From a2c671bfc9906963c5c18e6172e7fd1c9ebcf391 Mon Sep 17 00:00:00 2001 From: William Fullmer Date: Mon, 11 Nov 2019 11:18:51 -0500 Subject: [PATCH] first pass of QB chapter - Qualitative Benchmarks --- docs/source/index.rst | 1 + docs/source/qb/biseg.rst | 18 ++++ docs/source/qb/figs/boyce_sb_1908_small.png | Bin 0 -> 352070 bytes docs/source/qb/figs/granRT_1908_small.png | Bin 0 -> 345199 bytes docs/source/qb/figs/hcs_ke_1908.png | Bin 0 -> 5980 bytes docs/source/qb/figs/hcs_xy_1908.png | Bin 0 -> 973089 bytes docs/source/qb/figs/mehrdad_1908_small.png | Bin 0 -> 183844 bytes docs/source/qb/figs/netl_biseg_1908_small.png | Bin 0 -> 546542 bytes docs/source/qb/granRT.rst | 84 ++++++++++++++++++ docs/source/qb/hcs.rst | 84 ++++++++++++++++++ docs/source/qb/index.rst | 28 ++++++ docs/source/qb/mehrdadsbed.rst | 54 +++++++++++ docs/source/qb/refs.rst | 82 +++++++++++++++++ docs/source/qb/single_bubble.rst | 75 ++++++++++++++++ 14 files changed, 426 insertions(+) create mode 100644 docs/source/qb/biseg.rst create mode 100644 docs/source/qb/figs/boyce_sb_1908_small.png create mode 100644 docs/source/qb/figs/granRT_1908_small.png create mode 100644 docs/source/qb/figs/hcs_ke_1908.png create mode 100644 docs/source/qb/figs/hcs_xy_1908.png create mode 100644 docs/source/qb/figs/mehrdad_1908_small.png create mode 100644 docs/source/qb/figs/netl_biseg_1908_small.png create mode 100644 docs/source/qb/granRT.rst create mode 100644 docs/source/qb/hcs.rst create mode 100644 docs/source/qb/index.rst create mode 100644 docs/source/qb/mehrdadsbed.rst create mode 100644 docs/source/qb/refs.rst create mode 100644 docs/source/qb/single_bubble.rst diff --git a/docs/source/index.rst b/docs/source/index.rst index f1c57b7..9dc5462 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -29,6 +29,7 @@ the master branch at the beginning of each month. EB CITests NightlyTests + qb/index Debugging Notice diff --git a/docs/source/qb/biseg.rst b/docs/source/qb/biseg.rst new file mode 100644 index 0000000..2c01430 --- /dev/null +++ b/docs/source/qb/biseg.rst @@ -0,0 +1,18 @@ +.. _Chap:QB:biseg: + +Bidisperse Segregation +====================== + +wdf TODO ASAP + + +.. figure:: figs/netl_biseg_1908_small.png + :width: 16cm + :align: center + :alt: Sim comparison to bidisperse segregation experiment at NETL + + Comparison of experiment and MFiX-Exa simulaton for rapid segregation + of a bi-disperse particle mixture. + + + diff --git a/docs/source/qb/figs/boyce_sb_1908_small.png b/docs/source/qb/figs/boyce_sb_1908_small.png new file mode 100644 index 0000000000000000000000000000000000000000..22719f189ffedbe43237b7d81de0470a57a3ee04 GIT binary patch literal 352070 zcmeAS@N?(olHy`uVBq!ia0y~yU|z+*z!b#6#=yY1_bi780|NtNage(c!@6@aFBupZ zSkfJR9T^xl_H+M9WMyDr;4JWnEM{O3dj-ObPy3t&7#RL9^>lFzsfc?M%eq7K>aDoV 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of all multi-phase +flow instabilities [C81]_. The prototypical case involves two (traditional) +fluids at rest of differing densities with the heavier fluid being accelerated +into the lighter fluid. The instability manifests itself in a deformation of +the interface between the two fluids. The initial deformation grows into an +interpenetrating fingering pattern, commonly producing a mushroom cloud +pattern, before giving way to micro-scale mixing or bubble-droplet formation +if the fluids are immiscible. + + +Vinningland and coworkers [VJFTM07]_ devised a granular analogue of the classic +problem in which the heavier "fluid" is an assembly of particles penetrating +into a gas, in this case air. The particle assembly is generated by settling +under gravity into a random close packed array in a Hele-Shaw cell +(rectangular enclosure) which is quickly inverted around a pivot to bring the +heavier particle phase above the lighter gas phase. The instability evolution +is distinct from the classic fluid-fluid