Pneumatic Resistive Tube
Pneumatic pipe accounting for pressure loss and added heat due to flow resistance
Library
None (example custom library)
Description
Note
As of Release R2016b, the Gas block library replaces the Pneumatic library as the recommended way of modeling pneumatic systems. The former Pneumatic library is now included in the product installation as an example custom library. The pneumatic domain definition is still provided with the software, and all the pneumatic blocks in your legacy models continue to work as before. However, these blocks no longer receive full production support and can be removed in a future release.
The Pneumatic Resistive Tube block models the loss in pressure and heating due to viscous friction along a short stretch of pipe with circular cross section. Use this block with the Constant Volume Pneumatic Chamber block to build a model of a pneumatic transmission line.
The tube is simulated according to the following equations:
where
pi, po | Absolute pressures at the tube inlet and outlet, respectively. The inlet and outlet change depending on flow direction. For positive flow (G > 0), pi = pA, otherwise pi = pB. |
Ti, To | Absolute gas temperatures at the tube inlet and outlet, respectively |
G | Mass flow rate |
μ | Gas viscosity |
f | Friction factor for turbulent flow |
D | Tube internal diameter |
A | Tube cross-sectional area |
L | Tube length |
Re | Reynolds number |
The friction factor for turbulent flow is approximated by the Haaland function
where e is the surface roughness for the pipe material.
The Reynolds number is defined as:
where ρ is the gas density and v is the gas velocity. Gas velocity is related to mass flow rate by
For flows between Relam and Returb, a linear blend is implemented between the flow predicted by the two equations.
In a real pipe, loss in kinetic energy due to friction is turned into added heat energy. However, the amount of heat is very small, and is neglected in the Pneumatic Resistive Tube block. Therefore, qi = qo, where qi and qo are the input and output heat flows, respectively.
Variables
To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.
Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.
Basic Assumptions and Limitations
The gas is ideal.
The pipe has a circular cross section.
The process is adiabatic, that is, there is no heat transfer with the environment.
Gravitational effects can be neglected.
The flow resistance adds no net heat to the flow.
Parameters
- Tube internal diameter
Internal diameter of the tube. The default value is
0.01
m.- Tube length
Tube geometrical length. The default value is
10
m.- Aggregate equivalent length of local resistances
This parameter represents total equivalent length of all local resistances associated with the tube. You can account for the pressure loss caused by local resistances, such as bends, fittings, armature, inlet/outlet losses, and so on, by adding to the pipe geometrical length an aggregate equivalent length of all the local resistances. The default value is
0
.- Internal surface roughness height
Roughness height on the tube internal surface. The parameter is typically provided in data sheets or manufacturer catalogs. The default value is
1.5e-5
m, which corresponds to drawn tubing.- Reynolds number at laminar flow upper margin
Specifies the Reynolds number at which the laminar flow regime is assumed to start converting into turbulent flow. Mathematically, this value is the maximum Reynolds number at fully developed laminar flow. The default value is
2000
.- Reynolds number at turbulent flow lower margin
Specifies the Reynolds number at which the turbulent flow regime is assumed to be fully developed. Mathematically, this value is the minimum Reynolds number at turbulent flow. The default value is
4000
.
Ports
The block has the following ports:
A
Pneumatic conserving port associated with the tube inlet for positive flow.
B
Pneumatic conserving port associated with the tube outlet for positive flow.
Version History
Introduced in R2009b