Automatic differentiation through source code transformation is a very powerful strategy for gradient-based optimization studies. However, memory allocation is a significant challenge if the transformed code is used without any modifications because automatic differentiation requires huge memory space. A general strategy to calculate derivatives of CFD solutions analytically through automatic differentiation without the memory problem is proposed in this paper. The problem of memory allocation is avoided by wisely modifying the code generated by automatic differentiation, and by feeding a set of converged solutions to the modified code. This strategy is validated by comparing derivatives computed through automatic differentiation and finite differentiation. The proof of concept application is the optimization of airfoil shape in transonic speed regime using a general CFD software available on line.
The influence of propeller blade wake is emphasized at the performance design of propeller. The propeller wakes mainly consist of the wing tip vortex generated at the tip of blade and the vortex sheet from the trailing edge of the blade, which describe the helix in the wake. The source of these wakes is the surface of the blade, so the conditions of the flow on the surface are largely concerned with formation of the wake and the performance of propeller. Then the propeller blade was made under the condition of low Reynolds number flow, and the flow on surface is studied by empirical means of direct pressure measurement and tuft method. An exist of separation flow was revealed by the pressure measurement and the appearance of the cross flow on the blade could be observed by tuft method.
In this paper, we address simultaneous structure/controller design of flexible space structures. In particular, we consider optimal placement of sensors and actuators together with control design. Even though the original problem is non-convex, we transform it into a convex one via a novel approach. In particular, nonlinear parameter relationship is described as a bound of a convex region in a parameter space. Approximating the region from the inside by a set of successive LMIs, we seek optimal solutions that approach the bound of the region.
For validation of an ion beam optics code, the behavior of ion beam optics was experimentally observed and evaluated with a two-dimensional visualized ion thruster (VIT). Since the observed beam focus positions, sheath positions and measured ion beam currents were in good agreement with the numerical results, it was confirmed that the numerical model of this code was appropriated. In addition, it was also confirmed that the beam focus position was moved on center axis of grid hole according to the applied grid potentials, which differs from conventional understanding/assumption. The VIT operations may be useful not only for the validation of ion beam optics codes but also for the fundamental and intuitive understanding of the Child Law Sheath theory.
In this paper, precise position keeping of a deputy spacecraft with respect to a chief spacecraft is considered in the formation flight. Especially, the case where the deputy spacecraft is located at the certain distance from the chief spacecraft in the tangential direction is analyzed under the J2 perturbation. The relative position between the two spacecraft is affected by the J2 perturbation, and the state transition matrix of the relative position and velocity including the effects of J2 is derived. With the state transition matrix, the variation of the relative motion during the orbit period is evaluated. The initial velocity of the deputy spacecraft in terms of the Hill coordinates and the small eccentricity of the chief spacecraft orbit that alleviate the effects of J2 are obtained. Numerical studies are executed to validate the analytical results.
The Busemann biplane is well known as the airfoil that has zero wave drag at the supersonic flight in the linear theory. It is found that this airfoil has a hysteresis in drag values from the transonic speeds through the low supersonic speeds based on Computational Fluid Dynamics (CFD) analysis. This paper shows that this hysteresis is explained by the Kantrowitz-Donaldson Criteria that usually defines the start and unstart of the supersonic intake.