Analyse du fonctionnement d'un propulseur a éjection modulée

ONERA developed, for studying the response of a propellant to a pressure or velocity fluctuation, an experimental rocket engine whose nozzle throat area can be modulated by a toothed disk.The paper presents a linearized theory of the functioning of this engine in the low frequency domain, i.e. when there is no wave propagation within the combuster.To describe the functioning of this motor, the Ryazantsev-Novozhilov method, which assumes that the gas response is instantaneous, is used. This analysis takes into account the erosion and radiation effects, the combustion efficiency and the thermal losses through the walls.Two particular cases are described, for two values of the Damköhler parameter $\text{D}{}_1\text{=}\text{t}{}_{\mathrm{c}}\text{t}{}_{\mathrm{th}}$, where t_c is the residence time in the combuster and t_th the characteristic thermal time of the heat penetration into the solid propellant. These two cases correspond, one to a classical propellant D₁ > 1, the other to a particular propellant of low burning rate ($\text{J}{}_{\mathrm{b}}\text{? 0.2}\text{to}\text{0.4}\text{mm s}{}^{\mathrm{?1}}$) D₁ < 1. The stability conditions are analysed as well as the pressure amplitute and phase as a function of the nozzle throat modulation frequency.Still in linearized theory, the complete solutions of the problem are presented, using a method of numerical resolution.     

On the limiting mass of a dense stellar matter

In the present work, we have derived an expression $\text{M}{}_{\mathrm{L}}\text{? 4.738 M}{}_{\mathrm{\odot }}$ (M_⊙ = 1.985 × 10³³ g = mass of the Sun) giving the “limiting” value of the mass of a dense stellar matter, by introducing the concept of nuclear size correction in the theory of relativistic Thomas Fermi model for a compressed atom. We find that $\text{M}{}_{\mathrm{L}}\text{? 5.1571 M}{}_{\mathrm{<mtext>Ch</mtext>}}\text{and}\text{=3.2750(M}{}_{\mathrm{<mtext>O</mtext>}}\text{)}{}_{\mathrm{<mtext>Prev</mtext>}}$ [M_Ch and (M_O)_Prev denote respectively the Chandrasekhar and author's “limiting” masses]. By making a comparative study with those of previous results it has been shown that our present treatment would provide satisfactory results for the density ranges from ? ? 10⁸ up to $\text{? ? 10}{}^{11}\text{g}\text{/}\text{cm}{}^3$. Other results of cognate interest in the non-relativistic regime 10³ < ? ? 10⁵ (without the nuclear size effect) are presented. The astrophysical implications of the results are mentioned.     

A small parameter method in problems of maneuvering space vehicles with aerodynamic efficiency

The motion of a satellite with aerodynamic efficiency along a low near-circular orbit is considered in the paper. The controls of bank angle γ and lift coefficient C_y are used as control functions. The introduction of a small parameter ($\text{? = (}\text{?}{}_0\text{· S · g}{}_0\text{2G}\text{)}$) makes it possible to integrate an adjoint system of equations and to obtain an approximate solution to the complete problem in the class of piecewise-constant control functions. Maximum values for the coordinates of heading angle η and lateral derivation from the plane of a reference orbit ?, which are connected with orbit plane angle by the relation cos i = cos ? · cos h, are used as criteria of maneuvering capability for a satellite with aerodynamic efficiency. Optimal programs for bank angle and incidence variation are derived and the influence of lift-to-drag ratio on the vehicle maneuvering capabilities has been estimated.It is shown that the process of the optimal motion is a special kind of gravitational skipping similar to the Keplerian motion but with continuous descent.     

