Aeronautical Engineer

[Marenta]

I'm trying to find an aeronautical engineer because I want the fluid flow equations for turbulant, laminar, and turbulant/laminar flow for oil, water, steam, and air.

The purpose for this being in a turbo application. The most efficient flow is the turbulant flow with laminar in the middle. This flow will cause a cushion around the piping wall allowing the laminar flow to move quicker through the bends in the piping. However, I have a suspicion that it's based upon density, and really only applicable for higher density fluids like water and oil. If that's the case, then, in a turbo application the dual flow wouldn't be as efficient as completely laminar flow. The lower pressure (30 psi highest) for the air for the turbo isn't enough to see the effects of having a dual flow, vice the 1000s of psi that it'd have to be at.

I'm just trying to mathematically prove this, so, if anybody knows the equations for this, I'd appreciate it.

[nissangirl74]

Damnit Dee, it's too early for that s***.

[Marenta]

I've been up for 5 hours already, not too early for me! :P

[nissangirl74]

:p
Talk about way above my pay-grade. Sheesh. Anyway, I'll quit thread-jacking now.

Engineers = UNITE!

[Hijacker]

Where's Red Coupe? He's an engineer!

[C-Kwik]

I'm trying to find an aeronautical engineer because I want the fluid flow equations for turbulant, laminar, and turbulant/laminar flow for oil, water, steam, and air.

The purpose for this being in a turbo application. The most efficient flow is the turbulant flow with laminar in the middle. This flow will cause a cushion around the piping wall allowing the laminar flow to move quicker through the bends in the piping. However, I have a suspicion that it's based upon density, and really only applicable for higher density fluids like water and oil. If that's the case, then, in a turbo application the dual flow wouldn't be as efficient as completely laminar flow. The lower pressure (30 psi highest) for the air for the turbo isn't enough to see the effects of having a dual flow, vice the 1000s of psi that it'd have to be at.

I'm just trying to mathematically prove this, so, if anybody knows the equations for this, I'd appreciate it.

I'm not sure that having laminar flow in the middle with turbulent flow is possible. The velocity profile of laminar flow between two parallel surfaces is parabolic. In a pipe it would be a paraboloid. The velocity profile of turbulent flow tends to look flatter as the mixing effect that occurs perpendicular to the primary flow direction slow flow in the middle while speeding it up at the walls. This said, for a given fluid and pipe (or any flow surface) the difference between laminar and turbulent flow is the value of the Reynolds number. Which in the case of a given fluid and pipe will only vary with velocity. Turbulent flow occurs at higher velocities. Since the velocity profile of a laminar fluid is a paraboloid, the peak velocity occurs in the center of the pipe. I would think the turbulence propagates from the fastest moving part of the fluid. Regardless, the mixing effect is going to be quite strong and would be impossible to control in such a manner.

Given this, the effect you think may be occurring would not. Turbulent flow reduces or removes the boundary layer (the cushion you are describing). So even if such a circumstance of turbulence at the wall with laminar flow in the center could exist, your hypothesis would not hold. Its likely all moot anyways. You're likely dealing with turbulent flow in most if not all engine intake systems.

As for the math, there are analytical solutions for laminar flow. You can probably google laminar pipe flow for those. Turbulent flows have no analytical solutions. The math requires experimental data. Its been a couple of quarters since I took fluids, but you might look up head loss and Moody Diagrams as keywords to help you going in the right direction. I'm not sure what you might calculate as a qualitative analysis negates what you're seeking. Regardless, the fact that we do not have any analytical method for turbulent flows means there are many equations that may need to be considered depending on the specific scenario. A big part of that being the value of the Reynolds number. If you are really interested in quantitatively analyzing the turbulent flows, you might need something as comprehensive as a textbook.

[alms24sebring]

lots of physics and math...

[MinisterofDOOM]

lots of physics and math...

Also at least one potato.

[PapaSmurf2k3]

I'm trying to find an aeronautical engineer because I want the fluid flow equations for turbulant, laminar, and turbulant/laminar flow for oil, water, steam, and air.

