填充床中气体渗流与化学波耦合问题的研究

研究等温和显著气固反应条件下填充床内反应气体浓度(物质)波推进与混合气体渗流的相互作用,指出化学反应对流动的影响包括两个方面,反应过程中混合气体质量的变化和密度的变化。混合气体流动将反过来影响反应进程。分析表明,按耦合模型和非耦合模型得到的速度场完全不同;按耦合模型,反应气体的浓度(物质)波阵面的推进对混合气体的流场有显著影响,因此按耦合模型计算的混合气体流场强烈地依赖于时间;忽略化学反应引起的混合气体密度变化的耦合模型,将导致一个质量消失的汇(或质量生成的源),因此将引起混合气体渗流速度的明显变化,并可能导致物理上不合理的结果;按耦合模型和非耦合模型计算的浓度场也有很大差别;当反应气体与惰性气体摩尔质量相差较大时,不能忽略反应过程中混合气体密度的变化;研究表明对于显著气固反应不能忽略化学反应与气体渗流的相互作用。     

Combustion stability of a homogeneous mixture in a chamber lined with acoustic absorbers

Self-excited oscillations in cylindrical combustion chambers burning a homogeneous mixture are investigated theoretically and experimentally. It is shown that two low-order tangential-longitudinal modes differing slightly in frequency are excited in the model chamber. Judging from the closeness of the experimental and theoretical values obtained for the mass flow rate of the mixture at the self-excitation boundary, it is postulated that excitation is due to the dependence of chemical reaction rate on the pressure (temperature) of the medium.     

脉冲流在Y型和倒Y型微反应器中强化传质的格子Boltzmann模拟

连续流微反应器的迅速发展为化学合成技术提供了一条可精准控制的路径。微反应器中流体的流动、混合和传质是反应的物理基础,因此强化传递就能够合理改善混和效果,增加相接触面积,减小微通道尺寸,以缩短分子扩散距离。由于微反应器中对流传递数量级非常低,不容易控制。通过改进微混合器构型和引入脉冲流动等主被动强化措施,可以有效改善对流和传质,影响化合反应。如何量化分析这些影响,是微反应器强化传质和优化控制反应过程的基础。本文基于有效的虚拟串行竞争反应格子Boltzmann模型,通过对Y型和倒Y型的微反应器的流场结构、混合传质和化合反应进行数值研究,定量分析了脉冲流动在不同流场构型下传质和化学反应的影响,所得结论可为连续流微反应器设计以及微反应精准控制提供有意义的参考。     

Multicomponent diffusion and heat exchange during the flow of an ionized gas in chemical equilibrium about a body

In the present paper, we investigate the flow of a multicomponent, partially ionized gas mixture in the boundary layer around an impermeable surface; the state in the boundary layer being one of chemical equilibrium. As an example, the flow of partially ionized air about a sphere is considered. The chemical composition at every point of the boundary layer with running values of the pressure, temperature, and concentrations of the chemical elements was found by Newton's method, parallel with the integration of the fundamental system of nonself-similar differential equations by the curve-fitting method. Also discussed is another method of finding the composition, which is more economical from the point of view of expenditure of machine time. It is found that the dimensionless heat flux to the wall at the front critical point of the sphere can be 26% larger for constant concentrations of the chemical elements than it is for variable concentrations.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 53–59, May–June, 1972.The author thanks G. A. Tirskii for discussing the work.     

2D Mixture Fraction Studies in a Hot-Jet Ignition Configuration Using NO-LIF and Correlation Analysis

The problem of measuring mixture fraction (defined here as the fractional part of mass originating from the exhaust gas jet) during the mixing of an unsteady hot exhaust gas jet impinging into a quiescent premixed hydrogen/air mixture is addressed. The diagnostic method is based on planar Laser-Induced Fluorescence of nitric oxide (NO) that is seeded to the hot jet and used as a tag for mixture fraction. The research work presented in this paper focusses on the analytical and experimental data employed for the estimation of mixture fraction using NO as a tracer. Since the NO LIF-signal does not solely depend on the amount of NO, but also on temperature and overall chemical composition, additional information is normally required to transform LIF-signals into mixture fraction values. To provide this additional information, the concept of reduced state spaces is applied: Correlations between state variables (temperature and species) are exploited to establish relationships between the measured signal and the mixture fraction. Simple numerical model simulations are used in combination with spectroscopic calculations to check for correlations between NO-LIF signal and mixture fraction. The result is that sharp correlations between NO-LIF signals and mixture fraction exist, provided that chemical reactions have not yet significantly influenced the flow. These correlations display only little sensitivity with respect to changes of the jet temperature, amount of NO seeded to the jet, and jet velocity. Measurements of NO-LIF were then performed for a non-reacting case before ignition, and mixture fraction maps were obtained from the measured LIF-signals by exploiting the correlations. The resulting data reveal the different driving forces behind mixing at regions near to the jet tip and at the radial shear layers.     

