From bcb8897e9eaa94ab1b9d2a01256504e5ffa4f780 Mon Sep 17 00:00:00 2001 From: Matt Mitchell Date: Sun, 22 Mar 2020 15:25:52 -0600 Subject: [PATCH 1/5] update sky temperature docs --- .../climate-calculations.tex | 95 +++++++++---------- 1 file changed, 44 insertions(+), 51 deletions(-) diff --git a/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex b/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex index 5ae4dc01be3..af8582e7ead 100644 --- a/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex +++ b/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex @@ -44,86 +44,79 @@ \subsection{EnergyPlus Design Day Temperature Calculations}\label{energyplus-des \subsection{Sky Radiation Modeling}\label{sky-radiation-modeling} -EnergyPlus calculates the Horizontal Infrared Radiation Intensity in Wh/m\(^{2,}\) if it is missing on the weather file or for design days, from the Opaque Sky Cover field as shown in the following explanation. +EnergyPlus calculates the Horizontal Infrared Radiation ($IR_H$), if it is missing in the weather file or for design days, from the Dry Bulb Temperature, Dewpoint Temperature, and Opaque Cloud Cover as described below. -\begin{equation} -Horizontal\_IR = Sk{y_{emissivity}}\cdot Sigma\cdot Temperature_{drybulb}^4 -\end{equation} - -where - -Horizontal\_IR = horizontal IR intensity \{W/m\(^{2}\)\} - -Sky\(_{emissivity}\) = sky emissivity - -Sigma = Stefan-Boltzmann constant = 5.6697e-8 \{W/m\(^{2}\)-K\(^{4}\)\} - -Temperature\(_{drybulb}\) = drybulb temperature \{K\} - -By default, the clear sky emissivity is calculated by the Clark \& Allen (1978) model as +$IR_H$ is defined as the rate of infrared radiation emitted from the sky falling on a horizontal upward-facing surface, in \si{\watt\per\m\squared}. \begin{equation} -Sky_{clear-sky-emissivity} = 0.787 + 0.764\cdot \ln \frac {T_{dewpoint}}{T_{Kelvin}} +IR_H = \sigma \cdot T_{sky}^4 \end{equation} -where, T\(_{dewpoint}\) = dewpoint temperature \{K\}. +\noindent where: +\newline -Alternatively, the clear sky emissivity can also be calculated using different models set by the user from options using the \textbf{WeatherProperty:SkyTemperature} object, including the calibrated version of the Berdahl and Martin, Brunt and Idso models (2017), listed as follows. +$\sigma$ = Stefan-Boltzmann constant = \SI{5.6697e-8}{\watt\per\meter\squared\per\kelvin\tothe{4}} -Calibrated Berdahl and Martin model: +$T_{sky}$ = Effective mean sky temperature, or sky radiative temperature, \si{\kelvin}. +\newline -\begin{equation} -Sky_{clear-sky-emissivity} = 0.711 + 0.56\cdot(T_{dewpoint} / 100) + 0.73\cdot{T_{dewpoint} / 100}^2. -\end{equation} - -Calibrated Brunt model: +Walton (1983) proposed a fictitious quantity called the Sky Emissivity ($\epsilon_{sky}$) such that the following energy balance is satisfied: \begin{equation} -Sky_{clear-sky-emissivity} = 0.52 + 0.065\cdot(P_{water-vapor})^{0.5}, +IR_H = \epsilon_{sky} \cdot \sigma \cdot T_{db}}^4 \end{equation} -where, P\(_{water-vapor}\) = partial water vapor pressure \{hPa\}. - -Calibrated Idso model: +$\epsilon_{sky}$ = sky emissivity -\begin{equation} -Sky_{clear-sky-emissivity} = 0.70 + 5.95\cdot10E-5\cdot(P_{water-vapor} \cdot exp(1500/T_{drybulb})). -\end{equation} +$T_{db}$ = drybulb temperature, \si{\kelvin} +\newline - -Then the sky emissivity is given by: +Walton also proposed the following correlation for $\epsilon_{sky}$: \begin{equation} -Sky_{emissivity} = Sky_{clear-sky-emissivity} \cdot \left( {1. + .0224N - .0035{N^2} + .00028{N^3}} \right) +\epsilon_{sky} = \left(0.787 + 0.764 \cdot \ln\left(T_{dp}}/273\right)\right) \cdot \left(1 + 0.0224 \cdot N - 0.0035 \cdot N^2 + 0.00028 \cdot N^3) \end{equation} -where, N = opaque sky cover \{tenths\} +\noindent where: +\newline + +$T_{dp}$ = dewpoint temperature, in \si{\kelvin} -Example: Clear sky (N = 0), Temperature\(_{drybulb}\) = 273+20 = 293 K, Temperature\(_{dewpoint}\) = 273+10 = 283 K: +$N$ = opaque sky cover, in tenths. +\newline -Sky\(_{emissivity}\) = 0.787 + 0.764*0.036 = 0.815 +\noindent Example: -Horizontal\_IR = 0.815*5.6697e-8*(293**4) = 340.6 W/m\(^{2}\) +Clear sky ($N=0$), $T_{db} = 20 + 273.15 = \SI{293.15}{\kelivin}$, $T_{dp} = 10 + 273.15 = \SI{283.15}{\kelvin}$ +\newline -If specified in \textbf{WeatherProperty:SkyTemperature} object, Horizontal Infrared Radiation Intensity from the weather files can also be ignored and the values can be calculated directly from the specified sky emissivity model. +$\epsilon_{sky} = \left(0.787 + 0.764 \cdot \ln\left(283.15/273\right)\right) \cdot \left(1 + 0.0224 \cdot N - 0.0035 \cdot N^2 + 0.00028 \cdot N^3) = 0.815$ +\newline -References for these calculations are contained in the references subsection at the end of this section and include Walton (1983), Clark and Allen (1978), and Li et al (2017). +$IR_H = 0.815 \cdot 5.6697E-8 \cdot 293.15^4 = \SI{341.2}{\watt\per\meter\squared}$ \subsection{EnergyPlus Sky Temperature Calculation}\label{energyplus-sky-temperature-calculation} -The default calculation for sky temperature is: +By default the Sky Temperature ($T_{sky}$) is calculated from the Horizontal Infrared Radiation Intensity ($IR_H$): \begin{equation} -Sk{y_{Temperature}} = {\left( {\frac{{Horizontal\_IR}}{{Sigma}}} \right)^{.25}} - Temperatur{e_{Kelvin}} +T_{sky} = \left(IR_H / \sigma\right)^{0.25} - 273.15 \end{equation} -Where +\noindent where: +\newline + +$T_{sky}$ = Effective mean sky temperature, or sky radiative temperature, in \si{\celsius}. +\newline -Sky\(_{Temperature}\) = Sky radiative temperature \{C\} +$IR_H$ = rate of infrared radiation emitted from the sky falling on a horizontal upward-facing surface, in \si{\watt\per\meter\squared}. +\newline -Horiizontal\_IR = Horizontal Infrared Radiation Intensity as described in the previous section \{Wh/m\(^{2}\)\} +$\sigma$ = Stefan-Boltzmann constant = \SI{5.6697e-8}{\watt\per\meter\squared\per\kelvin\tothe{4}} +\newline -Temperature\(_{Kelvin}\) = Temperature conversion from Kelvin to C, i.e.~273.15 +(Note: T\{\si{\celsius}\} = T\{\si{\kelvin}\} - 273.15) +\newline The Sky Temperature can also be set by the user from several options using the~\textbf{WeatherProperty:SkyTemperature} object. @@ -153,13 +146,13 @@ \subsubsection{ASHRAE Clear Sky Solar Model}\label{ashrae-clear-sky-solar-model} % table 20 \begin{longtable}[c]{p{0.75in}p{0.75in}p{0.75in}p{0.75in}p{0.75in}p{0.75in}p{0.75in}} \caption{Extraterrestrial Solar Irradiance and Related Data Note: Data are for 21st day of each month during the base year of 1964. \label{table:extraterrestrial-solar-irradiance-and-related}}\\ -\toprule +\toprule ~ & I\(_{o}\)\{W/m\(^{2}\)\} & Equation of Time \{minutes\} & Declination \{degrees\} & A \{W/m\(^{2}\)\} & B \{\} & C \{\} \tabularnewline \midrule \endfirsthead \caption[]{Extraterrestrial Solar Irradiance and Related Data Note: Data are for 21st day of each month during the base year of 1964.