.Buildings.ThermalZones.Detailed.UsersGuide.MixedAir

Information

The model Buildings.ThermalZones.Detailed.MixedAir is a model of a room with completely mixed air. The room can have any number of constructions and surfaces that participate in the heat exchange through convection, conduction, infrared radiation and solar radiation.

Physical description

A description of the model assumptions and the implemention and validation of this room model can be found in Wetter et al. (2011). Note that this paper describes a previous version of the room model. The equations have not changed. However, what is shown in Figure 2 in the paper has in this version of the model been integrated directly into what is shown in Figure 1.

The room models the following physical processes:

1. Transient or steady-state heat conduction through opaque surfaces, using the model Buildings.HeatTransfer.Conduction.MultiLayer
2. Heat transfer through glazing system, taking into account solar radiation, infrared radiation, heat conduction and heat convection. The solar radiation is modeled using Buildings.HeatTransfer.Windows.BaseClasses.WindowRadiation. The overall heat transfer is modeled using the model Buildings.HeatTransfer.Windows.Window for the glass assembly, and the models Buildings.HeatTransfer.Windows.ExteriorHeatTransfer, Buildings.HeatTransfer.Windows.InteriorHeatTransferConvective and Buildings.HeatTransfer.Windows.BaseClasses.ShadeRadiation for the exterior and interior heat transfer. A window can have both, an overhang and a side fin. Overhangs and side fins are modeled using Buildings.HeatTransfer.Windows.Overhang and Buildings.HeatTransfer.Windows.SideFins, respectively. These models compute the reduction in direct solar irradiation due to the external shading device.
3. Convective heat transfer between the outside air and outside-facing surfaces using either a wind-speed, wind-direction and temperature-dependent heat transfer coefficient, or using a constant heat transfer coefficient, as described in Buildings.HeatTransfer.Convection.Exterior.
4. Solar and infrared heat transfer between the room enclosing surfaces, convective heat transfer between the room enclosing surfaces and the room air, and temperature, pressure and species balance inside the room volume. These effects are modeled as follows:
   1. The model Buildings.ThermalZones.Detailed.BaseClasses.MixedAirHeatMassBalance is used to compute heat convection between the room air and the surface of opaque constructions. It is also used to compute the heat and mass balance of the room air. This model is a composite model that contains Buildings.HeatTransfer.Windows.InteriorHeatTransferConvective to compute the convective heat balance of the window and a shade, if present. The convective heat transfer coefficient can be selected to be either temperature-dependent or constant. The convective heat transfer is computed using Buildings.HeatTransfer.Convection.Interior. The heat and mass balance of the room air is computed using Buildings.Fluid.MixingVolumes.MixingVolume, which assumes the room air to be completely mixed. Depending on the medium model, moisture and species concentrations, such as CO₂, can be modeled transiently.
   2. The latent heat gain of the room, which is a user-input, is converted to a moisture source using the model Buildings.ThermalZones.Detailed.BaseClasses.HeatGain.
   3. The radiant heat gains in the infrared spectrum are also a user input. They are distributed to the room enclosing surfaces using the model Buildings.ThermalZones.Detailed.BaseClasses.InfraredRadiationGainDistribution.
   4. The infrared radiative heat exchange between the room enclosing surfaces is modeled in Buildings.ThermalZones.Detailed.BaseClasses.InfraredRadiationExchange. This model takes into account the absorptivity of the surfaces and the surface area. However, the view factors are assumed to be proportional to the area of the receiving surface, without taking into account the location of the surfaces.
   5. The solar radiation exchange is modeled in Buildings.ThermalZones.Detailed.BaseClasses.SolarRadiationExchange. The assumptions in this model is that all solar radiation first hits the floor, and is then partially absorbed and partially reflected by the floor. The reflectance are diffuse, and the reflected radiation is distributed in proportion to the product of the receiving areas times their solar absorptivity.

Model instantiation

The next paragraphs describe how to instantiate a room model. To instantiate a room model,

1. make an instance of the room model in your model,
2. make instances of constructions from the package Buildings.HeatTransfer.Data.OpaqueConstructions to model opaque constructions such as walls, floors, ceilings and roofs,
3. make an instance of constructions from the package Buildings.HeatTransfer.Data.GlazingSystems to model glazing systems, and
4. enter the parameters of the room.

Entering parameters may be easiest in a textual editor.

