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% A meaningless sample of slides written by using
% ILASS-Americas Presentation, May 2005
% Brooks Moses
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% Command to create a new slide, with title given as argument.
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% presentation.
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  [here]
  {none}
  {\startcombination[2*1]
    {\scale[width=9.0cm]{#1}}
    {\bfc #2}
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    {\bfc #4}
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}


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% ACTUAL SLIDE TEXT BEGINS HERE
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% Title slide (not defined with a \NewSlide command, since the title slide
% doesn't use the standard graphics and layout.)

\page[blank]
\midaligned{
  \bfe\rm\mc \setupinterlinespace[0.9]
  2次元静電場と正則関数: \\
  \bfe\rm\mc \setupinterlinespace[0.9]
  静電誘導の簡単な例 \\

  \\  
  \externalfigure[Seal][width=60mm] \\
  \\
  
  \tfd \setupinterlinespace[0.9]
  鈴木太郎，中村九介 \\

  \\
      
  \itd
  Department of Mechanical Engineering \\
  \itd
  Sakura International University  
}
%
% ### The "\page" command here appears extraneous.
\page


% -----------------------------------------------------------------------------
% Set text size and spacing for remaining slides.
% ### This could probably go better in the \NewSlide command.)

\tfd \setupinterlinespace[0.85]

% -----------------------------------------------------------------------------
\NewSlide{Outline}

\startbullets
\item
 Motivation: Dense Sprays and LES Calculations.
 
\blank[2*big]

\item
 Spatial Filtering of Multiphase Flow Equations.

\blank[2*big]

\item
 An Example of a Partly-Resolved Particle Model. 例

\blank[2*big]

\item
 Results for Various Particle Sizes. 種々の粒子サイズに対する結果

\blank[2*big]

\item
 Grid Requirements for Filtered Multiphase Calculations.

\blank[2*big]

\item
 Filtering and Point Particle Models. 

\blank[2*big]

\item
 Conclusions.

\stopbullets


% -----------------------------------------------------------------------------
\NewSlide{Motivation}

\startbullets
\item
 Atomization models in combustion codes:
\stopbullets

\midaligned{
 \hbox{\externalfigure[pic][width=6cm]}
}

\startbullets
\item
 Dense-region mass, momentum transfers are significant.
 
    \startbullets
    \item
     How much transfer should there be?
    \item
     How should it be distributed?
    \stopbullets

\item
 Multiphase models need to be consistent with LES.

\item
 Filtered-Phase Method (FPM) provides analysis path.
\stopbullets


% -----------------------------------------------------------------------------
\NewSlide{What is the Filtered-Phase Method?}

\startbullets
\item
 Apply the turbulent LES methodology for fluid surfaces as well as turbulent eddies:
 
    \startbullets
    \item
     Rigorously extend fluid equations to cover entire domain, including regions outside the fluids.
    \item
     Flow phases and variable fields are divided into large- and small-scale parts by spatial filtering.
    \item
     Large-scale liquid features and gas-phase interaction appear directly in the resolved-scale calculation.
    \item
     Small-scale effects such as individual droplets and secondary breakup are included by models.
    \stopbullets

\item
 {\bfd As in LES, the interaction between small scales and large scales can be derived explicitly.}

\stopbullets


% -----------------------------------------------------------------------------
\NewSlide{Spatially-Filtered Multiphase Flow Equations}

\startbullets
\item Filtered momentum equation (simplified form):
\stopbullets

% Because ConTeXt's math setup is TeX-based rather than LaTeX-based, and the
% LaTeX/amsmath-compatibility functions aren't yet complete, the equations
% are generated in a separate LaTeX file and included here as a graphic.
%\midaligned{
% \hbox{\externalfigure[equation16a][scale=1800]}
% \hskip0.5in\relax
% \raise3.5cm\hbox{\externalfigure[equation16b][scale=1800]}
%}

% Normally, \vskip should be avoided in ConTeXt documents; this is a bit
% of a hack to get the spacing right, and should be replaced by better
% code once I figure out how.
\vskip-2mm\relax

\startbullets
\item
 Simplifying assumptions: one phase (plus particles), \crlf
 incompressible flow, constant properties, no outflow.

\item
 Unclosed terms:
 
    \startbullets
    \item \color[backa]{\vrule width3ex height1.7ex depth0.3ex}
      Correction terms for surface motion.
    \item \color[backb]{\vrule width3ex height1.7ex depth0.3ex}
      Surface stress term.
    \item \color[backc]{\vrule width3ex height1.7ex depth0.3ex}
      Subfilter-scale convection (LES model term).
    \stopbullets

\stopbullets


% -----------------------------------------------------------------------------
\NewSlideII{Model Problem}

\startbullets
\item
 Laminar flow around a fixed cylindrical ``particle''.
\stopbullets

%\placefigure
%  [here]
%  {}
%  {\scale[height=8.5cm]{\externalfigure[exact_flow]}}

\startbullets
\item
 Flow conditions: Uniform freestream, { ${\it Re}_D = 26$}.

