Flow through an orifice drops drops significantly at 0.5 times the spe 2

[apex]

I remember Porsche having issues in the 1998 racing season due to the size of the air restrictor for there turbo engine and also due to were they could place this restrictor on the intake. The reason was that the airflow approached the speed of sound. I would love someone to explain to me in laymen’s terms why the following happens. Flow through an orifice drops significantly at 0.5 times the speed of sound, i.e. mach index Z=0.5?

Paul Guincho
p_guincho@yahoo.com

 

[zdas04]

Looking at the graphs in my Compressible Flow text, the breakover in density vs. velocity is closer to 0.6 M. Above 0.6 M the gas density increases exponetially with velocity and at Mach 1.0 it is near the density of liquid and stops increasing (for a given upstream pressure). 1.0 Mach is called "choked flow" in most piping scenarios. As long as the pressure downstream of an orifice is adequately low (this is a function of ratio of specific heats, for air "adequately low" is 62% of upstream pressure in absolute units) the flow rate through the orifice is a constant regardless of changes in downstream pressure.

David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

 

[iainuts]

In simplified terms (I tried to point out where this simplified analogy differs from actual):

Imagine air (or any gas) being like a bunch of balls bouncing around. They zip around depending on how warm they are. The actual molecules don't all have this speed though, just the average molecule has that speed. The speed of sound in a gas like air is slightly lower, but that's not particularly important here. Imagine instead that all the balls have the same speed, and that speed is the speed of sound. If all the balls are trying to get through an orifice, and the forward (ie: through the orifice) velocity is less than the speed of sound, then some molecules are actually going upstream through this orifice, while slightly more are traveling downstream. Just the average overall velocity of the gas is positive through the orifice.

Now as downstream pressure drops, or upstream pressure increases, the overall average velocity of the gas continues to increase, and fewer and fewer molecules are actually traveling upstream through the orifice. In other words, as this large group of molecules travels through the orifice, they are bouncing around in random directions at the speed of sound, so some of them are actually going upstream.

At some point, the overall average velocity of the gas is equal to the velocity of the molecules (ie: sonic velocity of the gas has been reached) in which case, no more molecules are traveling upstream.

At this point, lowering the downstream pressure further does not increase the overall bulk velocity of the gas through the orifice, because the individual molecules can only go so fast. Thus, the individual molecules have all 'straightened out' as they go through this orifice, and are now zipping through as fast as they can run. They can't go any faster.

So the flow rate of gas through the orifice can't increase with a continued decrease in downstream pressure past a certain point. That point is where the pressure downstream is roughly 1/2 of the pressure upstream. The flow rate doesn't go DOWN when the downstream pressure continues to drop, it simply stops increasing.

 

[hacksaw]

Now if you porsche is cruising along at Mach 0.5, don't worry about it, you'll have everyone behind you all the way to the finish line...