Buildings.Airflow.Multizone.BaseClasses

Information

This package contains base classes that are used to construct the models in Buildings.Airflow.Multizone.

Extends from Modelica.Icons.BasesPackage (Icon for packages containing base classes).

Package Content

Name	Description
DoorDiscretized	Door model using discretization along height coordinate
PowerLawResistance	Flow resistance that uses the power law
TwoWayFlowElement	Flow resistance that uses the power law
TwoWayFlowElementBuoyancy	Flow resistance that uses the power law
ZonalFlow	Flow across zonal boundaries of a room
ErrorControl	Interface that defines parameters for error control
powerLaw	Power law used in orifice equations
powerLawFixedM	Power law used in orifice equations when m is constant
windPressureLowRise	Wind pressure coefficient for low-rise buildings
Examples	Collection of models that illustrate model use and test models

Buildings.Airflow.Multizone.BaseClasses.DoorDiscretized

Information

This is a partial model for the bi-directional air flow through a 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 compartment area dA is a variable, which allows using the model for a door that can be open or closed.

Extends from Buildings.Airflow.Multizone.BaseClasses.TwoWayFlowElementBuoyancy (Flow resistance that uses the power law).

Parameters

Type	Name	Default	Description
Boolean	forceErrorControlOnFlow	true	Flag to force error control on m_flow. Set to true if interested in flow rate
replaceable package Medium		PartialMedium
Velocity	vZer	0.001	Minimum velocity to prevent zero flow. Recommended: 0.001 [m/s]
Integer	nCom	10	Number of compartments for the discretization
Pressure	dp_turbulent	0.01	Pressure difference where laminar and turbulent flow relation coincide. Recommended: 0.01 [Pa]
Initialization
MassFlowRate	m1_flow.start	0	Mass flow rate from port_a1 to port_b1 (m1_flow > 0 is design flow direction) [kg/s]
Pressure	dp1.start	0	Pressure difference between port_a1 and port_b1 [Pa]
MassFlowRate	m2_flow.start	0	Mass flow rate from port_a2 to port_b2 (m2_flow > 0 is design flow direction) [kg/s]
Pressure	dp2.start	0	Pressure difference between port_a2 and port_b2 [Pa]
Density	rho_a1_inflow.start	1.2	Density of air flowing in from port_a1 [kg/m3]
Density	rho_a2_inflow.start	1.2	Density of air flowing in from port_a2 [kg/m3]
Geometry
Length	wOpe	0.9	Width of opening [m]
Length	hOpe	2.1	Height of opening [m]
Length	hA	2.7/2	Height of reference pressure zone A [m]
Length	hB	2.7/2	Height of reference pressure zone B [m]
Orifice characteristics
Real	CD	0.65	Discharge coefficient
Advanced
Initialization
SpecificEnthalpy	h_outflow_a1_start	Medium1.h_default	Start value for enthalpy flowing out of port a1 [J/kg]
SpecificEnthalpy	h_outflow_b1_start	Medium1.h_default	Start value for enthalpy flowing out of port b1 [J/kg]
SpecificEnthalpy	h_outflow_a2_start	Medium2.h_default	Start value for enthalpy flowing out of port a2 [J/kg]
SpecificEnthalpy	h_outflow_b2_start	Medium2.h_default	Start value for enthalpy flowing out of port b2 [J/kg]
MassFlowRate	m1_flow_small	1E-4*abs(m1_flow_nominal)	Small mass flow rate for regularization of zero flow [kg/s]
MassFlowRate	m2_flow_small	1E-4*abs(m2_flow_nominal)	Small mass flow rate for regularization of zero flow [kg/s]
Boolean	homotopyInitialization	true	= true, use homotopy method
Diagnostics
Boolean	show_V_flow	false	= true, if volume flow rate at inflowing port is computed
Boolean	show_T	false	= true, if actual temperature at port is computed (may lead to events)

Connectors

Type	Name	Description
FluidPort_a	port_a1	Fluid connector a1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_b	port_b1	Fluid connector b1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_a	port_a2	Fluid connector a2 (positive design flow direction is from port_a2 to port_b2)
FluidPort_b	port_b2	Fluid connector b2 (positive design flow direction is from port_a2 to port_b2)

Modelica definition

partial model DoorDiscretized 
  "Door model using discretization along height coordinate"
  extends Buildings.Airflow.Multizone.BaseClasses.TwoWayFlowElementBuoyancy;

  parameter Integer nCom=10 "Number of compartments for the discretization";

  parameter Modelica.SIunits.Pressure dp_turbulent(min=0) = 0.01 
    "Pressure difference where laminar and turbulent flow relation coincide. Recommended: 0.01";
  parameter Real CD=0.65 "|Orifice characteristics|Discharge coefficient";

  Modelica.SIunits.Pressure dpAB[nCom](nominal=1) 
    "Pressure difference between compartments";
  Modelica.SIunits.Velocity v[nCom](nominal=0.01) 
    "Velocity in compartment from A to B";
  Modelica.SIunits.Velocity vTop "Velocity at top of opening from A to B";
  Modelica.SIunits.Velocity vBot "Velocity at bottom of opening from A to B";

protected 
  parameter Modelica.SIunits.Length dh=hOpe/nCom "Height of each compartment";
  Modelica.SIunits.AbsolutePressure pA[nCom](nominal=101325) 
    "Pressure in compartments of room A";
  Modelica.SIunits.AbsolutePressure pB[nCom](nominal=101325) 
    "Pressure in compartments of room B";

