for moderately dense gas-particle flows. Int. J. Multiph. Flow\, 126
 :\n      103237\, 2020a.\n\n[5] S. Rauchenzauner and S. Schneiderbauer. A 
 Dynamic Spatially-Averaged Two-Fluid Model\n      for Heat Transport in Mo
 derately Dense Gas-Particle Flows. Phys. Fluids\, 32:063307\,\n      2020b
 .\n\n[6] D. K. Lilly. A proposed modification of the Germano subgrid-scale
  closure method. Phys.Fluids A\, 4(3):633–635\, 1992.\n\n[7] J. Capecela
 tro\, O. Desjardins\, and R. O. Fox. On fluid–particle dynamics in fully
  developed cluster-induced turbulence. J. Fluid Mech.\, 780:578–635\, 20
 15.\n
LOCATION:Centre for Mathematical Sciences\, meeting room MR14
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