Buildings.Fluid.FixedResistances

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Buildings.Fluid.FixedResistances

Package with models for fixed flow resistances (pipes, diffusers etc.)

Information

This package contains components models for fixed flow resistances. By fixed flow resistance, we mean resistances that do not change the flow coefficient

k = m ⁄ √ΔP.

For models of valves and air dampers, see Buildings.Fluid.Actuators. For models of flow resistances as part of the building constructions, see Buildings.Airflow.Multizone.

The model Buildings.Fluid.FixedResistances.FixedResistanceDpM is a fixed flow resistance that takes as parameter a nominal flow rate and a nominal pressure drop. The actual resistance is scaled using the above equation.

The model Buildings.Fluid.FixedResistances.LosslessPipe is an ideal pipe segment with no pressure drop. It is primarily used in models in which the above pressure drop model need to be replaced by a model with no pressure drop.

The model Buildings.Fluid.FixedResistances.SplitterFixedResistanceDpM can be used to model flow splitters or flow merges.

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

Package Content

Name	Description
FixedResistanceDpM	Fixed flow resistance with dp and m_flow as parameter
LosslessPipe	Pipe with no flow friction and no heat transfer
Pipe	Pipe with finite volume discretization along flow path
SplitterFixedResistanceDpM	Flow splitter with fixed resistance at each port
Examples	Collection of models that illustrate model use and test models
BaseClasses

Buildings.Fluid.FixedResistances.FixedResistanceDpM

Fixed flow resistance with dp and m_flow as parameter

Information

This is a model of a resistance with a fixed flow coefficient. The mass flow rate is computed as

ṁ = k √ΔP,

where k is a constant and ΔP is the pressure drop. The constant k is equal to k=m_flow_nominal/dp_nominal, where m_flow_nominal and dp_nominal are parameters. In the region abs(m_flow) < m_flow_turbulent, the square root is replaced by a differentiable function with finite slope. The value of m_flow_turbulent is computed as follows:

If the parameter use_dh is false (the default setting), the equation m_flow_turbulent = deltaM * abs(m_flow_nominal), where deltaM=0.3 and m_flow_nominal are parameters that can be set by the user.
Otherwise, the equation m_flow_turbulent = eta_nominal*dh/4*π*ReC is used, where eta_nominal is the dynamic viscosity, obtained from the medium model. The parameter dh is the hydraulic diameter and ReC=4000 is the critical Reynolds number, which both can be set by the user.

The figure below shows the pressure drop for the parameters m_flow_nominal=5 kg/s, dp_nominal=10 Pa and deltaM=0.3.

If the parameter show_T is set to true, then the model will compute the temperature at its ports. Note that this can lead to state events when the mass flow rate approaches zero, which can increase computing time.

The parameter from_dp is used to determine whether the mass flow rate is computed as a function of the pressure drop (if from_dp=true), or vice versa. This setting can affect the size of the nonlinear system of equations.

If the parameter linearized is set to true, then the pressure drop is computed as a linear function of the mass flow rate.

Setting allowFlowReversal=false can lead to simpler equations. However, this should only be set to false if one can guarantee that the flow never reverses its direction. This can be difficult to guarantee, as pressure imbalance after the initialization, or due to medium expansion and contraction, can lead to reverse flow.

Notes

For more detailed models that compute the actual flow friction, models from the package Modelica.Fluid can be used and combined with models from the Buildings library.

Implementation

The pressure drop is computed by calling a function in the package Buildings.Fluid.BaseClasses.FlowModels, This package contains regularized implementations of the equation

m = sign(Δp) k √ Δp

and its inverse function.

To decouple the energy equation from the mass equations, the pressure drop is a function of the mass flow rate, and not the volume flow rate. This leads to simpler equations.

Extends from Buildings.Fluid.BaseClasses.PartialResistance (Partial model for a hydraulic resistance).

