Buildings.Fluid.Actuators.BaseClasses

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Buildings.Fluid.Actuators.BaseClasses

Package with base classes for Buildings.Fluid.Actuators

Information

This package contains base classes that are used to construct the models in Buildings.Fluid.Actuators.

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

Package Content

Name Description

ActuatorSignal Partial model that implements the filtered opening for valves and dampers

PartialDamperExponential Partial model for air dampers with exponential opening characteristics

PartialThreeWayValve Partial three way valve

PartialTwoWayValve Partial model for a two way valve

ValveParameters Model with parameters for valves

der_equalPercentage Derivative of valve opening characteristics for equal percentage valve

equalPercentage Valve opening characteristics for equal percentage valve

exponentialDamper Damper opening characteristics for an exponential damper

Examples Collection of models that illustrate model use and test models

Name	Description
ActuatorSignal	Partial model that implements the filtered opening for valves and dampers
PartialDamperExponential	Partial model for air dampers with exponential opening characteristics
PartialThreeWayValve	Partial three way valve
PartialTwoWayValve	Partial model for a two way valve
ValveParameters	Model with parameters for valves
der_equalPercentage	Derivative of valve opening characteristics for equal percentage valve
equalPercentage	Valve opening characteristics for equal percentage valve
exponentialDamper	Damper opening characteristics for an exponential damper
Examples	Collection of models that illustrate model use and test models

Buildings.Fluid.Actuators.BaseClasses.ActuatorSignal

Partial model that implements the filtered opening for valves and dampers

Buildings.Fluid.Actuators.BaseClasses.ActuatorSignal

Information

This model implements the filter that is used to approximate the travel time of the actuator. Models that extend this model use the signal y_actual to obtain the current position of the actuator.

See Buildings.Fluid.Actuators.UsersGuide for a description of the filter.

Parameters

Type Name Default Description

Dynamics

Filtered opening

Boolean filteredOpening true = true, if opening is filtered with a 2nd order CriticalDamping filter

Time riseTime 120 Rise time of the filter (time to reach 99.6 % of an opening step) [s]

Init init Modelica.Blocks.Types.Init.I... Type of initialization (no init/steady state/initial state/initial output)

Real y_start 1 Initial value of output

Type	Name	Default	Description
Dynamics
Filtered opening
Boolean	filteredOpening	true	= true, if opening is filtered with a 2nd order CriticalDamping filter
Time	riseTime	120	Rise time of the filter (time to reach 99.6 % of an opening step) [s]
Init	init	Modelica.Blocks.Types.Init.I...	Type of initialization (no init/steady state/initial state/initial output)
Real	y_start	1	Initial value of output

Connectors

Type Name Description

input RealInput y Actuator position (0: closed, 1: open)

output RealOutput y_actual Actual valve position

Type	Name	Description
input RealInput	y	Actuator position (0: closed, 1: open)
output RealOutput	y_actual	Actual valve position

Modelica definition

model ActuatorSignal 
  "Partial model that implements the filtered opening for valves and dampers"

  parameter Boolean filteredOpening=true 
    "= true, if opening is filtered with a 2nd order CriticalDamping filter";
  parameter Modelica.SIunits.Time riseTime=120 
    "Rise time of the filter (time to reach 99.6 % of an opening step)";
  parameter Modelica.Blocks.Types.Init init=Modelica.Blocks.Types.Init.InitialOutput 
    "Type of initialization (no init/steady state/initial state/initial output)";
  parameter Real y_start=1 "Initial value of output";

  Modelica.Blocks.Interfaces.RealInput y(min=0, max=1) 
    "Actuator position (0: closed, 1: open)";

  Modelica.Blocks.Interfaces.RealOutput y_actual "Actual valve position";

  // Classes used to implement the filtered opening
protected 
  Modelica.Blocks.Interfaces.RealOutput y_filtered if filteredOpening 
    "Filtered valve position in the range 0..1";

  Modelica.Blocks.Continuous.Filter filter(
     order=2,
     f_cut=5/(2*Modelica.Constants.pi*riseTime),
     final init=init,
     final y_start=y_start,
     final analogFilter=Modelica.Blocks.Types.AnalogFilter.CriticalDamping,
     final filterType=Modelica.Blocks.Types.FilterType.LowPass,
     x(each stateSelect=StateSelect.always)) if 
        filteredOpening 
    "Second order filter to approximate valve opening time, and to improve numerics";

equation 
 connect(filter.y, y_filtered);
  if filteredOpening then
  connect(y, filter.u);
  connect(filter.y, y_actual);
  else
    connect(y, y_actual);
  end if;

end ActuatorSignal;

Buildings.Fluid.Actuators.BaseClasses.PartialDamperExponential

Partial model for air dampers with exponential opening characteristics

Buildings.Fluid.Actuators.BaseClasses.PartialDamperExponential

Information

Partial model for air dampers with exponential opening characteristics. This is the base model for air dampers and variable air volume flow boxes. The model implements the functions that relate the opening signal, the pressure drop and the mass flow rate. The model also defines parameters that are used by different air damper models.

For a description of the opening characteristics and typical parameter values, see the damper model Exponential.

Extends from Buildings.Fluid.BaseClasses.PartialResistance (Partial model for a hydraulic resistance), Buildings.Fluid.Actuators.BaseClasses.ActuatorSignal (Partial model that implements the filtered opening for valves and dampers).