  Modelica.SIunits.VolumeFlowRate dV_flow[nCom] 
    "Volume flow rate through compartment from A to B";
  Modelica.SIunits.VolumeFlowRate dVAB_flow[nCom] 
    "Volume flow rate through compartment from A to B if positive";
  Modelica.SIunits.VolumeFlowRate dVBA_flow[nCom] 
    "Volume flow rate through compartment from B to A if positive";

  Real m(min=0.5, max=1) "Flow exponent, m=0.5 for turbulent, m=1 for laminar";
  Real kVal "Flow coefficient for each compartment, k = V_flow/ dp^m";
  Modelica.SIunits.Area dA "Compartment area";

  parameter Medium.ThermodynamicState sta_default=Medium.setState_pTX(
      T=Medium.T_default,
      p=Medium.p_default,
      X=Medium.X_default);
  parameter Modelica.SIunits.Density rho_default=Medium.density(sta_default) 
    "Density, used to compute fluid volume";

equation 
  dA = A/nCom;

  for i in 1:nCom loop
    // pressure drop in each compartment
    pA[i] = port_a1.p + rho_a1_inflow*Modelica.Constants.g_n*(hA - (i - 0.5)*dh);
    pB[i] = port_a2.p + rho_a2_inflow*Modelica.Constants.g_n*(hB - (i - 0.5)*dh);
    dpAB[i] = pA[i] - pB[i];
    v[i] = dV_flow[i]/dA;
    // assignment of net volume flows
    dVAB_flow[i] = dV_flow[i]*
      Buildings.Utilities.Math.Functions.smoothHeaviside(x=dV_flow[i], delta=
      VZer_flow/nCom) + VZer_flow/nCom;
    dVBA_flow[i] = -dV_flow[i] + dVAB_flow[i] + 2*VZer_flow/nCom;
  end for;
  // add positive and negative flows
  VAB_flow = ones(nCom)*dVAB_flow;
  VBA_flow = ones(nCom)*dVBA_flow;
  vTop = v[nCom];
  vBot = v[1];
end DoorDiscretized;

Buildings.Airflow.Multizone.BaseClasses.PowerLawResistance

Information

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

    V_flow = k * dp^m,

The model is used as a base for the interzonal air flow models.

Extends from Buildings.Fluid.Interfaces.PartialTwoPortInterface (Partial model transporting fluid between two ports without storing mass or energy), Buildings.Airflow.Multizone.BaseClasses.ErrorControl (Interface that defines parameters for error control).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Boolean	forceErrorControlOnFlow	true	Flag to force error control on m_flow. Set to true if interested in flow rate
Real	m		Flow exponent, m=0.5 for turbulent, m=1 for laminar
Boolean	useConstantDensity	true	Set to false to use density based on state (as implemented by the Medium model)
Pressure	dp_turbulent	0.1	Pressure difference where laminar and turbulent flow relation coincide. Recommended = 0.1 [Pa]
Length	lWet	sqrt(A)	Wetted perimeter used for Reynolds number calculation [m]
Nominal condition
MassFlowRate	m_flow_nominal	rho_default*k*dp_turbulent	Nominal mass flow rate [kg/s]
Initialization
MassFlowRate	m_flow.start	0	Mass flow rate from port_a to port_b (m_flow > 0 is design flow direction) [kg/s]
Pressure	dp.start	0	Pressure difference between port_a and port_b [Pa]
Orifice characteristics
Area	A		Area of orifice [m2]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Advanced
MassFlowRate	m_flow_small	1E-4*abs(m_flow_nominal)	Small mass flow rate for regularization of zero flow [kg/s]
Boolean	homotopyInitialization	true	= true, use homotopy method
Diagnostics
Boolean	show_V_flow	true	= true, if volume flow rate at inflowing port is computed
Boolean	show_T	true	= true, if actual temperature at port is computed (may lead to events)

Connectors

Type	Name	Description
FluidPort_a	port_a	Fluid connector a (positive design flow direction is from port_a to port_b)
FluidPort_b	port_b	Fluid connector b (positive design flow direction is from port_a to port_b)

Modelica definition

partial model PowerLawResistance 
  "Flow resistance that uses the power law"
  extends Buildings.Fluid.Interfaces.PartialTwoPortInterface(final 
      m_flow_nominal=rho_default*k*dp_turbulent, final show_V_flow=true,
      final show_T=true);
  extends Buildings.Airflow.Multizone.BaseClasses.ErrorControl;

  parameter Modelica.SIunits.Area A "|Orifice characteristics|Area of orifice";

  parameter Real m(min=0.5, max=1) 
    "Flow exponent, m=0.5 for turbulent, m=1 for laminar";
  parameter Boolean useConstantDensity=true 
    "Set to false to use density based on state (as implemented by the Medium model)";
  Modelica.SIunits.Density rho "Fluid density at port_a";
  parameter Modelica.SIunits.Pressure dp_turbulent(min=0, displayUnit="Pa") = 0.1 
    "Pressure difference where laminar and turbulent flow relation coincide. Recommended = 0.1";
  Modelica.SIunits.Velocity v(nominal=1) "Average velocity";
  parameter Modelica.SIunits.Length lWet=sqrt(A) 
    "Wetted perimeter used for Reynolds number calculation";
  Real Re "Reynolds number";

