Optimal quasi-circular motion of a spacecraft with an energy storage device

The problem of using an energy storage device in spacecraft low-thrust propulsion systems with a constant-power thruster is considered and solved for optimal quasi-circular maneuvers in the near-Earth space. The maximum payload is the optimality criterion. The optimal control as a function of time and the optimal mass parameters of the spacecraft were determined. Domains of the mass parameters where the use of an energy storage device makes sense are shown. T. G. Shevchenko University, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 10, pp. 93–100, October, 1999.     

Optimization of spacecraft transfers between distant elliptical orbits

Optimization is made of the trajectories, controls, and the parameters of a low-thrust constant-power engine with energy storage of a spacecraft executing the maneuver of synchronous considerable change in the semimajor axis, eccentricity, and angle of an elliptical orbit in a spherical gravitational field. The gain in payload mass due to the energy storage is estimated. The optimal control law and the optimal ratio for the masses of the propulsion system are found     

Optimization of constant- and variable-thrust propulsion systems

The problem of the transfer of a spacecraft with maximum payload from a fixed circular orbit to a given noncoplanar circular orbit in a spherical gravity field is solved. The spacecraft is equipped with constant-power electric propulsion and energy storage. The cases of variable-thrust and constant-thrust propulsion are considered. The increase in the payload mass due to the energy storage is estimated in both cases. The optimal time dependence of controls and the optimal relations between the mass parameters of the propulsion system are established. The ranges of these parameters where it makes sense to store energy are identified     

Energy change due to the appearance of cavities in elastic solids

The paper presents an overview of the problem of assessing an increment of strain energy due to the appearance of small cavities in elastic solids. The following approaches are discussed: the compound asymptotic method by Mazja et al., the Eshelby-like method used in the classical works on the mechanics of composites, the homogenization method, and the topological derivative method proposed by Sokołowski and Żochowski. The increment of energy is expressed by a quadratic form with respect to strains referring to the virgin solid. All the methods lead to the same formula for the increment of energy. It is expressed by a quadratic form with respect to strains referring to the virgin solid. This quadratic form turns out to be unconditionally positive definite. Explicit formulae are derived for an elliptical hole and for a spherical cavity. The results derived determine the characteristic function of the bubble method of the optimal shape design of elastic 2D and 3D structures.     

Thermal analysis of a finned-tube LHTS module for a solar dynamic power system

 This paper investigates the transient behaviour of a finned tube latent heat thermal storage (LHTS) module that is put into use in space based power systems, or such similar energy storage applications. The shell side of the module is loaded with phase change material (PCM) while the tubes carry the heat transfer fluid (HTF). Thin circumferential fins are added externally onto the tube surface at equal spacings. The LHTS module is mathematically modeled with an enthalpy based method and the resulting system of conjugate governing equations is numerically solved for charging mode. The influence of various parameters viz. geometrical, thermophysical and various non-dimensional numbers on the performance of the unit is studied. Numerical results indicate an appreciable enhancement in the energy storage process with the addition of fins in the module for an effective utilisation of the available solar energy during the active phase of the orbit orcharging cycle. Received on 1 September 2000 / Published online: 29 November 2001     

Optimal disturbances of a dusty-gas plane-channel flow with a nonuniform distribution of particles

The classical stability theory for multiphase flows, based on an analysis of one (most unstable) mode, is generalized. A method for studying an algebraic (non-modal) instability of a disperse medium, which consists in examining the energy of linear combinations of three-dimensional modes with given wave vectors, is proposed. An algebraic instability of a dusty-gas flow in a plane channel with a nonuniform particle distribution in the form of two layers arranged symmetrically with respect to the flow axis is investigated. For all possible values of governing parameters, the optimal disturbances of the disperse flow have zero wavenumber in the flow direction, which indicates their banded structure (“streaks”). The presence of dispersed particles in the flow increases the algebraic instability, since the energy of optimal disturbances in the disperse medium exceeds that for the pure-fluid flow. It is found that for a homogeneous particle distribution the increase in the energy of optimal perturbations is proportional to the square of the sum of unity and the particle mass concentration and is almost independent of particle inertia. For a non-uniform distribution of the dispersed phase, the largest increase in the initial energy of disturbances is achieved in the case when the dust layers are located in the middle between the center line of the flow and the walls.     

