AirflowNetwork Model[LINK]
The AirflowNetwork model provides the ability to simulate the performance of an air distribution system, including supply and return leaks, and calculate multizone airflows driven by outdoor wind and forced air during HVAC system operation. The pressure and airflow model described here was developed based on AIRNET (Walton 1989). This detailed model is used to simulate thermal conduction and air leakage losses for constant volume air distribution systems (e.g., in residential or light commercial buildings). The multizone airflow calculations are performed at the HVAC system time step which, among other benefits, allows for modeling hybrid ventilation systems.
Model Description[LINK]
The input object AirflowNetwork:SimulationControl provides access to the airflow network method, which consists of a set of nodes connected by airflow components through linkages. The objects AirflowNetwork:Multizone:Zone, AirflowNetwork:Multizone:ExternalNode, and AirflowNetwork:Distribution:Node represent airflow nodes. The objects AirflowNetwork:Multizone:Surface and AirflowNetwork:Distribution:Linkage represent airflow linkages. The other objects with a relationship between pressure and airflow represent airflow components.
The AirflowNetwork model consists of three sequential steps:
Pressure and airflow calculations
Node temperature and humidity calculations
Sensible and latent load calculations
The pressure and airflow calculations determine pressure at each node and airflow through each linkage given wind pressures and forced airflows. Based on the airflow calculated for each linkage, the model then calculates node temperatures and humidity ratios given zone air temperatures and zone humidity ratios. Using these node temperatures and humidity ratios, the sensible and latent loads from duct system conduction and leakage are summed for each zone. The sensible and latent loads obtained in this step are then used in the zone energy balance equations to predict HVAC system loads and to calculate the final zone air temperatures, humidity ratios, and pressures.
The present AirflowNetwork model may only be applied to a single heating and cooling system that uses a single air distribution system (a single AirLoopHVAC object). The model excludes the impact of the air and duct system thermal capacitance.
Pressure and Airflow Calculations[LINK]
The EnergyPlus airflow network consists of a set of nodes linked by airflow components. Therefore, it is a simplified airflow model, compared to detailed models such as those used in computational fluid dynamics (CFD) models. The node variable is pressure and the linkage variable is airflow rate. A brief description is presented below. A detailed description of the airflow network model may be found in the work of Walton (1989), Dols and Walton (2002), and Walton and Dols (2003).
Initialization[LINK]
Newton’s method is used to solve for node air pressures and it requires an initial set of values for the node pressures. There are two initialization methods available. The first is linear initialization and equivalent to Initialization flag = 0. These initial values may be obtained by including in each airflow component a linear approximation relating airflow to pressure drop:
˙mi=CiρΔPiμ
where:
˙mi 
= Air mass flow rate at ith linkage [kg/s] 
Ci 
= Air mass flow coefficient [m3] 
ΔPi 
= Pressure difference across the ith linkage [Pa] 
μ 
= Air viscosity [Pas] 
This initialization handles stack effects very well and tends to establish the proper direction for the airflows. The linear approximation is provided by the laminar regime.
The second initialization method assumes the initial pressures are zero and uses Newton’s method directly.
Convergence criteria[LINK]
Conservation of air mass flow rate at each linkage provides the convergence criterion. When the sum of mass flow rates in all the linkages approaches zero within the convergence tolerance, the solution has converged. The solution is assumed to have converged when the sum is less than the convergence value, in order to reduce the number of iterations and obtain sufficient accuracy. There are two convergence criteria used in the AirflowNetwork model: Relative airflow convergence tolerance and Absolute airflow convergence tolerance.
Relative airflow tolerance 
= ∑˙mi∑˙mi

Absolute airflow tolerance 
= $ 
The relative airflow tolerance is equivalent to the ratio of the absolute value of the sum of all network airflows to the sum of the network airflow magnitudes. The absolute airflow tolerance is the summation of the absolute value of all network airflows. The solution has converged when both of these convergence criteria have been met.
Linkage models[LINK]
A linkage used in the AirflowNetwork model has two nodes, inlet and outlet, and is linked by a component which has a relationship between airflow and pressure. The pressure difference across each component in a linkage is assumed to be governed by Bernoulli’s equation:
ΔP=(Pn+ρV2n2)−(Pm+ρV2m2)+ρg(zn−zm)
where:
ΔP 
= Total pressure difference between nodes n and m [Pa] 
Pn,Pm 
= Entry and exit static pressures [Pa] 
Vn,Vm 
= Entry and exit airflow velocities [m/s] 
ρ 
= Air density [kg/m3] 
g 
= Acceleration due to gravity [9.81 m/s2] 
zn,zm 
= Entry and exit elevations [m] 
By rearranging terms and adding wind pressure impacts, the above equation may be rewritten in the format used by the airflow network model:
ΔP=Pn−Pm+PS+PW
where:
Pn,Pm 
= Total pressures at nodes n and m [Pa] 
PS 
= Pressure difference due to density and height differences [Pa] 
PW 
= Pressure difference due to wind [Pa] 
The Input Output Reference provides the relationship between airflow and pressure for the most of the components (Ref.AirflowNetwork Model). The relationship between airflow and pressure for the AirflowNetwork:Multizone:Component:DetailedOpening, AirflowNetwork:Multizone:Component:SimpleOpening, and AirflowNetwork:Multizone:Component:HorizontalOpening objects are provided in detail in this reference.
The schematic drawing of a possible air flow pattern through a detailed vertical opening (AirflowNetwork:Multizone:Component:DetailedOpening) is shown in Figure. The equations used below are extracted from the COMIS Fundamentals manual (1990).
