A Validation Uncertainty Quantification Analysis of a 1.5 MW Oxy-Coal Fired Furnace

Paper from the AFRC 2015 conference titled A Validation Uncertainty Quantification Analysis of a 1.5 MW Oxy-Coal Fired Furnace

A 1.5 MW pulverized coal-fired furnace at the University of Utah, the L1500, represents one scale in a multiscale Validation/Uncertainty Quantification (V/UQ) study undertaken by the Carbon-Capture Multidisciplinary Simulation Center (CCMSC) (http://ccmsc.utah.edu). This validation process seeks to obtain consistency between all measured and simulated quantities of interest (QOI). This paper discusses the V/UQ process applied to the oxy-fired pulverized coal experiments performed on the L1500 (described in a companion paper). In this study the simulations and measurement campaigns have been coordinated to maximize the information obtained by performing both the simulation and the experiments together and by requiring consistency within the uncertainty of the measurements. This analysis requires quantification of the real uncertainties in the measured QOIs and in the models used to obtain the QOIs in the simulation. For this analysis, the QOI is heat flux (to the wall and to the cooling tubes). To perform the analysis, two simulation parameters were selected that have a first order effect on the QOI: (1) a parameter in the coal devolatilization model and (2) the effective thickness of the furnace wall (assuming an effective thermal conductivity of 1 W/m-K). A suite of six simulations of the L1500 experiment was then performed over the parameter space defined by the uncertainty range of these two parameters. The simulations consisted of two parts. In the first part, the velocity and temperature fields at the exit plane of a low NOx burner equipped with swirl blocks were obtained with the commercial software package StarCCM+. In the second part, the main chamber of the L1500 was simulated with Arches, a Large Eddy Simulation code developed by ICSE researchers that uses the Discrete Quadrature Method of Moments to simulate the solid disperse phase (e.g. coal); the exit plane velocity and temperature fields from the StarCMM+ simulation were used as the boundary condition. The computational domain in Arches had 18.1 millions cells. Each simulation in the test suite required approximately one week of run time on 2808 cores. Upon completion of the simulation suite, a consistency analysis of the simulation and experimental data was performed. This presentation will provide an overview of the methodology, present results from the consistency analysis, and discuss how the analysis was enhanced due to the coordination of experimental and simulation work.

A Validation/Uncertainty Quantification Analysis of a 1.5 MW Oxy-Coal Fired Furnace Oscar H. Diaz-Ibarra, Jennifer Spinti, Andrew Fry, Benjamin Schroeder, Jeremy N. Thornock, Benjamin Issac, Derek Harris, Michal Hradisky, Sean Smith, Eric Eddings, Philip J. Smith Institute for Clean and Secure Energy, University of Utah, Salt Lake City, UT   Abstract     A  validation  and  uncertainty  quantification  study  of  a  1.5  MW  oxy-­‐coal  fired  furnace   is  presented.  In  this  study,  a  consistency  analysis  approach  was  applied  to   experimental  and  simulation  results  for  eight  quantities  of  interest:  thermocouple   measurements  in  five  locations  down  the  length  of  the  furnace  and  three  radiometer   measurements  in  the  first  three  sections  of  the  furnace.  Instrument  models  were   devised  for  both  the  thermocouples  and  radiometer  measurements  so  that   experimental  and  simulation  data  could  be  compared.  A  total  of  six  parameters  were   tested  through  the  consistency  analysis.  In  the  simulations,  two  parameters  were   tested,  the  thermal  wall  resistance  and  a  devolatilization  parameter.  In  the   instrument  models,  four  parameters  were  tested:  the  emissivity  of  the   thermocouple  in  the  thermocouple  model  and,  the  emissivity  of  the  wall  opposite  to   the  radiometer  in  the  radiometer  model.     Nomenclature       𝜀𝜀   Emissivity   [-­‐]   𝑞𝑞!"#!$%"&   Incident  radiation     [W/m2]   𝜎𝜎   Stefan-­‐Boltzmann  constant     5.670373  e-­‐8   [W/m2/K4]   𝑅𝑅   Thermal  resistance     [W/m2/K]   𝑇𝑇   Temperature   [K]   𝑘𝑘!   Thermal  conductivity     [W/m/K]   ∆𝑥𝑥!   Layer  thickness     [m]   𝑣𝑣!!"   Devolatilization  parameter   [-­‐]   𝑉𝑉!   Ultimate  volatile  yield     [-­‐]   𝑇𝑇!   Particle  temperature     [K]   𝑉𝑉   Volatile  yield     [-­‐]   𝐴𝐴   Pre-­‐exponential  factor     [1/s]   𝐸𝐸   Activation  temperature   [K]   𝜎𝜎!   Distribution's  standard  deviation     [K]   𝑍𝑍     max  (−4.0, min( 2.0 ∗ 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒(1.0 − 2.0 ∗ (𝑉𝑉! − 𝑉𝑉)/𝑣𝑣!!" , 4.0))   𝑞𝑞!"#$%&'   Heat  removed     [W/cell/m2]   1   𝑘𝑘   𝐿𝐿 ℎ   𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠_𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎   𝐼𝐼   𝐼𝐼!   𝑘𝑘!!!   ∆𝑥𝑥   𝑁𝑁!   𝐼𝐼!     Subscripts     𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐_𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡   𝑡𝑡𝑡𝑡   𝑔𝑔𝑔𝑔𝑔𝑔   𝑠𝑠ℎ𝑒𝑒𝑒𝑒𝑒𝑒   𝑤𝑤   p     Thermal  conductivity  over  thickness  of  the   thermocouple     Heat  transfer  coefficient  on  the  thermocouple     Solid  angle  for  the  radiometer   Intensity   𝜎𝜎𝑇𝑇!"#  !   𝜋𝜋 Absorption  coefficient     Resolution   Number  of  rays     Intensity  at  the  wall  oppose  to  radiometer         Heat  flux  gauge     Thermocouple  instrument     Gas   Shell   Wall   Particle   [W/m2/K]   [W/m2/K]     [W/m2]   [W/m2]   [1/m]   [m]     [W/m2]                   Acknowledgment This material is based upon work supported by the Department of Energy, National Nuclear Security Administration, under Award Number(s) DE-NA0002375. Disclaimer This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.     2     1. Introduction     The  Carbon  Capture  Multidisciplinary  Simulation  Center  (CCMSC)   (http://ccmsc.utah.edu), at  the  University  of  Utah  is  demonstrating  the  use  of  exascale   computing  with  verification,  validation,  and  uncertainty  quantification  as  a  means  of   accelerating  deployment  of  low  cost,  low  emission  coal-­‐fired  power  generation   technologies.  This  effort  employs  a  hierarchical  validation  approach  to  obtain   simultaneous  consistency  between  a  set  of  selected  experiments  at  different  scales   embodying  the  key  physics  components  (large  eddy  simulations,  multiphase  flow,   particle  combustion  and  radiation)  of  a  full-­‐scale,  oxy-­‐fired  boiler.  