Optimal aeroassisted return from high earth orbit with plane change

This paper gives a complete analysis of the problem of aeroassisted return from a high Earth orbit to a low Earth orbit with plane change. A discussion of pure propulsive maneuver leads to the necessary change for improvement of the fuel consumption by inserting in the middle of the trajectory an atmospheric phase to obtain all or part of the required plane change. The variational problem is reduced to a parametric optimization problem by using the known results in optimal impulsive transfer and solving the atmospheric turning problem for storage and use in the optimization process. The coupling effect between space maneuver and atmospheric maneuver is discussed. Depending on the values of the plane change i, the ratios of the radii, $\text{n =}\text{r}{}_1\text{r}{}_2$ between the orbits and $\text{a =}\text{r}{}_2\text{R}$ between the low orbit and the atmosphere, and the maximum lift-to-drag ratio E1 of the vehicle, the optimal maneuver can be pure propulsive or aeroassisted. For aeroassisted maneuver, the optimal mode can be parabolic, which requires only drag capability of the vehicle, or elliptic. In the elliptic mode, it can be by one-impulse for deorbit and one or two-impulse in postatmospheric flight, or by two-impulse for deorbit with only one impulse for final circularization. It is shown that whenever an impulse is applied, a plane change is made. The necessary conditions for the optimal split of the plane changes are derived and mechanized in a program routine for obtaining the solution.     

Small cryogenic propulsion unit for upper stage application

The feasibility study was conducted to use the cryogenic propulsion system for the third stage of the future H-1 vehicle. While the $\text{LO}{}_2\text{LH}{}_2$ third-stage mass fraction is less than the current solid propellant third stage, the 50% higher Isp results in a significantly higher payload. Two basic configurations of the new propulsion system were proposed: one pressure-fed system and two pump-fed systems. The first is a pressure-fed system providing a 700 kg thrust at an Isp of 441 sec with restart capability. The second is a pump-fed system, operating on an expander cycle principle. A midget turbopump with a 90 000 rpm shaft speed feeds the thrust chamber which delivers 1 ton of thrust at an Isp of 471 sec. The third proposed system is also a pump-fed design using a unique expander bleed cycle, and delivers a 1 ton thrust at an Isp of 470 sec with a turbopump speed of 80 000 rpm. The results of engine testing predict the performance feasibility of respective propulsion system designs.     

超临界压力下航空煤油RP-3在水平细圆管内对流换热特性实验研究

为探究超临界压力下碳氢燃料在水平管内的对流换热规律,文章针对超临界条件下航空煤油RP-3在水平细圆管内的对流换热,分析了热流密度、进口雷诺数及浮升力对对流换热的影响。研究表明:沿流动方向,管内表面传热系数随热流密度的增大先减小后增大;在低进口温度及低进口雷诺数情况下,管内换热均出现先恶化后强化的现象,而随着进口温度和雷诺数的增加,此现象消失;浮升力对换热的影响随热流密度的增加而增加;浮升力对下表面换热的加强使得入口效应的影响在下表面先于上表面结束;受浮升力影响,上下壁最大温差可达50 K;质量流速的增加会抑制浮升力对换热的影响;准则数Grq/Grth可以很好地反映浮升力的变化趋势。以上研究结果可为采用碳氢燃料作冷却介质的各类飞行器主动热防护技术方案提供技术支撑。     

Theoretical study about the Marangoni convection in a liquid column in zero-gravity

The thermal Marangoni effect on the surface of a liquid bridge induces a convection inside the liquid. For an imposed arbitrary periodic axial circumferential temperature distribution on the liquid surface the velocity distributions in radial-, angular- and axial direction are determined theoretically by solving the linearized Navier-Stokes equations. Of particular interest is the effect of the viscosity parameter $\text{v}\text{a}{}^2$ and axial wave length to diameter ratio $\text{l}\text{a}$. It was found that the increase of viscosity decreases the magnitude of the velocity distributions and that for small axial wave length to diameter ratios the radial- and axial velocities exhibit peak values close to the free surface of the liquid. This is in a less pronounced way also true for the angular velocity, which shows for increasing moderate values $\text{l}\text{a}\text{(0 ≤}\text{l}\text{a}\text{≤ 2}$) a strong increase in magnitude and for larger axial wavelength a decrease again. For increasing axial wavelength the peak value of the radial- and axial velocity shifts towards the center of the liquid bridge, of which for a further increase a decrease of the magnitude appears.     

