Cold gas wind tunnel experiments of a descending launcher first stage and generalization of the engine scaling parameter

In the Horizon Europe Project SALTO, a demonstrator of a vertically landing first stage with three Prometheus engines was investigated, the so-called T3. It shall be recovered with a downrange landing approach. In this paper, the results of cold gas experiments are presented where the engine plume was simulated with pressurized air. For that purpose, the engine scaling parameter, which is used to scale the engine parameters and thrust to the experimental conditions, was generalized. It is shown that the matching reduces to a single term, γₑMₑ² γ e M e 2 . With the parameter in this simplified form, it can be ensured that the relevant similarity parameters for retro-propulsion such as thrust coefficient, momentum flux ratio, and ambient pressure ratio can be matched at the same time. The test campaign showed that switches between the short and the long penetration mode occur for T3, since the re-entry burn is performed at comparatively low thrust coefficients. They cause significant changes of the pressure coefficients on the base area, the short penetration mode giving the lower values, and the lower pressure fluctuations. The transition was quantified from the bow shock stand-off distance extracted from high-speed Schlieren recordings. It exhibits a hysteresis in the thrust coefficient, at Mach 2.0 between C T = 1.896 and 2.905, so that the flow state is not determined by the instantaneous flight condition alone. The upper limit of the long penetration mode decreases monotonically with increasing Mach number, and the mode is confined to a narrow band of angles of attack around zero incidence. Consequences for the design of the flight trajectory are discussed.