Effect of external power supply to a shock layer on the shock wave structure

A physical model that describes the structure of a 1D shock wave in a gas containing a moving heat source is put forward. A stationary equation for the profile of a shock wave in a gas with an arbitrary-shape heat source that is at rest relative to this wave is derived. Analytical solutions to this equation make it possible to analyze the flow pattern in the case of external power supply.     

On wave radiation induced by a fast shock wave in an oblique magnetic field

The corrugation stability of the flat surface of a fast magnetohydrodynamic shock wave in a perfect monoatomic gas with a constant heat capacity is studied with numerical techniques. The magnetic field makes an arbitrary angle with the plane of discontinuity. It is shown that the shock wave remains stable only if it is strictly perpendicular to the magnetic field. At any other angle between the fast shock wave and magnetic field, the former may spontaneously radiate outwardly propagating magnetohydrodynamic waves under certain conditions. Incoming flow characteristics at which these waves are induced are determined.     

Impact of the external energy supply to the shock layer region on the shock wave parameters

A system of equations describing supersonic gas flow in the presence of a heat source near the shock front is obtained. Relations between the gas parameters in disturbed and undisturbed regions, which generalize the classical Hugoniot-Rankine relations, are derived. Formulas for calculation of the flow parameters in the presence of an energy supply to the shock layer region are presented. It is demonstrated that there exists a critical intensity of energy supply at which the system of equations of the conservation laws for the gas parameters on both sides of the shock layer possesses no stationary solution.     

Penetration of an ordinary wave into a weakly inhomogeneous magnetoplasma at oblique incidence

A theory is given describing the propagation of high-frequency electromagnetic waves in a plane-stratified weakly inhomogeneous plasma. The density gradient is supposed to be perpendicular to the external magnetic field and the wave vector is expected not to be generally parallel to the plane given by both the preceding vectors. The analysis points out that the ordinary wave can penetrate through the plasma resonance region if the direction of vacuum wave vector is chosen appropriately. Analytical expressions for the reflecion and transmission coefficients are obtained and their dependence on the direction cosines of the wave vector of the incident is studied. The paper further shows in outline that, after transmission through the plasma resonance, the ordinary wave is transformed into an extraordinary wave and the latter is reflected back to the region of the hybrid resonance. In this region the extraordinary wave is fully transformed into the Bernstein modes.     

Effect of heat transfer on the penetration of an electromagnetic pulse into a plasma layer and the inverse skin effect

Penetration of a heating pulse into a plasma layer was studied using the system of coupled nonlinear equations for electric field, electron, and ion temperatures. Numerical calculations of field structure and temperature evolution are performed both in the absence and in the presence of heat transfer. It is established that heat transfer leads to a more rapid penetration of the field near the illuminated surface of the layer and impairs penetration in regions of the layer far from this surface. We found that heat transfer promotes the creation of more favourable conditions for manifestation of the inverse skin effect.     

Design of guided-mode resonance filters with an antireflective surface at oblique incidence

A design approach of guided-mode resonance filter (GMRF) with an antireflective surface at oblique incidence is presented. For a given incident angle or grating filling factor, the required grating filling factor or incident angle can be expressed by the analytical forms of the quadratic equations at quarter-wavelength thickness. Long-range, low sidebands are obtainable for a single-layer GMRF under the TM mode wave illumination at oblique incidence. The reflection properties such as the symmetry of the lineshape and the sideband level in the logarithm scale can be further improved by slightly varying both the grating period and the grating thickness. Magnetic field enhancement occurs in these structures due to the coupling between the evanescent diffracted order and the waveguide mode.     

Effect of the structurally damaged surface layer of an isotropic solid on Rayleigh wave dispersion and damping

The effect of the structurally damaged isotropic surface layer on the free surface of an isotropic solid on the Rayleigh wave propagation has been considered. The phase velocity dispersion and inverse Rayleigh wave decay length in the second order of vanishing with respect to the ratio of the structurally damaged layer thickness to the wavelength have been obtained in an analytical form. For the dispersion and the inverse wave decay length, the long-wave limit has been studied when the wavelength is much larger than the characteristic size of layer inhomogeneity. The inverse decay length has been calculated numerically.     

