Shock waves traveling around corners

[Terry Giblin]

Can anyone in this section help me answer this question?

How many corners must a shock wave, or sonic boom for example, travel around before it loses the majority of its initial strength?

I have solved this question using the 'Reynolds Average Navier-Stokes Equations' and cannot believe the answer and would therefore appreciate an alternative solution...

Any help would be appreciated.

Terry Giblin

 

[enigma]

What do you mean by initial strength?

Expansion waves increase the mach number, but (IIRC) lose total pressure.

 

[Terry Giblin]

What if I re-phase the question.

Assume a super sonic shock wave, of strength or Energy "S", is traveling down a pipe or in inside a trench, each time the shock wave travels around a corner or edge ( at 90 Degrees to the direction of travel), its strength is decreased.

How much strength or energy is losted by the shock wave turning the corner?

 

[enigma]

Again, "strength" is not a typical definition of a shockwave. Shocks always travel at mach 1, the only thing supersonic is the object creating the wave to begin with.

That being said, discontinuities in a flow field (e.g. caused by a 90 deg corner) are impossible to analytically solve for. You need to run the simulation in some sort of CFD (computational fluid dynamics) program to find out for sure. It'll depend (among other things) on temperature, pressure, and density of the air.

I know that's not what you wanted to hear...

 

[Terry Giblin]

Again, "strength" is not a typical definition of a shockwave. Shocks always travel at mach 1, the only thing supersonic is the object creating the wave to begin with.

That being said, discontinuities in a flow field (e.g. caused by a 90 deg corner) are impossible to analytically solve for. You need to run the simulation in some sort of CFD (computational fluid dynamics) program to find out for sure. It'll depend (among other things) on temperature, pressure, and density of the air.

I know that's not what you wanted to hear...

Enigma, your absolutely correct, using finite elements CFD techniques using the RANS equations, you can calculate the energy loss of a shock wave round corners - I am trying to check my findings - I thought there would be tables or at least a general rule of thumb

 

[enigma]

Ah. I'm not sure.

There may be, but I do space systems, so aerodynamics are not my forte'.

 

[Terry Giblin]

What if the shockwave is the object?

Again, "strength" is not a typical definition of a shockwave. Shocks always travel at mach 1, the only thing supersonic is the object creating the wave to begin with.

That being said, discontinuities in a flow field (e.g. caused by a 90 deg corner) are impossible to analytically solve for. You need to run the simulation in some sort of CFD (computational fluid dynamics) program to find out for sure. It'll depend (among other things) on temperature, pressure, and density of the air.

I know that's not what you wanted to hear...

Enigma,

I agree with what you said, but have you considered what happens when the object making the wave can be considered the same as the wave - for example the gases coming out of the back of a large rocket ?

What happens when the gases themselves are traveling supersonic before the wave can be formed?

What does the shock wave look like then ?

Then feed this information back into the NS equations and you will be surprised at the results...

Regards

Terry Giblin

 

[enigma]

Are you talking about the diamond shock wave formations which form in the exhaust plumes or something else?

 

[Terry Giblin]

Diamond shock wave formation

I discovered my own solution to this problem in 1990.

When was the "Diamond shock wave formation" first coined?

It is obviously more advanced than my results, I was only interested in when the energy of the shock wave could be negelected, hence how many corners it had too travel around, before the majority of its energy was gone.

A diamond shock wave formation, sounds like a complete full solution, but I wouldn't be surprised if it could not be resolved down a more simple solution.

I would be interested in learning more to see how far this theory has progressed in the last 15 years...

Regards

Terry Giblin

 

[enigma]

I'm by no means an expert on this topic, so I'll relate what I learned from my aerodynamics classes...

The pattern appears as a result of oblique shock reflections. When the flow exits the supersonic nozzle (or hits an internal obstruction in a tunnel or engine), an oblique shock forms and travels to the other side of the flow. If you're outside the tunnel, you will have slipstreams in the flow. Those slipstreams act like walls to a shockwave, and it reflects back across the flow again.

I will check Anderson to see if it was covered there, or if it was merely a lecture topic.

 

[Terry Giblin]

Thank you for helping me solve half my problem

I'm by no means an expert on this topic, so I'll relate what I learned from my aerodynamics classes...

The pattern appears as a result of oblique shock reflections. When the flow exits the supersonic nozzle (or hits an internal obstruction in a tunnel or engine), an oblique shock forms and travels to the other side of the flow. If you're outside the tunnel, you will have slipstreams in the flow. Those slipstreams act like walls to a shockwave, and it reflects back across the flow again.

I will check Anderson to see if it was covered there, or if it was merely a lecture topic.

Enigma,

Thank you for your help. Knowning what it is now called I was able to get the answer I was looking for at the following web site.

http://www.allstar.fiu.edu/aero/rocket3.htm

It would still be interesting to discover when these results were predicted and calculated, before the proto-types were built.

Regards

Terry Giblin

 

[Terry Giblin]

Attention any math's anti_cranks

Under the new anti_crank policy, should this call not be moved to TD and closed, for proposing a visual solution to the NS's equations, before providing the valid mathematical proof.

His appears to be a hot thread but no one from the science community has answered a simiple question, which has been solved for over 50 years or more. Just like in the case RSA encryption.

But I am very surprised that there's no one who can answer this question.

If no one knows the answer then, to avoid any further embarrassment, I would close this call.

An unexpected result can be as useful as a valid answer.

We expected to discover a proton decay, but when we didn't get the answer we wanted we simply ignored the results and implications by simply increasing the expected result, until they appeared to match...

