diff --git a/doc/engineering-reference/src/surface-heat-balance-manager-processes/combined-heat-and-moisture-transfer-hamt.tex b/doc/engineering-reference/src/surface-heat-balance-manager-processes/combined-heat-and-moisture-transfer-hamt.tex index df9d09f3a7d..60efd8000af 100644 --- a/doc/engineering-reference/src/surface-heat-balance-manager-processes/combined-heat-and-moisture-transfer-hamt.tex +++ b/doc/engineering-reference/src/surface-heat-balance-manager-processes/combined-heat-and-moisture-transfer-hamt.tex @@ -2,11 +2,20 @@ \section{Combined Heat and Moisture Transfer (HAMT) Model}\label{combined-heat-a \subsection{Overview}\label{overview-011} -The combined heat and moisture transfer finite (HAMT) solution algorithm is a completely coupled, one-dimensional, finite element, heat and moisture transfer model simulating the movement and storage of heat and moisture in surfaces simultaneously from and to both the internal and external environments. As well as simulating the effects of moisture buffering, HAMT is also be able to provide temperature and moisture profiles through composite building walls, and help to identify surfaces with high surface humidity. +The combined heat and moisture transfer finite (HAMT) solution algorithm is +a completely coupled, one-dimensional, finite element, heat and moisture +transfer model simulating the movement and storage of heat and moisture in +surfaces simultaneously from and to both the internal and external +environments. As well as simulating the effects of moisture buffering, HAMT +is also be able to provide temperature and moisture profiles through +composite building walls, and help to identify surfaces with high surface +humidity. \subsection{HAMT Nomenclature}\label{hamt-nomenclature} -Dependencies on moisture content are indicated by a superscript \(^{w}\), on heat by a superscript \(^{h}\) and vapor pressure by a superscript \(^{v}\). +Dependencies on moisture content are indicated by a superscript \(^w\), +on heat by a superscript \(^h\) and vapor pressure by a superscript +\(^v\). \begin{longtable}[c]{p{1.5in}p{1.0in}p{3.5in}} \caption{Combined Heat and Moisture Transfer Model Nomenclature \label{table:combined-heat-and-moisture-transfer-model}} \tabularnewline @@ -21,7 +30,7 @@ \subsection{HAMT Nomenclature}\label{hamt-nomenclature} \midrule \endhead -T & °C & Temperature \tabularnewline +T & \si{\celsius} & Temperature \tabularnewline RH,$\varphi$ & \%, fraction & Relative humidity \tabularnewline W & $kg/m^3$ & Moisture Content \tabularnewline $\partial{H}/\partial{T}$ & $J/m^3C$ & Moisture dependent heat storage capacity \tabularnewline @@ -57,21 +66,29 @@ \subsection{HAMT Nomenclature}\label{hamt-nomenclature} \subsection{HAMT Model Description}\label{hamt-model-description} -Equations~\ref{eq:HAMTHeatBalanceEquation} and~\ref{eq:HAMTMoistureBalanceEquation} are derived from heat and moisture balance equations and are taken from {[}Künzel, H.M. (1995){]}. They describe a theoretical model for the transfer of heat and moisture through a material. +Equations~\ref{eq:HAMTHeatBalanceEquation} +and~\ref{eq:HAMTMoistureBalanceEquation} are derived from heat and moisture +balance equations and are taken from {[}K\"unzel, H.M. (1995){]}. They +describe a theoretical model for the transfer of heat and moisture through +a material. \begin{equation} \frac{{\partial H}}{{\partial T}}\frac{{\partial T}}{{\partial \tau }} = \frac{\partial }{{\partial x}}\left( {{k^w}\frac{{\partial T}}{{\partial x}}} \right) + {h_v}\frac{\partial }{{\partial x}}\left( {\frac{\delta }{\mu }\frac{{\partial T}}{{\partial x}}} \right) \label{eq:HAMTHeatBalanceEquation} \end{equation} -The three terms in Equation~\ref{eq:HAMTHeatBalanceEquation} describe the storage, transport and generation of heat respectively. +The three terms in Equation~\ref{eq:HAMTHeatBalanceEquation} describe the +storage, transport and generation of heat respectively. \begin{equation} \frac{{\partial w}}{{\partial \phi }}\frac{{\partial \phi }}{{\partial \tau }} = \frac{\partial }{{\partial x}}\left( {{D^w}\frac{{\partial w}}{{\partial \phi }}\frac{{\partial \phi }}{{\partial x}}} \right) + \frac{\partial }{{\partial x}}\left( {\frac{\delta }{\mu }\frac{{\partial T}}{{\partial x}}} \right) \label{eq:HAMTMoistureBalanceEquation} \end{equation} -The three terms in equation describe the storage