Stability of pressures in gas


First of all, apologizes from a newbie if I have passed over something obvious.

I would like to share and discuss some behaviour of gas phases I have observed in DualSPHysics4.0_LiquidGas distributed within the DualSPHysics 4.2 package.

It is mostly related with pressure. During simulation of an Oscillating Water Column energy device I suspected that pressure results took time to stabilize, and when it finally does the results seem incorrect.

Absolute pressure in the gas is defined when cs0, gamma and rhop0 is defined as speed of sound can be expressed the following way:

cs0 = (gamma*p0/rhop0)^0.5

So, absolute pressure can be deduced:

p0 = cs0^2*rhop0/gamma

DualSPHysics formulation for pressure is described in chapters 3.4 and 3.13 of "DualSPHysics_v4.2_GUIDE.pdf":

p = (cs0^2*rhop0/gamma) *((rhop/rhop0)^gamma-1)

As cs0^2*rhop0/gamma = p0 this can be written in the following manner:

(p0+p)/p0 = (rhop/rhop0)^gamma

That is the equation for isentropic processes, where p is not the absolute pressure, but the pressure over the main ambient pressure p0, or what is called in engineering as "gauge pressure" pg .

After some intermediate tests I reached to a very simple simulation to isolate ideal gas behaviour in DualSPHysics4.0_LiquidGas that is defined in a later posted XML definition case and can be run by anyone.
The bounday is a column shaped closed chamber 1 m heigh. It is filled with gas particles whose thermodynamic state is defined by the following variables:

rhop0 value="1.204"
gamma value="1.4"
cs0 value="343.28"

Those variables describe air at normal conditions (approx: 20ºC/273K, 100 kPa).

We should expect that after running this case, the air in the upper of column chamber should havean gauge pressure of 0 kPa. The lower gauge pressure should be 11.8 Pa higher due to the weight of the air column (1.2*9.81), and a gauge pressure gradient should be observed in the intermediate layers. And this results should be static, as no motion nor transient behaviour is defined. General pressure p0 is not postprocessed by the code, and so no field of absolute pressure is available, though it can be externally postprocessed.

When this case is run, we can see in a first output (first image) that the code has defined an initial state where upper gauge pressure is 0 and a correct 11.8 Pa gradient is defined.

In a second output (second image), a general increase of gauge pressure is observed: A general gauge pressure of 980 Pa is present with an additional gradient of 11.8 Pa.

The following time steps, main gauge pressure continue a more gradual increase until time step 960 approx (corresponding to 96 seconds, third image), where general gauge pressure stabilizes at 1644 Pa and no apparent gradient. Density results look correct.

1) Why this gradual increase in general gauge pressure?

2) Why this time of 96 seconds for this change in gauge pressure?
Changes of pressure should be governed by speed of sound and would take 1/343 = 0.003 s to be transmitted in a 1 m chamber.

3) Why no pressure gradient remains?

Anyone can help?


P.D. I attach the XML definition case in a following post.


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