Radiative gasdynamics of the nose surface of the Apollo-4 command module at its superobrital reentry

The problem of the radiative gasdynamics of the Apollo-4 command module superorbital entry in the dense terrestrial atmosphere is numerically solved in the two-dimensional formulation of flow past an aerodynamic nose shield on the entry velocity range V_∞ = 10.7?5.75 km/s and the altitude range H = 91.5?35.0 km. The specific regions of the trajectory with strongly nonequilibrium flow in the shock layer, the most high-heat areas of the trajectory, and the regions with strong radiative-gasdynamic interaction in a relatively dense and strongly rarefied oncoming flow are highlighted. The density distributions of the convective and radiative heat fluxes over the body surface are obtained. The spectral composition of the thermal radiation is studied. The results of the calculations are compared and found to be in good agreement with the experimental flight data.     

Delta Shock Wave Solution of the Riemann Problem for the Non-homogeneous Modified Chaplygin Gasdynamics

The motivation of the present study is to derive the solution of the Riemann problem for modified Chaplygin gas equations in the presence of constant external force. The analysis leads to the fact that in some special circumstances delta shock appears in the solution of the Riemann problem. Also, the Rankine–Hugoniot relations for delta shock wave which are utilized to determine the strength, position and propagation speed of the delta shocks have been derived. Delta shock wave solution to the Riemann problem for the modified Chaplygin gas equation is obtained. It is found that the external force term, appearing in the governing equations, influences the Riemann solution for the modified Chaplygin gas equation.

     

Solution of the Three-Dimensional Thermoelastic Problem in Stresses

A method is proposed for constructing a general solution to the three-dimensional thermoelastic equations in stresses (compatibility conditions and equilibrium equations). This general solution is valid for both an elastic half-space and an elastic layer. The second thermoelastic boundary-value problem for a half-space is studied in detail as an example     

Symmetry Groups and Non-Planar Collisionless Action-Minimizing Solutions of the Three-Body Problem in Three-Dimensional Space

Periodic and quasi-periodic solutions of the n-body problem can be found as minimizers of the Lagrangian action functional restricted to suitable spaces of symmetric paths. The main purpose of this paper is to develop a systematic approach to the equivariant minimization for the three-body problem in three-dimensional space. First we give a finite complete list of symmetry groups fitting to the minimization of the action, with the property that any other symmetry group can be reduced to be isomorphic to one of these representatives. A second step is to prove that the resulting (local and global) symmetric action-minimizers are always collisionless (when they are not already bound to collisions). Furthermore, we prove some results which address the question of whether minimizers are planar or non-planar; as a consequence of our theory we will give general criteria for a symmetry group to yield planar or homographic minimizers (either homographic or not, as in the Chenciner-Montgomery eight solution). On the other hand we will provide a rigorous proof of the existence of some interesting one-parameter families of periodic and quasi-periodic non-planar orbits. These include the choreographic Marchal's P₁₂ family with equal masses – together with a less-symmetric choreographic family (which anyway probably coincides with the P₁₂ family).     

Solving the Three-Dimensional Elastic Problem for a Cylinder of Finite Length Subject to Bending

A new technique is proposed for solving the three-dimensional antisymmetric elastic problem for a thick-walled shell of finite length. The boundary-value problem is reduced to a system of one-dimensional singular integral equations. Characteristic stresses are calculated     

Radiative heat transfer at the leading edge of a body during intense evaporation

The problem of the flow of a radiating gas near the leading part of a body during intense vaporization of its surface is solved. Significant radiative heating occurs when a sufficiently dense gas flows past the body, thus a gasdynamic model of the flow is used according to which the flow takes place in a shock layer and a vapor layer separated by the contact surface. The radiant energy flux from the shock layer is partially absorbed by a vapor layer and falls on the surface of the body, causing intense vaporization.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 190–192, March–April, 1975.     

空投鱼雷倾斜姿态落水冲击研究

利用轴长体假设和Ｔａｙｌｏｒ关于圆柱在不同浸深时的附加质量表达式，运用切片理论建立了空投鱼雷在其纵向平面内以倾斜姿态落水时的运动微分方程组，通过实例计算得到了空投鱼雷入水冲击时作用在其上的弯矩和剪力分布的规律，为理论预测空投鱼雷入水冲击时的强度破坏建立了基础。     

Determining Modes, Nodes and Volume Elements for Stationary Solutions of the Navier-Stokes Problem Past a Three-Dimensional Body

In this paper we show that every solution of the three-dimensional exterior Navier-Stokes boundary-value problem, corresponding to a given non-zero, constant velocity at infinity (flow past a body) and belonging to a very general functional class, , can be determined by a finite number of parameters. Our results extend the analogous classical results by Foiaş & Temam [6, 7], and by Jones & Titi [14] for the interior problem. This extension is by no means trivial, in that all fundamental tools used in the case of the interior problem – such as compactness of the Sobolev embeddings, Poincaré's inequality, and the special basis constituted by eigenfunctions of the Stokes operator – are no longer available for the exterior problem. An important consequence of our results is that any solution in is uniquely determined by the knowledge of the associated velocity field only ``near' the boundary. Just how ``near' it has to be depends only on the Reynolds number and on the body. Dedicated to John Heywood on the occasion of his 65th birthday     

Two-Valued Solutions in the Problem of Salt Precipitation during Groundwater Evaporation

The problem of the evaporation of groundwater containing a dissolved admixture is studied. It is shown that in the salt precipitation regime the solution is nonunique. At critical parameter values the solutions merge and in a certain region the solution of the problem disappears. The nonexistence of a solution corresponds to clogging of the pore space with precipitated salt.     

Radiative and convective heat transfer during blowing into a compressed hypersonic layer of two-phase products from the ablation of a covering

The study examines the screening of the radiative heat flux in conditions of hypersonic flow around blunt bodies with ablated carbon-based coverings. In contrast to the studies already known [1–3], allowance is made for the presence of condensed microscopic particles in the products of ablation. In [4] the problem of radiative transfer is considered in a layer of two-phase ablation products with parametrically prescribed dimensions, particle temperature, and layer thickness. The present study uses a closed system of equations which describes the processes of heat and mass transfer. This gives rise to considerable differences in the numerical results, according to the degree of screening.Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 161–166, November–December 1985.deceased     

Investigation of double-diffusive convection during the solidification of a binary mixture (NH4Cl–H2O) in a trapezoidal cavity

The solidification of binary mixture (NH₄Cl–H₂O) inside a trapezoidal cavity is investigated experimentally in this study. The effect of the initial concentration of ammonium chloride (0–19.8%) and boundary temperatures (−30 to 0°C) on the solidification process was investigated. Particle image velocimetry (PIV) technique was used for the visualization of the dynamic field in the melt. Thirty-two thermocouples were used to monitor the temperature distribution inside the cavity and on the cooling walls. The convective flow field, the temperature distribution, the frozen layer thickness and the moving solid/liquid interface were obtained for different initial concentrations of ammonium chloride and various boundary temperatures. The results obtained in the course of this study reveal that: (1) the process of solidification is slower with an increase in initial concentration levels of the binary solution: as the concentration increases, the time needed to get the same thickness of frozen layer increases; (2) an increase in the initial concentration of ammonium chloride solution reduce significantly the temperature in the melt; and (3) the initial concentration play a significant role in the evolution of convection flow patterns.