Parameters

Type Name Default Description

replaceable package Medium PartialMedium Medium in the component

MassFlowRate m_flow_turbulent if use_deltaM then deltaM*m_... Turbulent flow if |m_flow| >= m_flow_turbulent [kg/s]

Boolean use_deltaM true Set to true to use deltaM for turbulent transition, else ReC is used

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

Boolean use_v_nominal true Set to true to use face velocity to compute area

Velocity v_nominal 1 Nominal face velocity [m/s]

Area A m_flow_nominal/rho_default/v... Face area [m2]

Boolean roundDuct false Set to true for round duct, false for square cross section

Real ReC 4000 Reynolds number where transition to turbulent starts

Real kFixed Flow coefficient of fixed resistance that may be in series with damper, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2).

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

Boolean use_constant_density true Set to true to use constant density for flow friction

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)

Dynamics

Filtered opening

Boolean filteredOpening true = true, if opening is filtered with a 2nd order CriticalDamping filter

Time riseTime 120 Rise time of the filter (time to reach 99.6 % of an opening step) [s]

Init init Modelica.Blocks.Types.Init.I... Type of initialization (no init/steady state/initial state/initial output)

Real y_start 1 Initial value of output

Damper coefficients

Real a -1.51 Coefficient a for damper characteristics

Real b 0.105*90 Coefficient b for damper characteristics

Real yL 15/90 Lower value for damper curve

Real yU 55/90 Upper value for damper curve

Real k0 1E6 Flow coefficient for y=0, k0 = pressure drop divided by dynamic pressure

Real k1 0.45 Flow coefficient for y=1, k1 = pressure drop divided by dynamic pressure

Type	Name	Default	Description
replaceable package Medium	PartialMedium	Medium in the component
MassFlowRate	m_flow_turbulent	if use_deltaM then deltaM*m_...	Turbulent flow if \|m_flow\| >= m_flow_turbulent [kg/s]
Boolean	use_deltaM	true	Set to true to use deltaM for turbulent transition, else ReC is used
Real	deltaM	0.3	Fraction of nominal mass flow rate where transition to turbulent occurs
Boolean	use_v_nominal	true	Set to true to use face velocity to compute area
Velocity	v_nominal	1	Nominal face velocity [m/s]
Area	A	m_flow_nominal/rho_default/v...	Face area [m2]
Boolean	roundDuct	false	Set to true for round duct, false for square cross section
Real	ReC	4000	Reynolds number where transition to turbulent starts
Real	kFixed		Flow coefficient of fixed resistance that may be in series with damper, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2).
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
Boolean	use_constant_density	true	Set to true to use constant density for flow friction
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)
Dynamics
Filtered opening
Boolean	filteredOpening	true	= true, if opening is filtered with a 2nd order CriticalDamping filter
Time	riseTime	120	Rise time of the filter (time to reach 99.6 % of an opening step) [s]
Init	init	Modelica.Blocks.Types.Init.I...	Type of initialization (no init/steady state/initial state/initial output)
Real	y_start	1	Initial value of output
Damper coefficients
Real	a	-1.51	Coefficient a for damper characteristics
Real	b	0.105*90	Coefficient b for damper characteristics
Real	yL	15/90	Lower value for damper curve
Real	yU	55/90	Upper value for damper curve
Real	k0	1E6	Flow coefficient for y=0, k0 = pressure drop divided by dynamic pressure
Real	k1	0.45	Flow coefficient for y=1, k1 = pressure drop divided by dynamic pressure

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)

input RealInput y Actuator position (0: closed, 1: open)

output RealOutput y_actual Actual valve position

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)
input RealInput	y	Actuator position (0: closed, 1: open)
output RealOutput	y_actual	Actual valve position

Modelica definition

partial model PartialDamperExponential 
  "Partial model for air dampers with exponential opening characteristics"
   extends Buildings.Fluid.BaseClasses.PartialResistance(
      m_flow_turbulent=if use_deltaM then deltaM * m_flow_nominal else 
      eta_default*ReC*sqrt(area)*facRouDuc);
   extends Buildings.Fluid.Actuators.BaseClasses.ActuatorSignal;
 parameter Boolean use_deltaM = true 
    "Set to true to use deltaM for turbulent transition, else ReC is used";
 parameter Real deltaM = 0.3 
    "Fraction of nominal mass flow rate where transition to turbulent occurs";
 parameter Boolean use_v_nominal = true 
    "Set to true to use face velocity to compute area";
 parameter Modelica.SIunits.Velocity v_nominal=1 "Nominal face velocity";
 parameter Modelica.SIunits.Area A=m_flow_nominal/rho_default/v_nominal 
    "Face area";
 parameter Boolean roundDuct = false 
    "Set to true for round duct, false for square cross section";
 parameter Real ReC=4000 "Reynolds number where transition to turbulent starts";
 parameter Real a(unit="")=-1.51 "Coefficient a for damper characteristics";
 parameter Real b(unit="")=0.105*90 "Coefficient b for damper characteristics";
 parameter Real yL = 15/90 "Lower value for damper curve";
 parameter Real yU = 55/90 "Upper value for damper curve";
 parameter Real k0(min=0) = 1E6 
    "Flow coefficient for y=0, k0 = pressure drop divided by dynamic pressure";
 parameter Real k1(min=0) = 0.45 
    "Flow coefficient for y=1, k1 = pressure drop divided by dynamic pressure";
 parameter Boolean use_constant_density=true 
    "Set to true to use constant density for flow friction";
 Medium.Density rho "Medium density";
 parameter Real kFixed(unit="") 
    "Flow coefficient of fixed resistance that may be in series with damper, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2).";
 Real kDam(unit="") 
    "Flow coefficient of damper, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2)";
 Real k(unit="") 
    "Flow coefficient of damper plus fixed resistance, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2)";
protected 
 parameter Medium.Density rho_default=Medium.density(sta_default) 
    "Density, used to compute fluid volume";
 parameter Real[3] cL=
    {(Modelica.Math.log(k0) - b - a)/yL^2,
      (-b*yL - 2*Modelica.Math.log(k0) + 2*b + 2*a)/yL,
      Modelica.Math.log(k0)} "Polynomial coefficients for curve fit for y < yl";
 parameter Real[3] cU=
    {(Modelica.Math.log(k1) - a)/(yU^2 - 2*yU + 1),
    (-b*yU^2 - 2*Modelica.Math.log(k1)*yU - (-2*b - 2*a)*yU - b)/(yU^2 - 2*yU + 1),
    (Modelica.Math.log(k1)*yU^2 + b*yU^2 + (-2*b - 2*a)*yU + b + a)/(yU^2 - 2*yU + 1)} 
    "Polynomial coefficients for curve fit for y > yu";
 parameter Real facRouDuc= if roundDuct then sqrt(Modelica.Constants.pi)/2 else 1;
 parameter Modelica.SIunits.Area area=
    if use_v_nominal then m_flow_nominal/rho_default/v_nominal else A 
    "Face velocity used in the computation";
initial equation 
  assert(k0 > k1, "k0 must be bigger than k1.");
  assert(m_flow_turbulent > 0, "m_flow_turbulent must be bigger than zero.");
equation 
  rho = if use_constant_density then 
         rho_default else 
         Medium.density(Medium.setState_phX(port_a.p, inStream(port_a.h_outflow), inStream(port_a.Xi_outflow)));
  // flow coefficient, k=m_flow/sqrt(dp)
  kDam=sqrt(2*rho)*area/Buildings.Fluid.Actuators.BaseClasses.exponentialDamper(
    y=y_actual,
    a=a,
    b=b,
    cL=cL,
    cU=cU,
    yL=yL,
    yU=yU);
  k = if (kFixed>Modelica.Constants.eps) then sqrt(1/(1/kFixed^2 + 1/kDam^2)) else kDam;
  // Pressure drop calculation
  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
end PartialDamperExponential;

