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Pneumatic Resistive Tube

Pneumatic pipe accounting for pressure loss and added heat due to flow resistance

Library

None (example custom library)

  • Pneumatic Resistive Tube block

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:

pipo={RTipi·32μLAD2·Gfor Re < Relam(laminar flow)f·RTipi·LD·G22A2for Re > Returb(turbulent flow) 

where

pi, poAbsolute 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, ToAbsolute gas temperatures at the tube inlet and outlet, respectively
GMass flow rate
μGas viscosity
fFriction factor for turbulent flow
DTube internal diameter
ATube cross-sectional area
LTube length
ReReynolds number

The friction factor for turbulent flow is approximated by the Haaland function

f=(1.8log10(6.9Re+(e3.7D)1.11))2

where e is the surface roughness for the pipe material.

The Reynolds number is defined as:

Re=ρvD/μ

where ρ is the gas density and v is the gas velocity. Gas velocity is related to mass flow rate by

G=ρvA

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