An impingement of two-dimensional axisymmetric supersonic jet on a plate is simulated numerically to evaluate the jet flow configuration on the plate with a real gas assumption. An explicit TVD-Upwind scheme is used for the Euler equations to evaluate interaction between shock waves. An experimental study of the underexpanded axisymmetric supersonic N2 jets impinging on a plate is also discussed. Pressure measurements on the plate surface and Schlieren photometries are performed to investigate the impinging jets. Numerical results with the Euler equations have a good agreement with the experimental results at the shock structure and pressure distribution on the plate. The results show that three types for complicated shock-shock interactions are revealed and that a stagnation bubble is formed due to triple point near the plate.
This paper considers a numerical method to solve optimal control problems which are formulated by a mathematical programming. In this 2nd report, A new method named Block Diagonal Hessian (BDH) method is proposed. This proposed method transforms the optimal control problem into a new formulated nonlinear programming problem. Considering that the nonlinear programming problem is solved by using a sequential quadratic programming method, the diagonal form of the Hessian matrix for the Lagrange function is introduced in BDH method. The BDH method is applied to a simple optimization problem and its characteristics are compared with those of other methods. As a result, though the accuracy of the BDH method is lower than that of the other methods, the BDH converges quickly and has robust characteristics in the selection of the nominal solution. Through this study, the effectiveness of the BDH method was confirmed.
This paper discusses the estimation method of the satellite attitude when star sensors are the only attitude sensors. Among the previously proposed estimation methods, the algebraic method and the q-method are representative ones. The algebraic method is fast but less accurate, whereas the q-method gives the optimal solution but takes much more time. The proposed method uses the solution of the algebraic method as an initial estimate and applies Newton method to obtain a more accurate solution by iterations. The iteration procedure is simplified by using the estimate of the last iteration. Thus the calculation time is shortened. From numerical simulations, it is shown that the proposed method gives the same optimal solution as the q-method and is much faster than the q-method. The proposed method is fairly competitive in calculation time, compared with the Markley's method (a variation of the q-method) credited as the fastest optimal estimation method. Besides computation of four rules (+, -, × and ÷), Markley's method includes seven square roots computation, a trigonometric function and an inverse trigonometric function, whereas the proposed method includes only two square roots computation. Therefore, in view of on-board applications, the proposed method is more suitable.
The dynamics of a space robot can be quite complex, that is, the manipulator motion acts as a disturbance to the satellite attitude control system. But even when the manipulator is working, the main body of the space robot, which includes a communications antenna, must be stabilized to maintain the communication link to the ground control station. In this paper the method to estimate the angular velocity norm of the next control cycle from reference payload motion under the coordinated control is proposed. If the estimated angular velocity norm exceeds the maximum permissible angular velocity norm, reference payload motion must be reconstructed. This calculation can be realized on real-time. The validity and usefulness of this scheme are verified through results of the computer simulation with a three-dimensional space robot model.