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Annex60.Fluid.Actuators.Dampers

Package with air damper models

Information

This package contains components models for air dampers. For motor models, see Annex60.Fluid.Actuators.Motors.

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

Package Content

Name Description
Annex60.Fluid.Actuators.Dampers.Exponential Exponential Air damper with exponential opening characteristics
Annex60.Fluid.Actuators.Dampers.MixingBox MixingBox Outside air mixing box with interlocked air dampers
Annex60.Fluid.Actuators.Dampers.VAVBoxExponential VAVBoxExponential VAV box with a fixed resistance plus a damper model withe exponential characteristics
Annex60.Fluid.Actuators.Dampers.Examples Examples Collection of models that illustrate model use and test models

Annex60.Fluid.Actuators.Dampers.Exponential Annex60.Fluid.Actuators.Dampers.Exponential

Air damper with exponential opening characteristics

Annex60.Fluid.Actuators.Dampers.Exponential

Information

This model is an air damper with flow coefficient that is an exponential function of the opening angle. The model is as in ASHRAE 825-RP. A control signal of y=0 means the damper is closed, and y=1 means the damper is open. This is opposite of the implementation of ASHRAE 825-RP, but used here for consistency within this library.

For yL < y < yU, the damper characteristics is

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

Outside this range, the damper characteristic is defined by a quadratic polynomial that matches the damper resistance at y=0 and y=yL or y=yU and y=1, respectively. In addition, the polynomials are such that kd(y) is differentiable in y and the derivative is continuous.

The damper characteristics kd(y) is then used to compute the flow coefficient k(y) as

k(y) = (2 ρ ⁄ kd(y))1/2 A,

where A is the face area. The flow coefficient k(y) is used to compute the mass flow rate versus pressure drop relation as

m = sign(Δp) k(y) √ Δp  

with regularization near the origin.

ASHRAE 825-RP lists the following parameter values as typical:

opposed bladessingle blades
yL15/9015/90
yU55/9065/90
k01E61E6
k10.2 to 0.50.2 to 0.5
a-1.51-1.51
b0.105*900.0842*90

References

P. Haves, L. K. Norford, M. DeSimone and L. Mei, A Standard Simulation Testbed for the Evaluation of Control Algorithms & Strategies, ASHRAE Final Report 825-RP, Atlanta, GA.

Extends from Annex60.Fluid.Actuators.BaseClasses.PartialDamperExponential (Partial model for air dampers with exponential opening characteristics).

Parameters

TypeNameDefaultDescription
replaceable package MediumPartialMediumMedium in the component
MassFlowRatem_flow_turbulentif use_deltaM then deltaM*m_...Turbulent flow if |m_flow| >= m_flow_turbulent [kg/s]
Booleanuse_deltaMtrueSet to true to use deltaM for turbulent transition, else ReC is used
RealdeltaM0.3Fraction of nominal mass flow rate where transition to turbulent occurs
Booleanuse_v_nominaltrueSet to true to use face velocity to compute area
Velocityv_nominal1Nominal face velocity [m/s]
AreaAm_flow_nominal/rho_default/v...Face area [m2]
BooleanroundDuctfalseSet to true for round duct, false for square cross section
RealReC4000Reynolds number where transition to turbulent starts
RealkFixed0Flow coefficient of fixed resistance that may be in series with damper, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2).
Nominal condition
MassFlowRatem_flow_nominal Nominal mass flow rate [kg/s]
PressureDifferencedp_nominal(m_flow_nominal/kDam_default...Pressure drop at nominal mass flow rate [Pa]
Assumptions
BooleanallowFlowReversaltrue= false to simplify equations, assuming, but not enforcing, no flow reversal
Advanced
Diagnostics
Booleanshow_Tfalse= true, if actual temperature at port is computed
Booleanfrom_dpfalse= true, use m_flow = f(dp) else dp = f(m_flow)
BooleanhomotopyInitializationtrue= true, use homotopy method
Booleanlinearizedfalse= true, use linear relation between m_flow and dp for any flow rate
Booleanuse_constant_densitytrueSet to true to use constant density for flow friction
Dynamics
Filtered opening
BooleanfilteredOpeningtrue= true, if opening is filtered with a 2nd order CriticalDamping filter
TimeriseTime120Rise time of the filter (time to reach 99.6 % of an opening step) [s]
InitinitModelica.Blocks.Types.Init.I...Type of initialization (no init/steady state/initial state/initial output)
Realy_start1Initial value of output
Damper coefficients
Reala-1.51Coefficient a for damper characteristics
Realb0.105*90Coefficient b for damper characteristics
RealyL15/90Lower value for damper curve
RealyU55/90Upper value for damper curve
Realk01E6Flow coefficient for y=0, k0 = pressure drop divided by dynamic pressure
Realk10.45Flow coefficient for y=1, k1 = pressure drop divided by dynamic pressure

