Mathematical model for axisymmetric steady flow within layered structures with finite or infinitely high bulk viscosity

A mathematical model was developed for viscous incompressible medium; this model comprises a small parameter for regularization of ill-posed problem. Starting from the analogy with strain problems of axisymmetric laminar structures which include the elastic orthotropic and elastic volume-incompressible layers with a connection to viscous laminar fluid flow, we have developed a method providing a single algorithm for computation of velocity field, stresses, and other parameters of laminar composite material. The example of calculation for the binding agent flow during pultrusion formation is presented.     

Response of axisymmetric separated flow to its spatially localized perturbation

The flow past an axisymmetric body with laminar boundary-layer separation in a low-velocity air stream has been studied. The hot-wire technique was employed to identify the variation of velocity field induced by a local stationary perturbation of separation region at the stern of the experimental model. A large-scale influence upon the near-wall flow due to a cylinder roughness element provided on the model surface was observed. The obtained data substantiate the possibility of controlling the laminar boundary-layer separation on an axisymmetric body using a local external forcing.     

钝体驻定湍流扩散火焰的数值研究——燃烧模型比较

分别采用标量联合的概率密度函数方法、稳态火焰面模型、Euler非稳态火焰面模型和基于有限体积/Monte Carlo混合算法的完备PDF模型对钝体驻定的Sydney湍流扩散火焰HM1进行数值模拟,以比较不同燃烧模型的性能,并比较标量联合的概率密度函数方法和Euler非稳态火焰面模型对氮氧化物排放预测的差异.计算结果和实验数据的比较表明,采用概率密度函数方法计算化学反应可以得到更好的结果但计算量较大,而用火焰面模型求解计算量较小,在接近完全燃烧的情形下,其计算结果比较合理.     

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采用FLUENT软件分别对外加均匀横向磁场的等截面三维充分发展液态金属管流的层流模型和低雷诺数湍流Lam/Bremhost(LB)模型进行了数值模拟,分析了外加磁场对普通方管LB模型速度分布和压降的影响。比较在相同哈特曼数下,层流和湍流模型方管截面上速度分布和管道中MHD压降。其中,对电流的计算采用磁感应方程来求得。数值模拟结果证明了用低雷诺数LB湍流模型解决方管磁流体流动的可行性。通过层流模型和湍流模型的对比可知,层流模型有较短的入口长度,但管内流体的压降却很大;而湍流模型管内速度更加平均化,管内压降较小,但管内入口长度较长。     

Trajectories of para- and freeomagnetic particles in HGMS filters with axial configurations

The trajectories of para-and ferromagnetic particles with velocities between 0.04 and 2.5 cm s⁻¹ have been investigated in an HGMS model system with axial configuration. A single-wire system has been observed by a TV system. The trajectories were compared with the ideal (inviscid flow) and laminar (viscous flow) model. The results agree with laminar flow model.     

An elementary model for the validation of flamelet approximations in non-premixed turbulent combustion

The fundamental soundness of three flamelet models for non-premixed turbulent combustion is examined on the basis of their performance in an idealized model problem that merges ideas from the laminar asymptotic theory for non-premixed flames and rigorous homogenization theory for the diffusion of a passive scalar. The overall flame configuration is stabilized by a mean gradient in the passive scalar: large Damköhler number asymptotics results are available for the laminar case to quantify the finite-rate effects that cause the flame to depart from its equilibrium state; the same results can also be used to incorporate higher-order corrections in the approximation of the reactive variables in terms of the passive scalar. The use of such flamelet approximations has been extended well beyond the laminar regime as they lie at the core of practical strategies to simulate non-premixed flames in the turbulent regime: the flamelet representation avoids the problem of turbulence closure for the reactive variables by replacing it by the presumably much simpler closure problem for a passive scalar. It is precisely the validity of this substitution outside the laminar regime that is addressed here in the idealized context of a class of small-scale periodic flows for which extensive rigorous results are available for the passive scalar statistics. Results for this simplified problem are reported here for significant wide ranges of Peclet and Damköhler numbers. Asymptotic convergence is observed in terms of the Damköhler number, with a convergence rate that is found to match the laminar predictions and appears relatively insensitive to the Peclet number. The passive scalar dissipation plays a key role in achieving higher-order corrections for the finite-rate case: replacing its pointwise value by an averaged value is convenient practically and can be rigorously motivated for the class of flows studied here, but while it does achieve an overall improvement over the lower-order equilibrium model, the simplification compromises the higher asymptotic convergence observed with the original finite-rate flamelet model with exact local dissipation.(Some figures in this article are in colour only in the electronic version; see www.iop.org)     