} \tabularnewline -\toprule +\toprule ~ & I\(_{o}\)\{W/m\(^{2}\)\} & Equation of Time \{minutes\} & Declination \{degrees\} & A \{W/m\(^{2}\)\} & B \{\} & C \{\} \tabularnewline \midrule \endhead @@ -241,7 +234,7 @@ \subsubsection{ASHRAE Revised Clear Sky Model (``Tau Model'')}\label{ashrae-revi ad = 0.507 + 0.205 \cdot {\tau_b} - 0.080 \cdot {\tau_d} - 0.190 \cdot {\tau_b} \cdot {\tau_d} \end{equation} -The empirical equations coefficients of the 2017 ASHRAE HOF are also valid for the 2013 ASHRAE HOF hence the $\tau$\(_{b}\) and $\tau$\(_{d}\) values from the 2013 ASHRAE HOF can be used with ASHRAETau2017 solar model indicator if needed. +The empirical equations coefficients of the 2017 ASHRAE HOF are also valid for the 2013 ASHRAE HOF hence the $\tau$\(_{b}\) and $\tau$\(_{d}\) values from the 2013 ASHRAE HOF can be used with ASHRAETau2017 solar model indicator if needed. Studies done as part of ASHRAE research projects show that the revised tau model produces more physically plausible irradiance values than does the traditional clear sky model.~ In particular, diffuse irradiance values are more realistic. @@ -298,7 +291,7 @@ \subsection{References}\label{references-010} Clark, G. and C. Allen, ``The Estimation of Atmospheric Radiation for Clear and Cloudy Skies,'' Proceedings 2nd National Passive Solar Conference (AS/ISES), 1978, pp.~675-678. -Li, M., Jiang, Y. and Coimbra, C. F. M. 2017. On the determination of atmospheric longwave irradiance under all-sky conditions. Solar Energy 144, 40–48, +Li, M., Jiang, Y. and Coimbra, C. F. M. 2017. On the determination of atmospheric longwave irradiance under all-sky conditions. Solar Energy 144, 40–48, Watanabe, T., Urano, Y., and Hayashi, T. 1983. ``Procedures for Separating Direct and Diffuse Insolation on a Horizontal Surface and Prediction of Insolation on Tilted Surfaces'' (in Japanese), Transactions, No. 330, Architectural Institute of Japan, Tokyo, Japan. From 4cd3cfebcf15a5bfe7c7ec24f06568525bc4f73a Mon Sep 17 00:00:00 2001 From: Matt Mitchell Date: Tue, 24 Mar 2020 10:54:24 -0600 Subject: [PATCH 2/5] update sky radiation docs section --- .../climate-calculations.tex | 47 +++++++++++++++---- 1 file changed, 37 insertions(+), 10 deletions(-) diff --git a/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex b/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex index af8582e7ead..8e5e0415fa8 100644 --- a/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex +++ b/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex @@ -44,12 +44,12 @@ \subsection{EnergyPlus Design Day Temperature Calculations}\label{energyplus-des \subsection{Sky Radiation Modeling}\label{sky-radiation-modeling} -EnergyPlus calculates the Horizontal Infrared Radiation ($IR_H$), if it is missing in the weather file or for design days, from the Dry Bulb Temperature, Dewpoint Temperature, and Opaque Cloud Cover as described below. +EnergyPlus calculates the Horizontal Infrared Radiation Intensity ($IR_H$), if it is missing in the weather file or for design days, from the Dry Bulb Temperature, Dewpoint Temperature or Partial Pressure of Water Vapor, and Opaque Cloud Cover as described below. Regardless of whether or not $IR_H$ is present in the weather file, it can be specified in the \textbf{WeatherProperty:SkyTemperature} object to ignore the reported value of $IR_H$ and instead calculate it from the specified sky emissivity model as described below. $IR_H$ is defined as the rate of infrared radiation emitted from the sky falling on a horizontal upward-facing surface, in \si{\watt\per\m\squared}. \begin{equation} -IR_H = \sigma \cdot T_{sky}^4 +IR_H = \sigma