Distribution of radiant thermal flux over the surface of a sphere for hypersonic flow of a nonviscous radiating gas past the sphere

In the present study using the Newtonian approximation [1] we obtain an analytical solution to the problem of flow of a steady, uniform, hypersonic, nonviscous, radiating gas past a sphere. The three-dimensional radiative-loss approximation is used. A distribution is found for the gasdynamic parameters in the shock layer, the withdrawal of the shock wave and the radiant thermal flux to the surface of the sphere. The Newtonian approximation was used earlier in [2, 3] to analyze a gas flow with radiation near the critical line. In [2] the radiation field was considered in the differential approximation, with the optical absorption coefficient being assumed constant. In [3] the integrodifferential energy equation with account of radiation was solved numerically for a gray gas. In [4–7] the problem of the flow of a nonviscous, nonheat-conducting gas behind a shock wave with account of radiation was solved numerically. To calculate the radiation field in [4, 7] the three-dimensional radiative-loss approximation was used; in [5, 6] the self-absorption of the gas was taken into account. A comparison of the equations obtained in the present study for radiant flow from radiating air to a sphere with the numerical calculations [4–7] shows them to have satisfactory accuracy.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 44–49, November–December, 1972.In conclusion the author thanks G. A. Tirskii and É. A. Gershbein for discussion and valuable remarks.     

Some problems in the theory of plane jets of conducting fluid

Using the boundary-layer equations as a basis, the author considers the propagation of plane jets of conducting fluid in a transverse magnetic field (noninductive approximation).The propagation of plane jets of conducting fluid is considered in several studies [1–12]. In the first few studies jet flow in a nonuniform magnetic field is considered; here the field strength distribution along the jet axis was chosen in order to obtain self-similar solutions. The solution to such a problem given a constant conductivity of the medium is given in [1–3] for a free jet and in [4] for a semibounded jet; reference [5] contains a solution to the problem of a free jet allowing for the dependence of conductivity on temperature. References [6–8] attempt an exact solution to the problem of jet propagation in any magnetic field. An approximate solution to problems of this type can be obtained by using the integral method. References [9–10] contain the solution obtained by this method for a free jet propagating in a uniform magnetic field.The last study [10] also gives a comparison of the exact solution obtained in [3] with the solution obtained by the integral method using as an example the propagation of a jet in a nonuniform magnetic field. It is shown that for scale values of the jet velocity and thickness the integral method yields almost-exact values. In this study [10], the propagation of a free jet is considered allowing for conduction anisotropy. The solution to the problem of a free jet within the asymptotic boundary layer is obtained in [1] by applying the expansion method to the small magnetic-interaction parameter. With this method, the problem of a turbulent jet is considered in terms of the Prandtl scheme. The Boussinesq formula for the turbulent-viscosity coefficient is used in [12].This study considers the dynamic and thermal problems involved with a laminar free and semibounded jet within the asymptotic boundary layer, propagating in a magnetic field with any distribution. A system of ordinary differential equations and the integral condition are obtained from the initial partial differential equations. The solution of the derived equations is illustrated by the example of jet propagation in a uniform magnetic field. A similar solution is obtained for a turbulent free jet with the turbulent-exchange coefficient defined by the Prandtl scheme.     

Effect of surrounding gas on velocity distribution function of molecules in molecular beam

Molecular-beam methods have become widely used in recent times for the study of flows of rarefied gases [1]. However, the very first experiments with molecular beams for agasdynamic source [2] showed that the measured intensities fell below theoretical predictions. Most devices for the creation of a molecular beam by means of a gasdynamic source have pumping equipment of comparatively low capacity and beam formation in them occurs with residual gas present. It was shown [3] that the residual gas penetrates into the jet and significantly reduces the intensity of the molecular beam. This and subsequent work [4, 5] were confined to measurements of intensity (density) and there are no data in the literature on the effect of residual gas on other parameters of the distribution function. The present work was devoted to a study of the effect of residual gas on the distribution function in a molecular beam defined from a jet in the scattering mode [6]. The work was performed on the small molecular-beam generator [7] and on the VS-4 low-density gasdynamic tube [8] at the Institute of Thermal Physics, Siberian Branch, Academy of Sciences of the USSR. Measurements of the distribution function by the time-of-flight method [9] were performed on the small molecular-beam generator and measurements of gas density on the VS-4.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fizito, No. 4, pp. 11–19, July–August, 1976.The authors are grateful to A. K. Rebrov for valuable discussions.     