This  paper   presents  validation  and  uncertainty  quantification  (VUQ)  results  for  one  of  the   selected  datasets,  a  suite  of  oxycoal-­‐fired  experiments  conducted  in  the  L1500  (a  1.5   MW  furnace  at  the  University  of  Utah).    The  VUQ  method  used  was  a  consistency   analysis.  With  this  method,  regions  of  consistency  between  experimental  and   simulation  data  were  determined.  Details  about  the  L1500  furnace  and  the   experimental  data  can  be  found  in  the  accompanying  paper  by  Fry  et  al.  entitled   "Pilot-­‐scale  Investigation  of  Heat  Flux  and  Radiation  from  an  Oxy-­‐coal  Flame"  This   paper  focuses  on  the  L1500  simulations,  the  collection/processing  of  the  simulation   data,  and  the  VUQ  consistency  analysis.     2. Methodology       To  perform  a  VUQ  analysis,  the  quantity  (or  quantities)  of  interest  (QOI)  and  the   system  parameters  (scenario,  model,  numerical)  that  have  a  first  order  impact  on   the  QOI  are  identified.  In  this  experimental  dataset,  the  QOIs  all  relate  to  heat  flux:   wall  temperature,  heat  flux  measured  by  narrow-­‐angle  radiometers,  and  wall  heat   flux.  For  this  initial  analysis,  a  two-­‐parameter  study  was  selected  due  to  constraints   of  time  and  computer  resources.     2.1 Design  of  Experiments     The  two  parameters  explored  in  this  study  were  a  devolatilization  model  parameter   and  a  scenario  parameter  related  to  thermal  resistance  in  the  wall  heat  transfer   model.  These  parameters  were  selected  based  on  prior  experience  and  a  desire  to   have  one  model  parameter  that  was  investigated  at  all  relevant  levels  of  the   validation  hierarchy.     Within  the  simulation  tool,  the  models  for  coal  particle  physics  include  a   devolatilization  model  that  is  presented  in  equations  (1)  and  (2).  In  this  model,  the   ultimate  volatile  yield  is  determined  by  the  function  shown  in  Equation  (1):                        𝑉𝑉! = !!!" ! 1 − tanh  ( 𝑏𝑏 + 𝑐𝑐 ∗ 𝑣𝑣!!" ∗   3   !"#!!! !! + (𝑑𝑑 + 𝑒𝑒 ∗ 𝑣𝑣!!" )                (1)                               !" !!!! ∗! 𝑉𝑉! − 𝑉𝑉 ,        𝑖𝑖𝑖𝑖  𝑉𝑉! − 𝑉𝑉 ≤ 0                                                    (2)   0                                                                ,                  𝑒𝑒𝑒𝑒𝑠𝑠𝑠𝑠   In  equation  (1),  the  parameters  b,  c,  d  and  e  were  fitted  using  data  from  the   Chemical  Percolation  Devolatilization  (CPD)  model  [1].  The  parameter  𝑣𝑣!!"  was   explored  in  this  VUQ  analysis  in  the  range  of  0.5-0.9.  The  volatile  yield  was  used  in   equation  (2)  to  compute  the  rate  of  devolatilization.  More  detailed  information   about  this  new  devolatilization  model  can  be  found  in  [2].     A  scenario  parameter  called  the  "effective  thickness"  is  related  to  the  thermal   resistance  used  in  the  one-­‐dimensional  (1D)  wall  heat  transfer  model  equation   shown  in  equation  (3).  The  walls  of  the  L1500  furnace  consist  of  one  layer  of   refractory  material  and  three  insulation  layers  for  a  total  wall  thickness  of  0.34  m.   The  1D  heat  transfer  equation  for  this  multilayer  wall  is  given  in  equation  (4).   ! Finally,  the  "effective  thickness"  scenario  parameter,    ,  is  presented  in  equation  (5).   ! The  selected  range  for  this  parameter  was  0.1-0.4  based  on  uncertainty  in  the  wall   emissivity  and  on  temperature  dependence  of  the  thermal  conductivity.                                                                        𝜀𝜀 𝑞𝑞!"#!$%"& − 𝜎𝜎𝑇𝑇!! = 𝑅𝑅(𝑇𝑇! − 𝑇𝑇!!!""  )                                                                                          (3)     !                                                       𝑞𝑞!"#!$%"& − 𝜎𝜎𝑇𝑇!! = ! ∆!! 𝑇𝑇! − 𝑇𝑇!!!""                                                                                          (4)   !" = 𝐴𝐴 ∗ exp − !! !                                                                                                                 = ! ! !!! !! ! ∆!! 𝜀𝜀 !!! !                                                                                                                                          (5)   !   A  total  of  eight  cases  were  run  for  this  analysis.  Latin  hypercube  sampling  was  used   to  generate  the  sets  of  parameter  values  that  best  represented  the  two-­‐dimensional   parameter  space.  This  eight-­‐case  design  of  experiments  is  presented  in  Table  1.     Table  1.  Design  of  experiments  for  the  VUQ  analysis.       ! Case     𝑣𝑣!!"    [m2k/W]   ! 1   0.7738   0.10   2   0.5228   0.14   3   0.827   0.20   4   0.6019   0.23   5   0.729   0.25   6   0.6737   0.32   7   0.88022   0.35   8   0.5503   0.37     For  the  eight  cases  presented  in  Table  1,  the  following  simulation  tool,  geometry  and   operating  conditions  were  used.       4   2.2 Simulation  Tool     The  simulations  were  performed  with  Arches,  a  component  of  the  Uintah  software   suite  [3].  Uintah  is  a  solver  for  partial  differential  equations  on  structured  grids   using  hundreds  to  thousands  of  processors.     In  Arches,  the  turbulent  flow  is  resolved  by  the  filtered  Navier-­‐Stokes  equations.  In   this  Large  Eddy  Simulation  (LES)  approach,  the  large  scales  are  resolved,  and  the   subgrid  scales  are  modeled  with  the  dynamic  Smagorinsky  model.  For  the  LES   simulations  described  in  this  paper,  first  order  discretization  in  time  and  a  wall   upwind  convection  scheme  were  used.     The  solid  phase  was  modeled  using  the  direct  quadrature  method  of  moments   (DQMOM)  with  three  environments.  The  internal  coordinates  were  the  raw  coal   mass,  the  char  mass,  the  enthalpy  of  the  particle,  and  the  velocity  of  the  particle  (in   x,  y,  and  z).  In  addition,  the  weights  for  the  three  environments  were  solved.  An   upwind  discretization  scheme  was  used  to  solve  the  equations  for  the  internal   coordinates  and  for  the  weights.  The  particle  phase  was  coupled  with  the  gas  phase   through  source  terms  in  the  equations  for  momentum,  heat  and  mass.  More  detail   about  the  DQMOM  implementation  in  Arches  is  presented  in  [4].  The  coal  particle   physics  models  included  the  devolatilization  model  discussed  above  and  the   Shaddix  and  Murphy  char  oxidation  model  [5].     