Low-thrust Engines Research Articles

Estimating Expected Radiation Doses in a Flight to the Moon Using Low-Thrust Engines

Estimating Expected Radiation Doses in a Flight to the Moon Using Low-Thrust Engines

A novel calculation method for low-thrust transfer trajectories in the Earth-Moon restricted three-body problem

This paper introduces a novel trajectory calculation method for achieving continuous low-thrust transfers from the geostationary orbit to libration point orbits within the Earth-Moon restricted three-body framework. Low-thrust engines can offer benefits such as high specific impulse and long operating lifetimes, making them suitable for deep space exploration. However, the primary challenge lies in the low thrust level, leading to prolonged flight duration for spacecraft to overcome Earth's gravitational pull. Furthermore, the transfer trajectories exhibit multiple revolutions around the Earth, adding complexity to the calculations. To solve these difficulties, a novel trajectory computation method is presented, which for the first time discusses dynamical evolution beyond a predefined time interval in the context of an optimal control problem specific to low-thrust engines. This method employs a backward integration technique applied to the known optimized solution, coupled with a deliberate extension of the flight time to generate an initial guess for subsequent trajectory optimization, significantly simplifying the computational procedure. Several application scenarios involving transfer from the geostationary orbit to libration point orbits are demonstrated. The results confirm the effectiveness of this method, providing a rapid computational strategy for similar low-thrust transfer missions.

Двухуровневый параметрический метод оптимизации траектории перелета с малой тягой

A direct method is proposed for solving the optimal control problem of a spacecraft equipped with a low-thrust engine. The control function is parameterized using polynomials and switching moments between active and passive control modes. The essence of the method lies in separating optimization parameters: at the outer level, the switching time moments of control modes are optimized, while at the inner level, the coefficients of auxiliary polynomials are optimized. The method’s performance is demonstrated on problems of interplanetary flight to Mars and the conversion of impulse control to continuous control.

APPLICATION OF THE TEST-PARTICL STATISTICAL METHOD FOR THE SIMULATION OF RAREFIED PLUME FLOWS IN A VACUUM

The article substantiates the important role of the problem of the supersonic jet outflow into a vacuum to control the motion of the center of mass, orientation, and stabilization of the spacecraft’s position in space. The types of low-thrust engines and microrocket engines viewed have plumes that can pass through all regimes from continuum to free-molecular. In zones where motion is described at the molecular-kinetic level, statistical methods are most often used. The statistical Test Particle Method (TPM) has so far been used only in rarefied homogeneous flows. The aim of this work is to develop the TPM for numerical modelling plume flows. Below are the basic tenets of the TPM and changes in its algorithm. The initial drawing of the trajectories of molecules is carried out either from the nozzle exit (in the absence of a dense core) or from the initial surface, which is the virtual border of the continuity zone. Determining the distributions over the surface of the drawing of the coordinates of the start and the mass velocity of the plume flow is decisive for obtaining adequate results. Among the considered launch options, the most realistic one is uneven, with a concentration on the plume axis. The calculation of the mass velocity of the plume flow at the initial surface can be performed using numerical methods of continuum aerodynamics or using approximate methods. The testing of TPM in the far field of a rarefied nitrogen plume was carried out by comparing the relative density distribution with the data of the approximate method. The results obtained in the presence of the initial sphere and in its absence agree with each other. The TPM testing in the area adjacent to the nozzle was carried out by comparing the isolines of relative density and Mach numbers with the results of direct Monte Carlo simulation for the experimental conditions of helium outflow from a lowthrust engine into a vacuum. Satisfactory agreement has been obtained between the numerical simulation data of the TPM and the compared data

Analysis of Dynamics and Control During the Deployment of an Annular Tether Group of Spacecraft

The article considers a method for forming a rotating tether group of small spacecraft in the form of a regular polygon. To create an external torque acting on the entire system as a whole, low-thrust engines are used, and the directions of the reactive forces are unchanged in the coordinate systems associated with the spacecraft. The release of the cables is controlled by measuring their length and speed in accordance with the nominal program, which assumes that the mechanisms of the release of the cables work only for their braking. The nominal program is built according to a simplified model of the system's motion, built using the Lagrange equations. The feasibility of the deployment program is checked using a more complete model of the spatial motion of the system, written in a geocentric fixed coordinate system and taking into account the extensibility of the cables, the one-sidedness of the mechanical links corresponding to them, the operation of the control system, disturbances associated with the initial conditions of motion, etc. A more complete model of motion takes into account the motion of space vehicles relative to their centers of mass as solid bodies of finite dimensions, which leads to perturbations in the directions of action of reactive forces. Numerical examples are given of the deployment of ring tether groups of small spacecraft in the form of polygons with up to seven vertices, inclusive, under the action of disturbances.

