Buildings.Airflow.Multizone

Package with models for multizone airflow and contaminant transport

Information

Extends from Modelica.Icons.VariantsPackage (Icon for package containing variants).

Package Content

Name	Description
UsersGuide	User's Guide
Coefficient_V_flow	Power law with coefficient for volume flow rate
Coefficient_m_flow	Powerlaw with coefficient for mass flow rate
DoorDiscretizedOpen	Door model using discretization along height coordinate
DoorDiscretizedOperable	Door model using discretization along height coordinate
DoorOpen	Door model for bi-directional air flow between rooms
DoorOperable	Door model for bi-directional air flow between rooms that can be open or closed
EffectiveAirLeakageArea	Effective air leakage area
MediumColumn	Vertical shaft with no friction and no storage of heat and mass
MediumColumnDynamic	Vertical shaft with no friction and storage of heat and mass
Orifice	Orifice
Point_m_flow	Powerlaw with flow coeffient fitted based on flow exponent and 1 datapoint
Points_m_flow	Powerlaw with flow coefficient and flow exponent fitted based on 2 datapoints
Table_V_flow	Volume flow(y-axis) vs Pressure(x-axis) cubic spline fit model based on table data, with last two points linearly interpolated
Table_m_flow	Mass flow(y-axis) vs Pressure(x-axis) cubic spline fit model based from table data, with last two points linearly interpolated
ZonalFlow_ACS	Zonal flow with input air change per second
ZonalFlow_m_flow	Zonal flow with input air change per second
Types	Package with type definitions
Examples	Collection of models that illustrate model use and test models
Validation	Collection of validation models
BaseClasses	Package with base classes for Buildings.Airflow.Multizone

Buildings.Airflow.Multizone.Coefficient_V_flow

Power law with coefficient for volume flow rate

Information

This model describes the one-directional pressure driven air flow through an opening, using the equation

V̇ = C Δp^m,

where V̇ is the volume flow rate in m³/s, C is a flow coefficient, Δp is the pressure difference in Pa, and m is the flow exponent.

A similar model is also used in the CONTAM software (Dols and Walton, 2015). Dols and Walton (2002) recommend to use for the flow exponent m=0.6 to m=0.7 if the flow exponent is not reported with the test results.

References

• ASHRAE, 1997. ASHRAE Fundamentals, American Society of Heating, Refrigeration and Air-Conditioning Engineers, 1997.
• Dols and Walton, 2002. W. Stuart Dols and George N. Walton, CONTAMW 2.0 User Manual, Multizone Airflow and Contaminant Transport Analysis Software, Building and Fire Research Laboratory, National Institute of Standards and Technology, Tech. Report NISTIR 6921, November, 2002.
• W. S. Dols and B. J. Polidoro,2015. CONTAM User Guide and Program Documentation Version 3.2, National Institute of Standards and Technology, NIST TN 1887, Sep. 2015. doi: 10.6028/NIST.TN.1887.

Extends from Buildings.Airflow.Multizone.BaseClasses.PartialOneWayFlowElement (Partial model for flow resistance with one-way flow), Buildings.Airflow.Multizone.BaseClasses.PowerLawResistanceParameters (Power law resistance parameters).

Parameters

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Modelica definition

Buildings.Airflow.Multizone.Coefficient_m_flow

Powerlaw with coefficient for mass flow rate

Information

This model describes the one-directional pressure driven air flow through an opening, using the equation

ṁ = k Δp^m,

where ṁ is the mass flow rate in kg/s, k is a flow coefficient, Δp is the pressure difference in Pa, and m is the flow exponent.

A similar model is also used in the CONTAM software (Dols and Walton, 2015). Dols and Walton (2002) recommend to use for the flow exponent m=0.6 to m=0.7 if the flow exponent is not reported with the test results.

References

• ASHRAE, 1997. ASHRAE Fundamentals, American Society of Heating, Refrigeration and Air-Conditioning Engineers, 1997.
• Dols and Walton, 2002. W. Stuart Dols and George N. Walton, CONTAMW 2.0 User Manual, Multizone Airflow and Contaminant Transport Analysis Software, Building and Fire Research Laboratory, National Institute of Standards and Technology, Tech. Report NISTIR 6921, November, 2002. [1]
• W. S. Dols and B. J. Polidoro,2015. CONTAM User Guide and Program Documentation Version 3.2, National Institute of Standards and Technology, NIST TN 1887, Sep. 2015. doi: 10.6028/NIST.TN.1887.