The  gas-­‐phase  reactions  in  the  system  were  modeled  using  a  three-­‐stream  mixture   fraction  approach.  The  three  streams  are  recycled  flue  gas  (𝑚𝑚!"# ),  oxygen  (𝑚𝑚!! ),   and  coal  off  gas  (𝑚𝑚! ).  The  mixture  fractions  based  on  these  three  streams  are   defined  in  equations  (6),  (7)  and  (8).       !                                                                                                              (6)                                                                                                                            𝜂𝜂!,!"# = ! !"# !!     !"#                                                                                                                                𝜂𝜂! = !                                                                                                                            𝜂𝜂! = ! !!"# !! !"# !!!! !!! !! !"# !!!! !!!                                                                                                      (7)                                                                                                            (8)     Transport  equations  were  solved  for  𝜂𝜂!  and  𝜂𝜂!,!!" ;  𝜂𝜂!  was  computed  from  the  other   two  mass  fractions.  A  lookup  table  based  on  equilibrium  chemistry  assumptions  was   tabulated  a  priori  as  a  function  of  these  three  mixture  fractions  and  of  the  system   enthalpy.     The  discrete  ordinates  (DO)  method  was  used  to  compute  radiation  in  the   simulation.  For  the  cases  in  this  paper,  S8  quadrature,  representing  40  discrete   directions,  was  used.  The  radiation  equations  were  solved  every  20  iterations.     2.3 Geometry  and  Computational  Domain   5     The  L1500  reactor  is  15.5  m  long  with  a  1x1  m2  transversal  area  as  shown  in  Figure   1.  It  is  divided  into  10  sections,  and  each  section  has  several  ports  through  which  a   variety  of  measurements  can  be  taken.  The  L1500  has  a  swirling  burner  that  can   operated  in  a  range  of  modes  from  0%  swirl,  where  completely  straight  flow  can  be   achieved,  to  100%  swirl,  where  flow  with  a  32  m/s  tangential  velocity  and  22  m/s   axial  velocity  can  be  obtained.  The  L1500  can  be  operated  in  air-­‐fired  or  oxy-­‐fired   modes  and  can  burn  solid,  liquid,  or  gaseous  fuels.  In  oxy-­‐fired  mode,  recycled  flue   gas  (RFG)  is  brought  from  the  exit  of  the  convective  section  back  into  the  burner's   primary/secondary  oxidant  registers.  Oxygen  is  supplied  to  the  secondary  and   primary  RFG  streams  just  prior  to  entering  the  burner.  For  the  experiments  used  in   this  validation  study,  coal  was  fed  with  the  primary  stream  at  a  rate  of  0.0324  kg/s   in  order  to  produce  1  MW  of  heat.  More  information  about  this  reactor  and  burner   can  be  found  in  [6]  and  [7].     The  computational  geometry  for  the  entire  furnace  is  presented  in  Figure  2.  The   reactor  has  eight  sets  of  water-­‐cooled  tubes  that  remove  heat  from  the  first  four   sections.  Additionally,  there  is  a  water-­‐cooled  steel  grid  at  the  furnace  exit  to  reduce   the  temperature  of  the  combustion  gases  prior  to  entering  the  convection  section.   Also  seen  in  Figure  2  are  the  burner  quarl,  the  geometry  of  the  furnace  exit,  and  the   10  cm  step  up  in  the  bottom  of  the  furnace  between  sections  4  and  5.         Figure  1:  Photo  of  the  L1500  reactor  located  at  the  Industrial  Combustion  And   Gasification  Research  Facility  [8].     Several  simulations  using  the  entire  furnace  geometry  at  a  resolution  of  16  mm   were  carried  out  for  the  0%  swirl  case.  From  these  simulations,  it  was  clear  that   after  section  6,  gas  temperatures,  velocities  and  chemical  compositions  were   relatively  constant.  The  computational  geometry  was  shortened  to  7  m  and   additional  simulations  were  run.  Simulation  results  from  the  7  m  simulation  were   compared  with  results  from  the  15.5  m  simulation  and  the  differences  were   minimal.  Hence,  for  subsequent  simulations,  the  computational  geometry  was   shortened  to  7  m.  The  impact  of  mesh  resolution  on  simulation  results  was  also   6   tested  by  performing  a  simulation  with  12  mm  resolution.  While  the  differences  in   the  wall  temperature  profiles  for  the  12  mm  and  16  mm  resolution  cases  were   small,  there  were  larger  differences  in  gas  temperatures  near  the  burner.  Therefore,   a  12  mm  resolution  has  selected  for  the  VUQ  analysis.       The  shortened  geometry  of  the  L1500  with  a  12  mm  resolution  is  presented  in   Figure  3;  this  geometry  includes  the  cooling  tubes  and  the  step.  The  surface  area  of   the  cooling  tubes  in  the  computational  mesh  was  adjusted  to  match  the  actual   surface  of  the  tubes.  With  this  new  geometry,  comparisons  could  be  made  with  most   of  the  experimental  data,  including  narrow-­‐angle  radiometer  measurements  in   sections  1,  2,  and  3;  wall  temperatures  in  sections  1,  2,  3,  4  and  6;  gas  compositions   in  sections  4,  5,  and  6;  and  total  heat  flux  in  sections  1,  2,  and  3.  Gas  composition   data  from  sections  7,  8,  9  and  10  could  not  be  used,  but,  the  gas  composition  was   fairly  constant  through  these  sections.         Figure  2:  Computational  geometry  for  the  L1500  showing  the  eight  sets  of  cooling   tubes,  the  cooling  grid,  the  burner  quarl,  the  step  after  section  4,  and  the  exit.     The  L1500  simulations  were  run  on  two  linux  machines:  Ash,  a  machine  owned  by   the  Institute  for  Clean  and  Secure  Energy  and  operated  by  the  Center  for  High   Performance  Computing  at  the  University  of  Utah,  and  Syrah,  a  machine  operated  by   7   Lawrence  Livermore  National  Laboratory.  With  a  12  mm  mesh  resolution  (mesh  is   uniform  and  structured),  the  computational  domain  had  4,463,448  cells.  The   simulations  were  run  on  464  cores  long  enough  to  obtain  20  s  of  physical  time.  On   Syrah,  this  required  80  hours  of  run  time.           Figure  3:  Shortened  geometry  for  the  L1500  simulations  including  the  quarl,  the   eight  sets  of  cooling  tubes,  and  the  step  change  in  the  reactor  floor.     2.4 Coal  Characterization     A  Sufco  Utah  coal  was  used  in  the  experimental  campaign.  