前沿领域综述–多孔介质强制对流换热研究进展

多孔介质的强制对流换热主要涉及渗流、对流换热、热弥散和热辐射等方面的内容, 文中对这个几个方面的国内外研究进展和发展趋势进行了逐一综述. 同时对主要理论模型、实验研究和经验关联式进行了分类整理, 总结了它们的特点、适用范围和局限性, 并对主要研究成果进行了对比分析, 指出了将来进一步研究的方向和难点所在. 而且通过简化计算得到高温多孔介质冷却过程何时需要考虑辐射换热. 所有这些对多孔介质的理论研究和工程应用都具有指导性的意义. 关键词： 多孔介质 对流换热 渗流 热弥散     

多孔介质中盐指现象的数值模拟

运用基于杂交网格的高精度数值方法研究了多孔介质中的盐指现象.该算法将基于边界拟合坐标下的高精度有限差分法和高精度的泊松方程快速求解器有效地结合在一起,从而达到提高整体的计算精度、计算效率和稳定性的目的.通过比较不同孔隙率的多孔介质对盐指对流的传热传质效应的影响,发现在标准孔隙率较低的多孔介质中,盐度扩散的速度明显比热扩散的速度快,盐指很快触及上下壁面,使得上下层的盐度梯度迅速减小,这是与非多孔介质具有明显差异之处. 关键词： 多孔介质 双扩散对流 盐指     

Explicit analytical solutions of the anisotropic Brinkman model for the natural convection in porous media (II)

Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model—an improved Darcy model—describing the natural convection in porous media. Besides their important theoretical meaning (for example, in analyzing the non-Darcy and anisotropic effects on the convection), such analytical solutions can be the benchmark solutions that can promote the development of computational heat and mass transfer. Some solutions considering the anisotropic effect of permeability have been given previously by the authors, and this paper gives solutions including the anisotropic effect of thermal conductivity and the effect of heat sources.     

Explicit analytical solutions of the anisotropic Brinkman model for the natural convection in porous media (Ⅱ)

Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model―an improved Darcy model―describing the natural convection in porous media. Besides their important theoretical meaning (for example, in analyzing the non-Darcy and anisotropic effects on the convection), such analytical solutions can be the benchmark solutions that can promote the development of computational heat and mass transfer. Some solutions considering the anisotropic effect of permeability have been given previously by the authors, and this paper gives solutions including the anisotropic effect of thermal conductivity and the effect of heat sources.     

Characteristic regimes of premixed gas combustion in high-porosity micro-fibrous porous media

Dynamical behaviour of the premixed flame propagating in the inert high-porosity micro-fibrous porous media has been studied numerically. Effects of mixture filtration velocity, equivalence ratio and burner transverse size on the flame structure have been investigated and the regions of existence of different combustion regimes have been determined. It was found that the influence of the hydrodynamic instability on the flame dynamics is significant in the case of the moderate and high filtration velocities and this effect is negligible at the low velocities. At the moderate filtration velocities the effect of hydrodynamic instability manifests in the flame front deformation and in particular in the flame inclination. It was found that the flame can be stabilized within the whole interval of the filtration gas velocity, whereas in the ordinary porous media the standing wave is settled only at fixed value of gas filtration velocity. This finding is in line with recent experimental results on combustion in micro-fibrous porous media (Yang et al., Combust. Sci. Tech. 181 (2009), 1–16). Possible physical interpretation of the flame anchoring effect may be given on the base of present numerical analysis. At the high filtration velocities the hydrodynamic instability manifests itself in periodical appearance of the moving wrinkles on the flame front surface which forms non stationary high temperature trailing spots behind the leading part of the flame front. Such dynamics may be associated with splitting wave structures which were revealed in previous experiments (Yang et al., Combust. Sci. Tech. 181 (2009), 1–16).     

Modeling of heterogeneous combustion in porous media under free convection

A mathematical model and a numerical method, based on the combination of explicit and implicit finite difference schemes, have been developed for investigating the unsteady gas flows in porous objects with zones of heterogeneous combustion when gas pressure at object boundaries is known. Used approach enables to solve problems of filtration combustion for both forced filtration and free convection, so it can be efficiently applied for modeling the combustion zones in porous media, which may arise from natural or man-caused disasters. One-dimensional unsteady processes of heterogeneous combustion in porous object under free convection have been investigated using numerical experiment. Two regimes of combustion wave propagation have been revealed – wave movement up and down in the object – and it is shown that these regimes are significantly different in degree of burn of solid combustible material, the temperature in the combustion zone and propagation velocity of combustion wave.     