Effects of springs on a pendulum electromechanical energy harvester

This paper studies a model of energy harvester that consists of an electromechanical pendulum system subjected to nonlinear springs. The output power is analyzed in terms of the intrinsic parameters of the device leading to optimal parameters for energy harvesting. It is found that in an appropriate range of the springs constant, the power attains higher values as compared to the case without springs. The dynamical behavior of the device shows transition to chaos.     

Thermoplastic damage of a stretched plane caused by a moving energy source

A thermoplastic stress and strain calculation is made to analyze the energy distribution around an energy source traveling in a prestretched panel. The technique of finite element is applied such that the motion of the energy source is discretized into a finite number of time increments. Remeshing of the grid pattern is carried out for every time increment.The energy source may represent a welding torch or laser beam with a high local intensity that causes the material to deform beyond its elastic limit and experience permanent damage by evaporation. This reduces the local stiffness and can lead to global instability. The failure analysis is based on the application of the strain energy density theory which is into the incremental theory of thermoplasticity. The specific example involves examining the experimental data of a 7075-T651 aluminum panel subjected to tensile loading. The energy source is assumed to have a finite radius and travels along the line of symmetry being normal to the direction of applied tension. The possible failure location is predicted for each time increment by analyzing the fluctuation of the local strain energy density field. A critical point corresponding to incipient fracture is found. The panel has a width of 45.72 cm and length of 55.88 cm. The prediction is consistent with the experimental observation.     

Vibration Attenuation of a Nonlinear Oscillator by using the Bound on a system

This work examines dynamic optimization of an autonomous oscillator with nonlinearities in stiffness and damping. Lyapunov analysis is utilized to show boundedness of the solution. The ultimate bound on the system is found by using Lyapunov stability criterion. The optimal parameters are found by estimating the bound on the system. The proposed theory can predict the parameters of a nonlinear autonomous system to a relatively good precision and superior vibration attenuation can be predicted.     

Improvement of the Contour Method for Measurement of Near-Surface Residual Stresses from Laser Peening

A study was conducted to develop a methodology to obtain near-surface residual stresses for laser-peened aluminium alloy samples using the contour method. After cutting trials to determine the optimal cut parameters, surface contours were obtained and a new data analysis method based on spline smoothing was applied. A new criterion for determining the optimal smoothing parameters is introduced. Near-surface residual stresses obtained from the contour method were compared with X-ray diffraction and incremental hole drilling results. It is concluded that with optimal cutting parameters and data analysis, reliable near-surface residual stresses can be obtained by the contour method.     

Numerical and experimental investigations of a rotating nonlinear energy sink

In this work, passive nonlinear targeted energy transfer (TET) is addressed by numerically and experimentally investigating a lightweight rotating nonlinear energy sink (NES) which is coupled to a primary two-degree-of-freedom linear oscillator through an essentially nonlinear (i.e., non-linearizable) inertial nonlinearity. It is found that the rotating NES passively absorbs and rapidly dissipates a considerable portion of impulse energy initially induced in the primary oscillator. The parameters of the rotating NES are optimized numerically for optimal performance under intermediate and strong loads. The fundamental mechanism for effective TET to the NES is the excitation of its rotational nonlinear mode, since its oscillatory mode dissipates far less energy. This involves a highly energetic and intense resonance capture of the transient nonlinear dynamics at the lowest modal frequency of the primary system; this is studied in detail by constructing an appropriate frequency–energy plot. A series of experimental tests is then performed to validate the theoretical predictions. Based on the obtained numerical and experimental results, the performance of the rotating NES is found to be comparable to other current translational NES designs; however, the proposed rotating device is less complicated and more compact than current types of NESs.     