RT, which is described by +Vinningland et al. [VJFTM07]_: + + .. line-block:: + + The initially flat front defined by the grains subsequently develops + into a pattern of falling granular fingers separated by rising bubbles + of air. A transient coarsening of the front is observed right from the + start by a finger merging process. The coarsening is later stabilized + by new fingers growing from the center of the rising bubbles. + + +The granular-RT is simulated with MFiX-Exa 19.08 with the following setup. +The domain is 56 mm wide by 68 mm tall and 1 mm deep which is discretized +by a uniform mesh of :math:`224 \times 272 \times 4` CFD cells. No-slip walls +are applied at top, bottom, left and right domain extents. +The front and back walls are "removed" and treated as periodic in the +simulation as the depth is only resolved by four CFD cells. +No additional geometry definition is required. +The particles are assumed monodisperse with a constant diameter of +:math:`d_p = 140` microns (:math:`dx^* \approx 1.8`) and density of +:math:`\rho_p = 1050` kg/m\ :sup:`3` \. The resitution and sliding friction +coefficients are set to 0.9 and 0.25, which are believed to be representative +of the polystyrene material. The Wen and Yu drag law [WY66]_ is applied. +1.12M particles are initially randomly distributed throughout the domain. +The gravity force on the particles is modified by :math:`\tanh 100(t - 2)` +so that the particles initially settle upwards, and then the body force is +quickly inverted around :math:`t = 2` s, causing the particles to fall +downward into the quiescent air. + + +.. figure:: figs/granRT_1908_small.png + :width: 16cm + :align: center + :alt: Sim comparison to granular Rayleigh-Taylor experiment + + Progression of the granular Rayleigh-Taylor instability in the experiments + of Vinningland et al. [VJFTM07]_ (top row) + compared to the MFiX-Exa result (bottom row). + + +The figure above shows the progression of an MFiX-Exa 19.08 simulation compared +to the experimental results. There is a good match between the experimental and +numerical results for roughly the first half of the transien: an initially flat +interface gives way to many fingers falling into the gas which merge and form +a semi-stable bubble pattern. However, the simulated bubbles appear to be less +stable than those in the lab, which rise uniformily to the surface. However, in +the simulations the center bubble rises slighlty faster than the one on the +left, which shifts more weight over the left-hand bubble, which further impedes +its rise and eventually "squishes" the left-hand bubble into the center bubble +as it breaks the surface. Later, the right hand bubble also merges with (what +remains of) the center bubble, allowing a path of least resistance for its air +to escape without rupturing on the surface on its own. The bubble merging +significantly accelerates the second half of the transient (notice the +different times between experiment and simulation). Several different +variations of this setup were performed: different drag laws, slower inversion +time, different combinations of particle restitution and friction coefficients, +inclusion of front and back walls. Although all tests were slighlty different, +none were able to match the stability of the later time bubble pattern observed +experimentally. + + diff --git a/docs/source/qb/hcs.rst b/docs/source/qb/hcs.rst new file mode 100644 index 0000000..59332ca --- /dev/null +++ b/docs/source/qb/hcs.rst @@ -0,0 +1,84 @@ +.. _Chap:QB:hcs: + +Clustering in the HCS +====================== + + +The HCS is the simplest non-trivial particulate gas-solid system. The continuum +gas-phase is initially at rest. The particles are uniformily distributed in space +and have zero momentum in all three directions. However, the particle pecular +velocity is non-zero, quantified by an initial *granular* temperature, +:math:`T_0`. The system is periodic in all direcitons and no external forces act +on the system. Under homogeneous conditions, the granular temperature, :math:`T`, +is equivalent to two-thirds of the the (massless) mean particle kinetic energy. +In the HCS, the Eulerian kinetic theory (KT) model of Garzo et al. [GTSH12]_ +reduces to: + +.. math:: + \frac{dT}{dt} = - \frac{2 \gamma}{m} T - \zeta_0 T + +where :math:`m` is the particle mass, :math:`\gamma` is the thermal drag and +:math:`\zeta_0` is the zeroth-order cooling rate. The first term on the RHS +above represents viscous dissipation due to the interstitial gas while the +second term represents collisional dissipation due inelastic particle-particle +interactions. The ODE has an analytical solution given by Yin et al. [YZMH13]_ +(also see [LBFHHGS16]_ for the exact model used herein which also includes a +first-order thermal Reynolds number extension to :math:`\gamma`). In the absence +of clustering, the granular temperature in the HCS decays according to the +analytical solution, known as Haff's law [H83]_ in granular systems: +:math:`\gamma = 0`. However, at a critical system size [G05]_, :math:`L^*_c`, +(where :math:`L^* = L/d_p`), the initially homogeneous state gives way to the +most fundamental of gas-solid instabilities, the clustering instability, which +causes :math:`T` (or more accurately :math:`KE`) to deviate significantly from +KT solution due to regions of high and low concentration and correlated motion. + + +To test if MFiX-Exa predicts the expected clustering behavior, a system is set up +with the following non-dimensional parameters: + + * initial thermal Reynolds number: :math:`Re_{T_0} = \rho_g d_p \sqrt{T_0} / \mu_g = 20` + * density ratio: :math:`\rho^* = \rho_p / \rho_g = 1000` + * restitution coefficient: :math:`e = 0.8` + * solids concentration: :math:`\phi = \pi N_p / 6 L^*_x L^*_y L^*_z \approx 0.05` + +While not specifically studied by Fullmer et al. [FLYH18]_, their results +indicate that :math:`L_c^*` may be as large as 50 to 70 at these conditions. +In order to avoid the region near critical stability, we use a significnatly +larger system size: :math:`L^*_x = L^*_y = 256`. The system is thin in the +depth dimension, :math:`L^*_z = 8` in order to highlight the clustering +phenomena. Therefore, :math:`N_p = 50000`. Because the system is hypothetical, +the ideal ``BVK2`` DNS drag law is applied, see [BvK07]_, [TPKKv15]_. + + +.. figure:: figs/hcs_ke_1908.png + :width: 8cm + :align: center + :alt: kinetic energy decay in the HCS + + Decay of the particle mean kinetic energy compared to the KT analytical + soluiton of the GTSH model. + + +Three replicate systems are simulated with MFiX-Exa 19.08, differing only +in initial particle locations and pecular velocities. The particle kinetic +energy is averaged in the simulations (red) and compared to the analytical +granular temperature (black) of the HCS as a funciton of time in the figure +above. The kinetic energy :math:`KE / KE_0` decays by two to three orders of +magnitude in line with the HCS result until clustering and localized mean +motion cause a drastic deviation. The final result at :math:`t^* = 1000` +for one of the replicates is shown below (at right) compared to the seminal +result of Goldhirsch and Zanetti [GZ93]_ (true 2D), the original demonstration +of the clustering instability the HCS. + + +.. figure:: figs/hcs_xy_1908.png + :width: 12cm + :align: center + :alt: clustered state of the HCS + + Clustered state of the HCS observed by Goldhirsch and Zanetti [GZ93]_ + (left) compared to an MFiX-Exa result (right). + + + + diff --git a/docs/source/qb/index.rst b/docs/source/qb/index.rst new file mode 100644 index 0000000..22ffd29 --- /dev/null +++ b/docs/source/qb/index.rst @@ -0,0 +1,28 @@ +.. _Chap:QB: + +Qualitative Benchmarks +====================== + +MFiX-Exa uses a three level approach to regression testing spaning from simple +and/or short smoke tests to validation problems comparing against experimental +data. Most of the validation benchmarks target the physics of interest to +MFiX-Exa's intended audience, i.e., dense bubbling, fast fluidization and +pneumatic transport of particulate solids by a light gas. In an effort to widen +the phase-space in which MFiX-Exa may be (potentially) applied, a set of +qualitative benchmark problems are provided below which focus more on the +phenomenology of a given, problem rather than averaged statistical measures. +Animations of numerical soluitons to several of the qualitative benchmarks +can be seen in the +`Gallery `_ + + +.. toctree:: + :maxdepth: 1 + + hcs + granRT + mehrdadsbed + single_bubble + biseg + refs + diff --git a/docs/source/qb/mehrdadsbed.rst b/docs/source/qb/mehrdadsbed.rst new file mode 100644 index 0000000..ae35958 --- /dev/null +++ b/docs/source/qb/mehrdadsbed.rst @@ -0,0 +1,54 @@ +.. _Chap:QB:mehrdad: + +Mehrdad's Bed +============= + +Typically, bubbling fluidized beds are produced by uniformily--in space and +time--driving a gas flow through a particle bed. Slightly different bubbling +patterns are observed depending largely on the Geldart classification [G73]_ +of the particles and the size of the bed. Like gas bubbles in a liquid bed, +the dynamics are almost always highly irregular and chaotic in nature. +However, by periodically driving the gas flow, chaotic bubbling can be +suppressed yeilding quasi-regular periodic bubbling [PB98]_. Studying bubble +control methods, Coppens and coworkers [Cv03]_ realized that periodic bubbling +produces starkly regular patterns in thin beds, which may be useful for code +validation [WdLC16]_. Shahnam and coworkers took the problem even further and +reducing the latteral dimension to produce an oscillating Left-Right single +bubble pattern in a setup affectionately referred to as *Mehrdad's bed* [S18]_. + + +Mehrdad's bed is a rectangular geometry of width :math:`L_x` = 50 mm, +height :math:`L_y` = 160 mm, and depth :math:`L_z` = 5 mm. The domain is +resolved by a uniform CFD grid of :math:`80 \times 256 \times 8`. No-slip walls +are applied on the vertical domain extents with a mass inflow at the bottom and +a pressure outflow at the top of the domain. The mass inflow is defined in +`usr1.f90` as: + +.. code:: fortran + + real(rt), intent(in ) :: time + real(rt) :: usr_pi, usr_umf + + usr_pi = 4.0d0*ATAN(1.0d0) + usr_umf = MIN(0.15d0, 0.1d0*time) + + bc_u_g(1) = usr_umf*(1.3d0 + 0.7d0*DSIN(10.0d0*usr_pi*time)) + +The bed consists of 188500 particles which are assumed to be monodisperse with +constant diameter and density of :math:`d_p = 400` microns and +:math:`\rho_p = 2500` kg/m\ :sup:`3` \, respectively. + + +.. figure:: figs/mehrdad_1908_small.png + :width: 16cm + :align: center + :alt: Sim comparison to Mehrdad's experiment + + Comparison of the experiment (middle two rows) to the MFiX-Exa simulation + (top and bottom rows). + +The bed is simulated using MFiX-Exa 19.08 for an initial transient period of +10 s before an observation window of an additional 5 s. The desired left-right +pattern is seen as shown in the figure above. + + diff --git a/docs/source/qb/refs.rst b/docs/source/qb/refs.rst new file mode 100644 index 0000000..4631791 --- /dev/null +++ b/docs/source/qb/refs.rst @@ -0,0 +1,82 @@ +.. _Chap:QB:refs: + +References +========== + +.. [BvK07] R. Beetstra, M.A. van der Hoef, and J.A.M. + Kuipers. Drag force of intermediate Reynolds number flow past mono- + and bidisperse arrays of spheres. *AIChE Journal*, **53**, 489--501 (2007). + +.. [BPLPM19] C.M. Boyce, A. Penn, M. Lehnert, K.P. Pruessmann, and C.R. Müller. + Magnetic resonance imaging of single bubbles injected into incipiently + fluidized beds. *Chemical Engineering