燃烧学讲义（10湍流燃烧）

错误！未找到图形项目。 0. 绪论 1. 燃料 2. 燃料的燃烧计算 3. 输运现象[5] REF _Ref224654757 \r \h [7] MACROBUTTON MTEditEquationSection2 Equation Chapter (Next) Section 1[10] 输运什么呢？质量、动量、能量。The subject of transport phenomena includes three closely 4. 化学动力学基础 5. 燃烧学基本方程 任何一门成熟的学科都有它自己的模型体系，它能够在数学上描述这门学科所涉及的所有特征。人们通过解方程就可以预测这门学科所涉及的所有现象，比如在天体力学中通过解经典力学方程，就能确定行星（如海王星）的轨道；在分子物理中通过解薛定谔方程，就可以确定分子光谱。 这章介绍燃烧学基本方程。它是在流体力学方程基础上得到的。The dynamics and thermodynamics of a chemically reacting flow are governed by the conservation laws of mass, momentum, energy, and the concentration of the individual species. In this chapter, we shall first present a derivation of these conservation equations based on control volume considerations. 6. 预混可燃气着火理论 7. 层流预混可燃气火焰传播理论 8. 层流非预混燃烧 9. 火焰稳定 这一章与第6章的着火相对，考虑熄火问题。 10. 湍流燃烧 Most flows in practical combustion devices are turbulent, characterized by the presence of rapid, random fluctuations of the flow velocity and scalar properties at a given point in space. Nearly all mobile and stationary power plants operate in this manner because turbulence increases the mass consumption rate of the reactants, or reactant mixture, to values much greater than those that can be obtained with laminar fl ames. A greater mass consumption rate increases the chemical energy release rate and hence the power available from a given combustor or internal engine of a given size. Indeed, few combustion engines could function without the increase in mass consumption during combustion that is brought about by turbulence. 与清晰明亮的光滑层流火焰相比，湍流火焰较厚、皱折、火焰面模糊不清，但传播速度比层流大好多倍。随着湍流强度增加, 火焰传播速度增加，火焰更短，燃烧室尺寸更紧凑，向外界散热小，经济性更好。缺点是燃烧噪音很大。图 10‑1illustrates various canonical flow configurations that are often encountered in practical combustion systems: unconfined flows such as jets and mixing layers, semiconfined flows over solid surfaces, confined flows in ducts, reverse flows in wakes, and buoyant flows. 图 10‑1Schematic showing various classes of turbulent flows. Turbulence remains one of the most challenging and unsolved problems in physics. The complexity further increases when chemical reactions are also present. Because of these difficulties, studies on turbulent combustion have been mostly empirical until the late 1970s. Advances since then have identified fruitful paths for rational investigation. In this chapter we present a brief account of the current state of understanding. 10.1. 湍流概述 10.1.1. 湍流的产生 The most famous experiment on the transition to turbulence is the Reynolds experiment of a flow in a circular pipe (circular Poiseuille flow). It is interesting to go back to Reynolds’s article concerning one experiment where he introduced a fine line of dye upstream at the centre of the pipe inlet (which has a trumpet shape): The general results were as follows: (1) When the velocities are sufficiently low, the streak of colour extended in a beautiful straight line through the tube. (2) If the water in the tank had not quite settled to rest, at sufficiently low velocities, the streak would shift about the tube, but there was no appearance of sinusoity. (3) As the velocity was increased by small stages, at some point in the tube, always at considerable distance from the trumpet or intake, the colour band would all at once mix up with the surrounding water, and fill the rest of the tube with a mass of coloured water (...). Any increase in the velocity caused the point of break down to approach the trumpet, but with no velocities that were tried did it reach this. On viewing the tube by the light of an electric spark, the mass of colour resolved itself into a mass of more ore less distinct curls, showing eddies (. . . ). Reynolds introduced in 1883 the non -dimensional parameter MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.1) and showed experimentally that there was a critical value of Re above which the flow inside the tube became turbulent. U is an average velocity of the flow across the tube section (bulk velocity), D the diameter of the tube, and ν the molecular viscosity. The critical value Rc found by Reynolds was of the order of 2000. For R < Rc , the flow remained regular (laminar), and for R > Rc it became turbulent. Turbulence can only develop in rotational flows: it is due to the existence of shear in a basic flow that small perturbations will develop, through various instabilities, and eventually degenerate into turbulence. 通常认为给定初始和边界条件，方程就有唯一的解。但人们发现，当雷诺数比较大，离初始时刻和边界比较远时，N-S方程的解对初始条件和边界条件很敏感。非线性的对流项对流场结构起了控制作用，这时任何微小的扰动（包括初边条件，流体物性的微小变化）都会发展起来，原有的流动状态遭到破坏，变成新的流动状态，或继续发生不稳定，直至变成湍流。