Calling any math's anti_cranks

or

should I ignore my results and finding and simply join the club.

Regards

Terry Giblin

 

[Clausius2]

His appears to be a hot thread but no one from the science community has answered a simiple question, which has been solved for over 50 years or more.
But I am very surprised that there's no one who can answer this question.

I know something about shock waves but your question is very poor definited and clear. The definition of "Strenght" or energy S as you defined it above is naive and unknown in the Fluid Mechanics community. I advice you to reformulate your question employing a definited geometry, substance, and requirements of your desired answer, but do not scorn us for not answering a not clarified question.

 

[Terry Giblin]

I'm afraid I cannot provide the details you are looking for, as I said I was simply looking for a rule of thumb solution.

But the information given in the attachment, is exactly what I was expecting someone to tell me, if they already new the answer.

Would anyone care to guess?

Regards

Terry Giblin

 

[Clausius2]

I'm afraid I cannot provide the details you are looking for, as I said I was simply looking for a rule of thumb solution.

But the information given in the attachment, is exactly what I was expecting someone to tell me, if they already new the answer.

1) At Fluid Mechanics science there are neither thumb solutions nor vague questions.

2)How is it possible you are expecting someone here to give you such a concrete answer (a supersonic jet structure) for such a vague question?

Again, reformulate your question and here do will be someone to answer you. But never doubt of our knowledge for not understanding your question. Enigma has done a large effort not worth of your problem explanation.

 

[enigma]

Enigma,

It would still be interesting to discover when these results were predicted and calculated, before the proto-types were built.

If I had to hazard a guess, I'd say that they were observed and calculated when the first supersonic windtunnels were being built in (IIRC) the 20s and 30s. You'd have very similar patterns forming off of the walls leading into the test chamber.

 

[Terry Giblin]

Fluid mechanics or quantum Mechanics

1) At Fluid Mechanics science there are neither thumb solutions nor vague questions.

2)How is it possible you are expecting someone here to give you such a concrete answer (a supersonic jet structure) for such a vague question?

Again, reformulate your question and here do will be someone to answer you. But never doubt of our knowledge for not understanding your question. Enigma has done a large effort not worth of your problem explanation.

Enigma's contribution is not in question.

I was just surprized that no one could give a rule of thumb answer, so I will modify my question, so that it is easier to understand.

If I am standing in a maze of tunnels next to the entrance and someone creates a large shock wave, which travels through the maze at supersonic speeds.

"How many corners away from the source of the sock wave, can I withstand the sock, to report my observations"

Taking that information and working backwards, if you want to form a shape which is capable of surviving this type of environment, who many corners is best suited for job.

Where Fluid mechanic meets quantum mechanics.

Who said reality is more bizar than fiction?

Regards

Terry Giblin

 

[Clausius2]

Enigma's contribution is not in question.

I was just surprized that no one could give a rule of thumb answer, so I will modify my question, so that it is easier to understand.

If I am standing in a maze of tunnels next to the entrance and someone creates a large shock wave, which travels through the maze at supersonic speeds.

"How many corners away from the source of the sock wave, can I withstand the sock, to report my observations"

Taking that information and working backwards, if you want to form a shape which is capable of surviving this type of environment, who many corners is best suited for job.

Where Fluid mechanic meets quantum mechanics.

Who said reality is more bizar than fiction?

Regards

Terry Giblin

Yes, I see what you're getting at, but the question remains being very general. I have the opinion not a thumb rule exists for this problem. I have imagined for instance a detonation wave traveling inside the tunnels. At each corner, the detonation wave will lose a bit of velocity and pressure jump, due to external and internal irreversibilities. Also the proper plane form of the detonation front can be altered, and the detonation wave can deteriorate into a deflagration wave and finally into a combustion faliure. To be honest, I don't know how to make easy figures with this problem. But, hearing the way you talked, surely you know yet how to go about it.

 

[Terry Giblin]

Rule of thumb to the Navier Stokes Equ.s is 3

According to my own theory on the Navier Stokes equations the rule of thumb which can be applied is the answer 3.

So when I heard of the Diamond shock wave formation, I was initially surprised until I realized, the answer 3 applies only to 2-D, if you rotate 3 corners 360 degrees, do you not get the same result as shown in the following diagrams.

http://www.allstar.fiu.edu/aero/rocket3.htm

Regards

Terry Giblin

 

[Clausius2]

According to my own theory on the Navier Stokes equations the rule of thumb which can be applied is the answer 3.

My own? Have you got a proper theory? Where have you published it? I'm anxious to see your own theory. Three corners? Why? Is there some analytical demonstration or you have experimented it 10e5 times?

EDIT: You may as well take a look at my signature.

 

[Terry Giblin]

Do you agree the answer is 3?

I have not written my proof up, if that is what you are asking, but I know mathematically my answer is definitely 3.

Do you agree?

Regards

Terry Giblin

1) At Fluid Mechanics science there are neither thumb solutions nor vague questions.

2)How is it possible you are expecting someone here to give you such a concrete answer (a supersonic jet structure) for such a vague question?

Again, reformulate your question and here do will be someone to answer you. But never doubt of our knowledge for not understanding your question. Enigma has done a large effort not worth of your problem explanation.

 

[FredGarvin]

"According to my own theory on the Navier Stokes equations the rule of thumb which can be applied is the answer 3."

I am just curious how you managed to solve a system of 3 non-linear, second order, partial differential equations that are really for describing incompressible flow.

 

[enigma]

I don't see this thread progressing much further.

If the OP has actual formulation he wants to present, please send it to me in a PM and I'll consider unlocking the thread.