Fluid flow interaction with an obstacle near free surface

The two-dimensional problem of thin obstacle interaction with compressible fluid flow near free surface under microgravity was regarded. The fluid was assumed occupying infinite semi-space, gravity was neglected as compared with fluid inertia. The obtained exact solution shows that for relatively thin layer the resistance force does not depend on the layer thickness, but depend on body length and inclination angle, and surpasses twice the respective values for the infinite medium, which could be explained by additional wave resistance arising in the presence of free surface.     

Theoretical solution for the lift force of “ecranoplan” moving near rigid surface

This paper develops a theoretical solution for the problem of determining thin wing's lift force while moving near flat surface (a screen). The solution is determined under the assumption of fluid being ideal and incompressible. The Chaplygin–Zhukovsky hypothesis of rear-edge-limited solution is taken into consideration. The solution of a problem is reduced to the Fredholm equation that is solved numerically. The generalization of the Zhukovski solution was obtained, which provides the lift force dependence on the altitude of the flight. The behavior of the lift force is very peculiar: it increases on decreasing altitude above the rigid surface. The screen effect becomes essential on moving wing altitude being smaller than the wing's length. The effect was detected experimentally before and gave birth to construction of a special flying vehicle named “ecranoplan”. It is shown in the paper that the lift force could increase several orders of magnitude. This effect could be used in developing flying vehicles of high loading capacity, which could be used in the territories of smooth surface: savannas, steppes, deserts, lakes, swamps, etc. The effect could be used for developing vehicles for operation on other planets having not very dense atmosphere and relatively smooth surface (like Mars). Flights in such an atmosphere are energy consuming, while using the effect of lift force increase near the surface could be very effective.     

Hydrodynamic Analogy for the Solution to the Doubly Averaged Hill Problem Disturbed by Precession of the Orbit Plane of a Disturbing Body

A hydrodynamic analogy for the solution to a satellite version of the restricted three-body problem is considered with allowance made for precession of the disturbing body orbit. Applying, in the first approximation, the analytical solution to a doubly averaged equation system obtained in 1961 by M.L. Lidov, we consider the precession of the disturbing body orbit as some disturbing factor. The appropriate model enables us to describe the general pattern of integral curves in the entire area of their existence as a picture of flow lines of the potential motion of some fictitious homogeneous incompressible fluid. For the synthesis of an adequate mathematical model, a method similar to the Pade approximation is used. The obtained model and its discrete continual analog allow us to present, in a pictorial form, the disturbance of orbits under the effect of precession of the disturbing body orbit.     

The Impact of Variable Accelerations on Crystal Growth onboard Spacecraft by the Floating Zone Method

The numerical investigation of the impact of time-dependent accelerations (vibrations) on the flow and heat and mass transfer in the melt is carried out for the case of modeling the crystal growth by the floating zone method under conditions of microgravity that exist onboard spacecraft. The effects of the Archimedean buoyancy force and of vibrations of the free surface of fluid are considered separately. When solving the problem of the effect of the vibrations of the free surface of fluid, the previously obtained data were used. It is shown that vibrations of the free surface have a much stronger effect on the processes under consideration than the buoyancy. Some problems that are related to the newly discovered effects are discussed. The use of vibroprotected systems and a rotating magnetic field can help solve these problems. We plan to continue our investigations in future spacecraft experiments, in particular, at the International Space Station, which is under construction at the moment.     

Consequences of collisions of natural cosmic bodies with the Earth’s atmosphere and surface

Possible consequences of collisions of natural cosmic bodies with the Earth’s atmosphere and surface are described. The methodological basis of classification of consequences is the solution of meteor physics equations characterizing the trajectory of a body in the atmosphere, namely, the dependence of the body’s velocity and mass on the flight altitude. The solution depends on two dimensionless parameters characterizing the drag altitude and the role of mass loss by a meteoroid during its motion in the atmosphere. Depending on values of these parameters, the degree of effect on the planetary surface considerably changes. In particular, the conditions of cratering and meteorite fall on the planetary surface are obtained. The results are presented in a simple analytical form. They quite match to the real events considered in the paper. Recommendations are given on further investigations into the important problem of interaction of cosmic bodies with planetary atmospheres.     

