Model Turbines

I made the following spreadsheets to find the rotor velocity coefficients. In the spreadsheets I used the methods given by Dr. Balje in his report ‘A STUDY OF HIGH ENERGY LEVEL, LOW POWER OUTPUT TURBINES’ made in 1958 for finding the average rotor velocity coefficients. As you can see from the spreadsheets the average rotor velocity coefficients are dependent on the number of blades or pockets covered by the nozzle. The arc of admission, a, of Radial Turbine 5B is approximately 1.5 times as large as that of Axial Turbine 4A. This results in the average rotor velocity coefficient being much closer to the maximum rotor velocity coefficient. Even with this advantage, Tangential Turbine 5B has a much lower average rotor velocity coefficient than Axial Turbine 4A since its maximum rotor velocity coefficient is so much larger. This shows that the traditional axial turbine rotor is quite a bit higher in efficiency than the open pocket tangential turbine rotor. If you look at drawings shown in the 16/03/2023 post, you can see the incidence of the flow entering the blades is much less for Axial Turbine 4A. Also the blades and close clearance on the OD force the flow through a constant area closed on all sides. This keeps the flow from expanding to a lower velocity as it passes thru the blades. The open pockets allow this expansion, and the overlapping pockets have a much higher gap between the OD and housing bore in the center of the pockets so allow more leakage. I will try in the next posts to show how with this large advantage in rotor efficiency, Axial Turbine 4A could only turn the same size propellers the same maximum speed as Tangential Turbine 5B.

I made the following spreadsheets to calculate the hydraulic torque using the velocities found from a typical velocity diagram like shown below. I coded the velocities in the spreadsheets to match the velocity diagram. The propeller used for the test data was the largest propeller I have that had performance data down to speeds as low as 1,000 rpm. I thought that finding the torque at this low of a speed should be close to the stall torque since the rotational losses would be almost negligible. The hydraulic torque is determined by the entrance velocity in the rotor movement direction, Vw, and the exit velocity in the rotor movement direction, Vw1. As you can see from the spreadsheets, Axial Turbine 4A has a much lower Vw than Tangential Turbine 5B, but a much higher Vw1 so the net result is almost the same torque. These spreadsheets show the importance of the velocity coefficients and how they effect the torque. I will use similar spreadsheets in the next post to illustrate  their effect at higher speed using the GWS EP 2508 propeller.

Edited By Turbine Guy on 23/03/2023 17:45:35

The following spreadsheets, similar to the ones in the last post, show the effect of using a smaller propeller running at a higher speed of 28,000 rpm. This speed is high enough to start getting significant rotational losses so the hydraulic power must be larger than the actual power to absorb these losses. The rotational losses are larger with the blades than with the open pockets, but neither was very large at this speed. The most significant reason Tangential Turbine 5B almost matched the performance of Axial Turbine 4A was its better nozzle efficiency due to a much shorter throat length. This difference in throat length was caused by the center drills I use to create the nozzles that I will explain in the next post.

You can see in the following drawings showing the details of Axial Turbine 4A and Tangential Turbine 5B that I tried to get the center drill as close to the housing bore or face of the cover as I could. This is the best tool I have found to make a reasonably efficient nozzle and is only available with a 1/8” OD. It is the large OD that creates the problem. That is why I was excited about using an insert in Tangential Turbine 5C to get the nozzle throat length even shorter and provide a space for the gas to expand before contacting the rotor. I got a test of Tangential Turbine 5C running on steam described the 08/03/2023 post that made a significant improvement, but the insert quit working while running further tests on steam. I had to remove the insert to find what was causing the problem and decided to make a new insert with a smaller bore like I first planned to do. The used tailstock I ordered for my Unimat 3 lathe arrived and is in excellent condition as described by the seller in Ebay. I hope this will solve my problem of drilling the very tiny holes and plan to make a new insert and start testing Tangential Turbine 5C again. If I am able to drill the very small holes again, I will design a new cover for Axial Turbine 4A that will use this concept for what I will call Axial Turbine 4D.

The replacement tailstock did solve the problem of drilling the very tiny holes. I was able to make the insert shown in the following drawings on my first try. I added the insert in Axial Turbine 4A first that was going to be called Axial Turbine 4D. I made a few tests with Axial Turbine 4D and then removed the insert and added it to Tangential Turbine 5C as shown below. The insert performed better in Tangential Turbine 5C so I will use this turbine for the tests with steam that needed the 0.024” nozzle size. I will discuss the performance of the insert running both turbines on air in the next post.

