<commit_before>
%\section{Calibration and Validation}
\section{Validation}
\label{sec:validation}

%
% meshed vanes are 24x more expensive
%

The previous sections briefly outlined the physical regime under
consideration, the mathematical models we have developed to emulate
these conditions, and the software we are leveraging to solve these
equations for a variety of system configurations and scenarios. 
However, for our simulations to be useful for prediction, we
need to evaluate models against experimental data so
as to ensure that the entire formulation accurately reflects reality. 
Thus, this section discusses the validation of computational results
against existing experimental data and high fidelity simulations.

%
% experimental challenges
%

The general system configuration is depicted
in Figure \ref{fig:lab_image}. 
Notice that the experimental laboratory has numerous objects
in the immediate vicinity that may obstruct/manipulate the flow. These
objects may be moved or removed during PIV data gathering.  
Several challenges arise in performing a validation study between the
simulation output and the experimental data. These data were taken using
particle image velocimetery (PIV), and the errors in 
in measurement and sampling are not known. 


% The validation challenge is compounded by the fact that little is
% known about the uncertainties in the observation data. PIV is a
% non-intrusive technique, but it does rely upon large sample sizes 
% to generate reliable statistics. While several hundred PIV
% snapshots are available, no quantified uncertainties for the averaged fields
% presently exist.  

In addition, only velocity measurements are available. Several
potentially important quantities of interest, such as the pressure field
or the temperature, have not been measured, and cannot then be used for
the purposes of validation. 


%
%\subsection{Model Calibration}
%
%
% viscosity calibrated
% 
%
%
%\subsection{Model Validation}


  \begin{figure}[!htb]
    \begin{center}
     \includegraphics[width = 12 cm]{figs/lab_setup}
     \caption{The single tier straight vane laboratory configuration. The
     apparatus is shown with a turbine, but it was removed for data
     gathering.}
     \label{fig:lab_image}
    \end{center}
  \end{figure}

While no sensitivity analysis has been performed, it is likely that the
largest uncertainty in the laboratory simulation is a result of the
ventilation. The heated plate on the bottom of the laboratory
generates enough heat to cause a significant increase in room
temperature (30+ Kelvin). This also greatly impacts the SoV
performance, as the ground to air thermal gradient drives the
vortex. The laboratory therefore uses cooling to maintain
temperature, in particular, two inlet HVAC ducts into the room. While
efforts have been made to characterize the level of ventilation being
used, these numbers come with non-trivial uncertainties attached. One
vent runs continuously at 288 Kelvin with a flow rate of approximately 1 
$m^3$/s.
%(4-6 m/s with an approximate area of 0.2 $m^2$)
The other vent initializes only if the room exceeds 301 Kelvin
Finally, the air is expected to leave through the laboratory doors.
Preliminary results indicated that 
inflow rates consistent with the lower bound of those estimates result in an
unrealistic heating of the room, while inflow conditions at the high end
result in velocity profiles that exceed the laboratory measurements. In
other words, our simulations appear to be sensitive to the choice of
inflow rate, and it is likely that the laboratory is run where one of
the vents is operating intermittently. 

We have attempted to mimic these scenario conditions in our
simulations. To do so, we impose Dirichlet boundary conditions to
establish a constant inflow condition of cool air at the rates 
proscribed by our collaborators. The simulation uses adiabatic side
walls as a boundary condition. It is unclear how much of an impact this
may have on the simulation. It is also unclear if this is a realistic
boundary condition. The largest boundary condition disparity is that
flow is permitted to leave out the top of the boundary, instead of out
of the sides of the room. 

  \begin{figure}[!htb]
    \begin{center}
     \includegraphics[width = 12 cm]{figs/hybrid_profile}
     \caption{Azimuthal and vertical velocity profiles as a function of
     radius. The simulation and experimental data broadly agree, with
     the simulation also exhibiting the characteristic ``twin-peak''
     structure of the hybrid vanes in the azimuthal velocity. }
     \label{fig:lab}
    \end{center}
  \end{figure}

Figure \ref{fig:lab} shows direct comparisons between laboratory measurements for a simple 
two tier configuration ($55^{\circ}$ top, $30^{\circ}$ bottom) and 
a nominally identical simulation. The simulation and experiment broadly agree. The simulation 
correctly reproduces the twin peak structure in the azimuthal velocity 
observed for this configuration in the experiment. The radial location of peak vertical velocity also 
closely agrees with experiment. The largest observed difference is near the center, where the simulation predicts 
a downward vertical velocity, in contrast to the modest vertical flows measured in the laboratory. 

Similar validation comparisons have been made between several other configurations, notably the $30^{\circ}$ 
and $60^{\circ}$ singly tier straight vane cases, with similar levels of agreement. 
This represents the totality of quantitiative data available for comparison. Qualitative comparisons have been made
between the our simulation results with a mean velocity and with wind tunnel pictures. These images showed
roughly consistent structure between simulation and experiment. Finally. estimates of the energy fluxes between
the field configuration and our simulation results agreed within 15\%. These validation studies have provided a modest 
level of confidence that our simulations accurately reproduce the dynamics observed in real vane configurations. 