Asymptotic analysis of transonic flows

In this paper we derive the equations of the second and third approximations for the stream function of two-dimensional and axisymmetric potential transonic flow of an inviscid gas and find their particular solutions corresponding to certain transonic flows.A similar study concerning the second approximation of subsonic and supersonic flow was made by Van Dyke [1] and Hayes [2]. The second approximation for the velocity potential of transonic flow has been examined in detail by Hayes [3]. Euvrard [4, 5] has investigated the asymptotic behavior of transonic flow far from a body, while Fal'kovich, Chernov, and Gorskii [6] have studied the flow in a nozzle throat.The transonic asymptotic analysis for the stream function is presented in this paper.     

轴向拉伸下氮化钛纳米杆变形机制及力学性能的分子动力学研究

本文使用分子动力学软件包lammps并采用第二近邻改进型嵌入原子法(2NN MEAM)模拟了单晶氮化钛纳米杆的轴向拉伸破坏过程,分析了分别沿[100]、[111]晶向的不同截面尺寸、不同拉伸应变率、不同温度下的氮化钛纳米杆的力学性能,详细描述了氮化钛纳米杆拉伸变形过程。研究发现, 拉伸晶向、截面尺寸、拉伸应变率及温度均会对TiN纳米杆的拉伸变形过程及屈服强度、弹性模量等力学性能产生不同程度的影响。 沿[100]晶向的拉伸,截面尺寸越大,屈服强度越低;而沿[111]晶向,截面尺寸越大,屈服强度越大。应变率越大,屈服强度及屈服应变越大,但对于弹性模量几乎无影响。温度越高,材料的屈服强度、屈服应变及弹性模量越小,断裂应变越大。不同拉伸条件下的氮化钛纳米杆的拉伸过程均包括弹性变形、塑性变形与断裂阶段。[100]晶向的弹性模量都要高于[111]晶向。     

Nonisothermal Couette flow of a non-Newtonian fluid under the action of a pressure gradient

Nonisothermal Couette flow has been studied in a number of papers [1–11] for various laws of the temperature dependence of viscosity. In [1] the viscosity of the medium was assumed constant; in [2–5] a hyperbolic law of variation of viscosity with temperature was used; in [6–8] the Reynolds relation was assumed; in [9] the investigation was performed for an arbitrary temperature dependence of viscosity. Flows of media with an exponential temperature dependence of viscosity are characterized by large temperature gradients in the flow. This permits the treatment of the temperature variation in the flow of the fluid as a hydrodynamic thermal explosion [8, 10, 11]. The conditions of the formulation of the problem of the articles mentioned were limited by the possibility of obtaining an analytic solution. In the present article we consider nonisothermal Couette flows of a non-Newtonian fluid under the action of a pressure gradient along the plates. The equations for this case do not have an analytic solution. Methods developed in [12–14] for the qualitative study of differential equations in three-dimensional phase spaces were used in the analysis. The calculations were performed by computer.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 26–30, May–June, 1981.     