Connectors

TypeNameDescription
FluidPort_aport_aFluid connector a (positive design flow direction is from port_a to port_b)
FluidPort_bport_bFluid connector b (positive design flow direction is from port_a to port_b)
input RealInputyActuator position (0: closed, 1: open)
output RealOutputy_actualActual valve position

Modelica definition

model Exponential "Air damper with exponential opening characteristics" extends Annex60.Fluid.Actuators.BaseClasses.PartialDamperExponential( final dp_nominal=(m_flow_nominal/kDam_default)^2, dp(nominal=10), final kFixed=0); protected parameter Real kDam_default = sqrt(2*rho_default)*A/kThetaSqRt_default "Flow coefficient for damper, k=m_flow/sqrt(dp), with unit=(kg*m)^(1/2)"; parameter Real kThetaSqRt_default(min=0)= Annex60.Fluid.Actuators.BaseClasses.exponentialDamper( y=1, a=a, b=b, cL=cL, cU=cU, yL=yL, yU=yU) "Flow coefficient, kThetaSqRt = sqrt(pressure drop divided by dynamic pressure)"; initial algorithm assert(kThetaSqRt_default>0, "Flow coefficient must be strictly positive."); end Exponential;

Annex60.Fluid.Actuators.Dampers.MixingBox Annex60.Fluid.Actuators.Dampers.MixingBox

Outside air mixing box with interlocked air dampers

Annex60.Fluid.Actuators.Dampers.MixingBox

Information

Model of an outside air mixing box with air dampers. Set y=0 to close the outside air and exhast air dampers.

If dp_nominalIncludesDamper=true, then the parameter dp_nominal is equal to the pressure drop of the damper plus the fixed flow resistance at the nominal flow rate. If dp_nominalIncludesDamper=false, then dp_nominal does not include the flow resistance of the air damper.

Extends from Annex60.Fluid.Actuators.BaseClasses.ActuatorSignal (Partial model that implements the filtered opening for valves and dampers).

Parameters

TypeNameDefaultDescription
replaceable package MediumModelica.Media.Interfaces.Pa...Medium in the component
Booleanuse_deltaMtrueSet to true to use deltaM for turbulent transition, else ReC is used
RealdeltaM0.3Fraction of nominal mass flow rate where transition to turbulent occurs
Booleanuse_v_nominaltrueSet to true to use face velocity to compute area
Velocityv_nominal1Nominal face velocity [m/s]
BooleanroundDuctfalseSet to true for round duct, false for square cross section
RealReC4000Reynolds number where transition to turbulent starts
AreaAOutmOut_flow_nominal/rho_defaul...Face area outside air damper [m2]
AreaAExhmExh_flow_nominal/rho_defaul...Face area exhaust air damper [m2]
AreaARecmRec_flow_nominal/rho_defaul...Face area recirculation air damper [m2]
Nominal condition
Booleandp_nominalIncludesDamperfalseset to true if dp_nominal includes the pressure loss of the open damper
MassFlowRatemOut_flow_nominal Mass flow rate outside air damper [kg/s]
PressureDifferencedpOut_nominal Pressure drop outside air leg [Pa]
MassFlowRatemRec_flow_nominal Mass flow rate recirculation air damper [kg/s]
PressureDifferencedpRec_nominal Pressure drop recirculation air leg [Pa]
MassFlowRatemExh_flow_nominal Mass flow rate exhaust air damper [kg/s]
PressureDifferencedpExh_nominal Pressure drop exhaust air leg [Pa]
Dynamics
Filtered opening
BooleanfilteredOpeningtrue= true, if opening is filtered with a 2nd order CriticalDamping filter
TimeriseTime120Rise time of the filter (time to reach 99.6 % of an opening step) [s]
InitinitModelica.Blocks.Types.Init.I...Type of initialization (no init/steady state/initial state/initial output)
Realy_start1Initial value of output
Assumptions
BooleanallowFlowReversaltrue= false to simplify equations, assuming, but not enforcing, no flow reversal
Advanced
Booleanfrom_dptrue= true, use m_flow = f(dp) else dp = f(m_flow)
Booleanlinearizedfalse= true, use linear relation between m_flow and dp for any flow rate
Booleanuse_constant_densitytrueSet to true to use constant density for flow friction
Damper coefficients
Reala-1.51Coefficient a for damper characteristics
Realb0.105*90Coefficient b for damper characteristics
RealyL15/90Lower value for damper curve
RealyU55/90Upper value for damper curve
Realk01E6Flow coefficient for y=0, k0 = pressure drop divided by dynamic pressure
Realk10.45Flow coefficient for y=1, k1 = pressure drop divided by dynamic pressure