Extends from Buildings.Airflow.Multizone.BaseClasses.PartialOneWayFlowElement (Partial model for flow resistance with one-way flow), Buildings.Airflow.Multizone.BaseClasses.PowerLawResistanceParameters (Power law resistance parameters).

Parameters

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Modelica definition

Buildings.Airflow.Multizone.DoorDiscretizedOpen

Door model using discretization along height coordinate

Information

This model describes the bi-directional air flow through an open door.

To compute the bi-directional flow, the door is discretize along the height coordinate. An orifice equation is used to compute the flow for each compartment.

In this model, the door is always open. Use the model Buildings.Airflow.Multizone.DoorDiscretizedOperable for a door that can either be open or closed.

Extends from Buildings.Airflow.Multizone.BaseClasses.DoorDiscretized (Door model using discretization along height coordinate).

Parameters

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Modelica definition

Buildings.Airflow.Multizone.DoorDiscretizedOperable

Door model using discretization along height coordinate

Information

This model describes the bi-directional air flow through an open door.

To compute the bi-directional flow, the door is discretize along the height coordinate, and uses an orifice equation to compute the flow for each compartment.

The door can be either open or closed, depending on the input signal y. Set y=0 if the door is closed, and y=1 if the door is open. Use the model Buildings.Airflow.Multizone.DoorDiscretizedOpen for a door that is always closed.

Extends from Buildings.Airflow.Multizone.BaseClasses.DoorDiscretized (Door model using discretization along height coordinate).

Parameters

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Modelica definition

Buildings.Airflow.Multizone.DoorOpen

Door model for bi-directional air flow between rooms

Information

Model for bi-directional air flow through a large opening such as a door.

In this model, the air flow is composed of two components, a one-directional bulk air flow due to static pressure difference in the adjoining two thermal zones, and a two-directional airflow due to temperature-induced differences in density of the air in the two thermal zones. Although turbulent air flow is a nonlinear phenomenon, the model is based on the simplifying assumption that these two air flow rates can be superposed. (Superposition is only exact for laminar flow.) This assumption is made because it leads to a simple model and because there is significant uncertainty and assumptions anyway in such simplified a model for bidirectional flow through a door.

Main equations

The air flow rate due to static pressure difference is

V̇_ab,p = C_D w h (2/ρ₀)^0.5 Δp^m,

where V̇ is the volumetric air flow rate, C_D is the discharge coefficient, w and h are the width and height of the opening, ρ₀ is the mass density at the medium default pressure, temperature and humidity, m is the flow exponent and Δp = p_a - p_b is the static pressure difference between the thermal zones. For this model explanation, we will assume p_a > p_b. For turbulent flow, m=1/2 and for laminar flow m=1.

The air flow rate due to temperature difference in the thermal zones is V̇_ab,t for flow from thermal zone a to b, and V̇_ba,t for air flow rate from thermal zone b to a. The model has two air flow paths to allow bi-directional air flow. The mass flow rates at these two air flow paths are

ṁ_a1 = ρ₀   (+V̇_ab,p/2 +   V̇_ab,t),

and, similarly,

V̇_ba = ρ₀   (-V̇_ab,p/2 +   V̇_ba,t),

where we simplified the calculation by using the density ρ₀. To calculate V̇_ba,t, we again use the density ρ₀ and because of this simplification, we can write

ṁ_ab,t = -ṁ_ba,t = ρ₀   V̇_ab,t = -ρ₀   V̇_ba,t,

from which follows that the neutral height, e.g., the height where the air flow rate due to flow induced by temperature difference is zero, is at h/2. Hence,

V̇_ab,t = C_D ∫₀^h/2 w v(z) dz,

where v(z) is the velocity at height z. From the Bernoulli equation, we obtain

v(z) = (2 g z Δρ ⁄ ρ₀)^1/2.

The density difference can be written as

Δρ = ρ_a-ρ_b ≈ ρ₀ (T_b - T_a) ⁄ T₀,

where we used ρ_a = p₀ /(R T_a) and T_a T_b ≈ T₀². Substituting this expression into the integral and integrating from 0 to z yields

V̇_ab,t = 1⁄3 C_D w h (g h ⁄ (R T₀ ρ₀))^1/2 Δp^1/2.

The above equation is equivalent to (6) in Brown and Solvason (1962).