CoCrFeMnNi高熵合金冲击波响应与层裂强度的分子动力学研究

高熵合金未来有望应用于航空航天和深海探测等领域, 并且不可避免地会受到极端冲击载荷作用, 甚至会发生层裂. 本文采用分子动力学(MD)方法, 研究了CoCrFeMnNi单晶高熵合金冲击时的冲击波响应、层裂强度以及微观结构演化的取向相关性和冲击速度相关性. 模拟结果表明, 在沿[110]和[111]方向进行冲击时产生了弹塑性双波分离现象, 且随着冲击速度的增加呈现出先增强后减弱的变化趋势, 但在沿[100]方向冲击时未出现双波分离现象. 在冲击过程中, 大量无序结构产生且随冲击速度的增加而增加, 使得层裂强度随冲击速度的增加而减小. 此外, 层裂强度也具有取向相关性. 沿[100]方向冲击时产生了大量体心立方(BCC)中间相, 抑制了层错以及无序结构的产生, 使得[100]方向的层裂强度最高; 层裂初期微孔洞形核区域无序结构含量大小关系的转变, 使得[111]方向的层裂强度在冲击速度较低时(U_p≤0.9 km/s)大于[110]方向, 而在冲击速度较大时(U_p≥1.2 km/s)略小于[111]方向. 研究成果有望为 CoCrFeMnNi高熵合金在极端冲击条件下的应用提供理论支撑和数据积累.      

一类三维慢变振荡器周期解的奇摄动解

本文给出一类三维慢变振荡器周期解的求解方法,实例计算结果与文献[1]一致,利用本文的方法可研究文献[1]不能研究的问题。     

Equations of hydromechanics and compression shock in two-velocity and two-temperature continuum with phase transformations

The equations of motion of multiphase mixtures have been considered in [1–10] and several other studies. In [1] it is proposed that the mixture motion be considered as an interpenetrating motion of several continua when velocity, pressure, mean density, concentration, etc., fields for each phase are introduced in the flowfield. The equations of motion are written separately for each phase, and the force effect of the other components is considered by introducing the interaction forces, which for the entire system are internal. The assumption of component barotropy is used to close the system.The energy equations are used in [2, 3] in place of the component barotropy assumption. Moreover, mixtures without phase transformations are considered. In [4] an analysis is made of the equations of turbulent motion with account for viscous forces for a two-velocity, but single-temperature medium in which equilibrium phase transformations are assumed, i. e., a two-phase medium is considered in which the phase temperatures are the same, the composition is equilibrium, but the phase velocities are different. In [5] the equations are written on the interface in a multicomponent medium consisting of barotropic fluids. A discontinuity classification is also presented here. In the aforementioned work [3] the equations on the shock are written for a continuum with particles without the use of the property of barotropy of the carrier fluid. Various different aspects of the motion of multiphase mixtures are considered in [6–11], for example, the effect of particle collisions with one another, the effect of the volume occupied by the particles on the parameters stream, shock waves, etc. In [7] a study is made of the force effect of an agitated medium on a particle on the basis of the Basset-Boussinesq-Oseen equation.In the following we derive the equations of motion of a two-velocity and two-temperature continuum with drops or particles with nonequilibrium phase transformations, i. e., a medium in which the phase velocities and temperatures are different and the composition may be nonequilibrium. In addition, we study the effect of the presence of particles or drops on the gas parameters behind a shock. Further, the equations obtained here are used to study compression waves, and in particular shock waves.The author wishes to thank Kh. A. Rakhmatulin, S. S. Grigoryan, and Yu. A. Buevich for helpful discussions and valuable comments.     

Asymptotic solution of the euler equations in the shock layer on a blunt body in nonuniform flow with gas injection from the body surface

Supersonic nonuniform gas flow over blunt bodies without surface injection has previously been investigated by both numerical [1–3] and experimental [3] methods. The processes of surface vaporization under the influence of an intense heat flux, artificial gas injection and surface combustion [4] are all worthy of study. The problem of the interaction between a nonuniform supersonic flow and a body in the presence of intense gas injection from the surface is examined and an analytical solution is constructed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 126–134, November–December, 1989.     

Sound absorption near the boundary dividing two liquids

It is well known that sound absorption in finite media is caused mainly by fluid viscosity and thermal conductivity. Kirchhoff [1] developed a general theory describing the mechanism of such absorption and applied it to the particular case of sound propagating in tubes. Rayleigh [2] used Kirchhoff's theory to study sound absorption by a porous wall with normal incidence of the sound wave. Konstantinov [3] also used Kirchhoff's theory to solve the problem of sound absorption by a rigid, isothermal (with infinite thermal conductivity) and a thermally insulating plane wall with arbitrary angle of sound-wave incidence. A natural extension of these efforts is a study of sound absorption on the boundary dividing two liquids. Aside from its scientific interest, such a problem is of practical significance, for example, in hydroacoustics or in creating methods for visualization of sound in gases and liquids [4]. The present study will attempt to solve this problem. The results can be applied to both liquid and solid (resinlike) materials.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 6–9, January–February, 1984.The author thanks T. P. Zhizhina for much assistance in the study.     

