7th may 2024
this is the second part to my log/notes on building a gas turbine engine. here i plan to note down my steps to obtain somewhat realistic numbers i can base my further design upon.
i start with HX35, a common compressor wheel available offshelf. as i do not have one handy, i managed to find some engineering drawings on aliexpress (scroll down to see compressor diagram) from which i could approximate my required dimensions. i am listing my findings (may not be accurate) here,
> inlet hub diameter: 10 mm
> inlet tip diameter: 54 mm
> outlet diameter: 78 mm
> number of blades: 7
> number of splitters: 7
> outlet sweep angle: -30° (backward swept)
> inducer angle: 60°
assuming a maximum relative inlet (tip) velocity of mach one, we can get an upper limit for the revs. ofcourse, the upper limit is also decided by the material also, but given a device made of a metal with high yield strength, the maximum revs would be caped by aerodynamic reasons. we do not want to get into near mach 1 as shock losses will increase. we can decrease the relative inlet mach number by introducing prewhirl, but that would require a static inducer and would be too much effort. here i list some rev numbers and some relevant information.
| rpm [N/s] | Mrel | Vaxial[m/s] | ṁ [kg/s] | PR |
|---|---|---|---|---|
| 50000 | 0.47 | 81.62 | 0.211 | 1.31 |
| 60000 | 0.56 | 97.94 | 0.253 | 1.49 |
| 70000 | 0.66 | 114.26 | 0.295 | 1.72 |
| 80000 | 0.75 | 130.59 | 0.338 | 2.03 |
| 90000 | 0.84 | 146.91 | 0.380 | 2.46 |
| 100000 | 0.94 | 163.24 | 0.422 | 3.02 |
| 105000 | 0.99 | 171.40 | 0.443 | 3.37 |
| 110000 | 1.04 | 179.57 | 0.464 | 3.76 |
drop in a mail if you need the python script to calculate the params, the code is too messy for me to post publicly
looks like 110k rpm is too much, 105k rpm is the theoretical max that we could get before shock waves occur. this would be even lower at high altitudes where the temperature is low. lets assume that we are only worried about ground operation for the moment and lets just say that our engine maxes at 105k rpm producing a pressure ratio 3.76 (considering isentropic efficiency of 90%).
now lets do an ideal air cycle analysis to calculate the upper bound of thrust these numbers produce. lets assume we idle at 500 K and our max turbine entry temperature is 1100 K. 500 K for idling temperature is a guestimate, it might produce small amount of thrust or may not have enough heat released to drive the compressor. the upper limit is decided by material science. here are some parameters and assumptions i used for the cycle analysis.
> inlet isentropic efficiency: 0.995
> compressor isentropic efficiency: 0.890
> combustion chamber pressure loss: 0.035
> turbine isentropic efficiency loss: 0.900
> shaft mechanical efficiency: 0.995
> nozzle isentropic efficiency: 0.990
here are the results of brayton cycle analysis,
| state | rpm | tet [K] | pr | thrust [N] | tsfc [kg/N/s] |
|---|---|---|---|---|---|
| mil @ ISA | 105000 | 1100 | 3.37 | 249 | 2.83E-5 |
| mil @ ISA + 10 | 105000 | 1100 | 3.24 | 232 | 2.93E-5 |
| idle @ ISA | 50000 | 500 | 1.31 | 10.86 | 8.35E-5 |
| idle @ ISA + 10 | 50000 | 500 | 1.30 | 8.66 | 9.76E-5 |
looks like our guestimate of 500 K at idle was pretty decent. anyhow, we see that the maximum theoretical thrust possible is around 249 N at ISA. in a warm country like India, we get slightly lower thrust. i am expecting the final engine to give me atleast 20kgf.
next i am planning to size the combustion chamber. i am planning to reuse the same combustion chamber from the turbocharger based engine to the axial variant. so it is a high stakes job.
live long and prosper,
soorkie