Main assumptions

The main assumptions are as follows:

• The air flow rates due to static pressure difference and due to temperature-difference can be superposed.

• For buoyancy-driven air flow, a constant density can be used to convert air volume flow rate to air mass flow rate.

From these assumptions follows that the neutral height for buoyancy-driven air flow is at half of the height of the opening.

Notes

For a more detailed model, use Buildings.Airflow.Multizone.DoorDiscretizedOpen.

References

• Brown, W.G. and K. R. Solvason. Natural Convection through rectangular openings in partitions - 1. Int. Journal of Heat and Mass Transfer. Vol. 5, p. 859-868. 1962. doi:10.1016/0017-9310(62)90184-9.
  Also available at https://nrc-publications.canada.ca/eng/view/ft/?id=081c0ace-7c31-449c-9b3b-e6c14864b196.

Extends from Buildings.Airflow.Multizone.BaseClasses.Door (Partial door model for bi-directional flow).

Parameters

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Modelica definition

Buildings.Airflow.Multizone.DoorOperable

Door model for bi-directional air flow between rooms that can be open or closed

Information

Model for bi-directional air flow through a large opening such as a door which can be opened or closed based on the control input signal y.

For the control input signal y=1, this model is identical to Buildings.Airflow.Multizone.DoorOpen, and for y=0, the door is assumed to be closed and the air flow rate is set to the air flow rate through the crack posed by the open door, V̇_clo.

The air flow rate for the closed door is computed as

V̇_clo = C_clo Δp^mClo,

where V̇_clo is the volume flow rate, C_clo is a flow coefficient and mClo is the flow exponent. The flow coefficient is

C_clo = L_clo C_DCloRat Δp_Rat^(0.5-mClo) (2/ρ₀)^0.5,

where L_clo is the effective air leakage area, C_DCloRat is the discharge coefficient at the reference condition, Δp_Rat is the pressure drop at the rating condition, and ρ₀ is the mass density at the medium default pressure, temperature and humidity.

The effective air leakage area L_clo can be obtained, for example, from the ASHRAE fundamentals (ASHRAE, 1997, p. 25.18). In the ASHRAE fundamentals, the effective air leakage area is based on a reference pressure difference of Δp_Rat = 4 Pa and a discharge coefficient of C_DCloRat = 1. A similar model is also used in the CONTAM software (Dols and Walton, 2002). Dols and Walton (2002) recommend to use for the flow exponent mClo=0.6 to mClo=0.7 if the flow exponent is not reported with the test results.

For the open door, the air flow rate V̇_ope is computed as described in Buildings.Airflow.Multizone.DoorOpen with the parameters CDOpe and mOpe.

The actual air flow rate is computed as

V̇_clo = (y-1) V̇_clo + y V̇_ope,

where y ∈ [0, 1] is the control signal. Note that for values of y that are different from 0 and 1, the model simply interpolates the air flow rate between a fully open and a fully closed door. In practice, the air flow rate would likely increase quickly if the door is slightly opened, and hence we do not claim that the model is accurate for values other than y = 0 and y = 1.

References

• ASHRAE. ASHRAE Fundamentals, American Society of Heating, Refrigeration and Air-Conditioning Engineers, 1997.
• Dols and Walton. W. Stuart Dols and George N. Walton, CONTAMW 2.0 User Manual, Multizone Airflow and Contaminant Transport Analysis Software, Building and Fire Research Laboratory, National Institute of Standards and Technology, Tech. Report NISTIR 6921, November, 2002.

Extends from Buildings.Airflow.Multizone.BaseClasses.Door (Partial door model for bi-directional flow).

Parameters

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Modelica definition

Buildings.Airflow.Multizone.EffectiveAirLeakageArea

Effective air leakage area

Information

This model describes the one-directional pressure driven air flow through a crack-like opening, using the equation

V̇ = C Δp^m,

where V̇ is the volume flow rate, C is a flow coefficient and m is the flow exponent. The flow coefficient is

C = L C_D,Rat Δp_Rat^(0.5-m) (2/ρ₀)^0.5,

where L is the effective air leakage area, C_D,Rat is the discharge coefficient at the reference condition, Δp_Rat is the pressure drop at the rating condition, and ρ₀ is the mass density at the medium default pressure, temperature and humidity.

