Implement Carroll method for Interior Radiant Heat Exchange

design/FY2019/Carroll-MRT.md

@@ -0,0 +1,49 @@
+Carroll Mean Radiant Temperature option for Interior Radiant Exchange
+=====================================================================
+
+**Neal Kruis, Big Ladder Software, LLC**
+
+## Justification for New Feature ##
+
+A well-known performance bottleneck in EnergyPlus is the calculation of interior long-wave radiation exchange. This is a dense-matrix, linear algebra problem with O(n^2 ) complexity. One approach used in other programs with comparable accuracy is the Carroll method (see Carroll 1980, 1980a, & 1981). There are several similar MRT methods with linear complexity including methdods by Walton (used in BLAST) and Seem (used in TRNSYS). Unlike Walton's method, Carroll's method balances radiant heat without an additional term to balance the heat flow between surfaces.
+
+## Approach ##
+
+The Carroll method is an approximation of gray-body long-wave radiation exchange within an enclosure that simplifies the surface-to-surface radiation exchange by using a single, mean radiant temperature node, Tr, that act as a clearinghouse for the radiation heat exchange between surfaces. Instead of solving a dense-matrix, linear algebra problem, the mean radiant temperature can be calculated using a single equation, and subsequently used to determine the net long-wave radiation to/from each surface. Unlike the O(n^2 ) complexity of the current dense-matrix solution, this approach has linear complexity.
+
+The mean radiant temperature is calculated using three steps:
+
+1. Calculation of the mean radiant temperature “view factor”, Fi. These view factors represent each surface’s “view” to the mean radiant temperature node as though all surfaces were part of a spherical enclosure (i.e., they all have equal view of the node regardless of their orientation to each other). Fi is calculated as:
+
+    $$F_i=\frac{1}{1-\frac{A_i F_i}{\sum_1^n{A_j F_j} }}$$
+
+    Because of the circular reference in this equation, the collection of all “view factors” must be solved iteratively, but only once per simulation as surface areas do not change throughout. This converges for realistic enclosures but won’t necessarily converge for “enclosures” having only two or three surfaces, particularly if there are large area disparities.
+
+2. Calculating the gray-body radiation resistance, F’i. This calculation must be computed every time surface emissivity changes. F’i is calculated as:
+
+    $$F'_i=\frac{\sigma\varepsilon_i}{\frac{\varepsilon_i}{F_i} +1-\varepsilon_i}$$
+
+3. Finally, the mean radiant temperature, Tr, is:
+
+    $$T_r=\frac{\sum_1^nA_i F'_i T_i}{\sum_1^nA_i F'_i}$$
+
+Once the mean radiant temperature is known, the net radiation heat transfer for each surface can be calculated as:
+
+$$q=F'_i A_i (T_r^4-T_i^4)$$
+
+
+## Input Output Reference Documentation ##
+
+See proposed changes in [Energy+.idd.in](https://github.com/NREL/EnergyPlus/pull/7534/files#diff-23ccf090b80d26e885712256b9a6d888). Will draft document once IDD is reviewed.
+
+## Engineering Reference ##
+
+See approach.
+
+## References ##
+
+Carroll, J. A., 1980, An ‘MRT Method’ of Computing Radiant Energy Exchange in Rooms, Proceedings of the Second Systems Simulation and Economic Analysis Conference, San Diego, CA.
+
+Carroll, J. A., 1980a, "An MRT method of computing radiant energy exchange in rooms," Proceedings of the 2nd Systems Simulation and Economic Analysis Conference, San Diego, CA.
+
+Carroll, J. A., 1981, "A Comparison of Radiant Interchange Algorithms," Proceedings of the 3rd Annual Systems Simulation and Economics Analysis/Solar Heating and Cooling Operational Results Conference, Reno. Solar Engineering, Proceedings of the ASME Solar division.

doc/engineering-reference/src/surface-heat-balance-manager-processes/inside-heat-balance.tex

@@ -48,7 +48,11 @@ \subsubsection{LW Radiation Exchange Among Zone Surfaces}\label{lw-radiation-exc
 
 The limiting case of completely absorbing air has been used for load calculations and also in some energy analysis calculations.~ This model is attractive because it can be formulated simply using a combined radiation and convection heat transfer coefficient from each surface to the zone air.~ However, it oversimplifies the zone surface exchange problem, and as a result, the heat balance formulation in EnergyPlus treats air as completely transparent.~ This means that it does not participate in the LW radiation exchange among the surfaces in the zone. The model, which considers room air to be completely transparent, is reasonable physically because of the low water vapor concentrations and the short mean path lengths.~ It also permits separating the radiant and convective parts of the heat transfer at the surface, which is an important attribute of the heat balance method.
 