Effect of dielectric barrier discharge methane reforming products on the combustion performance of rocket engine

Although the low-thrust liquid oxygen/methane rocket engine has broad application prospects, the low flame propagation speed and low combustion rate of methane fuel make the liquid oxygen/methane engine still face key technical challenges. Methane fuel is partially converted into hydrogen and ethane with higher combustion rate before being injected into the combustion chamber, which is positive for the use of dielectric barrier to improve the combustion performance of the engine. Therefore, this paper studies the effect of the main four products of dielectric barrier discharge reforming with methane conversion rate of 10%, on the flow field of the combustion chamber. The results show that the addition of reforming products can effectively improve the combustion efficiency of the engine. H2 in the reforming product can also improve the specific impulse performance of the engine by increasing the total pressure of the engine chamber. C2H4 will not affect the maximum temperature of the engine, However, it can expand the medium-high temperature range of engine temperature to different degrees. The addition of H2 accelerates the oxygen consumption rate, which provides a feasible way to reduce the design size of the engine and improve the combustion efficiency of the low-thrust engine.

Automation of low-thrust engine testing

The article discusses the key role of the use of automation in the stands, as well as the ignition system of the stand of low-thrust engines and the features of its operation as part of the stand. The ignition system scheme was developed, assembled and worked out, on the basis of which the ignition of the components of the propulsion system mixture will be carried out. The ignition system was tested by directly connecting the power supply to the circuit, which during the tests showed its suitability for use due to the long and continuous operation of the system. The power was turned on by controlling relay switches based on the Arduino MEGA 2560. Also, an algorithm was developed for the operation of the automation system for switching on, off and checking the entire system before testing the propulsion system on the stand of low-thrust engines to ensure automation and safety of using the stand. This algorithm includes control of two channels of the oxidizer and fuel pipeline, emergency power off, opening and closing of cut-off valves, taking readings and checking pressure gauges and flow meters, as well as shutting down the system after testing low-thrust engines using an Arduino MEGA controller.

Assessing Parameters of the Coplanar Components of Perturbing Accelerations Using the Minimal Number of Optical Observations

The method presented in this paper is developed to assess the parameters (the application moment and the magnitude of a velocity impulse) of a maneuver-like perturbation of motion of the center of mass of a spacecraft in a near-circular orbit. The assessment is based on the information on the spacecraft’s trajectory before the maneuver and the optical observations of the spacecraft’s angular position (right ascension and declination angles) after the maneuver. This study considers the cases of solely transversal (in-track) or transversal and radial components of the velocity increment vector. A single pair of the values of angles is used for the assessment of the single transversal maneuver parameters and two pairs are used in the other cases. The method also makes it possible to estimate the parameters of a continuous maneuver performed with low-thrust engines. For this case the property of its symmetry is used. The approach described in this article makes it possible to determine the spacecraft’s orbit after the maneuver much faster and more accurately in comparison to traditional methods.

Formation of a rotating ring-shaped three-body tethered nanosatellite system with limited control

The problem of forming a rotating ring-shaped tethered system consisting of three nanosatellites is considered. To analyze the dynamics of the tether system, a mathematical model is developed in the orbital coordinate system using the Lagrange method. Using the sliding mode control method, two control programs for the deployment of tethers are proposed, in which tether tensions and thrust forces created by low-thrust engines are used as controls. In the first control program, the control actions are directly limited by the permissible limits of tether tensions forces and thrust forces, and when designing the second control program, an auxiliary dynamic system is added into the control system, which introduces control corrections that take into account the saturation effect. The stability of motion of the tethered formation system for both control programs is investigated using the Lyapunov theory. The results of numerical simulations confirmed the possibility of using the proposed control programs for the formation of a rotating triangular tethered system in the form of a regular triangle in the presence of disturbances and with account of the given constraints.