Shock wave structure in a binary mixture of viscous gases

Shock wave structure was studied in [1] using Struminskii's model [2] with the assumption that viscosity and thermal conductivity exist only as interactions between components. The present study will obtain asymptotic solutions of the problem of shock wave structure in the Navier-Stokes approximation.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 48–54, September–October, 1984.     

Comment on “Precise Control for vibration of rigid-flexible mechanical arm”

The results presented in a paper by Zichen et al. [1] has some flaws. The idea in [1] is to combine assumed modes method using an integration method with optimal control adaptive law for a spatial rigid-flexible mechanical arm as an underactuated mechanical systems (UMS). The nonlinear dynamic equation formulation from reference [6] is incorrectly used in [1]. Furthermore, the control law approach in [1] was to achieve a similar result for a UMS rigid manipulator as the one published by Spong [2] and a proper citation must have been credited.     

Plane incompressible fluid flow past an array of arbitrary profiles vibrating with arbitrary phase shift

We consider the problem of the vibration of an array of arbitrary profiles with arbitrary phase shift. Account is taken of the influence of the vortex wakes. The vibration amplitude is assumed to be small. The problem reduces to a system of two integral Fredholm equations of the second kind, which are solved on a digital computer. An example calculation is made for an array of arbitrary form.A large number of studies have considered unsteady flow past an array of profiles. Most authors either solve the problem for thin and slightly curved profiles or they consider the flow past arrays of thin curvilinear profiles [1].In [2] a study is made of the flow past an array of profiles of arbitrary form oscillating with arbitrary phase shift in the quasi-stationary formulation. The results are reduced to numerical values. Other approaches to the solution of the problem of unsteady flow past an array of profiles of finite thickness are presented in [3–5] (the absence of numerical calculations in [3, 4] makes it impossible to evaluate the effectiveness of these methods, while in [5] the calculation is made for a symmetric profile in the quasi-stationary formulation).     

On the Riemann-Hilbert's boundary value problem, for flow through porous inhomogeneous media

The present paper is an extension of other results concerning Emile Picard's Great Theorem [2], [3] used for the study of plane, stationary flow with free and seepage surfaces in porous inhomogeneous media of second type.     

胆碱杂环二酸离子液体水润滑添加剂的制备及结构-性能关系研究

以胆碱和杂环二酸为原料,在去离子水中原位制备了添加剂[Ch]₂[Hdc],并研究了它们的摩擦学性能、腐蚀性、水生生物毒性与分子结构之间的构效关系. 研究发现,水溶液的运动黏度随着水中生成的[Ch]₂[Hdc]浓度的增加而增大,并且当[Ch]₂[Hdc]的分子结构对称性较低、极性较大时,水的黏度增加值相对较大. 这是由于添加剂分子极性较大时,分子间相互作用力较大,导致溶液的黏度增幅更大. 摩擦学性能测试发现,当[Ch]₂[Hdc]的浓度相对较低时,水溶液的减摩抗磨性能与[Ch]₂[Hdc]分子在摩擦副表面的吸附能力有关,分子极性较大,吸附能力较强的[Ch]₂[Hdc]可在摩擦副表面形成更为牢固的润滑保护膜,因而能有效改善水的减摩抗磨性能,反之则不能. 当[Ch]₂[Hdc]的浓度相对较高时,水溶液的减摩性能与其黏度呈反相关关系,抗磨性能则与其黏度呈正相关关系. 这是由于润滑剂黏度相对较大时,其内摩擦力较大,因而表现出较高的摩擦系数,即较差的减摩性能;然而,黏度相对较大的润滑剂则可以在摩擦副表面形成更为牢固的润滑保护膜,因而表现出较低的磨损体积,即较好的抗磨性能. 腐蚀试验结果表明,[Ch]₂[Hdc]可显著降低水对金属基底材料的腐蚀性. 毒性试验显示[Ch]₂[Hdc]对绿藻和海虾毒性远远小于传统离子液体L-B104.      