-EnergyPlus uses a grey interchange model for the longwave radiation among zone surfaces.~ This model is based on the ``ScriptF'' concept developed by Hottel (Hottel and Sarofim, Radiative Transfer, Chapter 3, McGraw Hill, 1967).~ This procedure relies on a matrix of exchange coefficients between pairs of surfaces that include all exchange paths between the surfaces.~ In other words all reflections, absorptions and re-emissions~ from other surfaces in the enclosure are included in the exchange coefficient, which is called ScriptF.~ The major assumptions are that all surface radiation properties are grey and all radiation is diffuse.~ Both assumptions are reasonable for building zone interchange.
+EnergyPlus uses a grey interchange model for the longwave radiation among zone surfaces. EnergyPlus offers two algorithms for modeling long wave radiation: The ``ScriptF'' method, and the ``CarrollMRT'' methods. Users can select between these two algorithms using the ``PerformancePrecisionTradeoffs'' object.
+
+\paragraph{ScriptF}
+
+The ``ScriptF'' algorithm was developed by Hottel (Hottel and Sarofim, Radiative Transfer, Chapter 3, McGraw Hill, 1967).~ This procedure relies on a matrix of exchange coefficients between pairs of surfaces that include all exchange paths between the surfaces.~ In other words all reflections, absorptions and re-emissions~ from other surfaces in the enclosure are included in the exchange coefficient, which is called ScriptF.~ The major assumptions are that all surface radiation properties are grey and all radiation is diffuse.~ Both assumptions are reasonable for building zone interchange.
 
 ~The ScriptF coefficients are developed by starting with the traditional direct radiation view factors.~ In the case of building rooms and zones, there are several complicating factors in finding the direct view factors---the main one being that the location of surfaces such as thermal mass representing furniture and partitions are not known.~ The other limitation is that the exact calculation of direct view factors is computationally very intensive even if the positions of all surfaces are known. Accordingly, EnergyPlus uses a procedure to approximate the direct view factors.~ The procedure has two steps:
 
@@ -88,6 +92,48 @@ \subsubsection{LW Radiation Exchange Among Zone Surfaces}\label{lw-radiation-exc
 
 where \textbf{\emph{F}}\(_{i,j}\) is the ScriptF between surfaces i and j.
 
+\paragraph{CarrollMRT}
+
+The Carroll method is an approximation of gray-body long-wave radiation exchange within an enclosure that simplifies the surface-to-surface radiation exchange by using a single, mean radiant temperature node, $Tr$, that acts as a clearinghouse for the radiation heat exchange between surfaces. Instead of solving a dense-matrix, linear algebra problem, the mean radiant temperature can be calculated using a single equation, and subsequently used to determine the net long-wave radiation to/from each surface. Unlike the $O(n^2)$ complexity of the current dense-matrix solution, this approach has linear complexity.
+
+The mean radiant temperature is calculated using three steps:
+
+\begin{enumerate}
+\item Calculation of the mean radiant temperature ``view factor'', $Fi$. These view factors represent each surface's ``view'' to the mean radiant temperature node as though all surfaces were part of a spherical enclosure (i.e., they all have equal view of the node regardless of their orientation to each other). $Fi$ is calculated as:
+
+\begin{equation}
+    F_i=\frac{1}{1-\frac{A_i F_i}{\sum_1^n{A_j F_j} }}
+\end{equation}
+
+Because of the circular reference in this equation, the collection of all ``view factors'' must be solved iteratively, but only once per simulation as surface areas do not change throughout. This converges for realistic enclosures but won't necessarily converge for ``enclosures'' having only two or three surfaces, particularly if there are large area disparities.
+
+\item Calculating the gray-body radiation resistance, $F'i$. This calculation must be computed every time surface emissivity changes. $F'i$ is calculated as:
+
+\begin{equation}
+    F'_i=\frac{\sigma\varepsilon_i}{\frac{\varepsilon_i}{F_i} +1-\varepsilon_i}
+\end{equation}
+
+\item Finally, the mean radiant temperature, $Tr$, is:
+
+\begin{equation}
+    T_r=\frac{\sum_1^nA_i F'_i T_i}{\sum_1^nA_i F'_i}
+\end{equation}
+
+\end{enumerate}
+
+Once the mean radiant temperature is known, the net radiation heat transfer for each surface can be calculated as:
+
+\begin{equation}
+    q=F'_i A_i (T_r^4-T_i^4)
+\end{equation}
+
+Carroll, J. A., 1980, ``An `MRT Method' of Computing Radiant Energy Exchange in Rooms,'' Proceedings of the Second Systems Simulation and Economic Analysis Conference, San Diego, CA.
+
+Carroll, J. A., 1980a, ``An MRT method of computing radiant energy exchange in rooms,'' Proceedings of the 2nd Systems Simulation and Economic Analysis Conference, San Diego, CA.
+
+Carroll, J. A., 1981, ``A Comparison of Radiant Interchange Algorithms,'' Proceedings of the 3rd Annual Systems Simulation and Economics Analysis/Solar Heating and Cooling Operational Results Conference, Reno. Solar Engineering, Proceedings of the ASME Solar division.
+
+
 \subsubsection{Thermal Mass and Furniture}\label{thermal-mass-and-furniture}
 