Оптимізація перельотів між низькими орбітами з суттєвою різницею довгот висхідних вузлів

At present, satellite systems, each comprising hundreds of satellites, are, and are to be, deployed in low orbits. In addition, existing satellite systems are replenished. There has appeared a trend towards the development of modular satellites, which will lead to the development of easy-to-maintain spacecraft consisting of many small structural modules with standardized interface mechanisms. To extend the life of all these systems and reduce their maintenance cost, it is advisable to develop a system for their maintenance. Despite the relatively large number of works on the rendezvous problem, this problem is considered in a somewhat simplified formulation, which is not sufficient for spacecraft servicing in low orbits. As a rule, the consideration is limited to coplanar rendezvous problems in an impulse formulation. In real conditions, rendezvous maneuvers in low orbits are nontrivial. As is known, the orbital parameters of low-orbit spacecraft may differ significantly: the difference in the longitude of ascending nodes (LAN) may reach tens and even hundreds of degrees. Because of this, the energy consumption for an orbital plane change becomes unacceptably high for modern service spacecraft. This energy consumption can be reduced by using the precession of the line of nodes due to the non-centrality of the Earth's gravitational field. A waiting maneuver of a service spacecraft in a well-chosen orbit makes it possible to eliminate the mismatch between the LANs of the service spacecraft’s parking and destination orbits, thus significantly reducing the orbital transfer energy consumption. However, the long wait time of the service spacecraft in its parking orbit significantly increases the total orbital transfer time. The aim of this article is to develop a mathematical model of bicriteria optimization of a transfer of a service spacecraft with a low constant thrust engine between low near-circular orbits with significantly different LANs. This problem is solved by averaging the service spacecraft’s dynamics equations over a fast parameter and using a genetic algorithm of global Pareto optimization. The novelty of the results obtained lies in a formulation of a bicriteria optimization problem and the development of a mathematical model for choosing an optimal service spacecraft parking orbit. The mathematical model developed may be used in planning service spacecraft transfers between low near-circular orbits with significantly different LANs.

Математична модель роботи системи різномасштабних двокомпонентних реактивних двигунів малої тяги

The aim of this work is to modify a comprehensive mathematical model of a system of two-component low-thrust jet engines using the numerical method of characteristics in the propellant pipeline system with account for different sound speeds in the oxidizer and the fuel employing a unified method of pipeline discretization. This paper presents a unified approach to a numerical implementation of the method of characteristics for both fuel components and for regular computational cross-sections (internal for structural sections with constant geometrical and elastic parameters) and terminal cross-sections at the pipeline system inlets, the section joints, and the engine inlets for each propellant components. The approach accounts for the hydraulic resistances of the propellant injectors and electric propellant valves and the actual pressures in the engine combustion chambers. The performance of the mathematical model is illustrated by the example of the predesigning of a system of different-scale low-thrust engines to control the motion of a spacecraft relative to its center of mass in pitch, yaw, and roll and transfer the spacecraft to a new orbit (higher of lower) for maneuvering and docking with another spacecraft. The computed results show the possibility of determining the key hydraulic and gas-dynamic parameters of the system in transient conditions: the pressure and propellant component flow rate distribution at the inlet of any of the engines, the combustion chamber pressure and thrust characteristics of each engine, and the mutual effect of the engines on their thrust characteristics by the example of varying the flow areas of the propellant manifolds in the steady (continuous) and unsteady pulsed operation of all engines or some of them. The proposed mathematical model may be used in the computational justification of design parameters and operating conditions in the preparation of a draft proposal or in the predesign determination of an engine system configuration. Detailed information on the hydraulic and gas-dynamic performance parameters of an engine system is an important complement to the results of a ground tryout of both single engines and an engine system in conditions that simulate the flight environment.

Перспективи використання азотовмісних однокомпонентних ракетних па-лив

The goal of this work is to analyze the possibility of using existing monopropellant compositions based on aqueous solutions of high-energy nitrogen-containing substances as the main propellant for low-thrust engines, for example, for meteorological rockets, for upper-stage engines, and in spacecraft control engine systems. This paper presents an approach that considers the selection and justification of ingredients based on renewable energy sources, the analysis being carried out primarily from standpoint of the availability of propellant components and their safety and energy efficiency. It is proposed that the energy of unitary reducing agent – oxidizer chemical propellants (energy-saturated compositions) be used as an alternative source. The development of nonhydrocarbon nitrogen-containing alternative energy sources with the possibility of their conversion and accumulation into the planetary nitrogen, oxygen, and water cycles is an urgent problem. The paper presents detailed information on propellant mixtures of nitrogen-containing substances as oxidizers and considers a number of reducing agents, such as alcohols, amides, etc. in composition with high-energy additives (aluminum, magnesium). The calculated results obtained meet the objectives and demonstrate that the compositions considered can be used as the main propellant for low-thrust engines. The advantages of the new propellant technology: availability, a low cost, produceability, environmental friendliness, a relatively low toxicity, and, primarily, a simpler design of the propulsion system and launch equipment. The proposed propellant composition, which is under test, is planned for use in the sustainer engines of ultralight suborbital rockets with the possibility of further development to an orbital rocket system.

