Graduate Thermal shock wave question from my hydrodynamics simulation

[kjssag]

TL;DR

I wonder why the shock wave is generated.

This is a fluid dynamic simulation.
The top area has 100 degrees Celsius.
The bottom area has 0 degrees Celsius.
And both are filled with an ideal gas which is 1-atmosphere pressure.

Two areas are connected through the left small line. Another part is blocked.
So heat transfer can only happen through the left small area.

Now I understand both areas will go to about 50 degrees Celsius eventually.
But I don't know why the shock wave is generated early.

Can you explain why the shock wave is generated?

 

[Delta2]

Why do you call it a hydrodynamic simulation? You say that the two areas are filled with gas (not with water) and interact through a small opening at the left side where the shock wave starts.
Wouldn't it be more proper to call it a fluid dynamics simulation?

 

[kjssag]

Why do you call it a hydrodynamic simulation? You say that the two areas are filled with gas (not with water) and interact through a small opening at the left side where the shock wave starts.
Wouldn't it be more proper to call it a fluid dynamics simulation?

Thanks. That is my mistake. The fluid dynamic is right.

 

[Delta2]

Something else , the opening on the left, does it allow gas to pass through or it allows only heat to flow?

 

[kjssag]

Something else , the opening on the left, does it allow gas to pass through or it allows only heat to flow?

gas can move. so there is convection and conduction. I don't consider radiation.

 

[256bits]

gas can move. so there is convection and conduction. I don't consider radiation.

Doesn't seem to be much convection since the sphere(s) of temperature variation seem quite circular and moving radially outwards.
Also, movement of the gases can depend upon the relative density and viscosity of each.
Also, the size of 'hole' can determine the action of the movement, whether it would be more on the 'diffusion' side of behavior rather than bulk convection.
A lot depends upon how you set up the simulation.

To me it just seems to be the temperature of the gases is changing radially from the hole as if the gases were modeled as solid objects.

 

[kjssag]

Doesn't seem to be much convection since the sphere(s) of temperature variation seem quite circular and moving radially outwards.
Also, movement of the gases can depend upon the relative density and viscosity of each.
Also, the size of 'hole' can determine the action of the movement, whether it would be more on the 'diffusion' side of behavior rather than bulk convection.
A lot depends upon how you set up the simulation.

To me it just seems to be the temperature of the gases is changing radially from the hole as if the gases were modeled as solid objects.

Thank you for your answer.
I agree the simulation doesn't show the noticeable bulk convection.
So do you think that simulation doesn't look like real nature?
I hoped to model real gas which is around us.

 

[256bits]

Thank you for your answer.
I agree the simulation doesn't show the noticeable bulk convection.
So do you think that simulation doesn't look like real nature?
I hoped to model real gas which is around us.

Depends upon the constraints that are put on the situation.
Your simulation is quite nice. I do like it,

Example.
A hole 1 mm diameter would exhibit something different than that of a hole 1 cm diameter( or more ) ( convection could become more important ).
Are the gases the same in the upper and top sections?
If different gases are in each compartment, definitely there should be a diffusion effect ( if not convection with mixing ) as the gases move from higher concentration compartment to the lower. Which is the reason I mentioned this in the first place, Unfortunately, how this affects heat flow would have to be investigated as it should be density and specific heat dependent. SEE https://en.wikipedia.org/wiki/Thermal_conductivity Theoretical prediction for gases. Due to the mixing, this can have an effect upon the actual heat flow in and expanding viscinity around the hole as time progresses.

I think one try to can get more and more accurate in modelling, and really end up with some complex formula(s) ( which real systems actually are ) , so we model with the most simplified equations that entertain the process to necessary satisfaction.

Your off to a good start.
Someone with much more experience in these sorts of things would be quite able to exact what would be important, and what not in particular cases.

 

[Frabjous]

Why do you call it a hydrodynamic simulation? You say that the two areas are filled with gas (not with water) and interact through a small opening at the left side where the shock wave starts.
Wouldn't it be more proper to call it a fluid dynamics simulation?

Hydrodynamic simulation is an old term for simulations that solve the conservation of mass, momentum and energy.

 

[Frabjous]

What does ‘abnormal gas’ exactly mean?

 

[kjssag]

What does ‘abnormal gas’ exactly mean?

Also my mistake. It is not abnormal gas. The gas in the simulation is an ideal gas.

 

[Baluncore]

But I don't know why the shock wave is generated early.

As the thermal energy diffuses through the port, the isotherms that separate the different colours in the diagram move. That is why it looks like a wave radiating in both directions from the port. It looks reasonable to me.

 

[Frabjous]

Are you sure that the initial pressures are identical? Also check the speed of the wave. Is it faster than the sound speed of the undisturbed material?

Have you tried setting up a ‘1d’ problem and comparing to analytical solitions?

 

[Delta2]

Is your simulation solving for the velocity field as well? If yes can you post the plot of the velocity field?

 

[kjssag]

As the thermal energy diffuses through the port, the isotherms that separate the different colours in the diagram move. That is why it looks like a wave radiating in both directions from the port. It looks reasonable to me.

That is very helpful to understand my simulation.
Thank you and I will more think about your reply.

 

[kjssag]

Are you sure that the initial pressures are identical? Also check the speed of the wave. Is it faster than the sound speed of the undisturbed material?

Have you tried setting up a ‘1d’ problem and comparing to analytical solitions?

Yes, I set all regions to have the same pressure. But I believe I should check my simulation setting again. I will check again with your suggestions such as speed or 1D problem. Thanks for your reply.

 

[kjssag]

Is your simulation solving for the velocity field as well? If yes can you post the plot of the velocity field?

Well, I didn't check the velocity field, but I can. So I will check and upload that later. I think maybe it will take some time.

 

[Baluncore]

Are you sure that the initial pressures are identical?

If the pressure was not initially balanced, the isotherms across the port would immediately bulge one way or the other at the start of the simulation.

With time, the hot gas above will cool and contract, reducing the pressure above. The cold gas below will warm and expand, raising the pressure below. Then there will be some flow from the bottom chamber to the top chamber.

 

[Chestermiller]

Have you tried the calculation without convection, and only conduction? How do the results compare?