Thermomechanical instability in steady operating regime of continuous-flow chemical reactor with fixed catalyzer bed

A continuous-flow chemical reactor with fixed bed is a vessel filled with a porous catalyzer through which a liquid or gaseous reagent mixture is filtered. The motion of the mixture in this system is maintained by the pressure differential which compensates for the hydraulic resistance.The complete system of equations describing the mass-and heat-transfer processes in the continuous-flow chemical reactor includes the mass, momentum, and energy conservation equations [1], Usually, in the study of the existence and stability of steady reactor operating regimes, very simple reactor models are analyzed, in which only the mass-conservation equation in the form of the diffusion equation and the energy-conservation equation in the form of the heat-conduction equation are taken into account. The equation of motion drops out of consideration, since the velocity of the reagent mixture with the reaction products through the reactor is considered given and unvarying for disturbances of the steady operating regime.The purpose of the present study is to indicate the possibility of instability in the steady-process regime of a chemical reactor, which is associated with the fact that any temperature (and also concentration) variation within the reactor with disturbances of the steady regime will, generally speaking, lead to variation of the mixture viscosity and, consequently, to variation of the hydraulic resistance and the filtration velocity. This interconnection is an additional factor which may have a significant effect on the behavior of disturbances of the steady regime.In contrast with thermal, kinetic, and thermokinetic instability [2], it is natural to refer to the instability being investigated as thermomechanical instability. Let us consider an example.     

Conditions for different steady states in an adiabatic continuous-flow reactor with a catalyst layer

An adiabatic reactor with continuous flow and with a stationary fine-grained catalyst layer is examined. The mixture which passes through this layer undergoes chemical reaction on the surface of the grains. The reaction there is accompanied by liberation of heat and change in the concentration of the mixture with subsequent heat and mass exchange between this surface and the flow. The rate of the reaction depends on the temperature and concentration of the reagents, in which the relationship to the temperature is markedly nonlinear.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 153–159, July–August, 1970.     

Governing equations in non-isothermal diffusion

Generalizations of Fick's law for the diffusion flux are often considered in the literature by analogy with those for the heat flux. The paper reviews the balance equations for a fluid mixture and provides the equations for the diffusion fluxes. As a consequence, the mass densities are shown to satisfy a system of hyperbolic equations. Moreover, for a binary mixture of ideal gases in stationary conditions, Fick's law is recovered. Next, diffusion fluxes are regarded as constitutive functions and a whole set of thermodynamic restrictions are determined which account for diffusion, heat conduction, viscosity and inhomogeneities. Hyperbolic models for diffusion and heat fluxes are established which involve the co-rotational derivative. The driving term of diffusion turns out to be the gradient of chemical potential rescaled by the temperature.     

Determination of heat fluxes in the neighborhood of a double curvature stagnation point in a flow of dissociating gas of arbitrary chemical composition

