Turbine wheel questions

[dieselguy86]

Hi Chris,

As always, your answer is very thorough and well explained.

The moment the light bulb went off in my head is when John said that the lp turbo must be twice the size if the expansion ratio is to be equal to the hp. One of those aha, "I feel like an idiot".

Then once he explained how to correct flow, I was able to quickly follow along.

I felt like I had a pretty good understanding of things, then you and John come along and blow me out of the water.

I love this place lol

-Joe

[madpatty]

Sept 25, 2021 20:10:53 GMT -5 racket said:

Hi Joe

Yep , you need pitot tube total pressure gauges before each turbo turbine stage, as well as thermocouples .

Speed of sound is temp related , the hotter the faster, ~2,000 ft/sec isn't unusual in a glowing turbo , pressure isn't important .

As for the flow through the HP turb , I checked out the turb map www.garrettmotion.com/wp-content/uploads/2018/05/Turbine-Flow-GT47.jpg for the Gt47with a 1.39 housing and it gave 55 lbs Corrected , so added on a couple more for your bigger housing, I used 800 Deg C - 1073 K as the TIT

Now Corrected Flow = Actual Flow X sq root of TIT/288 all divided by the PR going in

Corrected Flow = 165 X sq root 1073/288 divided by 5

= 165 X 1.93 divided by 5

=63
Now 63lbs/min Corrected Flow is considerably bigger than the 57 lbs/min on the map , so to get 57 lbs/min Corrected I needed to increase the PR going in , basicaly increase the density .

165 X 1.93 /5.6 = 56.8 ..............Corrected now equals the map.

Hope this helps

Cheers
John

Hi John.
Turbine maps have always been confusing.
I always thought the mass flow on the y-axis of the turbine map is the maximum the turbine can flow and as we can see the flow sorta becomes constant once after a Certain PR value so no matter however much you increase the PR going into the turbine you cannot increase the mass flow going through it.
Is it true?

Is the PR on the x-axis of the turbine the PR going into the turbine or the PR across the turbine?

Or is it just that turbine maps show what maximum PR across the turbine, a given turbine can process(sorta like what maximum work a turbine can perform)

Thanks

[finiteparts]

Sept 26, 2021 19:26:38 GMT -5 madpatty said:

Hi John.
Turbine maps have always been confusing.
I always thought the mass flow on the y-axis of the turbine map is the maximum the turbine can flow and as we can see the flow sorta becomes constant once after a Certain PR value so no matter however much you increase the PR going into the turbine you cannot increase the mass flow going through it.
Is it true?

Is the PR on the x-axis of the turbine the PR going into the turbine or the PR across the turbine?

Or is it just that turbine maps show what maximum PR across the turbine, a given turbine can process(sorta like what maximum work a turbine can perform)

Thanks

Patty,

The mass flow on the y-axis is "Corrected Flow" not physical flow.  When the curve flattens out, it does mean that the the maximum corrected flow has been reached, but the physical flow can still be increased by changing the upstream conditions. Increasing pressure or decreasing temperature can achieve a higher physical flow through a given fixed physical area.

If you think back on compressible flow through a nozzle, you usually walk through the test process were you set the upstream conditions and then slowly reduce the exit pressure.  The nozzle chokes when the back pressure reach some minimum pressure condition.  Further reducing the exit pressure cannot cause the nozzle to flow any additional mass.  But, what is often left out, is that you can just change the upstream conditions and easily increase the mass flow through the nozzle.

If you look at the corrected flow equation, you can see how the pressure and temperature interplay between the corrected and the physical flows....

W_corr  = W_phy X [ SQRT((Tt +459.67) / 519) / (Pt / 14.7) ]

You can see that increasing pressure as well as reducing temperature can allow the physical flow to increase for a given corrected flow.

The PR on the x-axis is the pressure ratio across the turbine stage....inlet over outlet.  It depends on who made the plot, but it can be total to total pressure ratio, or a total to static pressure ratio.  Typically, turbines are tested without a diffused exhaust, thus the pressures are usually total to static and this is how the efficiency is calculated as well.  But, I haven't been able to determine how Garrett tests their turbos.

The curves are just a peak efficiency and flow point on the individual speed lines to build a full turbine map...but the map is a relatively good way to represent the data.

I hope that helps!

