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Axial Compressor/Turbine - Methodology to estimate thrust forces generated?

Axial Compressor/Turbine - Methodology to estimate thrust forces generated?

Axial Compressor/Turbine - Methodology to estimate thrust forces generated?

I'm trying to perform some base level calculations to estimate axial thrust forces within a gas turbine engine. Looking at this, I see four key components to the forces:

1. Compressor Axial Thrust - i.e. forces generated at each stage of the compressor
2. Turbine Axial Thrust - as item 1, but forces in reverse direction
3. Secondary Air Flow Systems - i.e. cooling flows etc, will result in specific pressures across specific areas outwith the primary flow plath area
4. Thrust Bearing Load - Essentially reacts against the imbalance of the above.

What I'd like some input on is the best method for estimating items 1 and 2. Currently, I'm modelling these based upon pressure differential and area per stage, i.e. annulus area (A1), inlet pressure (P1), outlet pressure (P2), axial force = A1*(P2 - P1). This gives some initial estimations, but I would love to have a more appropriate method for calculations without going to the level of CFD etc? (I assume this would require some consideration of aerofoil lift forces etc, but not sure how they would stack up with P2-P1 calculations)

I have spent some time searching for methodologies, which I believe must be out there, but so far have had no real luck.

In terms of items 3 and 4. Item 3 - I can estimate each of these relatively well by flow modeling calculations to find pressures, and I have detailed dimensional data available. Item 4 - I have solid operational data, which allows for a basic estimation of the magnitude and direction of this force.

Ultimately, the item I am hoping to calculate as accurately as possible is 'Item 2', the turbine axial force generated.

Any help/thoughts/input etc much appreciated.

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