Some of these instabilities, at least during the initial stage of their development, may be understood within the framework of linear-instability theory. The nonlinear instability studies may prove to be useful in the future in understanding transition to turbulence, but, to date, they are still in progress and have not led to a unified theory of transition. Extremely useful tools to understand the transition, and assess the various theories proposed to describe it, are direct-numerical simulations of Navier–Stokes equations. The growth of the disturbance can be limited by the finite viscosity of the fluid, which tends to damp the disturbance and thereby produce a stabilizing effect on the flow. If the viscous force is sufficiently large as compared to the inertial force, the damping is strong enough to render the flow stable and, hence, laminar. 10.1.2. 湍流特征 It can be said that a turbulent flow is a flow which is disordered in time and space. But this, of course, is not a precise mathematical definition. A common property which is required of them is that they should be able to mix transported quantities much more rapidly than if only molecular diffusion processes were involved. It is this latter property which is certainly the more important for people interested in turbulence because of its practical applications: the engineer, for instance, is mainly concerned with the knowledge of turbulent heat diffusion coefficients, or the turbulent drag (depending on turbulent momentum diffusion in the flow). The following definition of turbulence can thus be tentatively proposed and may contribute to avoiding the somewhat semantic discussions on this matter (在湍流燃烧问题中，湍流脉动对流场结构和燃烧速率起了很大的作用。在分析湍流燃烧问题之前，首先要认识湍流的特性。): (1)Firstly, a turbulent flow must be unpredictable, in the sense that a small uncertainty as to its knowledge at a given initial time will amplify so as to render impossible a precise deterministic prediction of its evolution. (2)Secondly, it has to satisfy the increased mixing property defined above. 湍流脉动要引起流场中动量，化学组分和能量的输运，而且湍流输运通量大约比分子输运通量大二至三个数量级，因此湍流燃烧的速度和强度都比层流燃烧大很多，了解湍流机理，并加以利用对工程设计有很大的指导意义。 (3)Thirdly, it must involve a wide range of spatial wave lengths(湍流中的尺度)。流动不稳定产生最大尺度的湍流运动，根据流动不稳定性理论，大尺度湍流运动仍是不稳定的，还会产生更小尺度的运动，这样也就把大尺度湍流运动的能量传递到更小尺度的运动。如此不断反复，直至产生最小尺度的湍流运动。在最小尺度的湍流运动中，雷诺数的数量级等于1，流动是稳定的，同时由于粘性作用很强。湍流运动本身也逐渐衰减，湍流脉动的能量最终耗散为热。上述的这个涡旋破碎和能量从大尺度向小尺度的传递过程，我们称为能量串级过程。流动不稳定产生最大尺度的湍流运动，在最小尺度的湍流运动，湍流能量耗散为热。 湍流中的尺度 湍流中的速度和状态参数都随空间位置 和时间t迅速脉动。我们可以把各种不同的流场参数都分解成平均值和脉动值之和，比如把流场中（ ，t）处的速度分解成 。把动能也分解为平均动能与脉动动能之和。用 代表脉动动能。湍流强度可用 表示，也可用相对值表示 。Weak turbulence corresponds to U’ / U < 1 and intense turbulence has U’ / U of the order unity. Most fl ows have at least one characteristic velocity, U , and one characteristic length scale, L , of the device in which the fl ow takes place. In addition there is at least one representative density ρ0 and one characteristic temperature T0 , usually the unburned condition when considering combustion phenomena. Thus, a characteristic kinematic viscosity ν0 = μ0 / ρ0 can be defi ned, where μ0 is the coeffi cient of viscosity at the characteristic temperature T0 . The Reynolds number for the system is then Re = UL / ν0 . It is interesting that ν is approximately proportional to T2 . Thus, a change in temperature by a factor of 3 or more, quite modest by combustion standards, means a drop in Re by an order of magnitude. Thus, energy release can damp turbulent fl uctuations. The kinematic viscosity ν is inversely proportional to the pressure P , and changes in P are usually small; the effects of such changes in ν typically are much less than those of changes in T Although a continuous distribution of length scales is associated with the turbulent flow, it is useful to focus on two widely disparate lengths that determine separate effects in turbulent fl ows. First, there is a length l0 , which characterizes the large eddies, those of low frequencies and long wavelengths; this length is sometimes referred to as the integral scale. Experimentally, l0 can be defi ned as a length beyond which various fl uid-mechanical quantities become essentially uncorrelated; typically, l0 is less than L but of the same order of magnitude. This length can be used in conjunction with U’ to defi ne a turbulent Reynolds number MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.2) which has more direct bearing on the structure of turbulence in fl ows than does Re. Large values of Rl can be achieved by intense turbulence, large-scale turbulence, and small values of ν produced, for example, by low temperatures or high pressures. The cascade view of turbulence dynamics is restricted to large values of Rl . From the characterization of U’and l0 , it is apparent that Rl < Re. The second length scale characterizing turbulence is that over which molecular effects are signifi cant; it