of moisture, the transport of liquid moisture and the transport of vapor respectively. The equation to calculate the vapor diffusion coefficient in air (\(\delta\)) used in the third term of both equations, is also taken from Künzel, +The three terms in equation describe the storage of moisture, the transport +of liquid moisture and the transport of vapor respectively. The equation to +calculate the vapor diffusion coefficient in air (\(\delta\)) used in the +third term of both equations, is also taken from K\"unzel, \begin{equation} \delta = \frac{{\left( {2 \times {{10}^{ - 7}} \times {{\left( {T + 273.15} \right)}^{0.81}}} \right)}}{{{P_{ambient}}}} @@ -83,29 +100,44 @@ \subsection{HAMT Model Description}\label{hamt-model-description} \frac{{\partial H}}{{\partial T}} = \left( {c\rho + {c^w}w} \right) \end{equation} -The moisture content of the material w and the vapor diffusion resistance factor $\mu$ depend on the relative humidity inside the material. The parameters \(\frac{\partial w}{\partial \phi}\), \({k^w}\) ~and \({D^w}\) are also moisture dependent parameters. +The moisture content of the material w and the vapor diffusion resistance +factor $\mu$ depend on the relative humidity inside the material. The +parameters \(\frac{\partial w}{\partial \phi}\), \(k^w\) ~and \(D^w\) are +also moisture dependent parameters. -The following sections describe how the above equations are used within the HAMT model. +The following sections describe how the above equations are used within +the HAMT model. \subsubsection{Surfaces, Material Layers and Cells}\label{surfaces-material-layers-and-cells} -``Surfaces'' are made of a number of layers of potentially any combination of materials. Each surface is split into its constituent materials and is then split up further into cells through its depth. HAMT will generate no more than 10 cells per material with widths that are thinner near the boundaries of each material where most changes are expected and detail is needed. +``Surfaces'' are made of a number of layers of potentially any combination +of materials. Each surface is split into its constituent materials and is +then split up further into cells through its depth. HAMT will generate no +more than 10 cells per material with widths that are thinner near the +boundaries of each material where most changes are expected and detail is +needed. \subsubsection{Heat Transfer}\label{heat-transfer} -Equation~\ref{eq:HAMTHeatBalanceEquation} can be re-written and used to describe the heat storage and transfer through the i\(^{th}\) cell in a surface. +Equation~\ref{eq:HAMTHeatBalanceEquation} can be re-written and used to +describe the heat storage and transfer through the i\(^{th}\) cell in a +surface. \begin{equation} -\left( {{c_i}{\rho_i} + {c^w}{w_i}} \right)\Delta {V_i}\frac{{T_i^{p + 1} - T_i^p}}{{\Delta \tau }} = \sum\limits_j {k_{ij}^w{A_{ij}}\frac{{T_j^{p + 1} - T_i^{p + 1}}}{{{x_{ij}}}}} + \sum\limits_j {{h_v}\frac{{{\delta_{ij}}}}{{{\mu_{ij}}}}{A_{ij}}\frac{{p_j^{p + 1} - p_i^{p + 1}}}{{{x_{ij}}}}} +\left( {{c_i}{\rho_i} + {c^w}{w_i}} \right)\Delta {V_i}\frac{{T_i^{p + 1} - T_i^p}}{{\Delta \tau }} = \sum\limits_j {k_{ij}^w{A_{ij}}\frac{{T_j^{p + 1} - T_i^{p + 1}}}{x_{ij}}} + \sum\limits_j {{h_v}\frac{{{\delta_{ij}}}}{\mu_{ij}}{A_{ij}}\frac{{p_j^{p + 1} - p_i^{p + 1}}}{x_{ij}}} \end{equation} -In the one dimensional case there are only two adjacent cells each labelled j. The heat generated due to vaporization \(q_i^v\) can be calculated separately. +In the one dimensional case there are only two adjacent cells each labelled +j. The heat generated due to vaporization \(q_i^v\) can be calculated +separately. \begin{equation} -q_i^v = \sum\limits_j {{h_v}\frac{{{\delta_{ij}}}}{{{\mu_{ij}}}}{A_{ij}}\frac{{p_j^{p + 1} - p_i^{p + 1}}}{{{x_{ij}}}}} +q_i^v = \sum\limits_j {{h_v}\frac{{{\delta_{ij}}}}{\mu_{ij}}{A_{ij}}\frac{{p_j^{p + 1} - p_i^{p + 1}}}{x_{ij}}} \end{equation} -Rearranging Equation~\ref{eq:HAMTHeatBalanceEquation} and including other sources of heat (\(q_i^{adds}\)) such as radiation from other surfaces in the calculation gives the temperature in a cell in the next time step as, +Rearranging Equation~\ref{eq:HAMTHeatBalanceEquation} and including other +sources of heat (\(q_i^{adds}\)) such as radiation from other surfaces in +the calculation gives the temperature in a cell in the next