My own experience of making jets for a model butane burner supports your conclusion about the importance of keeping the throat length very short. The bore in a series of jets that I made was 0.02” diam. The length of the bore (i.e. the thickness of the nozzle end, as shown in the drawing below) was varied from 0.109”, 0.05” and 0.024”. (Measurement of actual thickness was by inserting inside the jet body a small rod of known length and measuring the overall length of rod and jet). There was a very impressive improvement in performance of the burner at each stage of shortening.

As you know, in many turbines the nozzles have to be curved and text books that I’ve read advise that a convergent nozzle should narrow down over a short distance and have a short straight parallel section at the exit to help steam leave at the desired angle. The length of this section should be about the same as its width. For a straight nozzle like yours I imagine that length could be even shorter. So I bet the reducing the bore length to even less than 0.067” would be advantageous, if that could be done.

My own nozzles have a construction that allows the curved shape. The outlet is 0.027” wide and they have a straight parallel exit section 0.027” long, as shown in the drawing below. (The only trouble is I’ve not yet reached the stage of using them to turn a rotor).

Hello Mike,

Why don't you use sections of medical injection needles. There is a large variety of sizes. To doctors, they are consumer items and I get them free of charge!

Hello Werner

My design is based on my (possibly erroneous) understanding of how turbines should ideally be designed, but I cannot be sure to what extent the following is correct for a miniature turbine. Hopefully I’ll find out one day when I eventually get a working machine.

My nozzles need to fit in the narrow diaphragm that separates the stages of what I hope will one day be a multi-stage turbine. Also the outlets of the nozzles need to be at a small angle (18 degrees) to the plane of the rotor. Drilling holes at such a small angle would be very difficult and would not fit within the circumference of the diaphragm. As in full-size turbines of this type, the nozzles have to be curved so that steam entering from the previous stage has its direction of flow changed to give the correct exit angle. Another aspect is that, for best efficiency, the text books say that a convergent nozzle should taper down by a smoothly curved shape over a short distance to the exit width. This minimises losses due to friction and eddy formation. Frictional losses are greatest at the highest steam velocity and that is attained at the outlet. Also, frictional loss is highest at the narrowest part of a nozzle which is also at the exit of a convergent nozzle. Therefore the final and narrowest part should be kept just short enough to sufficiently control the direction of the steam. Further back in the nozzle the steam has not yet expanded /accelerated so much and nozzle width is greater. These factors all mean that steam velocities at those earlier parts of a nozzle are much lower and so friction is reduced. With my design I have almost full control of the nozzle profile. Another reason for favouring my nozzle design is that the steam path is rectangular and so matches the gaps between the rotor blades. This means that the steam should fill the gaps whereas steam jets from circular nozzles would not fill the corners. I doubt this aspect has much impact on a miniature turbine but I think it was considered important for full-size turbines.

Mike

Hi Mike and Werner,

Thanks for breathing a little life into this thread. I have very little time this morning, so I will be very brief. I totally agree with Mikes comments on his type of nozzle and believe that it would produce the highest efficiency for subsonic to sonic flows and is the most used by full size turbines for these conditions. The round nozzles with converging and diverging sections seem to be preferred for the supersonic flows. I'm not sure which type would be best for a converging only nozzle expanding to supersonic velocities outside the nozzle. I agree with Werner that it is a lot easier to make an insert from injection needles or surgical tubing than drilling a tiny hole.

Thanks for the comments,

Byron

The following test sheet shows the performance of Axial Turbine 4D and Tangential Turbine 5C running on air I said I was going to show after the 27/03/2023 post that also included the following drawings. I will look at the reasons for this performance in the next posts.