protected 
  parameter Real k "Flow coefficient, k = V_flow/ dp^m";

  parameter Medium.ThermodynamicState sta_default=Medium.setState_pTX(
      T=Medium.T_default,
      p=Medium.p_default,
      X=Medium.X_default);
  parameter Modelica.SIunits.Density rho_default=Medium.density(sta_default) 
    "Density, used to compute fluid volume";

  constant Real gamma(min=1) = 1.5 
    "Normalized flow rate where dphi(0)/dpi intersects phi(1)";
  parameter Real a = gamma 
    "Polynomial coefficient for regularized implementation of flow resistance";
  parameter Real b = 1/8*m^2 - 3*gamma - 3/2*m + 35.0/8 
    "Polynomial coefficient for regularized implementation of flow resistance";
  parameter Real c = -1/4*m^2 + 3*gamma + 5/2*m - 21.0/4 
    "Polynomial coefficient for regularized implementation of flow resistance";
  parameter Real d = 1/8*m^2 - gamma - m + 15.0/8 
    "Polynomial coefficient for regularized implementation of flow resistance";

  Modelica.SIunits.DynamicViscosity dynVis "Dynamic viscosity";

  Modelica.SIunits.Mass mExc 
    "Air mass exchanged (for purpose of error control only)";
initial equation 
  mExc=0;
equation 
  if forceErrorControlOnFlow then
    der(mExc) = port_a.m_flow;
  else
    der(mExc) = 0;
  end if;

  rho = if useConstantDensity then rho_default else Medium.density(sta_a);
  dynVis = Medium.dynamicViscosity(sta_a);
  port_a.m_flow = rho*Buildings.Airflow.Multizone.BaseClasses.powerLawFixedM(
    k=k,
    dp=dp,
    m=m,
    a=a,
    b=b,
    c=c,
    d=d,
    dp_turbulent=dp_turbulent);
  v = V_flow/A;
  Re = v*lWet*rho/dynVis;

  // Isenthalpic state transformation (no storage and no loss of energy)
  port_a.h_outflow = inStream(port_b.h_outflow);
  port_b.h_outflow = inStream(port_a.h_outflow);

  // Mass balance (no storage)
  port_a.m_flow + port_b.m_flow = 0;

  // Transport of substances
  port_a.Xi_outflow = inStream(port_b.Xi_outflow);
  port_b.Xi_outflow = inStream(port_a.Xi_outflow);

  port_a.C_outflow = inStream(port_b.C_outflow);
  port_b.C_outflow = inStream(port_a.C_outflow);
end PowerLawResistance;

Buildings.Airflow.Multizone.BaseClasses.TwoWayFlowElement

Information

This is a partial model for models that describe the bi-directional air flow through large openings.

Models that extend this model need to compute mAB_flow and mBA_flow, or alternatively VAB_flow and VBA_flow, and the face area area. The face area is a variable to allow this partial model to be used for doors that can be open or closed as a function of an input signal.

Extends from Buildings.Fluid.Interfaces.PartialFourPortInterface (Partial model transporting fluid between two ports without storing mass or energy), Buildings.Airflow.Multizone.BaseClasses.ErrorControl (Interface that defines parameters for error control).

Parameters

Type	Name	Default	Description
replaceable package Medium1		PartialMedium	Medium 1 in the component
replaceable package Medium2		PartialMedium	Medium 2 in the component
Boolean	forceErrorControlOnFlow	true	Flag to force error control on m_flow. Set to true if interested in flow rate
replaceable package Medium		Modelica.Media.Interfaces.Pa...
Velocity	vZer	0.001	Minimum velocity to prevent zero flow. Recommended: 0.001 [m/s]
Nominal condition
MassFlowRate	m1_flow_nominal	10/3600*1.2	Nominal mass flow rate [kg/s]
MassFlowRate	m2_flow_nominal	m1_flow_nominal	Nominal mass flow rate [kg/s]
Initialization
MassFlowRate	m1_flow.start	0	Mass flow rate from port_a1 to port_b1 (m1_flow > 0 is design flow direction) [kg/s]
Pressure	dp1.start	0	Pressure difference between port_a1 and port_b1 [Pa]
MassFlowRate	m2_flow.start	0	Mass flow rate from port_a2 to port_b2 (m2_flow > 0 is design flow direction) [kg/s]
Pressure	dp2.start	0	Pressure difference between port_a2 and port_b2 [Pa]
Assumptions
Boolean	allowFlowReversal1	false	= true to allow flow reversal in medium 1, false restricts to design direction (port_a -> port_b)
Boolean	allowFlowReversal2	false	= true to allow flow reversal in medium 2, false restricts to design direction (port_a -> port_b)
Advanced
Initialization
SpecificEnthalpy	h_outflow_a1_start	Medium1.h_default	Start value for enthalpy flowing out of port a1 [J/kg]
SpecificEnthalpy	h_outflow_b1_start	Medium1.h_default	Start value for enthalpy flowing out of port b1 [J/kg]
SpecificEnthalpy	h_outflow_a2_start	Medium2.h_default	Start value for enthalpy flowing out of port a2 [J/kg]
SpecificEnthalpy	h_outflow_b2_start	Medium2.h_default	Start value for enthalpy flowing out of port b2 [J/kg]
MassFlowRate	m1_flow_small	1E-4*abs(m1_flow_nominal)	Small mass flow rate for regularization of zero flow [kg/s]
MassFlowRate	m2_flow_small	1E-4*abs(m2_flow_nominal)	Small mass flow rate for regularization of zero flow [kg/s]
Boolean	homotopyInitialization	true	= true, use homotopy method
Diagnostics
Boolean	show_V_flow	false	= true, if volume flow rate at inflowing port is computed
Boolean	show_T	false	= true, if actual temperature at port is computed (may lead to events)