%
% turbine (explain why we dont need to do it)
%

%% Another significant validation challenge is in modeling the
%% turbines. This is in essence a new embedded 
%% submodel that we will add after validation of the initial configuration
%% is completed. 
<commit_msg>hiding this image for now<commit_after>
%\section{Calibration and Validation}
\section{Validation}
\label{sec:validation}

%
% meshed vanes are 24x more expensive
%

The previous sections briefly outlined the physical regime under
consideration, the mathematical models we have developed to emulate
these conditions, and the software we are leveraging to solve these
equations for a variety of system configurations and scenarios. 
However, for our simulations to be useful for prediction, we
need to evaluate models against experimental data so
as to ensure that the entire formulation accurately reflects reality. 
Thus, this section discusses the validation of computational results
against existing experimental data and high fidelity simulations.

%
% experimental challenges
%

The general system configuration is depicted
in Figure \ref{fig:lab_image}. 
Notice that the experimental laboratory has numerous objects
in the immediate vicinity that may obstruct/manipulate the flow. These
objects may be moved or removed during PIV data gathering.  
Several challenges arise in performing a validation study between the
simulation output and the experimental data. These data were taken using
particle image velocimetery (PIV), and the errors in 
in measurement and sampling are not known. 


% The validation challenge is compounded by the fact that little is
% known about the uncertainties in the observation data. PIV is a
% non-intrusive technique, but it does rely upon large sample sizes 
% to generate reliable statistics. While several hundred PIV
% snapshots are available, no quantified uncertainties for the averaged fields
% presently exist.  

In addition, only velocity measurements are available. Several
potentially important quantities of interest, such as the pressure field
or the temperature, have not been measured, and cannot then be used for
the purposes of validation. 


%
%\subsection{Model Calibration}
%
%
% viscosity calibrated
% 
%
%
%\subsection{Model Validation}


%  \begin{figure}[!htb]
%    \begin{center}
%     \includegraphics[width = 12 cm]{figs/lab_setup}
%     \caption{The single tier straight vane laboratory configuration. The
%     apparatus is shown with a turbine, but it was removed for data
%     gathering.}
%     \label{fig:lab_image}
%    \end{center}
%  \end{figure}

While no sensitivity analysis has been performed, it is likely that the
largest uncertainty in the laboratory simulation is a result of the
ventilation. The heated plate on the bottom of the laboratory
generates enough heat to cause a significant increase in room
temperature (30+ Kelvin). This also greatly impacts the SoV
performance, as the ground to air thermal gradient drives the
vortex. The laboratory therefore uses cooling to maintain
temperature, in particular, two inlet HVAC ducts into the room. While
efforts have been made to characterize the level of ventilation being
used, these numbers come with non-trivial uncertainties attached. One
vent runs continuously at 288 Kelvin with a flow rate of approximately 1 
$m^3$/s.
%(4-6 m/s with an approximate area of 0.2 $m^2$)
The other vent initializes only if the room exceeds 301 Kelvin
Finally, the air is expected to leave through the laboratory doors.
Preliminary results indicated that 
inflow rates consistent with the lower bound of those estimates result in an
unrealistic heating of the room, while inflow conditions at the high end
result in velocity profiles that exceed the laboratory measurements. In
other words, our simulations appear to be sensitive to the choice of
inflow rate, and it is likely that the laboratory is run where one of
the vents is operating intermittently. 

We have attempted to mimic these scenario conditions in our
simulations. To do so, we impose Dirichlet boundary conditions to
establish a constant inflow condition of cool air at the rates 
proscribed by our collaborators. The simulation uses adiabatic side
walls as a boundary condition. It is unclear how much of an impact this
may have on the simulation. It is also unclear if this is a realistic
boundary condition. The largest boundary condition disparity is that
flow is permitted to leave out the top of the boundary, instead of out
of the sides of the room. 

  \begin{figure}[!htb]
    \begin{center}
     \includegraphics[width = 12 cm]{figs/hybrid_profile}
     \caption{Azimuthal and vertical velocity profiles as a function of
     radius. The simulation and experimental data broadly agree, with
     the simulation also exhibiting the characteristic ``twin-peak''
     structure of the hybrid vanes in the azimuthal velocity. }
     \label{fig:lab}
    \end{center}
  \end{figure}

Figure \ref{fig:lab} shows direct comparisons between laboratory measurements for a simple 
two tier configuration ($55^{\circ}$ top, $30^{\circ}$ bottom) and 
a nominally identical simulation. The simulation and experiment broadly agree. The simulation 
correctly reproduces the twin peak structure in the azimuthal velocity 
observed for this configuration in the experiment. The radial location of peak vertical velocity also 
closely agrees with experiment. The largest observed difference is near the center, where the simulation predicts 
a downward vertical velocity, in contrast to the modest vertical flows measured in the laboratory. 

Similar validation comparisons have been made between several other configurations, notably the $30^{\circ}$ 
and $60^{\circ}$ singly tier straight vane cases, with similar levels of agreement. 
This represents the totality of quantitiative data available for comparison. Qualitative comparisons have been made
between the our simulation results with a mean velocity and with wind tunnel pictures. These images showed
roughly consistent structure between simulation and experiment. Finally. estimates of the energy fluxes between
the field configuration and our simulation results agreed within 15\%. These validation studies have provided a modest 
level of confidence that our simulations accurately reproduce the dynamics observed in real vane configurations. 

%
% turbine (explain why we dont need to do it)
%

%% Another significant validation challenge is in modeling the
%% turbines. This is in essence a new embedded 
%% submodel that we will add after validation of the initial configuration
%% is completed. 

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