Parameters

Type Name Default Description

replaceable package Medium PartialMedium Medium in the component

MassFlowRate m_flow_turbulent if (computeFlowResistance an... Turbulent flow if |m_flow| >= m_flow_turbulent [kg/s]

Boolean use_dh false Set to true to specify hydraulic diameter

Length dh 1 Hydraulic diameter [m]

Real ReC 4000 Reynolds number where transition to turbulent starts

Real deltaM 0.3 Fraction of nominal mass flow rate where transition to turbulent occurs

Nominal condition

MassFlowRate m_flow_nominal Nominal mass flow rate [kg/s]

Pressure dp_nominal Pressure drop at nominal mass flow rate [Pa]

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]

Assumptions

Boolean allowFlowReversal system.allowFlowReversal = true to allow flow reversal, false restricts to design direction (port_a -> port_b)

Advanced

Boolean homotopyInitialization true = true, use homotopy method

Boolean from_dp false = true, use m_flow = f(dp) else dp = f(m_flow)

Boolean linearized false = true, use linear relation between m_flow and dp for any flow rate

Diagnostics

Boolean show_T false = true, if actual temperature at port is computed

Type	Name	Default	Description
replaceable package Medium	PartialMedium	Medium in the component
MassFlowRate	m_flow_turbulent	if (computeFlowResistance an...	Turbulent flow if \|m_flow\| >= m_flow_turbulent [kg/s]
Boolean	use_dh	false	Set to true to specify hydraulic diameter
Length	dh	1	Hydraulic diameter [m]
Real	ReC	4000	Reynolds number where transition to turbulent starts
Real	deltaM	0.3	Fraction of nominal mass flow rate where transition to turbulent occurs
Nominal condition
MassFlowRate	m_flow_nominal		Nominal mass flow rate [kg/s]
Pressure	dp_nominal		Pressure drop at nominal mass flow rate [Pa]
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]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Advanced
Boolean	homotopyInitialization	true	= true, use homotopy method
Boolean	from_dp	false	= true, use m_flow = f(dp) else dp = f(m_flow)
Boolean	linearized	false	= true, use linear relation between m_flow and dp for any flow rate
Diagnostics
Boolean	show_T	false	= true, if actual temperature at port is computed

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

model FixedResistanceDpM 
  "Fixed flow resistance with dp and m_flow as parameter"
  extends Buildings.Fluid.BaseClasses.PartialResistance(
    final m_flow_turbulent = if (computeFlowResistance and use_dh) then 
                       eta_default*dh/4*Modelica.Constants.pi*ReC
                       elseif (computeFlowResistance) then 
                       deltaM * m_flow_nominal_pos
         else 0);
  parameter Boolean use_dh = false "Set to true to specify hydraulic diameter";
  parameter Modelica.SIunits.Length dh=1 "Hydraulic diameter";
  parameter Real ReC(min=0)=4000 
    "Reynolds number where transition to turbulent starts";
  parameter Real deltaM(min=0.01) = 0.3 
    "Fraction of nominal mass flow rate where transition to turbulent occurs";

  final parameter Real k(unit="") = if computeFlowResistance then 
        m_flow_nominal_pos / sqrt(dp_nominal_pos) else 0 
    "Flow coefficient, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2)";
protected 
  final parameter Boolean computeFlowResistance=(dp_nominal_pos > Modelica.Constants.eps) 
    "Flag to enable/disable computation of flow resistance";
initial equation 
 if computeFlowResistance then
   assert(m_flow_turbulent > 0, "m_flow_turbulent must be bigger than zero.");
 end if;

 assert(m_flow_nominal_pos > 0, "m_flow_nominal_pos must be non-zero. Check parameters.");
 if ( m_flow_turbulent > m_flow_nominal_pos) then
   Modelica.Utilities.Streams.print("Warning: In FixedResistanceDpM, m_flow_nominal is smaller than m_flow_turbulent."
           + "\n"
           + "  m_flow_nominal = " + String(m_flow_nominal) + "\n"
           + "  dh      = " + String(dh) + "\n"
           + "  To fix, set dh < " +
                String(     4*m_flow_nominal/eta_default/Modelica.Constants.pi/ReC) + "\n"
           + "  Suggested value: dh = " +
                String(1/10*4*m_flow_nominal/eta_default/Modelica.Constants.pi/ReC));
 end if;

