Designing a turbine for a turbopump is critical considering the work the pump will do is ultimately derived from the gas turbine efficiency that is driving the impeller on the same shaft. Being of such importance also results in the turbine being extremely complex to design. Even after weeks of research, we barely scrapped together a turbine design based off a few initial velocity triangles of the stator vanes that direct the gas into the rotor blades or the turbine itself.
The power produced by the turbine has to be equal to or greater than the combined power required of the impeller to produce desired flow rate along with the frictional losses due to off tolerances, bearing, or seal resistance. Thus the equation to derive the power from the turbine is as follows: Pt = nt mdott cpT1[1-(p2/p1)^(k-1)/k
Where P is power output of turbine, n is efficiency, m dot is mass flow rate(of the turbine), c is specific heat at a constant pressure, T is the absolute temperature, p1 is initial pressure of system, p2 is the exit pressure, and k is the ratio of specific heats. The equation to derive nt is as follows:
nt = LtNt/mdot*dh
Where L is torque produced, N is specific speed, and dh is change in enthalpy.
After attempting to plug in some parameters into bladegen, a feature in ANSYS to model turbomachinery, the geometry that resulted for the v1 turbine rotor blade is shown below.
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