Buildings.Fluid.Actuators.BaseClasses.PartialThreeWayValve

Partial three way valve

Buildings.Fluid.Actuators.BaseClasses.PartialThreeWayValve

Information

Partial model of a three way valve. This is the base model for valves with different opening characteristics, such as linear, equal percentage or quick opening. The three way valve model consists of a mixer where valves are placed in two of the flow legs. The third flow leg has no friction. The flow coefficient Kv for flow from port_1 -> port_2 is a parameter. The flow coefficient for the bypass flow from port_3 -> port_2 is computed as

         Kv(port_3 -> port_2)
  fraK = ----------------------
         Kv(port_1 -> port_2)

where 0 < fraK ≤ 1 is a parameter with a default value of fraK=0.7.

Since this model uses two way valves to construct a three way valve, see PartialTwoWayValve for details regarding the valve implementation.

Extends from Buildings.Fluid.BaseClasses.PartialThreeWayResistance (Flow splitter with partial resistance model at each port), Buildings.Fluid.Actuators.BaseClasses.ActuatorSignal (Partial model that implements the filtered opening for valves and dampers), Buildings.Fluid.Actuators.BaseClasses.ValveParameters (Model with parameters for valves).

Parameters

Type Name Default Description

replaceable package Medium PartialMedium Medium in the component

Real fraK 0.7 Fraction Kv(port_3->port_2)/Kv(port_1->port_2)

Real l[2] {0,0} Valve leakage, l=Kv(y=0)/Kv(y=1)

Flow Coefficient

CvTypes CvData Buildings.Fluid.Types.CvType... Selection of flow coefficient

Real Kv Kv (metric) flow coefficient [m3/h/(bar)^(1/2)]

Real Cv Cv (US) flow coefficient [USG/min/(psi)^(1/2)]

Area Av Av (metric) flow coefficient [m2]

Pressure-flow linearization

Real deltaM 0.02 Fraction of nominal flow rate where linearization starts, if y=1

Nominal condition

MassFlowRate m_flow_nominal Nominal mass flow rate [kg/s]

Pressure dpValve_nominal Nominal pressure drop of fully open valve, used if CvData=Buildings.Fluid.Types.CvTypes.OpPoint [Pa]

Pressure dpFixed_nominal[2] {0,0} Nominal pressure drop of pipes and other equipment in flow legs at port_1 and port_3 [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 m_flow_nominal 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]

Filtered opening

Boolean filteredOpening true = true, if opening is filtered with a 2nd order CriticalDamping filter

Time riseTime 120 Rise time of the filter (time to reach 99.6 % of an opening step) [s]

Init init Modelica.Blocks.Types.Init.I... Type of initialization (no init/steady state/initial state/initial output)

Real y_start 1 Initial value of output

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[2] {false,false} = true, use linear relation between m_flow and dp for any flow rate

Nominal condition

Density rhoStd Medium.density_pTX(101325, 2... Inlet density for which valve coefficients are defined [kg/m3]

