高能炸药散心爆轰波绕射传播的数值模拟

从曲面爆轰波的Hugoniot 关系式出发,应用燃烧模型模拟散心爆轰波的传播,分析了空间步长不是足够小时,不能同时准确给出爆轰波走时及波阵面物理量的原因。对球壳装药散心爆轰波的长程绕射作了二维计算,应用燃烧模型并细分空间网格。除起爆点附近,计算的爆轰波走时与实验相差均在0 .2s 以内;稳定传播的爆轰波波阵面压力计算值接近pJ。可见,应用燃烧模型模拟散心爆轰波的传播,化学反应区内的空间步长需足够小。最后对Program 燃烧模型不能很好地模拟多维效应作了分析。     

惰性颗粒抑爆过程的数值模拟

对高温火球诱导的爆炸及惰性颗粒的抑爆过程进行了数值研究。由于扰动特征时间 ,两相弛豫特征时间和化学平衡特征时间的差异 ,这种带激波的两相化学反应流守恒方程具有刚性。利用处理包括组元守恒方程的全耦合TVD格式和可处理方程源项的Lax Wendroff Rubin格式分别求解气相和颗粒相 ,并根据各特征时间的比值用分步法处理方程的刚性。计算结果反映了均温燃烧火球在可燃环境中形成加速火焰和激波 ,进而成长为爆轰波的过程 ,以及惰性颗粒对爆轰波的抑制过程 ,反映了激波、化学反应和惰性颗粒之间的相互作用和耦合。计算结果表明 ,仅当颗粒浓度大于某值时才能有效抑制爆轰 ,否则无论多大的颗粒散布区域 ,皆不能使爆轰波完全抑制 ,爆轰波或是在其中发展为两相爆轰波 ,或是穿越该区域后重新成长为气相爆轰。     

斜爆轰波面上复杂结构的数值研究

利用欧拉方程和单步化学反应模型, 对斜爆轰波进行了数值模拟, 重点研究了斜爆轰波面上多维复杂结构的形成机理. 数值结果显示在斜爆轰波面上, 存在两种小尺度的激波和火焰耦合结构: 第1种结构由一道横波和三角形火焰组成, 是斜爆轰波中特有的结构; 第2种结构由两道横波和凸起的火焰面组成, 类似于正爆轰波面上的胞格结构. 数值结果表明这两种结构具有相同的形成机理, 而且能够相互转化, 它们的形成和发展过程受到来流马赫数和化学反应放热速度等参数的影响.      

应用阵面追踪法对散心爆轰波传播的数值模拟

考虑到爆轰波阵面曲率及化学反应区宽度的作用 ,由修正Hugoniot关系式解析求解了波后状态 ,应用阵面追踪法 (FTM)数值模拟了曲面散心爆轰波的传播。计算给出的散心爆轰波走时及波阵面上物理量都达到了波阵面曲率的一阶精度。     

二维拟定常爆轰波反应区的初步研究

研究由现代爆轰渐近分析理论建立的关于二维拟定常爆轰波反应区的控制方程组，用数值积分方法求解该方程组，得到爆轰波反应区内压力、粒子速度、化学反应度随时间变化的规律。对乳化硝铵、PBX-9404和TATB炸药进行了计算，得到比较满意的结果。     

爆轰波管中铝粉尘爆轰的数值模拟

用两相流模型对爆轰波管中的铝粉尘的爆轰波进行了研究。模型考虑了气体和颗粒两相间速度和温度的不同及由于管壁引起的对流热传导和粘性引起的耗散,考虑了由于铝颗粒表面粗糙使得表面积增加的因素。铝颗粒的点火判据使用了新的判据,即铝颗粒在激波后的气流中温度达到铝的熔点且铝全部熔化即被点火。数值模拟了内径为15.2cm的爆轰波管中铝粉尘中爆轰波的传播和发展,得到了爆轰波速度及铝颗粒点火距离,还得到了爆轰流场中物理量的分布。从前导激波面到CJ面处,两相间的速度和温度有明显的差别。还考虑了粒子由于粗糙引起的表面积增加对爆轰波的影响,这个因素对铝颗粒的点火距离的影响较大,对这里计算的铝粉尘爆轰波的速度基本没有影响。结果表明,两相流模型可以较好地描述铝粉尘的爆轰过程,得到具有很粗糙表面、平均粒子直径为3.4m的铝粉尘浓度为304g/m3时爆轰波的速度为1.63km/s,点火距离为3mm,与实验值符合较好。     