Connectors

Type	Name	Description
replaceable package Medium1		Medium 1 in the component
replaceable package Medium2		Medium 2 in the component
FluidPort_a	port_a1	Fluid connector a1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_b	port_b1	Fluid connector b1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_a	port_a2	Fluid connector a2 (positive design flow direction is from port_a2 to port_b2)
FluidPort_b	port_b2	Fluid connector b2 (positive design flow direction is from port_a2 to port_b2)
replaceable package Medium

Modelica definition

partial model TwoWayFlowElement 
  "Flow resistance that uses the power law"
  extends Buildings.Fluid.Interfaces.PartialFourPortInterface(
    redeclare final package Medium1 = Medium,
    redeclare final package Medium2 = Medium,
    final allowFlowReversal1=false,
    final allowFlowReversal2=false,
    final m1_flow_nominal=10/3600*1.2,
    final m2_flow_nominal=m1_flow_nominal);
  extends Buildings.Airflow.Multizone.BaseClasses.ErrorControl;

  replaceable package Medium = Modelica.Media.Interfaces.PartialMedium;

  Modelica.SIunits.VolumeFlowRate VAB_flow(nominal=0.001) 
    "Volume flow rate from A to B if positive";
  Modelica.SIunits.VolumeFlowRate VBA_flow(nominal=0.001) 
    "Volume flow rate from B to A if positive";
  Modelica.SIunits.MassFlowRate mAB_flow(nominal=0.001) 
    "Mass flow rate from A to B if positive";
  Modelica.SIunits.MassFlowRate mBA_flow(nominal=0.001) 
    "Mass flow rate from B to A if positive";

  Modelica.SIunits.Velocity vAB(nominal=0.01) "Average velocity from A to B";
  Modelica.SIunits.Velocity vBA(nominal=0.01) "Average velocity from B to A";

  Modelica.SIunits.Density rho_a1_inflow(start=1.2) 
    "Density of air flowing in from port_a1";
  Modelica.SIunits.Density rho_a2_inflow(start=1.2) 
    "Density of air flowing in from port_a2";

  Modelica.SIunits.Area A "Face area";

  parameter Modelica.SIunits.Velocity vZer=0.001 
    "Minimum velocity to prevent zero flow. Recommended: 0.001";
protected 
  Modelica.SIunits.VolumeFlowRate VZer_flow(fixed=false) 
    "Minimum net volume flow rate to prevent zero flow";
protected 
  Modelica.SIunits.Mass mExcAB(start=0) 
    "Air mass exchanged (for purpose of error control only)";
  Modelica.SIunits.Mass mExcBA(start=0) 
    "Air mass exchanged (for purpose of error control only)";

equation 
  // enforcing error control on both direction rather than on the sum only
  // gives higher robustness. The reason may be that for bi-directional flow,
  // (VAB_flow - VBA_flow) may be close to zero.
  if forceErrorControlOnFlow then
    der(mExcAB) = mAB_flow;
    der(mExcBA) = mBA_flow;
  else
    der(mExcAB) = 0;
    der(mExcBA) = 0;
  end if;
  rho_a1_inflow = Medium.density(state_a1_inflow);
  rho_a2_inflow = Medium.density(state_a2_inflow);
  VZer_flow = vZer*A;

  mAB_flow = rho_a1_inflow*VAB_flow;
  mBA_flow = rho_a2_inflow*VBA_flow;
  // Average velocity (using the whole orifice area)
  vAB = VAB_flow/A;
  vBA = VBA_flow/A;

  port_a1.m_flow = mAB_flow;
  port_a2.m_flow = mBA_flow;

  // Energy balance (no storage, no heat loss/gain)
  port_a1.h_outflow = inStream(port_b1.h_outflow);
  port_b1.h_outflow = inStream(port_a1.h_outflow);
  port_a2.h_outflow = inStream(port_b2.h_outflow);
  port_b2.h_outflow = inStream(port_a2.h_outflow);

  // Mass balance (no storage)
  port_a1.m_flow = -port_b1.m_flow;
  port_a2.m_flow = -port_b2.m_flow;

  port_a1.Xi_outflow = inStream(port_b1.Xi_outflow);
  port_b1.Xi_outflow = inStream(port_a1.Xi_outflow);
  port_a2.Xi_outflow = inStream(port_b2.Xi_outflow);
  port_b2.Xi_outflow = inStream(port_a2.Xi_outflow);

  // Transport of trace substances
  port_a1.C_outflow = inStream(port_b1.C_outflow);
  port_b1.C_outflow = inStream(port_a1.C_outflow);
  port_a2.C_outflow = inStream(port_b2.C_outflow);
  port_b2.C_outflow = inStream(port_a2.C_outflow);

end TwoWayFlowElement;

Buildings.Airflow.Multizone.BaseClasses.TwoWayFlowElementBuoyancy

Information

This is a partial model for models that describe the bi-directional air flow through large openings.