time step as, \begin{equation} T_i^{p + 1} = \frac{{\sum\nolimits_j {\frac{{T_j^{p + 1}}}{{R_{ij}^h}}} + q_i^v + q_i^{adds} + C_i^h\frac{{T_i^p}}{{\Delta \tau }}}}{{\frac{{C_i^h}}{{\Delta \tau }} + \sum\nolimits_j {\frac{1}{{R_{ij}^h}}} }} @@ -114,86 +146,270 @@ \subsubsection{Heat Transfer}\label{heat-transfer} where \(C_i^h = \left( {{c_i}{\rho_i} + {c^w}{w_i}} \right)\Delta {V_i}\) is thermal heat capacitance of cell i and \(R_{ij}^h = \frac{x_{ij}}{k_{ij}A_{ij}}\) ~is the thermal resistance between cells i and j. -This equation can be solved using the Gauss-Seidel iteration technique. The i\(^{th}\) cell temperature is calculated whilst the j\(^{th}\) cell temperatures are kept as up to date as possible. The iteration is stopped when the maximum difference between two consecutive calculations in all cells is less than a threshold of 0.002°C. +This equation can be solved using the Gauss-Seidel iteration technique. The +i\(^{th}\) cell temperature is calculated whilst the j\(^{th}\) cell +temperatures are kept as up to date as possible. The iteration is stopped +when the maximum difference between two consecutive calculations in all +cells is less than a threshold of \SI{0.002}{\celsius}. \subsubsection{Moisture Content w}\label{moisture-content-w} -The moisture content (w) of a cell is needed for the calculation of the heat transfer through the cell as it affects the thermal resistance and heat capacitance. The moisture content of cells is calculated from the relative humidity (RH) of the material. The relationship between w and the RH for each material is known as the sorption isotherm and measured data points are entered into EnergyPlus as a series of coordinates. HAMT interpolates between the measurements to obtain the moisture content of a material for any RH value. The sorption isotherm input is via the MaterialProperty:HeatAndMoistureTransfer:SorptionIsotherm object and is described in the Input Output Reference document. +The moisture content (w) of a cell is needed for the calculation of the +heat transfer through the cell as it affects the thermal resistance and +heat capacitance. The moisture content of cells is calculated from the +relative humidity (RH) of the material. The relationship between w and the +RH for each material is known as the sorption isotherm and measured data +points are entered into EnergyPlus as a series of coordinates. HAMT +interpolates between the measurements to obtain the moisture content of a +material for any RH value. The sorption isotherm input is via the +MaterialProperty:HeatAndMoistureTransfer:SorptionIsotherm object and is +described in the Input Output Reference document. \subsubsection{Porosity P}\label{porosity-p} -The porosity of a material (P) is an input variable and defined as the maximum fraction, by volume, of a material that can be taken up with moisture. It is used to calculate the maximum point on the sorption isotherm curve. ~The porosity is entered for each material via the MaterialProperty:HeatAndMoistureTransfer:Settings object, as described in the Input Output Reference document. +The porosity of a material (P) is an input variable and defined as the +maximum fraction, by volume, of a material that can be taken up with +moisture. It is used to calculate the maximum point on the sorption +isotherm curve. The porosity is entered for each material via the +MaterialProperty:HeatAndMoistureTransfer:Settings object, as described in +the Input Output Reference document. \subsubsection{Moisture Dependant Thermal Conductivity k\(^{w}\)}\label{moisture-dependant-thermal-conductivity-kw} -The thermal conductivity (k\(^{w}\)) of the cell is determined by interpolating between data points of thermal conductivity versus the moisture content of the material, entered into EnergyPlus via the MaterialProperty:HeatAndMoistureTransfer:ThermalConductivity object. The moisture content is determined via the sorption isotherm which gives the moisture content as a function of Relative Humidity. +The thermal conductivity (k\(^{w}\)) of the cell is determined by +interpolating between data points of thermal conductivity versus the +moisture content of the material, entered into EnergyPlus via the +MaterialProperty:HeatAndMoistureTransfer:ThermalConductivity object. The +moisture content is determined via the sorption isotherm which gives the +moisture content