Connectors

TypeNameDescription
input RealInputyActuator position (0: closed, 1: open)
output RealOutputy_actualActual valve position
replaceable package MediumMedium in the component
FluidPort_aport_OutFluid connector a (positive design flow direction is from port_a to port_b)
FluidPort_bport_ExhFluid connector b (positive design flow direction is from port_a to port_b)
FluidPort_aport_RetFluid connector a (positive design flow direction is from port_a to port_b)
FluidPort_bport_SupFluid connector b (positive design flow direction is from port_a to port_b)

Modelica definition

model MixingBox "Outside air mixing box with interlocked air dampers" extends Annex60.Fluid.Actuators.BaseClasses.ActuatorSignal; replaceable package Medium = Modelica.Media.Interfaces.PartialMedium "Medium in the component"; import Modelica.Constants; parameter Boolean allowFlowReversal = true "= false to simplify equations, assuming, but not enforcing, no flow reversal"; VAVBoxExponential damOA(A=AOut, redeclare package Medium = Medium, dp_nominal=dpOut_nominal, dp_nominalIncludesDamper=dp_nominalIncludesDamper, from_dp=from_dp, linearized=linearized, use_deltaM=use_deltaM, deltaM=deltaM, use_v_nominal=use_v_nominal, v_nominal=v_nominal, roundDuct=roundDuct, ReC=ReC, a=a, b=b, yL=yL, yU=yU, k0=k0, k1=k1, use_constant_density=use_constant_density, allowFlowReversal=allowFlowReversal, m_flow_nominal=mOut_flow_nominal, final filteredOpening=false); 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 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 Modelica.SIunits.Area AOut=mOut_flow_nominal/rho_default/v_nominal "Face area outside air damper"; VAVBoxExponential damExh(A=AExh, redeclare package Medium = Medium, m_flow_nominal=mExh_flow_nominal, dp_nominal=dpExh_nominal, dp_nominalIncludesDamper=dp_nominalIncludesDamper, from_dp=from_dp, linearized=linearized, use_deltaM=use_deltaM, deltaM=deltaM, use_v_nominal=use_v_nominal, v_nominal=v_nominal, roundDuct=roundDuct, ReC=ReC, a=a, b=b, yL=yL, yU=yU, k0=k0, k1=k1, use_constant_density=use_constant_density, allowFlowReversal=allowFlowReversal, final filteredOpening=false) "Exhaust air damper"; parameter Modelica.SIunits.Area AExh=mExh_flow_nominal/rho_default/v_nominal "Face area exhaust air damper"; VAVBoxExponential damRec(A=ARec, redeclare package Medium = Medium, m_flow_nominal=mRec_flow_nominal, dp_nominal=dpRec_nominal, dp_nominalIncludesDamper=dp_nominalIncludesDamper, from_dp=from_dp, linearized=linearized, use_deltaM=use_deltaM, deltaM=deltaM, use_v_nominal=use_v_nominal, v_nominal=v_nominal, roundDuct=roundDuct, ReC=ReC, a=a, b=b, yL=yL, yU=yU, k0=k0, k1=k1, use_constant_density=use_constant_density, allowFlowReversal=allowFlowReversal, final filteredOpening=false) "Recirculation air damper"; parameter Modelica.SIunits.Area ARec=mRec_flow_nominal/rho_default/v_nominal "Face area recirculation air damper"; parameter Boolean dp_nominalIncludesDamper=false "set to true if dp_nominal includes the pressure loss of the open damper"; parameter Modelica.SIunits.MassFlowRate mOut_flow_nominal "Mass flow rate outside air damper"; parameter Modelica.SIunits.PressureDifference dpOut_nominal(min=0, displayUnit="Pa") "Pressure drop outside air leg"; parameter Modelica.SIunits.MassFlowRate mRec_flow_nominal "Mass flow rate recirculation air