Freezing around a finite heat sink immersed in an infinite phase change medium

Freezing around a spherical heat sink immersed in an infinite phase change medium — a free boundary problem involving growth and decay of the free boundary — is analysed here. A one-dimensional conduction model is formulated and the resulting partial differential equations are solved by finite difference methods. The energy discharged from the phase change medium during the heat transfer process is analysed for latent heat thermal energy storage applications. Results are presented for a wide range of parameters that are encountered in energy storage devices. The cases of slab/cylindrical heat sink are reexamined for a range of parameters not covered by the earlier investigators     

Studies of a Magnetocumulative Source of Electromagnetic Pulses with a Double Inductive Energy Storage

An energy source based on a helical magnetocumulative generator with simultaneous initiation of an explosive charge on the axis was developed. The generator operates on a double inductive energy storage with current circuit breakers in each storage. The main analytical dependences of the pulse amplitude and shape on the parameters of the double inductive energy storage were obtained. In an experiment with such an energy source, a voltage pulse of 770 – 800 kV was obtained on a breaker made of electrically exploding wires. The voltage at possible load points was 1300 – 1350 kV. The duration of the voltage pulse edge from 0.1U _max to 0.9U _max did not exceed 0.5 sec.     

Mechanical analysis of C/C composite grids in ion optical system

The ion thruster is an engine with high specific impulse for satellites and spacecrafts, which uses electric energy to boost the spacecraft. The ion optical system,also known as gate assemblies which consist of acceleration and screen grids, is the key component of the ion thruster. In this paper, the static mechanical properties of the C/C composite grids are evaluated based on the structural design. Representative volume element(RVE) is adopted to simplify the braded composite structure as a continuum material. The dynamical behavior of the 100 mm ion thruster optics in the launch environment(1 000 gshock-load) is numerically modeled and simulated with the half-sine pulse method. The impact response of the C/C and molybdenum gate assemblies on the stress distribution and deformation is investigated. The simulated results indicate that the magnitudes of the normal displacement of the composite grids subject to the uniformly distributed load are on the same level as molybdenum grids although the normal stiffness of the composite grids is much smaller. When sub ject to impact loading,the stress distribution in the C/C composite grids is similar to molybdenum grids while the stress magnitude is much smaller. This finding shows that the C/C gate assemblies outperform molybdenum grids and meet the requirement of long lifetime service in space travel.     

Atomistically determined phase-field modeling of dislocation dissociation,stacking fault formation,dislocation slip,and reactions in fcc systems

The purpose of the current work is the development of a phase field model for dislocation dissociation, slip and stacking fault formation in single crystals amenable to determination via atomistic or ab initio methods in the spirit of computational material design. The current approach is based in particular on periodic microelasticity (Wang and Jin, 2001, Bulatov and Cai, 2006, Wang and Li, 2010) to model the strongly non-local elastic interaction of dislocation lines via their (residual) strain fields. These strain fields depend in turn on phase fields which are used to parameterize the energy stored in dislocation lines and stacking faults. This energy storage is modeled here with the help of the ”interface” energy concept and model of Cahn and Hilliard (1958) (see also Allen and Cahn, 1979, Wang and Li, 2010). In particular, the “homogeneous” part of this energy is related to the “rigid” (i.e., purely translational) part of the displacement of atoms across the slip plane, while the “gradient” part accounts for energy storage in those regions near the slip plane where atomic displacements deviate from being rigid, e.g., in the dislocation core. Via the attendant global energy scaling, the interface energy model facilitates an atomistic determination of the entire phase field energy as an optimal approximation of the (exact) atomistic energy; no adjustable parameters remain. For simplicity, an interatomic potential and molecular statics are employed for this purpose here; alternatively, ab initio (i.e., DFT-based) methods can be used. To illustrate the current approach, it is applied to determine the phase field free energy for fcc aluminum and copper. The identified models are then applied to modeling of dislocation dissociation, stacking fault formation, glide and dislocation reactions in these materials. As well, the tensile loading of a dislocation loop is considered. In the process, the current thermodynamic picture is compared with the classical mechanical one as based on the Peach-Köhler force.     