Boundary layer flow and heat transfer of a Casson fluid past a symmetric porous wedge with surface heat flux

The aim of this paper is to investigate numerically the boundary layer forced convection flow of a Casson fluid past a symmetric porous wedge. Similarity transformations are used to convert the governing partial differential equations into ordinary ones. With the help of the shooting method, the reduced equations are then solved numerically. Comparisons are made with the previously published results in some special cases and they are found to be in excellent agreement with each other. The results obtained in this study are illustrated graphically and discussed in detail. The velocity is found to increase with an increasing Falkner-Skan exponent whereas the temperature decreases. With the rise of the Casson fluid parameter, the fluid velocity increases but the temperature is found to decrease in this case. Fluid velocity is suppressed with the increase of suction. The skin friction decreases with the increasing value of Casson fluid parameter. It is found that the temperature decreases as the Prandtl number increases and thermal boundary layer thickness decreases with the increasing value of Prandtl number. A significant finding of this investigation is that flow separation can be controlled by increasing the value of the Casson fluid parameter as well as by increasing the amount of suction.     

Unstable combustion induced by oblique shock waves at the non-attaching condition of the oblique detonation wave

The instability of oblique shock wave (OSW) induced combustion is examined for a wedge with a flow turning angle greater than the maximum attach angle of the oblique detonation wave (ODW), where archival results rarely exist for this case in previous literatures. Numerical simulations were carried out for wedges of different length scales to account for the ratio of the chemical and fluid dynamic time scales. The results reveal three different regimes of combustion. (1) No ignition or decoupled combustion was observed if a fluid dynamic time is shorter than a chemical time behind an OSW. (2) Oscillatory combustion was observed behind an OSW if a fluid dynamic time is longer than a chemical time behind an OSW and the fluid dynamic time is shorter than the chemical time behind a normal shock wave (NSW) at the same Mach number. (3) Detached bow shock-induced combustion (or detached overdriven detonation wave) was observed if a fluid dynamic time is longer than a chemical time behind a NSW. Since no ignition or decoupled combustion occurs as a very slow reaction and the detached wave occurs as an infinitely fast reaction, the finite rate chemistry is considered to be the key for the oscillating combustion induced by an OSW over a wedge of a finite length with a flow turning angle greater than the maximum attach angle for an ODW. Since this case has not been previously reported, grid independency was tested intensively to account for the interaction between the shock and reaction waves and to determine the critical time scale where the oscillating combustion can be observed.     

层状介质时域有限差分方法斜入射平面波引入新方式

应用二维时域有限差分方法分析层状介质中的目标散射时,在总场-散射场边界斜入射平面波源用常规方法难以引入,因为在总场-散射场边界处设置的入射波实际上包含了入射脉冲以及各分层界面的反射和多次反射.为解决这个问题,提出了斜入射平面波的混合引入方式,即对总场-散射场的四个边界面采取不同的处理方式.对于总场-散射场的纵向侧边界,用含有斜入射角度的修正一维时域有限差分方法,只要在自由空间位置加入入射脉冲就会自行产生由各分层界面形成的反射波,包括多次反射.同时,把纵向总场-散射场侧边界向下延伸,使得总场-散射场下边界位于完全匹配层内,这样透射波和散射波均为外向行波而被吸收.对于总场-散射场的上边界,由于完全位于自由空间中,边界上各点的入射波将是总场-散射场纵向边界角点处入射波的带有时间延迟的复制.数值模拟结果表明了本文所提出方法的正确性和有效性. 关键词： 时域有限差分 层状介质 斜入射平面波 修正一维麦克斯韦方程     

Effect of temperature-dependent surface heat transfer coefficient on the maximum surface stress in ceramics during quenching