equation 
  // Pressure drop calculation
  if computeFlowResistance then
    if linearized then
      m_flow*m_flow_nominal_pos = k^2*dp;
    else
      if homotopyInitialization then
        if from_dp then
          m_flow=homotopy(actual=Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_dp(dp=dp, k=k,
                                   m_flow_turbulent=m_flow_turbulent),
                                   simplified=m_flow_nominal_pos*dp/dp_nominal_pos);
        else
          dp=homotopy(actual=Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_m_flow(m_flow=m_flow, k=k,
                                   m_flow_turbulent=m_flow_turbulent),
                    simplified=dp_nominal_pos*m_flow/m_flow_nominal_pos);
         end if;  // from_dp
      else // do not use homotopy
        if from_dp then
          m_flow=Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_dp(dp=dp, k=k,
                                   m_flow_turbulent=m_flow_turbulent);
        else
          dp=Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_m_flow(m_flow=m_flow, k=k,
                                   m_flow_turbulent=m_flow_turbulent);
        end if;  // from_dp
      end if; // homotopyInitialization
    end if; // linearized
  else // do not compute flow resistance
    dp = 0;
  end if;  // computeFlowResistance

end FixedResistanceDpM;

Buildings.Fluid.FixedResistances.LosslessPipe

Pipe with no flow friction and no heat transfer

Information

Model of a pipe with no flow resistance, no heat loss and no transport delay. This model can be used to replace a replaceable pipe model in flow legs in which no friction should be modeled. This is for example done in the outlet port of the base class for three way valves, Buildings.Fluid.Actuators.BaseClasses.PartialThreeWayValve.

Extends from Buildings.Fluid.Interfaces.PartialTwoPortInterface (Partial model transporting fluid between two ports without storing mass or energy), Buildings.BaseClasses.BaseIcon (Base icon).

Parameters

Type Name Default Description

replaceable package Medium PartialMedium Medium in the component

Nominal condition

MassFlowRate m_flow_nominal 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]

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_T false = true, if actual temperature at port is computed

Type	Name	Default	Description
replaceable package Medium	PartialMedium	Medium in the component
Nominal condition
MassFlowRate	m_flow_nominal		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]
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_T	false	= true, if actual temperature at port is computed

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

model LosslessPipe "Pipe with no flow friction and no heat transfer"
  extends Buildings.Fluid.Interfaces.PartialTwoPortInterface;
  extends Buildings.BaseClasses.BaseIcon;
  final parameter Boolean from_dp=true "Used to satisfy replaceable models";
equation 
  dp=0;
  // 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 LosslessPipe;

Buildings.Fluid.FixedResistances.Pipe

Pipe with finite volume discretization along flow path

Information

Model of a pipe with flow resistance and optional heat exchange with environment.

If useMultipleHeatPorts=false (default option), the pipe uses a single heat port for the heat exchange with the environment. If useMultipleHeatPorts=true, then one heat port for each segment of the pipe is used for the heat exchange with the environment. If the heat port is unconnected, then the pipe has no heat loss.

The default value for the parameter diameter is computed such that the flow velocity is equal to v_nominal=0.15 for a mass flow rate of m_flow_nominal. Both parameters, diameter and v_nominal, can be overwritten by the user. The default value for dp_nominal is two times the pressure drop that the pipe would have if it were straight with no fittings. The factor of two that takes into account the pressure loss of fittings can be overwritten. These fittings could also be explicitely modeled outside of this component using models from the package Modelica.Fluid.Fittings. For mass flow rates other than m_flow_nominal, the model Buildings.Fluid.FixedResistances.FixedResistanceDpM is used to compute the pressure drop.

For a steady-state model of a flow resistance, use Buildings.Fluid.FixedResistances.FixedResistanceDpM instead of this model.

Extends from Buildings.Fluid.FixedResistances.BaseClasses.Pipe (Model of a pipe with finite volume discretization along the flow path).

