Shock wave through a liquid metal filled steel tube

[BrandonBerchtold]

TL;DR Summary

Would an A36 steel tube be able to axially transmit a shock wave with a peak pressure higher than the yield strength of the steel tube?

Would an A36 steel tube filled with liquid mercury be able to transmit a shock wave longitudinally through the liquid mercury with a peak pressure higher than the yield strength of the steel tube? My thinking is that since the shock wave is traveling normal to the tube wall, it should not be interacting with the tube wall. However, if the shock wave is pictured to be a disk of high pressure mercury, this disk should be exerting a force, equal to the peak shock pressure, outwards into the tube wall (granted this disk would be traveling at the speed of sound in mercury and not have long to exert said force on the walls).

 

[jrmichler]

If we assume a short duration pressure pulse normal to the tube wall, then the sequence of events is as follows:
1) The pressure pulse applies force to the tube wall. The force is large enough to yield the wall.
2) The tube wall has elasticity and inertial mass, so it starts to accelerate outward.
3) As the tube wall moves outward, the material stress increases.
4) If the pressure pulse ends before the tube wall yields, then the tube wall does not yield. This ignores tube wall inertia, but that effect should be small.
5) I am assuming that the shock wave exerts pressure equally in all directions.

So, yes it is possible for the pressure to be large enough to yield the tube wall, without yielding the tube wall. But it may or may not be possible to create a pressure pulse short enough for that to happen.

 

[Baluncore]

Will there actually be a “shock wave” ?

The speed of sound is 5,130 m/s in iron, but only 1,450 m/s in mercury. The pressure step that starts in the mercury will gradually enter the iron and race ahead of the pulse that remains in the mercury. Some of that energy will reenter the mercury well ahead of the pulse and so rapidly reduce the slope of the pressure step in the mercury.

The pulse in the mercury will be traveling along the steel wall, so some energy will couple across the impedance mismatch into the steel. I expect the low speed in mercury will form a greater amplitude step than it will in the iron. That may attenuate the stress that appears in the iron.

Pressure in a cylindrical tube causes a hoop stress that is twice the longitudinal stress, which explains why pipes split longitudinally. Will the same be true for a slow pressure step inside the tube?

 

[anorlunda]

How about something like water hammer?

 

[Baluncore]

Water hammer is a transmission line effect. The liquid is not compressible.

A shock wave pressure step compresses and heats a gas, which increases the speed of sound behind the step, so it accelerates the velocity of the shock front and keeps the step sharp.