What are typical Pressures in a test section of a shock tunnel?

[shreddinglicks]

TL;DR Summary

Shock Tunnel pressures

I'm writing a Matlab script to calculate various properties in a shock tunnel. While this might sound silly but I am not well acquainted with the subject and have very few resources to compare.

For a mach 6 test section is it reasonable to have a freestream pressure as low as 305 Pa?

 

[Astronuc]

Summary:: Shock Tunnel pressures

Mach 6

One should look into hypersonic wind tunnels, M > 5, which is an arbitrary cutoff, but a convention.

"A supersonic wind tunnel is a wind tunnel that produces supersonic speeds (1.2<M<5) The Mach number and flow are determined by the nozzle geometry. The Reynolds number is varied by changing the density level (pressure in the settling chamber)." Source: https://en.wikipedia.org/wiki/Supersonic_wind_tunnel
I would add that density of the atmosphere (gas) would be a factor on the pressure.

https://en.wikipedia.org/wiki/Hypersonic_wind_tunnel

An article on shock tubes indicates "shock waves with peak dynamic pressures of 7 MPa to 200 MPa and durations of a few hundred microseconds to several milliseconds."
https://en.wikipedia.org/wiki/Shock_tube

So at the low end, M = 6, the pressures should probably be on the order of low MPa, based on available examples. However, the absolute or dynamic pressure depends on the type of gas and ambient pressure (the pressure would be very low for a gas in a vacuum, i.e., very low gas density).

What kind of shock tube is one considering? What type of gas (atmospheric composition) and pressure?

See - Shock Tubes and Shock Tunnels: Design and Experiments
https://apps.dtic.mil/dtic/tr/fulltext/u2/a568015.pdf

A REVIEW OF SHOCK TUBES AND SHOCK TUNNELS
https://apps.dtic.mil/dtic/tr/fulltext/u2/832325.pdf

Edit/update: Other examples - https://www.osti.gov/servlets/purl/1338397
https://www.sciencedirect.com/science/article/pii/S1877705812027841
https://core.ac.uk/download/pdf/4414075.pdf

 

[shreddinglicks]

The shock tunnel I am modeling uses the reflective shock from the tube to produce a reservoir that feeds into the nozzle. I am using a helium driver with an air driven section at room conditions. I am assuming a calorically perfect gas and an isentropic nozzle. My test model is a plate at zero angle of attack. I am trying to achieve a Reynolds number on the plate edge of 1*10^6.

Incident shock mach = 1.55
reflective shock mach = 1.46
reservoir pressure = 619 kpa
test section pressure (free stream)= .392 kpa

I have calculated many values, density, temperature, etc. I want to make sure these pressure values are reasonable to give me confidence in my calculations.

 

[boneh3ad]

The typical test section pressures in a shock tunnel can vary greatly depending on application. In your case, it sounds like you can start with your desired $Re$ and work backward. What length scale are you using for the $Re$ you cited? If you are referencing free-stream conditions, it would be more appropriate to cite unit $Re$.

 

[shreddinglicks]

The typical test section pressures in a shock tunnel can vary greatly depending on application. In your case, it sounds like you can start with your desired $Re$ and work backward. What length scale are you using for the $Re$ you cited? If you are referencing free-stream conditions, it would be more appropriate to cite unit $Re$.

How would I do that? Maybe my logic is wrong. Don't I need to know the temperature to get the viscosity?

The way I have done it is:

1. Create a desired pressure ratio.
2. Calculate incident shock mach.
3. Calculate pressure, density, temperature ratios of incident shock.
4. Calculate reflective shock mach.
5. Calculate pressure, density, temperature ratios of reflective shock.
6. Obtain reservoir properties.
7. Use isentropic relations to obtain properties at nozzle outlet where mach = 6.
8. Get shock property ratios at plate.
9. Calculate pressure, density, temperature ratios at plate edge
10. I use the Sutherland eq for viscosity and velocity is found from m = u/sqrt(gamma*287*Tp)
287 is air gas constant and Tp is the temperature at the plate. This gives me the unit Reynolds number, rho*u/mu

 

[boneh3ad]

How would I do that? Maybe my logic is wrong. Don't I need to know the temperature to get the viscosity?

The way I have done it is:

1. Create a desired pressure ratio.
2. Calculate incident shock mach.
3. Calculate pressure, density, temperature ratios of incident shock.
4. Calculate reflective shock mach.
5. Calculate pressure, density, temperature ratios of reflective shock.
6. Obtain reservoir properties.
7. Use isentropic relations to obtain properties at nozzle outlet where mach = 6.
8. Get shock property ratios at plate.
9. Calculate pressure, density, temperature ratios at plate edge
10. I use the Sutherland eq for viscosity and velocity is found from m = u/sqrt(gamma*287*Tp)
287 is air gas constant and Tp is the temperature at the plate. This gives me the unit Reynolds number, rho*u/mu

Sure, but generally if you are designing a wind tunnel, you are starting with your desired free-stream conditions. If you know what $Re^{\prime}$ (or altitude or whatever target you are shooting for that stands in for pressure/density) and $h_0$ you want, you can set your desired pressure and temperature based on that and work backward. If you aren't shooting for high-enthalpy (seems unlikely if you are designing a reflected shock tunnel), then just enough $T_0$ to avoid liquefaction is sufficient.

 

[shreddinglicks]

Sure, but generally if you are designing a wind tunnel, you are starting with your desired free-stream conditions. If you know what $Re^{\prime}$ (or altitude or whatever target you are shooting for that stands in for pressure/density) and $h_0$ you want, you can set your desired pressure and temperature based on that and work backward. If you aren't shooting for high-enthalpy (seems unlikely if you are designing a reflected shock tunnel), then just enough $T_0$ to avoid liquefaction is sufficient.