Models that extend this model need to compute mAB_flow and mBA_flow, or alternatively VAB_flow and VBA_flow, and the face area area. The face area is a variable to allow this partial model to be used for doors that can be open or closed as a function of an input signal.

Extends from Buildings.Airflow.Multizone.BaseClasses.TwoWayFlowElement (Flow resistance that uses the power law).

Parameters

Type	Name	Default	Description
Boolean	forceErrorControlOnFlow	true	Flag to force error control on m_flow. Set to true if interested in flow rate
replaceable package Medium		PartialMedium
Velocity	vZer	0.001	Minimum velocity to prevent zero flow. Recommended: 0.001 [m/s]
Initialization
MassFlowRate	m1_flow.start	0	Mass flow rate from port_a1 to port_b1 (m1_flow > 0 is design flow direction) [kg/s]
Pressure	dp1.start	0	Pressure difference between port_a1 and port_b1 [Pa]
MassFlowRate	m2_flow.start	0	Mass flow rate from port_a2 to port_b2 (m2_flow > 0 is design flow direction) [kg/s]
Pressure	dp2.start	0	Pressure difference between port_a2 and port_b2 [Pa]
Density	rho_a1_inflow.start	1.2	Density of air flowing in from port_a1 [kg/m3]
Density	rho_a2_inflow.start	1.2	Density of air flowing in from port_a2 [kg/m3]
Geometry
Length	wOpe	0.9	Width of opening [m]
Length	hOpe	2.1	Height of opening [m]
Length	hA	2.7/2	Height of reference pressure zone A [m]
Length	hB	2.7/2	Height of reference pressure zone B [m]
Advanced
Initialization
SpecificEnthalpy	h_outflow_a1_start	Medium1.h_default	Start value for enthalpy flowing out of port a1 [J/kg]
SpecificEnthalpy	h_outflow_b1_start	Medium1.h_default	Start value for enthalpy flowing out of port b1 [J/kg]
SpecificEnthalpy	h_outflow_a2_start	Medium2.h_default	Start value for enthalpy flowing out of port a2 [J/kg]
SpecificEnthalpy	h_outflow_b2_start	Medium2.h_default	Start value for enthalpy flowing out of port b2 [J/kg]
MassFlowRate	m1_flow_small	1E-4*abs(m1_flow_nominal)	Small mass flow rate for regularization of zero flow [kg/s]
MassFlowRate	m2_flow_small	1E-4*abs(m2_flow_nominal)	Small mass flow rate for regularization of zero flow [kg/s]
Boolean	homotopyInitialization	true	= true, use homotopy method
Diagnostics
Boolean	show_V_flow	false	= true, if volume flow rate at inflowing port is computed
Boolean	show_T	false	= true, if actual temperature at port is computed (may lead to events)

Connectors

Type	Name	Description
FluidPort_a	port_a1	Fluid connector a1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_b	port_b1	Fluid connector b1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_a	port_a2	Fluid connector a2 (positive design flow direction is from port_a2 to port_b2)
FluidPort_b	port_b2	Fluid connector b2 (positive design flow direction is from port_a2 to port_b2)

Modelica definition

partial model TwoWayFlowElementBuoyancy 
  "Flow resistance that uses the power law"
  extends Buildings.Airflow.Multizone.BaseClasses.TwoWayFlowElement;

  parameter Modelica.SIunits.Length wOpe=0.9 "|Geometry|Width of opening";
  parameter Modelica.SIunits.Length hOpe=2.1 "|Geometry|Height of opening";

  parameter Modelica.SIunits.Length hA=2.7/2 
    "|Geometry|Height of reference pressure zone A";
  parameter Modelica.SIunits.Length hB=2.7/2 
    "|Geometry|Height of reference pressure zone B";

end TwoWayFlowElementBuoyancy;

Buildings.Airflow.Multizone.BaseClasses.ZonalFlow

Information

This is a partial model for computing the air exchange between volumes. Models that extend this model need to provide an equation for port_a1.m_flow and port_a2.m_flow.

Extends from Buildings.Fluid.Interfaces.PartialFourPortInterface (Partial model transporting fluid between two ports without storing mass or energy), Buildings.Airflow.Multizone.BaseClasses.ErrorControl (Interface that defines parameters for error control).