We study the difference in the maximum stress on a cylinder surface σ_max using the measured surface heat transfer coefficient h_m instead of its average value h_a during quenching. In the quenching temperatures of 200, 300, 400, 500, 600 and 800°C, the maximum surface stress σ_mmax calculated by h_m is always smaller than σ_amax calculated by h_a, except in the case of 800°C; while the time to reach σ_max calculated by h_m (f_mmax) is always earlier than that by h_a (f_amax). It is inconsistent with the traditional view that σ_max increases with increasing Biot number and the time to reach σ_max decreases with increasing Biot number. Other temperature-dependent properties also have a small effect on the trend of their mutual ratios with quenching temperatures. Such a difference between the two maximum surface stresses is caused by the dramatic variation of h_m with temperature, which needs to be considered in engineering analysis.     

Effect of porous surface layer on wave propagation in elastic cylinder immersed in fluid

To study the damage to an elastic cylinder immersed in fluid, a model of an elastic cylinder wrapped with a porous medium immersed in fluid is designed. This structure can both identify the properties of guided waves in a more practical model and address the relationship between the cylinder damage degree and the surface and surrounding medium. The principal motivation is to perform a detailed quantitative analysis of the longitudinal mode and flexural mode in an elastic cylinder wrapped with a porous medium immersed in fluid. The frequency equations for the propagation of waves are derived each for a pervious surface and an impervious surface by employing Biot theory. The influences of the various parameters of the porous medium wrapping layer on the phase velocity and attenuation are discussed. The results show that the influences of porosity on the dispersion curves of guided waves are much more significant than those of thickness, whereas the phase velocity is independent of the static permeability. There is an apparent "mode switching" between the two low-order modes. The characteristics of attenuation are in good agreement with the results from the dispersion curves. This work can support future studies for optimizing the theory on detecting the damage to cylinder or pipeline.     

Effect of boundary layer thickness before the flow separation on aerodynamic characteristics and heat transfer behind an abrupt expansion in a round tube

Results of numerical investigation of the boundary layer thickness on turbulent separation and heat transfer in a tube with an abrupt expansion are shown. The Menter turbulence model of shear stress transfer implemented in Fluent package was used for calculations. The range of Reynolds numbers was from 5·10³ to 105. The air was used as the working fluid. A degree of tube expansion was (D ₂/D ₁)² = 1.78. A significant effect of thickness of the separated boundary layer both on dynamic and thermal characteristics of the flow is shown. In particular, it was found that with an increase in the boundary layer thickness the recirculation zone increases, and the maximum heat transfer coefficient decreases. The work was financially supported by the Russian Foundation for Basic Research (project codes 07-08-00025 and 06-08-00300).     

Perturbation evolution at a metal-metal interface subjected to an oblique shock wave: Supersonic velocity of the point of contact

The perturbation evolution at the interface between identical metals (metal plates) that is exposed to high-speed oblique shock waves is observed experimentally for the first time (the waves are attached to the point of contact, so that a cumulative jet cannot form). The experiments are numerically simulated by the two-dimensional Lagrange method. An elastoplastic model where the dynamic yield strength is a function of material state parameters is employed. An analytical technique to treat instability development under given loading conditions is suggested. High strains produce a high-temperature zone near the interface (thermal softening zone). A short-lived shear flow with a high velocity gradient depending on the angle and velocity of plate collision is observed. In this zone, the shear modulus and the yield strength are appreciably lower than under normal conditions, which favors instability development.     

Investigation of the third heat transfer crisis on a vertical surface

The process of development of the third heat transfer crisis for vertical orientation of the heating surface was studied experimentally. Experiments were carried out with acetone under the conditions of saturation for the pressures in the working volume from 20 to 28 kPa. In all experiments, the third heat transfer crisis was preceded by propagation of evaporation front along the heating surface. The threshold values of heat flux densities, above which a stable vapor film is formed on the whole heating surface, are lower for vertical orientation of this heating surface than for the horizontal one. Data on the threshold heat flux densities and overheating before boiling-up were obtained. Above these values, formation of evaporation fronts was observed. The range of operation parameters corresponding to formation of the sites of unstable film boiling on the heating surface after boiling-up was determined.