Density vs shaft speed

[dieselguy86]

Hi all,

In my Hugh MacInnes turbo book, he talks about turbocharging at altitude(pg 105). He corrects the absolute temp at 16,000' to show how the denser air slows down the shaft speed.

In my mind the turbo doesn't "see" hot or cold air, rather if the air is thin or thick. If I run his same correction for a high pressure stage in a compound turbo system, it says the shaft speed goes up, due to the heat, despite the inlet air being at a 2.25dr.

Instead of sq/rt the temp ratio, could I sq/rt the density ratio to correct shaft speed?

The caterpillar hp turbo uses a 43 trim compressor, I'm wondering if the large exducer was too keep peripheral speed high with a slower shaft speed.

-Joe

[racket]

Hi Joe

In your high pressure stage at 2.25 dr we still need to "correct" , because comp maps don't work with density ratios only pressure ratios, I wouldn't try using sq rt density .

The CAT 43 Trim comp is probably trying to maximise efficiency as the inducer relative tip speed at max PR is trying to stay subsonic to minimise shock losses etc etc

Cheers
John

[finiteparts]

Hi Joe,

The corrected spool speed equation is based on matching the tip velocity, which can also be represented as a Mach number divided by the local speed of sound. The square root of the temperature comes from the equation for the local speed of sound (sqrt(gamma*R*T)). As gamma, tip radius and R will be assumed fixed, they drop out when the equation is differentiated. The remaining equation is Nc = N /(compressor inlet total temperature / standard day total temperature).

The speed of sound is not impacted by pressure in this formulation because the pressure effects are implied through the gas constant, the ratio of specific heats and the fact that we assume adiabatic conditions and that the gas behaves as an ideal gas.  By assuming the system behaves adiabatically, we means that within the system, there are no losses and no heat is lost from the system.  SO for an ideal gas if no heat leaves the system, if we compress it, we just change the gas temperature somewhat.

For real gases, pressure does have a small impact, but nowhere close to the effect of temperature on the speed of sound, thus it is "safe" to ignore this for small changes in pressure (i.e less than 1000 psia).

So, if you wanted to scale by density, you would have to reformulate the equations form start and differentiate them to get the corrected equation, you can't just swap sqrt(T/Tstd) to sqrt(rho/rho_std) as that would likely not correctly satisfy the starting equation. My guess is that it would make a complicated corrected equation.

The next "problem" with this idea is that you can't directly measure density. You can measure the local temperature fairly accurately, so there is that error , but it is a much smaller error than measuring the local static pressure and temperature, then calculating the density from them, with the calculation's associated rounding errors.

In response to this comment,

"In my mind the turbo doesn't "see" hot or cold air, rather if the air is thin or thick. If I run his same correction for a high pressure stage in a compound turbo system, it says the shaft speed goes up, due to the heat, despite the inlet air being at a 2.25pr.",

I think you might be thinking of this incorrectly. What the corrected equation is telling you is that to get to that pressure ratio, you need to drive the compressor to a higher speed. It is harder to put work into air that has been heated as opposed to cold air. If you look at the equation for specific work (click to open below):



you can see that if the inlet temperature increases, the specific work (work per lbm or kg of flow) needed to meet a given pressure ratio increases (T01 and due to Cp increasing).  It is not  telling you that if you increase the inlet temperature, the rotor will speed up.  The given speed of the compressor impeller is really up to the amount of work that the turbine is providing.  If the turbine was somehow limited so as to only be able to provide a fixed power, the rotor would slow down as you are saying.

I hope that helps,

Chris

[dieselguy86]

Hi Chris,

Doing the turbine temp and pressure drop calcs it's really easy to see the extra work required. So it's safe to assume then the corrected raised shaft speed goes along with the additional t and p drops? I didn't know that before, that definitely changes things now when looking at compressor maps.

So would that be the reason for the low trim compressor wheel on the second stage? To keep the pr's up while keeping shaft speed "normal"?

Thanks again- Joe

[racket]

Hi Chris/Joe

Heres an interesting article people.unica.it/tizianoghisu/files/2020/05/rodgers-geiser.pdf

The only problem is I think theres a mistake in the throat area of the gasifier NGV , I can't get 6.52 lbs/sec through its 10.6 sq ins :-(

Cheers
John

[finiteparts]

Joe,

The lower trim could be the result of so many things that it is hard to say. If they wanted to use an existing impeller that they could just modify the shroud profile, then it could just be a result of the inlet Mach number. It could be a result of expansion ratio available across the HP turbine, which will be limited based on back-pressure produced by the LP turbine. Without working through the calculations, it is hard for me to say.

I am not sure what you are asking here, "So it's safe to assume then the corrected raised shaft speed goes along with the additional t and p drops? "

- Chris

[dieselguy86]

John,

At the end of the article, it says they had to open up both nozzles 3% to improve the surge margin with a stalled pt. Does 10.92in² work any better?

-Joe

[finiteparts]

John,
That is a good paper, but then again, almost all of Colin Roger's papers are excellent. I heard he passed away a yr or two ago, which is very disappointing because I always hoped that he would write a book about radial turbomachinery.

When I do the calcs., I get the critical throat area, for the inlet conditions of Tt=1910R and Pt = 58 psia, is 9.394 in ^2. So that means that if he was quoting geometric area at 10.6 in^2, it would only choke if the NGV Cd = 0.886 or lower. If he was quoting the 10.6 in^2 as the throat effective area, then the Mach number at the throat would only have been 0.662.