Transfer between the planar Lyapunov orbits around the Earth–Moon L2 point using low-thrust engine

We present a study of the low-thrust transfer problem near the secondary body in the Earth–Moon circular restricted three-body problem (CRTBP). Based on the Pontryagin maximum principle, the time-optimal, energy-optimal and fuel-optimal transfers between the planar Lyapunov orbits around the L2 point of the Earth–Moon system are constructed as a two-point boundary value problem (TPBVP). A criterion for identifying the best trajectory is also described. The Lyapunov orbit structure is used to deal with the potential difficulties of initial guess. As a result, the final transfer trajectory follows a multi-revolution structure, which takes a long time of flight. The homoclinic connection configuration is investigated by introducing the relevant invariant manifolds, allowing for faster transfer and less fuel consumption in the same case. It is designed a linear time-varying model predictive control (MPC) algorithm to perform trajectory tracking in the presence of initial orbit error and deviations in engine operation. Numerical simulations show the efficiency and practicability of the optimal transfer trajectory design strategy and trajectory tracking controller proposed in this paper for future lunar exploration missions.

The Investigation of Plume-Regolith Interaction and Dust Dispersal during Chang’E-5 Descent Stage

The plume-surface interaction that occurs as a result of a variable-thrust engine exhaust plume impinging on soil during landings is critical for future lunar mission design. Unique lunar environmental properties, such as low gravity, high vacuum, and the regolith layer, make this study complex and challenging. In this paper, we build a reliable simulation model, with constraints based on landing photos, to characterize the erosion properties induced by a low-thrust engine plume. We focus on the low-thrust plume-surface erosion process and erosion properties during the Chang’E-5 mission, aiming to determine the erosion difference between high- and low-thrust conditions; this is a major concern, as the erosion process for a low-thrust lunar mission is rarely studied. First, to identify the entire erosion process and its relative effect on the flat lunar surface, a one-to-one rocket nozzle simulation model is built; ground experimental results are utilized to verify the simulated inlet parameters of the vacuum plume flow field. Following that, plume flow is considered using the finite volume method, and the Roberts erosion model, based on excess shear stress, is adopted to describe plume-surface interaction properties. Finally, a Lagrangian framework using the discrete phase model is selected to investigate the dynamic properties of lunar dust particles. Results show that erosion depth, total ejected mass, and the maximum particle incline angle during the Chang’E-5 landing period are approximately 0.2 cm, 335.95 kg, and 4.16°, respectively. These results are not only useful for the Chang’E-5 lunar sample analysis, but also for future lunar mission design.

ЭКСПЕРИМЕНТАЛЬНОЕ ОПРЕДЕЛЕНИЕ ВРЕМЕНИ ОСАЖДЕНИЯ ТОПЛИВА В СФЕРИЧЕСКОМ БАКЕ ПЕРЕД ПОВТОРНЫМ ВКЛЮЧЕНИЕМ МАРШЕВОГО ДВИГАТЕЛЯ

The paper deals with the case of fuel deposition in the oxidizer tank of the space stage of the rocket using two low-thrust engines before re-starting the main engine. In addition, confirmed a computational-experimental method for determining the required time for fuel deposition, which combines experimental testing and numerical simulation of fuel deposition, which allows carrying out the necessary research with the required accuracy and significantly reducing the amount of testing and the need for material and technical equipment of the experimental base.