In the here presented example, we assume we made several instances of data records for the construction material by dragging them from the package Buildings.HeatTransfer.Data to create the following list of declarations:

  Buildings.HeatTransfer.Data.OpaqueConstructions.Insulation100Concrete200
    matLayExt "Construction material for exterior walls"
    annotation (Placement(transformation(extent={{-60,140},{-40,160}})));
  Buildings.HeatTransfer.Data.OpaqueConstructions.Brick120 matLayPar 
    "Construction material for partition walls"
    annotation (Placement(transformation(extent={{-20,140},{0,160}})));
  Buildings.HeatTransfer.Data.OpaqueConstructions.Generic matLayRoo(
        material={
          HeatTransfer.Data.Solids.InsulationBoard(x=0.2),
          HeatTransfer.Data.Solids.Concrete(x=0.2)},
        final nLay=2) "Construction material for roof"
    annotation (Placement(transformation(extent={{20,140},{40,160}})));
  Buildings.HeatTransfer.Data.OpaqueConstructions.Generic matLayFlo(
        material={
          HeatTransfer.Data.Solids.Concrete(x=0.2),
          HeatTransfer.Data.Solids.InsulationBoard(x=0.1),
          HeatTransfer.Data.Solids.Concrete(x=0.05)},
        final nLay=3) "Construction material for floor"
    annotation (Placement(transformation(extent={{60,140},{80,160}})));
  Buildings.HeatTransfer.Data.GlazingSystems.DoubleClearAir13Clear glaSys(
    UFra=2,
    shade=Buildings.HeatTransfer.Data.Shades.Gray(),
    haveExteriorShade=false,
    haveInteriorShade=true) "Data record for the glazing system"
annotation (Placement(transformation(extent={{100,140},{120,160}})));

Note that construction layers are assembled from the outside to the room-side. Thus, the construction matLayRoo has an exterior insulation. This constructions can then be used in the room model.

Before we explain how to declare and parametrize a room model, we explain the different models that can be used to compute heat transfer through the room enclosing surfaces and constructions. The room model Buildings.ThermalZones.Detailed.MixedAir contains the constructions shown in the table below. The first row of the table lists the name of the data record that is used by the user to assign the model parameters. The second row lists the name of the instance of the model that simulates the equations. The third column provides a reference to the class definition that implements the equations. The forth column describes the main applicability of the model.

With these constructions, we may define a room as follows:

  Buildings.ThermalZones.Detailed.MixedAir roo(
    redeclare package Medium = MediumA,
    AFlo=6*4,
    hRoo=2.7,
    nConExt=2,
    datConExt(layers={matLayRoo, matLayExt},
           A={6*4, 6*3},
           til={Buildings.Types.Tilt.Ceiling, Buildings.Types.Tilt.Wall},
           azi={Buildings.Types.Azimuth.S, Buildings.Types.Azimuth.W}),
    nConExtWin=nConExtWin,
    datConExtWin(layers={matLayExt}, A={4*3},
              glaSys={glaSys},
              hWin={2},
              wWin={2},
              fFra={0.1},
              til={Buildings.Types.Tilt.Wall},
              azi={Buildings.Types.Azimuth.S}),
    nConPar=1,
    datConPar(layers={matLayPar}, each A=10,
           each til=Buildings.Types.Tilt.Wall),
    nConBou=1,
    datConBou(layers={matLayFlo}, each A=6*4,
           each til=Buildings.Types.Tilt.Floor),
    nSurBou=1,
    surBou(each A=6*3, each absIR=0.9, each absSol=0.9, each til=Buildings.Types.Tilt.Wall),
    linearizeRadiation = true ,
    energyDynamics=Modelica.Fluid.Types.Dynamics.FixedInitial) "Room model"
    annotation (Placement(transformation(extent={{46,20},{86,60}})));

The following paragraphs explain the different declarations.

The statement

    redeclare package Medium = MediumA,
    AFlo=20,
    V=20*2.5,

declares that the medium of the room air is set to MediumA, that the floor area is 20 m² and that the room air volume is 20*2.5 m³. The floor area is used to scale the internal heat gains, which are declared with units of W/m² using the input signal qGai_flow.

The next entries specify constructions and surfaces that participate in the heat exchange.

The entry

    nConExt=2,

declares that there are two exterior constructions.

The lines

    datConExt(layers={matLayRoo, matLayExt},
           A={6*4, 6*3},
           til={Buildings.Types.Tilt.Ceiling, Buildings.Types.Tilt.Wall},
           azi={Buildings.Types.Azimuth.S, Buildings.Types.Azimuth.W}),

declare that the material layers in these constructions are set the records matLayRoo and matLayExt. What follows are the declarations for the surface area, the tilt of the surface and the azimuth of the surfaces. Thus, the surface with construction matLayExt is 6*3 m² large and it is a west-facing wall.

Next, the declaration

    nConExtWin=nConExtWin,
    datConExtWin(layers={matLayExt}, A={4*3},
              glaSys={glaSys},
              hWin={2},
              wWin={2},
              fFra={0.1},
              til={Buildings.Types.Tilt.Wall},
              azi={Buildings.Types.Azimuth.S}),

declares the construction that contains a window. This construction is built using the materials defined in the record matLayExt. Its total area, including the window, is 4*3 m². The glazing system is built using the construction defined in the record glaSys. The window area is h_win=2 m high and w_win=2 m wide. The ratio of frame to total glazing system area is 10%.

