Air velocity calculation through thin slot

[globalsoaring]

Hi,

I am trying to calculate the air velocity at a certain distance after it has exited a thin slot (600 mm x 0.5 mm). I know the air pressure inside the plenum, i.e. before the air exits the slot. The air is discharged into atmosphere where it obviously expands and slows down. Any hints on how I can calculate the remaining airspeed at 150 mm, 300 mm and 450 mm distance?
Also on my mind are any ideas as to whether a plenum shape can be theoretically determined to generate the best air flow through a thin slot.
Thanks for your help!

Marcus.

 

[poetix99]

This is a relatively simple example of a plume/jet/wake type of problem, which can, in general, become rather complex for hand calculations.

I'll need to consult some references that I don't have at hand, and will respond again in the days ahead.

In the meantime, a few comments about the simplifying assumptions that the jet calculations will depend upon, and a question or two about your actual design objective.

You should verify that your "problem" fits within these constraints. I am thinking that you might not have asked the question that you really want an answer to:

FOR A 1-D JET PROBLEM THAT IS CALCULABLE:
- This is a one-dimensional problem, provided that you are interested in the velocity of the "jet" at the mid point of the 0.5mm dimension, and well within the mid range of the 600 mm dimension. In other words, we can assume symmetry and neglect edge effects.
- The jet discharge is into an undisturbed, EFFECTIVELY "infinite" plenum; there are no other solid boundaries to disturb the jet.
- There is no (residual) velocity of the air. If the jet discharges into a relatively small plenum (see previous assumption), you will induce circulating flows and these will effect the (theoretical) jet velocities.
- There are no density effects which would change the phenomenon. Buoyant plumes are similar jet/wake/plume flows, but the solution of the combined momentum flux & buoyant plume will not be so easy. If the jet flow is not in the direction of the buoaynt flow, the symmetry is gone and any approximate closed-form solution is beyond hope.
- If the jet discharge is pressurizing the plenum, this transient problem is more complicated in two ways. One, the discharge velocity is obviously diminsihing with time. Two, because jet plumes are the spreading out of the initial jet momentum due to turbulence (we assume the momentum is undiminished, just spread out), the momentum diffusion will change as the free stream (plenum) density changes.

Your actual design intentions are unclear to me because of your last comment: If you want the plenum to influence the discharge from the jet, you will BY DESIGN, violate some of the assumptions I've described. Indeed, it is not really a "plenum" if the boundaries are that close. But regardless of what you might call the "plenum", I am left to wonder what you wish to achieve.

- Enhanced mixing within the plenum?
- Does your desire to "generate the best air flow" mean to maximize the mass flow discharging from the slot? The slot is an orifice, and will be influenced more by the upstream geometry, rather than the downstream geometry. (a sharp edged orifice has a flow coeff. of about .62 and a flow nozzle with rounded entrance has a flow coeff. of about .97)

You might be better off with a full size model and some hot-wire anemometers. Beware of reduced-scale testing; depending upon what you want, the jet or mixing phenomena of interest might not scale geometrically.