一维与二维爆轰传播的时空关联特性数值研究

一维爆轰传播的理论完备、计算准确, 二维斜爆轰传播由于壁面与黏性效应, 大尺度、高精度预测还有一定难度. 利用Euler方程和H₂-Air基元反应模型, 对二维有限长楔面诱导的斜爆轰和活塞驱动一维非定常正爆轰进行计算比较研究, 从时空两个维度方面, 分析了两者在起爆过程、稀疏波传播、爆轰波面演化中的关联特性. 研究结果表明: 在过驱动度相同的条件下, 经过时空变换的活塞驱动一维爆轰传播与二维驻定斜爆轰在起爆区波系结构、波面演化特征和主要参数分布规律方面无论定性或者定量对比均符合较好, 所以, 一维非定常爆轰和二维驻定斜爆轰具有时空相关性. 两者的差异主要体现在过驱动斜爆轰受稀疏波影响过渡到近Chapman-Jouguet (C-J)爆轰状态所需的弛豫时间不同, 原因可能是起源于活塞和壁面稀疏波强度的差异. 本文提出的一维与二维爆轰传播的时空关联方法不仅有助于认知斜爆轰起爆、过驱爆轰产生、胞格爆轰演化的三阶段规律, 还可以对比揭示壁面、边界层和黏性效应的影响, 应用在斜爆轰发动机燃烧室设计中能够有效节约计算时间和成本, 并降低复杂度.      

Thermal analysis of composite superconductors subjected to time-dependent disturbances

A one-dimensional heat conduction equation with time- and temperature-dependent heat sources was employed to study the steady-state and transient response of a composite superconductor subjected to a thermal disturbance. An integral formulation was used to solve the steady-state problem of current redistribution and heat generation. The results of the integral formulation are compared with those of an analytical solution. The two solutions agree with each other except when the analytical solution fails as the temperature in the superconductor begins to exceed the critical temperature. Transient solutions were obtained by the finite-difference technique and the results are compared with a known analytical solution. Results of numerical calculations of the transient response of a composite superconductor subjected to an initial pulsed disturbance are presented. It is demonstrated that the superconductor can switch between the superconducting and the current-sharing state. The transient response and the stability of the composite conductor depend on the magnitude and duration of the disturbance, the dimensionless temperature θ^*, and the dimensionless parameter φ. Received on 18 November 1996     

One-Dimensional Steady Infiltration with Water Extraction

Exact solutions of the one-dimensional steady infiltration with water extraction are obtained for a particular but realistic form of the soil–water conductivity. The results are compared with numerical solutions for slightly different forms of the soil–water conductivity function, showing the sensitivity of the shape of the profiles on the exact representation of the soil–water conductivity. The exact solutions are an extension of Warrick's (1974) solution for the case where the soil can become saturated.     

可燃介质中飞行圆球诱导斜爆轰的流场结构

基于带化学反应的二维轴对称Euler方程,利用带有Superbee限制函数的波传播算法,对氢/氧/ 氮预混气中飞行圆球诱导斜爆轰进行了数值模拟。结果表明,在达姆科勒数Da略大于临界情形时,圆球诱导 的驻定爆轰是一个由强过驱斜爆轰、弱过驱斜爆轰、反应激波和惰性激波组合而成的复合结构。波后的圆球 绕流流场内存在2个亚音速区和1个超音速区。在圆球背风表面,还形成了第2道斜激波。     