Type	Name	Default	Description
replaceable package Medium	PartialMedium	Medium in the component
Real	fraK	0.7	Fraction Kv(port_3->port_2)/Kv(port_1->port_2)
Real	l[2]	{0,0}	Valve leakage, l=Kv(y=0)/Kv(y=1)
Flow Coefficient
CvTypes	CvData	Buildings.Fluid.Types.CvType...	Selection of flow coefficient
Real	Kv		Kv (metric) flow coefficient [m3/h/(bar)^(1/2)]
Real	Cv		Cv (US) flow coefficient [USG/min/(psi)^(1/2)]
Area	Av		Av (metric) flow coefficient [m2]
Pressure-flow linearization
Real	deltaM	0.02	Fraction of nominal flow rate where linearization starts, if y=1
Nominal condition
MassFlowRate	m_flow_nominal		Nominal mass flow rate [kg/s]
Pressure	dpValve_nominal		Nominal pressure drop of fully open valve, used if CvData=Buildings.Fluid.Types.CvTypes.OpPoint [Pa]
Pressure	dpFixed_nominal[2]	{0,0}	Nominal pressure drop of pipes and other equipment in flow legs at port_1 and port_3 [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	m_flow_nominal	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]
Filtered opening
Boolean	filteredOpening	true	= true, if opening is filtered with a 2nd order CriticalDamping filter
Time	riseTime	120	Rise time of the filter (time to reach 99.6 % of an opening step) [s]
Init	init	Modelica.Blocks.Types.Init.I...	Type of initialization (no init/steady state/initial state/initial output)
Real	y_start	1	Initial value of output
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[2]	{false,false}	= true, use linear relation between m_flow and dp for any flow rate
Nominal condition
Density	rhoStd	Medium.density_pTX(101325, 2...	Inlet density for which valve coefficients are defined [kg/m3]

Connectors

Type Name Description

FluidPort_a port_1

FluidPort_b port_2

FluidPort_a port_3

input RealInput y Actuator position (0: closed, 1: open)

output RealOutput y_actual Actual valve position

Type	Name	Description
FluidPort_a	port_1
FluidPort_b	port_2
FluidPort_a	port_3
input RealInput	y	Actuator position (0: closed, 1: open)
output RealOutput	y_actual	Actual valve position

Modelica definition

partial model PartialThreeWayValve "Partial three way valve"
  extends Buildings.Fluid.BaseClasses.PartialThreeWayResistance(
      final mDyn_flow_nominal = m_flow_nominal,
        redeclare replaceable Buildings.Fluid.Actuators.BaseClasses.PartialTwoWayValve
            res1 constrainedby 
      Buildings.Fluid.Actuators.BaseClasses.PartialTwoWayValve(
               deltaM=deltaM,
               dp(start=dpValve_nominal/2),
               from_dp=from_dp,
               redeclare final package Medium = Medium,
               final l=l[1],
               final linearized=linearized[1],
               final homotopyInitialization=homotopyInitialization,
               final CvData=Buildings.Fluid.Types.CvTypes.OpPoint,
               final m_flow_nominal=m_flow_nominal,
               final dpValve_nominal=dpValve_nominal,
               final dpFixed_nominal=dpFixed_nominal[1],
               final filteredOpening=false),
        redeclare FixedResistances.LosslessPipe res2(
          redeclare package Medium = Medium, m_flow_nominal=m_flow_nominal),
        redeclare replaceable Buildings.Fluid.Actuators.BaseClasses.PartialTwoWayValve
            res3 constrainedby 
      Buildings.Fluid.Actuators.BaseClasses.PartialTwoWayValve(
               deltaM=deltaM,
               dp(start=dpValve_nominal/2),
               from_dp=from_dp,
               redeclare final package Medium = Medium,
               final l=l[2],
               final linearized=linearized[2],
               final homotopyInitialization=homotopyInitialization,
               final CvData=Buildings.Fluid.Types.CvTypes.OpPoint,
               final m_flow_nominal=m_flow_nominal,
               final dpValve_nominal=dpValve_nominal/fraK^2,
               final dpFixed_nominal=dpFixed_nominal[2],
               final filteredOpening=false));
    extends Buildings.Fluid.Actuators.BaseClasses.ActuatorSignal;
    extends Buildings.Fluid.Actuators.BaseClasses.ValveParameters(
      rhoStd=Medium.density_pTX(101325, 273.15+4, Medium.X_default));
  parameter Modelica.SIunits.Pressure dpFixed_nominal[2](each displayUnit="Pa",
                                                         each min=0) = {0, 0} 
    "Nominal pressure drop of pipes and other equipment in flow legs at port_1 and port_3";

  parameter Real fraK(min=0, max=1) = 0.7 
    "Fraction Kv(port_3->port_2)/Kv(port_1->port_2)";
  parameter Real[2] l(each min=0, each max=1) = {0, 0} 
    "Valve leakage, l=Kv(y=0)/Kv(y=1)";
  parameter Real deltaM = 0.02 
    "Fraction of nominal flow rate where linearization starts, if y=1";

  parameter Boolean[2] linearized = {false, false} 
    "= true, use linear relation between m_flow and dp for any flow rate";

protected 
  Modelica.Blocks.Math.Feedback inv "Inversion of control signal";
  Modelica.Blocks.Sources.Constant uni(final k=1) 
    "Outputs one for bypass valve";
equation 

  connect(uni.y, inv.u1);
end PartialThreeWayValve;

Buildings.Fluid.Actuators.BaseClasses.PartialTwoWayValve

Partial model for a two way valve

Buildings.Fluid.Actuators.BaseClasses.PartialTwoWayValve

Information

Partial model for a two way valve. This is the base model for valves with different opening characteristics, such as linear, equal percentage or quick opening.

Modelling options

The following options have been adapted from the valve implementation in Modelica.Fluid and are described in Buildings.Fluid.Actuators.BaseClasses.ValveParameters.

In contrast to the model in Modelica.Fluid, this model uses the parameter Kv_SI, which is the flow coefficient in SI units, i.e., it is the ratio between mass flow rate in kg/s and square root of pressure drop in Pa.

To prevent the derivative d/dP (m_flow) to be infinite near the origin, this model linearizes the pressure drop vs. flow relation ship. The region in which it is linearized is parameterized by

  m_turbulent_flow = deltaM * m_flow_nominal

Because the parameterization contains Kv_SI, the values for deltaM and dp_nominal need not be changed if the valve size changes.