I estimated the nozzle velocity coefficient of Axial Turbine 4D to be approximately 0.69 and 0.73 for Tangential Turbine 5C for the tests shown in the last post. These velocity coefficients were determined by starting with the velocity coefficient of 0.93 for the conical nozzle as explained in the 17/03/2023 post then finding the reduction for the pressure drop due to friction. The reduction due to pressure drop was 0.94 for both turbines since they had the same nozzle throat length. This reduced the nozzle velocity coefficient to 0.87. I then found the reduction for expanding to supersonic velocities with a converging only nozzle shown in the following diagram as line A. In the tests shown in the previous post, the Mach number for Axial Turbine 4D was 1.47 and for Tangential Turbine 5C was 1.43. The reduction for expanding supersonic is approximately 0.97 for both turbines when rounded to two decimal places. This reduces the nozzle velocity coefficient to 0.84 for both turbines. The last reduction was for the distance between the nozzle outlet to the rotor. This was 0.186” for Axial Turbine 4D and 0.113” for Tangential Turbine 5C as shown on the two drawings of the last post. The reduction in nozzle velocity coefficient for this was 0.82 for Axial Turbine 4D and 0.87 for Tangential Turbine 5C. This reduced the nozzle velocity coefficient to 0.69 for Axial Turbine 4D and to .73 for Tangential Turbine 5C as stated at the first of this post. The reduction in rotor velocity coefficient for supersonic velocity was 0.98 for both turbines. The rotor velocity coefficient found from the static torque test explained in the 23/03/2023 post were 0.68 for Axial Turbine 4A and 0.27 for Tangential Turbine 5B. Neither of these turbines had the insert and the discharge velocity of the nozzles were approximately sonic, so using the correction for supersonic velocities reduces the rotor velocity coefficient to 0.67 for Axial Turbine 4D and to 0.26 for Tangential Turbine 5C. I will show in the next post how the test results in the last post compare with the velocity diagrams like shown in the 23/03/2023 post.

Edited By Turbine Guy on 29/03/2023 21:20:09

The following spreadsheets show the results of Axial Turbine 4D and Tangential Turbine 5C using the rotor velocity coefficients and nozzle velocity coefficient shown in the last post. These values worked well for Axial Turbine 4D but not for Tangential Turbine 5C. The rotor velocity coefficient found by the stall torque in the 23/03/2023 post appears to be quite a bit low. I will see if I can find the error.

I couldn’t find the reason for the velocity coefficients only working for Axial Turbine 4D as discussed in the last post, so I made a stall torque test for Tangential Turbine 5C like described in the 21/03/2023 post. The air pressure used in the test of Tangential Turbine 5C was the same as shown in the last post. The weight of the load used was 0.094 oz. The radius to the load was 2.93” so the maximum static torque was 0.275 in-oz. I used the nozzle velocity coefficient determined in the 29/03/2023 post in the following spreadsheet to find the rotor velocity coefficient. This rotor velocity coefficient is more like I expected and works better as shown in the following velocities spreadsheet.

I found an error in the nozzle velocity coefficient for Tangential Turbine 5C I described in the 29/03/2023 Post. The correction for the distance from the nozzle to the rotor should have been 0.95 instead of 0.87. This changed the nozzle velocity coefficient from 0.73 to 0.81 and resulted in the rotor velocity coefficient shown in the 31/03/2023 post changing from 0.63 to 0.51. The following spreadsheets show the effect of this change. The estimated hydraulic power at 28,000 rpm is greater than the actual power like it must be.

Mike Tilby pointed out that the angle theta of the flow approaching the blade or pocket inlet shown on my velocities spreadsheets could be different than the rotor inlet angle, so I made the rotor inlet angle theta b. I also added the other flow angles shown on the following velocity diagram. We started the discussion with the spreadsheets shown in the 23/03/2023 post so I updated the following velocities spreadsheets for Axial Turbine 4A that uses the rotor he made for me and sent him copies. Mike checked the angles and after a few corrections we agreed the equations used in these spreadsheets appear to be correct. Hopefully these angles will be helpful in showing the changes in direction of the flow as it approaches, runs through the blades, and exits the rotor. I will use these updated spreadsheets for future tests. I encourage anyone that believes they have found an error in anything I add to this thread to please let me know.

I ran a test of Tangential Turbine 5C on steam using my Stuart Twin Drum boiler. I was not able to run the test continuously at 40 psig but was able to run it for short periods at this pressure, so the actual mass flow at 40 psig is not known. Since only the dry steam does useful work, I calculated the mass flow and enthalpy drop for dry saturated steam at 40 psig for a 0.024” nozzle and used them in the following spreadsheet. The values of the nozzle velocity coefficient and rotor velocity coefficient were as previously found running on air as discussed in the 31/03/2023 and following posts. Hopefully this will give a reasonable comparison of running on air and saturated steam at the same pressure. I used the updated spreadsheet running on air shown below for comparison. Using the same velocity coefficients for steam as were found for air seems to give reasonable results.