as a function of Relative Humidity. -\subsubsection{Moisture Dependant Moisture Diffusion Coefficient μ}\label{moisture-dependant-moisture-diffusion-coefficient-ux3bc} +\subsubsection{Moisture Dependant Moisture Diffusion Coefficient $\mu$}\label{moisture-dependant-moisture-diffusion-coefficient-ux3bc} -This is used in the third term of Equation~\ref{eq:HAMTHeatBalanceEquation} to describe the heat transfer due to vapor movement. It is determined by interpolating between data points of moisture diffusion coefficient versus the moisture content of the material, entered into EnergyPlus via the MaterialProperty:HeatAndMoistureTransfer:Diffusion object. A simple linear interpolation is used to obtain the conductivity between measured points. +This is used in the third term of Equation~\ref{eq:HAMTHeatBalanceEquation} +to describe the heat transfer due to vapor movement. It is determined by +interpolating between data points of moisture diffusion coefficient versus +the moisture content of the material, entered into EnergyPlus via the +MaterialProperty:HeatAndMoistureTransfer:Diffusion object. A simple linear +interpolation is used to obtain the conductivity between measured points. \subsubsection{Moisture Transfer}\label{moisture-transfer} -Moisture, as well as heat, is transported through materials as either liquid (w) or vapor (p). There are two different potentials that control the movement though the material. Liquid transfer is driven by differences in relative humidity whereas vapor transfer is driven by differences in vapor pressure. Materials also have a capacity to store moisture. Equation~\ref{eq:HAMTMoistureBalanceEquation} can be re-written for a discrete cell in a continuous material. +Moisture, as well as heat, is transported through materials as either +liquid (w) or vapor (p). There are two different potentials that control +the movement though the material. Liquid transfer is driven by differences +in relative humidity whereas vapor transfer is driven by differences in +vapor pressure. Materials also have a capacity to store moisture. +Equation~\ref{eq:HAMTMoistureBalanceEquation} can be re-written for a +discrete cell in a continuous material. \begin{equation} \frac{{dw}}{{d{\phi_i}}}\Delta {V_i}\frac{{\phi_i^{p + 1} - \phi_i^p}}{{\Delta \tau }} = \sum\limits_j {{k_{ij}}{A_{ij}}\frac{{\phi_j^{p + 1} - \phi_i^{p + 1}}}{{{x_{ij}}}}} + \sum\limits_j {\frac{{{\delta_{ij}}}}{{{\mu_{ij}}}}{A_{ij}}\frac{{p_j^{p + 1} - p_i^{p + 1}}}{{{x_{ij}}}}} \label{eq:HAMTMoistureBalanceEquationDiscreteCell} \end{equation} -Equation~\ref{eq:HAMTMoistureBalanceEquationDiscreteCell} can be rearranged to provide the relative humidity of the i\(^{th}\) cell in the next time step. +Equation~\ref{eq:HAMTMoistureBalanceEquationDiscreteCell} can be rearranged +to provide the relative humidity of the i\(^{th}\) cell in the next time +step. \begin{equation} \phi_i^{p + 1} = \frac{{\sum\nolimits_j {\frac{{\phi_j^{p + 1}}}{{R_{ij}^w}}} + \sum\nolimits_j {\frac{{p_i^{p + 1}}}{{R_{ij}^v}}} + C_i^w\frac{{\phi_i^p}}{{\Delta \tau }}}}{{\frac{{C_i^w}}{{\Delta \tau }} + \sum\nolimits_j {\frac{1}{{R_{ij}^w}} + \sum\nolimits_j {\frac{{p_i^{sat}}}{{R_{ij}^v}}} } }} \label{eq:RelativeHumidityIthCell} \end{equation} -where \(C_i^w = \frac{dw}{d\phi_{i}}\Delta {V_i}\) ~is the ``Moisture Capacitance'' of cell i, +where \(C_i^w = \frac{dw}{d\phi_{i}}\Delta {V_i}\) ~is the ``Moisture +Capacitance'' of cell i, \begin{equation} R_{ij}^w = \frac{{{x_{ij}}}}{{{A_{ij}}D_{ij}^w\frac{{dw}}{{d\phi }}}} \end{equation} -is the moisture resistance between cells i and j and \(R_{ij}^v = \frac{\mu_{ij}x_{ij}}{A_{ij}\delta_{ij}}\) ~is the vapor resistance~between cells i and j. +is the moisture resistance between cells i and j and +\(R_{ij}^v = \frac{\mu_{ij}x_{ij}}{A_{ij}\delta_{ij}}\) is the vapor +resistance between cells i and j. -Equation~\ref{eq:RelativeHumidityIthCell} can be used together with the heat equation~\ref{eq:TemperatureIthCell} in an alternate step by step fashion to calculate the new temperature and relative humidity profiles for each cell for the next time step. +Equation~\ref{eq:RelativeHumidityIthCell} can be used together with the +heat equation~\ref{eq:TemperatureIthCell} in an alternate step by step +fashion to calculate the new temperature and relative humidity profiles +for each cell for the next time step. -Surfaces