The  ultimate  analysis  for   this  coal  is  presented  in  Table  2.       Table  2.  Ultimate  analysis  for  the  Sufco  Utah  Coal.  Data  are  averaged  and  normalized   from  the  analysis  of  five  samples.       Coal   %  Mass   C   66.89   H   4.51   N   1.17   S   0.36   O   13.6   8   Ash   H2O   HHV  [J/kg]   7.88   5.58   27364.93     To  determine  the  particle  size  distribution  (PSD)  of  the  Sufco  coal,  the  bags  of  coal  to   be  burned  during  the  experimental  campaign  were  sampled  at  different  depths.     Both  a  sieving  analysis  and  a  Beckman-­‐Coulter  diffraction  analysis  were  performed   on  the  collected  samples.  As  seen  in  Figure  4,  data  from  both  methods  were  fitted  to   a  Rosin-­‐Rammler  distribution.  From  this  analysis,  it  was  concluded  that  the  PSD   distribution  could  be  approximated  by  three  particle  sizes:  15  𝜇𝜇𝜇𝜇,  60  𝜇𝜇𝜇𝜇,  and   200  𝜇𝜇𝜇𝜇,  with  mass  weights  of  57.4%,  26.2%  and  16.4%  respectively.  Assuming  that   the  particle  velocities  were  the  same  as  the  gas  velocity,  these  mass  weights  were   !" converted  to  particles  per  cubic  meter  using  a  coal  density  of  1300   !  and  the   ! volume  corresponding  to  each  particle  size.  Thus,  the  inputs  to  DQMOM  were  the   number  of  particles  per  𝑚𝑚!  for  each  of  the  three  particles  size.       Figure  4:  Experimental  PSD  and  fitted  Rosin-­‐Rammler  PSD.    Sieving  was  performed   for  different  times  to  determine  the  effect  on  the  resulting  PSD.  Based  on  this   analysis,  only  the  30-­‐minute  sieving  data  was  used  for  the  Rosin-­‐Rammler  fit.     2.5 Operating  Conditions       An  experimental  campaign  was  carried  out  for  a  week  in  the  L1500  where  both  0%   swirl  and  100%  swirl  operating  conditions  were  tested.  The  L1500  operating   parameters  that  were  used  as  inputs  to  the  Arches  simulations  are  shown  in  Table  3.   These  inputs  were  computed  from  the  mass  flow  of  the  RFG  to  the  primary  and   secondary  registers,  the  oxygen  mass  flow  to  the  primary  and  secondary  inlets,  the   9   coal  mass  flow  rate,  the  gas  temperatures  for  each  of  these  streams,  and  the   composition  of  RFG.  All  of  these  parameters  were  recorded  and  controlled  during   the  experimental  campaign.  For  the  0%  swirl  operating  condition,  a  constant   velocity  profile  at  the  tip  of  the  burner  was  assumed  for  the  primary  and  secondary   oxidant  streams.     Table  3.  L1500  operating  conditions  used  as  inputs  for  Arches  simulations.     Stream    Mass  flow  [kg/s]   Temperature  [K]   Coal  (ash  and  moisture  free)   0.0324   338   Primary   0.0688   338   Secondary     0.2995   500   Mass  Fraction   Primary     Secondary   O2   0.1739   0.2385   CO2   0.6746   0.6245   H2O   0.1043   0.0966   SO2   0.0020   0.0018   N2   0.0450   0.0416     These  operating  conditions  were  generally  stable  during  the  experiment.  However,   there  was  an  air  leak  in  the  RFG  stream  as  evidenced  by  the  outlet  CO2   concentration  being  lower  than  expected.  To  compensate  for  this  air  leak  in  the   simulations,  an  overall  mass  balance  was  performed  on  the  furnace.  The  leaked  air   and  the  coal's  moisture  were  included  in  the  compositions  of  the  RFG  flow  shown  in   Table  3.       During  the  experimental  campaign,  radiative  heat  flux  was  measured  through  the   center  port  of  sections  1,  2,  and  3  using  a  narrow-­‐angle  radiometer.  A  cold  plate   serving  as  a  heat  flux  gauge  was  installed  in  the  port  opposite  from  the  radiometer   to  measure  total  heat  flux  to  the  wall  and  to  provide  a  known  boundary  condition   for  the  radiometer  measurements.  In  practice,  the  cold  surface  became  coated  with   radiating  particles,  introducing  uncertainty  into  the  radiometer  measurement.  Mass   flow  rates  and  inlet/outlet  temperatures  of  the  water  flowing  through  the  cold  plate   heat  flux  gauges  were  recorded.  Mass  flow  rates  and  inlet/outlet  temperatures  of   the  water  flowing  through  the  cooling  tubes  were  measured  as  well.  "Wall"   temperature  measurements  were  taken  in  sections  1,  2,  3,  4,  6,  7  and  8  using  Type  B   thermocouples  encased  in  ceramic  sheaths  that  were  then  inserted  into  small  holes   in  the  furnace  ceiling  located  in  the  middle  of  each  section  (see  Figure  5).  Each   sheath  was  inserted  until  it  was  flush  with  the  inside  wall  of  the  furnace.  Gas  phase   composition  was  continuously  measured  at  the  furnace  outlet.  In  addition,  a  mobile   gas  probe  was  used  to  record  centerline  and  radial  gas  phase  compositions  between   sections  4  and  10.  Finally,  detailed  shell  temperature  profiles  were  taken  of  each  of   the  10  sections.     10     Figure  5:  Thermocouple  placement  in  furnace  wall.  Section  4  is  shown  but  the   placement  is  similar  for  all  thermocouple  measurements.     In  scoping  simulations,  it  was  determined  that  simulation  results  (specifically   radiative  heat  flux  and  wall  temperatures)  were  not  sensitive  to  the  shell   temperature  of  the  furnace.  Therefore,  constant  values  were  used  for  each  of  the   four  sides  of  the  furnace.  Table  4  presents  the  values  of  shell  temperature  used  in   the  simulations.     Table  4.  Shell  temperatures  averaged  over  all  measurements  made  on  a  side.     Location   Shell  Temperature  (K)   Quarl     434   Main  chamber  south  side   362   Main  camber  north  side     396   Main  chamber  bottom  side   362   Main  chamber  top  side   427.2     2.6 Heat  Removal  by  the  Cooling  Tubes     Figure  6  shows  the  heat  removed  by  cooling  tubes  1  and  2  (both  in  section  1)  as  a   function  of  time  during  the  last  day  of  the  experiment.  The  quantity  of  heat  removed   generally  decreased  until  the  burner  was  switched  from  0%  to  100%  swirl   (represented  by  the  vertical  black  line  at  109  hours  in  the  figure).  After  the  brief   jump  with  the  change  in  swirl,  the  heat  removal  continued  its  general  decline.  This   behavior  was  due  to  ash  deposition  on  the  cooling  tube  surface.  However,   sometimes  the  heat  removal  increased,  which  could  have  been  due  to  ash  material   falling  from  the  tubes.  