Investigation of thermosolutally caused convection during -growth of BiSbTe3-mixed crystals at normal and reduced gravity

BiSbTe₃-mixed crystals have been grown at normal and reduced gravity (during the MIR'97-mission) using a -configuration of the TITUS facility. The distribution of the components in the melt, and so the homogeneity of the growing crystal, is strongly influenced by the flow in the melt even in the case of weak convection. The flow configuration in the melt especially in front of the solid-liquid phase boundary can be investigated by means of a segregation analysis of the system components and an additional Pb-dopant. The BiSbTe₃-system is because of its hydro-dynamic properties a typical representative of semiconductor melts (low number, high number) but there are also some special properties relating to the segregationally caused enrichment of the lighter tellurium at the phase boundary and the resulting solutal destabilities. Experimental experiences from segregation analysis have shown that the mass transport in the melt at normal gravity is mainly influenced by convective mixing determined by thermally and solutally caused buoyancy forces. Numerical simulations have been performed for the real experimentally used configurations. These simulations have shown that a strong coupling of thermal and solutal effects exists and have given axial as well as radial segregation profiles being in excellent agreement with the experimental results for the vertical normal gravity grown crystals. For micro gravity conditions a reduction of the flow velocity of more than two orders of magnitude (depending on the micro gravity level and the direction of the residual acceleration) resulting in diffusion controlled component segregation has been predicted.The results of the two micro gravity grown crystals, especially the axial and radial segregation profiles as a sensitive indicator for the flow configuration in front of the phase boundary will be given and discussed in the paper. They will be compared with the results of numerical simulations of the melt flow for the real processing parameters measured during the TITUS growth processes and with experimental as well as numerical results for vertical normal gravity grown reference Samples.     

Investigation of thermosolutally caused convection during Bridgman-growth of BiSbTe3-mixed crystals at normal and reduced gravity

BiSbTe₃-mixed crystals have been grown at normal and reduced gravity (during the MIR'97-mission) using a Bridgman-configuration of the TITUS facility. The distribution of the components in the melt, and so the homogeneity of the growing crystal, is strongly influenced by the flow in the melt even in the case of weak convection. The flow configuration in the melt especially in front of the solid-liquid phase boundary can be investigated by means of a segregation analysis of the system components and an additional Pb-dopant. The BiSbTe₃-system is because of its hydro-dynamic properties a typical representative of semiconductor melts (low Prandtl number, high Schmidt number) but there are also some special properties relating to the segregationally caused enrichment of the lighter tellurium at the phase boundary and the resulting solutal destabilities. Experimental experiences from segregation analysis have shown that the mass transport in the melt at normal gravity is mainly influenced by convective mixing determined by thermally and solutally caused buoyancy forces. Numerical simulations have been performed for the real experimentally used configurations. These simulations have shown that a strong coupling of thermal and solutal effects exists and have given axial as well as radial segregation profiles being in excellent agreement with the experimental results for the vertical normal gravity grown crystals. For micro gravity conditions a reduction of the flow velocity of more than two orders of magnitude (depending on the micro gravity level and the direction of the residual acceleration) resulting in diffusion controlled component segregation has been predicted.The results of the two micro gravity grown crystals, especially the axial and radial segregation profiles as a sensitive indicator for the flow configuration in front of the phase boundary will be given and discussed in the paper. They will be compared with the results of numerical simulations of the melt flow for the real processing parameters measured during the TITUS growth processes and with experimental as well as numerical results for vertical normal gravity grown reference Samples.     