Implementation

The two way valve models are implemented using this partial model, as opposed to using different functions for the valve opening characteristics, because each valve opening characteristics has different parameters.

Extends from Buildings.Fluid.BaseClasses.PartialResistance (Partial model for a hydraulic resistance), Buildings.Fluid.Actuators.BaseClasses.ValveParameters (Model with parameters for valves), Buildings.Fluid.Actuators.BaseClasses.ActuatorSignal (Partial model that implements the filtered opening for valves and dampers).

Parameters

Type Name Default Description

replaceable package Medium PartialMedium Medium in the component

MassFlowRate m_flow_turbulent deltaM*abs(m_flow_nominal) Turbulent flow if |m_flow| >= m_flow_turbulent [kg/s]

Real l 0.0001 Valve leakage, l=Kv(y=0)/Kv(y=1)

Nominal condition

MassFlowRate m_flow_nominal Nominal mass flow rate [kg/s]

Pressure dp_nominal dpValve_nominal + dpFixed_no... Pressure drop at nominal mass flow rate [Pa]

Pressure dpValve_nominal Nominal pressure drop of fully open valve, used if CvData=Buildings.Fluid.Types.CvTypes.OpPoint [Pa]

Pressure dpFixed_nominal 0 Pressure drop of pipe and other resistances that are in series [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]

Flow Coefficient

CvTypes CvData Buildings.Fluid.Types.CvType... Selection of flow coefficient

Real Kv Kv (metric) flow coefficient [m3/h/(bar)^(1/2)]

Real Cv Cv (US) flow coefficient [USG/min/(psi)^(1/2)]

Area Av Av (metric) flow coefficient [m2]

Pressure-flow linearization

Real deltaM 0.02 Fraction of nominal flow rate where linearization starts, if y=1

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_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)

Nominal condition

Density rhoStd Medium.density_pTX(101325, 2... Inlet density for which valve coefficients are defined [kg/m3]

Dynamics

Filtered opening

Boolean filteredOpening true = true, if opening is filtered with a 2nd order CriticalDamping filter

Time riseTime 120 Rise time of the filter (time to reach 99.6 % of an opening step) [s]

Init init Modelica.Blocks.Types.Init.I... Type of initialization (no init/steady state/initial state/initial output)

Real y_start 1 Initial value of output

Type	Name	Default	Description
replaceable package Medium	PartialMedium	Medium in the component
MassFlowRate	m_flow_turbulent	deltaM*abs(m_flow_nominal)	Turbulent flow if \|m_flow\| >= m_flow_turbulent [kg/s]
Real	l	0.0001	Valve leakage, l=Kv(y=0)/Kv(y=1)
Nominal condition
MassFlowRate	m_flow_nominal		Nominal mass flow rate [kg/s]
Pressure	dp_nominal	dpValve_nominal + dpFixed_no...	Pressure drop at nominal mass flow rate [Pa]
Pressure	dpValve_nominal		Nominal pressure drop of fully open valve, used if CvData=Buildings.Fluid.Types.CvTypes.OpPoint [Pa]
Pressure	dpFixed_nominal	0	Pressure drop of pipe and other resistances that are in series [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]
Flow Coefficient
CvTypes	CvData	Buildings.Fluid.Types.CvType...	Selection of flow coefficient
Real	Kv		Kv (metric) flow coefficient [m3/h/(bar)^(1/2)]
Real	Cv		Cv (US) flow coefficient [USG/min/(psi)^(1/2)]
Area	Av		Av (metric) flow coefficient [m2]
Pressure-flow linearization
Real	deltaM	0.02	Fraction of nominal flow rate where linearization starts, if y=1
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_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)
Nominal condition
Density	rhoStd	Medium.density_pTX(101325, 2...	Inlet density for which valve coefficients are defined [kg/m3]
Dynamics
Filtered opening
Boolean	filteredOpening	true	= true, if opening is filtered with a 2nd order CriticalDamping filter
Time	riseTime	120	Rise time of the filter (time to reach 99.6 % of an opening step) [s]
Init	init	Modelica.Blocks.Types.Init.I...	Type of initialization (no init/steady state/initial state/initial output)
Real	y_start	1	Initial value of output

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)
input RealInput	y	Actuator position (0: closed, 1: open)
output RealOutput	y_actual	Actual valve position

Modelica definition

partial model PartialTwoWayValve "Partial model for a two way valve"

  extends Buildings.Fluid.BaseClasses.PartialResistance(
       final dp_nominal=dpValve_nominal + dpFixed_nominal,
       dp(nominal=6000),
       final m_flow_turbulent = deltaM * abs(m_flow_nominal));

  extends Buildings.Fluid.Actuators.BaseClasses.ValveParameters(
      rhoStd=Medium.density_pTX(101325, 273.15+4, Medium.X_default));