Slip boundary conditions and through flow effects on double-diffusive convection in internally heated heterogeneous Brinkman porous media

A model for double-diffusive convection in a heterogeneous porous layer with a constant throughflow is explored, with penetrative convection being simulated via an internal heat source using the Brinkman model. In particular, we analyse the effect of slip boundary conditions on the stability of the model. Because of the many applications in micro-electro-mechanical systems (MEMS) and other microfluidic devices, a study of this problem is necessary. Both linear instability analysis and nonlinear stability analysis are employed. We accurately analyse when stability and instability will commence and determine the critical Rayleigh number as a function of the slip coefficient.     

A random field model for anomalous diffusion in heterogeneous porous media

Heterogeneity, as it occurs in porous media, is characterized in terms of a scaling exponent, or fractal dimension. A feature of primary interest for two-phase flow is the mixing length. This paper determines the relation between the scaling exponent for the heterogeneity and the scaling exponent which governs the mixing length. The analysis assumes a linear transport equation and uses random fields first in the characterization of the heterogeneity and second in the solution of the flow problem, in order to determine the mixing exponents. The scaling behavior changes from long-length-scale dominated to short-length-scale dominated at a critical value of the scaling exponent of the rock heterogeneity. The long-length-scale-dominated diffusion is anomalous.     

Numerical simulation for separation of multi-phase immiscible fluids in porous media

Based on a lattice Boltzmann method and general principles of porous flow, a numerical technique is presented for analysing the separation of multi-phase immiscible fluids in porous media. The total body force acting on fluid particles is modified by axiding relative permeability in Nithiarasu＇s expression with an axiditional surface tension term. As a test of this model, we simulate the phase separation for the case of two immiscible fluids. The numerical results show that the two coupling relative permeability coefficients K12 and K21 have the same magnitude, so the linear flux-forcing relationships satisfy Onsager reciprocity. Phase separation phenomenon is shown with the time evolution of density distribution and bears a strong similarity to the results obtained from other numerical models and the flows in sands. At the same time, the dynamical rules in this model are local, therefore it can be run on massively parallel computers with well computational efficiency.     

A new method for deriving analytical solutions of partial differential equations — Algebraically explicit analytical solutions of two-buoyancy natural convection in porous media

Analytical solutions of governing equations of various phenomena have their irreplaceable theoretical meanings. In addition, they can also be the benchmark solutions to verify the outcomes and codes of numerical solutions, and even to develop various numerical methods such as their differencing schemes and grid generation skills as well. A hybrid method of separating variables for simultaneous partial differential equation sets is presented. It is proposed that different methods of separating variables for different independent variables in the simultaneous equation set may be used to improve the solution derivation procedure, for example, using the ordinary separating method for some variables and using extraordinary methods of separating variables, such as the separating variables with addition promoted by the first author, for some other variables. In order to prove the ability of the above-mentioned hybrid method, a lot of analytical exact solutions of two-buoyancy convection in porous media are successfully derived with such a method. The physical features of these solutions are given. Supported by the National Natural Science Foundation of China (Grant No. 50576097) and the National Basic Research Development Program of China (Grant No. 2007CB206902)     

缝洞型介质流动模拟的多尺度分解法

缝洞型介质通常具有非均质性强、结构多尺度的特征.传统数值方法在解决此类多尺度流动问题时,难以兼顾计算精度与计算效率,无法实际应用.对此,本文提出了多孔介质流体流动的多尺度分解法,并应用于缝洞介质流动模拟,能够大幅减小计算的复杂度,同时,可以通过控制均化程度控制计算精度.该方法将求解空间分为若干个子空间的正交直和,从而获得一个近线性的计算复杂度;以分层计算的方式实现了快速计算,另外这种方法是一种无网格方法,具有较好的地层适应性.同时,采用离散缝洞模型简化缝洞结构,进一步提高了计算效率.详细阐述了基于多尺度分解法的多孔介质流体流动数值计算格式的建立,重点介绍了如何在不同的层次上计算基函数.数值结果表明,本文提出的计算方法不仅能够准确捕捉多孔介质中的精细流动特征,而且具有很高的计算效率,是一种有效的流动模拟方法.     