On radiative and conductive heat transfer in spacecraft

The “radiative” boundary condition in a heat conduction problem relates the heat flux in a point of the wall to the temperatures in all the other points of the surface system.That is, this condition is of a “functional” type. This “functional” can be solved in discrete terms by using the conventional technique of dividing the body in small discrete elements or “nodes”. This paper instead presents an approach on a continuous scheme, by which the functional is solved in terms of “spacewise harmonics” of the temperature inside the body; the heat conduction problem is thus reduced to an ordinary form differential system whose unknowns are these “harmonics”. An interative linearized procedure to solve this system is also suggested, by which “exact” solutions are obtained. The merits of these solutions, with respect to practical discrete element computations, are in the better spacewise resolution and in the consequent more accurate treatment of both radiation and conduction. The application of the procedure is, however, limited to particular geometries. It is relevant to note that among these possible geometries many are included of practical interest, like hollow cylinders and polygons, cubic boxes etc. A numerical example completes the work.     

利用喷气装置卸载航天器积累角动量的最小工质损耗控制

讨论利用喷气装置卸载航天器积累的外扰角动量过程中 ,实现最小工质损耗的问题。提出了在航天器绕自己质心转动的过程中实现对这一角动量进行卸载的新思路。文中采用极大值原理求得了最优工质损耗并举出了实例     

自由返回轨道的P平面参数快速设计方法

针对自由返回轨道求解过程中地心轨道类型变化造成的B平面参数方法计算失败问题,提出一种基于P平面参数的自由返回轨道快速设计方法。首先,基于轨道半通径参数的普适性,给出了不同轨道类型的P平面参数定义,建立了以P平面参数为求解目标量的自由返回轨道求解模型。其次,给出了基于P平面参数的自由返回轨道快速设计方法,在构建的瞬时地月惯性系下,以平面双二体自由返回轨道作为初值,实现了高精度力模型下的自由返回轨道快速求解。对8种构型自由返回轨道的设计结果表明,P平面参数具有类似于B平面参数的大收敛域,且有效解决了轨道类型变化对计算的影响,可直接应用于中国后续月球探测任务轨道设计。     

星历模型下地月自由返回全飞行过程轨道设计

面向载人登月任务需要,针对星历模型下具备自由返回能力的地月转移轨道设计问题进行了研究。在三体模型下对地月三维自由返回轨道进行了求解,得到了地月空间内的自由返回轨道分布情况。在二体模型假设下对近月段的三脉冲变轨进行了求解,给出了变平面机动的计算方法。进一步提出了两轮逐次优化修正策略,分别以高度和再入走廊为主要约束,采用内点法和SQP算法在高精度星历模型下对自由返回轨道初值进行逐次优化修正。之后,采用SQP算法在星历模型下对近月三脉冲变轨进行优化修正,得到了星历模型下的自由返回+近月三脉冲变轨地月转移策略。仿真校验结果表明本文提出的方法能够在给定约束下有效求解星历模型下具备自由返回能力的地月转移轨道,为载人登月任务的转移轨道设计提供参考。     

Optimal Control of a Programmed Turn of a Spacecraft

A problem of optimal turn of a spacecraft is considered. The time of turn is minimized, as well as the functional having a meaning of the propellant consumption. An analytical solution to the problem stated is derived. It is demonstrated that the solution optimal in this sense belongs to a class of two-impulse controls, under which a spacecraft executes the turn along the trajectory of its free motion. The solution obtained in this paper differs from earlier available solutions considerably. The estimations of the propellant consumption for a realization of the programmed turn are made.     

