From fc6fd82f61f72d359c1f6db8fd0f987e10880779 Mon Sep 17 00:00:00 2001
From: William Fullmer <william.fullmer@netl.doe.gov>
Date: Wed, 13 Nov 2019 13:05:46 -0500
Subject: [PATCH] adding very short write up for QB case biseg
---
docs/source/qb/biseg.rst | 34 ++++++++++++++++++++++++++++++--
docs/source/qb/granRT.rst | 12 +++++------
docs/source/qb/hcs.rst | 2 +-
docs/source/qb/refs.rst | 4 ++++
docs/source/qb/single_bubble.rst | 2 +-
5 files changed, 44 insertions(+), 10 deletions(-)
diff --git a/docs/source/qb/biseg.rst b/docs/source/qb/biseg.rst
index 2c01430..9873497 100644
--- a/docs/source/qb/biseg.rst
+++ b/docs/source/qb/biseg.rst
@@ -3,8 +3,38 @@
Bidisperse Segregation
======================
-wdf TODO ASAP
-
+In this simple test conducted at NETL, a uniform, random mixture
+of nylon
+(:math:`d_p = 3.19` mm, :math:`\rho_p = 1130` kg/m\ :sup:`3` \)
+and ceramic
+(:math:`d_p = 4.25` mm, :math:`\rho_p = 2580` kg/m\ :sup:`3` \)
+particles. When fluidized, the smaller, lighter nylon particles
+(:math:`U_{mf} ~ 1.1` m/s) segregate out of the mixture to the top,
+with the larger, heavier ceramic particles (:math:`U_{mf} ~ 1.8` m/s)
+remaining at the bottom. The batch segregation test was conducted in
+a small bed with a square cross-section of side length 60.325 mm.
+Similar to previous observations of fluidized segregation of
+bidisperse mixtures [GLMK03]_, the optimal separation was found to
+occur just above the larger of the two minimum fluidization velocities.
+Below the larger :math:`U_{mf}`, lack of fluidization inhibits particle
+movement and too much above :math:`U_{mf}` vigorous bubbling promotes
+mixture in the bed.
+
+
+The optimal batch segregation experiment is simulated with MFiX-Exa 19.08
+discretized onto a :math:`8 \times 24 \times 8` mesh. No-slip walls are
+set at vertical domain extents with a mass inflow and pressure outflow at
+bottom and top, respectively. The :cpp:`Gidaspow` drag law is applied.
+A defluidization curve of all ceramic particles was traced to find
+:math:`U_{mf} \approx 1.9` m/s, close to the experimental value. The inflow
+velocity is set to `2.0` m/s. The image below shows the simulated segregation
+(inset) occurs much more rapidly than observed experimentally. In this case,
+as the nylon particles begin to leave the mixture, the ceramic particles
+defluidize. In the final state, the ceramic particles are essentially static
+with a fluidized layer of nylon particles floating on top, in contrast to the
+experiment, in which the full bed showed signs of fluidization. Investigation
+into the over-segregation in this case is on-going.
+
.. figure:: figs/netl_biseg_1908_small.png
:width: 16cm
diff --git a/docs/source/qb/granRT.rst b/docs/source/qb/granRT.rst
index 7846f18..f0ad225 100644
--- a/docs/source/qb/granRT.rst
+++ b/docs/source/qb/granRT.rst
@@ -43,12 +43,12 @@ 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.
+of the polystyrene material. The :cpp:`WenYu` drag law of Wen and Yu drag
+[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
diff --git a/docs/source/qb/hcs.rst b/docs/source/qb/hcs.rst
index 59332ca..4c43d9e 100644
--- a/docs/source/qb/hcs.rst
+++ b/docs/source/qb/hcs.rst
@@ -47,7 +47,7 @@ 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]_.
+the ideal :cpp:`BVK2` DNS drag law is applied, see [BvK07]_, [TPKKv15]_.
.. figure:: figs/hcs_ke_1908.png
diff --git a/docs/source/qb/refs.rst b/docs/source/qb/refs.rst
index 4631791..fb7b68b 100644
--- a/docs/source/qb/refs.rst
+++ b/docs/source/qb/refs.rst
@@ -7,6 +7,10 @@ References
Kuipers. Drag force of intermediate Reynolds number flow past mono-
and bidisperse arrays of spheres. *AIChE Journal*, **53**, 489--501 (2007).
+.. [GLMK03] M.J.V. Goldschmidt, J.M. Link, S. Mellema, and J.A.M. Kuipers.
+ Digital image analysis measurements of bed expansion and segregation dynamics
+ in dense gas-fluidised beds. *Powder Technology*, **138** (2-3), 135--159 (2003).
+
.. [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).
diff --git a/docs/source/qb/single_bubble.rst b/docs/source/qb/single_bubble.rst
index 3f62e5a..4e37890 100644
--- a/docs/source/qb/single_bubble.rst
+++ b/docs/source/qb/single_bubble.rst
@@ -37,7 +37,7 @@ 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
+:math:`U_{mf} \approx 0.66` m/s using the :cpp:`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
--
GitLab