I haven't thought of that. I'll try a script where I'll pick a Reynolds number and work my way to the pressure ratio.

 

[shreddinglicks]

Sure, but generally if you are designing a wind tunnel, you are starting with your desired free-stream conditions. If you know what $Re^{\prime}$ (or altitude or whatever target you are shooting for that stands in for pressure/density) and $h_0$ you want, you can set your desired pressure and temperature based on that and work backward. If you aren't shooting for high-enthalpy (seems unlikely if you are designing a reflected shock tunnel), then just enough $T_0$ to avoid liquefaction is sufficient.

I tried to work backwards. I chose a Reynolds number and varied the pressure to obtain it. Then worked backwards:

1. calculated the shock at the plate.
2. Obtained property ratios.
3. With the free stream properties I used the isentropic relations to get ratios of free stream and reservoir properties at the nozzle.
4. The equation I have for the reflected shock is a function of specific heat ratio and incident shock mach number so I am stuck.

 

[shreddinglicks]

I tried to work backwards. I chose a Reynolds number and varied the pressure to obtain it. Then worked backwards:

1. calculated the shock at the plate.
2. Obtained property ratios.
3. With the free stream properties I used the isentropic relations to get ratios of free stream and reservoir properties at the nozzle.
4. The equation I have for the reflected shock is a function of specific heat ratio and incident shock mach number so I am stuck.

If I assume an incident shock mach number. I am able to work my way back to p4/p1 and values of the pressures.

 

[boneh3ad]

Ultimately, this is a design problem, so you have more than just free-stream conditions constraining you, for example, strength of materials. Ultimately, you might not want your driver tube to go over a certain pressure or temperature for safety reasons, so that gives you another constraint or two.

 

[shreddinglicks]

Ultimately, this is a design problem, so you have more than just free-stream conditions constraining you, for example, strength of materials. Ultimately, you might not want your driver tube to go over a certain pressure or temperature for safety reasons, so that gives you another constraint or two.

True, but that would be another topic of focus. Astronuc, mentioned a wiki article stating early designs achieving pressures of 200 MPa. I am interested in what modern designs are capable of.

 

[boneh3ad]

True, but that would be another topic of focus. Astronuc, mentioned a wiki article stating early designs achieving pressures of 200 MPa. I am interested in what modern designs are capable of.

I wouldn't put any weight in Wikipedia articles like that. You can follow the citations in them and see where they lead, but the translation by random people on topics like this is often poor.

You might checking out the pages for various well known shock tunnels around the world. Some examples:
T5 at Caltech
HIEST at JAXA
T4 at UQ
LENS at CUBRC
HEG at DLR Göttingen

 

[shreddinglicks]

I wouldn't put any weight in Wikipedia articles like that. You can follow the citations in them and see where they lead, but the translation by random people on topics like this is often poor.

You might checking out the pages for various well known shock tunnels around the world. Some examples:
T5 at Caltech
HIEST at JAXA
T4 at UQ
LENS at CUBRC
HEG at DLR Göttingen

LENS at CUBRC claims to achieve Reynolds number of 10^8.

 

[Frabjous]

True, but that would be another topic of focus. Astronuc, mentioned a wiki article stating early designs achieving pressures of 200 MPa. I am interested in what modern designs are capable of.

That actually sounds reasonable. In some ways, they knew more about this stuff in the 1960‘s. At a certain point, you will be limited by material strength of the barrel, so I would be surprised by anything over 1GPa in a non-disposable system.

There is a modern book on shock tubes
https://www.amazon.com/dp/3319237446/?tag=pfamazon01-20

 

[boneh3ad]

LENS at CUBRC claims to achieve Reynolds number of 10^8.

That's honestly not all that hard to do. Lower $Re'$ is harder since you have less pressure to start the tunnel.

 

[boneh3ad]

That actually sounds reasonable. In some ways, they knew more about this stuff in the 1960‘s. At a certain point, you will be limited by material strength of the barrel, so I would be surprised by anything over 1GPa in a non-disposable system.

There is a modern book on shock tubes
https://www.amazon.com/dp/3319237446/?tag=pfamazon01-20

I wouldn't say that we knew more about it in the '60s than now, but it's fair to say that wind tunnel design hasn't evolved much since then.

 

[shreddinglicks]

That actually sounds reasonable. In some ways, they knew more about this stuff in the 1960‘s. At a certain point, you will be limited by material strength of the barrel, so I would be surprised by anything over 1GPa in a non-disposable system.

There is a modern book on shock tubes
https://www.amazon.com/dp/3319237446/?tag=pfamazon01-20

I have that book.

 

[shreddinglicks]

Thanks to everyone who replied. I have one final question. I've been searching the net but can not find any freely available literature. Can someone give me a quick lesson on boundary layer instability and its frequencies? I have an equation that claims to scale the instability frequency by:

F = U/2*delta

U is leading edge velocity
delta is layer thickness

What information does this give me? Does this tell me the likelihood of transition from laminar to turbulence?

 

[Frabjous]

Thanks to everyone who replied. I have one final question. I've been searching the net but can not find any freely available literature. Can someone give me a quick lesson on boundary layer instability and its frequencies? I have an equation that claims to scale the instability frequency by:

F = U/2*delta

U is leading edge velocity
delta is layer thickness

What information does this give me? Does this tell me the likelihood of transition from laminar to turbulence?

You will probably get a better response if you put this in a new posting.

 

[shreddinglicks]

You will probably get a better response if you put this in a new posting.

Will do.