  extends Buildings.Fluid.Actuators.BaseClasses.ActuatorSignal;
  parameter Modelica.SIunits.Pressure dpFixed_nominal(displayUnit="Pa", min=0) = 0 
    "Pressure drop of pipe and other resistances that are in series";
  parameter Real l(min=1e-10, max=1) = 0.0001 
    "Valve leakage, l=Kv(y=0)/Kv(y=1)";
  Real phi "Ratio actual to nominal mass flow rate of valve, phi=Kv(y)/Kv(y=1)";
protected 
 parameter Real kFixed(unit="") = if dpFixed_nominal > Modelica.Constants.small
    then m_flow_nominal / sqrt(dpFixed_nominal) else 0 
    "Flow coefficient of fixed resistance that may be in series with valve, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2).";
 Real kVal(unit="", min=Modelica.Constants.small) 
    "Flow coefficient of valve, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2).";
 Real k(unit="", min=Modelica.Constants.small) 
    "Flow coefficient of valve and pipe in series, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2).";
initial equation 
  // Since the flow model Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_m_flow computes
  // 1/k^2, the parameter l must not be zero.
  assert(l > 0, "Valve leakage parameter l must be bigger than zero.");
  assert(dpFixed_nominal > -Modelica.Constants.small, "Require dpFixed_nominal >= 0. Received dpFixed_nominal = "
        + String(dpFixed_nominal) + " Pa.");
equation 
 kVal = phi*Kv_SI;
 k = if (dpFixed_nominal > Modelica.Constants.eps) then sqrt(1/(1/kFixed^2 + 1/kVal^2)) else kVal;

 if linearized then
   // This implementation yields m_flow_nominal = phi*kv_SI * sqrt(dp_nominal)
   // if m_flow = m_flow_nominal and dp = dp_nominal
   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;
   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;
    end if; // homotopyInitialization
 end if; // linearized
end PartialTwoWayValve;

Buildings.Fluid.Actuators.BaseClasses.ValveParameters

Model with parameters for valves

Information

Model that computes the flow coefficients of valves. This base class allows the following modeling options, which have been adapted from the valve implementation in Modelica.Fluid to specify the valve flow coefficient in fully open conditions:

CvData = Buildings.Fluid.Types.CvTypes.Av: the flow coefficient is given by the metric Av coefficient (m^2).
CvData = Buildings.Fluid.Types.CvTypes.Kv: the flow coefficient is given by the metric Kv coefficient (m^3/h).
CvData = Buildings.Fluid.Types.CvTypes.Cv: the flow coefficient is given by the US Cv coefficient (USG/min).
CvData = Buildings.Fluid.Types.CvTypes.OpPoint: the flow is computed from the nominal operating point specified by dp_nominal and m_flow_nominal.

The treatment of parameters Kv and Cv is explained in detail in the Users Guide.

In contrast to the model in Modelica.Fluid, this model uses the protected parameter Kv_SI, which is the flow coefficient in SI units, i.e., it is the ratio between mass flow rate in kg/s and square root of pressure drop in Pa. The value of Kv_SI is computed based on the parameters Av, Kv, Cv, or, if CvData = Buildings.Fluid.Types.CvTypes.OpPoint, based on m_flow_nominal and dpValve_nominal. Conversely, if CvData <> Buildings.Fluid.Types.CvTypes.OpPoint, then dpValve_nominal is computed based on Av, Kv, or Cv, and the nominal mass flow rate m_flow_nominal. Therefore, if CvData <> Buildings.Fluid.Types.CvTypes.OpPoint, then specifying a value for dpValve_nominal is a syntax error.

Parameters

Type Name Default Description

Flow Coefficient

CvTypes CvData Buildings.Fluid.Types.CvType... Selection of flow coefficient

Real Kv Kv (metric) flow coefficient [m3/h/(bar)^(1/2)]

Real Cv Cv (US) flow coefficient [USG/min/(psi)^(1/2)]

Area Av Av (metric) flow coefficient [m2]

Pressure-flow linearization

Real deltaM 0.02 Fraction of nominal flow rate where linearization starts, if y=1

Nominal condition

MassFlowRate m_flow_nominal Nominal mass flow rate [kg/s]

Pressure dpValve_nominal Nominal pressure drop of fully open valve, used if CvData=Buildings.Fluid.Types.CvTypes.OpPoint [Pa]

Advanced

Nominal condition

Density rhoStd Inlet density for which valve coefficients are defined [kg/m3]

Type	Name	Default	Description
Flow Coefficient
CvTypes	CvData	Buildings.Fluid.Types.CvType...	Selection of flow coefficient
Real	Kv		Kv (metric) flow coefficient [m3/h/(bar)^(1/2)]
Real	Cv		Cv (US) flow coefficient [USG/min/(psi)^(1/2)]
Area	Av		Av (metric) flow coefficient [m2]
Pressure-flow linearization
Real	deltaM	0.02	Fraction of nominal flow rate where linearization starts, if y=1
Nominal condition
MassFlowRate	m_flow_nominal		Nominal mass flow rate [kg/s]
Pressure	dpValve_nominal		Nominal pressure drop of fully open valve, used if CvData=Buildings.Fluid.Types.CvTypes.OpPoint [Pa]
Advanced
Nominal condition
Density	rhoStd		Inlet density for which valve coefficients are defined [kg/m3]

Modelica definition

partial model ValveParameters "Model with parameters for valves"

  parameter Buildings.Fluid.Types.CvTypes CvData=Buildings.Fluid.Types.CvTypes.OpPoint 
    "Selection of flow coefficient";
  parameter Real Kv(
    fixed= if CvData==Buildings.Fluid.Types.CvTypes.Kv then true else false) 
    "Kv (metric) flow coefficient [m3/h/(bar)^(1/2)]";
  parameter Real Cv(
    fixed= if CvData==Buildings.Fluid.Types.CvTypes.Cv then true else false) 
    "Cv (US) flow coefficient [USG/min/(psi)^(1/2)]";
  parameter Modelica.SIunits.Area Av(
    fixed= if CvData==Buildings.Fluid.Types.CvTypes.Av then true else false) 
    "Av (metric) flow coefficient";