with Ground exterior boundary condition assumes saturated air ({100\%} relative humidity) condition to calculate the exterior mass transfer coefficient, which is used to model mass transport through a ground contact surfaces. +Surfaces with Ground exterior boundary condition assumes saturated air +({100\%} relative humidity) condition to calculate the exterior mass +transfer coefficient, which is used to model mass transport through a +ground contact surfaces. \subsubsection{Liquid Transport Coefficient D\(^{w}\)}\label{liquid-transport-coefficient-dw} -The Moisture Dependant Liquid Transport Coefficient is entered as a series of moisture density and liquid transport coefficient data points. There are two different coefficients, one for suction, where the surface is wet due to rain, and one for redistribution where the surface is no longer wet. If the weather file has a rain flag it is used to switch between these two types of coefficient. HAMT-SUCTION and HAMT-REDISTRIBUTION. +The Moisture Dependant Liquid Transport Coefficient is entered as a series +of moisture density and liquid transport coefficient data points. There are +two different coefficients, one for suction, where the surface is wet due +to rain, and one for redistribution where the surface is no longer wet. If +the weather file has a rain flag it is used to switch between these two +types of coefficient. HAMT-SUCTION and HAMT-REDISTRIBUTION. \subsubsection{Moisture Dependent Moisture Capacity \(\frac{\partial w}{\partial \phi}\)}\label{moisture-dependent-moisture-capacity-fracpartial-wpartial-phi} -This is simply the gradient of moisture sorption isotherm at the RH of the material. +This is simply the gradient of moisture sorption isotherm at the RH of the +material. \subsubsection{Convective Heat Transfer}\label{convective-heat-transfer} -The internal and external heat transfer coefficients are used to calculate the thermal resistance of the boundary layer between the zone air and the surface of the surface. They are either supplied by the user via the advanced surface concepts object ``SurfaceProperty:ConvectionCoefficients'' or, if these are not provided, dynamic values are calculated. +The internal and external heat transfer coefficients are used to calculate +the thermal resistance of the boundary layer between the zone air and the +surface of the surface. They are either supplied by the user via the +advanced surface concepts object ``SurfaceProperty:ConvectionCoefficients'' +or, if these are not provided, dynamic values are calculated. \subsubsection{Convective Vapor Transfer}\label{convective-vapor-transfer} -The internal and external vapor transfer coefficients are used to calculate the resistance to vapour transfer of the boundary layer between the zone air and the surface of the surface. They are also either supplied by the user via the advanced surface concept object SurfaceProperties:VaporCoefficients. If these are not provided then dynamic values are calculated based on the convective heat transfer coefficients. +The internal and external vapor transfer coefficients are used to calculate +the resistance to vapour transfer of the boundary layer between the zone +air and the surface of the surface. They are also either supplied by the +user via the advanced surface concept object +SurfaceProperties:VaporCoefficients. If these are not provided then dynamic +values are calculated based on the convective heat transfer coefficients. \subsubsection{Initial Moisture Content}\label{initial-moisture-content} -At the start of an EnergyPlus simulation ``warm up'' days are used to ensure that the temperatures of surfaces come to equilibrium with the environment before the simulation starts proper. Moisture content within some building fabrics can take a very long time to come to equilibrium with its environment and it is therefore necessary to set initial or typical values of moisture content for each material to be used at the start of the simulation. These initial values are entered for each material via the MaterialProperty:HeatAndMoistureTransfer:Settings object as described in the Input Output Reference document. +At the start of an EnergyPlus simulation ``warm up'' days are used to +ensure that the temperatures of surfaces come to equilibrium with the +environment before the simulation starts proper. Moisture