can be introduced in terms of a representative rate of dissipation of velocity fl uctuations, essentially the rate of dissipation of the turbulent kinetic energy. This rate of dissipation, which is given by the symbol ε0 , is MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.3) is a representative value at a suitable reference point. This rate estimate corresponds to the idea that the time scale over which velocity fl uctuations (turbulent kinetic energy) decay by a factor of (1/ e ) is the order of the turning time of a large eddy. The rate ε0 increases with turbulent kinetic energy (which is due principally to the large-scale turbulence) and decreases with increasing size of the large-scale eddies. For the small scales at which molecular dissipation occurs, the relevant parameters are the kinematic viscosity, which causes the dissipation, and the rate of dissipation. The only length scale that can be constructed from these two parameters is the so-called Kolmogorov length (scale): MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.4) However, note that Therefore MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.5) This length is representative of the dimension at which dissipation occurs and defi nes a cut-off of the turbulence spectrum. For large Rl there is a large spread of the two extreme lengths characterizing turbulence. This spread is reduced with the increasing temperature found in combustion of the consequent increase in ν0 . 从能量串级的观点来看，the energy dissipated at the smallest eddies is transferred from the turbulent kinetic energy contained in eddies of the integral scale, and the rate of energy transfer ε0 is constant throughout the entire inertial subrange, so we have MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.6) where is the velocity of Kolmogorov scale. Considerations analogous to those for velocity apply to scalar fi elds as well, and lengths analogous to lk have been introduced for these fi elds. They differ from lk by factors involving the Prandtl and Schmidt numbers, which differ relatively little from unity for representative gas mixtures. Therefore, to a fi rst approximation for gases, lk may be used for all fi elds and there is no need to introduce any new corresponding lengths. An additional length, intermediate in size between l0 and lk , which often arises in formulations of equations for average quantities in turbulent fl ows is the Taylor length ( λ ) (应变率尺度), which is representative of the dimension over which strain occurs in a particular viscous medium. The strain can be written as ( U’ / l0 ). As before, the length that can be constructed between the strain and the viscous forces is MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.7) and then MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.8) In a sense, the Taylor microscale is similar to an average of the other scales, l0 and lk , but heavily weighted toward lk . Recall that there are length scales associated with laminar fl ame structures in reacting fl ows. One is the characteristic thickness of a premixed fl ame, δL . It may be expected, then, that the nature of the various turbulent fl ows, and indeed the structures of turbulent fl ames, may differ considerably and their characterization would depend on the comparison of these chemical and fl ow scales in a manner specifi ed by the following inequalities and designated fl ame type: The nature, or more precisely the structure, of a particular turbulent fl ame implied by these inequalities cannot be exactly established at this time. Thereason is that values of δL , lk , λ , or l0 cannot be explicitly measured under a given fl ow condition or analytically estimated. Many of the early experiments with turbulent fl ames appear to have operated under the condition δL < lk , so the early theories that developed specifi ed this condition in expressions for ST 相干结构（拟序结构）。 前面已经说了，我们可以把湍流看作随机过程，但测量和观察都表明，湍流不完全是随机的，湍流中有相干结构存在。所谓相干结构是指流场中重复出现的，有一定流场结构的组织，但相干结构在什么时间和什么地方出现是随机的，不同时刻出现的流场结构也不完全相同。相干结构（也称拟序结构）的存在会使流场中温度，化学组分或凝结相的分布发生变化，因而影响燃烧过程。 图 10‑2 Spark-shadowgraph of the mixing layer in a two-dimensional shear flow, showing the characteristics of coherent structures (Brown & Roshko 1974). 10.1.3. 湍流模拟（数学描述） 由于初边条件稍有变化，其解就差的很远，即使用今天速度最快和精度最高的计算机也很难分辨出这些变化。因此无论从实际应用，还是理论分析角度看，采用统计方法都是可取的。因为很难对初始条件和边界条件进行精确的控制。使方程给出唯一的解，我们可以假定初边条件仅仅在统计意义上给定，方程的解是一些统计量。化学反应湍流可以看作是一个随机过程，把注意力集中在给出随机参数的解。 湍流中的速度和状态参数都随空间位置 和时间t迅速脉动。最基本的统计描述方法是引进几率密度函数，如流场中某点（ ，t）第i方向速度分量的几率密度函数P(u )定义为速度分量u 在 和 之间的几率是 ，符号 表示在函数空间内的一个体积微元。除了定义几率密度函数P(u )，P( ),P(T)以外，还可以定义联合几率密度函数，如速度分量u 和密度 的联合几率密度函数 定义为，流场中某点（ ，t）速度分量 在u 至 之间，密度 在 至 之间的几率是 。从质量、动量、能量等守恒方程，我们可以推出联合几率密度函数 的方程。原则上说，联合几率密度函数的方程包含了湍流的所有统计信息，把湍流燃烧归结为这类方程的求解问题。