T_{sky}^4 \end{equation} \noindent where: @@ -60,10 +60,10 @@ \subsection{Sky Radiation Modeling}\label{sky-radiation-modeling} $T_{sky}$ = Effective mean sky temperature, or sky radiative temperature, \si{\kelvin}. \newline -Walton (1983) proposed a fictitious quantity called the Sky Emissivity ($\epsilon_{sky}$) such that the following energy balance is satisfied: +Over the years authors have proposed a fictitious quantity called the Sky Emissivity ($\epsilon_{sky}$) such that the following energy balance is satisfied: \begin{equation} -IR_H = \epsilon_{sky} \cdot \sigma \cdot T_{db}}^4 +IR_H = \epsilon_{sky} \cdot \sigma \cdot T_{db}^4 \end{equation} $\epsilon_{sky}$ = sky emissivity @@ -71,29 +71,56 @@ \subsection{Sky Radiation Modeling}\label{sky-radiation-modeling} $T_{db}$ = drybulb temperature, \si{\kelvin} \newline -Walton also proposed the following correlation for $\epsilon_{sky}$: +Four correlations for $\epsilon_{sky}$ under clear-sky conditions, proposed by four sets of authors, are available in EnergyPlus. The default correlation is from Clark \& Allen (1978): -\begin{equation} -\epsilon_{sky} = \left(0.787 + 0.764 \cdot \ln\left(T_{dp}}/273\right)\right) \cdot \left(1 + 0.0224 \cdot N - 0.0035 \cdot N^2 + 0.00028 \cdot N^3) -\end{equation} +\begin{table}[hbtp] +\centering +\begin{tabular}{cl} +\textbf{Author} & \epsilon_{sky, clear} \\ \\ +Clark \& Allen & $= 0.787 + 0.764 \ln\left(T_{dp}/273\right)$ \\ \\ +Martin \& Berdahl & $= 0.711 + 0.56 \left(T_{dp}/100\right) + 0.73 \left(T_{dp} / 100\right)^2$ \\ \\ +Brunt & $= 0.52 + 0.065 \left(P_{wv}\right)^{0.5}$ \\ \\ +Idso & $= 0.70 + 5.95\times10^{-5} \left(P_{wv}\right) e^{1500/T_{db}} $ +\end{tabular} +\end{table} \noindent where: \newline +$\epsilon_{sky, clear}$ = $\epsilon_{sky}$ under clear-sky conditions +\newline + $T_{dp}$ = dewpoint temperature, in \si{\kelvin} +\newline + +$P_{wv}$ = partial pressor of water vapor, in \si{\hecto\pascal} +\newline + +The clear sky emissivity is modified for partially-cloudy conditions using the correlation from Walton (1983) which uses the opaque cloud cover fraction: + +\begin{equation} +\epsilon_{sky} = \epsilon_{sky, clear} \left(1 + 0.0224 N - 0.0035 N^2 + 0.00028 N^3\right) +\end{equation} + +\noindent where: +\newline $N$ = opaque sky cover, in tenths. \newline \noindent Example: +\newline Clear sky ($N=0$), $T_{db} = 20 + 273.15 = \SI{293.15}{\kelivin}$, $T_{dp} = 10 + 273.15 = \SI{283.15}{\kelvin}$ \newline -$\epsilon_{sky} = \left(0.787 + 0.764 \cdot \ln\left(283.15/273\right)\right) \cdot \left(1 + 0.0224 \cdot N - 0.0035 \cdot N^2 + 0.00028 \cdot N^3) = 0.815$ +$\epsilon_{sky} = \left(0.787 + 0.764 \ln\left(283.15/273\right)\right) \left(1 + 0.0224 N - 0.0035 N^2 + 0.00028 N^3) = 0.815$ +\newline + +$IR_H = 0.815 5.6697E-8 293.15^4 = \SI{341.2}{\watt\per\meter\squared}$ \newline -$IR_H = 0.815 \cdot 5.6697E-8 \cdot 293.15^4 = \SI{341.2}{\watt\per\meter\squared}$ +References for these calculations are contained in the references section at the end of this list of fields. (Walton, 1983) (Clark \& Allen, 1978), (Li et al, 2017). \subsection{EnergyPlus Sky Temperature Calculation}\label{energyplus-sky-temperature-calculation} From fc2927c464d8ed957df38ee9831f08f5060b81dc Mon Sep 17 00:00:00 2001 From: Matt Mitchell Date: Tue, 24 Mar 2020 19:37:45 -0600 Subject: [PATCH 3/5] fix spelling and non-ascii char --- .../climate-calculations.