Figure  7  shows  a  photo  of  one  set  of  cooling  tubes  after  the   experiment.  In  this  photo,  it  can  be  seen  that  the  ash  layer  on  the  tubes  is  not   uniform  and  there  are  some  locations  where  the  ash  material  has  fallen  off.       11   Figure  6:  Heat  removal  by  cooling  tubes  1  and  2.  The  vertical  line  represents  the   point  where  operating  conditions  were  switched  from  0%  swirl  to  100%  swirl.         Figure  7:  Cooling  tubes  after  the  experiment.       Heat  removal  by  the  cooling  tubes  is  an  important  parameter  that  ideally  would  be   computed  and  then  compared  to  experimental  values  as  part  of  the  VUQ  analysis.   However,  Arches  does  not  currently  have  a  model  to  compute  ash  deposition  and   the  resultant  changes  in  emissivity  and  conductivity  of  the  cooling  tubes.   Additionally,  ash  deposition  is  a  slow  process  in  comparison  with  an  LES  simulation.   A  preliminary  simulation  was  run  assuming  clean  tubes.  However,  temperature  and   heat  flux  profiles  from  the  simulation  did  not  agree  with  the  experimental  values.   Therefore,  it  was  decided  that  heat  removal  by  the  cooling  tubes  would  be  used  as   an  input  parameter  instead  of  an  output.     To  include  the  heat  removed  as  an  input  parameter,  an  energy  balance,  given  in   equation  (9),  was  performed  on  each  set  of  cooling  tubes.  The  parameter  R,  defined   in  equation  (5),  was  computed  using  equation  (10).  Equation  (9)  assumes  a  constant   heat  removal  along  the  length  of  each  set  of  cooling  tubes.  The  value  for  qremoval,  the   total  heat  removal  for  a  set  of  tubes,  was  obtained  from  the  experimental  data.  Since   the  diameter  of  the  tubes  was  equal  to  the  cell  size,  this  value  was  divided  by  the   12   total  number  of  cells  representing  each  set  of  tubes  in  the  computational  domain  to   obtain  the  heat  removal  per  cell.                                                                                                                                                                                                                                    𝑅𝑅 𝑇𝑇! − 𝑇𝑇!!!""   = 𝑞𝑞!"#$%&'                                                                                          (9)     !                                                                                                                          𝑅𝑅 = !"#$%&'                                                                                                                              (10)     ! !!   ! !!!""   Because  the  parameter  R  (a  strong  function  of  ash  deposition  along  the  entire  tube   length)  was  not  controlled  in  the  experiment,  experimental  data  from  a  small   window  in  time  were  used  for  the  VUQ  analysis.  By  choosing  a  small  window,  the   ash  layer  on  the  cooling  tubes  was  assumed  to  be  constant  and  R  was  computed   using  equation  (10).  For  future  studies,  this  parameter  will  be  included  as  one  of  the   variable  parameters  in  the  VUQ  analysis.     2.7 Quantities  of  Interest  for  the  VUQ  Analysis     As  noted  previously,  the  QOIs  for  this  study  were  related  to  the  radiative  heat  flux  in   the  furnace  under  oxycoal  firing  conditions.  Specifically,  the  QOIs  were  "wall"   temperatures  measured  by  thermocouples  in  sections  1,  2,  3,  4,  and  6;  radiative  heat   flux  measured  by  the  narrow-­‐angle  radiometer  in  sections  1,  2,  and  3;  and  the  total   heat  flux  at  the  wall  measured  in  sections  1,  2,  and  3.  These  data  were  used  in  the   VUQ  analysis  that  follows.     2.8 Description  of  VUQ  Approach     The  VUQ  methodology  employed  for  this  study  was  a  consistency  measure  analysis   referred  as  bounds  to  bounds  consistency.  This  methodology  was  developed  by   Michael  Frenklach  and  Andrew  Packard  at  the  University  of  California  Berkeley  [2].   The  basic  concept  of  this  consistency  analysis  boils  down  to  comparing  modeling   outputs  with  experimental  data  using  equation  (11).  In  equation  (11),  the   discrepancy  𝑢𝑢!  between  the  model  data  (𝑦𝑦!,! 𝒙𝒙 )  and  the  experimental  data  (𝑦𝑦! )  is   computed.  If  𝑢𝑢!    is  lower  than  the  error  in  the  experimental  measurement,  the   simulation  and  experimental  data  are  consistent.  If  the  data  are  not  consistent,  the   simulation  scientist  must  reassess  whether  the  models  and  model  parameter  ranges   are  appropriate  for  the  system  being  studied  and  the  experimentalist  must   reevaluate  the  experimental  methods  and  data  to  see  if  there  are  unaccounted  for   errors  that  might  increase  the  uncertainty  in  the  measurement.  As  discussed  in   Section  3,  identifying  regions  of  consistency  may  help  reduce  the  uncertainty  in  the   parameter  space.     𝑦𝑦!,! 𝒙𝒙 − 𝑦𝑦! ≤ 𝑢𝑢!                                                                                                              (11)           13   3 VUQ  Results       Here,  the  consistency  analysis  is  applied  to  thermocouple  and  radiometer   measurements.  In  order  to  compare  experimental  data  and  simulation  data,   instrument  models  for  the  thermocouple  and  the  radiometer  were  devised.       3.1 Temperature  Measurement  Analysis     The  instrument  model  for  the  thermocouple  in  the  ceramic  sheath  was  shown   schematically  in  Figure  5.  In  the  instrument  model,  the  energy  equation  (12)  was   solved  for  𝑇𝑇!" ,  the  temperature  that  would  be  measured  by  the  thermocouple  shown   in  Figure  5  given  the  simulated  conditions  of  the  furnace.  The  value  for  𝑇𝑇!"  is  then   directly  comparable  to  the  thermocouple  temperature  measured  experimentally.       ! ! + 𝑇𝑇!" − 𝑇𝑇!!!""   + ℎ 𝑇𝑇!"# − 𝑇𝑇!" = 0                                                  (12)                                𝜀𝜀!" 𝑞𝑞!"#!$%"& − 𝜎𝜎𝑇𝑇!" !   For  a  given  case,  the  incident  radiation  𝑞𝑞!"#!$%"&  and  the  gas  temperature  𝑇𝑇!"#  in   equation  (12)  were  obtained  from  the  simulation  by  extracting  data  at  the   thermocouple's  location  and  averaging  the  data  over  two  seconds.    The  thermal   ! resistance    of  the  thermocouple  was  obtained  from  product  literature.  The  value  of   ! 𝑇𝑇!!!""  was  obtained  from  Table  4  for  the  "Main  chamber  top  side."  