damper"; parameter Modelica.SIunits.PressureDifference dpRec_nominal(min=0, displayUnit="Pa") "Pressure drop recirculation air leg"; parameter Modelica.SIunits.MassFlowRate mExh_flow_nominal "Mass flow rate exhaust air damper"; parameter Modelica.SIunits.PressureDifference dpExh_nominal(min=0, displayUnit="Pa") "Pressure drop exhaust air leg"; parameter Boolean from_dp=true "= true, use m_flow = f(dp) else dp = f(m_flow)"; parameter Boolean linearized=false "= true, use linear relation between m_flow and dp for any flow rate"; parameter Boolean use_constant_density=true "Set to true to use constant density for flow friction"; parameter Real a=-1.51 "Coefficient a for damper characteristics"; parameter Real b=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=1E6 "Flow coefficient for y=0, k0 = pressure drop divided by dynamic pressure"; parameter Real k1=0.45 "Flow coefficient for y=1, k1 = pressure drop divided by dynamic pressure"; Modelica.Fluid.Interfaces.FluidPort_a port_Out(redeclare package Medium = Medium, m_flow(start=0, min=if allowFlowReversal then -Constants.inf else 0)) "Fluid connector a (positive design flow direction is from port_a to port_b)"; Modelica.Fluid.Interfaces.FluidPort_b port_Exh(redeclare package Medium = Medium, m_flow(start=0, max=if allowFlowReversal then +Constants.inf else 0)) "Fluid connector b (positive design flow direction is from port_a to port_b)"; Modelica.Fluid.Interfaces.FluidPort_a port_Ret(redeclare package Medium = Medium, m_flow(start=0, min=if allowFlowReversal then -Constants.inf else 0)) "Fluid connector a (positive design flow direction is from port_a to port_b)"; Modelica.Fluid.Interfaces.FluidPort_b port_Sup(redeclare package Medium = Medium, m_flow(start=0, max=if allowFlowReversal then +Constants.inf else 0)) "Fluid connector b (positive design flow direction is from port_a to port_b)"; Modelica.Blocks.Sources.Constant uni(k=1) "Unity signal"; Modelica.Blocks.Math.Add add(k2=-1) "Adder"; protected parameter Medium.Density rho_default=Medium.density(sta_default) "Density, used to compute fluid volume"; parameter Medium.ThermodynamicState sta_default= Medium.setState_pTX(T=Medium.T_default, p=Medium.p_default, X=Medium.X_default) "Default medium state"; equation connect(uni.y, add.u1); connect(add.y, damRec.y); connect(damOA.port_a, port_Out); connect(damExh.port_b, port_Exh); connect(port_Sup, damOA.port_b); connect(damRec.port_b, port_Sup); connect(port_Ret, damExh.port_a); connect(port_Ret, damRec.port_a); connect(y_actual, add.u2); connect(y_actual, damOA.y); connect(y_actual, damExh.y); end MixingBox;

Annex60.Fluid.Actuators.Dampers.VAVBoxExponential Annex60.Fluid.Actuators.Dampers.VAVBoxExponential

VAV box with a fixed resistance plus a damper model withe exponential characteristics

Annex60.Fluid.Actuators.Dampers.VAVBoxExponential

Information

Model of two resistances in series. One resistance has a fixed flow coefficient, the other resistance is an air damper whose flow coefficient is an exponential function of the opening angle.

If dp_nominalIncludesDamper=true, then the parameter dp_nominal is equal to the pressure drop of the damper plus the fixed flow resistance at the nominal flow rate. If dp_nominalIncludesDamper=false, then dp_nominal does not include the flow resistance of the air damper.