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex b/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex index 8e5e0415fa8..3e1f6545cfa 100644 --- a/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex +++ b/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex @@ -93,7 +93,7 @@ \subsection{Sky Radiation Modeling}\label{sky-radiation-modeling} $T_{dp}$ = dewpoint temperature, in \si{\kelvin} \newline -$P_{wv}$ = partial pressor of water vapor, in \si{\hecto\pascal} +$P_{wv}$ = partial pressure of water vapor, in \si{\hecto\pascal} \newline The clear sky emissivity is modified for partially-cloudy conditions using the correlation from Walton (1983) which uses the opaque cloud cover fraction: @@ -318,7 +318,7 @@ \subsection{References}\label{references-010} Clark, G. and C. Allen, ``The Estimation of Atmospheric Radiation for Clear and Cloudy Skies,'' Proceedings 2nd National Passive Solar Conference (AS/ISES), 1978, pp.~675-678. -Li, M., Jiang, Y. and Coimbra, C. F. M. 2017. On the determination of atmospheric longwave irradiance under all-sky conditions. Solar Energy 144, 40–48, +Li, M., Jiang, Y. and Coimbra, C. F. M. 2017. On the determination of atmospheric longwave irradiance under all-sky conditions. Solar Energy 144, 40-48, Watanabe, T., Urano, Y., and Hayashi, T. 1983. ``Procedures for Separating Direct and Diffuse Insolation on a Horizontal Surface and Prediction of Insolation on Tilted Surfaces'' (in Japanese), Transactions, No. 330, Architectural Institute of Japan, Tokyo, Japan. From 769b7aa4af58ef81893af535ccea21fecdf5480a Mon Sep 17 00:00:00 2001 From: xuanariel Date: Wed, 25 Mar 2020 14:39:45 -0700 Subject: [PATCH 4/5] fix sky temp equations --- .../climate-calculations.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex b/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex index 3e1f6545cfa..316ceeed069 100644 --- a/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex +++ b/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex @@ -78,9 +78,9 @@ \subsection{Sky Radiation Modeling}\label{sky-radiation-modeling} \begin{tabular}{cl} \textbf{Author} & \epsilon_{sky, clear} \\ \\ Clark \& Allen & $= 0.787 + 0.764 \ln\left(T_{dp}/273\right)$ \\ \\ -Martin \& Berdahl & $= 0.711 + 0.56 \left(T_{dp}/100\right) + 0.73 \left(T_{dp} / 100\right)^2$ \\ \\ -Brunt & $= 0.52 + 0.065 \left(P_{wv}\right)^{0.5}$ \\ \\ -Idso & $= 0.70 + 5.95\times10^{-5} \left(P_{wv}\right) e^{1500/T_{db}} $ +Martin \& Berdahl & $= 0.758 + 0.521 \left(T_{dp}/100\right) + 0.625 \left(T_{dp} / 100\right)^2$ \\ \\ +Brunt & $= 0.618 + 0.056 \left(P_{wv}\right)^{0.5}$ \\ \\ +Idso & $= 0.685 + 3.2\times10^{-5} \left(P_{wv}\right) e^{1699/T_{db}} $ \end{tabular} \end{table} From 02a21f11818e3e4e990b1751fdaa0642c3a72035 Mon Sep 17 00:00:00 2001 From: mjwitte Date: Wed, 25 Mar 2020 17:14:59 -0500 Subject: [PATCH 5/5] Sky temp calcs Tdp units clarification --- .../climate-calculations.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex b/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex index 316ceeed069..cf1e0321744 100644 --- a/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex +++ b/doc/engineering-reference/src/climate-sky-and-solar-shading-calculations/climate-calculations.tex @@ -90,7 +90,7 @@ \subsection{Sky Radiation Modeling}\label{sky-radiation-modeling} $\epsilon_{sky, clear}$ = $\epsilon_{sky}$ under clear-sky conditions \newline -$T_{dp}$ = dewpoint temperature, in \si{\kelvin} +$T_{dp}$ = dewpoint temperature, in \si{\kelvin} for Clark \& Allen, in \si{\celsius} for Martin \& Berdahl \newline $P_{wv}$ = partial pressure of water vapor, in \si{\hecto\pascal}