Boundary layer on a rotating disk with account for the Hall effect

The steady rotation of a disk of infinite radius in a conducting incompressible fluid in the presence of an axial magnetic field leads to the formation on the disk of a three-dimensional axisymmetric boundary layer in which all quantities, in view of the symmetry, depend only on two coordinates. Since the characteristic dimension is missing in this problem, the problem is self-similar and, consequently, reduces to the solution of ordinary differential equations.Several studies have been made of the steady rotation of a disk in an isotropically conductive fluid. In [1] a study was made of the asymptotic behavior of the solution at a large distance from the disk. In [2] the problem is linearized under the assumption of small Alfven numbers, and the solution is constructed with the aid of the method of integral relations. In the case of small magnetic Reynolds numbers the problem has been solved by numerical methods [3,4]. In [5] the method of integral relations was used to study translational flow past a disk. The rotation of a weakly conductive fluid above a fixed base was studied in [6,7], The effect of conductivity anisotropy on a flow of a similar sort was studied approximately in [8], In the following we present a numerical solution of the boundary-layer problem on a disk with account for the Hall effect.     

Flow stability of viscous liquid layer with moment stresses on an inclined plane

The flow stability of a liquid layer on an inclined plane with account for molecular spin [1, 2] has been considered in [3] in the absence of moment stresses within the liquid. It was shown in [3] that molecular spin has a destabilizing effect on the flow. In the following we study the combined effect of molecular spin and internal moment stresses on the behavior of three-dimensional disturbances. The validity of Squire's theorem is established. The flow stability of a layer of relatively long-wave disturbances is studied by the method of sequential approximations [4, 5] under the assumption that the rotational viscosity coefficient _r is significantly smaller than the Newtonian viscosity coefficient .     

Passage of a supersonic flow over intersecting surfaces

Using the linear formulation, the problem of passage of a supersonic flow over slightly curved intersecting surfaces whose tangent planes form small dihedral angles with the incident flow velocity at every point is considered. Conditions on the surfaces are referred to planes parallel to the incident flow forming angles 0≤γ≤2π at their intersection [1]. The problem reduces to finding the solution of the wave equation for the velocity potential with boundary conditions set on the surfaces flowed over and the leading characteristic surface. The Volterra method is used to find the solution [2]. This method has been applied to the problem of flow over a nonplanar wing [3] and flow around intersecting nonplanar wings forming an angle γ=π/n (n=1, 2, 3, ...) with consideration of the end effect on the wings forming the angle [4]. In [5] the end effect was considered for nonplanar wings with dihedral angle γ=m/nπ. In the general case of an arbitrary angle 0≤γ≤2π the problem of finding the velocity potential reduces to solution of Volterra type integrodifferential equations whose integrands contain singularities [1]. It was shown in [6] that the integrodifferential equations may be solved by the method of successive approximation, and approximate solutions were found differing slightly from the exact solution over the entire range of interaction with the surface and coinciding with the exact solution on the characteristic lines (the boundary of the interaction region, the edge of the dihedral angle). The solution of the problem of flow over intersecting plane wings (the conic case) for an arbitrary angle γ was obtained in terms of elementary functions in [7], which also considered the effect of boundary conditions set on a portion of the leading wave diffraction. In [8, 9] the nonstationary problem of wave diffraction at a plane angle π≤γ≤2π was considered. On the basis of the wave equation solution found in [8], this present study will derive a solution which permits solving the problem of supersonic flow over nonplanar wings forming an arbitrary angle π≤γ≤2π in quadratures. The solutions for flow over nonplanar intersecting surfaces for the cases 0≤γ≤π [6] and π≤γ≤2π, found in the present study, permit calculation of gasdynamic parameters near a wing with a prismatic appendage (fuselage or air intake). The study presents a method for construction of solutions in various zones of wing-air intake interaction.