The effective air leakage area L can be obtained, for example, from the ASHRAE fundamentals (ASHRAE, 1997, p. 25.18). In the ASHRAE fundamentals, the effective air leakage area is based on a reference pressure difference of Δp_Rat = 4 Pa and a discharge coefficient of C_D,Rat = 1. A similar model is also used in the CONTAM software (Dols and Walton, 2002). Dols and Walton (2002) recommend to use for the flow exponent m=0.6 to m=0.7 if the flow exponent is not reported with the test results.

References

• ASHRAE, 1997. ASHRAE Fundamentals, American Society of Heating, Refrigeration and Air-Conditioning Engineers, 1997.
• Dols and Walton, 2002. W. Stuart Dols and George N. Walton, CONTAMW 2.0 User Manual, Multizone Airflow and Contaminant Transport Analysis Software, Building and Fire Research Laboratory, National Institute of Standards and Technology, Tech. Report NISTIR 6921, November, 2002.
• Michael Wetter. Multizone Airflow Model in Modelica. Proc. of the 5th International Modelica Conference, p. 431-440. Vienna, Austria, September 2006.

Extends from Buildings.Airflow.Multizone.Coefficient_V_flow (Power law with coefficient for volume flow rate).

Parameters

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Modelica definition

Buildings.Airflow.Multizone.MediumColumn

Vertical shaft with no friction and no storage of heat and mass

Information

This model describes the pressure difference of a vertical medium column. It can be used to model the pressure difference caused by stack effect.

Typical use and important parameters

The model can be used with the following three configurations, which are controlled by the setting of the parameter densitySelection:

• top: Use this setting to use the density from the volume that is connected to port_a.
• bottom: Use this setting to use the density from the volume that is connected to port_b.
• actual: Use this setting to use the density based on the actual flow direction.

The settings top and bottom should be used when rooms or different floors of a building are connected since multizone airflow models assume that each floor is completely mixed. For these two seetings, this model will compute the pressure between the center of the room and an opening that is at height h relative to the center of the room. The setting actual may be used to model a chimney in which a column of air will change its density based on the flow direction.

In this model, the parameter h must always be positive, and the port port_a must be at the top of the column.

Dynamics

For a dynamic model, use Buildings.Airflow.Multizone.MediumColumnDynamic instead of this model.

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Modelica definition

Buildings.Airflow.Multizone.MediumColumnDynamic

Vertical shaft with no friction and storage of heat and mass

Information

This model contains a completely mixed fluid volume and models that take into account the pressure difference of a medium column that is at the same temperature as the fluid volume. It can be used to model the pressure difference caused by a stack effect.

Typical use and important parameters

Set the parameter use_HeatTransfer=true to expose a heatPort. This heatPort can be used to add or subtract heat from the volume. This allows, for example, to use this model in conjunction with a model for heat transfer through walls to model a solar chimney that stores heat.

Dynamics

For a steady-state model, use Buildings.Airflow.Multizone.MediumColumn instead of this model.

In this model, the parameter h must always be positive, and the port port_a must be at the top of the column.

Extends from Buildings.Fluid.Interfaces.LumpedVolumeDeclarations (Declarations for lumped volumes).

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Buildings.Airflow.Multizone.Orifice

Orifice

Information

This model describes the mass flow rate and pressure difference relation of an orifice in the form

V̇ = C Δp^m,

where V̇ is the volume flow rate, C is a flow coefficient and m is the flow exponent. The flow coefficient is

C = C_D A (2/ρ₀)^0.5,

where C_D is the discharge coefficient, A is the cross section area and ρ₀ is the mass density at the medium default pressure, temperature and humidity.

For turbulent flow, set m=1/2 and for laminar flow, set m=1. Large openings are characterized by values close to 0.5, while values near 0.65 have been found for small crack-like openings (Dols and Walton, 2002).

References

• W. Stuart Dols and George N. Walton, CONTAMW 2.0 User Manual, Multizone Airflow and Contaminant Transport Analysis Software, Building and Fire Research Laboratory, National Institute of Standards and Technology, Tech. Report NISTIR 6921, November, 2002.
• Michael Wetter. Multizone Airflow Model in Modelica. Proc. of the 5th International Modelica Conference, p. 431-440. Vienna, Austria, September 2006.

Extends from Buildings.Airflow.Multizone.Coefficient_V_flow (Power law with coefficient for volume flow rate).

Parameters

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Modelica definition

Buildings.Airflow.Multizone.Point_m_flow

Powerlaw with flow coeffient fitted based on flow exponent and 1 datapoint

Information

Model that fits the flow coefficient of the massflow version of the orifice equation based on 1 datapoint of mass flow rate and pressure difference, and given flow exponent.

