Modelica.Fluid.Fittings

Information

This sublibrary contains models and functions providing pressure loss correlations. All models in this library have the property that no mass and no energy is stored in the component. Therefore, none of the models have a state.

All functions are continuous and have a finite, non-zero, smooth, first derivative. The functions are all guaranteed to be strict monotonically increasing. The mentioned properties guarantee that a unique inverse of every function exists. Note, the usual quadratic pressure loss correlation

• in the form m_flow = f(dp) has an infinite derivative at zero mass flow rate and is therefore problematic to use.
• in the form dp = f(m_flow) has a zero derivative at zero mass flow rate and is therefore problematic to invert, since the inverse function has then an infinite derivative at zero mass flow rate.

The two mentioned problems are solved in this package by approximating the characteristics around zero mass flow rates with appropriate polynomials. The monotonicity is guaranteed using results from:

Fritsch F.N. and Carlson R.E. (1980):

Monotone piecewise cubic interpolation. SIAM J. Numerc. Anal., Vol. 17, No. 2, April 1980, pp. 238-246

Package Content

Name	Description
Bends	Flow models for bends
Orifices	Flow models for orifices
GenericResistances	Flow models for generic resistances
SimpleGenericOrifice	Simple generic orifice defined by pressure loss coefficient and diameter (only for flow from port_a to port_b)
SharpEdgedOrifice	Pressure drop due to sharp edged orifice (for both flow directions)
AbruptAdaptor	Pressure drop in pipe due to suddenly expanding or reducing area (for both flow directions)
MultiPort	Multiply a port; useful if multiple connections shall be made to a port exposing a state
TeeJunctionIdeal	Splitting/joining component with static balances for an infinitesimal control volume
TeeJunctionVolume	Splitting/joining component with static balances for a dynamic control volume
BaseClasses	Base classes used in the Fittings package (only of interest to build new component models)

Modelica.Fluid.Fittings.SimpleGenericOrifice

Information

This pressure drop component defines a simple, generic orifice, where the loss factor ζ is provided for one flow direction (e.g., from loss table of a book):

   Δp = 0.5*ζ*ρ*v*|v|
      = 8*ζ/(π^2*D^4*ρ) * m_flow*|m_flow|

where

• Δp is the pressure drop: Δp = port_a.p - port_b.p
• D is the diameter of the orifice at the position where ζ is defined (either at port_a or port_b). If the orifice has not a circular cross section, D = 4*A/P, where A is the cross section area and P is the wetted perimeter.
• ζ is the loss factor with respect to D that depends on the geometry of the orifice. In the turbulent flow regime, it is assumed that ζ is constant.
  For small mass flow rates, the flow is laminar and is approximated by a polynomial that has a finite derivative for m_flow=0.
• v is the mean velocity.
• ρ is the upstream density.

Since the pressure loss factor zeta is provided only for a mass flow from port_a to port_b, the pressure loss is not correct when the flow is reversing. If reversing flow only occurs in a short time interval, this is most likely uncritical. If significant reversing flow can appear, this component should not be used.

Parameters

Name	Description
replaceable package Medium	Medium in the component
pathLength	Length flow path [m]
diameter	Diameter of orifice [m]
zeta	Loss factor for flow of port_a -> port_b
use_zeta	= false to obtain zeta from dp_nominal and m_flow_nominal
Nominal operating point
m_flow_nominal	Mass flow rate for dp_nominal [kg/s]
dp_nominal	Nominal pressure drop [Pa]
Assumptions
allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Dynamics
momentumDynamics	Formulation of momentum balance
Advanced
dp_start	Guess value of dp = port_a.p - port_b.p [Pa]
m_flow_start	Guess value of m_flow = port_a.m_flow [kg/s]
m_flow_small	Small mass flow rate for regularization of zero flow [kg/s]
use_Re	= true, if turbulent region is defined by Re, otherwise by m_flow_small
from_dp	= true, use m_flow = f(dp) else dp = f(m_flow)
Diagnostics
show_T	= true, if temperatures at port_a and port_b are computed
show_V_flow	= true, if volume flow rate at inflowing port is computed

Connectors

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

Modelica.Fluid.Fittings.SharpEdgedOrifice

Information

Parameters

Name	Description
replaceable package Medium	Medium in the component
data	Loss factor data
length	Length of orifice [m]
diameter	Inner diameter of pipe (= same at port_a and port_b) [m]
leastDiameter	Smallest diameter of orifice [m]
alpha	Angle of orifice [deg]
Nominal operating point
m_flow_nominal	Nominal mass flow rate [kg/s]
Assumptions
allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Advanced
dp_start	Guess value of dp = port_a.p - port_b.p [Pa]
m_flow_start	Guess value of m_flow = port_a.m_flow [kg/s]
m_flow_small	Small mass flow rate for regularization of zero flow [kg/s]
use_Re	= true, if turbulent region is defined by Re, otherwise by m_flow_small
from_dp	= true, use m_flow = f(dp) else dp = f(m_flow)
Diagnostics
show_T	= true, if temperatures at port_a and port_b are computed
show_V_flow	= true, if volume flow rate at inflowing port is computed
show_Re	= true, if Reynolds number is included for plotting

Connectors

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

Modelica.Fluid.Fittings.AbruptAdaptor

Information

Parameters

Name	Description
replaceable package Medium	Medium in the component
data	Loss factor data
diameter_a	Inner diameter of pipe at port_a [m]
diameter_b	Inner diameter of pipe at port_b [m]
Nominal operating point
m_flow_nominal	Nominal mass flow rate [kg/s]
Assumptions
allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Advanced
m_flow_start	Guess value of m_flow = port_a.m_flow [kg/s]
m_flow_small	Small mass flow rate for regularization of zero flow [kg/s]
Diagnostics
show_T	= true, if temperatures at port_a and port_b are computed
show_V_flow	= true, if volume flow rate at inflowing port is computed
show_Re	= true, if Reynolds number is included for plotting
show_totalPressures	= true, if total pressures are included for plotting
show_portVelocities	= true, if port velocities are included for plotting

Connectors

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

Modelica.Fluid.Fittings.MultiPort

Information

This model is useful if multiple connections shall be made to a port of a volume model exposing a state, like a pipe with ModelStructure av_vb. The mixing is shifted into the volume connected to port_a and the result is propagated back to each ports_b.

If multiple connections were directly made to the volume, then ideal mixing would take place in the connection set, outside the volume. This is normally not intended.

Parameters

Name	Description
replaceable package Medium

Connectors

Name	Description
replaceable package Medium
port_a
ports_b[nPorts_b]

Modelica.Fluid.Fittings.TeeJunctionIdeal

Information

Parameters

Name	Description
replaceable package Medium	Medium in the component

Connectors

Name	Description
port_1
port_2
port_3

Modelica.Fluid.Fittings.TeeJunctionVolume

Information

Parameters

Name	Description
replaceable package Medium	Medium in the component
fluidVolume	Volume [m3]
V	Mixing volume inside junction [m3]
Assumptions
Dynamics
energyDynamics	Formulation of energy balance
massDynamics	Formulation of mass balance
Initialization
p_start	Start value of pressure [Pa]
use_T_start	= true, use T_start, otherwise h_start
T_start	Start value of temperature [K]
h_start	Start value of specific enthalpy [J/kg]
X_start[Medium.nX]	Start value of mass fractions m_i/m [kg/kg]
C_start[Medium.nC]	Start value of trace substances

Connectors

Name	Description
port_1
port_2
port_3