2021-08期封面

铝粉反应模型是对悬浮铝粉尘气-固两相爆轰进行数值模拟研究的关键。通过考虑铝粉燃烧产物氧化铝（Al₂O₃）在高温下的分解吸热反应,改进了铝粉的扩散燃烧模型。将该模型嵌入到三维的气-固两相爆轰数值计算程序中,分别对铝粉/空气混合物以及铝粉/氧气混合物的爆轰进行了数值模拟,计算得到的稳定爆轰波速度与实验结果、文献值均吻合较好,误差小于5.5%,表明改进的铝粉反应模型适用于不同氧化气体氛围中铝粉尘爆轰的模拟计算。此外,对两相爆轰参数及爆轰流场的物理量分布进行分析,获得了铝粉反应模型对爆轰波结构的影响规律。     

动态存储方法在气相爆轰波数值模拟中的应用

为减少反应流计算花费的时间,采用动态存储建立热力学数据表（In situ adaptive tabulation, ISAT）的方法来取代反应流计算中化学反应的直接积分（Direct integral, DI）,并针对气相H2/O2爆轰波的传播过程进行了数值模拟。采用两种不同的ISAT误差放大判据对一维爆轰波的压力、温度及组分变化进行了计算,并和DI的结果进行了比较以考察其计算精度。此外,还探讨了ISAT方法的效率。计算结果表明,和DI方法相比,在爆轰波传播计算中ISAT方法计算误差小于3％,化学反应计算速度提高了8倍。     

临界爆轰的稳定条件和螺旋爆轰波

本文应用耗散结构热力学理论和微扰的方法,研究临界爆轰波对二维扰动的稳定性问题。在忽略粘性、热传导、浓度扩散、外力和交叉效应的情况下,作出了扰动在爆轰波结构内传播的稳定性判据。对Arrhenius反应率,当化学反应活化能E大于某一临界值E_c之后,对反应率随温度增加而增加的放热反应,临界爆轰波对二维扰动是不稳定的,扰动的振幅在反应燃烧区内随时间的增加而增长,直至扰动最后离开爆轰波结构进入波后产物区。当考虑了粘性的影响之后,扰动振幅的增长和衰减依赖于扰动本身的频率,在反应放热量超过某临界值后,频率愈小亦即扰动波长愈长的扰动振幅,随时间增长愈快,以致最长波长的扰动增长掩盖了其它波长的扰动,或者只有最长波长的扰动振幅维持不变,其它波长的扰动振幅都逐渐衰减,最后形成有规则的螺旋爆轰波。所得结果当忽略化学反应以及粘性对扰动传播相速度的微小影响之后,结论与N.Monson和J.A.Fay等所作的声波理论结果相一致,比较成功地解释了螺旋爆轰的一些实验现象。     

爆轰合成纳米氧化铝颗粒的生成时间估算

利用胶体理论中的快速聚沉动力学模拟尺寸为20nm 的氧化铝球形颗粒在爆轰化学反应区的 生成过程,估算出其生长时间为0.11s,该时间值在爆轰化学反应区的时间长度(约1.0s)内。理论计算证 明该尺度的纳米氧化铝颗粒是在爆轰反应区内形成的,这与实验证明的结果一致。根据爆轰反应机理可知爆 轰化学反应区的长度可以通过改变炸药的爆轰参数来改变,因此通过人为改变混合炸药的爆轰参数可以控 制纳米氧化铝在反应区的生长时间,进而可以控制其最终的生长尺寸。     

Shock-wave formation in flowing bubbly mixtures by steepening of compression waves

The formation and propagation of shock waves in a two-component flowing bubbly mixture has been investigated experimentally. The structure of shock waves formed by steepening of compression waves is compared with the corresponding features of shocks produced spontaneously in shock tubes. Experimentally determined values of the speed of propagation of the shock compare favorably with the Hugoniot relationship based upon a homogeneous two-phase model. The effect of the gravitational and frictional pressure gradients on the shock characteristics is also examined.     

Convective heat transfer in porous media with columnar structure

An analysis is made of convective heat transport, produced by uniform heating from below, in a horizontal layer of a porous medium consisting of vertical slabs or columns of different permeabilities. Estimates of the heat flux are made on the assumption that flow in one column does not interact with flow in adjacent columns. The results are compared with those for a homogeneous layer, for which previous work is reviewed. It is found that an inhomogeneous layer transports less heat than a homogeneous layer for which the mean Rayleigh number is the same, if the Rayleigh number is supercritical throughout the layer. If the Rayleigh number is subcritical in part of the layer, the inhomogeneous layer may transport more heat than the equivalent homogeneous layer.     

