- Jan 26, 2022
- Reaction score
Hi Toymaker, just some clarification of my understanding of De Laval nozzles.
As you are sending gas at the orifice from the pressure of the liquid, to a space beyond the nozzle at "some other pressure", I think the divergent nozzle shape is critical, both to the pressures, the density of gas at the end of the nozzle, and also the speed of sound for the gas at the pressure within the chamber at the end of the nozzle.I think that if the nozzle is too wide, you won't develop the velocity of gas that would be achieve with a correct nozzle. I also think that if the nozzle is too long it will choke the flow and reduce performance of the gas stream, both mass and velocity.
- I agree the total CSA of the combined set of nozzles (throat CSA) determines the total flow, subject to pressure difference across the throat.
- I do not know how to design the converging nozzle.
- I have read about the diverging nozzle with gas mixtures accelerating to sonic velocities. BUT the sonic limit (speed of sound) varies as the pressure and density of fluid (gas mixture). In rocketry, the diverging nozzle is different for an atmospheric and vacuum environment, and some nozzles have variable bells to optimise the shape as the rocket passes through the thinning atmosphere with altitude. I think that the nozzle can choke the output (velocity) if the wrong shape.
Please research this as I am not an expert, just a novice at the early stages of learning these subjects. I am quite likely to be wrong.....
From what I've learned about nozzles, choking is not usually a big problem. Induced turbulent flow is the biggest concern, which happens when the gases are allowed to expand too quickly, but as long as the nozzle expansion angle stays somewhere close to 15°, there shouldn't be a problem. Here are couple of images of real existing ORC nozzles. The color images were generated using CFD (Computational Fluid Dynamics) software; notice how the upper portion of the nozzle is not fully complete, but instead relies on the fluid flow from the adjacent nozzle to help shape the flow. The convergent-divergent shape is also obvious, and exists only in 2 dimensions as these nozzles are not round holes.
Also notice how thin the nozzle material becomes at the nozzle exit; when you actually machine these nozzles you will find that compromises will need to be made as the designed material thickness becomes less than 0.010", which from a practical standpoint, wont work.
In a multi-stage axial flow design, you should also keep the expansion angle of the entire turbine housing close to 15° so as to avoid turbulent flow through the blades and stators.
Also, in the 2 dimensional plan view, notice how both the second stage blades and stators (black & white drwg above) roughly form convergent-divergent nozzles, the entrance to all the blades and stators is larger then the exit, forcing the gases to accelerate through the blade row.
Finally, here's my nozzle and blading design. Ignore purple lines as they're only construction lines from my CAD drawing. The gap between adjacent nozzles is 1.5mm. Notice the nozzles convergent-divergent geometry.
Added one final pic,...this is my actual nozzle. It's not easy to see, but if you focus on the root area you can see the convergent-divergent geometry.