Thanks,

Chris

[racket]

Hi Chris

Yep , some good Papers :-)

One thing that has always concerned me about my NGV throat areas is how the gases behave in the semi vaneless space between throat and turb tip , do the gases speed up or stay at the same speed , I'm thinking of comp wheels here where the air slows between comp exducer and diffuser throat .

If the NGV is running choked then I'd imagine the gas speeds couldn't increase as the area becomes less as it gets closer to the wheel, but then again , if the NGV vane shapes were such that there was an increase in area then supersonic flow could result .

LOL......I've search the net for years looking for easy to understand info on radial wheels used with an axial freepower but its a bit thin on the ground .

This Paper helps , but the radial wheel has a HUGE exducer at nearly twice the area of the inducer unlike our "normal??" turbo ones which are down ~30% bigger where we need to have higher exit speeds if we want to get our mass flows through them .

Wishing you guys are Merry Christmas , just over 12 hours to go for us, a busy time ahead :-)

Cheers
John

[finiteparts]

Hi John,

Merry Christmas to you also, somewhat belated! I hope you had a wonderful time with family and friends.

The flow in the nozzle-rotor interspace is usually treated as a free vortex, since the bulk of the flow there is "free". For our purposes, neglecting the wall effects on the free vortex flow will be ok and hopefully, not drive too much error. In general, the flow will speed up, but that neglects any NGV wake mixing and frictional effects that could reduce the bulk gas mean speed. The free vortex is just a result of the conservation of angular momentum, which has the classic example of the figure skater. When they pull there arms inward and concentrate mass at a smaller radius (from the axis of rotation) they speed up to maintain the angular momentum. Similarly, when the swirling flow from the NGVs moves into a tighter radius, it will accelerate.

If you look at Moustafa, Zelensky, Baines and Japikse's book, "Axial and Radial Turbines", sections 8.5.4 and 8.5.5 cover the nozzle-turbine interspace and supersonic expansion in the NGVs. They suggest that there are three basic paths to achieve supersonic flows at the turbine inlet.

1. A high subsonic exit condition at the exit of the NGVs, with the NGV throat being unchoked. Then the flow would accelerate in the interscape and enter the turbine at some form of supercritical condition. I am not able to rationalize this in my mind since the general construct for a subsonic to supersonic acceleration is to choke at a minimal area and then accelerate to supersonic via an area increase...so I will have to think about this one for a bit.

2. Choke the NGV throat and then via an expansion fan attached to the NGV trailing edge, accelerate to supersonic flow conditions. The problem with this is that the expansion fan turns the flow radially inward, so any flow speed acceleration achieved does little to help the specific work of the turbine. This is because the work done by the gas on the turbine is due to the change in the angular momentum of the gas through the turbine stage, when the expansion fan turns the flow inward, it is not helping to increase the angular momentum and possibly, it reduces it.

3. Design the NGVs such that they are converging-diverging nozzles.

They also suggest using Watanbe's equation for max efficiency of the interspace as:

(r_NGVexit - r_turbineInlet) / b3* cos(NGV_exit_angle) = 2 (where b3 is the inlet height of the turbine)

or, in a general sense, they suggest a radius ratio (r_NGVexit / r_turbineInlet) of 1.1 to minimize pressure pulse coupling between the passing turbine blades and NGV blades and give time for any NGV wakes to mix out.

Whitfield and Baines suggest similar things in their "Design of Radial Turbomachines".

Here is a older paper on the work that Garrett Airesearch did on their GTCP305-2 that has a coupled radial to axial turbine arrangement. Even though it is not a free-turbine design, the information on flow matching should still be relevant and provide some useful insight...plus, they are loaded with great tid-bits of other information of interest.

ntrs.nasa.gov/citations/19820011347

Further information on the GTCP305 can be found here,

apps.dtic.mil/sti/pdfs/AD0754903.pdf

and

apps.dtic.mil/sti/pdfs/ADA087838.pdf

What specifically are you looking to understand about radial to axial turbine matching? Maybe if I had an idea of the question, I could better help you to understand or point you to the relevant information. My guess from your comments is, how to determine the pressure drop through the first stage due to the presence of the second stage...maybe?

Axial turbines after radial turbines are quite common in older (70's and 80's) literature. Several of the automotive gas turbines used them and there was a big resurgence in research them for use in compact, high temperature helicopter engines were proposed and maybe built. I will try to dig around and get a list of some of the better documented ones. I have a pile of SAE and ASME tech reports on turbine matching, but I will have to dig to find online information.

- Chris

[racket]

Hi Chris

Thanks for the Links , I've been having a read , lots to process :-)

I'm trying to find a reason for my engines odd behaviour with regards the largish temp increases once past mid power , and have been looking at the turb stage as a candidate .

I'm limited in what I can manufacture and source so my NGV isn't ideally matched with regards vane angle vs throat area , I need a certain angle to get the gases into the wheel , but that angle doesn't produce the correct throat area with the vanes I can make , so I'm trying to understand the actual velocities achieved with what I have .

The Paper I gave a Link to has a relatively much larger turbine for its mass flow than I'm using , so I'm not certain just how representative it is for my application .

I'm not too concerned about the freepower side of things as I can always measure the jetpipe energy and go from there as theres plenty of axial turbine wheel design material available but not much in the way of using a radial wheel with less than full expansion through it unlike with a turbo arrangement.

I don't want to run a choked NGV as I'd like a fair velocity out of the exducer to maximise flow through my stage .

On another subject , I've pulled the engine apart and alls still OK inside though there has been "differences" with changing fuel type , theres now more soft carbon inside the end of the flametube with the higher kero content, I'm seriously considering going back to vapouriser and "aircaps" like I had in the 12/118 as I'm not burning fuel in the first half of the flametube :-(

Cheers
John