modelExponential

Air damper with exponential opening characteristics

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

Information

Model of two flow resistances in series:

one resistance has a fixed flow coefficient;
the other resistance represents a damper whose flow coefficient is an exponential function of the opening angle.

The lumped flow coefficient k(y) (function of the fractional opening y) is used to compute the mass flow rate versus pressure drop relation as:

ṁ = sign(Δp) k(y) √ Δp

with regularization near the origin.

For a description of the damper opening characteristics and typical parameter values, see the partial model Buildings.Fluid.Actuators.BaseClasses.PartialDamperExponential.

Parameters

Type	Name	Default	Description
Boolean	homotopyInitialization (from PartialResistance)	true	= true, use homotopy method
Modelica.Units.SI.MassFlowRate	m_flow_turbulent (from PartialResistance)		Turbulent flow if \|m_flow\| >= m_flow_turbulent
Boolean	use_deltaM (from PartialDamperExponential)	true	Set to true to use deltaM for turbulent transition, else ReC is used
Real	deltaM (from PartialDamperExponential)	0.3	Fraction of nominal mass flow rate where transition to turbulent occurs
Modelica.Units.SI.Velocity	v_nominal (from PartialDamperExponential)	(2/rho_default/k1*dpDamper_nominal)^0.5	Nominal face velocity
Modelica.Units.SI.Area	A (from PartialDamperExponential)	m_flow_nominal/rho_default/v_nominal	Face area
Boolean	roundDuct (from PartialDamperExponential)	false	Set to true for round duct, false for square cross section
Real	ReC (from PartialDamperExponential)	4000	Reynolds number where transition to turbulence starts
Real	kFixed (from PartialDamperExponential)	if dpFixed_nominal > Modelica.Constants.eps then m_flow_nominal/sqrt(dpFixed_nominal) else Modelica.Constants.inf	Flow coefficient of fixed resistance that may be in series with damper, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2).
Assumptions
Boolean	allowFlowReversal (from PartialTwoPort)	true	= false to simplify equations, assuming, but not enforcing, no flow reversal
Nominal condition
Modelica.Units.SI.MassFlowRate	m_flow_nominal (from PartialTwoPortInterface)		Nominal mass flow rate
Modelica.Units.SI.PressureDifference	dp_nominal (from PartialResistance)		Pressure drop at nominal mass flow rate
Modelica.Units.SI.PressureDifference	dpDamper_nominal (from PartialDamperExponential)		Pressure drop of fully open damper at nominal mass flow rate
Modelica.Units.SI.PressureDifference	dpFixed_nominal (from PartialDamperExponential)	0	Pressure drop of duct and resistances other than the damper in series, at nominal mass flow rate
Advanced
Modelica.Units.SI.MassFlowRate	m_flow_small (from PartialTwoPortInterface)	1E-4*abs(m_flow_nominal)	Small mass flow rate for regularization of zero flow
Boolean	from_dp (from PartialResistance)	false	= true, use m_flow = f(dp) else dp = f(m_flow)
Real	n (from PartialResistance)	2	Flow exponent, n=1 for laminar, n=2 for turbulent
Boolean	linearized (from PartialResistance)	false	= true, use linear relation between m_flow and dp for any flow rate
Boolean	use_constant_density (from PartialDamperExponential)	true	Set to true to use constant density for flow friction
Advanced › Diagnostics
Boolean	show_T (from PartialTwoPortInterface)	false	= true, if actual temperature at port is computed
Dynamics › Actuator position
Boolean	use_strokeTime (from ActuatorSignal)	true	Set to true to continuously open and close valve using strokeTime
Modelica.Units.SI.Time	strokeTime (from ActuatorSignal)	120	Time needed to fully open or close actuator
Modelica.Blocks.Types.Init	init (from ActuatorSignal)	Modelica.Blocks.Types.Init.InitialOutput	Type of initialization (no init/steady state/initial state/initial output)
Real	y_start (from ActuatorSignal)	1	Initial position of actuator
Damper coefficients
Real	a (from PartialDamperExponential)	-1.51	Coefficient a for damper characteristics
Real	b (from PartialDamperExponential)	0.105*90	Coefficient b for damper characteristics
Real	yL (from PartialDamperExponential)	15/90	Lower value for damper curve
Real	yU (from PartialDamperExponential)	55/90	Upper value for damper curve
Real	k0 (from PartialDamperExponential)	2rho_default(A/kDamMin)^2	Loss coefficient for y=0 (pressure drop divided by dynamic pressure)
Real	k1 (from PartialDamperExponential)	0.45	Loss coefficient for y=1 (pressure drop divided by dynamic pressure)
Real	l (from PartialDamperExponential)	0.0001	Damper leakage, ratio of flow coefficients k(y=0)/k(y=1)