The  heat  transfer   ! coefficient  h  was  set  to  4.0   ! ∙!.  Because  the  surface  emissivity  𝜀𝜀!"  had  a  strong   ! effect  on  measured  temperature,  it  was  varied  between  0-1  in  the  instrument   model.  With  all  these  values  set,  equation  (12)  was  used  to  solve  for  𝑇𝑇!" .  This   process  was  repeated  using  results  from  each  of  the  eight  simulations  presented  in   Table  1.     Three  dimensional  surfaces  (e.g.  surrogate  models)  for  𝑇𝑇!"#  and  𝑞𝑞!"#!$%"&  were   constructed  with  a  Gaussian  Process  [9]  using  the  data  obtained  from  the  eight   simulations.    The  set  of  surrogate  models  created  for  𝑇𝑇!"#  is  shown  in  Figure  8,  one   for  each  section.  The  measurement  location  in  each  section  was  the  middle  of  the   ceiling.  The  black  dots  in  the  plots  are  the  𝑇𝑇!"# values  from  the  eight  simulations.     14           Figure  8:  Gas  temperature  at  five  different  positions  on  the  ceiling  of  the  L1500.  The   black  dots  correspond  to  simulation  data;  the  surface  represents  the  surrogate   model.   15         The  behavior  of  the  two  parameters  is  similar  for  sections  1,  3,  4  and  5  but  is   different  for  section  2.  This  behavior  may  be  related  to  the  recirculation  patterns   present  in  section  2.  From  this  figure,  it  can  be  seen  that  the  gas  temperature   ! increases  as        increases  because  the  heat  lost  through  the  wall  is  decreasing.  The   ! gas  temperature  also  increases  with  𝑣𝑣!!" ,  but  the  surface  in  section  2  has  an  odd   maximum,  possibly  due  to  recirculation.     Figure  9  shows  the  simulation  and  experimental  data  with  their  associated   uncertainty  ranges  at  the  five  measurement  locations.  For  a  given  location  and  case   (e.g.  𝑞𝑞!"#!$%"&  and  𝑇𝑇!"#  fixed)  in  Figure  9,  the  range  in  the  thermocouple  temperature   (±100𝐾𝐾)  results  from  varying  𝜀𝜀!"  from  0.2  to  1.0.  For  a  given  location  considering  all   cases,  the  overall  range  of  computed  temperatures  (±500𝐾𝐾)  is  determined  by   varying  𝑞𝑞!"#!$%"&  and    𝑇𝑇!"# .  Since  the  instrument  model  shown  in  equation  (12)  is   most  sensitive  to  𝑞𝑞!"#!$%"&  and    𝑇𝑇!"# and  since  𝑞𝑞!"#!$%"&  and    𝑇𝑇!"# are  functions  of     ! !  and  𝑣𝑣!!" ,  the  three  parameters  explored  for  the  thermocouple  model  in  the  VUQ   ! analysis  were      ,  𝑣𝑣!!" ,  and    𝜀𝜀!" .  Figure  9  presents  the  range  of  temperatures  values   ! obtained  at  each  location  by  varying  these  three  parameters.  Also  shown  in  the   figure  are  the  experimental  data  averaged  over  a  five-­‐minute  window  with  the   range  determined  by  the  maximum  and  minimum  values  of  the  temperature  in  that   window.     Figure  9:  Thermocouple  temperature  at  five  positions  along  the  L1500.  The   simulation  error  bars  correspond  to  emissivities  of  1  and  0.2  for  the  eight  cases   presented  in  Table  1.  The  red  line  corresponds  to  the  experimental  data.     16     3.2   Radiometer  Measurement  Analysis     A  narrow-­‐angle  radiometer  was  used  to  measure  the  radiative  heat  flux  in  sections   1,  2  and  3  in  the  L1500.  The  instrument  model  for  the  radiometer  used  a  reverse-­‐ Monte  Carlo  ray  tracing  approach  to  compute  the  radiative  heat  flux  by  summing  up   the  radiative  intensities  over  all  the  rays  comprising  the  field  of  view  of  the   radiometer  as  seen  in  equation  (13).  The  radiative  intensity  in  each  solid  angle,  𝐼𝐼!   was  computed  with  equation  (14).  For  this  analysis,  𝑁𝑁! = 1.       ! !!                                                                                            𝑞𝑞 = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠_𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 !!! 𝐼𝐼! 𝑐𝑐𝑐𝑐𝑐𝑐𝜃𝜃!                                                                                        (13)   !!                                                                              𝐼𝐼!!! = 1 − exp −𝑘𝑘!!! ∆𝑥𝑥 𝐼𝐼! + exp −𝑘𝑘!!! ∆𝑥𝑥 𝐼𝐼!                                            (14)   !! !                                                                                                  where  𝐼𝐼! = !"#   !   In  order  to  compute  the  radiative  intensity  with  Equation  (14),  the  gas  temperature   𝑇𝑇!"# ,  used  to  compute  the  blackbody  intensity  𝐼𝐼! ,  and  the  gas  absorption  coefficient   𝑘𝑘!!!  were  obtained  from  the  simulations.  These  two  parameters  were  extracted   along  one  ray  from  wall  across  from  the  radiometer  to  the  inlet  of  the  radiometer.     While  a  cooled  target  was  used  on  the  wall  opposite  the  radiometer  to  reduce  the   radiation  from  the  reactor  wall,  ash  built  up  on  the  target  surface  during  the   experiments,  so  the  condition  of  this  surface  was  unknown.  To  compute  𝐼𝐼! ,  the   intensity  of  the  target,  the  wall  temperature  from  the  simulation  was  used,  and  the   emissivity  of  this  surface,  𝜀𝜀!"#$_!"#$%! ,  was  taken  as  other  parameter  for  the   instrument  model.  Because  of  the  unknown  surface  condition  of  the  three  cooled   targets  and  the  strong  effect  of  the  target  emissivity  on  the  radiometer   measurements,  the  target  in  each  section  (1,  2,  and  3)  was  assumed  to  have  a   different  𝜀𝜀!"#$_!"#$%! .  Therefore,  this  instrument  model  had  five  parameters.     !! !                                                                                                                          𝐼𝐼! = 𝜀𝜀!"#$_!"#$%! !"##                                                                                              (15)   !   Figure  10  compares  the  experimental  radiometer  measurements  (points  connected   by  the  dotted  line)  with  the  results  from  the  eight  simulation  cases  in  this  study.  The   uncertainty  ranges  for  the  experimental  data  were  obtained  by  applying  equations   (13)  and  (14)  to  the  radiometer  calibration  with  a  black  body.  For  the  simulation   data,  the  maximum  values  correspond  to  the  case  where  the  emissivity  of  the  cooled   target  was  assumed  to  be  1  and  the  wall  temperature  was  equal  to  the  simulated   wall  temperature.  The  minimum  values  correspond  to  the  case  where  the  emissivity   was  0.     17     Figure  10:  Comparison  of  experimental  and  simulation  radiative  heat  flux   measurements  in  sections  1,  2,  and  3  of  the  L1500.       