Science*, **200**, 147--166 (2019). + +.. [C81] S. Chandrasekhar. *Hydrodynamic and hydromagnetic stability*. + Dover Publications (1981). + +.. [Cv03] M.O. Coppens and J.R. van Ommen. Structuring chaotic fluidized beds. + *Chemical Engineering Journal*, **96**, 117--124 (2003). + +.. [FLYH18] W.D. Fullmer, X. Li, X. Yin and C.M. Hreyna. Notes on clustering + in hte gas-solid HCS. `arxiv:1809.04173 `_ + (2018). + +.. [G73] D. Geldart. Types of gas fluidization. *Powder Technology*, **7** (5), 285--292 (1973) + +.. [G05] V. Garzó. Instabilities in a Free Granular Fluid Described by the + Enskog Equation. *Physical Review E*, **72** (2), 021106 (2005). + +.. [GTSH12] V. Garzó, S. Tenneti, S. Subramaniam, and C.M. Hrenya. Enskog + kinetic theory for monodisperse gas-solid flows. *Journal of Fluid Mechanics*, + **712**, 129--168 (2012). + +.. [GZ93] I. Goldhirsch and G. Zanetti. Clustering instability in dissipative + gases. *Physical Review Letters*, **70** (11), 1619--1622 (1993). + +.. [H83] P.K. Haff. Grain Flow as a Fluid-Mechanical Phenomenon. + *Journal of Fluid Mechanics*, **134**, 401--430 (1983). + +.. [LBFHHGS16] P. Liu, T. Brown, W.D. Fullmer, T. Hauser, C.M. Hrenya, + R. Grout and H. Sitaraman. Comprehensive benchmark suite for simulation + of particle laden flows using the discrete element method with performance + profiles from the multiphase flow with interface exchanges (MFiX) code. + Technical report, National Renewable Energy Lab.(NREL), Golden, CO + (United States), (2016). url: https://www.nrel.gov/docs/fy16osti/65637.pdf + +.. [PB98] D.V. Pence and D.E. Beasley, Chaos suppression in gas-solid + fluidization, *Chaos*, **8**, 514--519 (1998). + +.. [TPKKv15] Y. Tang, E.A.J.F. Peters, J.A.M. Kuipers, + S.H.L. Kriebitzsch, and M.A. van der Hoef. A new drag correlation + from fully resolved simulations of flow past monodisperse static arrays + of spheres. *AIChE Journal*, **61** (2), 688--698 (2015). + +.. [S18] A. Bakshi, M. Shahnam, A. Gel, T. Li, C. Altantzis, W. Rogers, and A.F. Ghoniem. + Comprehensive multivariate sensitivity analysis of CFD-DEM simulations: + Critical model parameters and their impact on fluidization hydrodynamics. + *Powder Technology*, **338**, 519--537 (2018). + + J.E. Higham, M. Shahnam, and A. Vaidheeswaran. On the Dynamics of a + Quasi-Two-Dimensional Pulsed-Fludized Bed. + `arxiv:1809.05033 `_ (2018). + +.. [VJFTM07] J.L. Vinningland, Ø. Johnsen, E.G. Flekkøy, R. Toussaint, + and K.J. Måløy. Granular Rayleigh-Taylor instability: Experiments and + simulations. *Physical Review Letters*, **99** (4), 048001 (2007). + + J.L. Vinningland, Ø. Johnsen, E.G. Flekkøy, R. Toussaint, + and K.J. Måløy. Experiments and simulations of a gravitational granular + flow instability. *Physical Review E*, **76** (5), 051306 (2007). + +.. [WY66] C.Y.Wen and Y.H. Yu. Mechanics of fluidization. + *Chemical Engineering Progress Symposium*, **62**, 100--111 (1966). + +.. [WdLC16] K. Wu, L. de Martin, Luca, M. and M.-O. Coppens. Pattern formation + in fluidized beds as a tool for model validation: A two-fluid model based study. + *Powder Technology*, **295**, 35--42 (2016). + +.. [YZMH13] X. Yin, J.R. Zenk, P.P. Mitrano, and C.M. Hrenya. Impact of + Collisional Versus Viscous Dissipation on Flow Instabilities in + Gas-Solid Systems. *Journal of Fluid Mechanics*, **727**, R2 (2013). + + diff --git a/docs/source/qb/single_bubble.rst b/docs/source/qb/single_bubble.rst new file mode 100644 index 0000000..3f62e5a --- /dev/null +++ b/docs/source/qb/single_bubble.rst @@ -0,0 +1,75 @@ +.. _Chap:QB:singbub: + +Single Bubble Injection +======================= + +Another variation on bubbling typically observed in bubbling fluidized beds +is the detailed single-bubble study of Boyce and coworkers [BPLPM19]_. In the +experiment, a cylinderical bed is brought to incipient fluidization +(just *under* minimum fluidization) by