点阵结构空气舵及内部流体热流固耦合研究

开展了钛合金TC4材料激光粉末床熔融(LPBF)工艺研究,在此基础上设计了多孔轻质空气舵模型,并基于有限差分法(FDM),采用三维流固耦合共轭传热数值计算方法,利用流体体积法(VOF)追踪流体自由液面,研究了典型的点阵夹层结构的空气舵内部冷却液动态换热过程的相互影响过程,考虑了冷却液与钛合金材料蒙皮间的耦合传热及湍流换热。结果表明,空气舵的内部流体压强随速度的增加而增加,从而导致流体出口的速度增加。当压强增加到一定程度时,流体的出口以水柱形式喷出。虽然较大的流体速度可以带走较多的热量,但是影响远小于对压强的影响。综合考虑空气舵的服役要求,获得了合适的冷却水入口速度。     

Exact analytic solution for the spin-up maneuver of an axially symmetric spacecraft

The problem of spinning-up an axially symmetric spacecraft subjected to an external torque constant in magnitude and parallel to the symmetry axis is considered. The existing exact analytic solution for an axially symmetric body is applied for the first time to this problem. The proposed solution is valid for any initial conditions of attitude and angular velocity and for any length of time and rotation amplitude. Furthermore, the proposed solution can be numerically evaluated up to any desired level of accuracy. Numerical experiments and comparison with an existing approximated solution and with the integration of the equations of motion are reported in the paper. Finally, a new approximated solution obtained from the exact one is introduced in this paper.     

A hydrodynamic analogy of the solution to double-averaged Hill problem

A hydrodynamic analogy for the solution of doubly averaged Hill problem obtained by M.L. Lidov [1] is discussed. S.A. Chaplygin used a similar analogy reducing the two-dimensional problem of motion of a compressible fluid to the same problem for some fictitious incompressible fluid [2]. In this case, we are led to the range of ideas which go back to the work by N.E. Zhukowski [3]. Two versions of this hydrodynamic analogy, on the basis of the model of a stratified fluid (exact analogy) and on the basis of the model of a homogeneous fluid (approximate analogy), are considered as well as some consequences of them.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 2, 2005, pp. 126–134.Original Russian Text Copyright © 2005 by Rabinovich, Prokhorenko.     

非凸二次约束下航天器姿态机动路径迭代规划方法

针对复杂约束下航天器姿态机动路径规划问题,首先描述和分析了航天器姿态机动过程中面临的动力学和运动学约束、有界约束、姿态指向约束,把姿态指向约束利用非凸二次型进行表述;其次从能量最优角度出发,将该约束机动问题归纳为非凸二次约束二次规划问题;然后引入线性松弛技术,将该问题转化成双线性规划问题,求出其中一个变量的凸包络和凹包络,降低求解复杂度,从而求出原问题的一个线性松弛。同时为了提高求解精度,提出一种基于评价函数的迭代规划算法,利用线性松弛求出的解作为初值,通过评价函数进行迭代规划,最终求出原问题的最优解。仿真结果表明该方法不仅可以满足复杂的姿态约束,得到全局姿态优化路径,而且能够降低能量消耗。     

Optimal control of reorientation of a spacecraft using free trajectory method

The problem of optimal control over spatial reorientation of a spacecraft is considered. The functional having a sense of propellant consumption is minimized. The analytical solution to the formulated problem is presented. It is shown that the optimal solution can be found in the class of two-impulse control at which the spacecraft’s turn is performed along a free motion trajectory. In order to improve the accuracy of spacecraft guidance into a specified angular position, methods of control are suggested that realize the method of free trajectories. The synthesized controls are invariant with respect to both external perturbations and parametric errors. The results of mathematical modeling are presented that demonstrate high efficiency of developed control algorithms. Propellant consumption for realizing a programmed turn is numerically estimated taking into account considerable gravitational and aerodynamic moments acting upon the spacecraft.     