但联合几率密度函数方程的求解却遇到了很大的困难。 在很多包含湍流问题的工程和实际应用中，我们感兴趣的流场信息是比较有限的，比如只须知道各种流场参数的平均值，参数在平均值周围的变化大小，以及不同参数之间相关的程度等。因此，我们可以把各种不同的流场参数都分解成平均值和脉动值之和，比如把流场中（ ，t）处的速度分解成 。如果平均值 随时间的变化很慢，我们可以把这种湍流近似看作是统计定常的。平均值与时间无关。对统计定常的随机过程，平均值可以用对时间求平均获得。对不满足统计定常的随机过程，平均值可以采用系综平均的方法获得。用平均方法推出的湍流平均量方程很简洁，分析也很方便。 Direct Numerical Simulation Reynolds-Averaged Navier–Stokes Models Large Eddy Simulation Probability Density Functions Closure of the Reaction Rate Term 10.2. 预混湍流燃烧 To examine the effect of turbulence on fl ames, and hence the mass consumption rate of the fuel mixture, it is best to fi rst recall the tacit assumption that in laminar fl ames the fl ow conditions alter neither the chemical mechanism nor the associated chemical energy release rate. Now one must acknowledge that, in many fl ow confi gurations, there can be an interaction between the character of the fl ow and the reaction chemistry. When a fl ow becomes turbulent, there are fl uctuating components of velocity, temperature, density, pressure, and concentration. The degree to which such components affect the chemical reactions, heat release rate, and fl ame structure in a combustion system depends upon the relative characteristic times associated with each of these individual parameters. In a general sense, if the characteristic time ( τc ) of the chemical reaction is much shorter than a characteristic time ( τm ) associated with the fl uid-mechanical fl uctuations, the chemistry is essentially unaffected by the fl ow fi eld. But if the contra condition ( τc>τm ) is true, the fl uid mechanics could infl uence the chemical reaction rate, energy release rates, and fl ame structure. Under premixed fuel–oxidizer conditions the turbulent fl ow fi eld causes a mixing between the different fl uid elements, so the characteristic time was given the symbol τm . In general with increasing turbulent intensity, this time approaches the chemical time, and the associated length approaches the fl ame or reaction zone thickness. Essentially the same is true with respect to nonpremixed fl ames. The fuel and oxidizer (reactants) in non-premixed fl ames are not in the same fl ow stream; and, since different streams can have different velocities, a gross shear effect can take place and coherent structures (eddies) can develop throughout this mixing layer. These eddies enhance the mixing of fuel and oxidizer. The same type of shear can occur under turbulent premixed conditions when large velocity gradients exist. The complexity of the turbulent reacting fl ow problem is such that it is best to deal fi rst with the effect of a turbulent fi eld on an exothermic reaction in a plug fl ow reactor. Then the different turbulent reacting fl ow regimes will be described more precisely in terms of appropriate characteristic lengths, which will be developed from a general discussion of turbulence. Finally, the turbulent premixed fl ame will be examined in detail. 10.2.1. 湍流对反应速率的影响 The effect of turbulence on the rate of an exothermic reaction is typical of those occurring in a turbulent fl ow reactor. Here, the fl uctuating temperatures and concentrations could affect the chemical reaction and heat release rates. Then, there is the situation in which combustion products are rapidly mixed with reactants in a time much shorter than the chemical reaction time. (This latter example is the so-called stirred reactorn.容积燃烧) In both of these examples, no fl ame structure is considered to exist. As an excellent, simple example of how fl uctuating parameters can affect a reacting system, one can examine how the mean rate of a reaction would differ from the rate evaluated at the mean properties when there are no correlations among these properties. In fl ow reactors, time-averaged concentrations and temperatures are usually measured, and then rates are determined from these quantities. Only by optical techniques or very fast response thermo couples could the proper instantaneous rate values be measured, and these would fl uctuate with time. 化学反应速率 在湍流流场中，温度和浓度都随在不断脉动，这里只考虑温度脉动的影响。