content within +some building fabrics can take a very long time to come to equilibrium with +its environment and it is therefore necessary to set initial or typical +values of moisture content for each material to be used at the start of the +simulation. These initial values are entered for each material via the +MaterialProperty:HeatAndMoistureTransfer:Settings object as described in +the Input Output Reference document. \subsubsection{Using the Model}\label{using-the-model} -As an illustration of the use of the Heat and Moisture Transfer (HAMT) model, the material properties for a small sample of six generic materials have been provided in the EnergyPlus Reference DataSets (MoistureMaterials.idf). The properties were synthesised from the Annex 24 database {[}Kumar Kumaran, M. (1996){]}, supplemented, when required, by data from the database of the WUFI model {[}WUFI (1999){]} and are therefore not related to any unique, measured material. Users should consult material property catalogues and other primary sources when the properties of a specific material are required. +As an illustration of the use of the Heat and Moisture Transfer (HAMT) +model, the material properties for a small sample of six generic materials +have been provided in the EnergyPlus Reference DataSets +(MoistureMaterials.idf). The properties were synthesised from the Annex 24 +database {[}Kumar Kumaran, M. (1996){]}, supplemented, when required, by +data from the database of the WUFI model {[}WUFI (1999){]} and are +therefore not related to any unique, measured material. Users should +consult material property catalogues and other primary sources when the +properties of a specific material are required. + +Moisture and heat from the surfaces are used by EnergyPlus to calculate the +room air temperature and moisture content. EnergyPlus with HAMT works best +with as short a time step as possible. However the optimum time step which +gives a good prediction for a short computing time will very much depend +on the nature of the weather and type of building. Buildings with frequent +and large changes in internal and external temperature will need a small +time step, maybe even 60 steps per hour. Slowly evolving temperatures and +relative humidity's will not require such a short time step and 20, or +even 6, steps per hour may be sufficient. + +\subsection{Moisture Source and Transport Mechanisms}\label{hamt-moisture-sources} +Air movements may transport vapor through the envelope and deposit moisture +within envelope components, acting as a source in the HAMT equations. This +may be modeled in on of three ways. The first method is a simple constant +airflow through the building component, the second calculates the air leakage +based on stack pressure and overpressure from mechanical ventilation equipment, +and the third method uses the computed airflow through building components +from the AirflowNetwork calculation in Energy Plus. The mathematical model and +additional test results of this model are described by Antretter and Pallin (2019). + +\subsubsection{User-Defined Constant Airflow } +This method uses a simplistic assumption of constant airflow through an +envelope component. User defined air-flow rates are assumed to be in the range +between \SI{0.07}{\meter\cubed\per\hour\per\meter\squared} +(\IP{0.0038}{\CFM\per\ft\squared}) for very airtight buildings to +\SI{0.33}{\meter\cubed\per\hour\per\meter\squared} +(\IP{0.018}{\CFM\per\ft\squared}) for buildings without requirements on their + air-tightness. the air leakage ratio can be expressed as +% +\begin{equation}\label{ALRconstant} +ALR = \text{constant}. +\end{equation} +% +The airflow depends on dynamic wind induced pressure differences and on +differences in stack effect due to varying temperature differences between +outside and inside. Also, mechanical ventilation equipment does often operate +intermittently, causing dynamic changes in pressure differences and therefore +airflow through leaks. However, a simple assumption like a constant airflow +allows for assessment of the impact of different air-tightness levels on the +moisture conditions in building envelopes and related risks. + +\subsubsection{Calculated Airflow Based on Stack Pressure and Over-Pressure from Mechanical Ventilation Equipment} +A dynamic model by K\"unzel, Zirkelbach and Schafaczek (K\"unzel et