Newbie to Gas Turbine Modeling: How do I Model a Free-Turbine Turboprop in T-MATS?

[Marwa]

 I'm attempting to model a 600hp turboprop loosely based on the PT6A. I've tried 2 approaches so far and both only seem to work for the steady state design condition. Any attempt to perform off-design runs causes "unwanted" results. I think possible causes for this include: 

1. Modeling assumptions/decision errors
   
2. Model component linkage errors and/or misuse of component data
   
3. Component Map errors

Being a newbie, I suspect I am making all of the above mistakes. I've attached 2 files in an attempt to show exactly how I modeled the system.

My next approach is to use the gas generator section paired with a solver. However I would have to create a new free turbine block which only takes in the mass flow from the high power turbine and has torque and rpm as outputs. ( I think this last statement sums up my question: how do I model a free turbine in T-MATS? )

[J Chapman]

Marwa, 

Thanks for posting. 

A free turbine is essentially the same as any other turbine,  it just isn't attached to a compressor.  If you are making a gas generator you would use the turbine block and another shaft block. Turbine torque and a torque demand that you define would be fed to the shaft creating an Ndot. This Ndot could then be integrated (for dynamic operation) or fed into the solver (in SS) to generate a shaft speed. To get this running you would need to have an idea about the steady state shaft speed (for initial conditions) and Torque (for your demand).

There is also a block called PGenerator that creates a Torq demand based on a power demand if you want to work in energy. Note, if you use the gearbox to get a speed to match the grid, make sure to verify you have the efficiency and Gear ratio set up correctly. If side A and B are flipped the reciprocals of GR and eff will need to be used.

A second, perhaps easier, way to do this is to just use the mass flow and enthalpies then assume all the energy is converted.  To do this you could use 

Pwr = W*(h_turb - h_exit) * 1.41

to get ht_exit: you need the to have the temperature at the exit of the system. For this use the TP2S block with the turbine exit temp and pressure to get the entropy, then use the SP2T (inputing ambient pressure) to get exit temp at the exit entropy. With the exit temperature you can then get the enthalpy (h_exit) using the Temp2Enth block.
W and h_turb would come out of the bus coming from the gas generator's turbine. Obviously this would give you no information about frequency, but it could give you a ball park figure to help you tune the other method.

Hope this helps

-Jeff

[Marwa]

Jeff,

Thanks for responding. I'm going to implement both methods - and use the enthalpy-conversion method to get ballpark figures for the first method. I already suspected as much.

- Marwa

[J Chapman]

Sounds good.  

A couple more comments on convergin though

Converging these systems can be a pain. 

Sometimes it is best to develop simple models of the system to compare against or divide the system into small portions that can be verified against something known. Also, if you use iDesign it is a good idea to look at the scalars it comes up with to verify the they are good. IDesign is a dumb process and can potentially create values that don't make sense.

I have not created a gas generator in T-MATS, but both methods you show look like they should work, however there are a couple of things you should look out for. When using the nozzle with low pressure ratios you can potentially get a "backflow" situation where the solver will attempt to push the input pressure lower than ambient (this will typically lead to a crash). Second, T-MATS does not have a free turbine example, so (if you are using the T-MATS map for the free turbine) it may not be the correct form. Of course this shouldn't have any effect when using iDesign and running to the design point. 

It is also useful to look at where you are in the maps to verify you are where you think you are.  I have attached a .m file that can be used to generate plot the maps easily. 

Convergence is also affected by the solver itself,  changing the perturbation size (usually smaller  ~ 0.01) or changing the dx (usually smaller around 1) can sometimes help. Additionally the convergence criteria should be set very low (esspecially when running idesign),  it is not a bad idea to see the errors at 10^-8 or so (this can be especially true with Ndot where even a small error can create a drift situation during convergence). I think the default is 0.1 which is way too high, can set this in the order of 0.00000001.

GL

-Jeff

[Marwa]

Convergence has been the bane of my T-MATS experience. So far, I've been loose with solver tolerances, intending to achieve quick convergence and short simulation run times without worrying too much about the accuracy. I was planning on using tighter tolerances down the road but I suppose I can do that from the onset.

Also thank you for the map plotting utility. It is mightily handy. In my model I was interpolating the HPC HPT (...etc) map data to see exactly where the model was "running at" - see image below.

I worked my way up from simple models - first running each component at the design point, then running incremental component stacks before putting the whole engine together. I had just finished doing this when I saw the GitHub "Component Verification" utilities. 

I will be distracted by finals over the next 2 weeks but after that I will try to put together a "free-turbine block". 

[I'm a master's student with a focus in aerodynamics and propulsion. I plan on using T-MATS results in my thesis - that's my incentive.]

-Marwa

[J Chapman]

FYI,  I just posted a update to the solvers.  The update allows for multiple perturbations to be defined. This has been shown to make jacobean generation a bit more robust (typically having two,  one pos and one neg works much better than the single perturbation, for the gas turbine SS example it cut my convergence time in a third). 

The new perturbation can be added by adding another row on the perturbation vector.  So, for example, if you have 3 independents your pert matrix could be   [ 0.01 0.01 0.01; -0.01 -0.01 -0.01],   would perturb each independent in the pos and neg direction by 0.01,  two Jacobeans would be generated and then averaged together for use.

Note:  if you define the new solver for a single perturbation it must be a row vector.  This is different than the old block, which could be defined either as a column or row vector. If you have it set up with the wrong vector you will get an error when you plop the new block in, but you can easily fix it by transposing the input.

Hope this helps, GL. 

-Jeff 

[Philipp M.]

Marwa,

I know this post is quite old, but did you succeed in creating the free-turbine block?

Cheers,

Philipp