The purpose for this being in a turbo application. The most efficient flow is the turbulant flow with laminar in the middle. This flow will cause a cushion around the piping wall allowing the laminar flow to move quicker through the bends in the piping. However, I have a suspicion that it's based upon density, and really only applicable for higher density fluids like water and oil. If that's the case, then, in a turbo application the dual flow wouldn't be as efficient as completely laminar flow. The lower pressure (30 psi highest) for the air for the turbo isn't enough to see the effects of having a dual flow, vice the 1000s of psi that it'd have to be at.

I'm just trying to mathematically prove this, so, if anybody knows the equations for this, I'd appreciate it.

I'm not sure that having laminar flow in the middle with turbulent flow is possible. The velocity profile of laminar flow between two parallel surfaces is parabolic. In a pipe it would be a paraboloid. The velocity profile of turbulent flow tends to look flatter as the mixing effect that occurs perpendicular to the primary flow direction slow flow in the middle while speeding it up at the walls. This said, for a given fluid and pipe (or any flow surface) the difference between laminar and turbulent flow is the value of the Reynolds number. Which in the case of a given fluid and pipe will only vary with velocity. Turbulent flow occurs at higher velocities. Since the velocity profile of a laminar fluid is a paraboloid, the peak velocity occurs in the center of the pipe. I would think the turbulence propagates from the fastest moving part of the fluid. Regardless, the mixing effect is going to be quite strong and would be impossible to control in such a manner.

Given this, the effect you think may be occurring would not. Turbulent flow reduces or removes the boundary layer (the cushion you are describing). So even if such a circumstance of turbulence at the wall with laminar flow in the center could exist, your hypothesis would not hold. Its likely all moot anyways. You're likely dealing with turbulent flow in most if not all engine intake systems.

As for the math, there are analytical solutions for laminar flow. You can probably google laminar pipe flow for those. Turbulent flows have no analytical solutions. The math requires experimental data. Its been a couple of quarters since I took fluids, but you might look up head loss and Moody Diagrams as keywords to help you going in the right direction. I'm not sure what you might calculate as a qualitative analysis negates what you're seeking. Regardless, the fact that we do not have any analytical method for turbulent flows means there are many equations that may need to be considered depending on the specific scenario. A big part of that being the value of the Reynolds number. If you are really interested in quantitatively analyzing the turbulent flows, you might need something as comprehensive as a textbook.

This post is 100% true, at least when compared to what I've learned. I couldn't have said it any better.

[IanS]

You deserve a ticket for exceeding the physichs limit on a Monday.

You should all be a ashamed of yourselves.

Also, C-K's answer is the longest and most technical, he's probably righht......

[PapaSmurf2k3]

I'm really not kidding, I read the entire thing and every bit of it covers what I was going to say. He's absolutely right.

[C-Kwik]

I'm really not kidding, I read the entire thing and every bit of it covers what I was going to say. He's absolutely right.

That makes me feel better. But frankly, just don't ask me to do the math. It would take me days to figure it out and I have some idea of what to look for. Turbulent flow is intensely complicated.

You deserve a ticket for exceeding the physichs limit on a Monday.

I've actually been calculating crap all weekend, so this was actually a break for me. I don't know what possessed me to tackle 2 internships this summer.

[nissangirl74]

I've actually been calculating crap all weekend, so this was actually a break for me. I don't know what possessed me to tackle 2 internships this summer.

Because you are crazy smart. After reading your answer, I KNOW I need to get my a** back in school because you lost me after the first three sentences.

[Marenta]

C-Kwik,

I generally agree with what you're saying about laminar flow, specifically for turbo applications.

However, I know in certain high-pressure applications (many thousands of #s of pressure) it is most beneficial to have turbulant flow around the edges of the piping to create a "ball bearing" situation so that the laminar flow in the middle may not only flow faster, but not impinge the piping when it hits bends. Now, I know that the equations for this I've used before (I just can't find them, because that was when I was in Nuke training, and that's classified material) have a density dependant component meaning that while I might be able to possibly get water or a very thin viscous oil to behave in the environment, I wasn't sure if steam or air would be able to act in much the same way.

