The discharge current and potential difference between cathode and ground of a Hall thruster were predicted sequentially by Recurrent Neural Network (RNN) in order to optimize operating conditions. The prediction accuracy and calculation cost for three RNN models, the standard Echo State Network (simpleESN), cycle-groupedESN, and Long Short-Term Memory (LSTM) were compared. The ESN model structures were chosen using Bayesian optimization. We calculated the normalized root mean square error (NRMSE) of the model output against the experimental results of a 200 W class Hall thruster developed at Kyushu University. The NRMSE of the simpleESN model output against discharge current was 0.0407, about 1/10 that of the LSTM. The NRMSE of the simpleESN model against the potential difference between cathode and ground was 0.0981, about 1/7 that of the LSTM. Moreover, cycle-groupedESN reduced the calculation time for the optimization process to 24 seconds, compared to 303 seconds with simpleESN, though the NRMSE against discharge current of the cycle-grouped ESN was 0.1179. These results show that the simpleESN and cycle-groupedESN models are superior to the LSTM in both prediction accuracy and calculation costs for prediction of discharge current and voltage between ground and cathode in Hall thrusters in the considered settings.

To realize a propeller-driven Mars airplane, the propeller-wing flow interaction characteristics should be clarified. Thus, we conducted numerical simulations of the propeller-wing interaction at low Reynolds number conditions (Re = 3.0 × 10⁴) corresponding to Mars atmosphere, focusing on the propeller slipstream effects on the fixed wing. Solutions for the tractor case (propeller in front of the fixed wing) and the wing only case were compared. The results showed that in the tractor case, the lift coefficient (C_L) of the fixed wing increased with the angle of attack (α) more linearly than for the wing only case and showed delayed stall because the propeller slipstream favorably suppressed the expansion of the recirculation region over the fixed wing in the time-averaged flow fields, supporting the experimental result. The flow over the fixed wing separated from near the leading-edge in both low and high thrust conditions even at a moderate angle of attack (α = 5°), whereas previous studies at relatively high Reynolds numbers (Re ∼ O(10⁵)) showed that almost attached flow fields were formed under the propeller slipstream influence. Additionally, it was observed that the C_L fluctuation of the fixed wing increased even when the time-averaged C_L was lower than that of the wing only case.

This paper presents a method of propellant balancing to maximize the mission lifetime in spacecraft formation flying. The proposed method considers the initial remaining propellant, which was not considered in previous studies. This method optimizes the reference orbit for the virtual chief spacecraft so that the control effort of the deputy spacecraft is adjusted to balance the remaining propellant. The authors formulate the problem as an optimization problem and build new algorithms for propellant balancing, including the coordinate transformation for the chief spacecraft. A propellant-optimal solution is also analytically derived for an equilateral triangle of three spacecraft. The analytical solution is computationally inexpensive since it can be calculated using only the remaining propellant at the desired time and some pre-computed parameters. Finally, the analytical solution was compared with the results of numerical optimization, and the analytical solution was confirmed to be sufficiently practical.

The flow features of shock-containing jets from elliptical convergent nozzles operating under slightly off-design conditions have been studied analytically, where the jet mixing layer is approximated by a vortex sheet and the shock-cell structure is confined to the interior of the vortex sheet. Perturbation conservation equations are solved using eigenfunction expansion, and shock-cell structures for the elliptical jets are obtained explicitly. Only the first Fourier mode of the eigenvalue problem is considered for simplicity. The effects of flow parameters such as the nozzle pressure ratio, aspect ratio, and design Mach number on the shock-cell structure and shock-cell spacings are investigated.