Design of a Working Fluid Versatile Supersonic Turbine for Micro Launchers
Authors: Cuciumita Cleopatra , Vilag Valeriu 
Published: November 2019

Abstract
Launch systems development today is heading in two, seemingly divergent, directions. A first direction is towards bigger launchers, designed to carry more than 50 tons into low Earth orbit (LEO). On the other hand, there’s growing interest from government agencies and start-up companies alike in very small vehicles for dedicated launches of small satellites, vehicles that can place just a few hundred, or even a few dozen, kilograms into LEO. At the same time, space programs are starting to look into the possibility of using the existing turbines of rocket engines turbopumps working on classical fuels to work on alternative fuels. The desired characteristics of being a simple, lightweight, high specific work output, low mass flow rate turbine easily translate into supersonic turbines and outweigh the disadvantage of having low efficiency compared to subsonic turbines. Such a turbine needs proof of concept because, at small scales, the flow changes dramatically due to end wall losses which may cause the turbine to choke prematurely and combined with the effect of shock wave losses, characteristic to a supersonic flow, this effect can turn out to be critical. This paper presents a methodology to design such a turbine, taking into account the requirements derived from an application represented by a micro launcher with a maximum payload of 100 kg. As compared to the design of a classical turbine, this methodology is focused on geometrical limitations, to ensure the manufacturability of the turbine, as well as aerodynamic efficiency. The methodology was applied for obtaining the geometry of a turbine for the aforementioned application using a classical fuel as design point. 3D numerical simulations were computed for this geometry, and the efficiency of the turbine was obtained within 8% of the analytical data. To facilitate the use of different fuels, a simple and fast method was also developed for predicting the performance of a turbine of known geometry and performance for an initial working fluid when changing the nature of this working fluid. Benefiting from having the performance already estimated for another working fluid (the design fluid), the Mach numbers similarity criterion can be used to estimate the performance of the same geometry when changing the working fluid, as a known practice in the gas-turbine field. The Mach number appears as a scaling parameter in many of the equations for compressible flows, shock waves, and expansions. Not only is it suited for similarity of a classical turbine, it is also appropriate for a supersonic turbine, due to the fact the conditions behind shock waves are only dependent on the Mach number and the fluid’s properties. Using this method, the performance of the designed turbine was computed for a completely different working fluid than the design one. The largest difference in power output generated by changing the working fluid is of 170%. A new set of numerical simulations was done, and the results confirmed the validity of the method by obtaining a value of the power output within 6.5% for four other working fluids.