a uniform disributor. Then, an +additional volume of gas is abruptly injected from a nozzle located in the +center of the bed causing a single bubble to form and rise through the bed. +Measurement of the evolution of the bubble formation, rise and +is captured with high-speed, high-resolution magnetic resonance imaging (MRI) +in a 10 mm thick slice through the center of the bed. Two particle types +are studied experimentally, only the larger of which is currently used +for qualitative benchmarking. + + +The experimental test section is a cylinderical bed 190 mm in diameter and +300 mm tall. The system is modeled in a domain of size 192 mm square by 384 mm +tall with a cylinderical EB geometry centered at :math:`(x,z) = (96, 96)` mm. +The modeled bed height is larger than the experimentso that it can be resolved +by a uniform uniform CFD grid of power 2. Specifically, the applied grid is +:math:`32 \times 64 \times 32`, such that :math:`dx^* \approx 2.0`. +:math:`N_p = 260`-thousand particles make up a bed of approximately +:math:`h_{bed} = 200` static bed height. The particles are of diameter +:math:`d_p = 2.93` mm and density +:math:`\rho_p = 1040` kg/m\ :sup:`3` \, respectively. Mass inlet and pressure +outlet boundary conditions are specified at the bottom and top of the domain, +respectively. The nozzle is modeled with a secondary mass inlet covering the +center (in x,z) four CFD cells. We note that, as modeled, the area of the +injector is roughly three times that of the experimental nozzle, a tube of +:math:`7.95` mm diameter. The injection times are adjusted slightly to +:math:`\delta t_{inj} = 154.2`, :math:`101.7`, :math:`66.7`, :math:`51.4`, +and :math:`25.0` ms so that a uniform jet velocity of :math:`50` m/s can be +applied in all cases. + + +A separate defluidization simulation was first carried out first to determine +:math:`U_{mf} \approx 0.66` m/s using the `WenYu` [WY66]_ drag law, slightly +below the experimentally measured value of :math:`U_{mf} = 0.7` m/s. The bed +was prepared with two initialization simulations. First, the particle initial +condition is fluidized above :math:`U_{mf}` at :math:`0.8` m/s for one second +using both the uniform distributor and jet sections. Then, the jet section is +shut off (velocity in BC set to zero) and the flow in the uniform distributor +section is reduced to incipient fluidization at :math:`0.66` m/s for an +additional two seconds. Then, beginning at :math:`t = 3` s, the jet region is +set to :math:`50` m/s for a specified injection duration given previously. +The jet is switched on and off with a step change in `usr1.f90`. + + +.. figure:: figs/boyce_sb_1908_small.png + :width: 16cm + :align: center + :alt: Sim comparison to single bubble injection experiment of Boyce + + Comparison of experiment and MFiX-Exa simulaton for single bubbles + injected into incipiently fluidized beds for increasing (left to right) + injection times. + + +The figure above provides a comparison between MFiX-Exa `19.08` simulation +results and the experimental measurements. In both cases, the particle data +has been averaged onto a :math:`10` mm thick grid of :math:`21 \times 32` +For the longer injection times, :math:`\delta t_{inj} \approx 100` and +:math:`150` ms, the simulated bubbles are larger and more elongated than +observed experimentally. However, this trend is not universal, at shorter +injection times, the bubble is too small and actually collapses before +erupting at the surface. Above, the bubble produced from a :math:`50` ms +injection is currently in the process of collapsing. Another interesting +feature (perhaps most apparent at :math:`66` ms), is the V-shaped region +of particle down flow centered around the bubble centeroid, which appears +to be captured rather well by the simulation. + + -- GitLab

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