Head-on Collision of a Detonation with a Planar Shock Wave

The phenomenon that occurs when a Chapman–Jouguet (CJ) detonation collides with a shock wave is discussed. Assuming a one-dimensional steady wave configuration analogous to a planar shock–shock frontal interaction, analytical solutions of the Rankine–Hugoniot relationships for the transmitted detonation and the transmitted shock are obtained by matching the pressure and particle velocity at the contact surface. The analytical results indicate that there exist three possible regions of solutions, i.e. the transmitted detonation can have either strong, weak or CJ solution, depending on the incident detonation and shock strengths. On the other hand, if we impose the transmitted detonation to have a CJ solution followed by a rarefaction fan, the boundary conditions are also satisfied at the contact surface. The existence of these multiple solutions is verified by an experimental investigation. It is found that the experimental results agree well with those predicted by the second wave interaction model and that the transmitted detonation is a CJ detonation. Unsteady numerical simulations of the reactive Euler equations with both simple one-step Arrhenius kinetic and chain-branching kinetic models are also carried out to look at the transient phenomena and at the influence of a finite reaction thickness of a detonation wave on the problem of head-on collision with a shock. From all the computational results, a relaxation process consisting of a quasi-steady period and an overshoot for the transmitted detonation subsequent to the head-on collisions can be observed, followed by the asymptotic decay to a CJ detonation as predicted theoretically. For unstable pulsating detonations, it is found that, due to the increase in the thermodynamic state of the reactive mixture caused by the shock, the transmitted pulsating detonation can become more stable with smaller amplitude and period oscillation. These observations are in good agreement with experimental evidence obtained from smoked foils where there is a significant decrease in the detonation cell size after a region of relaxation when the detonation collides head-on with a shock wave.     

Stability of shallow arches under constant load

Design of large span roof structures requires an analysis of static and dynamic behavior of shallow arches under various loads. In this paper the exact solution is established when the initial shape and the load are given by a linear combination of sinusoidal functions. The load is assumed to be time-independent. Then, the asymptotic stability of the arch is analyzed. For the one-dimensional solutions the arch is shown to have at most three equilibria. The arch motion exhibits a snap-through motion. In the two-dimensional case the location and the stability of equilibria is established under various conditions on the load-free shape, and the load parameters. An interesting phenomenon of a zigzag pattern of the critical pairs is discovered and studied numerically.     

A numerical study of the mechanisms of self-reignition in low-overdrive detonations

Below a threshold in overdrive, both stability analysis and numerical simulations predict that one-dimensional detonations in high activation energy mixtures behave as a chaotic sequence of failures followed by reignition. Instead, less chaotic, cellular detonations almost invariably occur in experiments. Numerical simulation, based on the Euler equations with single step chemistry, shows that a ZND detonation initially fails in that regime. The detonation splits into a weaker shock, a surface discontinuity separating reacted from unreacted fluid, and a rarefaction wave. However, the detonation is eventually reignited by the explosion of a small gas pocket, in a process reminiscent of deflagration to detonation transition. In the fluid heated by the leading shock, the chemical reaction occurs slowly at first, but becomes faster as heat is released, until the pocket explodes. Small differences in initial temperature result in large enough differences in reaction time sufficient for one pocket of fluid to explode. In two dimensions, the explosion occurs earlier because an oblique shock structure develops which unevenly heats the fluid that passes through the leading shock. Hence, pockets that underwent more heating will explode sooner. As it moves upstream, the two-dimensional explosion, meets the leading shock and the detonation quickly develops a transverse wave structure. An abridged version of this paper was presented at the 15th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Boulder, Colorado, from July 30 to August 4, 1995.     

高速弹丸诱导斜爆轰激波结构实验研究

斜爆轰推进系统在高超声速推进领域具有广阔的应用前景,其释热迅速、比冲高、燃烧室结构简单的优点吸引研究人员的持续关注.然而,斜爆轰的地面试验同时涉及到高速试验环境模拟、燃料与氧化剂混合、高温燃烧流场结构测量等技术难点,当前国内外系统的试验研究仍然十分有限,难以支撑斜爆轰发动机的研制.为了研究自持传播的斜爆轰激波结构与波面流动特性,基于爆轰驱动二级轻气炮开展了高速弹丸诱导斜爆轰实验研究,使用直径30 mm球头圆柱形弹丸发射进入充满氢/氧可燃混合气体的实验舱中以起爆斜爆轰波,并采用两种阴影技术对实验流动结构进行测量.实验中在不同速度、不同充气压力下观察到三种弹丸诱导激波结构,即激波诱导燃烧、弹丸起爆爆轰波和相对弹丸驻定的斜爆轰波,实验舱充气压力下降则会造成爆轰横波尺度增加与波面流动失稳.实验中,斜爆轰激波角与理论分析结果吻合较好,弹丸气动不稳定带来较大的弹丸攻角会对激波角测量带来一定偏差.通过对斜爆轰波波面法向传播速度的测量发现,随着远离弹丸,斜爆轰传播速度由弹丸飞行速度衰减至接近实验气体CJ速度,弹丸速度的降低会加速斜爆轰波传播速度的衰减.     