Parameters

Type	Name	Default	Description
replaceable package Medium1		PartialMedium	Medium 1 in the component
replaceable package Medium2		PartialMedium	Medium 2 in the component
Boolean	forceErrorControlOnFlow	true	Flag to force error control on m_flow. Set to true if interested in flow rate
replaceable package Medium		Modelica.Media.Interfaces.Pa...
Nominal condition
MassFlowRate	m1_flow_nominal	10/3600*1.2	Nominal mass flow rate [kg/s]
MassFlowRate	m2_flow_nominal	m1_flow_nominal	Nominal mass flow rate [kg/s]
Initialization
MassFlowRate	m1_flow.start	0	Mass flow rate from port_a1 to port_b1 (m1_flow > 0 is design flow direction) [kg/s]
Pressure	dp1.start	0	Pressure difference between port_a1 and port_b1 [Pa]
MassFlowRate	m2_flow.start	0	Mass flow rate from port_a2 to port_b2 (m2_flow > 0 is design flow direction) [kg/s]
Pressure	dp2.start	0	Pressure difference between port_a2 and port_b2 [Pa]
Assumptions
Boolean	allowFlowReversal1	false	= true to allow flow reversal in medium 1, false restricts to design direction (port_a -> port_b)
Boolean	allowFlowReversal2	false	= true to allow flow reversal in medium 2, false restricts to design direction (port_a -> port_b)
Advanced
Initialization
SpecificEnthalpy	h_outflow_a1_start	Medium1.h_default	Start value for enthalpy flowing out of port a1 [J/kg]
SpecificEnthalpy	h_outflow_b1_start	Medium1.h_default	Start value for enthalpy flowing out of port b1 [J/kg]
SpecificEnthalpy	h_outflow_a2_start	Medium2.h_default	Start value for enthalpy flowing out of port a2 [J/kg]
SpecificEnthalpy	h_outflow_b2_start	Medium2.h_default	Start value for enthalpy flowing out of port b2 [J/kg]
MassFlowRate	m1_flow_small	1E-4*abs(m1_flow_nominal)	Small mass flow rate for regularization of zero flow [kg/s]
MassFlowRate	m2_flow_small	1E-4*abs(m2_flow_nominal)	Small mass flow rate for regularization of zero flow [kg/s]
Boolean	homotopyInitialization	true	= true, use homotopy method
Diagnostics
Boolean	show_V_flow	false	= true, if volume flow rate at inflowing port is computed
Boolean	show_T	false	= true, if actual temperature at port is computed (may lead to events)

Connectors

Type	Name	Description
replaceable package Medium1		Medium 1 in the component
replaceable package Medium2		Medium 2 in the component
FluidPort_a	port_a1	Fluid connector a1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_b	port_b1	Fluid connector b1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_a	port_a2	Fluid connector a2 (positive design flow direction is from port_a2 to port_b2)
FluidPort_b	port_b2	Fluid connector b2 (positive design flow direction is from port_a2 to port_b2)
replaceable package Medium

Modelica definition

partial model ZonalFlow "Flow across zonal boundaries of a room"
  extends Buildings.Fluid.Interfaces.PartialFourPortInterface(
     redeclare final package Medium1 = Medium,
     redeclare final package Medium2 = Medium,
     final allowFlowReversal1 = false,
     final allowFlowReversal2 = false,
     final m1_flow_nominal = 10/3600*1.2,
     final m2_flow_nominal = m1_flow_nominal);
  extends Buildings.Airflow.Multizone.BaseClasses.ErrorControl;

   replaceable package Medium = Modelica.Media.Interfaces.PartialMedium;

equation 
  // Energy balance (no storage, no heat loss/gain)
  port_a1.h_outflow = inStream(port_b1.h_outflow);
  port_b1.h_outflow = inStream(port_a1.h_outflow);
  port_a2.h_outflow = inStream(port_b2.h_outflow);
  port_b2.h_outflow = inStream(port_a2.h_outflow);

  // Mass balance (no storage)
  port_a1.m_flow = -port_b1.m_flow;
  port_a2.m_flow = -port_b2.m_flow;

  port_a1.Xi_outflow = inStream(port_b1.Xi_outflow);
  port_b1.Xi_outflow = inStream(port_a1.Xi_outflow);
  port_a2.Xi_outflow = inStream(port_b2.Xi_outflow);
  port_b2.Xi_outflow = inStream(port_a2.Xi_outflow);

  // Transport of trace substances
  port_a1.C_outflow = inStream(port_b1.C_outflow);
  port_b1.C_outflow = inStream(port_a1.C_outflow);
  port_a2.C_outflow = inStream(port_b2.C_outflow);
  port_b2.C_outflow = inStream(port_a2.C_outflow);

end ZonalFlow;

Buildings.Airflow.Multizone.BaseClasses.ErrorControl

Information

This is an interface that defines parameters used for error control.

Dymola does error control on state variables, such as temperature, pressure and species concentration. Flow variables such as m_flow are typically not checked during the error control. This can give large errors in flow variables, as long as the error on the volume's state variables that are coupled to the flow variables is small. Obtaining accurate flow variables can be achieved by imposing an error control on the exchanged mass, which can be defined as

  dm/dt = m_flow.

Parameters

Type	Name	Default	Description
Boolean	forceErrorControlOnFlow	true	Flag to force error control on m_flow. Set to true if interested in flow rate

Modelica definition

model ErrorControl 
  "Interface that defines parameters for error control"
  parameter Boolean forceErrorControlOnFlow = true 
    "Flag to force error control on m_flow. Set to true if interested in flow rate";
end ErrorControl;

Buildings.Airflow.Multizone.BaseClasses.powerLaw

Information

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

V = k sign(Δp) |Δp|^m

The model is used for the interzonal air flow models.

Implementation

For |Δp| < Δp_t, the equation is regularized so that it is twice continuously differentiable in Δp, and that it has an infinite number of continuous derivatives in m and in k.

If m is not a function of time, then a, b, c and d can be pre-computed. In this situation, use Buildings.Airflow.Multizone.BaseClasses.powerLawFixedM, which allows to compute these values outside of this function, for example as parameters of a model.