Extends from Annex60.Fluid.Actuators.BaseClasses.PartialDamperExponential (Partial model for air dampers with exponential opening characteristics).

Parameters

TypeNameDefaultDescription
replaceable package MediumPartialMediumMedium in the component
MassFlowRatem_flow_turbulentif use_deltaM then deltaM*m_...Turbulent flow if |m_flow| >= m_flow_turbulent [kg/s]
Booleanuse_deltaMtrueSet to true to use deltaM for turbulent transition, else ReC is used
RealdeltaM0.3Fraction of nominal mass flow rate where transition to turbulent occurs
Booleanuse_v_nominaltrueSet to true to use face velocity to compute area
Velocityv_nominal1Nominal face velocity [m/s]
AreaAm_flow_nominal/rho_default/v...Face area [m2]
BooleanroundDuctfalseSet to true for round duct, false for square cross section
RealReC4000Reynolds number where transition to turbulent starts
RealkFixedsqrt(kResSqu)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
MassFlowRatem_flow_nominal Nominal mass flow rate [kg/s]
PressureDifferencedp_nominal Pressure drop at nominal mass flow rate [Pa]
Booleandp_nominalIncludesDampertrueset to true if dp_nominal includes the pressure loss of the open damper
Assumptions
BooleanallowFlowReversaltrue= false to simplify equations, assuming, but not enforcing, no flow reversal
Advanced
Diagnostics
Booleanshow_Tfalse= true, if actual temperature at port is computed
Booleanfrom_dpfalse= true, use m_flow = f(dp) else dp = f(m_flow)
BooleanhomotopyInitializationtrue= true, use homotopy method
Booleanlinearizedfalse= true, use linear relation between m_flow and dp for any flow rate
Booleanuse_constant_densitytrueSet to true to use constant density for flow friction
Dynamics
Filtered opening
BooleanfilteredOpeningtrue= true, if opening is filtered with a 2nd order CriticalDamping filter
TimeriseTime120Rise time of the filter (time to reach 99.6 % of an opening step) [s]
InitinitModelica.Blocks.Types.Init.I...Type of initialization (no init/steady state/initial state/initial output)
Realy_start1Initial value of output
Damper coefficients
Reala-1.51Coefficient a for damper characteristics
Realb0.105*90Coefficient b for damper characteristics
RealyL15/90Lower value for damper curve
RealyU55/90Upper value for damper curve
Realk01E6Flow coefficient for y=0, k0 = pressure drop divided by dynamic pressure
Realk10.45Flow coefficient for y=1, k1 = pressure drop divided by dynamic pressure

Connectors

TypeNameDescription
FluidPort_aport_aFluid connector a (positive design flow direction is from port_a to port_b)
FluidPort_bport_bFluid connector b (positive design flow direction is from port_a to port_b)
input RealInputyActuator position (0: closed, 1: open)
output RealOutputy_actualActual valve position

Modelica definition

model VAVBoxExponential "VAV box with a fixed resistance plus a damper model withe exponential characteristics" extends Annex60.Fluid.Actuators.BaseClasses.PartialDamperExponential( dp(nominal=dp_nominal), final kFixed=sqrt(kResSqu)); parameter Boolean dp_nominalIncludesDamper = true "set to true if dp_nominal includes the pressure loss of the open damper"; protected parameter Modelica.SIunits.PressureDifference dpDamOpe_nominal(displayUnit="Pa")= k1*m_flow_nominal^2/2/Medium.density(sta_default)/A^2 "Pressure drop of fully open damper at nominal flow rate"; parameter Real kResSqu(unit="kg.m", fixed=false) "Resistance coefficient for fixed resistance element"; initial equation kResSqu = if dp_nominalIncludesDamper then m_flow_nominal^2 / (dp_nominal-dpDamOpe_nominal) else m_flow_nominal^2 / dp_nominal; assert(kResSqu > 0, "Wrong parameters in damper model: dp_nominal < dpDamOpe_nominal" + "\n dp_nominal = " + String(dp_nominal) + "\n dpDamOpe_nominal = " + String(dpDamOpe_nominal)); end VAVBoxExponential;
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