3.3 Consistency  Analysis  for  the  Thermocouple  and  Radiometer  Measurements     A  consistency  analysis  (described  in  Section  2.8)  was  performed  using  the   ! thermocouple  temperature  and  the  radiative  heat  flux  measurements  as  QOIs  and    ,   ! 𝑣𝑣!!" ,  and    𝜀𝜀!" /𝜀𝜀!"#$_!"#$%!  as  parameters.  The  combined  dataset  included  five   thermocouple  values  and  three  radiometer  measurements  for  a  total  of  eight  QOIs.   ! The  total  number  of  parameters  is  six  (  ,  𝑣𝑣!!" ,  𝜀𝜀!" ,  𝜀𝜀!,!"#$_!"#$%! ,  𝜀𝜀!,!"#$_!"#$%! ,   ! 𝜀𝜀!,!"#$_!"#$%! ),  two  from  the  simulation  and  four  from  the  instrument  models.     The  instrument  models  for  the  thermocouple  and  for  the  radiometer  were  used  to   produce  64  cases  using  the  original  eight  cases  presented  in  Table  1  and  eight   emissivity  values  between  0.0  and  1.0  for  each  of  the  four  emissivity  parameters.    To   test  for  consistency,  a  surrogate  model  for  each  QOI  was  created  using  a  Gaussian   Process  with  the  64  cases  and  the  six  parameters.  These  surrogate  models  were   then  used  to  compare  with  the  experimental  data.         To  perform  the  consistency  analysis,  the  average  values  and  uncertainty  of  the   experimental  data  were  required.  All  of  the  averages  were  computed  over  a  five-­‐ minute  window.  The  uncertainty  of  the  radiometer  measurements  was   approximated  from  an  analysis  of  the  radiometer  calibration  data  with  a  black  body.   18   The  uncertainty  for  the  thermocouple  measurements  was  approximated  from  the   scaled  standard  deviation  for  a  five-­‐minute  window,  assuming  a  distribution  for  the   error  and  a  90%  confidence  interval.  For  the  first  three  locations,  the  scaling  factor   was  30.  For  the  last  two  locations,  the  scaling  factor  was  60.  The  factor  was  applied   because,  based  on  experience,  the  errors  in  the  thermocouple  measurements  were   not  reflected  in  the  measured  standard  deviations  of  1  K.  Also,  without  a  larger   experimental  error  range,  there  was  no  consistency  between  experimental  and   simulation  data.  The  factor  was  larger  for  the  last  two  points  because  those   thermocouples  were  not  calibrated  prior  to  the  experimental  campaign.  These  input   values  for  all  the  QOIs  are  listed  in  Table  5.     Table  5.  Inputs  to  the  consistency  analysis.       QOI   Average   Uncertainty   Units   Value   Radiometer  1   63.76   8.98   [W/m2]   Radiometer  2   89.59   9.74   [W/m2]   Radiometer  3   88.66   11.11   [W/m2]   Thermocouple  1   1319.38   83.65   [K]   Thermocouple  2   1491.52   161.93   [K]   Thermocouple  3   1484.35   78.20   [K]   Thermocouple  4   1399.27   138.71   [K]   Thermocouple  5   1373.11   73.30   [K]     Using  the  inputs  in  Table  5  and  the  surrogate  model  previously  described,  an  initial   Monte-­‐Carlo  sampling  of  the  parameter  space  was  made  with  10,000  points  to  find  a   consistent  region.  This  consistent  region  was  then  sub-­‐sampled  with  an  additional   10,000  points  to  better  identify  its  shape.  The  results  of  the  analysis  are  presented   in  Figure  11(a)  for  the  thermocouple  measurements  and  Figure  11(b)  for   radiometer  measurements.  The  figure  includes  the  uncertainty  ranges  for  the   simulation  data  and  the  experimental  data  as  well  as  the  consistent  region  between   the  two  datasets.  The  uncertainty  range  for  the  simulation  is  large  due  to  the  size  of   the  parameter  space  that  was  explored.  The  parameter  range  was  chosen  to  be  large   in  order  to  encompass  all  the  experimental  data  within  the  uncertainty  of  the   simulation  outputs.  By  requiring  consistency  between  the  experiment  and   simulation,  the  uncertainty  range  is  greatly  reduced  for  both  datasets.     19   a)   Figure  11:  Results  of  consistency  analysis:  (a)  Thermocouple  measurements,  (b)   radiometer  measurements.     20   b)   Figure  12  shows  the  region  of  parameter  space  ("consistent  sample")  where   consistency  is  achieved  with  experimental  and  simulation  data.  In  these  plots  the   color  of  each  point  is  a  normalized  value  of  the  discrepancy  (𝑢𝑢!  in  equation  (11)).   The  boxes  represent  the  bounds  of  the  parameter  space  containing  the  consistent   region.  While  the  parameter  space  has  been  reduced  compared  to  the  original   parameter  space  (represented  by  the  axes  of  the  grid),  some  of  the  parameter   ranges  are  still  large.  For  example,  the  original  range  for  𝜀𝜀!"  was  reduced  from  0-1   to  0.4-1.  Also  of  note  in  Figure  12  are  the  strong  correlations  between  some  of  the   ! parameters  such  as)    and  𝜀𝜀!"  in  Figure  12(a).     !   a)   21   b)   c)   22   d)   e)     ! Figure  12:  Consistent  space  for  thermocouple  and  radiometer  measurements.  (a)     ! ! ! ! and  𝑣𝑣!!"  for  all  emissivities,  (b)  )   ,  𝑣𝑣!!"  and  𝜀𝜀!" ,  (c)    ,  𝑣𝑣!!"  and  𝜀𝜀!,!"#$_!"#$%! ,  (d))    ,   ! ! ! 𝑣𝑣!!"  and  𝜀𝜀!,!"#$_!"#$%! .,  and  (e)    ,  𝑣𝑣!!"  and  𝜀𝜀!,!"#$_!"#$%! .   !   23   ! Table  6  presents  the  new  uncertainty  bounds  for  the  six  parameters  resulting  from   the  consistency  analysis.  From  this  table,  it  is  clear  that  the  range  for  𝑣𝑣!!"  does  not   change,  𝜀𝜀!"  is  similar  to  𝜀𝜀!,!"#$_!"#$%! ,  and  the  values  𝜀𝜀!,!"#$_!"#$%!    and  𝜀𝜀!,!"#$_!"#$%!   ! are  really  low.  Also,  the  range  for    is  reduced  from  0.1-0.4  to  0.14-0.30.   !   Table  6.  Consistent  parameter  ranges  found  using  uncertainties  from  Table  5.     Parameter 𝑣𝑣!!" !   ! 𝜀𝜀!" Minimum 0.545 Maximum 0.900 0.139 0.320 0.306 1.00 𝜀𝜀!,!"#$_!"#$%! 𝜀𝜀!,!"#$_!"#$%! 𝜀𝜀!,!"#$_!"#$%! 0.352 0.990 0.00133 0.341 0.00565 0.203   The  consistency  region  depends  of  the  error  bounds  used  in  equation  (11).   However,  the  error  in  the  thermocouple  measurement  is  not  well  known.  In  order  to   see  the  impact  of  the  thermocouple  error  on  the  size/shape  of  the  consistency   region  in  Figure  12,  the  uncertainty  range  shown  in  Table  5  was  reduced  for   thermocouples  1,  2,  and  3.  For  these  first  three  locations,  the  scaling  factor  applied   to  the  standard  deviation  was  reduced  from  30  to  15.  