I know that air is far less dense than water, but at what pressure and size piping would the turbulant/laminar flow work, or could it work at all based upon the fact that even if you did get the turbulant flow going at the edges of the pipe, would that be enough cushion to maintain the laminar flow going around bends without disrupting the fluid wall that the turblant flow is creating.

Did I explain it a bit better?

[C-Kwik]

OK...I think I do see what you are getting at. Ultimately, it sounds like you are seeking the Reynolds number. The Reynolds number relates the density of the fluid (in a given state) with its viscosity, velocity and a characteristic dimension of a surface its acting on. Where a proportional geometry is used (say a plane and a scale model of the same plane), different fluids will act on the surface in the same way so long as the Reynolds number is the same. So if you increase the density of the fluid, you can alter any combination of the other parameters to achieve the same Reynolds number and observe the same behavior with a different or higher pressure fluid.

Where I think you might be confused is what constitutes turbulent flow. Turbulent flow is where particles of fluid move in directions normal to the streamlines. The effect you sound like you are referring to is likely just laminar flow. Containing turbulent flow along the surface contradicts the very definition of turbulent flow. The ball bearing effect would just be the shear occurring at the surface where a no slip condition will be present. That said, if the only thing you are actually trying to prove is if turbulent flow is less efficient than laminar flow, then that can be done qualitatively. Laminar flow will only have the minimum amount of shear occurring to maintain the flow rate through the pipe. Turbulent flow has shear in many directions that aren't necessarily conducive to the movement of the fluid in the overall direction of travel. As heat is produced by the shear forces, more shear forces equates to more heat. More heat means energy is being lost from the fluid.

Lastly, I need to correct a statement I made earlier. Turbulence is not propagated at the point of highest velocity in laminar flow. Its propagated at the walls. But the boundary layer thickness grows and will envelop all the fluid in the cross section of the pipe. The shear forces in a fluid are induced by the no slip condition at the surface. And its these shear forces that will convert a laminar flow into a turbulent flow.

[alms24sebring]

yay science

[Marenta]

It is the Reynolds number that I was looking for:

Nr (Reynolds Number) = ((density)(velocity)(pipe diameter))/((viscosity)(gravity))

Any viscous fluid would have to have such a large pressure and precisely measured piping diameter in order to achieve the "transitional flow" required to provide that fluid wall at the edge of the piping. I just needed the equations so that I could prove the feasibility of the application in a turbo setup.

Thanks for the 411, C-Kwik. Although, I can't say I'm too enthused by getting help from a Bronie. :P

[frapjap]

[C-Kwik]

Any viscous fluid would have to have such a large pressure and precisely measured piping diameter in order to achieve the "transitional flow" required to provide that fluid wall at the edge of the piping. I just needed the equations so that I could prove the feasibility of the application in a turbo setup.

We didn't study transitional flows too much in fluids, but from what I've seen in studying videos of flow is that transitional flows tend to shift back and forth between laminar and turbulent. It seemed like it oscillated in fact. I don't know if that is actually the case, but I don't recall seeing any kind of dual flow characteristics other than in non-fully developed flow. So such a dual flow could only exist in a very small section, likely after some disturbance.

But as I mentioned in my first post, I doubt this is even relevant. You are likely going to have turbulent flow throughout the intake. At a temperature of 25C, pipe diameter of 3" and pressure ratio of 3, Re=13664 * velocity. This is in SI units. This means the velocity needs to be in the range of 0.169 to 0.293 m/s (Transitional Re is 2300 to 4000 in a pipe). That is 0.655 mph or less. According to my calculations, a 2.4L motor would move air through the same pipe at 3.5 m/s at 800 RPM (100% V.E.). And since density is on the top of the fraction, increasing it would require an even lower velocity. Might be an interesting analysis in general, but not practical for a real engine.