A similar model is also used in the CONTAM software (Dols and Walton, 2015).

References

• W. S. Dols and B. J. Polidoro,2015. CONTAM User Guide and Program Documentation Version 3.2, National Institute of Standards and Technology, NIST TN 1887, Sep. 2015. doi: 10.6028/NIST.TN.1887.

Extends from Buildings.Airflow.Multizone.Coefficient_m_flow (Powerlaw with coefficient for mass flow rate).

Parameters

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Modelica definition

Buildings.Airflow.Multizone.Points_m_flow

Powerlaw with flow coefficient and flow exponent fitted based on 2 datapoints

Information

Model that fits the flow coefficient of the massflow version of the orifice equation based on 2 datapoints of mass flow rate and pressure difference.

A similar model is also used in the CONTAM software (Dols and Walton, 2015).

References

• W. S. Dols and B. J. Polidoro,2015. CONTAM User Guide and Program Documentation Version 3.2, National Institute of Standards and Technology, NIST TN 1887, Sep. 2015. doi: 10.6028/NIST.TN.1887.

Extends from Buildings.Airflow.Multizone.Coefficient_m_flow (Powerlaw with coefficient for mass flow rate).

Parameters

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Modelica definition

Buildings.Airflow.Multizone.Table_V_flow

Volume flow(y-axis) vs Pressure(x-axis) cubic spline fit model based on table data, with last two points linearly interpolated

Information

This model describes the one-directional pressure driven air flow through an opening based on user-provided tabular data describing the relation between volume flow rate and pressure difference over the component.

V̇ = f(Δp),

where V̇ is the volume flow rate and Δp is the pressure difference.

Based on the table input, a cubic hermite spline is constructed between all points except for the two last pairs of points. These point are connected linearly.

The constructed curve is the direct relation between V̇ and Δp.

A similar model is also used in the CONTAM software (Dols and Walton, 2015).

References

• W. S. Dols and B. J. Polidoro,2015. CONTAM User Guide and Program Documentation Version 3.2, National Institute of Standards and Technology, NIST TN 1887, Sep. 2015. doi: 10.6028/NIST.TN.1887.

Extends from Buildings.Airflow.Multizone.Table_m_flow (Mass flow(y-axis) vs Pressure(x-axis) cubic spline fit model based from table data, with last two points linearly interpolated).

Parameters

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Modelica definition

Buildings.Airflow.Multizone.Table_m_flow

Mass flow(y-axis) vs Pressure(x-axis) cubic spline fit model based from table data, with last two points linearly interpolated

Information

This model describes the one-directional pressure driven air flow through an opening based on user-provided tabular data describing the relation between mass flow rate and pressure difference over the component.

ṁ = f(Δp),

where ṁ is the volume flow rate and Δp is the pressure difference.

Based on the table input, a cubic hermite spline is constructed between all points except for the two last pairs of points. These point are connected linearly.

The constructed curve is the direct relation between ṁ and Δp.

A similar model is also used in the CONTAM software (Dols and Walton, 2015).

References

• W. S. Dols and B. J. Polidoro,2015. CONTAM User Guide and Program Documentation Version 3.2, National Institute of Standards and Technology, NIST TN 1887, Sep. 2015. doi: 10.6028/NIST.TN.1887.

Extends from Buildings.Airflow.Multizone.BaseClasses.PartialOneWayFlowElement (Partial model for flow resistance with one-way flow).

Parameters

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Modelica definition

Buildings.Airflow.Multizone.ZonalFlow_ACS

Zonal flow with input air change per second

Information

This model computes the air exchange between volumes.

Input is the air change per seconds. The volume flow rate is computed as

  V_flow = ACS * V

where ACS is an input and the volume V is a parameter.

Extends from Buildings.Airflow.Multizone.BaseClasses.ZonalFlow (Flow across zonal boundaries of a room).

Parameters

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Modelica definition

Buildings.Airflow.Multizone.ZonalFlow_m_flow

Zonal flow with input air change per second

Information

This model computes the air exchange between volumes.

Input is the mass flow rate from port_a1 to port_b1 and from port_a2 to port_b2.

Extends from Buildings.Airflow.Multizone.BaseClasses.ZonalFlow (Flow across zonal boundaries of a room).

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Modelica definition