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With the uniform charge density in the magnetically insulated transmission line (MITL) of parallel plate, a laminar flow model with pressure balance and a new model without the assumption of laminar flow and pressure balance are solved analytically, respectively. The results of laminar flow model and non-laminar flow model are compared. It is shown that the charge density is smaller and electric field, magnetic field on anode is bigger in laminar flow model as without radial velocity of electrons. Then, the result of particle-in-cell simulation is compared for the two theories and shows that the accuracy of non-laminar model is higher than laminar model. Finally, the pressure balance equation and two models of laminar and non-laminar with the uniform charge density have been promoted to coaxial MITL and cone MITL.     

均匀电荷密度下的磁绝缘理论研究

在平行板磁绝缘传输线中均匀电荷密度下,分别对压力平衡下的修正层流模型和非压力平衡和非层流模型进行了求解,比较了两种理论模型下的结果。分析表明：相对于非层流模型而言,层流模型因未考虑径向速度,其电荷密度偏低,阳极电场、阳极磁场及阳极电流都偏大。此外,粒子模拟结果显示非层流模型具有更高的精度。最后,对压力平衡条件、均匀电荷密度下的层流以及非层流模型,从平行板理论推广到一般构型。     

层流预混庚烷火焰中PAHs的形成与机理的简化

本文使用详细的化学反应机理模拟了C7H16／空气层流预混火焰中多环芳烃的生成动力学过程．反应机理包括108种组分的572个基元反应．通过数值计算分析了层流预混火焰的结构和主要反应物、中间物质和反应产物的浓度变化,并对A1-A4组分的反应灵敏度进行了分析。并初步得到可以用于CFD的简化机理．     

1-庚烯/空气的高压层流火焰传播研究

本文使用定容圆柱形燃烧弹,在初始温度373 K和初始压力1、2、5、10 atm的条件下,对当量比从0.7到1.5的1-庚烯/空气混合物的层流火焰传播进行了研究.利用记录的纹影图像处理得到层流火焰传播速度和马克斯坦长度.基于先前报道的1-己烯燃烧反应动力学模型,发展了1-庚烯的模型.该模型验证了本工作测量的1-庚烯层流火焰传播速度数据及文献中的1-庚烯着火延迟时间数据.通过开展敏感性分析和路径分析,帮助理解了1-庚烯在不同压力下的高温化学及其对层流火焰传播的影响.另外,比较了1-庚烯/空气和先前报道的正庚烷/空气的层流火焰传播.由于更强的放热性及反应活性,1-庚烯/空气的层流火焰传播速度在绝大多数条件下均快于正庚烷/空气的结果.     

竖壁膜状凝结过程的相似解

本文建立了含有液膜和汽膜的竖壁凝结物理模型和基于边界层方程组的数学模型，应用相似理论进行了无因次变换，确定了无因次方程的系数及变换函数的形式，并对控制方程组进行了数值求解，推导了考虑液膜对流因素的竖壁膜状凝结局部努谢尔特数的表达式，进而得出了雷诺数范围较宽的竖壁膜状凝结准则的统一表达式。     

飞行器低Reynolds数层流分离理论探讨

低Reynolds数流动由于自身特点导致气动特性严重恶化,非定常、非线性效应突出且预测困难,加之相关基础理论研究不足,给以临近空间低速飞行器和高性能微小型飞行器为代表的低Reynolds数飞行器的开发和研制带来了瓶颈和挑战.首先概述了飞行器低Reynolds数的范畴、低Reynolds数空气动力学的主要问题与挑战.随后从低Reynolds数层流分离基础理论出发,依次介绍了低Reynolds数层流分离经典理论、低Reynolds数层流分离非定常流动特性、低Reynolds数后缘层流分离泡.在此基础上,通过对经典长层流分离泡与后缘层流分离泡力学特性的差异以及随攻角和Reynolds数的演化规律的详细分析,逐步揭示了一些低Reynolds数复杂气动效应的本质,如小攻角升力系数的非线性效应,翼型随Reynolds数下降气动特性的二次恶化效应等.最后对低Reynolds数流动基础理论的发展过程进行了总结,并对层流分离诱导转捩及再附效应等复杂流动问题进行了展望.      