Numerical solutions are obtained for the equations of a uniform compressible boundary layer with variable physical properties in the vicinity of a stagnation point with different principal curvatures in the presence of an injected gas with the same properties as the incident flow. The results of the numerical solutions are approximated for the heat flux in the form of a relation that depends on the variation of the product of viscosity and density across the boundary layer and on the ratio of the principal radii of curvature.Using the concepts of effective diffusion coefficients in a multicomponent boundary layer, previously introduced by the author in [1], and the generalized analogy between heat and mass transfer in the presence of injection, together with the numerical solutions obtained, it is always possible, even without additional solutions of the boundary-layer equations, to derive final formulas for the heat fluxes in a flow of dissociating gas of arbitrary chemical composition, provided that we make the fundamental assumption that all recombination reactions take place at the surface.By way of example, formulas are given for the heat transfer to the surface of a body from dissociating air, regarded as a five-component mixture of the gases O, N, NO, O₂, N₂, and from a dissociating mixture of carbon dioxide and molecular nitrogen of arbitrary composition, regarded as an eleven-component mixture of the gases O, N, C, NO, C₂, O₂, N₂, CO, CN, C₃, CO₂.In the process of obtaining and analyzing these solutions it was found that, in computing the heat flux, a multicomponent mixture can be replaced with an effective binary mixture with a single diffusion coefficient only when the former can be divided into two groups of components with different (but similar) diffusion properties. In this case the concentrations of one group at the surface must be zero, while the diffusion flows of the second group at the surface are expressible, using the laws of mass conservation of the chemical elements, in terms of the diffusion flows of the first. Then the single effective diffusion coefficient is the binary diffusion coefficient D(A,M), where A relates to one group of components and M to the other.In view of the small amount of NO(c(NO) < 0.05), the diffusion transport of energy in dissociated air maybe described with the aid of a single binary diffusion coefficient D(A, M)(A=O, N, M=O₂, N₂, NO). However even in the case of complete dissociation into O and C atoms at the outer edge of the boundary layer, the diffusion transport of energy in dissociated carbon dioxide can not be described accurately enough by means of a model of a binary mixture with a single diffusion coefficient, since the diffusion properties of the O and C atoms are distinctly different.     

High‐resolution methods for preserving the sum of mass fractions: improved χ‐scheme and an alternative

When high resolution convection schemes are used for discretizing chemical species mass balance equations, the mass fractions are not guaranteed to add to one. We show that a proposed remedy called χ —scheme (Darwish and Moukalled, Comput. Methods Appl. Mech. Engrg. 192 (2003): 1711) will degrade to a diffusive first‐order scheme when a chemical species vanishes from the mixture, for example, because of chemical reactions. We propose an improvement to the χ ‐scheme to overcome this problem. Furthermore, a computationally efficient alternative scheme is proposed and evaluated with several examples, to quantify the improvements in the accuracy and the computational time. Published 2013. This article is a U.S. Government work and is in the public domain in the USA.     

固体炸药爆轰与惰性介质相互作用的一种扩散界面模型

提出一种保持热力学一致性的扩散界面模型,用来数值模拟固体炸药爆轰与惰性介质的相互作用问题。基于混合网格内各组分物质间可以达到力学平衡状态而不能达到热学平衡状态的假设,由混合网格能量守恒以及压力相等条件,推导出每种组分物质的体积分数演化方程。由此获得的扩散界面模型包括组分物质的质量守恒方程、混合物质的动量及总能量守恒方程,同时包括组分物质的体积分数演化方程和混合物质的压力演化方程。该扩散界面模型的主要特点是考虑了化学反应以及热学非平衡的影响。提出的扩散界面模型在物质界面附近不会出现物理量的非物理振荡现象、适用于任意表达形式的物质状态方程以及任意数目的惰性介质。     