    \startbullets
    \item Steady flow, with significant recirculation zone.
    \item Wake continues for many diameters downstream.
    \item Can be simulated with a 2-D calculation.
    \stopbullets

\stopbullets


% -----------------------------------------------------------------------------
\NewSlideII{Parametric Particle Model}

%\twoplots
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle_surfaceforce]}
%  }
%  {Exact surface force, ${\it r}_{filter} = 0.25 {\it D}_{particle}$}
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle_sfsforce]}
%  }
%  {Exact subfilter convection, ${\it r}_{filter} = 1.0 {\it D}_{particle}$}

\startbullets
\item
 Unclosed terms approximated by parametric models:

   \startbullets
   \item Surface force represented by a multi-point \crlf interpolation over the particle surface.

   \item Subfilter-scale convection represented by three filtered point forces.
   \stopbullets

\stopbullets


% -----------------------------------------------------------------------------
\NewSlideII{Initial Model Results}

%\twoplots
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle5e3f]}
%  }
%  {Computed streamwise velocity, ${\it r}_{filter} = 1.0 {\it D}_{particle}$}
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle5e-exact]}
%  }
%  {Filtered ``exact'' velocity, ${\it r}_{filter} = 1.0 {\it D}_{particle}$}

\startbullets
\item
 Computation parameters (in units of { ${\it D}_{particle}$}):
   \startbullets
   \item { $16 \times 16$} flow domain.
   \item { $\Delta {\it x}_{grid} = 1/16$}, for grid-converged results.
   \stopbullets

\item
 The resulting simulation is a close match for the exact filtered flow, both qualitatively and quantitatively.

\stopbullets


% -----------------------------------------------------------------------------
\NewSlideII{Results from Partial Models}

%\twoplots
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle5e]}
%  }
%  {Computed velocity, no subfilter-scale model.}
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle5e-exact]}
%  }
%  {Filtered ``exact'' velocity, ${\it r}_{filter} = 1.0 {\it D}_{particle}$.}

\startbullets
\item
 With the subfilter-scale convection neglected:
   \startbullets
   \item Wake centerline velocity is higher.
   
   \item Volume-displacement effects are greatly reduced.
   
   \item Total wake momentum defect, however, is the same.
   
   \stopbullets

\stopbullets


% -----------------------------------------------------------------------------
\NewSlideII{Results from Partial Models}

%\twoplots
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle5m]}
%  }
%  {Computed velocity, single-point surface force.}
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle5e]}
%  }
%  {Computed velocity, 128-point surface force.}

\startbullets
\item
 With the drag force uniformly distributed over the particle's surface (and without the subfilter term):
   \startbullets
   \item The wake is offset downstream because the centroid of the force is in the wrong place.
   
   \item The results are otherwise nearly identical.
   
   \stopbullets

\stopbullets


% -----------------------------------------------------------------------------
\NewSlideII{Initial and Partial Model Results}

\oneplot
  {\clip[width=10cm, height=5cm, hoffset=0.0in, voffset=0.0in]
        {\externalfigure[pic][height=4.5cm]}
  }
  {Momentum flux defects (in units of $\rho {\bi U}_0^2$).}

\startbullets
\item
 The wake defect consists of two parts:

    \startbullets
    \item Momentum loss due to drag force (all models).
    \item Momentum flux temporarily ``hidden'' in subfilter scales (with subfilter convection term).
    \stopbullets

\item
 The surface force distribution has very little effect. 

\stopbullets


% -----------------------------------------------------------------------------
\NewSlideII{Results for Various Particle Sizes}

%\twoplots
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle5c3f]}
%  }
%  {Filtered-computation results, ${\it r}_{filter} = 0.5 {\it D}_{particle}$}
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle5c-exact]}
%  }
%  {Filtered ``exact'' results, ${\it r}_{filter} = 0.5 {\it D}_{particle}$.}

\startbullets
\item
 Filter = 0.5 particle diameter:
   \startbullets
   \item Results are still very good.

   \item Some minor effects from limited sfs-term coverage.
   \stopbullets

\stopbullets


% -----------------------------------------------------------------------------
\NewSlideII{Results for Various Particle Sizes}

%\twoplots
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle5a]}
%  }
%  {Filtered-computation results, ${\it r}_{filter} = 0.1 {\it D}_{particle}$}
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle-exact]}
%  }
%  {Unfiltered ``exact'' results.}

\startbullets
\item
 Filter = 0.1 particle diameter:
   \startbullets
   \item No sfs term (three-point is insufficient)

   \item Results close, but sfs term still needed even at this fine resolution.
   \stopbullets

\stopbullets


% -----------------------------------------------------------------------------
\NewSlideII{Results for Various Particle Sizes}

%\twoplots
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle5h3f]}
%  }
%  {Filtered-computation results, ${\it r}_{filter} = 4.0 {\it D}_{particle}$}
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle5h-exact]}
%  }
%  {Filtered ``exact'' results, ${\it r}_{filter} = 4.0 {\it D}_{particle}$.}

\startbullets
\item
 Filter = 4.0 particle diameter:
   \startbullets
   \item Still reasonably good results (comparable to 1.0 case).