Inputs

Type	Name	Default	Description
Real	k		Flow coefficient, k = V_flow/ dp^m
Pressure	dp		Pressure difference [Pa]
Real	m		Flow exponent, m=0.5 for turbulent, m=1 for laminar
Pressure	dp_turbulent	0.001	Pressure difference where regularization starts [Pa]

Outputs

Type	Name	Description
VolumeFlowRate	V_flow	Volume flow rate [m3/s]

Modelica definition

function powerLaw "Power law used in orifice equations"
  input Real k "Flow coefficient, k = V_flow/ dp^m";
  input Modelica.SIunits.Pressure dp "Pressure difference";
  input Real m(min=0.5, max=1) 
    "Flow exponent, m=0.5 for turbulent, m=1 for laminar";
  input Modelica.SIunits.Pressure dp_turbulent(min=0)=0.001 
    "Pressure difference where regularization starts";
  output Modelica.SIunits.VolumeFlowRate V_flow "Volume flow rate";
protected 
  constant Real gamma(min=1) = 1.5 
    "Normalized flow rate where dphi(0)/dpi intersects phi(1)";
  Real a 
    "Polynomial coefficient for regularized implementation of flow resistance";
  Real b 
    "Polynomial coefficient for regularized implementation of flow resistance";
  Real c 
    "Polynomial coefficient for regularized implementation of flow resistance";
  Real d 
    "Polynomial coefficient for regularized implementation of flow resistance";
  Real pi "Normalized pressure";
  Real pi2 "Square of normalized pressure";
algorithm 
 if (dp >= dp_turbulent) then
   V_flow := k*dp^m;
 elseif (dp <= -dp_turbulent) then
   V_flow :=-k*(-dp)^m;
 else
   a := gamma;
   b := 1/8*m^2 - 3*gamma - 3/2*m + 35.0/8;
   c := -1/4*m^2 + 3*gamma + 5/2*m - 21.0/4;
   d := 1/8*m^2 - gamma - m + 15.0/8;
   pi  := dp/dp_turbulent;
   pi2 := pi*pi;
   V_flow := k*dp_turbulent^m * pi * ( a + pi2 * ( b + pi2 * ( c + pi2 * d)));
 end if;

end powerLaw;

Buildings.Airflow.Multizone.BaseClasses.powerLawFixedM

Information

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

V = k sign(Δp) |Δp|^m

The model is used for the interzonal air flow models. It is identical to Buildings.Airflow.Multizone.BaseClasses.powerLaw but it requires the polynomial coefficients as an input. This allows a more efficient simulation if m and therefore also a, b, c and d are constant.

Implementation

For |Δp| < Δp_t, the equation is regularized so that it is twice continuously differentiable in Δp, and that it has an infinite number of continuous derivatives in m and in k.

If m, and therefore also a, b, c and d, change with time, then it is more convenient and efficient to use Buildings.Airflow.Multizone.BaseClasses.powerLaw.

Inputs

Type	Name	Default	Description
Real	k		Flow coefficient, k = V_flow/ dp^m
Pressure	dp		Pressure difference [Pa]
Real	m		Flow exponent, m=0.5 for turbulent, m=1 for laminar
Real	a		Polynomial coefficient
Real	b		Polynomial coefficient
Real	c		Polynomial coefficient
Real	d		Polynomial coefficient
Pressure	dp_turbulent	0.001	Pressure difference where regularization starts [Pa]

Outputs

Type	Name	Description
VolumeFlowRate	V_flow	Volume flow rate [m3/s]

Modelica definition

function powerLawFixedM 
  "Power law used in orifice equations when m is constant"
  input Real k "Flow coefficient, k = V_flow/ dp^m";
  input Modelica.SIunits.Pressure dp "Pressure difference";
  input Real m(min=0.5, max=1) 
    "Flow exponent, m=0.5 for turbulent, m=1 for laminar";
  input Real a "Polynomial coefficient";
  input Real b "Polynomial coefficient";
  input Real c "Polynomial coefficient";
  input Real d "Polynomial coefficient";
  input Modelica.SIunits.Pressure dp_turbulent(min=0)=0.001 
    "Pressure difference where regularization starts";
  output Modelica.SIunits.VolumeFlowRate V_flow "Volume flow rate";
protected 
  constant Real gamma(min=1) = 1.5 
    "Normalized flow rate where dphi(0)/dpi intersects phi(1)";
  Real pi "Normalized pressure";
  Real pi2 "Square of normalized pressure";
algorithm 
 if (dp >= dp_turbulent) then
   V_flow := k*dp^m;
 elseif (dp <= -dp_turbulent) then
   V_flow :=-k*(-dp)^m;
 else
   pi  := dp/dp_turbulent;
   pi2 := pi*pi;
   V_flow := k*dp_turbulent^m * pi * ( a + pi2 * ( b + pi2 * ( c + pi2 * d)));
 end if;

end powerLawFixedM;

Buildings.Airflow.Multizone.BaseClasses.windPressureLowRise

Information

This function computes the wind pressure coefficient for low-rise buildings with rectangular shape. The correlation is the data fit from Swami and Chandra (1987), who fitted a function to various wind pressure coefficients from the literature. The same correlation is also implemented in CONTAM (Persily and Ivy, 2001).

The wind pressure coefficient is computed based on the natural logarithm of the side ratio of the walls, which is defined as

G = ln(x ⁄ y)

where x is the length of the wall that will be connected to this model, and y is the length of the adjacent wall as shown in the figure below.

