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Martin Johnson 113/03/2019 16:53:46
112 forum posts
1 photos

Thanks for making me think, chaps.

You are right for constant momentum, but greater mass flow, the TORQUE would remain constant for a given design of blades, but at the same time the optimum running speed would fall in the ratio of the mass flow increase (same as velocity decrease). Hence power falls as the ratio of mass flow increase or velocity decrease. All assuming motive and entrained fluids of identical density.

BUT earlier in this thread TG is reporting a blade speed to fluid speed ratio of 0.022 - way down on where it should be for a two velocity staged machine. AND even if he can get the running speed up to where it should be, how long will the bearings stand up to it? Or, indeed, how long will the blades stay attached to the hub? AND what losses would there be in a wee gearbox to reduce the speed to something manageable?

So, the question remains for tiny turbines, would an ejector lose more than it gains?

For all that, I am in awe of the tiny rotor and blade cutting that TG is undertaking. Also, the methodical way it is being thought through. Keep the reports on progress coming, please.


Turbine Guy13/03/2019 18:54:24
79 forum posts
35 photos

The following is a similar analysis as in the 13/03/2019 posts for the GH ½ B model jet pump

Air inlet pressure of 0 psig

Air inlet temperature of 70 F

Air inlet enthalpy of 126.7 btu/lb

Steam pressure of 120 psig,

Steam temperature is 351 F

Steam enthalpy is 1192 btu/lb.

Suction capacity is approximately 54 SCFM.

½ B Capacity factor is 0.030.

1½ model steam consumption is 390 lb/hr

½ B model steam consumption is 11.7 lb/hr

½ B air pumped = 1.6 SCFM

½ B mass flow of air is 7.2 lb/hr

Discharge pressure is 12 psig,

Discharge temperature is 300 F

Discharge enthalpy is 1192 btu/lb

Discharge mass flow is 18.9 lb/hr.

The mixture isentropic enthalpy drop to a pressure of 0 psig is 1192 – 1144 = 48 btu/lb. The exit velocity from a nozzle with this enthalpy drop is 1550 ft/sec. The energy of the mixture is 48 btu/lb x 18.9 lb/hr = 907 btu/hr

The isentropic enthalpy drop from the 120 psig and 351 F to a pressure of 0 psig is 1192 – 1045 = 147 btu/lbm. The exit velocity from a nozzle with this enthalpy drop is 2,713 ft/sec. The energy of the steam is 147 btu/lb x 11.7 lb/hr = 1720 btu/hr.

This model jet pump was designed to move higher flows with less steam and works better. The extra mass flow and lower velocity increases the nozzle size or quantity which can make a substantial difference on small turbines.

I'll read the discussions on momentum exchange and respond.  

Edited By Turbine Guy on 13/03/2019 19:00:55

Turbine Guy13/03/2019 23:13:27
79 forum posts
35 photos


The equation I use for the power of an ideal impulse turbine might help show the effect of changes.

P =2MW(V-W)/g
P is the power
M is the mass flow
W is the rotor speed at the blade location
g is the acceleration of gravity
V is the spouting velocity of the nozzle

Increasing the mass flow or spouting velocity without any other changes will always increase the power. Increasing the rotor speed up to a maximum of ½ the spouting velocity will also increase power in the ideal case but rotational losses have to be dealt with in real turbines.

What I found in the last post is starting to convince me using an ejector might actually help. I'm going to look at this a little more.

I appreciate you comments on my methodical approach and machining the tiny blades. I enjoy the engineering and design as much as making the models. Because of the cost of the tools required and my limited machining skills, It will be a while before I try making the model Terry turbine. I have an improved version of the open pocket rotor I plan to make next.