Chris

[dieselguy86]

John, Chris,

I'm curious about total pressure, it's the added affect of gas speed correct? What role does it play in the calcs on the turbine side? Using previous example of a pr drop of 2 for a turbine, is the total pressure "added on" to the static? So that 2 pr drop is still 2 but static pressure wise it looks to be less because a portion of that is from the gas speed?

I'm trying to not make a long post, but my idea is this... currently figured of a 5.6pr in the manifold, which is static. Let's say total pressure is 6pr. Is the pr drop through the turbo still 2 but say only 1.5 of it is static while the other 1.3 is total. So it would look like (5.6 static/ 1.5 static = 3.7)

Or is it with total pressure the pr drop is higher. I'm just making sure these expansion ratios im figuring are realistic.

-Joe

[racket]

Hi Joe

Yep , total pressure has the velocity component added on to static pressure .

Assuming the gases are static entering the turb stage , then the pressure drop will need to be higher than whats required to just satisfy the comps demands because of the velocity out of the exducer , but then the LP turb stage has the "advantage" of that "free" velocity at its entry which will compensate for its exhaust velocity , so "less" pressure drop required.

There really are too many variables to be able to accurately forcast what will happen , a ballpark set of assumptions is probably as good as we can get , once in operation some fine tuning required .

Cheers
John

[finiteparts]

Hi Joe,

Total pressure in compressible flow is more complicated than the incompressible flow idea of static plus dynamic pressure.  Incompressible dynamic pressure is the additional pressure head than can be gained from recovering the kinetic energy of the local gas flow.  But, compressible flow includes the "elastic" energy of the gas, which can be easily understood from the term "compressible".  Generally, the assumption is that if the local Mach number is below 0.3, then the error in assuming that total pressure and static pressure are equal is good enough.  But in reality, assuming that the total and static pressure are equal is incorrect at any condition other than a fully static flow (velocity = 0).

The rule of thumb to when to use total verses static gas properties is based on what you are trying to calculate.  If you are calculating energy related parameters, such as power or enthalpy changes, you would want to use the total gas properties, because they include all the forms of energy that is contained in the gas flow.  But, it has to be stressed that total properties are a conceptual property that you do not ever see in actuality. Total conditions exist when you bring the flow to rest isentropically.  Isentropic means that there is no change in entropy (totally lossless flow) and we know that in the real world, diffusing a flow without loss is really not realistic. But, when you are looking to calculate local gas flow properties, you really should be using static gas properties,  The  static gas properties are what the turbomachinery components"feel".  There are some exceptions to this logic, but for the most part, this logic works.

As for the question of which pressure ratio you should be using, that depends on the equations that you are using.  You need to understand the equations and properly select the pressures or temperatures appropriately.  I will mention that  almost all of the manufacturer's turbine maps are based on total to static properties.  While most maps do not explicitly state that they are based on total to static or total to total, knowing the testing process it becomes clear.  Here is a Garrett map that states the the Expansion ratio and efficiency is based on T-S properties:

 When the testing includes a downstream diffuser to recover the exit flow kinetic energy, then a total to total property ratio is relevant because you know both the total and static gas properties well (because they are essentially the same).  But when there is not a downstream diffuser, there is still a substantial difference in the total and static gas properties. If you read the manufacturer literature, you will see that they do not diffuse the flow downstream of the turbine, probably because the actual implementation  would likely have a long tube downstream of the turbine exit.  If you know the mass flow and static properties downstream of the turbine, calculating the static or total pressure from either one is relatively simple.

I would also say that another reason to choose either static or total pressure may be on how you are measuring the local conditions.  Static pressure ports are easy to add into manifolds, but can be very difficult to use because the sensitivity to local velocities can lead to large errors.  Total pressure probes are more challenging to implement and their recovery coefficients are hard to estimate without lab equipment.  They never fully recover the full total conditions and can have large errors if the flow does not approach the probe at a straight on angle.  Angle errors can be compounded with instrumentation accuracy, making it tough to get a tight accuracy.  But when you use both the static an total at a properly designed location you can get some pretty good results without having to get crazy lab-grade equipment.  Now, don't think that I am discouraging the use of static or total probes, I am just trying to bound expectations.  I would say that getting a 10-20% accuracy is definitely achievable.  I would say that if you have the manifolds instrumented with static ports, then you would want to make sure that you calculations are done so that you have the results in the static gas conditions and thus you can see if your predictions match the testing results quickly.

I hope that helps,

Chris