Vector triangles and radial turbines.

[ripcrow]

Working the maths out for a free power on my turbo jet build. Mass flow is .8139 lbs per second and 30 psi which gives a thrust of 31 lbs.  gas velocity at jet nozzle is 1262 ft/ second with density of 38.95 cuft/ lb. my free power is a radial turbine with a mean blade circumference of .75 ft and a mean blade speed of 333 ft over second giving 15000 rpm per minute. At these figures I achieve 31.48 hp but the velocity triangle gives me angles of 30 degree and 40 degrees. Can this be correct. 

I ran ran another set of numbers at 40psi which gave a thrust of 38.4 lbs. drawing the velocity triangles if I run the same free power at 80000 rpm I can achieve 37.48 hp but my vectors are 30 and 90 degree respectively. Is that even possible. I admit I have trouble understanding velocity triangles. The free power has a diameter of 94 mill at the exducer and 110 mill at the inducer. My calcs are based on a mean blade speed of .75 ft per rev 

[racket]

Hi Rodney

First off we need to assume a total pressure coming out of the gas producer , lets assume 6 psit or 1.4 PR , at a temp of 650 C -923 K , we need to use degrees K for the calcs .

Next we square root the 1.4 so that we have a division of the pressure drop available , so 1.18 PR drop in the NGV , so ~33 C degree drop in the NGV and roughly the same in the turb wheel .

33 C degrees will produce a velocity of ~900 ft/sec , with density at 890 K and 1.18 PR of ~34 cubic feet per pound , so ~27 CFS need to pass through your NGV throats at 900 ft/sec , so total throat area of 4.75 sq inches .

Now your 110 mm inducer should have a tip height of ~16 or 17 mm , lets go for 16 mm , so an annulus going in of 110 X Pi X 16 = 5530 sq mms - 8.57 sq ins 0.0595 sq ft , so a radial inflow speed of ~450 ft/sec , so yep , your NGV angle needs to be at ~30 degrees.

Density out will be a tad different at say 860 K of ~39 cf/lb so ~31 CFS , going out through the wheels exducer , we can use an angle of ~35 degrees for the exducer , and our rough 900 ft/sec gas velocity .

Because of the low blade speed at 333 ft/sec the max HP I seem to get is ~18 HP .

If the freepower rpm were increased so that we had a blade velocity up near 700 ft/sec ( ~50,000 rpm ) then HP goes up to ~30 hp .

Cheers
John

[ripcrow]

I've got a lot to understand about velocity triangles then John. Do you have a simple description of how to draw them.

[racket]

Hi Rodney

Have you looked at the DIY freepower stuff jetandturbineowners.proboards.com/thread/680/diy-turbines

Cheers
John

[ripcrow]

That's what I've been using. Some things I'm not sure how they work out is the gas deflection. As that instruction goes on the numbers just appear and I've been unable to work out how they obtained the data. It also seems to be directed towards an axial turbine. Not sure if the same mathematics are used as it uses a ngv with temp drops that affect data outcome. It says gas speed is halved as a sin of 30 degrees but the turbine equation still uses the gas at 933 ft per second not 480 ft per second. The vector triangles use 933 ft per second and gives a relative velocity of 700 ft per second which I don't understand how they got that figure. I know I should've studied maths a bit more.

[racket]

Hi Rodney

LOL, as they're my drawings and calcs I guess I should be able to answer you :-)

There could be some variation in "numbers" as these were done over a period of time and are probably a consolidation of various bits of info , they were originally on the Yahoo DIY Site .

The gas velocity obtained is a direct result of the pressure drop and its associated temperature drop.

If the gases are going into the turbine wheel at a 30 degree angle , then the rate of axial speed is halved , and its this speed that we use to see if the area is big enough .

Relative speeds and direction are the speeds and directions one would measure if travelling on the turbine wheel .

Next time you're up my way, maybe set aside a couple of hours for a tutorial , I'll be happy to go through it in more detail.