Parameters

Type Name Default Description

replaceable package Medium PartialMedium Medium in the component

Integer nSeg 10 Number of volume segments

Length thicknessIns Thickness of insulation [m]

ThermalConductivity lambdaIns Heat conductivity of insulation [W/(m.K)]

Length diameter sqrt(4*m_flow_nominal/rho_de... Pipe diameter (without insulation) [m]

Length length Length of the pipe [m]

Velocity v_nominal 0.15 Velocity at m_flow_nominal (used to compute default diameter) [m/s]

Length roughness 2.5e-5 Absolute roughness of pipe, with a default for a smooth steel pipe (dummy if use_roughness = false) [m]

Boolean useMultipleHeatPorts false = true to use one heat port for each segment of the pipe, false to use a single heat port for the entire pipe

Nominal condition

MassFlowRate m_flow_nominal Nominal mass flow rate [kg/s]

Pressure dp_nominal 2*dpStraightPipe_nominal Pressure [Pa]

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]

Dynamics

Equations

Dynamics energyDynamics Modelica.Fluid.Types.Dynamic... Formulation of energy balance

Dynamics massDynamics energyDynamics Formulation of mass balance

Initialization

AbsolutePressure p_start Medium.p_default Start value of pressure [Pa]

Temperature T_start Medium.T_default Start value of temperature [K]

MassFraction X_start[Medium.nX] Medium.X_default Start value of mass fractions m_i/m [kg/kg]

ExtraProperty C_start[Medium.nC] fill(0, Medium.nC) Start value of trace substances

ExtraProperty C_nominal[Medium.nC] fill(1E-2, Medium.nC) Nominal value of trace substances. (Set to typical order of magnitude.)

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

Flow resistance

Boolean from_dp false = true, use m_flow = f(dp) else dp = f(m_flow)

Boolean linearizeFlowResistance false = true, use linear relation between m_flow and dp for any flow rate

Real deltaM 0.1 Fraction of nominal flow rate where flow transitions to laminar

Real ReC 4000 Reynolds number where transition to turbulent starts

Type	Name	Default	Description
replaceable package Medium	PartialMedium	Medium in the component
Integer	nSeg	10	Number of volume segments
Length	thicknessIns		Thickness of insulation [m]
ThermalConductivity	lambdaIns		Heat conductivity of insulation [W/(m.K)]
Length	diameter	sqrt(4*m_flow_nominal/rho_de...	Pipe diameter (without insulation) [m]
Length	length		Length of the pipe [m]
Velocity	v_nominal	0.15	Velocity at m_flow_nominal (used to compute default diameter) [m/s]
Length	roughness	2.5e-5	Absolute roughness of pipe, with a default for a smooth steel pipe (dummy if use_roughness = false) [m]
Boolean	useMultipleHeatPorts	false	= true to use one heat port for each segment of the pipe, false to use a single heat port for the entire pipe
Nominal condition
MassFlowRate	m_flow_nominal		Nominal mass flow rate [kg/s]
Pressure	dp_nominal	2*dpStraightPipe_nominal	Pressure [Pa]
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]
Dynamics
Equations
Dynamics	energyDynamics	Modelica.Fluid.Types.Dynamic...	Formulation of energy balance
Dynamics	massDynamics	energyDynamics	Formulation of mass balance
Initialization
AbsolutePressure	p_start	Medium.p_default	Start value of pressure [Pa]
Temperature	T_start	Medium.T_default	Start value of temperature [K]
MassFraction	X_start[Medium.nX]	Medium.X_default	Start value of mass fractions m_i/m [kg/kg]
ExtraProperty	C_start[Medium.nC]	fill(0, Medium.nC)	Start value of trace substances
ExtraProperty	C_nominal[Medium.nC]	fill(1E-2, Medium.nC)	Nominal value of trace substances. (Set to typical order of magnitude.)
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
Flow resistance
Boolean	from_dp	false	= true, use m_flow = f(dp) else dp = f(m_flow)
Boolean	linearizeFlowResistance	false	= true, use linear relation between m_flow and dp for any flow rate
Real	deltaM	0.1	Fraction of nominal flow rate where flow transitions to laminar
Real	ReC	4000	Reynolds number where transition to turbulent starts

