# Gas Turbine Engine Compressor Discharge Air Temperature Calculation

1. Mar 11, 2013

### MisterDynamics

Is this gas turbine engine compressor discharge air temperature calculation relatively accurate?

Problem:

Calculate the compressor discharge air temperature in ºF of the following gas turbine engine compressor core specifications.

Gas Turbine Engine Compressor Core Specifications:

75% Compressor Efficiency
23:1 Compressor Pressure Ratio
Outside Air Temperature = 65º F

Solution:

Formula:

Tout = [Tin] + [(Tin) x ((PR)^0.263 - (1)) / (CE)]

Tout = Compressor Discharge Air Temperature in ºR
Tin = Outside Air Temperature in ºR
PR = Compressor Pressure Ratio
CE = Compressor Efficiency
ºR = [(ºF + 460)]

Tin = [(65 + 460)] = 525º R
PR = 23
CE = 0.75

(23)^0.263 – 1 ====> Compressor Pressure Ratio to the 0.263 power minus 1 = 1.28

1.28 x 525 ===> 1.28 multiplied times outside air temperature in absolute temp R = 672

672 / 0.75 ===> 672 divided into compressor efficiency in decimal form = 896

896 + 525 ===> 896 plus outside air temperature in absolute temp R = 1,421

Compressor Discharge Air Temperature = 1,421º R

1,421 – 460 ===> 1,421 degrees R absolute temperature minus 460 = 961º F

Compressor Discharge Air Temperature at given compressor specifications = 961º F

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2. Mar 14, 2013

### etudiant

Seems in the right ballpark, maybe a bit low.
In the real world, the compressor exit temperature is a real obstacle to improving gas turbines. It is already high enough to distress most metals and there is no source of relatively cool compressed air available to cool the blades. So industry is looking at fairly exotic materials to allow the greater compression ratios needed to make more efficient engines. Any good ideas that help move the ball forward in this space would be very welcome.

3. Mar 15, 2013

### MisterDynamics

To: etudiant

So if I were to place a Temperature Sensing Probe right at the compressor discharge nozzle after the last stage of the compressor right in the Diffuser section of the given compressor and take the CDT (Compressor Discharge Air Temperature) experimentally, would this theoretical CDT calculation above be relatively accurate?

If not, the CDT calculation is a bit low then?

Is there an exponential coefficient aside from ^0.263 that would reflect a more accurate calculation reflecting any gas turbine compressor core industry standards?

I have been trying to find an approximate formulation from various applicable sources and I never receive a reply.

It's apparent that much CFD and FEA is done by manufacturers via complex software algorithms.

My goal was to extract a basic formulation to predict CDT so that accurate temp rise (delta T) can be used to compute Compressor Horsepower:

Compressor HP: [(Delta D) x (0.24) x (Compressor Mass Airflow) x (778)] / [550]

Based on watching many videos of gas turbine core laboratory tests and listening to the approximate CDT temp rise at standard temp and pressure during Sea Level Max Static Thrust tests, especially for the GE-CF6 the narrator always states a CDT air temp rise of about 1,000 degrees F.

This particular formula up above was taken from a centrifugal flow compressor CDT calculation.

Axial flow compressors apparently aren't as efficient at lower power settings but reach very high efficiency at max power setting. Where as centrifugal flow compressors tend to remain efficient at all power settings.

Core designs are all different and may not reflect a standard based on one formulation, but perhaps formulation per given turbine core. I was just eager to find an approximate formulation that reflects a relatively accurate CDT for all gas turbine engine cores.

Instead of the old school turbine cores with several centrifugal flow compressors in series today's turbine compressor cores have many axial flow stages with the stator cascade vane effect for air pressure rise while limiting air velocity increase throughout the compressor stages. This apparently is the standard for commercialized high efficiency turbine engine compressor cores in this day and age.

Unlike the old school commercial turbine compressor cores from the 1940's and 1950's using two to three series centrifugal flow compressors ending with one single stage axial flow out to the diffuser. Or vice versa such as the Allison 250C turboshaft engine with a many stages of axial flow ending with a centrifugal flow stage out to the diffuser, developed in the 1950's and still very popular today for helicopters and smaller turboprops.