  parameter Real deltaM = 0.02 
    "Fraction of nominal flow rate where linearization starts, if y=1";
  parameter Modelica.SIunits.MassFlowRate m_flow_nominal 
    "Nominal mass flow rate";
  parameter Modelica.SIunits.Pressure dpValve_nominal(displayUnit="Pa",
                                                      min=Modelica.Constants.small,
                                                      fixed= if CvData==Buildings.Fluid.Types.CvTypes.OpPoint then true else false) 
    "Nominal pressure drop of fully open valve, used if CvData=Buildings.Fluid.Types.CvTypes.OpPoint";

  parameter Modelica.SIunits.Density rhoStd 
    "Inlet density for which valve coefficients are defined";

protected 
  parameter Real Kv_SI(
    min=0,
    fixed= false) 
    "Flow coefficient for fully open valve in SI units, Kv=m_flow/sqrt(dp) [kg/s/(Pa)^(1/2)]";
initial algorithm 
  if  CvData == Buildings.Fluid.Types.CvTypes.OpPoint then
    Kv_SI :=           m_flow_nominal/sqrt(dpValve_nominal);
    Kv    :=           Kv_SI/(rhoStd/3600/sqrt(1E5));
    Cv    :=           Kv_SI/(rhoStd*0.0631/1000/sqrt(6895));
    Av    :=           Kv_SI/sqrt(rhoStd);
  elseif CvData == Buildings.Fluid.Types.CvTypes.Kv then
    Kv_SI :=           Kv*rhoStd/3600/sqrt(1E5) 
      "Unit conversion m3/(h*sqrt(bar)) to kg/(s*sqrt(Pa))";
    Cv    :=           Kv_SI/(rhoStd*0.0631/1000/sqrt(6895));
    Av    :=           Kv_SI/sqrt(rhoStd);
    dpValve_nominal := (m_flow_nominal/Kv_SI)^2;
  elseif CvData == Buildings.Fluid.Types.CvTypes.Cv then
    Kv_SI :=           Cv*rhoStd*0.0631/1000/sqrt(6895) 
      "Unit conversion USG/(min*sqrt(psi)) to kg/(s*sqrt(Pa))";
    Kv    :=           Kv_SI/(rhoStd/3600/sqrt(1E5));
    Av    :=           Kv_SI/sqrt(rhoStd);
    dpValve_nominal := (m_flow_nominal/Kv_SI)^2;
  else
    assert(CvData == Buildings.Fluid.Types.CvTypes.Av, "Invalid value for CvData.
Obtained CvData = " + String(CvData) + ".");
    Kv_SI :=           Av*sqrt(rhoStd);
    Kv    :=           Kv_SI/(rhoStd/3600/sqrt(1E5));
    Cv    :=           Kv_SI/(rhoStd*0.0631/1000/sqrt(6895));
    dpValve_nominal := (m_flow_nominal/Kv_SI)^2;
  end if;

end ValveParameters;

Buildings.Fluid.Actuators.BaseClasses.der_equalPercentage

Derivative of valve opening characteristics for equal percentage valve

Information

This function computes the derivative of the opening characteristics of an equal percentage valve.

The function is the derivative of TwoWayValveEqualPercentage.

Inputs

Type Name Default Description

Real y Valve opening signal, y=1 is fully open

Real R Rangeability, R=50...100 typically

Real l Valve leakage, l=Kv(y=0)/Kv(y=1)

Real delta Range of significant deviation from equal percentage law

Real der_y Derivative of valve opening signal

Type	Name	Description
Real	y	Valve opening signal, y=1 is fully open
Real	R	Rangeability, R=50...100 typically
Real	l	Valve leakage, l=Kv(y=0)/Kv(y=1)
Real	delta	Range of significant deviation from equal percentage law
Real	der_y	Derivative of valve opening signal

Outputs

Type Name Description

Real der_phi Derivative of ratio actual to nominal mass flow rate, dphi/dy

Type	Name	Description
Real	der_phi	Derivative of ratio actual to nominal mass flow rate, dphi/dy

Modelica definition

function der_equalPercentage 
  "Derivative of valve opening characteristics for equal percentage valve"

  input Real y "Valve opening signal, y=1 is fully open";
  input Real R "Rangeability, R=50...100 typically";
  input Real l(min=0, max=1) "Valve leakage, l=Kv(y=0)/Kv(y=1)";
  input Real delta "Range of significant deviation from equal percentage law";
  input Real der_y "Derivative of valve opening signal";
  output Real der_phi 
    "Derivative of ratio actual to nominal mass flow rate, dphi/dy";
protected 
   Real a "Polynomial coefficient";
   Real b "Polynomial coefficient";
   Real c "Polynomial coefficient";
   Real logR "=log(R)";
   Real z "Auxiliary variable";
   Real q "Auxiliary variable";
   Real p "Auxiliary variable";
algorithm 
  if y < delta/2 then
    der_phi := (R^(delta-1) - l) / delta * der_y;
  else
    if (y > (3/2 * delta)) then
      der_phi := R^(y-1)*Modelica.Math.log(R) * der_y;
    else
      logR := Modelica.Math.log(R);
      z := (3*delta/2);
      q := delta*R^z*logR;
      p := R^z;
      a := (q - 2*p + 2*R^delta)/(delta^3*R);
      b := (-5*q + 12*p - 13*R^delta + l*R)/(2*delta^2*R);
      c := (7*q - 18*p + 24*R^delta - 6*l*R)/(4*delta*R);
      der_phi  := (c + y * ( 2*b + 3*a*y)) * der_y;
    end if;
  end if;
end der_equalPercentage;

Buildings.Fluid.Actuators.BaseClasses.equalPercentage

Valve opening characteristics for equal percentage valve

Information

This function computes the opening characteristics of an equal percentage valve.