把温度分解为 MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.9) 为在一个足够长的时间段内的积分平均： MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.10) In this hypothetical simplifi ed problem one assumes further that the temperature T fl uctuates with time around some mean represented by the form MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.11) where an is the amplitude of the fl uctuation and f ( t ) is some time-varying function in which MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.12) Ignoring the temperature dependence in the pre-exponential, one writes the instantaneous–rate constant as MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.13) and the rate constant evaluated at the mean temperature as MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.14) Dividing the two expressions, one obtains MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.15) Obviously, then, for small fl uctuations MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.16) The expression for the mean rate is written as MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.17) But recall MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.18) Examining the third term, it is apparent that MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.19) since the integral of the function can never be greater than 1. Thus, MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.20) If the amplitude of the temperature fl uctuations is of the order of 10% of the mean temperature （弱湍流）, one can take an = 0.1; and if the fl uctuations are considered sinusoidal, then MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.21) Thus for the example being discussed, MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.22) For most hydrocarbon fl ame or reacting systems the overall order of reaction is about 2, E / R is approximately 20,000 K , and the fl ame temperature is about 2000 K. Thus, MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.23) a 25% difference in the two rate constants. This result could be improved by assuming a more appropriate distribution function of T instead of a simple sinusoidal fl uctuation; however, this example— even with its assumptions—usefully illustrates the problem. Normally, probability distribution functions are chosen. If the concentrations and temperatures are correlated, the rate expression becomes very complicated. 10.2.2. 湍流与火焰相互作用 A turbulent fl ow fi eld dominated by largescale, low-intensity turbulence will affect a premixed laminar fl ame so that it appears as a wrinkled laminar fl ame. The fl ame would be contiguous throughout the front. As the intensity of turbulence increases, the contiguous fl ame front is partially destroyed and laminar fl amelets exist within turbulent eddies. Finally, at very high-intensity turbulence, all laminar fl ame structure disappears and one has a distributed reaction zone. Time-averaged photographs of these three fl ames show a very bushy fl ame front that looks very thick in comparison to the smooth thin zone that characterizes a laminar fl ame. However, when a very fast response thermocouple is inserted into these three fl ames, the fl uctuating temperatures in the fi rst two cases show a bimodal probability density function with well-defi ned peaks at the temperatures of the unburned and completely burned gas mixtures. But a bimodal function is not found for the distributed reaction case. To expand on the understanding of the physical nature of turbulent fl ames, it is also benefi cial to look closely at the problem from a chemical point of view, exploring how heat release and its rate affect turbulent fl ame structure. Damkohler numbers One begins with the characteristic time for chemical reaction designated τc , which was defi ned earlier. (Note that this time would be appropriate whether a fl ame existed or not.) Generally, in considering turbulent reacting fl ows, chemical lengths are constructed to be Uτc or U τc . Then comparison of an appropriate chemical length with a fl uid dynamic length provides a nondimensional parameter that has a bearing on the relative rate of reaction. Nondimensional numbers of this type are called Damkohler numbers and are conventionally given the symbol Da. An example appropriate to the considerations here is MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.24) where τm is a mixing (turbulent) time defi ned as ( l0 / U ), and the last equality in the expression applies when there is a fl ame structure. Following the earlier development, it is also appropriate to defi ne another turbulent time based on the Kolmogorov scale MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.25) For large Damkohler numbers, the chemistry is fast (i.e., reaction time is short) and reaction sheets of various wrinkled types may occur. For small Da numbers, the chemistry is slow and well-stirred flames （.