Gravitational Convection of a Liquid Mixture in a Horizontal Cylindrical Gap at Moderate Grashof Numbers

Weak concentration convection which arises in the process of diffusion of impurities into the solvent filling a gap between two coaxial cylinders is studied experimentally. It is found that convective motion in the range of Grashof numbers 10³–5 × 10⁴ has a clear boundary-layer character. Near the inner porous cylinder, which is a source of impurity, a diffusion boundary layer passing into a two-dimensional convective plume is formed. The data on the structure and thickness of this layer are presented depending on the integral flux of impurity. The prospects of making an experiment in order to discover concentration convection onboard an orbital station are discussed.     

Directional Solidification Using a Baffle in Microgravity

Numerical simulations were performed to optimize the conditions and parameters for directional solidification of Te-doped GaSb in reduced gravity ranging from 10⁻³ to 10⁻⁵g₀. Our key goal was to quantify the velocity and concentration fields with and without a baffle present in the melt. The effect of the distance of the baffle from the solid–liquid interface was investigated. When the baffle is placed 0.5 cm from the solid–liquid interface, acceleration of 10⁻³g₀ does not cause significant interference with segregation. Furthermore, the flow between the baffle and the interface (low Reynolds number “creeping” flow) does not depend on fluid properties (viscosity).     

Implementation of a semianalytic satellite theory with recovery of short period terms

First order averaging is applied to the artificial satellite problem to obtain the averaged orbit which includes the secular, long and medium period effects of the oblateness of the Earth and the third body perturbations of the moon and sun. Perturbation theory is then used to recover the short period effects due to J₂, the moon, and sun. The perturbation analysis is carried out by means of Lie series and is developed through the first order. Optimization of the resulting short period series was then accomplished in several steps: first all separate algebraic coefficients were precalculated and stored; then all redundant SIN/COS calls were eliminated; next all repetition of numeric and algebraic coefficients were precalculated in pairs; application of the distributive principle allowed a significant reduction in additions and multiplications; finally trigonometric identities were used to further reduce the SIN/COS computations. The result of this optimization along with an interpolator for the averaged equations of motion results in a computer program which requires only $\text{1}\text{6}$ the CPU time (with no loss in accuracy) of the original non-optimized test program.     

Results of the early orbit manoeuvres of the ampte-uks

The Active Magnetospheric Particle Tracer Explorers (AMPTE) program consists of three satellites which were launched on 16th August 1984. The scientific aim of the mission is to inject lithium and barium tracer ions inside and outside the Earth's magnetosphere and to detect and monitor these ions as they diffuse through the inner magnetosphere. The first of these three satellites, the U.S. Charge Composition Explorer (CCE) was launched into an elliptical orbit of apogee 8 R_e. The other two satellites are the West German Ion Release Module (IRM) and the U.K. Subsatellite (UKS), both of which were launched on the same vehicle into a highly elliptical orbit of apogee 18 R_e. At discreet intervals during the mission the IRM will release ions into the solar wind, and the movement of these ions will be monitored by the UKS. Depending on the particular scientific requirement, the UKS has to be positioned accurately at a given distance behind the IRM. Initially the UKS has to be located 100 km behind the IRM, and held there for ～9 months. It will then be moved a distance of ～1 R_e behind the IRM. In order to manoeuvre the UKS around its orbit, a cold gas jet system is incorporated on the satellite, allowing impulses to be applied both along and perpendicular to the orbit velocity vector. The orbit control system also has to cater for relative orbit changes due to air drag at perigee, as the IRM and the UKS have different $\text{area}\text{mass}$ ratios. This paper presents an account of the orbit control system implemented on the UKS, together with the mathematical approach adopted, and results from manoeuvres made in the first weeks of the mission.     