If I get time today I'll draw up your vectors and post a pic :-)

Cheers
John

[racket]

Test

[racket]

[ripcrow]

Thanks John it's getting back up your way that could be challenging. Is the speed halved simply as a result if turning the gas 30 degrees

[racket]

Hi Rodney

The gases exit the NGV throat at 30 degrees above the tangent to the inducer tip, at 900 ft/sec , its radial velocity into the wheel is only half its actual velocity ( sine 30 = 0.5) , we use the radial velocity to make sure the inducer area is big enough , if we find it isn't , then we need to increase the 30 degrees to maybe 35 degrees , this will then increase the radial velocity of the triangle , but decrease the gas deflection component effectively reducing power output a tad , but this is made up for my having the "greater" mass flow the higher inlet speed will produce, conversely, if the wheel inlet area is a tad large we can reduce the angle to 25 degrees which will increase gas deflection and horsepower , I've got a NGV for my ALCO locomotive turbo turbine wheel that has a NGV angle of only 15 degrees , this maximises deflection and horsepower , though at the expense of some extra NGV losses due to the "tight" NGV angle ..........trade offs :-(

The 900 ft/sec at the 30 degree angle represents ~750 ft/sec of tangential velocity and 450 ft/sec of radial velocity , the ~750 ft/sec part is "reduced" by the ~250 ft/sec tip speed of the wheel , think of that "loss" of velocity as energy transferred to the wheel and going out as part of the shaft horsepower.

Cheers
John

[ripcrow]

Starting to make sense. Am I right in assuming we have a design speed for the freepower and then work the angles to suit rpm requirements matched to gas flow and velocity density etc. with max torque at 0 rpm max hp (rpm) shouldn't really be a priority

[racket]

Hi Rodney

Generally we work from the opposite direction to full scale stuff , they start with a certain horsepower/thrust outcome then design the engine to produce it whereas us DIY'ers generally want as much power as we can get from whatever turbo/rotating assembly we can find to use.

Now, with your engine , you need to determine what sort of transmission you want to use and how it will influence what rpm you can use , for karting chain ~15,000 rpm is a reasonable number with possible short bursts to 20,000 if using good quality racing chain , but horsepower will be limited to what the kart engines turn out , so maybe 20-30 hp max .

If using a gearbox then the freepower will be able to be run up to its best horsepower output , with blade speeds on the turb wheel matched to the gas velocities , which in your case would be a rpm of ~45,000 rpm .

If you redraw the velocity triangles for 45,000 rpm then the gases exiting the NGV at 900 ft/sec at 30 degrees above the wheel will in reality enter the wheel roughly vertically at ~450 ft/sec and exit the wheel in an axial direction at ~500 ft/sec.

The horsepower calculation is roughly, 750 ft/sec blade speed squared ( gas deflection is the same as blade speed) , times your mass flow of 0.8 lbs/sec ,divided by 32.2 ( constant) divided by 550 ( 550 ft lbs/sec/hp) , which will give us a horsepower output of ~ 25 HP.

This is roughly twice the horsepower of our 15,000 rpm blade speed , but with 3 times the rpm .

Your turbine wheels stall torque will stay the same at the turb shaft , but with the extra 3 :1 ratio, the gearbox output shaft will have 3 times the torque

Hope this helps :-)

Cheers
John

[ripcrow]

Chow do you harness that 45000 rpm. I intended using the schwitzer turbine scroll and bearing housing. I'd imagine the stock bearings and turbine shaft won't like a sideways pull from a chain or belt. Option is to custom build a gearbox to mount on the Turbo housing

[racket]

You could always fit a ball race on the shaft quill to take the side loads , 45,000 rpm could be easily handled by a small sealed bearing.

Chains and belts have speed limits so won't be able to be used at those sort of rpm , so a gearbox is required if you want to use the full rpm capability of the gas speeds .

You'll only have ~3 ft lbs of torque at 25 HP at 45,000 so very lightweight gearing is all thats needed.

[ripcrow]

3 ft lbs of torque. This engine is getting more disappointing. Oh well a experience we'll call it.