Propagation mechanism of dust detonations

This paper summarizes the studies on dust detonations at the Stosswellenlabor of RWTH Aachen since 1987. The onset and propagation mechanism of heterogeneous dust detonations are similar to those of marginal gas phase detonations. A self-sustained dust detonation has transverse wave structures that provide the coupling between shock and reaction. Large transition distances and transverse wave spacings require large sized tubes for the propagation of self-sustained dust detonations. The Hugoniot analysis of the Chapman-Jouguet detonation predicts equilibrium detonation states being in reasonable agreement with the self-sustained dust detonations observed. Shock matching calculations at the triple point adequately determine the wave structures of those stable dust detonations.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Three-dimensional cellular structure of detonations in suspensions of aluminium particles

Recently, we have used scarce available data on the detonation cell size in suspensions of aluminium particles in air and oxygen to adjust the kinetic parameters of our two-phase model of detonations in these mixtures. The calculated detonation cell width was derived by means of two-dimensional (2D) unsteady simulations using an assumption of cylindrical symmetry of the flow in the tube. However, in reality, the detonation cells are three-dimensional (3D). In this work, we have applied the same detonation model which is based on the continuous mechanics of two-phase flows, for 3D numerical simulations of cellular detonation structures in aluminium particle suspensions in oxygen. Reasonable agreement on the detonation cell width was obtained with the aforementioned 2D results. The range of tube diameters where detonations in $\text{ Al/O}_2$ mixture at a given particle size and concentration would propagate in the spinning mode has been estimated (these results make a complement to our previous analysis of spinning detonations in Al/air mixtures). Coupling these results with the dependencies of detonation cell size on the mean particle diameter is of great interest for the understanding of fundamental mechanisms of detonation propagation in solid particle suspensions in gas and can help to better guide the experimental studies of detonations in aluminium suspensions. It is shown that the part of detonation wave energy used for transverse kinetic energy of both gas and particles is quite small, which explains why the propagation velocity of spinning and multi-headed detonations reasonably agrees with the ideal CJ values.     

Modelling detonation waves in condensed energetic materials: multiphase CJ conditions and multidimensional computations

A hyperbolic multiphase flow model with a single pressure and a single velocity but several temperatures is proposed to deal with the detonation dynamics of condensed energetic materials. Temperature non-equilibrium effects are mandatory in order to deal with wave propagation (shocks, detonations) in heterogeneous mixtures. The model is obtained as the asymptotic limit of a total non-equilibrium multiphase flow model in the limit of stiff mechanical relaxation only (Kapila et al. in Phys Fluids 13:3002–3024, 2001). Special attention is given to mass transfer modelling, that is obtained on the basis of entropy production analysis in each phase and in the system (Saurel et al. in J Fluid Mech 607:313–350, 2008). With the help of the shock relations given in Saurel et al. (Shock Waves 16:209–232, 2007) the model is closed and provides a generalized ZND formulation for condensed energetic materials. In particular, generalized CJ conditions are obtained. They are based on a balance between the chemical reaction energy release and internal heat exchanges among phases. Moreover, the sound speed that appears at sonic surface corresponds to the one of Wood (A textbook of sound, G. Bell and Sons LTD, London, 1930) that presents a non-monotonic behaviour versus volume fraction. Therefore, non-conventional reaction zone structure is observed. When heat exchanges are absent, the conventional ZND model with conventional CJ conditions is recovered. When heat exchanges are involved interesting features are observed. The flow behaviour presents similarities with non ideal detonations (Wood and Kirkwood in J Chem Phys 22:1920–1924, 1950) and pathological detonations (Von Neuman in Theory of detonation waves, 1942; Guenoche et al. in AIAA Prog Astron Aeronaut 75: 387–407, 1981). It also present non-conventional behaviour with detonation velocity eventually greater than the CJ one. Multidimensional resolution of the corresponding model is then addressed. This poses serious difficulties related to the presence of material interfaces and shock propagation in multiphase mixtures. The first issue is solved by an extension of the method derived in Saurel et al. (J Comput Phys 228(5):1678–1712, 2009) in the presence of heat and mass transfers. The second issue poses the difficult mathematical question of numerical approximation of non-conservative systems in the presence of shocks associated to the physical question of energy partition among phases for a multiphase shock. A novel approach is used, based on extra evolution equations used to retain the information of the material initial state. This method insures convergence in the post-shock state. Thanks to these various theoretical and numerical ingredients, one-dimensional and multidimensional unsteady detonation waves computations are done, eventually in the presence of material interfaces. Convergence of the numerical hyperbolic solver against ZND multiphase solution is reached. Material interfaces, shocks, detonations are solved with a unified formulation where the same equations are solved everywhere with the same numerical scheme.     