Optionally, each window can have an overhang, side fins or both. If the above window were to have an overhang of 2.5 m width that is centered above the window, and hence extends each side of the window by 0.25 m, and has a depth of 1 m and a gap between window and overhang of 0.1 m, then its declaration would be

              ove(wL={0.25}, wR={0.25}, gap={0.1}, dep={1}),

This line can be placed below the declaration of wWin. This would instanciate the model Buildings.HeatTransfer.Windows.Overhang to model the overhang. See this class for a picture of the above dimensions.

If the window were to have side fins that are 2.5 m high, measured from the bottom of the windows, and hence extends 0.5 m above the window, are 1 m depth and are placed 0.1 m to the left and right of the window, then its declaration would be

              sidFin(h={0.5}, gap={0.1}, dep={1}),

This would instanciate the model Buildings.HeatTransfer.Windows.SideFins to model the side fins. See this class for a picture of the above dimensions.

The lines

              til={Buildings.Types.Tilt.Wall},
              azi={Buildings.Types.Azimuth.S}),

declare that the construction is a wall that is south exposed.

Note that if the room were to have two windows, and one window has side fins and the other window has an overhang, the following declaration could be used, which sets the value of dep to 0 for the non-present side fins or overhang, respectively:

              sidFin(h  = {0.5, 0}, gap = {0.1, 0.0}, dep = {1, 0}),
              ove(wL = {0.0, 0.25}, wR = {0.0, 0.25}, gap = {0.0, 0.1}, dep = {0, 1}),

What follows is the declaration of the partition constructions, as declared by

    nConPar=1,
    datConPar(layers={matLayPar}, each A=10,
           each til=Buildings.Types.Tilt.Wall),

Thus, there is one partition construction. Its area is 10 m² for each surface, to form a total surface area inside this thermal zone of 20 m².

Next, the declaration

    nConBou=1,
    datConBou(layers={matLayFlo}, each A=6*4,
           each til=Buildings.Types.Tilt.Floor),

declares one construction whose other surface boundary condition is exposed by this room model (through the heat port surf_conBou).

Note that by default, there is a temperature state at the surface of this wall. Therefore, connecting to the heat port surf_conBou a prescribed temperature boundary condition such as Modelica.Thermal.HeatTransfer.Sources.PrescribedTemperature would lead to an error and the model won't translate. The reason is that both, the state defines the temperature at the surface, and Modelica.Thermal.HeatTransfer.Sources.PrescribedTemperature prescribes the value of this temperature, leading to an overspecification. To avoid this, add between surf_conBou and the prescribed boundary condition a thermal conductance such as Modelica.Thermal.HeatTransfer.Components.ThermalConductor or a thermal convection model such as Buildings.HeatTransfer.Convection.Exterior. Alternatively, you could remove the state from the surface by declaring

    nConBou=1,
    datConBou(layers={matLayFlo}, each A=6*4,
           each til=Buildings.Types.Tilt.Floor,
           each stateAtSurface_a = false),

The declaration

    nSurBou=1,
    surBou(each A=6*3, each absIR=0.9, each absSol=0.9, each til=Buildings.Types.Tilt.Wall),

is used to instantiate a model for a surface that is in this room. The surface has an area of 6*3 m², absorptivity in the infrared and the solar spectrum of 0.9 and it is a wall. The room model will compute infrared radiative heat exchange, solar radiative heat gains and infrared radiative heat gains of this surface. The surface temperature and heat flow rate are exposed by this room model at the heat port surf_surBou. A model builder may use this construct to couple this room model to another room model that may model the construction.

The declaration

    linearizeRadiation = true,

causes the equations for radiative heat transfer to be linearized. This can reduce computing time at the expense of accuracy.

The declaration

    energyDynamics=Modelica.Fluid.Types.Dynamics.FixedInitial)

is used to initialize the air volume inside the thermal zone.

Modeling of contaminants

The model has a parameter use_C_flow. If set to true, then an input connector C_flow is enabled, which allows adding trace substances to the room air. Note that this requires a medium model that has trace substances enabled. See the example Buildings.ThermalZones.Detailed.Examples.MixedAirCO2.

Notes

To connect two rooms, the model Buildings.HeatTransfer.Conduction.MultiLayer can be connected to the ports surf_surBou of the two rooms. However, make sure to set stateAtSurface_a = true and stateAtSurface_b = true in the instance of the heat conduction model, as this allows to avoid a nonlinear system of equation to compute the radiative heat transfer, thereby leading to faster simulation. See Buildings.ThermalZones.Detailed.Validation.BESTEST.Cases9xx.Case960 for an example.

By setting linearizeRadiation = false, nonlinear equations will be used to compute the infrared radiation exchange among surfaces. This can lead to slower computation.

References

Michael Wetter, Wangda Zuo and Thierry Stephane Nouidui.
Modeling of Heat Transfer in Rooms in the Modelica "Buildings" Library.
Proc. of the 12th IBPSA Conference, p. 1096-1103. Sydney, Australia, November 2011.