The function is used by the model TwoWayValveEqualPercentage.

For y < delta/2, the valve characteristics is linear. For y > 3*delta/2 the valve characteristics is equal percentage. In between, a cubic spline is used to ensure that the valve characteristics is once continuously differentiable with respect to y.

Inputs

Type	Name	Description
Real	y	Valve opening signal, y=1 is fully open
Real	R	Rangeability, R=50...100 typically
Real	l	Valve leakage, l=Kv(y=0)/Kv(y=1)
Real	delta	Range of significant deviation from equal percentage law

Outputs

Type Name Description

Real phi Ratio actual to nominal mass flow rate, phi=Cv(y)/Cv(y=1)

Type	Name	Description
Real	phi	Ratio actual to nominal mass flow rate, phi=Cv(y)/Cv(y=1)

Modelica definition

function equalPercentage 
  "Valve opening characteristics for equal percentage valve"
  annotation(derivative=der_equalPercentage);

  input Real y "Valve opening signal, y=1 is fully open";
  input Real R "Rangeability, R=50...100 typically";
  input Real l(min=0, max=1) "Valve leakage, l=Kv(y=0)/Kv(y=1)";
  input Real delta "Range of significant deviation from equal percentage law";
  output Real phi "Ratio actual to nominal mass flow rate, phi=Cv(y)/Cv(y=1)";
protected 
   Real a "Polynomial coefficient";
   Real b "Polynomial coefficient";
   Real c "Polynomial coefficient";
   Real d "Polynomial coefficient";
   Real logR "=log(R)";
   Real z "Auxiliary variable";
   Real q "Auxiliary variable";
   Real p "Auxiliary variable";
algorithm 
  if y < delta/2 then
    phi := l + y * (R^(delta-1) - l) / delta;
  else
    if (y > (3/2 * delta)) then
      phi := R^(y-1);
    else
      logR := Modelica.Math.log(R);
      z := (3*delta/2);
      q := delta*R^z*logR;
      p := R^z;
      a := (q - 2*p + 2*R^delta)/(delta^3*R);
      b := (-5*q + 12*p - 13*R^delta + l*R)/(2*delta^2*R);
      c := (7*q - 18*p + 24*R^delta - 6*l*R)/(4*delta*R);
      d := (-3*q + 8*p - 9*R^delta + 9*l*R)/(8*R);
      phi  := d + y * ( c + y * ( b + y * a));
    end if;
  end if;
end equalPercentage;

Buildings.Fluid.Actuators.BaseClasses.exponentialDamper

Damper opening characteristics for an exponential damper

Information

This function computes the opening characteristics of an exponential damper.

The function is used by the model Dampers.Exponential.

For yL < y < yU, the damper characteristics is

k = exp(a+b (1-y)).

Outside this range, the damper characteristic is defined by a quadratic polynomial.

Note that this implementation returns sqrt(k) instead of k. This is done for numerical reason since otherwise k may be an iteration variable, which may cause a lot of warnings and slower convergence if the solver attempts k < 0 during the iterative solution procedure.

Inputs

Type Name Default Description

Real y Control signal, y=0 is closed, y=1 is open

Real a Coefficient a for damper characteristics

Real b Coefficient b for damper characteristics

Real cL[3] Polynomial coefficients for curve fit for y < yl

Real cU[3] Polynomial coefficients for curve fit for y > yu

Real yL Lower value for damper curve

Real yU Upper value for damper curve

Type	Name	Description
Real	y	Control signal, y=0 is closed, y=1 is open
Real	a	Coefficient a for damper characteristics
Real	b	Coefficient b for damper characteristics
Real	cL[3]	Polynomial coefficients for curve fit for y < yl
Real	cU[3]	Polynomial coefficients for curve fit for y > yu
Real	yL	Lower value for damper curve
Real	yU	Upper value for damper curve

Outputs

Type Name Description

Real kThetaSqRt Flow coefficient, kThetaSqRT = =sqrt(kTheta) = sqrt(pressure drop/dynamic pressure)

Type	Name	Description
Real	kThetaSqRt	Flow coefficient, kThetaSqRT = =sqrt(kTheta) = sqrt(pressure drop/dynamic pressure)

Modelica definition

function exponentialDamper 
  "Damper opening characteristics for an exponential damper"
  input Real y(min=0, max=1, unit="") 
    "Control signal, y=0 is closed, y=1 is open";
  input Real a(unit="") "Coefficient a for damper characteristics";
  input Real b(unit="") "Coefficient b for damper characteristics";
  input Real[3] cL "Polynomial coefficients for curve fit for y < yl";
  input Real[3] cU "Polynomial coefficients for curve fit for y > yu";
  input Real yL "Lower value for damper curve";
  input Real yU "Upper value for damper curve";
  output Real kThetaSqRt(min=0) 
    "Flow coefficient, kThetaSqRT = =sqrt(kTheta) = sqrt(pressure drop/dynamic pressure)";
protected 
  Real yC(min=0, max=1, unit="") 
    "y constrained to 0 <= y <= 1 to avoid numerical problems";
algorithm 
  if y < yL then
    yC :=max(0, y);
    kThetaSqRt := sqrt(Modelica.Math.exp(cL[3] + yC * (cL[2] + yC * cL[1])));
  else
    if (y > yU) then
      yC := min(1, y);
      kThetaSqRt := sqrt(Modelica.Math.exp(cU[3] + yC * (cU[2] + yC * cU[1])));
    else
      kThetaSqRt := sqrt(Modelica.Math.exp(a+b*(1-y))) "y=0 is closed";
    end if;
  end if;
end exponentialDamper;

Automatically generated Wed May 15 11:55:07 2013.