LumpedStraightPipe#
Copyright © EDF 2002 - 2026#
ThermoSysPro Version 4.2#
This component model is documented in Sect. 13.5 of the ThermoSysPro book.
Lumped straight pipe#
The lumped straight pipe models the pressure loss of a fluid circulating inside a pipe. It must be connected to volumes in order to have a complete model featuring mass, energy, and momentum balance equations.
Following assumptions are made:
The flow inside pressure losses is adiabatic. Non-adiabatic pipes must be
modeled by connecting pressure losses to volumes.The specific enthalpy inside the components is equal to the specific enthalpy at the inlet.
The properties of the fluid are computed for the average pressure..
Inertia due to momentum inside pipes is neglected.
The fluid density \(\rho\) is assumed constant along the pipe.
Modelica component model#
The equations mentioned below are implemented in the component LumpedStraightPipe, located in the WaterSteam.PressureLosses sub-library.
This component has 2 connectors:
C1: fluid inlet,
C2: fluid outlet.
Nomenclature#
Symbol |
Description |
Unit |
Definition |
Modelica name |
|---|---|---|---|---|
\(A\) |
Internal cross section of the pipe |
\(\mathrm{m}^{2}\) |
\(\pi \cdot D^{2} / 4\) |
A |
\(D\) |
Internal diameter of the pipe |
\(\mathrm{m}\) |
D |
|
\(g\) |
Gravity constant |
\(\mathrm{m} / \mathrm{s}^{2}\) |
g |
|
\(h\) |
Fluid specific enthalpy |
\(\mathrm{J} / \mathrm{kg}\) |
h |
|
\(L\) |
Length of the pipe |
\(\mathrm{m}\) |
L |
|
\(\dot{m}\) |
Fluid mass flow rate |
\(\mathrm{kg} / \mathrm{s}\) |
Q |
|
\(P_{\mathrm{i}}\) |
Fluid pressure at the pipe inlet |
\(\mathrm{Pa}\) |
C1.P |
|
\(P_{\mathrm{o}}\) |
Fluid pressure at the pipe outlet |
\(\mathrm{Pa}\) |
C2.P |
|
\(R e\) |
Fluid Reynolds number |
\(-\) |
\(\frac{4 \cdot \lvert \dot{m} \rvert}{\pi \cdot D \cdot \mu}\) |
Re |
\(z_{\mathrm{i}}\) |
Inlet altitude of the pipe |
\(\mathrm{m}\) |
z1 |
|
\(z_{0}\) |
Outlet altitude of the pipe |
\(\mathrm{m}\) |
z2 |
|
\(\Delta P\) |
Pressure loss of the fluid between the pipe inlet and outlet |
\(\mathrm{Pa}\) |
\(P_{\mathrm{i}}-P_{\mathrm{o}}\) |
deltaP |
\(\Delta P_{\mathrm{f}}\) |
Friction pressure loss between the pipe inlet and outlet |
\(\mathrm{Pa}\) |
deltaPf |
|
\(\Delta P_{\mathrm{g}}\) |
Gravity pressure loss |
\(\mathrm{Pa}\) |
\(\rho \cdot \mathrm{g} \cdot\left(z_{\mathrm{o}}-z_{\mathrm{i}}\right)\) |
- |
\(\varepsilon\) |
Pipe roughness |
\(\mathrm{m}\) |
rugosrel |
|
\(\Lambda_{\mathrm{f}}\) |
Friction pressure loss coefficient |
\(\mathrm{Pa} . \mathrm{s}\) |
lam |
|
\(\mu\) |
Fluid dynamic viscosity |
\(\mathrm{kg} /\) |
mu |
|
\(\rho\) |
Fluid density |
\(\mathrm{m}^{3}\) |
rho |
Governing equations#
Dynamic momentum balance equation#
Validity domain:
\(\forall \dot{m}\)
Mathematical formulation:
Comments:
This is valid only if the mass flow rate wavelength is large as compared to the pipe length \(L\), i.e. if there is no water hammer effect inside the pipe. It can for instance be used to model water level oscillations in tanks communicating through a pipe.
Static momentum balance equation#
Validity domain:
\(\forall \dot{m}\)
Mathematical formulation:
Comments:
Friction pressure losses#
Validity domain:
\(\forall \dot{m}\)
Mathematical formulation:
Comments:
References#
El Hefni, Baligh and Bouskela, Daniel (2019). Modeling and Simulation of Thermal Power Plants with ThermoSysPro, sect. 13.5. Springer Nature Switzerland AG.