Heat flux-flow coupling effects in the stability of vapour generators

A study has been carried out to investigate the dynamics of two-phase flow in vapour generators, with special reference to the effect of flux-flow couplings on density wave instability. A distributed parameter time-varying theoretical analysis of the conservation equations, together with the constitutive laws of two-phase flow, has been derived. The analysis takes into account the dynamics of the heater wall, revealing the predominant role of the heat flux-flow couplings on the stability of the system. A digital computer program has been written and developed to implement the theoretical analysis. Results from the analysis are used for comparison with the available data and the effect of the flux-flow couplings on instability is demonstrated and discussed. These results are also used to explain the dynamic behaviour of a specially constructed “Arcton-113”¹ closed loop comprising a helical, electrically heated, once-through vapour generator in a parallel channel arrangement with high thermal capacitance. Kopplungseffekte zwischen Wärmefluß und Strömung bei der Stabilität von Dampferzeugern     

Stability analysis of soret-driven double-diffusive convection of Maxwell fluid in a porous medium

Stability analysis of double-diffusive convection for viscoelastic fluid with Soret effect in a porous medium is investigated using a modified-Maxwell-Darcy model. We use the linear stability analysis to investigate how the Soret parameter and the relaxation time of viscoelastic fluid effect the onset of convection and the selection of an unstable wavenumber. It is found that the Soret effect is to destabilize the system for oscillatory convection. The relaxation time also enhances the instability of the system. The effects of Soret coefficient and relaxation time on the heat transfer rate in a porous medium are studied using the nonlinear stability analysis, the variation of the Nusselt number with respect to the Rayleigh number is derived for stationary and oscillatory convection modes. Some previous results can be reduced as the special cases of the present paper.     

井筒气液两相流对致密气压裂水平井试井的影响

多段压裂水平井技术是目前开采致密气最常用的方法之一,在致密气压裂水平井试井测试中常常伴随着一定的产水量,井筒气液两相流会增加井筒流体的流动阻力,加大井筒流体流动对试井解释的影响.为了明确井筒气液两相流对致密气藏压裂水平井试井的影响,提高产水致密气压裂水平井的试井解释精度,建立了一种井筒气液两相流与地层渗流耦合的试井模型,采用数值方法对模型进行求解,获得了考虑井筒气液两相流的压裂水平井试井理论曲线、压力场分布及裂缝产量分布.研究结果表明:井筒气液两相流会增加试井理论曲线中压力和压力导数值,造成靠近入窗点的压力扩散要快于远离入窗点的压力扩散,引起靠近入窗点的裂缝产量要高于远离入窗点的裂缝产量.现场实例分析进一步说明,不考虑井筒两相流可能会对产水压裂水平井的试井解释结果产生很大误差,主要表现为水平井筒假设为无限大导流能力会使得拟合得到的表皮系数偏大,将测试点视为入窗点会使得拟合得到的原始地层压力偏小.所建立的考虑井筒两相流的压裂水平井试井模型为产水致密气井试井资料的正确解释提供了重要技术保障.      

Stress relaxation as a microstructural probe for immiscible polymer blends

Relaxation has been investigated in immiscible blends that consist of slightly viscoelastic components. Both the shear and normal stresses have been measured after cessation of steady shear flow as well as after transient shear histories. The latter can generate a fibrillar structure which can relax by either retraction or break-up via end-pinching or Rayleigh instabilities. Each of these three relaxation mechanisms is reflected in the shape of the stress curves, from which also the corresponding structural time scales can be deduced. The experimental results have been used to evaluate the Doi-Ohta and Lee-Park models for immiscible blends. The scaling relations by Doi-Ohta are confirmed by the experimental results, but none of the existing models can correctly predict the complex relaxation behaviour observed for a highly deformed droplet phase. In the present study an alternative approach has been proposed. The stress relaxation due to fibril break-up via Rayleigh instabilities has been predicted successfully by combining physical models for the structural changes with the basic approach of the Doi-Ohta model.     

Effect of diameter on two-phase pressure drop in narrow tubes

The effect of tube diameter on two-phase frictional pressure drop was investigated in circular tubes with inner diameters of 0.6, 1.2, 1.7, 2.6 and 3.4 mm using air and water. The gas and liquid superficial velocity ranges were 0.01-50 m/s and 0.01-3 m/s, respectively. The gas and liquid flow rates were measured and the two-phase flow pattern images were recorded using high-speed CMOS camera. Unique flow patterns were observed for smaller tube diameters. Pressure drop was measured and compared with various existing models such as homogeneous model and Lockhart-Martinelli model. It appears that the dominant effect of surface tension shrinking the flow stratification in the annular regime is important. It was found that existing models are inadequate in predicting the pressure drop for all the flow regimes visualized. Based on the analysis of present experimental frictional pressure drop data a correlation is proposed for predicting Chisholm parameter “C” in slug annular flow pattern. For all other flow regimes Chisholm’s original correlation appears to be adequate except the bubbly flow regime where homogeneous model works well. The modification results in overall mean deviation of pressure drop within 25% for all tube diameters considered. This approach of flow regime based modification of liquid gas interaction parameter appears to be the key to pressure drop prediction in narrow tubes.