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Copy file name to clipboardExpand all lines: Manuals/FDS_User_Guide/FDS_User_Guide.tex
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\subsection{Two-Dimensional and Axially-Symmetric Calculations}
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\label{info:2D}
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The governing equations solved in FDS are written in terms of a three dimensional Cartesian coordinate system. However, a two dimensional Cartesian or two dimensional cylindrical (axially-symmetric) calculation can be performed by setting the \ct{J} in the \ct{IJK} triplet to 1 on the \ct{MESH} line. For axial symmetry, add \ct{CYLINDRICAL=T} to the \ct{MESH} line, and the coordinate $x$ is then interpreted as the radial coordinate $r$. If more than one mesh is used, all the meshes must be specified as 2-D or \ct{CYLINDRICAL}---you cannot mix 2-D, 3-D and cylindrical geometries. No boundary conditions should be set at the planes $y=\hbox{\tt YMIN=XB(3)}$ or $y=\hbox{\tt YMAX=XB(4)}$, nor at $r=\hbox{\tt XMIN=XB(1)}$ in an axially-symmetric calculation if $r=\hbox{XB(1)=0}$ (Note that \ct{XB(1)} does not have to be 0). For better visualizations, the difference between \ct{XB(4)} and \ct{XB(3)} should be small so that the Smokeview rendering appears to be in 2-D. An example of an axially-symmetric helium plume is given in Sec.~\ref{baroclinic_torque}.
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When processing results for a \ct{CYLINDRICAL} simulation, note that integrated output quantities with the \ct{SPATIAL_STATISTIC} attribute apply only to the specified 2-D or cylindrical coordinates. Thus, the cylindrical coordinates define a cylindrical sector, like a slice of cake, even though Smokeview will not render it this way. The fully integrated quantity can be calculated by multiplying the reported value by $2 \pi \, \delta\theta$, where $\delta\theta$ is the difference between \ct{YMAX} and \ct{YMIN} in radians. The values chosen for \ct{YMAX} and \ct{YMIN} do not matter as long as the rendering in Smokeview is to your liking.
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The governing equations solved in FDS are written in terms of a three-dimensional Cartesian coordinate system. However, a two-dimensional Cartesian or two-dimensional cylindrical (axially-symmetric) calculation can be performed by setting the \ct{J} in the \ct{IJK} triplet to 1 on the \ct{MESH} line. For axial symmetry, add \ct{CYLINDRICAL=T} to the \ct{MESH} line, and the coordinate $x$ is then interpreted as the radial coordinate $r$. If more than one mesh is used, all the meshes must be specified as 2-D or \ct{CYLINDRICAL}---you cannot mix 2-D, 3-D and cylindrical geometries. No boundary conditions should be set at the planes $y=\hbox{\tt YMIN=XB(3)}$ or $y=\hbox{\tt YMAX=XB(4)}$, nor at $r=\hbox{\tt XMIN=XB(1)}$ in an axially-symmetric calculation if $r=\hbox{XB(1)=0}$ (Note that \ct{XB(1)} does not have to be 0). For better visualizations, the difference between \ct{XB(4)} and \ct{XB(3)} should be small so that the Smokeview rendering appears to be in 2-D. An example of an axially-symmetric helium plume is given in Sec.~\ref{baroclinic_torque}.
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When performing solid phase heat transfer while using a 2-D \ct{CYLINDRICAL} coordinate system, you must designate \ct{GEOMETRY='CYLINDRICAL'} on a surface (\ct{SURF} line) that is facing radially outward (positive $r$ direction) or \ct{GEOMETRY='INNER CYLINDRICAL'} on a surface that is facing radially inward (negative $r$ direction). In the latter instance, you must also specify the \ct{INNER_RADIUS} (m) of the cylinder. For the outer cylindrical boundary, specify an \ct{INNER_RADIUS} if appropriate. Its default value is 0~m. Because your inward and outward facing boundaries might occur at various radii, you must create separate \ct{SURF} lines for each with the appropriate values of \ct{GEOMETRY} and \ct{INNER_RADIUS}. For an obstruction (\ct{OBST}), use \ct{SURF_ID6} to assign individual \ct{SURF ID}s to each of the six faces. Because this is a 2-D simulation, the third and fourth entries representing the \ct{SURF ID}s in the $y$ or angular direction can just be designated \ct{'INERT'}.
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When processing results for a \ct{CYLINDRICAL} simulation, note that integrated output quantities with the \ct{SPATIAL_STATISTIC} attribute refer to the volume or surface area of the entire cylinder, not just the wedge. Smokeview renders the wedge as a 2-D slice. The values chosen for \ct{YMAX} and \ct{YMIN} do not matter as long as the rendering in Smokeview is to your liking. For a 2-D, non-cylindrical geometry, spatially integrated quanties shall be output in units of the quantity per unit meter.
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\subsection{Multiple Meshes}
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\label{info:multimesh}
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\end{lstlisting}
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would output the total surface area in the volume \ct{XB} where the total heat flux exceeds 10~\unit{kW/m^2}.
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\subsubsection{Two-Dimensional and Cylindrical Coordinate Systems}
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If the computational domain is two-dimensional or cylindrical, some spatially-integrated quantities are adjusted to eliminate the dependence on the arbitrarily chosen $\delta y$ or $\delta \theta$. For a 2-D domain, a reported volume output will have units of m$^3$/m and an area output will have units of m$^2$/m. For a cylindrical domain, volume and area outputs are reported for the entire cylinder rather than the thin wedge on which the simulation is performed. This might cause confusion in cases where both the input parameters and simulation results involve volumetric or areal quantities; thus, it is good practice to perform a simple test case with a known result to verify that these adjustments have been performed properly.
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