Temperature distribution in pipes using simscape

Andreas

2013 12 10

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Hello,

I currently try to model a large pipe buried in the ground and have to deliver step responses for temperature steps and a given mass flow. The idea is similar to ssc_tl_oil_pipeline, except my pipe is very long (100 m) and therefore has to be discretisized.

I used the pipe component from the simscape thermal liquid library and put several of them (including attached walls) in series.

In the following scope you'll see the differences between different discretization behaviors.

When the number of elements goes up, you'll nearly get sharp 90° rising and falling edges and can read out runtime of your fluid.

With a smaller number, that is also possible (nearly 50 s), but how can you find the right n for discretizations? When it is too large, the temperature wave comes in to sharp. In reality you'll find a lot of mixing due to turbulences and the velocity profile in the tube.

Source: http://discoverarmfield.com/data/f6/images/f6_velocity_schem.jpg

So n should be right somewhere between 10 and 100. But how can you match it to Reynolds number and the current mass flow?

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Andreas 2013-12-23

When you look at the documentation for the pipeline model from the hydraulic domain, you will find the following: <http://www.mathworks.de/de/help/physmod/hydro/ref/segmentedpipeline.html>

Hydraulic pipelines, which are inherently distributed parameter elements, are represented with sets of identical, connected in series, lumped parameter segments. It is assumed that the larger the number of segments, the closer the lumped parameter model becomes to its distributed parameter counterpart.

It will be the same way with thermal liquid elements, but how could you determine the right n? At a certain point your model gets quite lame...