## Hypothesis re Diffuser Action

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larry cottrill
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### Hypothesis re Diffuser Action

Here is a simple hypothesis on the action of a diffuser. Someone who has a handle on the maths (e.g. Forrest, Mike, et al) can look at this and perhaps validate whether this is essentially correct, or just hogwash. My description is illustrated in the attached drawing, although the drawing by itself is inadequate without understanding the text.
A set of air molecules at rest, entering a diffuser at speed, and then
leaving the diffuser. Drawing Copyright 2008 Larry Cottrill
The drawing illustrates a handful of cool air molecules, with associated velocity vectors. The exact location of the molecules is unimportant; note that the molecules are always shown in the same relative locations only as a way to identify them; in reality, their relative locations would radically change in passing through the diffuser! At the left, I show the molecules as they exist in free air just in front of the approaching diffuser. Their speeds (relative to an observer) are approximately equal, and their directions are completely at random. In other words, the observer would macroscopically observe them as a tiny sample of "stationary" air at a certain pressure and temperature.

In the center, the observer is now moving along with the approaching ramjet diffuser. Due to the forward motion of the engine, the relative motion V1 is added (as a vector) to each of the individual molecular velocities, shown as they are just entering the diffuser. This changes the velocity magnitude and direction of each molecule. The "longitudinal" part of their velocity (i.e. in the direction of air motion, relative to the diffuser) is now toward the engine in every case. The "transverse" velocity is exactly what it was in the "stationary observer" view (this MUST be true, since V1 is purely longitudinal velocity, by definition). The speeds (i.e. just the lengths of the vectors) represent a certain kinetic energy for each molecule (again, as measured by the moving observer); most of these kinetic energies are larger than in the "stationary air" case, due to the relative air speed. In the drawing, the longitudinal velocity vector is represented by the green line and the transverse vector by the red line (I've only shown this on one particular molecule, but it applies in the same manner to every one, of course).

My hypothesis is shown in the rightmost view, which represents the molecules as they leave the rear of the diffuser, at reduced longitudinal velocity V2. What I hypothesize is this: The kinetic energy of the molecules is unmodified in their passage through the diffuser. This is because in the diffuser, we can assume isentropic flow (or VERY close to it) -- i.e. the air molecules experience NO addition or loss of heat (remember, we are still ahead of the combustion zone). Because of this, the molecular speeds are not changed, but their exact directions are altered to be less longitudinal and more transverse. So, the velocity vectors don't change in magnitude, but are rotated "outward" in direction. This means that the longitudinal velocity vectors have become smaller, while the transverse vectors have become larger. This corresponds to a reduction in "velocity pressure" and an increase in "static pressure" due to passage through the diffuser (this is based on the well-known principle of "pressure" being basically a measure of average molecular momentum, which is simply molecular mass x velocity).

So to summarize, my hypothesis is that in passing through a diffuser (and assuming isentropic flow), there is conservation of molecular kinetic energy accompanied by a rotation of molecular velocity vectors to a less longitudinal, more transverse direction, which can be directly measured as decreased flow velocity and increased static pressure.

Obviously, I have not considered the effect of the increase in air temperature that will inevitably accompany the pressure rise. In very fast ramjets, this would be a significant effect, of course.

All right, gentlemen, go ahead and prove me wrong.

L Cottrill

PyroJoe
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### Re: Hypothesis re Diffuser Action

I think that if you increase the velocity of each molecule, work had to be done on the molecules at some point. Is this considered drag in the above example? Otherwise chemical energy probably does increase the path of the molecules in normal jet operation. I would guess the reason vectors end up exiting the aft section of running engines, is probably do to that specific direction presents the least resistance/(density). Almost a partial laser effect. Molecules bouncing around until finding the path of least resistance.

One can also see why the rejection of heat by the CC becomes important. That bouncing around before ejection will heat the CC, if the heat is absorbed, it robs the molecules of their KE. If the heat is rejected the molecule will retain its KE.

Also the skinny CCs appear to focus the paths more quickly than fat CC, also adding to the laser action. Of course this is my own fringe speculation from looking around and tinkering with things.

Joe

larry cottrill
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### Re: Hypothesis re Diffuser Action

PyroJoe wrote:I think that if you increase the velocity of each molecule, work had to be done on the molecules at some point. Is this considered drag in the above example?
Don't let yourself think of molecular velocity as the same thing as flow velocity. They are vastly different ideas. There is no mechanical work perfomed at all in a nozzle or diffuser, if we assume isentropic flow (no loss or gain of heat to/from the outside). This is why the velocity vectors of the molecules are shown rotated (between pix 2 and 3), not lengthened or shortened.