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)

HeatPort_a heatPort Single heat port that connects to outside of pipe wall (default, enabled when useMultipleHeatPorts=false)

HeatPorts_a heatPorts[nSeg] Multiple heat ports that connect to outside of pipe wall (enabled if useMultipleHeatPorts=true)

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)
HeatPort_a	heatPort	Single heat port that connects to outside of pipe wall (default, enabled when useMultipleHeatPorts=false)
HeatPorts_a	heatPorts[nSeg]	Multiple heat ports that connect to outside of pipe wall (enabled if useMultipleHeatPorts=true)

Modelica definition

model Pipe "Pipe with finite volume discretization along flow path"
  extends Buildings.Fluid.FixedResistances.BaseClasses.Pipe(
   diameter=sqrt(4*m_flow_nominal/rho_default/v_nominal/Modelica.Constants.pi),
   dp_nominal=2*dpStraightPipe_nominal,
   res(dp(nominal=length*10)));
  // Because dp_nominal is a non-literal value, we set
  // dp.nominal=100 instead of the default dp.nominal=dp_nominal,
  // because the latter is ignored by Dymola 2012 FD 01.

  parameter Modelica.SIunits.Velocity v_nominal = 0.15 
    "Velocity at m_flow_nominal (used to compute default diameter)";
  parameter Modelica.SIunits.Length roughness(min=0) = 2.5e-5 
    "Absolute roughness of pipe, with a default for a smooth steel pipe (dummy if use_roughness = false)";
  final parameter Modelica.SIunits.Pressure dpStraightPipe_nominal=
      Modelica.Fluid.Pipes.BaseClasses.WallFriction.Detailed.pressureLoss_m_flow(
      m_flow=m_flow_nominal,
      rho_a=rho_default,
      rho_b=rho_default,
      mu_a=mu_default,
      mu_b=mu_default,
      length=length,
      diameter=diameter,
      roughness=roughness,
      m_flow_small=m_flow_small) 
    "Pressure loss of a straight pipe at m_flow_nominal";

  parameter Boolean useMultipleHeatPorts=false 
    "= true to use one heat port for each segment of the pipe, false to use a single heat port for the entire pipe";

  Modelica.Thermal.HeatTransfer.Components.ThermalConductor conPipWal[nSeg](
      each G=2*Modelica.Constants.pi*lambdaIns*length/nSeg/Modelica.Math.log((
        diameter/2.0 + thicknessIns)/(diameter/2.0))) 
    "Thermal conductance through pipe wall";
  Modelica.Thermal.HeatTransfer.Components.ThermalCollector colAllToOne(m=nSeg) if 
       not useMultipleHeatPorts 
    "Connector to assign multiple heat ports to one heat port";

  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPort if not 
    useMultipleHeatPorts 
    "Single heat port that connects to outside of pipe wall (default, enabled when useMultipleHeatPorts=false)";
  Modelica.Fluid.Interfaces.HeatPorts_a heatPorts[nSeg] if 
       useMultipleHeatPorts 
    "Multiple heat ports that connect to outside of pipe wall (enabled if useMultipleHeatPorts=true)";
    
equation 

  connect(conPipWal.port_b, vol.heatPort);
  if useMultipleHeatPorts then
    connect(heatPorts, conPipWal.port_a);
  else
    connect(colAllToOne.port_a, conPipWal.port_a);
    connect(colAllToOne.port_b, heatPort);

  end if;
end Pipe;

Buildings.Fluid.FixedResistances.SplitterFixedResistanceDpM

Flow splitter with fixed resistance at each port

Information

Model of a flow splitter or mixer with a fixed resistance in each flow leg. In each flow lag, a pressure drop can be modelled, and at the fluid junction, a mixing volume can be modelled.