Convergence of Anisotropically Decaying Solutions of a Supercritical Semilinear Heat Equation

We consider the Cauchy problem for a semilinear heat equation with a supercritical power nonlinearity. It is known that the asymptotic behavior of solutions in time is determined by the decay rate of their initial values in space. In particular, if an initial value decays like a radial steady state, then the corresponding solution converges to that steady state. In this paper we consider solutions whose initial values decay in an anisotropic way. We show that each such solution converges to a steady state which is explicitly determined by an average formula. For a proof, we first consider the linearized equation around a singular steady state, and find a self-similar solution with a specific asymptotic behavior. Then we construct suitable comparison functions by using the self-similar solution, and apply our previous results on global stability and quasi-convergence of solutions.     

Hydrodynamic stability of evaporation fronts in porous media

The stability of phase transition fronts in water flows through porous media is considered. In the short-wave approximation a linear stability analysis is carried out and a sufficient condition of hydrodynamic instability of the phase discontinuity is proposed. The problem of injection of a water-vapor mixture into a two-dimensional mixture-saturated formation is solved and its numerical solution is compared with an exact solution of the corresponding one-dimensional self-similar problem. It is discovered that, instead of the unstable discontinuities in the one-dimensional formulation, in the two-dimensional case a lengthy mixing zone with a characteristic scale that increases self-similarly with time is formed.     

Structure and multiplicity of detonation regimes in heterogeneous hybrid mixtures

The problem of propagation of steady nonideal detonations in heterogeneous hybrid mixtures is studied in the case of a hydrogen-air gaseous mixture with suspended fine aluminum particles. Due to the difference in the order of magnitude of the characteristic induction and combustion times of gaseous mixture and solid particles, the process of energy release behind the leading shock front occurs over an extended period of time and in a nonmonotonic way. An approximate numerical model has been improved to find the steady propagation regimes and investigate their structure. The problem is analyzed in the frame of the theory of the mechanics of multiphase media with mass, momentum and heat exchanges between particles and gases. The one-dimensional ZND model of detonation with losses to the lateral boundaries is used. It is shown that three different steady propagation regimes may exist: the Pseudo-Gas Detonation (PGD), the Single-Front Detonation (SFD) and the Double-Front Detonation (DFD). The numerical results match the available experimental results obtained previously. The influence of the fundamental parameters of the system on the domains of existence of the different regimes is displayed. Moreover, it is shown that, according to the theory of nonideal detonations with nonmonotonic energy release, there may exist a multiplicity of detonation modes. However, the total number of solutions actually obtained by numerical calculations differs from that predicted by the theory. The reasons for these discrepancies are discussed.     

On the local stability analysis of the approximate harmonic balance solutions

Periodic response of nonlinear oscillators is usually determined by approximate methods. In the "steady state" type methods, first an approximate solution for the steady state periodic response is determined, and then the local stability of this solution is determined by analyzing the equation of motion linearized about this predicted "solution". An exact stability analysis of this linear variational equation can provide erroneous stability type information about the approximate solutions. It is shown that a consistent stability type information about these solutions can be obtained only when the linearized variational equation is analyzed by approximate methods, and the level of accuracy of this analysis is consistent with that of the approximate solutions. It is demonstrated that these consistent stability results do not imply that the approximate solution is qualitatively correct. It is also shown that the difference between an approximate and the next higher order stability analysis can be used to "guess" the role of higher harmonics in the periodic response. This trial and error procedure can be used to ensure the qualitatively correct and numerically accurate nature of the approximate solutions and the corresponding stability analysis.     

