WOLFRAM SYSTEM MODELER
DynamicPipeDynamic pipe model with storage of mass and energy |
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Diagram
Wolfram Language
In[1]:=
SystemModel["Modelica.Fluid.Pipes.DynamicPipe"]
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Information
This information is part of the Modelica Standard Library maintained by the Modelica Association.
Model of a straight pipe with distributed mass, energy and momentum balances. It provides the complete balance equations for one-dimensional fluid flow as formulated in UsersGuide.ComponentDefinition.BalanceEquations.
This generic model offers a large number of combinations of possible parameter settings. In order to reduce model complexity, consider defining and/or using a tailored model for the application at hand, such as HeatExchanger.
DynamicPipe treats the partial differential equations with the finite volume method and a staggered grid scheme for momentum balances. The pipe is split into nNodes equally spaced segments along the flow path. The default value is nNodes=2. This results in two lumped mass and energy balances and one lumped momentum balance across the dynamic pipe.
Note that this generally leads to high-index DAEs for pressure states if dynamic pipes are directly connected to each other, or generally to models with storage exposing a thermodynamic state through the port. This may not be valid if the dynamic pipe is connected to a model with non-differentiable pressure, like a Sources.Boundary_pT with prescribed jumping pressure. The modelStructure can be configured as appropriate in such situations, in order to place a momentum balance between a pressure state of the pipe and a non-differentiable boundary condition.
The default modelStructure is av_vb (see Advanced tab). The simplest possible alternative symmetric configuration, avoiding potential high-index DAEs at the cost of the potential introduction of nonlinear equation systems, is obtained with the setting nNodes=1, modelStructure=a_v_b. Depending on the configured model structure, the first and the last pipe segment, or the flow path length of the first and the last momentum balance, are of half size. See the documentation of the base class Pipes.BaseClasses.PartialTwoPortFlow, also covering asymmetric configurations.
The HeatTransfer component specifies the source term Qb_flows of the energy balance. The default component uses a constant coefficient for the heat transfer between the bulk flow and the segment boundaries exposed through the heatPorts. The HeatTransfer model is replaceable and can be exchanged with any model extended from BaseClasses.HeatTransfer.PartialFlowHeatTransfer.
The intended use is for complex networks of pipes and other flow devices, like valves. See, e.g.,
Parameters (40)
| length |
Value: Type: Length (m) Description: Length |
|---|---|
| isCircular |
Value: true Type: Boolean Description: = true, if cross sectional area is circular |
| diameter |
Value: Type: Diameter (m) Description: Diameter of circular pipe |
| crossArea |
Value: Modelica.Constants.pi * diameter * diameter / 4 Type: Area (m²) Description: Inner cross section area |
| perimeter |
Value: Modelica.Constants.pi * diameter Type: Length (m) Description: Inner perimeter |
| roughness |
Value: 2.5e-5 Type: Roughness (m) Description: Average height of surface asperities (default: smooth steel pipe) |
| V |
Value: crossArea * length * nParallel Type: Volume (m³) Description: Volume size |
| height_ab |
Value: 0 Type: Length (m) Description: Height(port_b) - Height(port_a) |
| 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: fill(length / n, n) Type: Length[n] (m) Description: Lengths of flow segments |
| crossAreas |
Value: fill(crossArea, n) Type: Area[n] (m²) Description: Cross flow areas of flow segments |
| dimensions |
Value: fill(4 * crossArea / perimeter, n) Type: Length[n] (m) Description: Hydraulic diameters of flow segments |
| roughnesses |
Value: fill(roughness, n) Type: Roughness[n] (m) Description: Average heights of surface asperities |
| dheights |
Value: height_ab * dxs 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 Description: Number of distributed flow models |
| nFMLumped |
Value: if modelStructure == Types.ModelStructure.a_v_b then 2 else 1 Type: Integer Description: Number of lumped flow models |
| 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 |
| use_HeatTransfer |
Value: false Type: Boolean Description: = true to use the HeatTransfer model |
| dxs |
Value: lengths / sum(lengths) Type: Real[n] Description: Normalized lengths |
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 |
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Connectors (3)
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port_a |
Type: FluidPort_a Description: Fluid connector a (positive design flow direction is from port_a to port_b) |
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port_b |
Type: FluidPort_b Description: Fluid connector b (positive design flow direction is from port_a to port_b) |
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heatPorts |
Type: HeatPorts_a[nNodes] Description: HeatPort connector with filled, large icon to be used for vectors of HeatPorts (vector dimensions must be added after dragging) |
Components (7)
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system |
Type: System Description: System properties |
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mediums |
Type: BaseProperties[n] Description: Base properties (p, d, T, h, u, R_s, MM and, if applicable, X and Xi) of a medium |
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state_a |
Type: ThermodynamicState Description: State defined by volume outside port_a |
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state_b |
Type: ThermodynamicState Description: State defined by volume outside port_b |
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statesFM |
Type: ThermodynamicState[nFM + 1] Description: State vector for flowModel model |
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flowModel |
Type: FlowModel Description: Flow model |
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heatTransfer |
Type: HeatTransfer Description: Heat transfer model |
Used in Examples (5)
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Modelica.Fluid.Examples Simple model of a heating system |
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Modelica.Fluid.Examples.AST_BatchPlant Model of an experimental batch plant |
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Modelica.Fluid.Examples Multi-way connections of pipes and incompressible medium model |
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Modelica.Fluid.Examples Comparing a circular with a non-circular pipe |
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Modelica.Fluid.Examples.TraceSubstances Demonstrates a room volume with CO2 controls |
Used in Components (1)
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Modelica.Fluid.Examples.HeatExchanger.BaseClasses Simple heat exchanger model |