al., 2012) + takes in to account the pressure difference due to stack effect only. This is due + to pressure differences due to wind are difficult to determine, due to the erratic + nature of wind and the dependence of the stagnation pressure on building + specifics and its surroundings. Also, when wind-induced pressure differences + peak, the increased flow rate may switch the ``moisture leak'' into an +``energy leak''. + +K\"unzel et al. (2012) used Equation~\ref{hamt-stack-and-over-press} for calculating +the pressure difference due to the stack effect with the assumption of a neutral +pressure level in the middle of the connected airspace. +% +\begin{equation}\label{hamt-stack-and-over-press} +\Delta P_{stack}= \rho ^{ext}\frac{T^{ext}-T^{int}}{T^{int}} g \frac{h}{2} +\end{equation} +% +They have also added a pressure difference due to overpressure from a +mechanical ventilation system as +% +\begin{equation}\label{hamt-over-press} +\Delta P_{mech}=-\Delta P^{mech}. +\end{equation} +% +Equations~ref{hamt-stack-and-over-press} and \ref{hamt-over-press} can be +superimposed to give the total pressure difference due to stack effect and +mechanical system overpressure as + +\begin{equation} +\Delta P=\rho ^{ext} \frac{T^{ext}-T^{int}}{T^{int}} g \frac{h}{2} -\Delta P^{mech}. +\end{equation} + +This may be further simplified by assuming laminar flow (Maref et al. 2009): + +\begin{equation}\label{hamt-k-dp} +ALR = K \Delta P. +\end{equation} + +According to K\"unzel et al. (2012) the components moisture specific air +permeance $K$ can range from +\SI{0.004}{\meter\cubed\per\meter\squared\per\hour\per\pascal} +(\IP{0.00022}{\CFM\per\ft\squared\per\pascal}) for very airtight buildings +to \SI{0.06}{\meter\cubed\per\meter\squared\per\hour\per\pascal} +(\IP{0.0033}{\CFM\per\ft\squared\per\pascal}) for standard construction. +K\"unzel et al. (2012) also assumes that moisture leaks are represented by +approximately 10\% of the total component air permeance. -Moisture and heat from the surfaces are used by EnergyPlus to calculate the room air temperature and moisture content. EnergyPlus with HAMT works best with as short a time step as possible. However the optimum time step which gives a good prediction for a short computing time will very much depend on the nature of the weather and type of building. Buildings with frequent and large changes in internal and external temperature will need a small time step, maybe even 60 steps per hour. Slowly evolving temperatures and relative humidity's will not require such a short time step and 20, or even 6, steps per hour may be sufficient. +\subsubsection{Airflow from Multizone AirflowNetwork} +To be added. \subsection{References}\label{references-012} -Künzel, H.M. (1995) Simultaneous Heat and Moisture Transport in Building Components. One- and two-dimensional calculation using simple parameters. IRB Verlag 1995 +K\"unzel, H.M. (1995) Simultaneous Heat and Moisture Transport in Building +Components. One- and two-dimensional calculation using simple parameters. +IRB Verlag 1995 Holman, J.P. (2002) Heat Transfer, Ninth Edition. McGraw-Hill -Winterton, R.H.S. (1997) Heat Transfer. (Oxford Chemistry Primers; 50) Oxford University Press +Winterton, R.H.S. (1997) Heat Transfer. (Oxford Chemistry Primers; 50) +Oxford University Press Kumar Kumaran, M. (1996) IEA ANNEX 24, Final Report, Volume 3 -WUFI (1999) version 2.2 Simultaneous Heat and Moisture Transport in Building components. Fraunhofer IBP, Holzkirchen, Germany +WUFI (1999) version 2.2 Simultaneous Heat and Moisture Transport in +Building components. Fraunhofer IBP, Holzkirchen, Germany + +Antretter, F., Pallin, S. B. (2019). Modelling moisture sources due to air +leakage with the HAMT extension for EnergyPlus. Oak Ridge National Lab (ORNL), +Oak Ridge, TN (United States). + +K\"unzel, H.M. (Ed.), 2012. Modeling Air Leakage in Hygrothermal Envelope +Simulation. + +K\"unzel, H.M., Zirkelbach, D., Schafaczek, B., 2012. Modelling the Effect of Air +Leakage in Hygrothermal Envelope Simulation. Proceedings of the BEST 3, 2-4. + +Maref, W., Elmahdy, A., Swinton, M., Tariku, F., 2009. Assessment of energy rating of PU spray foam walls. NRC-CNRC report NRCC-50847. + +Sherman, M.H., 1987. Estimation of infiltration from leakage and climate indicators. Energy and Buildings 10 (1), 81-86.10.1016/0378-7788(87)90008-9. +