High-pressure left

This is a classical single-phase shock tube filled with air. The test is available in the folder ./libTests/referenceTestCases/euler/1D/shockTubes/HPLeft/. The corresponding uncommented line in ECOGEN.xml is:

<testCase>./libTests/referenceTestCases/euler/1D/shockTubes/HPLeft/</testCase>

Fig. 40 Initial condition for single-phase shock tube.

The initial characteristics of the run are:

Characteristic	Value
dimension	1 m
initial mesh size	100
AMR max level	3
diaphragm position	0.4 m
boundary conditions	non-reflecting
final solution time	0.6 ms
solution printing frequency	0.06 ms
precision	2nd order (VanLeer)

Solution of this Riemann problem induces 3 waves:

• expansion waves propagating in high-pressure chamber,

• a right-facing shock wave propagating in low-pressure chamber,

• a contact discontinuity.

These waves are clearly observable on the results:

Fig. 41 Shock tube filled with air. Visualization using Paraview software.

This test is also equipped with 3 Eulerian sensors. For example, two sensors are positionned at \(x = 0.6 m\) and \(x= 0.8 m\). They record the following pressures:

Fig. 42 Pressure recorded by sensors at \(x = 0.6 m\) (pink) and \(x = 0.8 m\) (green). Visualization using gnuplot software.

The first sensor sees its pressure rising first because of the shock wave. Because this Riemann problem generates a supersonic flow after the shock wave, the tail of the expansion waves is seen by the sensor after 0.5 ms.