空气横掠波纹管束流动与传热性能的数值模拟

本文应用层流模型和湍流模型的数值模拟方法,对空气外掠8排波纹管束时的流动与传热性能进行了研究,并将数值结果与实验结果进行了对比,结果表明:层流模型数值模拟结果较湍流更接近于实验值。同时,对两种模型的数值模拟结果拟合出了Nu-Re的关联式。     

How fast can we burn, 2.0

We review the state of the art in measurements and simulations of the behavior of premixed laminar and turbulent flames, subject to differential diffusion, stretch and curvature. The first part of the paper reviews the behavior of premixed laminar flames subject to flow stretch, and how it affects the accuracy of measurements of unstrained laminar flame speeds in stretched and spherically propagating flames. We then examine how flow field stretch and differential diffusion interact with flame propagation, promoting or suppressing the onset of thermodiffusive instabilities. Secondly, we survey the methodology for and results of measurements of turbulent flame speeds in the light of theory, and identify issues of consistency in the definition of mean flame speeds, and their corresponding mean areas. Data for methane at a single operating condition are compared for a range of turbulent conditions, showing that fundamental issues that have yet to be resolved for Bunsen and spherically propagating flames. Finally, we consider how the laminar flame scale response of flames to flow perturbations interacting with differential diffusion leads to very different outcomes to the overall sensitivity of the burning rate to turbulence, according to numerical simulations (DNS). The paper concludes with opportunities for future measurements and model development, including the perennial recommendation for robust archival databases of experimental and DNS results for future testing of models.     

A Four-Equation Eddy-Viscosity Approach for Modeling Bypass Transition

It is very important to predict the bypass transition in the simulation of flows through turbomachinery. This paper presents a four-equation eddy-viscosity turbulence transition model for prediction of bypass transition. It is based on the SST turbulence model and the laminar kinetic energy concept. A transport equation for the non-turbulent viscosity is proposed to predict the development of the laminar kinetic energy in the pre-transitional boundary layer flow which has been observed in experiments. The turbulence breakdown process is then captured with an intermittency transport equation in the transitional region. The performance of this new transition model is validated through the experimental cases of T3AM, T3A and T3B. Results in this paper show that the new transition model can reach good agreement in predicting bypass transition, and is compatible with modern CFD software by using local variables.     

Detailed and simplified kinetic models of n-dodecane oxidation: The role of fuel cracking in aliphatic hydrocarbon combustion

A detailed kinetic model is proposed for the combustion of normal alkanes up to n-dodecane above 850 K. The model was validated against experimental data, including fuel pyrolysis in plug flow and jet-stirred reactors, laminar flame speeds, and ignition delay times behind reflected shock waves, with n-dodecane being the emphasis. Analysis of the computational results reveal that for a wide range of combustion conditions, the kinetics of fuel cracking to form smaller molecular fragments is fast and may be decoupled from the oxidation kinetics of the fragments. Subsequently, a simplified model containing a minimal set of 4 species and 20 reaction steps was developed to predict the fuel pyrolysis rate and product distribution. Combined with the base C₁-C₄ model, the simplified model predicts fuel pyrolysis rate and product distribution, laminar flame speeds, and ignition delays as close as the detailed reaction model.     

Analysis and measurement of candle flame shapes

A combined analytical and experimental study was performed to determine the length and width of a candle flame. Measurements were made of laminar steady flames from photographs of straight-wick candles composed of n-tetracosane and normal paraffin waxes. The wicks studied ranged in diameter from about 1 to 9 mm, and in height from about 2 to 10 mm, with aspect ratios (diameter to length) of 0.1 to 2. The flame length from the pool surface and the flame width at the top of the wick were found. It was also noted and recorded that the flame attachment point along the vertical wick varied. The attachment point was found to depend on the aspect ratio of the wick. A model based on stagnant layer burning for a finite cylinder was used, along with the Roper laminar burner model for flame height. With slight adjustment to a constant, the width of the flame was well predicted, and the prediction for the flame height was about 60% too high and offset. In addition, the model gave insight to produce an accurate simple correlation for flame height in terms of wick aspect ratio and Rayleigh number.     