Turbine Guy14/03/2019 18:14:21
79 forum posts
35 photos

I finally have enough information to give an indication of how effective using an ejector could be for small turbines. A Penberthy GL ½ A ejector has the following performance.
Air inlet pressure of 0 psig
Air inlet temperature of 70 F
Steam pressure of 80 psig,
Steam temperature of 324 F
Steam enthalpy of 1186 btu/lb
Steam consumption of 8.3 lb/hr
Amount of air pumped = 1.77 SCFM
Mass flow of air is 8.0 lb/hr
Discharge pressure is 6 psig,
Discharge temperature is 290 F
Discharge specific volume is 21 ft^3/lb
Discharge enthalpy at 6 psig is 1186 btu/lb
Discharge enthalpy at 0 psig is 1154 btu/lb
Discharge mass flow is 16.3 lb/hr.
Discharge isentropic enthalpy drop to a pressure of 0 psig of 32 btu/lb.
Steam enthalpy at 0 psig is 1047 btu/lb
Steam isentropic enthalpy drop to a pressure of 0 psig is 139 btu/lb.
Steam specific volume at 0 psig of 24 ft^3/lb

With this information I can use the following chart to estimate the performance with and without the ejector. This chart estimates the maximum performance for the given specific speed Ns and specific diameter Ds. It is intended to be used by first deciding the speed you would like to run and then calculating the specific speed Ns. You then use Ns to find the Ds that gives the best efficiency. You can then find the optimum rotor diameter from the Ds. I am using a turbine speed of 10,000 rpm for this comparison.

For the ejector, Q3 = 0.095 ft^3/sec, Had = 24,896 ft-lb/lb, and Ns = 1.56
From the chart for Ns = 1.56 the maximum efficiency is approximately 34% with Ds =18
For Ds = 18, the rotor diameter is 5.30 in. The power is 0.070 hp.

Without the ejector, Q3 = 0.055 ft^3/sec, Had = 108,142 ft-lb/lb, and Ns = 0.39
From the chart for Ns = 0.39 the maximum efficiency is approximately 17% with Ds =40
For Ds = 40, the rotor diameter is 6.21 in. The power is 0.076 hp.

Using the ejector, the efficiency of the turbine is double that of the turbine without the ejector. The ejector definitely improves the transfer of energy in the turbine. However, the discharge mixture from the ejector has so much less energy that the power ends up almost the same.
Ns Ds Diagram

Turbine Guy15/03/2019 12:05:30
79 forum posts
35 photos

The heavy solid lines in the chart of the preceding post are for axial turbines. The dashed lines are for Terry turbines. The thin solid lines are for Drag turbines. The drag turbines are like turbine pumps. The blades circulate the flow in a way that increases the drag force on the rotor.  The units for the volume flow are ft*3/sec and for the gas density lb/ft^3.

Edited By Turbine Guy on 15/03/2019 12:08:55

Turbine Guy26/03/2019 19:13:22
79 forum posts
35 photos

In the post of 08/03/2019 I showed a revised rotor and stated that it could get a rotor velocity coefficient of up to 1.64 times that of my existing turbine rotor. I built this rotor almost as shown on the drawing attached to the 08/03/2019 post. The following photo shows the new rotor (aluminum) next to the original rotor (brass) I tested this rotor with the same air pressure and flow used in the test of my original rotor that had a maximum speed of 17,000 rpm. The maximum speed with the new rotor was 18,250 rpm. The required power of the EP2508 propeller used in these tests is approximately 1.9 watts at 17,000 rpm and 2.4 watts at 18,250 rpm. The average rotor velocity coefficients for these output powers are 0.34 for 1.9 watts and 0.53 for 2.4 watts. The increase in rotor velocity coefficient with the new rotor is 1.56 times. I didn't quite get the maximum I thought was possible, but this is a very significant increase. The original rotor has 24 pockets and the new rotor has 48 pockets. In Dr. Balje's study of high energy level, low output turbines the highest average rotor velocity coefficient for a Terry turbine with a single nozzle and 45 blades was 0.53 The open pockets appear to be as efficient as the Terry turbine blades.