The  scaling  factor  (60)  was   not  reduced  for  the  last  two  locations  based  on  the  lack  of  calibration  data  for  those   two  thermocouples.  The  new  uncertainty  bounds  are  given  in  Table  7.     Table  7.  Inputs  to  the  consistency  analysis  with  reduced  uncertainty  range  for   thermocouples  1,  2,  and  3.     QOI   Average   Uncertainty   Units   Value   Radiometer  1   63.76   8.98   [W/m2]   Radiometer  2   89.59   9.74   [W/m2]   Radiometer  3   88.66   11.11   [W/m2]   Thermocouple  1   1319.38   41.83   [K]   Thermocouple  2   1491.52   80.96   [K]   Thermocouple  3   1484.35   39.09   [K]   Thermocouple  4   1399.27   138.71   [K]   Thermocouple  5   1373.11   73.30   [K]     Figure  13  and  Figure  14  show  the  new  bounds  and  consistent  space  based  on  the   inputs  in  Table  7.  Reducing  the  uncertainty  by  a  factor  of  two  for  three  of  the  eight   QOIs  reduced  the  consistent  region  to  a  small  fraction  of  the  original  space  for  all  six   parameters.  The  consistent  space  clearly  depends  very  strongly  on  the  error  in  the   thermocouple  measurements.  The  reduced  parameter  ranges  associated  with  this   analysis  are  given  in  Table  8.   24   a)   Figure  13:  Results  of  consistency  analysis:  (a)  Thermocouple  measurements,  (b)   radiometer  measurements       25   b)   a)   b)   26   c)   d)   27   e)     ! Figure  14:  Consistent  space  for  thermocouple  and  radiometer  measurements.  (a)     ! ! ! ! and  𝑣𝑣!!"  for  all  emissivities,  (b)  )   ,  𝑣𝑣!!"  and  𝜀𝜀!" ,  (c)    ,  𝑣𝑣!!"  and  𝜀𝜀!,!"#$_!"#$%! ,  (d))    ,   ! ! ! 𝑣𝑣!!"  and  𝜀𝜀!,!"#$_!"#$%! .,  and  (e)    ,  𝑣𝑣!!"  and  𝜀𝜀!,!"#$_!"#$%! .   !   Table  8.  Consistent  parameter  ranges  found  using  uncertainties  from  Table  7.     Parameter 𝑣𝑣!!"   1 𝑅𝑅 𝜀𝜀!"   Minimum Maximum 0.240   0.402   0.429   0.0602   0.105   0.265   0.440   0.474   0.0665   0.116   0.761   𝜀𝜀!,!"#$_!"#$%!   𝜀𝜀!,!"#$_!"#$%!   𝜀𝜀!,!"#$_!"#$%!   ! 0.841     The  consistency  analysis  shows  some  interesting  results.  First,  the  𝑣𝑣!!"  parameter   has  a  weaker  effect  than  the  other  five  parameters.  Second,  the  𝜀𝜀!"  parameter  has  a   value  that  is  really  close  to  𝜀𝜀!,!"#$_!"#$%! .  Third,  𝜀𝜀!,!"#$_!"#$%!    and  𝜀𝜀!,!"#$_!"#$%!  values   are  very  low.  Therefore,  the  contribution  of  the  radiation  flux  from  the  wall  is  small   for  sections  2  and  3  with  the  major  radiation  contribution  from  coming  from  the  gas.             28   4. Conclusions     A  VUQ  analysis  using  a  consistency  method  was  used  to  study  experimental  and   simulation  data  from  an  oxy-­‐coal  fired  furnace.  The  dataset  included  eight  QOIs:  five   thermocouple  measurements  and  three  radiometer  measurements.  Two  simulation   ! parameters  were  chosen  for  the  analysis:  a  scenario  parameter,   ,  and  a  model   ! parameter,  𝑣𝑣!!" .  To  look  for  consistency  between  the  experimental  and  simulation   data  for  the  eight  QOIs,  it  was  necessary  to  develop  two  instrument  models.  For   these  instrument  models,  four  additional  parameters  were  studied:  which  the   emissivity  of  the  thermocouple,  𝜀𝜀!" ,  and  the  emissivities  of  the  wall  opposite  from   the  radiometer,  𝜀𝜀!,!"#$_!"#$%! ,  𝜀𝜀!,!"#$_!"#$%! ,  and  𝜀𝜀!,!"#$_!"#$%! .  Based  on  this  analysis,  it   was  concluded  that  𝑣𝑣!!"  has  the  weakest  effect  on  the  QOIs  of  the  six  parameters   tested.  In  the  case  of  the  parameters  𝜀𝜀!,!"#$_!"#$%! ,  and  𝜀𝜀!,!"#$_!"#$%! ,  low  values  of   emissivity  were  obtained,  which  means  that  the  contribution  of  the  wall  to  the   overall  radiometer  measurement  is  low  and  that  most  of  the  radiation  comes  from   the  gas.  These  low  values  also  indicate  that  there  was  not  much  ash  deposition  on   the  cooled  targets.  Even  though  the  emissivities  of  the  thermocouple,  𝜀𝜀!" ,  and  of  the   opposite  wall  in  section  1,    𝜀𝜀!,!"#$_!"#$%! ,  were  not  related,  the  values  obtained  for   these  two  emissivities  were  similar.  This  result  could  be  due  to  the  surfaces  on  the   cold  target  and  on  the  wall  thermocouple  being  covered  with  a  similar  particle   material       For  the  next  experimental  campaign,  the  cold  targets  will  be  removed  so  as  to   reduce  the  three  emissivity  parameters  from  the  study.  This  change  will  simplify  the   analysis.  Also,  because  of  the  large  sensitivity  of  the  consistent  region  to  the   uncertainty  range  for  thermocouple  measurements  in  sections  1,  2,  and  3,  a   different  method  with  better  quantified  errors  will  be  used  in  future  experiments  to   measure  the  wall  temperatures.       5.   References     [1]   [2]   [3]   T.  Fletcher,  A.  Kerstein,  R.  J.  Pugmire,  M.  Solum,  and  D.  M.  Grant,  "A  chemical   percolation  model  for  devolatilization:  summary,"  …  Rep.  SAND92-­‐8207,  pp.  1- 66,  1992.   B.  B.  Schroeder,  "Scale-­‐bridging  model  development  and  increased  model   credibility,"  The  University  of  Utah,  2015.   J.  S.  Justin  Luitjens,  John  Schmidt,  Alan  Humphrey,  J.  Davison  de  St.  Germain,   Todd  Harman,  Jim  Guilkey,  Charles  Reid,  Dan  Hinckley,  Jeff  Burghardt,  John  M.   Schreiner,  Joseph  Peterson,  Jeremy  Nicholas  Thornock,  Brian  Leavy,  Qingyu   Meng,  Jennifer  Spinti,  Chuck  W,  "http://www.uintah.utah.edu/."  [Online].   Available:  http://www.uintah.utah.edu/.   29   [4]   [5]   [6]   [7]   [8]   [9]   J.  Pedel,  J.  N.  Thornock,  and  P.  J.  Smith,  "Ignition  of  co-­‐axial  turbulent  diffusion   oxy-­‐coal  jet  flames:  Experiments  and  simulations  collaboration,"  Combust.   Flame,  vol.  160,  no.  6,  pp.  1112-1128,  2013.   J.  J.  Murphy  and  C.  R.  Shaddix,  "Combustion  kinetics  of  coal  chars  in  oxygen-­‐ enriched  environments,"  Combust.  Flame,  vol.  144,  no.  4,  pp.  710-729,  Mar.   2006.   J.  Ahn,  R.  Okerlund,  A.  Fry,  and  E.  G.  Eddings,  "Sulfur  trioxide  formation  during   oxy-­‐coal  combustion,"  Int.  J.  Greenh.  Gas  Control,  vol.  5,  pp.  S127-S135,  2011.   A.  Fry,  B.  Adams,  K.  Davis,  D.  Swensen,  S.  Munson,  and  W.  Cox,  "An   investigation  into  the  likely  impact  of  oxy-­‐coal  retrofit  on  fire-­‐side  corrosion   behavior  in  utility  boilers,"  Int.  J.  Greenh.  Gas  Control,  vol.  5,  pp.  S179-S185,   2011.   "http://www.icse.utah.edu/multifuel-­‐furnace/."  .   C.  E.  Rasmussen  and  C.  K.  I.  Williams,  Gaussian  processes  for  machine  learning.   2006.     30