WOLFRAM SYSTEMMODELER

PartialTwoPortFlow

Base class for distributed flow models

Diagram

Wolfram Language

In[1]:=
SystemModel["Modelica.Fluid.Pipes.BaseClasses.PartialTwoPortFlow"]
Out[1]:=

Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

Base class for distributed flow models. The total volume is split into nNodes segments along the flow path. The default value is nNodes=2.

Mass and Energy balances

The mass and energy balances are inherited from Interfaces.PartialDistributedVolume. One total mass and one energy balance is formed across each segment according to the finite volume approach. Substance mass balances are added if the medium contains more than one component.

An extending model needs to define the geometry and the difference in heights between the flow segments (static head). Moreover it needs to define two vectors of source terms for the distributed energy balance:

  • Qb_flows[nNodes], the heat flow source terms, e.g., conductive heat flows across segment boundaries, and
  • Wb_flows[nNodes], the work source terms.

Momentum balance

The momentum balance is determined by the FlowModel component, which can be replaced with any model extended from BaseClasses.FlowModels.PartialStaggeredFlowModel. The default setting is DetailedPipeFlow.

This considers

  • pressure drop due to friction and other dissipative losses, and
  • gravity effects for non-horizontal devices.
  • variation of flow velocity along the flow path, which occur due to changes in the cross sectional area or the fluid density, provided that flowModel.use_Ib_flows is true.

Model Structure

The momentum balances are formulated across the segment boundaries along the flow path according to the staggered grid approach. The configurable modelStructure determines the formulation of the boundary conditions at port_a and port_b. The options include (default: av_vb):

  • av_vb: Symmetric setting with nNodes-1 momentum balances between nNodes flow segments. The ports port_a and port_b expose the first and the last thermodynamic state, respectively. Connecting two or more flow devices therefore may result in high-index DAEs for the pressures of connected flow segments.
  • a_v_b: Alternative symmetric setting with nNodes+1 momentum balances across nNodes flow segments. Half momentum balances are placed between port_a and the first flow segment as well as between the last flow segment and port_b. Connecting two or more flow devices therefore results in algebraic pressures at the ports. The specification of good start values for the port pressures is essential for the solution of large nonlinear equation systems.
  • av_b: Asymmetric setting with nNodes momentum balances, one between nth volume and port_b, potential pressure state at port_a
  • a_vb: Asymmetric setting with nNodes momentum balance, one between first volume and port_a, potential pressure state at port_b

When connecting two components, e.g., two pipes, the momentum balance across the connection point reduces to

pipe1.port_b.p = pipe2.port_a.p

This is only true if the flow velocity remains the same on each side of the connection. Consider using a fitting for any significant change in diameter or fluid density, if the resulting effects, such as change in kinetic energy, cannot be neglected. This also allows for taking into account friction losses with respect to the actual geometry of the connection point.

Parameters (30)

allowFlowReversal

Value: system.allowFlowReversal

Type: Boolean

Description: = true to allow flow reversal, false restricts to design direction (port_a -> port_b)

n

Value: nNodes

Type: Integer

Description: Number of discrete volumes

energyDynamics

Value: system.energyDynamics

Type: Dynamics

Description: Formulation of energy balances

massDynamics

Value: system.massDynamics

Type: Dynamics

Description: Formulation of mass balances

substanceDynamics

Value: massDynamics

Type: Dynamics

Description: Formulation of substance balances

traceDynamics

Value: massDynamics

Type: Dynamics

Description: Formulation of trace substance balances

p_a_start

Value: system.p_start

Type: AbsolutePressure (Pa)

Description: Start value of pressure at port a

p_b_start

Value: p_a_start

Type: AbsolutePressure (Pa)

Description: Start value of pressure at port b

ps_start

Value: if n > 1 then linspace(p_a_start, p_b_start, n) else {(p_a_start + p_b_start) / 2}

Type: AbsolutePressure[n] (Pa)

Description: Start value of pressure

use_T_start

Value: true

Type: Boolean

Description: Use T_start if true, otherwise h_start

T_start

Value: if use_T_start then system.T_start else Medium.temperature_phX((p_a_start + p_b_start) / 2, h_start, X_start)

Type: Temperature (K)

Description: Start value of temperature

h_start

Value: if use_T_start then Medium.specificEnthalpy_pTX((p_a_start + p_b_start) / 2, T_start, X_start) else Medium.h_default

Type: SpecificEnthalpy (J/kg)

Description: Start value of specific enthalpy

X_start

Value: Medium.X_default

Type: MassFraction[Medium.nX] (kg/kg)

Description: Start value of mass fractions m_i/m

C_start

Value: Medium.C_default

Type: ExtraProperty[Medium.nC]

Description: Start value of trace substances

nParallel

Value: 1

Type: Real

Description: Number of identical parallel flow devices

lengths

Value:

Type: Length[n] (m)

Description: lengths of flow segments

crossAreas

Value:

Type: Area[n] (m²)

Description: cross flow areas of flow segments

dimensions

Value:

Type: Length[n] (m)

Description: hydraulic diameters of flow segments

roughnesses

Value:

Type: Roughness[n] (m)

Description: Average heights of surface asperities

dheights

Value: zeros(n)

Type: Length[n] (m)

Description: Differences in heights of flow segments

momentumDynamics

Value: system.momentumDynamics

Type: Dynamics

Description: Formulation of momentum balances

m_flow_start

Value: system.m_flow_start

Type: MassFlowRate (kg/s)

Description: Start value for mass flow rate

nNodes

Value: 2

Type: Integer

Description: Number of discrete flow volumes

modelStructure

Value: Types.ModelStructure.av_vb

Type: ModelStructure

Description: Determines whether flow or volume models are present at the ports

useLumpedPressure

Value: false

Type: Boolean

Description: =true to lump pressure states together

nFM

Value: if useLumpedPressure then nFMLumped else nFMDistributed

Type: Integer

Description: number of flow models in flowModel

nFMDistributed

Value: if modelStructure == Types.ModelStructure.a_v_b then n + 1 else if modelStructure == Types.ModelStructure.a_vb or modelStructure == Types.ModelStructure.av_b then n else n - 1

Type: Integer

nFMLumped

Value: if modelStructure == Types.ModelStructure.a_v_b then 2 else 1

Type: Integer

iLumped

Value: integer(n / 2) + 1

Type: Integer

Description: Index of control volume with representative state if useLumpedPressure

useInnerPortProperties

Value: false

Type: Boolean

Description: =true to take port properties for flow models from internal control volumes

Inputs (1)

fluidVolumes

Default Value: array(crossAreas[i] * lengths[i] for i in 1:n) * nParallel

Type: Volume[n] (m³)

Description: Discretized volume, determine in inheriting class

Connectors (2)

port_a

Type: FluidPort_a

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

port_b

Type: FluidPort_b

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

Components (6)

system

Type: System

Description: System properties

mediums

Type: BaseProperties[n]

state_a

Type: ThermodynamicState

Description: state defined by volume outside port_a

state_b

Type: ThermodynamicState

Description: state defined by volume outside port_b

statesFM

Type: ThermodynamicState[nFM + 1]

Description: state vector for flowModel model

flowModel

Type: FlowModel

Description: Flow model

Extended by (1)

DynamicPipe

Modelica.Fluid.Pipes

Dynamic pipe model with storage of mass and energy