Based on the wind incidence angle α and the side ratio of the walls, the model computes how much the wind pressure is attenuated compared to the reference wind pressure Cp0. The reference wind pressure Cp0 is a user-defined parameter, and must be equal to the wind pressure at zero wind incidence angle, i.e., α = 0. Swami and Chandra (1987) recommend C_p0 = 0.6 for all low-rise buildings as this represents the average of various values reported in the literature. The attenuation factor is

C_p ⁄ C_p0 = ln(1.248 - 0.703 sin(α ⁄ 2) - 1.175 sin²(α) - 0.131 sin³(2 α G) + 0.769 cos(α ⁄ 2) +0.071 G² * sin²(α ⁄ 2) + 0.717 cos²(α ⁄ 2)),

This function is used in Buildings.Fluid.Sources.Outside_CpLowRise which can be used directly with components of this package.

References

• Muthusamy V. Swami and Subrato Chandra. Procedures for Calculating Natural Ventilation Airflow Rates in Buildings. Florida Solar Energy Center, FSEC-CR-163-86. March, 1987. Cape Canaveral, Florida.
• Andrew K. Persily and Elizabeth M. Ivy. Input Data for Multizone Airflow and IAQ Analysis. NIST, NISTIR 6585. January, 2001. Gaithersburg, MD.

Implementation

Symmetry requires that the first derivative of the wind pressure coefficient with respect to the incidence angle is zero for incidence angles of zero and π. However, the correlation of Swami and Chandra has non-zero derivatives at these values. In this implementation, the original function is therefore slightly modified for incidence angles between 0 and 5 degree, and between 175 and 180 degree. This leads to a model that is differentiable in the incidence angle, which generally leads to better numeric performance.

Inputs

Type	Name	Default	Description
Real	Cp0		Wind pressure coefficient for normal wind incidence angle
Angle	incAng		Wind incidence angle (0: normal to wall) [rad]
Real	G		Natural logarithm of side ratio

Outputs

Type	Name	Description
Real	Cp	Wind pressure coefficient

Modelica definition

function windPressureLowRise 
  "Wind pressure coefficient for low-rise buildings"
  input Real Cp0(min=0) 
    "Wind pressure coefficient for normal wind incidence angle";
  input Modelica.SIunits.Angle incAng 
    "Wind incidence angle (0: normal to wall)";
  input Real G "Natural logarithm of side ratio";
  output Real Cp "Wind pressure coefficient";
protected 
  Modelica.SIunits.Angle aR "alpha, restricted to 0...pi";
  Modelica.SIunits.Angle incAng2 "0.5*wind incidence angle";
  Real sinA2 "=sin(alpha/2)";
  Real cosA2 "=cos(alpha/2)";
  Real a "Attenuation factor";
  constant Modelica.SIunits.Angle pi2 = 2*Modelica.Constants.pi;
  constant Modelica.SIunits.Angle aRDel = 5*Modelica.Constants.pi/180 
    "Lower bound where transition occurs";
  constant Modelica.SIunits.Angle aRDel2 = aRDel/2 
    "Half-width of transition interval";
  constant Modelica.SIunits.Angle aRMax = 175*Modelica.Constants.pi/180 
    "Upper bound where transition occurs";
  constant Real a180 = Modelica.Math.log(1.248 - 0.703 +
      0.131*Modelica.Math.sin(2*Modelica.Constants.pi*G)^3
      + 0.071*G^2) "Attenuation factor at 180 degree incidence angle";
algorithm 
  // Restrict incAng to [0...pi]

  // Change sign to positive
  aR := if incAng < 0 then -incAng else incAng;
  // Constrain to [0...2*pi]
  if aR > pi2 then
    aR := aR - integer(aR/pi2)*pi2;
  end if;
  // Constrain to [0...pi]
  if aR > Modelica.Constants.pi then
    aR := pi2-aR;
  end if;

  // Evaluate eqn. 2-1 from FSEC-CR-163-86
  incAng2 :=aR/2;
  sinA2 :=Modelica.Math.sin(incAng2);
  cosA2 :=Modelica.Math.cos(incAng2);
  // Implementation of the wind pressure coefficient that is once
  // continuously differentiable for all incidence angles
  if aR < aRDel then
    Cp :=Cp0*Buildings.Utilities.Math.Functions.spliceFunction(
        pos=  Modelica.Math.log(1.248 - 0.703*sinA2 - 1.175*Modelica.Math.sin(aR)^2 +
        0.131*Modelica.Math.sin(2*aR*G)^3 + 0.769*cosA2 + 0.071*G^2*sinA2^2 + 0.717*cosA2^2),
        neg=1,
        x=aR-aRDel2,
        deltax=aRDel2);
  elseif aR > aRMax then
    Cp := Cp0*Buildings.Utilities.Math.Functions.spliceFunction(
        pos=  a180,
        neg=Modelica.Math.log(1.248 - 0.703*sinA2 - 1.175*Modelica.Math.sin(aR)^2 +
        0.131*Modelica.Math.sin(2*aR*G)^3 + 0.769*cosA2 + 0.071*G^2*sinA2^2 + 0.717*cosA2^2),
        x=aR+aRDel2-Modelica.Constants.pi,
        deltax=aRDel2);
  else
    Cp :=Cp0*Modelica.Math.log(1.248 - 0.703*sinA2 - 1.175*Modelica.Math.sin(aR)^2 +
      0.131*Modelica.Math.sin(2*aR*G)^3 + 0.769*cosA2 + 0.071*G^2*sinA2^2 + 0.717*cosA2^2);
  end if;
end windPressureLowRise;