Nozzle Design, Key to Turbine Efficiency
October -- my favorite time of the year. Fall colors are in full swing, we've had an early snow already -- it didn't stick for long, but we are taking the hint. Time to get our wood supply in and plan for winter activities.
Our minpins (miniature Doberman pinschers) are beginning to hibernate & demand more food for their winter fat, and the smaller birds are flocking south. But you won't find me in Florida again. You'd have to kill and bury me there to get me back to that hell on earth -- no, I'll take the North. The farther north the better!
Last month we reviewed turbine basics -- similar to the article we recently wrote for Steve Elswick's "ExtraOrdinary Technology" magazine (July/August/September edition).
This month we are revisiting inlet nozzle design.
Three Keys to Tesla Turbine Efficiency
According to Nikola Tesla, the three key efficiency points of his turbine are:
Disk geometry is a simple matter of using the right material with the right spacing and the right number & position of spacers, or sandwiched elements.
Starting with materials, use a good high strength stainless steel like 361 or 461 with as bright a polish as possible.
Space the disks anywhere from 0.032 inch to 0.125 inch, with the narrow spacing developing higher torque, lower horsepower -- and conversely.
Spacers should consist of a star type for the center, with 0.5 inch round washers placed at the mid and outer periphery positions. On a 10-inch turbine you would use six washers at the midpoint, 12 at the outer periphery.
The exit nozzle is located at the center of the engine and controls key elements such as backpressure, horsepower, and overall efficiency. Generally speaking, the larger the exhaust opening, the higher the horsepower and torque, but efficiency suffers.
The Inlet Nozzle
Now on to the main subject of the matter -- the inlet nozzle. This is by far the most important element in achieving and fine tuning the efficiency of the disk turbine. A properly designed nozzle has a complex shape that determines the efficiency of converting gas pressure to shaft horsepower.
The inlet nozzle is responsible for two important functions:
With this in mind, let's take a look at a couple of nozzle designs. First of all, we'll start with the traditional convergent-divergent nozzle, as shown in Figure 1.
Traditional convergent-divergent nozzle
The shape of the nozzle is extremely important in efficiently converting gas pressure, or potential energy, into gas kinetic energy.
Steam or gas enters the nozzle at A and increases in velocity to point d (vena contracta). Beyond point d the increase in volume causes a rapid expansion of the gas, which in turn increases the velocity enormously and simultaneously cools the gas. After passing through the divergent portion of the nozzle, it is important to straighten out the flow with a parallel section on the end.
A properly designed nozzle will efficiently convert a pressurized non-moving air mass into a high velocity gas moving several times the speed of sound (up to 4,000+ ft./second). The trans-sonic region of the nozzle is at the smallest throat diameter d, after which the gas goes supersonic in the divergent region.
To design an efficient convergent-divergent nozzle, we start from the nozzle exit point and work backward. The parallel tube diameter must match the width of the disk pack -- or slightly less to guarantee that gas does not blow around the end plates. (For wider disk packs the nozzle would be elongated rather than round.)
Let's take for example a disk pack that is 0.5 inch between the end plates. The nozzle parallel region would then be 0.5 inch in diameter. Working back from there, the Divergent angle is about 10 degrees, and the Divergent length is as long as possible or practical.
The diameter d is based on:
Generally speaking, we want to keep diameter d as small as possible and still develop sufficient high velocity gas to fully utilize turbine horsepower potential. In our example above, we may want to use a diameter d of about 0.125 inch to 0.25 inch.
The last calculation we have to make is the radius R -- which is simply R = 3/2 d.
For advanced experimental work a tunable nozzle could easily be made using a moveable tapered rod from point A to partially close off throat d.
Finally we'll take a look at a nozzle design that follows the same convergent-divergent principles as the traditional nozzle, but allows a much easier method of construction.
In Figure 2 we see basically a straight tube into which we center a carefully shaped insert.
Nozzle designed for simplified construction
The insert must follow the same calculations as the traditional nozzle, and it must also be fastened exactly in the center of the tube.
Next month we'll work on boiler basics, and then pull it all together in December. Until then, keep those projects rolling.
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Last updated: July 02, 2008 11:21 PM
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