Compressible flow or incompressible flow equation?

• ulfaazmi
In summary: I want to get the result of velocity, pressure, and temperature...The particle is labeled as traveling at 6.5km/s (!), which puts it solidly in the hypersonic flow regime, and compressibility will be necessary.

ulfaazmi

Hello everyone..
I am using 2-dimension Navier Stokes equation, but I confused that my problem is compressible or incompressible flow form, because if I have initial pressure and temperature and velocity for x-axis only in one grid that they are so very high but the others grid are zero. Can I consider the equation is compressible flow??Thank you

Is it a liquid or a gas?

ulfaazmi
Chestermiller said:
Is it a liquid or a gas?
It is Nitrogen gas.

ulfaazmi said:
It is Nitrogen gas.
Then the flow is compressible. Can you provide more details on your difficulty?

ulfaazmi
Chestermiller said:
Then the flow is compressible.
But the effects of compressibility might be negligible. You should compute the highest local Mach number $$Ma=U/c$$ in your flow. If it is smaller than say 0.1, the effects of compressibility can be ignored and you can use the incompressible Navier Stokes equations. If it is higher than 0.3, then you should definitely use the compressible form.

ulfaazmi
Chestermiller said:
Then the flow is compressible. Can you provide more details on your difficulty?

Not necessarily. Gas flows can be simplified as incompressible depending on the details - you should look at pressure variation thoughout your flowfield, as well as local mach numbers. If your pressure variations are small relative to the overall static pressure and the local mach number never exceeds 0.3 or so, you can reasonably treat the problem as incompressible.

ulfaazmi
bigfooted said:
But the effects of compressibility might be negligible. You should compute the highest local Mach number $$Ma=U/c$$ in your flow. If it is smaller than say 0.1, the effects of compressibility can be ignored and you can use the incompressible Navier Stokes equations. If it is higher than 0.3, then you should definitely use the compressible form.

Thank you for your help, actually the driving force of flow is caused by pressure. So, initially the flow is in a steady state in a closed horizontal pipe until pressure is introduced into that flow caused by a high speed projectile hits the wall of pipe. It also affecting temperature becomes higher at the area exactly in the center of the left side of pipe. Can I guess the velocity can be obtained from the equation :
P = ρ/U ?

cjl said:
Not necessarily. Gas flows can be simplified as incompressible depending on the details - you should look at pressure variation thoughout your flowfield, as well as local mach numbers. If your pressure variations are small relative to the overall static pressure and the local mach number never exceeds 0.3 or so, you can reasonably treat the problem as incompressible.
Chestermiller said:
Then the flow is compressible. Can you provide more details on your difficulty?
Thank you for your help, actually I have problem to get the correct equation of my study. I am difficult to converting the equation into the non dimensional system because the condition is not clear yet. If it doesn't bother you, would you like to check my equation, I will send it in a picture because it is difficult to write here, also include with the illustration of my problem??

ulfaazmi said:

Thank you for your help, actually I have problem to get the correct equation of my study. I am difficult to converting the equation into the non dimensional system because the condition is not clear yet. If it doesn't bother you, would you like to check my equation, I will send it in a picture because it is difficult to write here, also include with the illustration of my problem??
Sure. Let's see what you got. Just upload it.

ulfaazmi
An illustration of your problem would be very helpful for us to determine the best approach to take.

ulfaazmi

I attached my picture file in this link (https://drive.google.com/drive/u/0/folders/1CTWibwiW33ngNlEEWQLOIKGgMj5I9-sv), I am really pleasure if you would like to help me.

Thank you very much.

cjl said:
I am so sorry about that. Actually, I did not find any tool to send an attachment directly from here. So, as you mentioned like "imgur", I tried to upload my images there, and this is the link "https://imgur.com/a/zFtoldc". I hope it can be loaded.
Thank you very much.

So what exactly are you trying to calculate? The particle is labeled as traveling at 6.5km/s (!), which puts it solidly in the hypersonic flow regime, and compressibility will be necessary.

cjl said:
So what exactly are you trying to calculate? The particle is labeled as traveling at 6.5km/s (!), which puts it solidly in the hypersonic flow regime, and compressibility will be necessary.
I want to get the result of velocity, pressure, and temperature after iteration until reaching steady state and make a simulation using Fortran. But, I don't know whether the illustration of horizontal pipe is correct or not, because it is nonsymmetric. If I illustrate in a half of pipe like the third picture, is it right?

1. What is the difference between compressible and incompressible flow?

Compressible flow refers to the movement of a fluid in which its density changes significantly due to changes in pressure, temperature, or velocity. Incompressible flow, on the other hand, refers to the movement of a fluid in which its density remains constant regardless of changes in pressure, temperature, or velocity.

2. What is the equation for compressible flow?

The equation for compressible flow is the continuity equation, which states that the mass flow rate remains constant throughout a fluid system. It is represented by the equation ρAv = constant, where ρ is the density of the fluid, A is the cross-sectional area, and v is the velocity of the fluid.

3. What is the equation for incompressible flow?

The equation for incompressible flow is the Bernoulli's equation, which relates the pressure, velocity, and elevation of a fluid at different points within a system. It is represented by the equation P1 + ½ρv1^2 + ρgh1 = P2 + ½ρv2^2 + ρgh2, where P is the pressure, ρ is the density, v is the velocity, g is the acceleration due to gravity, and h is the height.

4. How do you determine if a flow is compressible or incompressible?

A flow is considered to be compressible if its Mach number (the ratio of the fluid's speed to the speed of sound) is greater than 0.3. If the Mach number is less than 0.3, the flow is considered to be incompressible.

5. What are the applications of compressible and incompressible flow equations?

The equations for compressible and incompressible flow have various real-world applications. Compressible flow is commonly used in aerodynamics, gas dynamics, and rocket propulsion. Incompressible flow is often used in fluid mechanics, hydraulic engineering, and HVAC systems.