Fluid pressure response in poroelastic materials subjected to cyclic loading

When cyclic loading is applied to poroelastic materials, a transient stage of interstitial fluid pressure occurs, preceding a steady state. In each stage, the fluid pressure exhibits a characteristic mechanical behavior. In this study, an analytical solution for fluid pressure in two-dimensional poroelastic materials, which is assumed to be isotropic, under cyclic axial and bending loading is presented, based on poroelasticity. The obtained analytical solution contains transient and steady-state responses. Both of these depend on three dimensionless parameters: the dimensionless stress coefficient; the dimensionless frequency; and, the axial-bending loading ratio. We focus particularly on the transient behavior of interstitial fluid pressure with changes in the dimensionless frequency and the axial-bending loading ratio. The transient properties, such as half-value period and contribution factor, depend largely on the dimensionless frequency and have peak values when its value is about 10. This suggests that, under these conditions, the transient response can significantly affect the mechanical behavior of poroelastic materials.     

Stability of dual solutions in stagnation-point flow and heat transfer over a porous shrinking sheet with thermal radiation

An analysis is carried out to study the steady two-dimensional stagnation-point flow and heat transfer of an incompressible viscous fluid over a porous shrinking sheet in the presence of thermal radiation. A set of similarity transformations reduce the boundary layer equations to a set of non-linear ordinary differential equations which are solved numerically using fourth order Runge-Kutta method with shooting technique. The analysis of the result obtained shows that as the porosity parameter β increases, the range of region of existence of similarity solution increases. It is also observed that multiple solutions exist for a certain range of the ratio of the shrinking velocity to the free stream velocity (i.e., α) which again depends on β. We then discuss the stability of the unsteady solutions about each steady solution, showing that one steady state solution corresponds to a stable solution whereas the other corresponds to an unstable solution. The stable solution corresponds to the physically relevant solution. Further we obtain numerical results for each solution, which enable us to discuss the features of the respective solutions.     

Transient heat and mass transfer in a natural circulation loop

Comprehensive work has been performed by theoretical and numerical methods in order to study the steady state, transient and stability characteristics of a double diffusive natural circulation loop. It was found that the behavior of the flow in the system depends on the initial conditions and on the location of the state in the seven-parameter space of the thermal and saline Rayleigh numbers,Ra _T ,Ra _S , the modified Prandtl and Schmidt numbers,Pr, Sc, the dimensionless heat and mass transfer coefficients,H _T ,H _S , and the “aspect ratio” (between the height and width) of the loop, γ. Numerical results are presented here, showing the flow in each of the five regions formed in the stability chart. The steady state solutions include convection (constant velocity flow), conduction (no-flow) and periodic with constant amplitude and frequency. Two main new results were obtained: long term periodic oscillations where the amplitude is not symmetric around the conduction solution, and an overshoot of the velocity in transients before reaching the stable convection solutions. In the monotonic instability region of the conduction solution, convection solutions (constant velocity flow) develop, and in the global stability region the flow decays to the conduction solution (no flow), regardless of the initial conditions.     

斜爆轰发动机的推力性能理论分析

爆轰燃烧具有释热快、循环热效率高的特点. 斜爆轰发动机利用斜爆轰波进行燃烧组织, 在高超声速吸气式推进系统中具有重要地位. 以往研究主要关注斜爆轰波的起爆、驻定以及波系结构等, 缺少从整体层面出发对斜爆轰发动机开展推力性能分析. 本文将斜爆轰发动机内的流动和燃烧过程分解成进气压缩、燃料掺混、燃烧释热和排气膨胀4个基本模块并分别进行理论求解, 建立了斜爆轰发动机推力性能的理论分析模型. 在斜爆轰波系研究成果的基础上, 选取了过驱动斜爆轰、Chapman?Jouguet斜爆轰、过驱动正爆轰和斜激波诱导等容燃烧等4种燃烧模式来描述燃烧室内的燃烧释热过程, 并对比分析了不同燃烧模式对发动机比冲性能的影响. 此外, 还获得了不同来流参数、燃烧室参数和进排气参数等对发动机推力的影响规律, 发现来流马赫数和尾喷管的膨胀面积比是发动机理论燃料比冲的主要影响因素. 最后, 结合以往关于受限空间内斜爆轰波驻定特性等方面的研究成果, 提出了斜爆轰发动机燃烧室的设计方向.      

