Choked Flow Across Turbines - I Need Some More Understanding

[easye]

Hey everyone,

I'm obviously new here, but I was wandering the internet looking for info for a couple of schemes I've been mulling over and stumbled on this site.  It's really nice to see a forum where everyone honestly does seem to be trying to help each other out, I must say.

Anyway, a little background:  I'm a mechanical engineer with a love for a nice spreadsheet, and a habit of scheming up excessively complicated solutions to problems that don't exist.  Which is what brings me here to this thread.  A lot of my ideas involve using gas turbines for things that are probably better served by another using another engine, but gas turbines are sweet, so I do it anyway.

I'm specifically wondering about the effect that choked flow has on a turbine though (the turbine only, i.e. not including the compressor).  So from thermo the power developed across a machine is Power = Mass flow * Specific Heat * Delta-T * Efficiency.  And the delta-T is controlled by the following:  T2 = T1 * (PR) ^ (k-1)/k.  Btw, feel free to correct me anywhere you see that I've made a mistake or overlooked something important....

Using the equations above and the turbine map below, let discuss some hypotheticals.

GTX5533R Turbine Map

Looking at the 1.24 A/R characteristic, am I correct in the following observations:

• that the flow chokes at ~67ish lbm/min and a PR of 2.5?
• if we keep the inlet temperature the same, then regardless of the increase in pressure upstream of the turbine, we cannot get more mass flow through?

Assuming the 2 statements above are correct, I have more questions....  Let's say there is sufficient flow through the turbine such that a PR of >2.5 is created, and the TIT is low enough that that we have choked flow.

• Does this relationship still hold true above the choked threshold?  T2 = T1 * (PR) ^ (k-1)/k ?
• If so, then the power output of the turbine (not thinking about the upstream compressor, just the turbine) should still keep increasing based on the greater PR and therefore lower turbine outlet temp.
• How is the efficiency of the turbine (again, just the turbine itself, not the compressor) effected by the operating above the choked threshold?

I'm sure I'll have more questions as we go, but that's plenty to get the discussion started.

Thanks.

[racket]

Hi

Welcome to the Forum :-)

The 65 lbs/min in the GT55 map is "Corrected" mass flow , so more mass flow can be forced through the turbine if the inlet pressure is increased .

Corrected Flow = Actual flow times sq root of (absolute gas temp deg R/519) , divided by (the absolute pressure/outlet "ambiant" pressure) .

Its easier to explain if you have some "numbers" .

Cheers
John

[easye]

Thanks for the reply, John.
 
So if M-corr = 65 lbm/min, assuming 1500F TIT and a PR of 2.5 then M-act = 65 / sqrt( (1500+460)/519) / 2.5) = 65 / 1.23 = 53 lbm/min.  Also, can you explain the physical significance of the corrected vs. actual mass flow rate?  

And regarding choked flow, is it correct to say that the mass flow rate through an orifice/nozzle/turbine/etc. is still dependent on the upstream gas density * area * speed of sound at local conditions?

-Eric

[racket]

Hi Eric

Checkout this info jetandturbineowners.proboards.com/thread/561/information-small-gas-turbine-engines?page=6 .

Are you trying to find the maximum flow through the turbine stage ?

Generally turb maps are used the other way around , to see if a known "actual" mass flow can be processed by a certain turb stage at the pressures/temperatures/pressure ratios, we want to use in the engine .

Your maths in the example have come out wrong, I'd better try to explain the process a bit better .

If Corrected Flow of 65 lbs/min = x lbs/min Actual Flow, times the square root of ( 1500 +460/519)
----------------------------------------------------
2.5 PR

= 65 X 2.5 = x lbs/min X sq root 3.77


= 162.5 = x lbs/min X 1.94

162.5 div by 1.94 = actual flow in lbs/min

Therefore actual flow = 83.7 lbs/min

Which means a comp flowing 83.7 lbs/min ( neglecting fuel addition)through the engine that provides a T I T of 1500 deg F at a PR of 2.5 out of the combustor can be used with that turbine stage .

Corrected flow calculations brings various temp and pressures within a flow back to a "standard" common "number" that can be compared with other temp/pressure flows.

If for instance you wished to use the GT55 turb stage as a freepower stage with a PR of say 1.7 :1 across it at the same temps then actual max flow would be reduced 57 lbs/min

But if you wished to run a 4:1 PR into the stage as part of a gas producer then max actual flow would be increased to 134 lbs/min - 2.23 lbs/sec , which is exactly in the right position on the comp map IF you had full expansion through the turb stage down to ambiant pressure , but you'd only be needing an ~2:1 PR across the turb stage at those temperatures to power the comp, so according to the map a max flow of only 67 lbs/min through that turb stage because of the "high?" exhaust pressure in the interstage duct going to the freepower stage, but this is where I'm not sure how "accurate" the turb maps actually indicate whats going on as they would normally assume the gases are exhausting to atmosphere .

Hope that helps :-)

Cheers
John

[easye]

That was extremely helpful!

I did some more looking around and calculating yesterday, and noticed that I had botched the math. I reworked it and got the numbers you obtained above.

I'm just generally trying to get an understanding of how to determine the effective flow ranges of many turbine sizes/styles. Which dovetails into several schemes I'm thinking about.

So I think my final question on this subject is regarding the turbine efficiency. What happens to the turbine efficiency as I increase the PR across is? That map listed a peak of 82%, though not where that occurred. And that map shows the characteristic curve over a range of PRs from ~1.2 to 3.5, but what if I want to run a PR of 4.0 or more across it? Does the efficiency drop off rapidly?

-Eric

[racket]

Hi Eric

Because the turbine wheel is an 84 Trim they aren't designed for high pressure ratios across them , they're OK for a turbo with limited pressure drop and because of the lack of "tip" the moment of inertia is "low??" , but for a high pressure ratio with good efficiency the Trim probably needs to be lower.

Best efficiency will most likely be near a 2:1 PR than a 4:1 PR , but theres very little information available for turbines , its only in the last decade that turbine maps have become available, and then only for Garrett stuff in any quantity, once the stage starts to choke the efficiency starts dropping, how far ...........only trial and error testing will give you the numbers .

Why do you need to use a PR of 4.0 or more ??

Cheers
John

[gtbph]

Hi Eric,

My favourite formula for estimating the PR is:

   PR = (1 - v_tip*v_gas_tan/(cp*T*eff))^(-k/(k - 1)

where
   v_tip = tip speed in m/s
   v_gas_tan = tangential gas speed (swirl) in m/s
   cp = heat capacity at constant pressure in J/kg/K
   T = Temperature in degree kelvin
   eff = Efficiency
   k = heat capacity ratio

For simplicity you can also set v_gas_tan = v_tip, but efficiency is best when v_gas_tan is a bit lower than v_tip.

For v_tip = 400 m/s, v_gas_tan = 350 m/s, cp = 1154 J/kg/K, T = 1023 °K (750 °C), eff = 0.8, k = 1.33 it gives

   PR = 1.91

This is the reason why these things have to spin so insanely fast.

Regards,
Alain

[easye]

Alain- I'll give that formula a try when I get a chance to get back to my spreadsheet. That will be helpful when looking at operating speeds.

John- I don't need a pr of 4.0 per se, it's that I'd like to use a gas turbine as a way to augment the power of a car, specifically an electric car. And if I use a turbocharger the turbine wheels have a temp limit that gives most efficient system operation at a pr of around 4-5ish.