   \item Some domain-size issues.
   \stopbullets

\stopbullets


% -----------------------------------------------------------------------------
\NewSlideII{Results for Various Particle Sizes}

%\twoplots
%  {\clip[width=9.5in, height=7.02in, hoffset=1.0in, voffset=1.105in]
%        {\externalfigure[wakeplot_3fb]}
%  }
%  {Wake momentum defects \crlf (in units of $\rho {\bi U}_0^2$).}
%  {\clip[width=9.5in, height=7.02in, hoffset=1.0in, voffset=1.105in]
%        {\externalfigure[wakeplot_3fa2]}
%  }
%  {Wake width \crlf (in units of ${\it D}_{particle}$).}

\startbullets
\item
 SFS momentum term increases with increasing filter.

\item
 Net wake defect is constant.

\item
 Wake width converges to same size downstream..

\stopbullets


% -----------------------------------------------------------------------------
\NewSlideII{Results for Grid Resolution Study}

%\twoplots
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle5e3f]}
%  }
%  {Filtered-computation results, $\Delta {\it x}_{grid} = 1/16 {\it r}_{filter}$}
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle5k3f]}
%  }
%  {Filtered-computation results, $\Delta {\it x}_{grid} = 1/2 {\it r}_{filter}$}

\startbullets
\item
 Grid = 0.5 filter radius:
   \startbullets
   \item Qualitatively very good results

   \item Some primary grid-coarsening effects. 
    (Max wake defect slightly washed-out.)
   \stopbullets

\stopbullets


% -----------------------------------------------------------------------------
\NewSlideII{Results for Grid Resolution Study}

%\twoplots
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle5e3f]}
%  }
%  {Filtered-computation results, $\Delta {\it x}_{grid} = 1/16 {\it r}_{filter}$}
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle5l3f]}
%  }
%  {Filtered-computation results, $\Delta {\it x}_{grid} = 1.0 {\it r}_{filter}$}

\startbullets
\item
 Grid = 1.0 filter radius:
   \startbullets
   \item Expected to be ill-resolved.

   \item Qualitatively still reasonable.
   
   \item Wake defect very ``smeared out''.
   \stopbullets

\stopbullets


% -----------------------------------------------------------------------------
\NewSlideII{Results for Grid Resolution Study}

%\oneplot
%  {\clip[width=9.5in, height=7.125in, hoffset=1.0in, voffset=1.0in]
%        {\externalfigure[wakeplot_4fa2]}
%  }
%  {Wake width (in units of ${\it D}_{particle}$).}

\startbullets
\item
 Wake width results are good over all grid range, even for most ill-resolved case.

\stopbullets


% -----------------------------------------------------------------------------
% \NewSlide{Filtering and the Point Particle Model}

% \startbullets
% \item
%  Comments here about how this relates to the point-particle model
%  
% \item
%  Why this is relevant?

%     \startbullets
%     \item is rigorous derivation for particles in LES
%     \stopbullets

% \item
%  Limit behavior of SGS term

%     \startbullets
%     \item graph; example
%     \stopbullets

% \stopbullets


% -----------------------------------------------------------------------------
\NewSlideII{Filtering and the Point Particle Model}

%\twoplots
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle-f50-surface]}
%  }
%  {Exact surface force, ${\it r}_{filter} = 50 {\it D}_{particle}$}
%  {\clip[width=8.75in, height=6.75in, hoffset=1.375in, voffset=1.00in]
%        {\externalfigure[particle-f50-sfs]}
%  }
%  {Exact subfilter convection, ${\it r}_{filter} = 50 {\it D}_{particle}$}

\startbullets
\item
 Even for a case where the particle is two orders of magnitude smaller than the filter, the subfilter-scale convection term is a significant fraction (around 25\%, at peak) of the filtered surface force.

\stopbullets

\setupinterlinespace[5]

\setuptables[rulethickness=2pt]
\midaligned{\tfc\rm\mc
\starttable[|l|l|]
\HL
\VL りんご \VL 110円 \VL\FR
\VL なし   \VL 70円  \VL\MR
\VL みかん \VL 90円  \VL\LR
\HL
\stoptable
}

\setupinterlinespace[0.85]
% -----------------------------------------------------------------------------
\NewSlide{Summary and Conclusions}

\startbullets
\item
 We have derived LES-compatible equations for multiscale, multiphase flow by spatial filtering, and used these equations to develop models for typical partly-resolved particles.

\item
 The particle models produce accurate results over a range of scales.

\item
 Grid resolution requirements are comparable to requirements for turbulence LES.

\item
 Subfilter-scale term is important over a wide range of scales, well into the ``resolved'' and ``point-particle'' regimes.

\item
 This provides clear, rigorous guidance for distributing particle forces in particle-laden LES computations.
\stopbullets


% -----------------------------------------------------------------------------
% Close environments at end of document.
\stopcolor
\stoptext