Transient Solution for the Energy Balance in Porous Media Considering Viscous Dissipation and Expansion/Compression Effects Using Integral Transforms

Monitoring of downhole flowing temperatures in oil wells is gaining attention in the recent years due to the possibility of exploring these data for reservoir characterization and determination of inflow profiles along the well completions, leading to an increased interest in the development of solutions for the equations governing the thermal behavior of a reservoir. In this work, it is proposed to use the generalized integral transform technique (GITT) to provide solutions for the energy balance equation, considering the thermal effects related to fluid flow. A formal and general solution for the energy balance in the porous media is presented and validated. It is presented the application of the proposed solution to one-dimensional and two-dimensional problems in the Cartesian coordinate system. The two-dimensional problem, which considers heat transfer to the surrounding impermeable formations, is tackled by a single domain formulation. The mathematical approach taken in these solutions is rigorous, valid for all flow regimes (transient, late-transient and pseudo-steady-state/steady-state) and for any orthogonal coordinate system, presenting the possibility of achieving differentiable and stable solutions with controlled accuracy. The solution comprises an important contribution to support the application of temperature data to reservoir engineering problems.     

Viscous and Inviscid Instabilities of Flow Along a Streamwise Corner

Here we consider the stability of flow along a streamwise corner formed by the intersection of two large flat plates held perpendicular to each other. Self-similar solutions for the steady laminar mean flow in the corner region have been obtained by solving the boundary layer equations for zero and nonzero streamwise pressure gradients. The stability of the mean flow is investigated using linear stability analysis. An eigensolver has been developed to solve the resulting linear eigenvalue problem either in a global mode to obtain an approximation to all the dominant eigenmodes or in a local mode to refine a particular eigenmode. The stability results indicate that the entire spectrum of two-dimensional and oblique viscous modes of a two-dimensional Blasius boundary layer is active in the case of a corner layer as well, but away from the cornerline. In a corner region of finite spanwise extent, the continuous spectrum of oblique modes degenerates to a discrete spectrum of modes of increasing spanwise wave number. The effect of the corner on the two-dimensional viscous instability is small and decreases the growth rate. The growth rate of outgoing oblique disturbances is observed to decrease, while the growth rate of incoming oblique disturbances is enhanced by the corner. This asymmetry between the outgoing and incoming viscous modes increases with increasing obliqueness of the disturbance. The instability of a zero pressure gradient corner layer is dominated by the viscous modes; however, an inviscid corner mode is also observed. The critical Reynolds number of the inviscid mode rapidly decreases with even a small adverse streamwise pressure gradient and the inviscid mode becomes the dominant one. Received 17 March 1998 and accepted 28 April 1999     

One-dimensional steady magnetogasdynamic flow in oblique fields and the structure of shock waves

Summary An exact solution in closed form, in terms of elliptic functions, is obtained for the one-dimensional steady flow of a polytropic gas with finite constant electrical conductivity which is influenced by an oblique magnetic field and a transverse electric field in the absence of viscosity, thermal conductivity and all other non-electrical dissipative mechanisms. The solution is presented in terms of elementary functions and the many possible flow patterns are discussed in detail in the case when, at some position, the transverse momentum equals the transverse Maxwell stress; a case which is appropriate to the structure of switch-on and switch-off shock waves.The research reported in this paper was supported in part by the United States Air Force under Grant No. AF-EOAR-65-58 and monitored by the European Office, Office of Aerospace Research.