Turbine Rotors

Turbine Guy10/04/2019 21:06:52
79 forum posts
35 photos

Based on the success of the new rotor that verified the importance of using as many blades or pockets as practical, I’m going to try velocity staging next. I looked at making a Terry turbine with a reversing chamber as shown on the drawing of the 04/03/2019 post. I was able to come up with ways to machine the blades but since the performance of the open pockets appeared to be about the same as with blades, I’m looking at other possibilities. I compared the estimated performance of the Terry turbine with an open pocket design that used two rows of blades on the rotor and an open pocket reversing chamber as shown on the following drawing. Since a new housing is needed, I increased the number of pockets from 48 to 60. I also made the ratio’s of the nozzle admission length (a), reversing chamber admission length (ar), and the rotor pitch length (t) approximately even multiples (a/t = 0.103/.051= 2.02 and ar/t = 0.051/0.051 = 1). With these improvements to the open pocket design, the estimated maximum power was about the same as for the Terry design. The wider blades required for the corkscrew type of flow of the Terry turbine resulted in about 2.5 times the flow length of the open pocket design per stage. Both types allow the flow to expand as it travels, so the length of travel is very important. Dr. Balje’s methods of estimating performance take this into account and were what I used to in my comparison.

Tangential Turbine 3 VS 2

DrDave10/04/2019 21:29:34
157 forum posts
30 photos

I was wondering how you were going to machine the reversing chamber around the whole internal circumference: I had forgotten that you only need a short length. A very elegant design! I hope that it runs well.

Martin Johnson 113/04/2019 09:58:57
112 forum posts
1 photos

Turbine Guy,

I have just caught up with your post of 14/3/19 doing outline design calculations for a turbine and a turbine / ejector combination. Carefully thought through again, and interesting that it shows things to be roughly the same - i.e. ejector losses balance turbine efficiency gains. Thanks for that.

How well do you think the Ds Vs. Ns chart reflects things in your tiny turbines?

I will be very interested to see what you get from the two stage open pocket design. - I dare say you will be as well.

Thanks for a great thread,


Turbine Guy13/04/2019 18:31:22
79 forum posts
35 photos


Thanks for your kind remarks. I hope the new turbine meets my expectations. I’ll start turning out the parts when the indexer I ordered arrives.

The with ejector and without ejector analysis was an interesting project. I didn’t have any idea what the results would be. I hope this answered your question.

The last test of my turbine with the new rotor had a Specific Speed Ns of 0.7 and a Specific Diameter Ds of 11.9. From the Ns Ds chart the adiabatic efficiency of the optimum axial impulse turbine is about 15% for these values. The adiabatic efficiency of my model turbine was approximately 13%. My design is relatively simple to make and I am pleased it gets this close to the performance of a well designed axial turbine.

I’m anxious to see how well the Curtis type velocity staging works with my open pocket design. I believe the momentum of the air will keep the flow against the pockets until it is almost through the rotor. I feel the very short flow length is what allows the open pockets to work.

Turbine Guy18/04/2019 21:56:20
79 forum posts
35 photos

I looked at the axial rotor and nozzle that would give the efficiency given in the last post. The rotor and nozzle assumptions used by Dr. Balje in the Ns Ds Diagram are:
a*/D = 0.015, s/h = 0.02, t/te = .02, and r1= a*. The cutter diameter (a*), blade height (h), blade pitch (t), blade entrance thickness (te), and the blade inside radius (r1) are shown in the following drawing. The clearance between the top of the blades and the housing (s) would need to be about 0.001 in. Another assumption is the flow leaving the nozzle should be at 16 degrees including the 6 degrees it deflects due to the angular discharge opening. The blade inlet and discharge angles are equal and designed to have no incidence at design speed. The drawing shows the values of these parameters for Ns = 0.7 and Ds = 11.9 of the last post. The speed (N) is 18,250 rpm, the exhaust volume flow (Q3) is 0.0064 ft^3/sec, and the expansion head (Had) is 27,230 ft-lb/lb for this example.
One of the most significant advantages of the axial turbine compared with the tangential turbine is the small angles that can be used on the nozzles and blades. The efficiency increases due to the flow being closer to perpendicular to the direction of the rotor movement and the increase in admission length (a). The tangential turbine is very limited in making the blade and nozzle angles small. Dr. Balje assumed a nozzle angle including the 6 degrees of flow deflection of 20 degrees for the Terry turbine.
Axial Nozzle & Rotor 1