The air density is assumed to be a linear function of height:
ρi(z)=ρ0i+biz
The pressure difference is assumed to be linear and simulate the effect of turbulence:
ΔPt=Pt0+btz
The reference pressures on each side are given at the bottom of the opening. By assuming the Bernoulli hypothesis on both sides, the pressure difference can be defined at any level of z as:
P1(z)−P2(z)=(P01−P02)−g[(ρ01z+b1z2/2)−(ρ02z+b2z2/2)]+(Pt0+btz)
The velocity at any level z is given by
v(z)=√2P1(z)−P
AirflowNetwork Model[LINK]
Overview[LINK]
The AirflowNetwork model provides the ability to simulate the performance of an air distribution system, including supply and return leaks, and calculate multizone airflows driven by outdoor wind and forced air during HVAC system operation. The pressure and airflow model described here was developed based on AIRNET (Walton 1989). This detailed model is used to simulate thermal conduction and air leakage losses for constant volume air distribution systems (e.g., in residential or light commercial buildings). The multizone airflow calculations are performed at the HVAC system time step which, among other benefits, allows for modeling hybrid ventilation systems.
Model Description[LINK]
The input object AirflowNetwork:SimulationControl provides access to the airflow network method, which consists of a set of nodes connected by airflow components through linkages. The objects AirflowNetwork:Multizone:Zone, AirflowNetwork:Multizone:ExternalNode, and AirflowNetwork:Distribution:Node represent airflow nodes. The objects AirflowNetwork:Multizone:Surface and AirflowNetwork:Distribution:Linkage represent airflow linkages. The other objects with a relationship between pressure and airflow represent airflow components.
The AirflowNetwork model consists of three sequential steps:
Pressure and airflow calculations
Node temperature and humidity calculations
Sensible and latent load calculations
The pressure and airflow calculations determine pressure at each node and airflow through each linkage given wind pressures and forced airflows. Based on the airflow calculated for each linkage, the model then calculates node temperatures and humidity ratios given zone air temperatures and zone humidity ratios. Using these node temperatures and humidity ratios, the sensible and latent loads from duct system conduction and leakage are summed for each zone. The sensible and latent loads obtained in this step are then used in the zone energy balance equations to predict HVAC system loads and to calculate the final zone air temperatures, humidity ratios, and pressures.
The present AirflowNetwork model may only be applied to a single heating and cooling system that uses a single air distribution system (a single AirLoopHVAC object). The model excludes the impact of the air and duct system thermal capacitance.
Pressure and Airflow Calculations[LINK]
The EnergyPlus airflow network consists of a set of nodes linked by airflow components. Therefore, it is a simplified airflow model, compared to detailed models such as those used in computational fluid dynamics (CFD) models. The node variable is pressure and the linkage variable is airflow rate. A brief description is presented below. A detailed description of the airflow network model may be found in the work of Walton (1989), Dols and Walton (2002), and Walton and Dols (2003).
Initialization[LINK]
Newton’s method is used to solve for node air pressures and it requires an initial set of values for the node pressures. There are two initialization methods available. The first is linear initialization and equivalent to Initialization flag = 0. These initial values may be obtained by including in each airflow component a linear approximation relating airflow to pressure drop:
˙mi=CiρΔPiμ
where:
This initialization handles stack effects very well and tends to establish the proper direction for the airflows. The linear approximation is provided by the laminar regime.
The second initialization method assumes the initial pressures are zero and uses Newton’s method directly.
Convergence criteria[LINK]
Conservation of air mass flow rate at each linkage provides the convergence criterion. When the sum of mass flow rates in all the linkages approaches zero within the convergence tolerance, the solution has converged. The solution is assumed to have converged when the sum is less than the convergence value, in order to reduce the number of iterations and obtain sufficient accuracy. There are two convergence criteria used in the AirflowNetwork model: Relative airflow convergence tolerance and Absolute airflow convergence tolerance.
The relative airflow tolerance is equivalent to the ratio of the absolute value of the sum of all network airflows to the sum of the network airflow magnitudes. The absolute airflow tolerance is the summation of the absolute value of all network airflows. The solution has converged when both of these convergence criteria have been met.
Linkage models[LINK]
A linkage used in the AirflowNetwork model has two nodes, inlet and outlet, and is linked by a component which has a relationship between airflow and pressure. The pressure difference across each component in a linkage is assumed to be governed by Bernoulli’s equation:
ΔP=(Pn+ρV2n2)−(Pm+ρV2m2)+ρg(zn−zm)
where:
By rearranging terms and adding wind pressure impacts, the above equation may be rewritten in the format used by the airflow network model:
ΔP=Pn−Pm+PS+PW
where:
The Input Output Reference provides the relationship between airflow and pressure for the most of the components (Ref.AirflowNetwork Model). The relationship between airflow and pressure for the AirflowNetwork:Multizone:Component:DetailedOpening, AirflowNetwork:Multizone:Component:SimpleOpening, and AirflowNetwork:Multizone:Component:HorizontalOpening objects are provided in detail in this reference.
The general problem of gravitational flow through a vertical opening
The schematic drawing of a possible air flow pattern through a detailed vertical opening (AirflowNetwork:Multizone:Component:DetailedOpening) is shown in Figure. The equations used below are extracted from the COMIS Fundamentals manual (1990).
The air density is assumed to be a linear function of height:
ρi(z)=ρ0i+biz
The pressure difference is assumed to be linear and simulate the effect of turbulence:
ΔPt=Pt0+btz
The reference pressures on each side are given at the bottom of the opening. By assuming the Bernoulli hypothesis on both sides, the pressure difference can be defined at any level of z as:
P1(z)−P2(z)=(P01−P02)−g[(ρ01z+b1z2/2)−(ρ02z+b2z2/2)]+(Pt0+btz)
The velocity at any level z is given by
v(z)=√2P1(z)−P