The pressure drop is implemented using the model Buildings.Fluid.FixedResistances.FixedResistanceDpM. If its nominal pressure drop is set to zero, then the pressure drop model will be removed. For example, the pressure drop declaration

  m_flow_nominal={ 0.1, 0.1,  -0.2},
  dp_nominal =   {500,    0, -6000}

would model a mixer that has the nominal flow rates and associated pressure drops as shown in the figure below. Note that port_3 is set to negative values. The negative values indicate that at the nominal conditions, fluid is leaving the component.

Optionally, at the fluid junction, a control volume can be modelled. This is implemented using the model Buildings.Fluid.Delays.DelayFirstOrder. The fluid volume is modelled if dynamicBalance=true, and it is removed if dynamicBalance=false. The control volume has the size

  V = sum(abs(m_flow_nominal[:])/3)*tau/rho_nominal

where tau is a parameter and rho_nominal is the density of the medium in the volume at nominal condition. Setting dynamicBalance=true can help reducing the size of the nonlinear system of equations.

Extends from Buildings.BaseClasses.BaseIcon (Base icon), Buildings.Fluid.BaseClasses.PartialThreeWayResistance (Flow splitter with partial resistance model at each port).

Parameters

Type Name Default Description

replaceable package Medium PartialMedium Medium in the component

Boolean use_dh false Set to true to specify hydraulic diameter

Real deltaM 0.3 Fraction of nominal mass flow rate where transition to turbulent occurs

Length dh[3] {1,1,1} Hydraulic diameter [m]

Real ReC[3] {4000,4000,4000} Reynolds number where transition to turbulent starts

Nominal condition

MassFlowRate m_flow_nominal[3] Mass flow rate. Set negative at outflowing ports. [kg/s]

Pressure dp_nominal[3] Pressure. Set negative at outflowing ports. [Pa]

Dynamics

Equations

Dynamics energyDynamics Modelica.Fluid.Types.Dynamic... Formulation of energy balance

Dynamics massDynamics energyDynamics Formulation of mass balance

Boolean dynamicBalance true Set to true to use a dynamic balance, which often leads to smaller systems of equations

MassFlowRate mDyn_flow_nominal sum(abs(m_flow_nominal[:])/3) Nominal mass flow rate for dynamic momentum and energy balance [kg/s]

Nominal condition

Time tau 10 Time constant at nominal flow for dynamic energy and momentum balance [s]

Initialization

AbsolutePressure p_start Medium.p_default Start value of pressure [Pa]

Temperature T_start Medium.T_default Start value of temperature [K]

MassFraction X_start[Medium.nX] Medium.X_default Start value of mass fractions m_i/m [kg/kg]

ExtraProperty C_start[Medium.nC] fill(0, Medium.nC) Start value of trace substances

ExtraProperty C_nominal[Medium.nC] fill(1E-2, Medium.nC) Nominal value of trace substances. (Set to typical order of magnitude.)

Advanced

Boolean from_dp true = true, use m_flow = f(dp) else dp = f(m_flow)

Boolean homotopyInitialization true = true, use homotopy method

Boolean linearized false = true, use linear relation between m_flow and dp for any flow rate