Generation of Artificial Halo Orbits in Near-Moon Space Using Low-Thrust Engines

Generation of Artificial Halo Orbits in Near-Moon Space Using Low-Thrust Engines

Orbital perturbation analysis and generation of nominal near rectilinear halo orbits using low-thrust propulsion

The near rectilinear halo orbit (NRHO) is a potential orbit for the establishment of lunar space station. This research is focused on the analysis of major orbital perturbations on NRHOs and the generation of nominal orbit using a low-thrust engine in the ephemeris model. First, the NRHO family is defined in the circular restricted three-body problem (CRTBP). Then, different perturbations are performed to integrate the spacecraft motion along the NRHOs; meanwhile, a modified momentum integral is employed to calculate the orbit deviation in the case of each perturbation examined independently. By this way, these perturbations are classified according to the magnitude of impact on NRHOs. Finally, combined with a fuel-optimal control, a target-point strategy generating the nominal-controlled NRHO in the real Earth–Moon system is proposed using low-thrust technology. By selecting a fixed point from the original NRHO, the spacecraft is forced to depart from this point and then return to it, thereby forming a controlled closed trajectory. This provides an alternative nominal orbit for the future application of the low-thrust engine to lunar exploration missions.

Optimal Control of Transfer to Vertical Orbits from Lyapunov Orbits Using Low-Thrust Engine

There are many different families of periodic orbits in the Earth-Moon system, such as Lyapunov orbits, halo orbits, vertical orbits, etc. The establishment of a lunar space station requires a spacecraft to be able to transfer among these orbits. Lyapunov orbits have been used by some missions and are well-studied orbits, while periodic vertical orbits can provide large amplitudes of spacecraft motion outside the plane of the Moon’s motion, which makes it possible to avoid shadowing of the orbits and use them as relay satellite in cislunar space. Modern researchers mainly consider the use of high-thrust engines for transfer. With the development of electric propulsion technology, the use of low, but long-acting thrust for deep space exploration has become especially relevant. This is due to the high specific characteristics of the propulsion systems of this type. In this article, an algorithm has been developed for determining the optimal control with a low-thrust engine for a transfer from Lyapunov orbit to a vertical orbit. The minimum time of flight or the minimum costs of the working body are used as criteria for optimality. In the calculation for solving the two-point boundary value problem of the optimal control theory, the parameter continuation algorithm is used, which allows to gradually get the transfer from some simple results to the final transfer trajectory. The results obtained make it possible to assert that the use of intermediate axial orbits allows the use of propulsion systems with lower thrust levels. In this case, the duration of the flight increases slightly with an almost unchanged consumption of the working body. Moreover, the homotopy method makes it possible to reduce the consumption of working body, while the control of the engine throttling becomes discrete. The results of this study and the algorithms proposed in this article can be used to determine the optimal program control and ballistic design of lunar missions.

Altitude Maximization for Small Subsonic Low-Power Unguided Rockets

This paper addresses the problem of maximizing the altitude that can be reached by small, unguided rockets propelled with low-thrust engines. A physical–mathematical model of a launcher device using exhaust gas recovery to increase the initial velocity of the rocket is presented. A case study related to a small-scale model used in amateur rocketry competitions is described. The analysis shows the constructive parameters of the piston launcher that optimize the performance of the rocket. The best thrust profile of the available motorizations, which potentially include delayed ignition of the sustainer, is identified, as well as the optimal distribution of the masses between the stages. Finally, the possibility of further increasing the initial velocity with a piston launcher through the use of retention mechanisms to increase the pressure in the tube or through the use of auxiliary gas generators is investigated. The results show the considerable performance benefits of using a piston launcher.

Численное исследование влияния физико-химических свойств жидкого горючего на эффективность рабочего процесса ракетного двигателя малой тяги

Low-thrust rocket engines are widely used in rocket and space technology for correcting the position of a spacecraft in orbit, for controlling motion along a trajectory, etc. Their number in the propulsion system can be from one to tens of units. Accordingly, the efficiency of their work significantly affects the perfection of the propulsion system as a whole. The object of the study was the low-thrust rocket engine combustion chamber operating according to the gas-liquid scheme. There were performed computational and parametric studies of various factor effects on the characteristics of the working process in the combustion chamber. The dependences of the coefficient of the consumable complex and parameters of the working process of the low-thrust rocket engine chamber on the influencing factors when using ethanol and kerosene as a fuel were calculated. A comparative analysis of the results of using these two components under similar conditions was carried out, which made it possible to reveal the influence of the physicochemical properties of the combustible component on the efficiency of the working process organization. The results obtained can be used in the design of low-thrust engines operating on the kerosene–oxygen and ethanol–oxygen propellants.