Similar solution of laminar boundary layer equations with a flame front

This paper is devoted to the general question of the effect of chemical reactions taking place in the boundary layer with the release of heat on the heat transfer, mass transfer, and friction. In the most general formulation the problem is associated with extremely complex computations because of the presence of many components in the mixture of gases. Moreover, to date the chemical kinetics have received little study, and there are simply no reliable data that can be used in the calculations. Therefore we consider in the following a simplified case in which the chemical reaction proceeds in an infinitely narrow region-a flame front. Mathematically this front is a surface of discontinuity of the concentration and temperature derivatives. Physically this corresponds to the limiting case of chemical equilibrium, in which equilibrium occurs with complete combustion and is realized at moderate temperatures and quite high pressures.This formulation of the problem simplifies the calculation considerably, since the gas mixture may be considered everywhere binary. In this case it is not necessary to introduce into consideration either the chemical kinetics or the chemical equilibrium constants. Moreover, in the case of this formulation we may make use of a similar solution of the boundary layer equations. The extreme simplification of the computations does not alter the physical essence of the problem-the effect of the heat sources within the boundary layer on friction, heat transfer and mass transfer. A large number of computations was made to permit clarification of the specific nature of the dependences of the coefficients of friction, and heat and mass transfer on the rate of fuel injection.Several studies have been published in which a similar assumption was made. Avduevskii and Obroskova [1] consider the case when the flame front is located right at the wall. Harnett and Eckert [2] calculated the boundary layer for a flame front on the assumption that the physical parameters do not depend on temperature. This assumption gives a picture which is inaccurate both quantitatively and qualitatively. Finally, when the present study was nearly completed, the article of Libby and Pierucci [3] appeared. In that study the external flow (air) is a mixture of oxygen and an inert gas (argon). Therefore there is a three-component mixture in the boundary layer at every point. This significantly complicates the computation. At the same time, the dependence of the physical parameters on temperature and the concentrations of the mixture components is taken in simplified form (an unjustified simplification, in our view). The authors of [3] carried out only a limited number of computations, which did not make it possible to clarify the characteristic features of the variation of the friction, heat transfer, and mass transfer coefficients as a function of the rate of combustible gas injection.Notation x coordinate along plate in flow direction - y coordinate along normal to plate - u, v velocity components - T absolute temperature - c mass concentration - volume concentration - density - c_p specific heat at constant pressure - viscosity coefficient - D diffusion coefficient - h specific enthalpy - heat conductivity - M Mach number in external stream - k adiabatic exponent in external stream The author wishes to thank V. S. Avduevskii for guiding this investigation.     

Material removal associated with condensation on a droplet in motion

This paper treats a three-phase, multicomponent fluid mechanics-heat and mass transfer problem. Solutions to the nonlinear, coupled boundary layer equations that govern laminar condensation heat and mass transfer in the vicinity of the forward stagnation point of a spherical cold water drop translating in a saturated mixture of five components are presented. The environment surrounding the drop is composed of a condensable (steam), a noncondensable and nonabsorbable (air), a noncondensable but absorbable (e.g. elemental iodine), a chemically reactive component (e.g. methyl iodide), and a particulate substance. The dispersed and the continuous phases have been treated simultaneously. The effect of chemical reaction between a reactive component in the continuous phase and an additive (e.g. hydrazine) in the droplet liquid has also been considered. The droplet sizes, the thermodynamic range, and the nature of chemical constituents chosen for the illustrative calculations are closely related to the operating conditions that are likely to prevail in the containment spray atmosphere of a nuclear reactor following a loss of coolant accident. The choice of elemental iodine and methyl iodide has an added feature. The mass transfer resistance for elemental iodine is almost entirely in the gaseous phase while the absorption of methyl iodide could be regarded as a liquid-phase resistance-controlled process. Mass transport, in the presence of condensation, is seen to depend in a rather complicated manner on droplet radius.     

A two-fluid model for reactive dilute solid–liquid mixtures with phase changes

Based on the Eulerian spatial averaging theory and the Müller–Liu entropy principle, a two-fluid model for reactive dilute solid–liquid mixtures is presented. Initially, some averaging theorems and properties of average quantities are discussed and, then, averaged balance equations including interfacial source terms are postulated. Moreover, constitutive equations are proposed for a reactive dilute solid–liquid mixture, where the formation of the solid phase is due to a precipitation chemical reaction that involves ions dissolved in the liquid phase. To this end, principles of constitutive theory are used to propose linearized constitutive equations that account for diffusion, heat conduction, viscous and drag effects, and interfacial deformations. A particularity of the model is that the mass interfacial source term is regarded as an independent constitutive variable. The obtained results show that the inclusion of the mass interfacial source term into the set of independent constitutive variables permits to easily describe the phase changes associated with precipitation chemical reactions.     

Chemical composition of PM_(2.5) during winter in Tianjin,China

PM2.5 samples for 24 h were collected during winter in Tianjin,China. The ambient mass concentration and chemical composition of the PM2.5 were determined. Ionic species were analyzed by ion chromatog-raphy,while carbonaceous species were determined with the IMPROVE thermal optical reectance(TOR) method,and inorganic elements were measured by inductively coupled plasma-atomic emission spec-trometer. The daily PM2.5 mass concentrations ranged from 48.2 to 319.2 g/m3 with an arithmetic average of 144.6 g/m3. ...     