Optimizing energy input for fracture by analysis of the energy required to initiate dynamic mode I crack growth

A problem for a central crack in a plate subjected to plane strain conditions is investigated. Mode I crack loading is created by a dynamic pressure pulse applied at large distance from the crack. It was found that for a certain combination of amplitude and duration of the pulse applied, energy transmitted to the sample has a strongly marked minimum, meaning that with the pulse amplitude or duration moving away from the optimal values minimum energy required for initiation of crack growth increases rapidly. Results received indicate a possibility to optimize energy consumption of different industrial processes connected with fracture. Much could be gained in for example drilling or rock pounding where energy input accounts for the largest part of the process cost. Presumably further investigation of the effect observed can make it possible to predict optimal energy saving parameters, i.e., frequency and amplitude of impacts, for industrial devices, e.g., bores, grinding machines, etc. and hence significantly reduce the process cost. The prediction can be given based on the parameters of the media fractured (material parameters, prevalent crack length and orientation, etc.).     

Influence of load amplitude and uniaxial tensile properties on fatigue crack growth

The rate at which energy is accumulated within a unit volume of material in fatigue is assumed to depend not only on load-time history but also on the specimen size and geometry in addition to material type. A threshold level for the hysteresis strain energy density function accumulated in the material is used for predicting macrocrack growth. This is accomplished by application of the incremental theory of plasticity for each increment of crack growth. The accumulated hysteresis strain energy density factor ΔS to crack growth increment Δa ratio is found to be constant for fixed specimen size and loading, i.e., . Results are obtained for the cylindrical bar specimens with a penny-shaped defect at the center subjected to a constant amplitude and frequency loading. The resistance curves in the ΔS versus Δa plot are parallel lines as specimen size is altered. This information provides a rational means for predicting the influence of specimen size on fatigue lifetime.The results are also compared with those found for geometrically similar plate specimens with line cracks. Cylinder bar specimens of the same material are found to sustain more load cycles prior to catastrophic failure.     

Nonlinear response of an initially buckled beam with 1:1 internal resonance to sinusoidal excitation

The nonlinear response of an initially buckled beam in the neighborhood of 1:1 internal resonance is investigated analytically, numerically, and experimentally. The method of multiple time scales is applied to derive the equations in amplitudes and phase angles. Within a small range of the internal detuning parameter, the first mode; which is externally excited, is found to transfer energy to the second mode. Outside this region, the response is governed by a unimodal response of the first mode. Stability boundaries of the unimodal response are determined in terms of the excitation level, and internal and external detuning parameters. Boundaries separating unimodal from mixed mode responses are obtained in terms of the excitation and internal detuning parameters. Stationary and non-stationary solutions are found to coexist in the case of mixed mode response. For the case of non-stationary response, the modulation of the amplitude depends on the integration increment such that the motion can be periodically or chaotically modulated for a choice of different integration increments. The results obtained by multiple time scales are qualitatively compared with those obtained by numerical simulation of the original equations of motion and by experimental measurements. Both numerical integration and experimental results reveal the occurrence of multifurcation, escaping from one well to the other in an irregular manner. and chaotic motion.     

Size effect of cylindrical specimens with fatigue cracks

The rate at which energy is accumulated within a unit volume of material in fatigue is assumed to depend not only on load-time history but also on the specimen size and geometry in addition to material type. A threshold level for the hysteresis strain energy density function accumulated in the material is used for predicting macrocrack growth. This is accomplished by application of the incremental theory of plasticity for each increment of crack growth. The accumulated hysteresis strain energy density factor ΔS to crack growth increment Δa ratio is found to be constant for fixed specimen size and loading, i.e., $\text{ΔS}\text{Δa}\text{=}\text{const}$. Results are obtained for the cylindrical bar specimens with a penny-shaped defect at the center subjected to a constant amplitude and frequency loading. The resistance curves in the ΔS versus Δa plot are parallel lines as specimen size is altered. This information provides a rational means for predicting the influence of specimen size on fatigue lifetime.The results are also compared with those found for geometrically similar plate specimens with line cracks. Cylinder bar specimens of the same material are found to sustain more load cycles prior to catastrophic failure.     

Energy transfer from an inductive storage by means of an explosive current disconnect

Energy transfer from an inductive storage is considered for two types of systems: a disconnect with an intrinsic parasitic inductance for an inductive load and a purely resistive disconnect for a resistive load. Solutions are obtained for the voltage, power, and energy transferred to the load. The dependence of the efficiency of the device on its parameters is established.