 Furniture in a zone has the effect of increasing the amount of surface area that can participate in the radiation and convection heat exchanges.~ It also adds participating thermal mass to the zone.~ These two changes both affect the response to temperature changes in the zone and also affect the heat extraction characteristics.

doc/input-output-reference/src/overview/group-simulation-parameters.tex

@@ -792,7 +792,7 @@ \subsubsection{Inputs}\label{inputs-15-014}
 
 \subsection{PerformancePrecisionTradeoffs}\label{performanceprecisiontradeoffs}
 
-The PerformancePrecisionTradeoffs object can be used to control tradeoffs between performance (speed) and precision for certain EnergyPlus features. This object enables users to choose to use selected options that are intended to shorten the time needed for the computer to run EnergyPlus simulations, but may tend to decrease the accuracy of results compared to methods that require longer computing time. 
+The PerformancePrecisionTradeoffs object can be used to control tradeoffs between performance (speed) and precision for certain EnergyPlus features. This object enables users to choose to use selected options that are intended to shorten the time needed for the computer to run EnergyPlus simulations, but may tend to decrease the accuracy of results compared to methods that require longer computing time.
 
 \paragraph{Field: Use Coil Direct Solutions}\label{use-coil-direct-solutions}
 
@@ -886,11 +886,18 @@ \subsection{PerformancePrecisionTradeoffs}\label{performanceprecisiontradeoffs}
 
 Note: The choice of Load in the Control Type of the AirLoopHVAC:UnitarySystem object is required for all coils listed in the above table.
 
+\paragraph{Field: Zone Radiant Exchange Algorithm}\label{zone-radiant-exchange-algorithm}
+
+Allowed choices are: ScriptF (default) and CarrollMRT. ScriptF uses view factors among all surfaces in a zone and calculates radiant heat transfer from each surface in the zone to each other surface in the zone based on their respective temperatures and emissivities. The CarrollMRT algorithm calculates radiant heat transfer between surfaces which exchange heat through a central, mean radiant temperature (MRT) node.
+
+Although, defined view factors cannot be used with CarrollMRT, the algorithm approximates ``view factors'' based on relative areas of the surfaces in a similar way to how EnergyPlus determines its default view factors. One exception is that with CarrollMRT, every surface can ``view'' every other surface in the zone regardless of orientation. For enclosed prism shapes, this approximation is very accurate.
+
 An IDF example:
 
 \begin{lstlisting}
 PerformancePrecisionTradeoffs,
-  Yes;                      !- Use Coil Direct Solutions
+  Yes,                      !- Use Coil Direct Solutions
+  CarrollMRT;               !- Zone Radiant Exchange Algorithm
 \end{lstlisting}
 
 \subsection{HVACSystemRootFindingAlgorithm}\label{hvacystemrootfindingalgorithm}

idd/Energy+.idd.in

@@ -443,18 +443,25 @@ SimulationControl,
       \type integer
       \minimum 1
       \default 1
-      
+
 PerformancePrecisionTradeoffs,
       \unique-object
       \memo This object enables users to choose certain options that speed up EnergyPlus simulation,
       \memo but may lead to small decreases in accuracy of results.
-  A1; \field Use Coil Direct Solutions
-      \note If Yes, an analytical or empirical solution will be used to replace iterations in 
+  A1, \field Use Coil Direct Solutions
+      \note If Yes, an analytical or empirical solution will be used to replace iterations in
       \note the coil performance calculations.
       \type choice
       \key Yes
       \key No
       \default No
+  A2; \field Zone Radiant Exchange Algorithm
+      \note Determines which algorithm will be used to solve long wave radiant exchange among surfaces within a zone.
+      \type choice
+      \key ScriptF
+      \key CarrollMRT
+      \default ScriptF
+
 
 Building,
        \memo Describes parameters that are used during the simulation

src/EnergyPlus/DataViewFactorInformation.hh

@@ -76,6 +76,8 @@ namespace DataViewFactorInformation {
         Array1D<Real64> Emissivity;         // Surface emissivity
         Array1D<Real64> Azimuth;            // Azimuth angle of the surface (in degrees)
         Array1D<Real64> Tilt;               // Tilt angle of the surface (in degrees)
+        Array1D<Real64> FMRT;               // Mean Radiant Temperature "View Factor" used in Carroll method
+        Array1D<Real64> Fp;                 // F' (Oppenheim surface resistance used in Carroll method)
         Array1D_int SurfacePtr;             // Surface number for surfaces in this enclosure
         Real64 FloorArea;                   // Floor area of zone(s) in enclosure
         Real64 ExtWindowArea;               // Exterior window area