Type	Name	Default	Description
replaceable package Medium	PartialMedium	Medium in the component
Boolean	use_dh	false	Set to true to specify hydraulic diameter
Real	deltaM	0.3	Fraction of nominal mass flow rate where transition to turbulent occurs
Length	dh[3]	{1,1,1}	Hydraulic diameter [m]
Real	ReC[3]	{4000,4000,4000}	Reynolds number where transition to turbulent starts
Nominal condition
MassFlowRate	m_flow_nominal[3]		Mass flow rate. Set negative at outflowing ports. [kg/s]
Pressure	dp_nominal[3]		Pressure. Set negative at outflowing ports. [Pa]
Dynamics
Equations
Dynamics	energyDynamics	Modelica.Fluid.Types.Dynamic...	Formulation of energy balance
Dynamics	massDynamics	energyDynamics	Formulation of mass balance
Boolean	dynamicBalance	true	Set to true to use a dynamic balance, which often leads to smaller systems of equations
MassFlowRate	mDyn_flow_nominal	sum(abs(m_flow_nominal[:])/3)	Nominal mass flow rate for dynamic momentum and energy balance [kg/s]
Nominal condition
Time	tau	10	Time constant at nominal flow for dynamic energy and momentum balance [s]
Initialization
AbsolutePressure	p_start	Medium.p_default	Start value of pressure [Pa]
Temperature	T_start	Medium.T_default	Start value of temperature [K]
MassFraction	X_start[Medium.nX]	Medium.X_default	Start value of mass fractions m_i/m [kg/kg]
ExtraProperty	C_start[Medium.nC]	fill(0, Medium.nC)	Start value of trace substances
ExtraProperty	C_nominal[Medium.nC]	fill(1E-2, Medium.nC)	Nominal value of trace substances. (Set to typical order of magnitude.)
Advanced
Boolean	from_dp	true	= true, use m_flow = f(dp) else dp = f(m_flow)
Boolean	homotopyInitialization	true	= true, use homotopy method
Boolean	linearized	false	= true, use linear relation between m_flow and dp for any flow rate

Connectors

Type Name Description

FluidPort_a port_1

FluidPort_b port_2

FluidPort_a port_3

Type	Name	Description
FluidPort_a	port_1
FluidPort_b	port_2
FluidPort_a	port_3

Modelica definition

model SplitterFixedResistanceDpM 
  "Flow splitter with fixed resistance at each port"
    extends Buildings.BaseClasses.BaseIcon;
    extends Buildings.Fluid.BaseClasses.PartialThreeWayResistance(
    mDyn_flow_nominal = sum(abs(m_flow_nominal[:])/3),
      redeclare Buildings.Fluid.FixedResistances.FixedResistanceDpM res1(
         redeclare package Medium=Medium,
            final allowFlowReversal=true,
            from_dp=from_dp,
            final m_flow_nominal=m_flow_nominal[1],
            final dp_nominal=dp_nominal[1],
            final ReC=ReC[1],
            final dh=dh[1],
            linearized=linearized,
            homotopyInitialization=homotopyInitialization,
            deltaM=deltaM),
      redeclare Buildings.Fluid.FixedResistances.FixedResistanceDpM res2(
         redeclare package Medium=Medium,
            final allowFlowReversal=true,
            from_dp=from_dp,
            final m_flow_nominal=m_flow_nominal[2],
            final dp_nominal=dp_nominal[2],
            final ReC=ReC[2],
            final dh=dh[2],
            linearized=linearized,
            homotopyInitialization=homotopyInitialization,
            deltaM=deltaM),
      redeclare Buildings.Fluid.FixedResistances.FixedResistanceDpM res3(
         redeclare package Medium=Medium,
            final allowFlowReversal=true,
            from_dp=from_dp,
            final m_flow_nominal=m_flow_nominal[3],
            final dp_nominal=dp_nominal[3],
            final ReC=ReC[3],
            final dh=dh[3],
            linearized=linearized,
            homotopyInitialization=homotopyInitialization,
            deltaM=deltaM));

  parameter Boolean use_dh = false "Set to true to specify hydraulic diameter";
  parameter Modelica.SIunits.MassFlowRate[3] m_flow_nominal 
    "Mass flow rate. Set negative at outflowing ports.";
  parameter Modelica.SIunits.Pressure[3] dp_nominal(each displayUnit = "Pa") 
    "Pressure. Set negative at outflowing ports.";
  parameter Real deltaM(min=0) = 0.3 
    "Fraction of nominal mass flow rate where transition to turbulent occurs";

  parameter Modelica.SIunits.Length[3] dh={1, 1, 1} "Hydraulic diameter";
  parameter Real[3] ReC(each min=0)={4000, 4000, 4000} 
    "Reynolds number where transition to turbulent starts";
  parameter Boolean linearized = false 
    "= true, use linear relation between m_flow and dp for any flow rate";
  parameter Boolean homotopyInitialization = true "= true, use homotopy method";

end SplitterFixedResistanceDpM;

Automatically generated Thu Oct 24 15:08:28 2013.