三维有序排列多孔介质对流换热的数值研究

利用CFD软件数值研究了颗粒三维有序堆积多孔介质的对流换热问题. 采用颗粒直径分别为14 mm,9.4 mm和7 mm的球形颗粒有序排列构成多孔介质骨架,在多孔骨架的上方有一恒热流密度的铜板. 采用流固耦合的方法研究了槽通道内温度分布和局部对流换热系数的分布以及对流换热的影响因素. 研究结果表明:热渗透的厚度和温度边界层的厚度在流动方向上逐渐增大,并且随流量的增加而减小;当骨架的导热系数比较高时,对流换热随颗粒直径的减小而略有增大;对流换热系数随聚丙烯酰胺溶液浓度的增大而减小,黏性耗散减弱了对流换热. 关键词： 多孔介质 温度场 局部对流换热系数 数值模拟     

Numerical investigation of the partial oxidation process in porous media based reformer

Numerical investigation of the thermal partial oxidation process of Methane in porous media based reformer is performed. A finite volume based CFD code, including radiation modeling, in combination with a detailed chemical kinetics scheme is used to perform the numerical simulation. A heterogeneous approach for the heat transport modeling in porous media (separate coupled energy equations for the gas and solid phases) was used. Validation of the model with experimental data is also performed. The model was able to predict the temperature behavior in the reformer reasonably well. However, the concentrations of H₂ and CO were under predicted while the H₂O concentration was over predicted.     

封闭腔内纳米流体强化自然对流换热的数值模拟

采用F luen软件对封闭腔内Cu-H2O纳米流体强化自然对流换热进行了数值模拟,重点分析Cu纳米粒子添加量和Gr数对换热性能的影响,并解释其换热机理。研究结果表明:在水基液中加入Cu纳米粒子可以显著提高基液的自然对流换热特性。对于一给定的Gr数,随着纳米粒子质量分数的增加,纳米流体的速度组成部分增加,纳米流体质量分数越大,x方向和y方向的速度峰越大,因此加速了流体中能量传输。另一方面,随着Gr数的增加,流线图中旋涡逐渐变大,流线间强度增加,说明换热效果逐渐增强。当Gr数较小时,传热主要是由热壁和冷壁之间的热传导引起的,随着Gr数的增大,换热逐渐变为由对流换热占主导地位。     

The propagation of ultrasound in porous media

The equations of Ying and Truell, and Waterman and Truell, describing the propagation of ultrasound in two-phase materials are solved numerically for porous solids, and are found to give unphysical results for high porosity. A new self-consistent theory, which can be solved analytically, is presented and is shown to have reasonable behaviour at high porosity.     

复杂多孔介质腔体内自然对流换热的数值研究

采用曲线坐标系下压力与速度耦合的SIMPLEC算法,数值研究复杂多孔介质腔体内的自然对流换热问题.腔体的曲面温度分别保持恒定,上下表面绝热.在曲线坐标系中用有限容积法离散方程,并采用Brinkman扩展达西模型及局部非热平衡模型求解,综合研究Rayleigh数,Darcy数、孔隙率等参数对腔体内自然对流换热的影响.计算结果表明:Rayleigh数和Darcy数的影响最大而孔隙率的影响很小,同时存在使得腔体内换热达到最强的最佳纵横比.     

Calculation of the permeability of porous media using hydrodynamic cellular automata

The permeability of two-dimensional porous media is calculated numerically as a function of porosity using the hydrodynamic cellular automata (lattice gas) approach. Results are presented for systems with up to 22 million sites (8192×2688). For randomly distributed solid obstacles whose macroscopic dimensions are much longer than the mean free path of particles in the fluid, the permeability varies with porosity as (–0.6)/(1–) for>0.7. When the solid obstacles are much smaller than the mean free path of particles in the fluid, i.e., when they form a dust of point objects, then such a relationship no longer holds and the permeability is more than an order of magnitude smaller than for the former case. The program used for the simulations is discussed and a listing is presented in the Appendix which achieved a sustained speed of 185 million sites updated per second on a single processor of the Cray-YMP. (On a Sun Sparc Workstation, the same program ran about 100 times slower.)     

A multi-length-scale theory of the anomalous mixing-length growth for tracer flow in heterogeneous porous media

We develop a multi-length-scale (multifractal) theory for the effect of rock heterogeneity on the growth of the mixing layer of the flow of a passive tracer through porous media. The multifractal exponent of the size of the mixing layer is determined analytically from the statistical properties of a random velocity (permeability) field. The anomalous diffusion of the mixing layer can occur both on finite and on asymptotic length scales.     

用格子玻尔兹曼方法研究流动-反应耦合的非线性渗流问题

根据格子玻尔兹曼计算技术以及相应渗流理论，对多孔介质内流动-反应(矿物介质的溶解等)耦合这一非线性渗流问题进行了数值研究，计算结果与解析解基本符合.数字图像重构技术反映的结果表明流体流动和反应之间可以发生强烈的耦合和反耦合作用，同时可以形成条带结构这一自组织现象，与实验和其他理论分析结果符合也很好. 关键词： 非线性渗流 耦合反应 数值模型