Operational modal analysis via image based technique of very flexible space structures

Vibrations represent one of the most important topics of the engineering design relevant to flexible structures. The importance of this problem increases when a very flexible system is considered, and this is often the case of space structures. In order to identify the modal characteristics, in terms of natural frequencies and relevant modal parameters, ground tests are performed. However, these parameters could vary due to the operative conditions of the system. In order to continuously monitor the modal characteristics during the satellite lifetime, an operational modal analysis is mandatory. This kind of analysis is usually performed by using classical accelerometers or strain gauges and by properly analyzing the acquired output. In this paper a different approach for the vibrations data acquisition will be performed via image-based technique. In order to simulate a flexible satellite, a free flying platform is used; the problem is furthermore complicated by the fact that the overall system, constituted by a highly rigid bus and very flexible panels, must necessarily be modeled as a multibody system. In the experimental campaign, the camera, placed on the bus, will be used to identify the eigenfrequencies of the vibrating structure; in this case aluminum thin plates simulate very flexible solar panels. The structure is excited by a hammer or studied during a fast attitude maneuver. The results of the experimental activity will be investigated and compared with respect to the numerical simulation obtained via a FEM-multibody software and the relevant results will be proposed and discussed.     

空间机器人抓取未知目标的质量特性参数辨识

根据动量守恒定理,研究了单臂自由飘浮空间机器人抓取未知目标的质量特性参数辨识问题。已有文献中基于动量守恒原理进行的参数辨识只适用于系统线动量和角动量为零的情况,当两者不为零时无法得到正确的辨识结果。为解决此问题,本文首先在惯性系而非本体系下推导得到了机械臂抓取未知目标后的系统线动量和角动量,保证了其各分量的守恒特性。然后基于此特性,通过在轨测量两个时刻机器人本体的线速度、角速度以及机械臂各关节的角速度和转角信息,建立了含有未知目标质量特性参数的动量增量方程。最后根据三组测量信息,从联立的动量增量方程组中求解得到未知目标的质量特性参数。数值仿真表明,此方法在系统线动量和角动量为零和不为零两种情况下都能实现高精度的参数辨识,同时还避免了方程求解的奇异问题。     

Application of the method of potentials in problems of fracture mechanics

The theory of generalized elastic potentials is used for solving the problem of a space with cracks of arbitrary shape. Two solutions are proposed. In the first case, the solution is represented by a double-layer potential and a functional equation for determination of the unknown density is constructed in which difficulties stipulated by high polarity of the integrand may be eliminated. The other method consists of an analysis of a space with a thin smooth cavity and the solution of corresponding singular integral equations.Methods to improve the convergence of successive approximations used in solution of the equations are described and some particular cases of three-dimensional solids are considered. A special function is introduced on the external surface of the solid, which allows consideration of a whole space with cracks having fictitious stresses on their edges; this solution has some bearing on the main problem and also provides an integral equation for the auxiliary function. Another approach consists of the elimination of cracks by introduction of corresponding potentials and solution of the auxiliary problem for a continuous solid with special boundary conditions.     

High order optimal control of space trajectories with uncertain boundary conditions

A high order optimal control strategy is proposed in this work, based on the use of differential algebraic techniques. In the frame of orbital mechanics, differential algebra allows to represent, by high order Taylor polynomials, the dependency of the spacecraft state on initial conditions and environmental parameters. The resulting polynomials can be manipulated to obtain the high order expansion of the solution of two-point boundary value problems. Since the optimal control problem can be reduced to a two-point boundary value problem, differential algebra is used to compute the high order expansion of the solution of the optimal control problem about a reference trajectory. Whenever perturbations in the nominal conditions occur, new optimal control laws for perturbed initial and final states are obtained by the mere evaluation of polynomials. The performances of the method are assessed on lunar landing, rendezvous maneuvers, and a low-thrust Earth–Mars transfer.