Perhaps there is no "one formulation" to calculate all turbine engine compressor CDT temp rises and that formulation is model-specific.

Are there any improvements you can provide me with to make this formula more accurate? Or even provide me a different formulation reflecting accurate gas turbine CDT calculation?

Thanks etudiant!

- MisterDynamics -

March 15, 2013

Last edited: Mar 15, 2013
4. Mar 15, 2013

### etudiant

There are surely more capable formulae to determine CDT, but afaik the formulations are model specific and not shared.
You might want to look at NASA publications, they often provide specific examples using well established hardware. That should allow more exact estimates.

5. Mar 16, 2013

### MisterDynamics

But on an approximate or general level could I use this formula to publish approximate CDT air temperature rise in a technical training manual?

Provided I state that this is a very general approximation of CDT and that each make and model gas turbine engine core has its own specific and accurate CDT formulation?

And that the analyst or technician needs to research accurate CDT formulation based on each make & model in order to determine CDT mathematically?

If this is so I can proceed onward with the gas turbine engine chapter in the aeronautics technical training manual I am working on. But list a disclaimer that this formulation is an approximation for all gas turbine compressor cores.

I have spent a lot of time at the nasa.gov site studying aerodynamic wing lift & drag along with propeller static thrust formulation(s) but not so much CDT formulation(s).

Regards,

- MisterDynamics -

March 16, 2013

6. Mar 16, 2013

### etudiant

I see no reason why your text should not include this formula, provided you include the caveat that it is a guide, not an exact solution.
I'm unfamiliar with its derivation, so if you could introduce it with a bit of explanatory language, to help explain that parameters such as the 0.263 factor are empirical, your students would be aware that this is rough guide and use it as such.
Good on you for pulling this kind of stuff together in a manual! I think we often forget to teach what we know.

7. Mar 17, 2013

### MisterDynamics

It seems as though formulation like this one should be readily presented along with the given physics theory. Apparently this isn't the case in many publications. It's almost like the idea is to make people search out for what should already be presented.

Most of this publication is complete. But I was looking for more peer review with this particular CDT formulation. Noting the wisdom that CDT is slightly different for each make, model and variation. This general CDT formulation seems to be publication-worthy.

Thank You etudiant. I very much appreciate your assistance and oversight!

If you would like to chat online or through E-mail please let me know.

Regards,

- MisterDynamics -

March 17, 2013

8. Mar 17, 2013

### AlephZero

Your formula is just the standard formula for adabatic compression or an ideal gas (which is where the magic number of 0.263 comes from), plus an "efficiency factor" to compensate for the fact that real compressors are not perfectly adiabatic.

The efficiency factor CE is purely empirical for any particular real compressor. If you don't like the answer you get, just change the value of CE.

9. Mar 21, 2013

### MisterDynamics

To: AlephZero

Compressor Efficiency (CE) of course would vary based on power setting and environment, wouldn't it?

Let's say this particular gas turbine engine application is a TurboFan application used on an airliner. As in a twin spool gas turbine core whereby the low speed compressor-turbine spool (N1) drives the large fan as a torque application and the high speed compressor-turbine spool (N2) maintains most of the compression to keep the engine running as a limited propulsion application. Resulting in most (80%) of the thrust developed by cold air acceleration out through the fan exhaust nozzle and the rest (20%) of thrust from accelerating from hot gas jet velocity out through the core exhaust nozzle.

The CE seems as if it would also change or vary with higher altitudes which include lower air density and a drop in air temperature compared to near Sea Level operation.

This formulation is just a basic explanation of a theoretical gas turbine engine at a given CE, PR & Tin, representing Adiabatic Compression.

Wouldn't a real gas turbine engine compressor fall within a blend of Adiabatic, Polytropic & Isobaric compression variations amongst each other?

Compressor Efficiency represents roughly the ratio between the amount of energy required to drive the compressor divided into the energy the compressor develops in heat-of-air-compression.

I was going generally by manufacturer's make & model listing of CE more than anything else to compute CDT Air Temp Rise as a basic calculation.

Are there any other factors to consider pertaining to CDT Air Temp rise calculations aside from these given these parameters?

Regards,

- Mister Dynamics -

March 21, 2013