Connectors

Type	Name	Description
Modelica.Fluid.Interfaces.FluidPort_a	port_a (from PartialTwoPort)	Fluid connector a (positive design flow direction is from port_a to port_b)
Modelica.Fluid.Interfaces.FluidPort_b	port_b (from PartialTwoPort)	Fluid connector b (positive design flow direction is from port_a to port_b)
Modelica.Blocks.Interfaces.RealInput	y (from ActuatorSignal)	Actuator position (0: closed, 1: open)
Modelica.Blocks.Interfaces.RealOutput	y_actual (from ActuatorSignal)	Actual actuator position

Components

Type	Name	Default	Description
Modelica.Units.SI.MassFlowRate	m_flow (from PartialTwoPortInterface)	port_a.m_flow	Mass flow rate from port_a to port_b (m_flow > 0 is design flow direction)
Modelica.Units.SI.PressureDifference	dp (from PartialTwoPortInterface)	port_a.p - port_b.p	Pressure difference between port_a and port_b
Medium.ThermodynamicState	sta_a (from PartialTwoPortInterface)	if allowFlowReversal then Medium.setState_phX(port_a.p, noEvent(actualStream(port_a.h_outflow)), noEvent(actualStream(port_a.Xi_outflow))) else Medium.setState_phX(port_a.p, noEvent(inStream(port_a.h_outflow)), noEvent(inStream(port_a.Xi_outflow)))	Medium properties in port_a
Medium.ThermodynamicState	sta_b (from PartialTwoPortInterface)	if allowFlowReversal then Medium.setState_phX(port_b.p, noEvent(actualStream(port_b.h_outflow)), noEvent(actualStream(port_b.Xi_outflow))) else Medium.setState_phX(port_b.p, noEvent(port_b.h_outflow), noEvent(port_b.Xi_outflow))	Medium properties in port_b
Medium.Density	rho (from PartialDamperExponential)		Medium density
Real	kDam (from PartialDamperExponential)		Flow coefficient of damper, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2)
Real	k (from PartialDamperExponential)		Flow coefficient of damper plus fixed resistance, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2)

Revisions

June 10, 2021, by Michael Wetter:
Changed implementation of the filter and changed the parameter order to a constant as most users need not change this value.
This is for #1498.
April 12, 2021, by Michael Wetter:
Guarded against division by zero if the pressure equation is removed. This then leads to a more meaningful error message.
This is for IBPSA, #1243.
December 23, 2019, by Antoine Gautier:
Added the pressure drop calculation as it is no longer in the base class.
This is for IBPSA, #1188.
March 22, 2017, by Michael Wetter:
Updated documentation.
April 14, 2014 by Michael Wetter:
Improved documentation.
September 26, 2013 by Michael Wetter:
Moved assignment of kDam_default and kThetaSqRt_default from initial algorithm to the variable declaration, to avoid a division by zero in OpenModelica.
December 14, 2012 by Michael Wetter:
Renamed protected parameters for consistency with the naming conventions.
June 22, 2008 by Michael Wetter:
Extended range of control signal from 0 to 1 by implementing the function Buildings.Fluid.Actuators.BaseClasses.exponentialDamper.
June 10, 2008 by Michael Wetter:
Introduced new partial base class, PartialDamperExponential.
June 30, 2007 by Michael Wetter:
Introduced new partial base class, PartialActuator.
July 27, 2007 by Michael Wetter:
Introduced partial base class.
July 20, 2007 by Michael Wetter:
First implementation.