Turbine Guy28/04/2019 16:27:23
79 forum posts
35 photos

The following picture of my Excel spreadsheet shows how I document the performance from my testing and compare the results with the guidelines given by Dr. Balje. This is the spreadsheet I made for the tangential turbine described in the post of 26/03/2019. I can check the estimated performance with the actual performance using this spreadsheet. The spreadsheet shows the pressures, temperatures, and mass flow of the air used in the test and the estimated and actual performance with these values. The spreadsheet also shows all the applicable turbine dimensions used in the calculations. The spreadsheet includes the estimated velocities of the air at each stage of its passage from the nozzle through the rotor. Fig. IV.24 is the Ns Ds diagram for axial turbines with approximately 40 blades and Fig. IV.42 is the Ns Ds diagram for Terry turbines with approximately 40 blades from Dr. Balje’s report. The Ns Ds diagram shown in the 14/03/2019 post is for axial turbines with approximately 66 blades.

Tangential Turbine 2 Excel

Werner Jeggli12/05/2019 23:09:44
9 forum posts


I just hit upon your thread - and I'm very interested. Obviously, you are all professionals and I'm trying to follow your arguments. But I'm confused! You started out with the idea of a steam turbine. But in the later posts, the discussion is based on air turbines - right ? That are totally different kettles of fish.

I think that your method of measuring the turbine output is not very accurate. Using a brushless generator gives you shaft power and rpm - see ME Vol.207, No.4412, September 2011 (Dampfsprinter) and ME Vol 215, No.4514 (Turbomotive). There, I also tried to determine turbine efficiency.

My latest project, the PRR-S2 is also quite successful (search YouTube under "PRR-S2, Jeggli". The good performance I reached more or less by trial and error. I'd love to get them supported by a more scientific approach. The problem is the turbulent steam flow in the turbine. I do not think to being able to build a more efficient multistage turbine, reducing the pressure drop to the required 0.8 Bar/stage, which would insure laminary steam flow.

At present I'm working on a lost wax cast turbine design, hopefully delivering 10 Watt shaft power at 35'000 rpm.

Turbine Guy13/05/2019 15:01:45
79 forum posts
35 photos

Thank you for your post Werner. This thread was intended to share information on model turbine designs for air, steam, or any other medium. In the case of my model turbine it has run on both steam and air. I prefer to do the testing on air since the output of my airbrush compressor is more consistent and it is much easier to set up and run.
I don’t know how the accuracy of measuring the power with a brushless generator compares with using a propeller. Both require a means of measuring the speed and require the efficiency of the measuring devices. I use a laser speed sensing device that has a +/- 0.05% accuracy. I found the volts and amps used by an electric motor to turn the EP2508 propeller I use at a speed approximately the same as my turbine test speed. The manufacturer of the electric motor gave the efficiency of the electric motor at about the same speed. I used the power the propeller required to run at the given speed as a base. I assume the efficiency of the propeller and the electric motor is relatively constant for a small range of speeds. The range of speeds for the tests I have done with this propeller is from 14,500 rpm to 18,250 rpm. The speed of the propeller in the test with the electric motor was 15,600 rpm. I don’t have access to the ME reports you mentioned, but I am very interested in any information you can give on better methods of testing.
I watched the You Tube testing of your PPR-S2 project and was very impressed by the performance of you model train. I am very interested in the details of the turbine used in this project and would appreciate any detailed information you can provide.
Good luck with your next project.

Werner Jeggli15/05/2019 20:40:42
9 forum posts

David Carpenter approached me about an input for his . I sent him details of my past contributions to the SMEE Journal. I hope, David will tell us when they will be online.

On my side, I would love to hear about any other successful model steam turbine application - with pictures/videos and performance data if possible.