Influence of simulated high-G on the weld size of aL–lI alloy

Whether welding processes are used on earth or in space, they have the same objective: to obtain defect-free welds. To fully understand the effect of gravity on the weld pool geometry and solidification one should perform experiments within a broad range of gravitational acceleration. High-gravity arc welding experiments were done on Al–Li alloy using the centrifuge called Multi-Gravity Research Welding System (MGRWS). At a high “g” level, buoyancy-driven flow is the dominant force in the weld pool over the Marangoni and the electromagnetic forces. Preliminary results show that the average grain size in the fusion zone at 1g is smaller that at 5g.     

Collisions of stars by oscillating orbits of the second kind

Ordinary estimations of the number of star collisions in our galaxy—by simple kinematic considerations—lead to a very small number of such collisions: about one or even less every millions of years. However star collisions can occur through the following indirect way which has a much higher probability. (a) Binary stars are very common in our galaxy, about 30–50% of the stars. (b) If two binary stars meet a triple system can be formed by an ordinary exchange type motion. (c) A triple system is generally decomposed into the “inner orbit” (i.e. the relative orbit of the two nearest stars) and the “outer orbit” (i.e. the relative orbit of the third star with respect to the center of mass of the two nearest stars). The major axes of these two orbits have generally small perturbations and it is the same for the eccentricity of the outer orbit. On the contrary, if the relative inclination of the two orbits is large, the perturbations of the eccentricity of the inner orbit are important and can even in some cases lead to an eccentricity equal to one, that is to a collision of the two stars of the inner orbit.Such orbits can be called “oscillating orbits of the second kind”, indeed the first oscillating orbits—conceived by Khilmi and described for the first time in an example by Sitnikov—have unbounded mutual distances r_ij, but the system always come back to small sizes, it has an infinite number of very large expansions followed by strong contractions and, in the three-body case, an upper bound of lim inf (r_1.2 + r_1.3 + r_2.3) can be given in terms of the three masses and the integrals of motion. For the oscillating orbits of the second kind the mutual distances r_ij are bounded, but the velocities are unbounded (i.e. lim inf r_ij = 0 for at least one r_ij) and the system goes to a collision if the bodies have non-zero radius even small. The analytical study of the oscillating orbits of the second kind is a part of the general analytical study of the three-body problem, a part which must be valid for large eccentricities and large inclinations. The use of Delaunay's variables and of a Von Zeipel transformation lead to a first order integrable approximation, valid for any eccentricities and any inclinations, and giving the following results: (a) The oscillating orbits of the second kind occur when the angular momentum of the outer orbit has a modulus sufficiently close to the modulus of the total angular momentum of the three-body system. Hence these orbits occur for inclinations in the vicinity of 90°. (b) The oscillating orbits represent a set of positive measure of phase space and the first order study allows to give a rough estimation of the probability of collisions—even for stars of infinitely small radius. This probability, for given initial major axes and eccentricities and for isotropic arbitrary initial orientations, is generally of the order of m₃$\text{R}\text{M}$ (m₃ being the mass of the outer star, M the total mass and R the ratio of the period of the inner orbit to that of outer orbit).One question remains to be solved: how many collisions of stars are due to that phenomenon? That question is difficult because the probability of formation of a triple system by a random meeting of two binaries is very uneasy to estimate. However it seems that, compared to the usual evaluations based on pure kinematic considerations without gravitational effects, the number of collisions must be multiplied by a factor between one thousand and one million.     

不同压力条件下水平平板的表面换热实验研究

为了解不同压力下水平平板的气体对流换热变化情况,搭建了一个提供不同气压和环境温度的实验舱,开展了在不同压力(0.1 Pa、0.1 k Pa、0.2 k Pa、0.5 k Pa、1 k Pa、10 k Pa、50 k Pa和常压)与几种加热量(75、150、300 W/m~2)组合条件下的水平平板换热实验研究。通过对辐射换热和自然对流换热的比较,得到不同压力下气体的对流换热系数。结果表明:对流换热系数在环境气体压力小于1 k Pa时非常小,而在1 k Pa以上时才较大;在大于1 k Pa时,对流换热系数随压力的升高呈二次方增加。