Author Topic: De Laval Nozzle  (Read 34977 times)

Offline DonPMitchell

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De Laval Nozzle
« on: July 01, 2008, 12:27:13 PM »
Goddard describes how the De Laval nozzle increased his rocket's exhaust speed from 314 meters/sec to 2434 m/s (Mach 7!).  It's an amazingly simple and efficient way to convert heat of combustion into kinetic energy, like 50 - 70 percent efficient.

But I have never completely groked this.  You constrict the gas until it is forced to the speed of sound.  Then when it flows into the bell of the nozzle it expands and goes supersonic.  Why doesn't this happen if you don't reach the speed of sound in the constriction?

I've looked at the math (the Russian wiki page has a really clear derivation of the fluid mechanics).  I've looked in Landau and Lif****z book on fluid mech (I took a course in that at Caltech).  I get the math, I am just trying to get clear intuition.  Why does the gas have to be forced to the speed of sound before the magic happens?

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Offline Bob B.

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Re: De Laval Nozzle
« Reply #1 on: July 01, 2008, 03:59:44 PM »
You might want to google “choked flow” (or "critical flow") and do some reading on that.  Choked flow occurs when the flow through a restricted area, such as an orifice or nozzle, can no longer be increased by a reduction in the downstream pressure.  This occurs when the sonic velocity is reached at some point along the flow path.

Say, for example, you have a high-pressure air line with a small valve on the end.  When the valve is opened, air will rush out the opening until the air flow reaches sonic velocity, at which time the flow will become choked and there will be no further increase in velocity.  If the flow is choked, further lowering the downstream pressure has no effect on the gas flow.  Although the gas has a velocity limit, a higher mass flow rate can be attained by increasing the upstream pressure, which increases the density of the gas as it flows through the opening.

A De Laval nozzle is an example of choked flow.  We have a very high upstream pressure in the combustion chamber and a very low downstream pressure at the nozzle exit.  The flow as it passes through the throat will become choked, and therefore, will be at sonic velocity.

I don’t understand the dynamics enough to explain why there is a sonic velocity limitation -- there just is.  It probably has something to do with pressure waves and the like.  It is not my area of expertise.

EDIT:
Why doesn't this happen if you don't reach the speed of sound in the constriction?

Anytime the pressure difference across the throat exceeds a minimum value, the flow will become choked.  A rocket engine far exceeds the minimum value, thus the flow is always choked and the velocity at the throat is always sonic velocity.  I believe that for air, the flow will become choked when the upstream pressure is about twice the downstream pressure.  In a rocket engine, the upstream pressure can be hundreds of times greater than the downstream pressure.  The divergent part of the nozzle will accelerate the exhaust gas whether the flow is choked at the throat or not, but for the flow not to be choked, the pressure in the combustion chamber would be so low that we would have a very non-effective rocket engine.

« Last Edit: July 02, 2008, 03:06:17 PM by Bob B. »

Offline DonPMitchell

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Re: De Laval Nozzle
« Reply #2 on: July 06, 2008, 06:29:30 PM »
I remember from fluid mechanics (ugh, like 30 years ago), some types of flow have two solutions to the equation.

For example, when water from faucet hits the bottom of your sink, it flows in a fast thin sheet for a few inches, then switches to the other mode, a thicker slower flow.  So perhaps choking the flow to sonic velocity allows it to go into a supersonic mode of flow.

But it may not be a two-mode thing, like you said, it may just be that chocking the flow is what lets you have high combustion chamber pressure.

Speaking of which, I never get tired of this video: http://science.nasa.gov/headlines/y2007/images/methaneblast/testfiring.wmv
« Last Edit: July 06, 2008, 06:32:35 PM by DonPMitchell »
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Offline Bob B.

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Re: De Laval Nozzle
« Reply #3 on: July 08, 2008, 08:41:17 PM »
Speaking of which, I never get tired of this video: http://science.nasa.gov/headlines/y2007/images/methaneblast/testfiring.wmv

That video definitely demands that the volumn be turned up full. :D