T型管内流动气体中爆轰绕射过程的数值模拟

基于带化学反应的二维Euler方程,对H₂、O₂、Ar体积比为2:1:1的混合气体系统在T型管内的爆轰绕射进行了数值模拟。用二阶附加半隐的Runge-Kutta法和五阶WENO格式分别离散欧拉方程的时间和空间导数项,采用9组分48步基元反应简化模型描述爆轰波在静止系统和流动系统中的传播过程,得到了温度、压力、典型组元H质量分数的分布及数值胞格结构。结果表明:在流动系统中,迎风面上波阵面为斜爆轰结构,静止系统两侧和顺风面上的波阵面为完全解耦的前导激波;在水平管中,波阵面与上下壁面经历一系列马赫碰撞后,最终形成正爆轰;在流动系统中,胞格结构明显向下游偏移;横向爆轰波的产生对爆轰波的再生起到了关键作用。     

Analysis of coupled thermo-hydro-mechanical behavior of unsaturated soils based on theory of mixtures I

This paper analyzes a coupled thermo-hydro-mechanical behavior of unsaturated soils based on the theory of mixtures. Unsaturated soil is considered as a mixture composed of soil skeleton, liquid water, vapor, dry air, and dissolved air. In addition to the mass and momentum conservation equations of each component and the energy conservation equation of the mixture, the system is closed using other 37 constitutive （or restriction） equations. As the change in water chemical potential is identical to the change in vapor chemical potential, a thermodynamic restriction relationship for the phase transition between pore water and pore vapor is formulated, in which the impact of the change in gas pressure on the phase transition is taken into account. Six final govern- ing equations are given in incremental form in terms of six primary variables, i.e., three displacement components of soil skeleton, water pressure, gas pressure, and temperature. The processes involved in the coupled model include thermal expansions of soil skeleton and soil particle, Soret effect, phase transition between water and vapor, air dissolution in pore water, and deformation of soil skeleton.     

Reactive Constrained Mixtures for Modeling the Solid Matrix of Biological Tissues

This article illustrates our approach for modeling the solid matrix of biological tissues using reactive constrained mixtures. Several examples are presented to highlight the potential benefits of this approach, showing that seemingly disparate fields of mechanics and chemical kinetics are actually closely interrelated and may be elegantly expressed in a unified framework. Thus, constrained mixture models recover classical theories for fibrous materials with bundles oriented in different directions or having different reference configurations, that produce characteristic fiber recruitment patterns under loading. Reactions that exchange mass among various constituents of a mixture may be used to describe tissue growth and remodeling, which may also alter the material’s anisotropy. Similarly, reactions that describe the breaking and reforming of bonds may be used to model free energy dissipation in a viscoelastic material. Therefore, this framework is particularly well suited for modeling biological tissues.     

Effect of chemical reactivity on the detonation initiation in shock accelerated flow in a confined space

The interactions of a spherical flame with an in- cident shock wave and its reflected shock wave in a confined space were investigated using the three-dimensional reactive Navier-Stokes equations, with emphasis placed on the effect of chemical reactivity of mixture on the flame distortion and detonation initiation after the passage of the reflected shock wave. It is shown that the spatio-temporal characteristics of detonation initiation depend highly on the chemical reactivity of the mixture. When the chemical reactivity enhances, the flame can be severely distorted to form a reactive shock bifurcation structure with detonations initiating at different three-dimensional spatial locations. Moreover, the detonation initiation would occur earlier in a mixture of more enhanced reactivity. The results reveal that the detonations arise from hot spots in the unburned region which are initiated by the shock-detonation-transition mechanism.     

Application of a coupled solid/fluids mixture theory: Process of squeezing a sponge

In this paper, we present the details of the solution of one of three problems obtained via the application of a coupled solid/fluids mixture theory developed recently by Chen. The problem is that of the process of squeezing a sponge. A fluid saturated solid is sandwiched between two infinitely stiff plates, one plate is held fixed and the other applies increasing pressure at its interface with the solid. Results concerning the stress of the solid, volume fraction, bulk density, chemical potential and pressures of the fluid, and the characteristics of fluid mass discharge are reported. The results are consistent with our expectations and experiences.