Turbine Guy15/05/2019 20:54:39
79 forum posts
35 photos

A friend was able to send me a copy of the LMS Turbomotive article. To say the article was impressive is an understatement. You should be very proud of this accomplishment. About the only place I believe I can help is with the turbine nozzles. For the 200 Ws/g turbine energy input you showed in the article, the nozzle discharge velocity is supersonic. Supersonic nozzles require a converging inlet section and a diverging outlet section similar to the following picture. The higher the mach number gets, the more unstable the flow becomes. You have an additional complication with the wet steam. The wet steam will cause the flow to be two phase, liquid and gas. Your article doesn’t show the design of your nozzles, but if you are using a simple converging nozzle like I am, you will need to make a supersonic nozzle to get stable performance with your turbine energy input. My boiler has a pressure of approximately 1.7 bar and a steam temperature of 193 C. The turbine energy input from my boiler is 63 btu/lb (146 Ws/g if I converted right). This energy level is about the highest amount recommended by my turbine books for a converging (sonic) nozzle with dry steam. With this energy the spouting velocity is slightly supersonic and has worked well for me. If you want to go the extra step to make a supersonic nozzle I would be glad to help. There are many examples for turbines using wet steam at pressures higher than yours. One example is the Terry turbine I described in the post of 18/02/2019 in this thread.

Supersonic nozzle

Werner Jeggli18/05/2019 16:53:08
9 forum posts

Hello Turbine Guy,

Thank you for the flowers. You are right of course with your nozzle proposal, which is in line with the real world technology. The thing is, it doesn't work for my small model turbines. I'm not a watch maker, and with a 0.8mm orifice I'd have problems producing it. Then, in our locos, the space available for nice straight and smooth steam runs is limited. Thirdly (and probably most importantly), the steam leaving the nozzle will be turbulent, creating complete chaos in the turbine housing. This makes nice calculations to the third digit irrelevant! My best results so far I got with doctors injection needles 0.8mm ID and 1.2mm OD, suitably bent and silver soldered in.

In the next days, should be receiving improved sets of lost wax cast nozzle units, eliminating the need for injection needles and also new lost wax cast turbine wheels. Well - I'm hopeful.

Martin Johnson 118/05/2019 20:27:48
112 forum posts
1 photos

If it makes Turbine Guy feel better, my old company that I trained with (W.H. Allen & Co, Bedford - see **LINK**) used to have an air turbine testing rig that was used for developing blading on steam turbines. So there is every good reason for using air as a convenient medium for development purposes.


Mark Rand18/05/2019 23:22:04
684 forum posts

Likewise, GEC turbines/Alstom/GE, who paid me money for most of my life, have a model air turbine* in the Aerodynamics labs at Willans Works in Rugby. Due to reorganisation and politics, it's the only meaningful part of the labs left now.

*single stage 1000hp with air provided in a closed loop by the compressor stages of a J57 turbojet, driven by a geared up variable speed electric motor.

Turbine Guy19/05/2019 16:24:25
79 forum posts
35 photos

Hi Werner,
I fully understand the compromises that we must make. I went to the open pocket design of my rotor because I don’t think I can machine blades to the tolerances required for optimum efficiency. I was only partially correct on suggesting a supersonic nozzle for your turbine. The following chart shows the efficiencies of various nozzle designs with changes in pressure. The line marked ‘A’ is a subsonic convergent only nozzle. The line marked ‘B’ is a slightly supersonic with a small divergent section. The lines marked ‘C, D, E, and F’ have progressively longer divergent sections for expansions to larger pressure drops. The dashed vertical line is sonic velocity. You can see from the chart that the subsonic nozzle ‘A’ can be used for pressure ratios well into the supersonic region with efficiencies over 88%. You can also see from the chart that nozzles specifically designed for high pressure drops only operate at maximum efficiency near their design pressures. As you probably have already noticed I get locked into finding the maximum efficiency of each component and sometimes miss the big picture.

Thanks Martin and Mark for pointing out that others are using air instead of steam for testing and development. In my case, being able to just push a button and have air at the set pressure immediately available is a big advantage.

Supersonic Nozzles Chart

Edited By Turbine Guy on 19/05/2019 16:26:46

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