A theoretical and numerical evaluation of the steady-state burning rate of vertically oriented PMMA slabs

The steady state burning rate of vertically oriented slabs of poly-methyl-methacrylate (PMMA) is numerically investigated. Model predictions are compared with measurements and results of the laminar boundary layer (LBL) theory. The numerical model provides a solution of the Favre-averaged Navier–Stokes equations coupled with sub-models for turbulence, combustion, soot production and radiation. The modelling of condensed phase processes is based on the one-dimensional heat transfer equation and pyrolysis is treated as a phase change using the latent heat approach. Results show that the pyrolysing region can be divided into three regions. In the laminar part of the flow (Gr _x < 4.3 × 10⁷), the predicted normalised burning rate, [mdot]″ _p x/μ_∞, is a power-law function of Gr _x with an exponent close to that of the LBL theory, surface re-radiation being the primary source of discrepancies. From the LBL theory for free flow, it is demonstrated that the local burning rate is inversely proportional to the shear velocity gradient. This is globally confirmed by numerical model results. At Gr _x = 4.3 × 10⁷ the change in slope of the burning rate observed experimentally, which indicates the end of the laminar flow region, is reproduced numerically. From Gr _x = 2.5 × 10⁹ model results show that the surface mass flux of pyrolyzate increases with x, in agreement with experimental data in literature.     

Experimental and kinetic study of 2,4,4-trimethyl-1-pentene and iso-octane in laminar flames

Laminar flame speeds of 2,4,4-trimethyl-1-pentene are investigated at equivalence ratios of 0.7–1.6, initial temperatures of 298–453 K and initial pressures of 0.1–0.5 MPa. The comparison between 2,4,4-trimethyl-1-pentene and iso-octane is also performed. Results show that 2,4,4-trimethyl-1-pentene has faster laminar flame speed than iso-octane. Chemical kinetic models (Metcalfe model, Modified model I) were tested against the present experimental data. The laminar flame speeds are apparently over-estimated by the Metcalfe model and under-predicted by the Modified model I. Therefore, high-level quantum mechanical calculations were used to revise the Modified model I to obtain Modified model II and it can give fairly good prediction at various conditions on laminar flame speeds. In addition, the chemical kinetic analysis was conducted. The analysis indicates both thermal and kinetic effects result in the discrepancy of laminar flame speeds between 2,4,4-trimethyl-1-pentene and iso-octane. Furthermore, IC₄H₈ plays a dominant role in laminar flame speeds of 2,4,4-trimethyl-1-pentene and iso-octane.     

Measurement of unstable burning velocities of iso-octane–air mixtures at high pressure and the derivation of laminar burning velocities

A new technique is reported for measuring burning velocities at high pressures in the final stages of two inwardly propagating flame kernels in an explosion bomb. The flames were initiated at diametrically opposite spark electrodes, close to the wall, in quiescent mixtures. Measurements of pressure and flame kernel propagation speeds by high-speed photography showed the burning velocities to be elevated above the corresponding laminar burning velocities as a result of the developing flame instabilities. The enhancement increased with increase in pressure and decreased with increase in Markstein number. When the Markstein number was negative, instabilities could be appreciable, as could the enhancement. For the iso-octane–air mixtures investigated, where the mixtures had well-characterised Markstein numbers or critical Peclet numbers at the relevant pressures and temperatures, it was possible to explain the enhancement quantitatively by the spherical explosion flame instability theory of Bechtold and Matalon, provided the critical Peclet number was that observed experimentally, and allowance was made for the changing pressure. With this theoretical procedure, it was possible to derive values of laminar burning velocity from the measured values of burning velocity over a wide range of equivalence ratios, pressures, and temperatures. The values became less reliable at the higher temperatures and pressures as the data on Markstein and critical Peclet numbers became less certain. It was found that with iso-octane as the fuel the laminar burning velocity decreased during isentropic compression.