The static pressure of a flowing fluid can only be measured with the flow running past the measuring port. For example, on an aircraft, the "airspeed indicator" system is really a Pitot tube system measuring a pressure difference. The "static port" of the system is carefully located on the fuselage surface so that the flow across it is non-accelerated flow (i.e. there will be no appreciable Bernoulli effect at that point); that way, an accurate barometric pressure for the outside air is obtained, even at maximum airspeed. That "sideways" orientation is absolutely necessary because it is the only orientation that eliminates the effect of airspeed on pressure. In the little measuring wand I sent you, you were able to see reduced static pressure, but that was because of the venturi action (i.e. bernoulli effect) of the intake (with its large flare) -- of course, there were other (wave-related) factors, too, in that case (this was a valveless pulsejet intake, for those who didn't see it).

What it all boils down to is that what I show as the "transverse" velocity vector component represents the "transverse" molecular momentum that we would measure at any point along the inner surface of the diffuser as static pressure (we could actually do this with a series of small ports and an appropriately sensitive gauge, for convenience). According to Bernoulli's law, the total energy remains constant for isentropic flow. So, if a diffuser smoothly slows the air in terms of overall flow and the average molecular speeds remain the same (by virtue of constant energy), the only other component of the velocity vector is its direction and that must be what changed! An outward rotation of the velocity vector would explain the simultaneous gain in static pressure and reduction in flow velocity.
Otherwise chemical energy probably does increase the path of the molecules in normal jet operation.
Ah, but that is not part of my example; I'm talking about the diffuser only. Recall that in the ramjet, pressure development is in the diffuser; expansion (via chemical heating) in the combustion chamber develops velocity within essentially a "constant pressure" environment. The "back pressure" from the exhaust nozzle equalizes automatically to the pressure established by the diffuser at the other end (think of the nozzle as a whole, not just the narrow throat). So the action we see in the chamber is constant high pressure with flow speed that increases from front to rear (until flow enters the nozzle region).
I would guess the reason (higher magnitude) vectors end up exiting the aft section of running engines, is probably due to that specific direction present(ing) the least resistance/(density). Almost a partial laser effect. Molecules bouncing around until finding the path of least resistance.
Actually, that's one way of looking at it, although I don't much like the "laser effect" part ;-) My first grab at analyzing this, away back in 2001, was to assume that the molecules bounced off the walls at an opposite angle on the other side of the "normal" line to the surface -- exactly like an optical reflection. Needless to say, this did NOT predict the real action of a fluid flow! What I neglected is the fact that most of the molecular collisions are against other molecules! That is something like the collisions of billiard balls (although even that is far too "predictable", since air molecules do not look like perfect spheres to one another). There is a huge degree of "randomization" to the molecular path problem. Thus, my picture really has to be taken to represent molecules as they are just about to collide with the diffuser surface, with no other molecules in the way.

It can be a hard thing to picture mentally at a microscopic level. We usually think about air flow velocities in tens of metres/second or some such, while molecular velocities in "still air" are on the order of 500 metres/sec at normal pressure and temperature. What we call flow velocity is just a sort of smoothed-out average "drift" of what is really a terrifically chaotic mass of little mutually repelling fragments. (But, you knew that ;-)

L Cottrill

larry cottrill
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### Re: Hypothesis re Diffuser Action

PyroJoe wrote:I think that if you increase the velocity of each molecule, work had to be done on the molecules at some point.
Joe, it now occurs to me that here you might be referring to the increase in speed between the first and second pictures. If so, then yes -- there was work performed. It was the work required to move the engine forward at velocity V1. That could be from combustion that's already happened, or it could be from a JATO rocket unit that's bringing the engine up to speed before starting, or whatever. But in any case, it's work that has been done BEFORE the molecules enter the intake. The important fact is that there is still no "loss" or "recovery" of energy between pix 2 and 3.

Sorry if I misunderstood what you were saying earlier.

L Cottrill

PyroJoe
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### Re: Hypothesis re Diffuser Action

No worries, this topic is interesting. Surprised so few have participated.
How do you see the diffusor action take effect, if you submerged the diffusor in water and move it along?
Something in the resulting velocity of the water as it exits?
Joe

larry cottrill
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### Re: Hypothesis re Diffuser Action

PyroJoe wrote:How do you see the diffusor action take effect, if you submerged the diffusor in water and move it along?
Something in the resulting velocity of the water as it exits?
You bet -- the water would exit at a decreased flow velocity. The only important difference would be that the water is essentially incompressible, so its density at the tail end of the diffuser would be no different from that of the surrounding water. In air, the compression would bring about a corresponding density increase. Similarly, the flow speed of the water at any point would be precisely determined by the area ratio (at that point) alone. In air, the flow velocity would be affected by compressibility, although this would be pretty insignificant at low speeds.

L Cottrill