Edited By Turbine Guy on 07/04/2023 15:18:09

I was given a copy of the article shown in This Link and found it very interesting. They used a rotor like shown below that was made with the dimensions given in the article. I call it 3 Blade Rotor for its small number of blades. The concept is very unique, since the flow enters the channel like a tangential turbine, then runs down the channel like a drag turbine, and exits the channel like an axial turbine. The article explains the process in much more detail and shows how they estimated the performance and how their estimates compared with test results. I made a housing using the few dimensions they gave in the article and combined it with the 3 Blade rotor to make the following drawing of the 3 Blade Turbine. I will show a velocities spreadsheet for this turbine in the next post.

I decided to use the pressures, areas ratio, and speed shown in Figure 9 of the article in the link given in the last post. This is a 3 Bar inlet pressure, approximately 1.1 Bar channel pressure, Kp = 0.66, and a speed of 5,000 rpm. The rotor channel is 7mm wide and 11mm high, so the channel area is 77 square millimeters. The nozzle throat area is 0.66 x 77 = 51 square millimeters. Since the 1.1 Bar pressure occurs almost the entire filling time this will be considered the channel pressure and the exhaust pressure is assumed to be atmospheric. The mass flow through the nozzle is larger than mass flow out of the channel with these pressures so I am assuming the difference is leakage. With these assumptions I made the following velocities spread sheet. My method of estimating the efficiency came close to the test results of Figure 19 for the approximately 0.1 U/Co of this example. I showed the following velocities spreadsheet for Axial Turbine 4A for comparison since this turbine had an efficiency of 24.2% that is the best of all the turbines I have tested so far. You can see that even with the lower nozzle and rotor velocity coefficients of Axial Turbine 4A  it reached almost as high an efficiency. I am trying to see if I can come up design using the 3 blade rotor that will have efficiencies in this range with the low mass flows and pressures of my airbrush compressor and boilers. 

Edited By Turbine Guy on 18/04/2023 21:06:41

I studied the analysis in ‘Theoretical and experimental analysis of new compressible flow small power turbine prototype’ by Silvio Barbarelli, Gaetano Florio, and Nino Michele Scornaienchi shown in This Link and although I was not able to follow it completely, I thought this type of turbine would work reasonably well with my airbrush compressor and boilers.I looked at different combinations of using a new 3 Blade Rotor with existing turbine housings and designing a new turbine housing specifically for this type of rotor. Although a housing designed specifically for this application showed the most promise, I think that the rotor shown in the following drawing used in the existing Housing 3 SD Gap has quite a bit of potential. I had to make a few compromises to the design of the rotor to fit in this housing and use the existing nozzle. The design of the rotor makes it possible to be printed or cast. The long channel works like in a drag turbine for the middle of the cycle, so the rougher surface helps get extra drag force to partially offset the loss in exit velocity. Since I only need to make the rotor and shaft, I decided to have the rotor printed in aluminum and will make the shaft out of precision machined stainless steel like in all my other turbines. The following drawings show the dimensions I am going to try to obtain for 3 Blade Turbine 2.

I assumed the pressures shown in ‘Theoretical and experimental analysis of new compressible flow small power turbine prototype’ by Silvio Barbarelli, Gaetano Florio, and Nino Michele Scornaienchi shown in This Link were gage pressures when I made the velocities spreadsheet shown in the last post. That is why I showed the pressure in the spreadsheet as 44.1 psig. When I do my analysis, all the pressures are converted to absolute which is required when using the gas equations. I assume this was done in the article, but I don’t know if the pressures shown were gage pressures or the gage pressures were converted to absolute pressure and then shown. After calculating the pressure drop in the channel of the 3 Blade Turbine described in the 18/04/2023 post, I found that the pressure drop in the channel was very low. The pressure drop I calculated was very close to the 1.1 Bar given for that example if it was absolute. I decided to revise the 3 Blade Turbine Velocities spreadsheet shown below with the assumption that the pressures given are absolute. I used the case shown in Fig. 19 where U/Co is 0.11, the efficiency is 30%, the inlet pressure is 3 Bar, and Kp is 0.5. The velocities were calculated the same way I did for the tangential and axial turbines. Where the spouting velocity is based on the full enthalpy drop, the nozzle velocity coefficient assumes the pressure downstream of the nozzle is exhaust pressure, and the rotor velocity coefficient includes all leakage and pressure drop losses. I used a nozzle velocity coefficient of 0.95 based on a converging only nozzle expanding to a Mach 1.3 velocity like shown in the chart of the 29/03/2023 post. I found the 0.80 velocity coefficient of the rotor gave the velocity required to pass almost all the mass flow. The resulting hydraulic efficiency of 32.8% would allow for the rotational and leakage losses if they are as low as the report indicates.