容积燃烧）may occur. Frank-Kamenetskii numbers Two other nondimensional numbers relevant to the chemical reaction aspect of this problem [42] have been introduced by Frank-Kamenetskii and others. These Frank-Kamenetskii numbers (FK) are the nondimensional heat release MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.26) where Qp is the chemical heat release of the mixture and Tf is the fl ame (or reaction) temperature; and the nondimensional activation energy MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.27) also called the Arrhenius number. Combustion, in general, and turbulent combustion, in particular, are typically characterized by large values of these numbers. When FK 1 is large, chemistry is likely to have a large infl uence on turbulence. When FK 2 is large, the rate of reaction depends strongly on the temperature. It is usually true that the larger the FK 2 , the thinner will be the region in which the principal chemistry occurs. Thus, irrespective of the value of the Damkohler number, reaction zones tend to be found in thin, convoluted sheets in turbulent fl ows, for both premixed and non-premixed systems having large FK 2 . For premixed fl ames, the thickness of the reaction region has been shown to be of the order δL /FK 2 . Different relative sizes of δL /FK 2 and fl uid-mechanical lengths, therefore, may introduce additional classes of turbulent reacting fl ows. 湍流尺度与火焰形状 Most open flames created by a turbulent fuel jet exhibit a wrinkled fl ame type of structure. Indeed, short-duration Schlieren photographs suggest that these fl ames have continuous surfaces. Measurements of fl ames have been taken at different time intervals and the instantaneous fl ame shapes verify the continuous wrinkled fl ame structure. A plot of these instantaneous surface measurements results in a thick fl ame region ( 右图), just as the eye would visualize that a larger number of these measurements would result in a thick fl ame. Indeed, turbulent premixed fl ames are described as bushy fl ames. The thickness of this turbulent fl ame zone appears to be related to the scale of turbulence. Essentially, this case becomes that of severe wrinkling and is categorized by lk < δL< λ . Increased turbulence changes the character of the fl ame wrinkling, and fl amelets begin to form. These fl ame elements take on the character of a fl uid-mechanical vortex rather than a simple distorted wrinkled front, and this case is specifi ed by λ< δL , l0 . For δL << l0 , some of the fl amelets fragment from the front and the fl ame zone becomes highly wrinkled with pockets of combustion. To this point, the fl ame is considered practically contiguous. When l0<δL , contiguous fl ames no longer exist and a distributed reaction front forms. Under these conditions, the fl uid mixing processes are very rapid with respect to the chemical reaction time and the reaction zone essentially approaches the condition of a stirred reactor. In such a reaction zone, products and reactants are continuously intermixed. For a better understanding of this type of fl ame occurrence and for more explicit conditions that defi ne each of these turbulent fl ame types, it is necessary to introduce the fl ame stretch concept. 火焰拉伸 图 10‑3 Defl ection of the velocity vector through an oblique fl ame. Now with regard to stretch, consider fi rst a plane oblique fl ame. Because of the increase in velocity demanded by continuity, a streamline through such an oblique fl ame is defl ected toward the direction of the normal to the fl ame surface. The velocity vector may be broken up into a component normal to the fl ame wave and a component tangential to the wave (图 10‑3). Because of the energy release, the continuity of mass requires that the normal component increase on the burned gas side while, of course, the tangential component remains the same. A consequence of the tangential velocity is that fl uid elements in the oblique fl ame surface move along this surface. If the surface is curved (原因见下), adjacent points traveling along the fl ame surface may move either farther apart (fl ame stretch，) or closer together (fl ame compression). An oblique fl ame is curved if the velocity U of the approach fl ow varies in a direction y perpendicular to the direction of the approach fl ow（因为法向速度须持不变，等于SL，这导致y+dy点的切向速度增加，从而y和y+dy点两点的微元相互远离）. Strehlow showed that the quantity MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.28) which is known as the Karlovitz fl ame stretch factor, is approximately equal to the ratio of the fl ame thickness δL to the fl ame curvature. The Karlovitz school has argued that excessive stretching can lead to local quenching of the reaction. Klimov [50] , and later Williams [51] , analyzed the propagation of a laminar fl ame in a shear fl ow with velocity gradient in terms of a more general stretch factor MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.29) where Λ is the area of an element of fl ame surface, dΛ / dt is its rate of increase, and δL / SL is a measure of the transit time of the gases passing through the fl ame. Stretch ( K2 > 0) is found to reduce the fl ame thickness and to increase reactant consumption per unit area of the fl ame and large stretch (K2 >> 0) may lead to extinction. On the other hand, compression ( K2 < 0) increases fl ame thickness and reduces reactant consumption per unit incoming reactant area. These fi ndings are relevant to laminar fl amelets in a turbulent fl ame structure. Stability concerns Since the concern here is with the destruction of a contiguous laminar fl ame in a turbulent fi eld, consideration must also be given to certain inherent instabilities in laminar fl ames themselves. There is a fundamental hydrodynamic instability as well as an instability arising from the fact that mass and heat can diffuse at different rates; that is, the Lewis number (Le) is nonunity. In the latter mechanism, a fl ame instability can occur when the Le number ( α / D ) is less than 1. 图 10‑4Convergence–divergence of the fl ow streamlines due to a wrinkle in a laminar fl ame. Consider initially the hydrodynamic instability—that is, the one due to the fl ow—fi rst described by Darrieus [52] , Landau [53] , and Markstein [54] . If nowrinkle occurs in a laminar fl ame, the fl ame speed SL is equal to the upstream unburned gas velocity U0 . But if a minor wrinkle occurs in a laminar fl ame, the approach fl ow streamlines will either diverge or converge as shown in 图 10‑4. Considering the two middle streamlines, one notes that, because of the curvature due to the wrinkle, the normal component of the velocity, with respect to the fl ame, is less than U0 . Thus, the streamlines diverge as they enter the wrinkled fl ame front. Since there must be continuity of mass between the streamlines, the unburned gas velocity at the front must decrease owing to the increase of area. Since SL is now greater than the velocity of unburned approaching gas, the fl ame moves farther downstream and the wrinkle is accentuated. For similar reasons, between another pair of streamlines if the unburned gas velocity increases near the fl ame front, the fl ame bows in the upstream direction. It is not clear why these instabilities do not keep growing. Some have attributed the growth limit to nonlinear effects that arise in hydrodynamics. When the Lewis number is nonunity, the mass diffusivity can be greater than the thermal diffusivity. This discrepancy in diffusivities is important with respect to the reactant that limits the reaction. Ignoring the hydrodynamic instability, consider again the condition between a pair of streamlines entering a wrinkle in a laminar fl ame. This time, however, look more closely at the fl ame structure that these streamlines encompass, noting that the limiting reactant will diffuse into the fl ame zone faster than heat can diffuse from the fl ame zone into the unburned mixture. Thus, the fl ame temperature rises, the fl ame speed increases, and the fl ame wrinkles bow further in the downstream direction. The result is a fl ame that looks very much like the fl ame depicted for the hydrodynamic instability in 图 10‑4. The fl ame surface breaks up continuously into new cells in a chaotic manner, as photographed by Markstein [54] . There appears to be, however, a higher-order stabilizing effect. The fact that the phenomenon is controlled by a limiting reactant means that this cellular condition can occur when the unburned premixed gas mixture is either fuelrich or fuel-lean. It should not be surprising, then, that the most susceptible mixture would be a lean hydrogen–air system. 火焰对湍流的影响 The fl ames themselves can alter the turbulence. In simple open Bunsen fl ames whose tube Reynolds number indicates that the fl ow is in the turbulent regime, some results have shown that the temperature effects on the viscosity are such that the resulting fl ame structure is completely laminar. In all fl ames there is a large increase in velocity as the gases enter the burned gas state. Thus, it should not be surprising that the heat release itself can play a role in inducing turbulence. Such velocity changes in a fi xed combustion confi guration can cause shear effects that contribute to the turbulence phenomenon. Large mean velocity gradients are therefore produced. The streamlines in the unburned gas are defl ected away from the fl ame. There is no better example of some of these aspects than the case in which turbulent fl ames are stabilized in ducted systems. The growth of axial turbulence in the fl ame zone of these ducted systems is attributed to the mean velocity gradient resulting from the combustion. Regimes of turbulent combustion 图 10‑5Characteristic parametric relationships of premixed turbulent combustion. The Klimov–Williams criterion is satisfi ed below the heavy line lk = δL . Earlier it was stated that the structure of a turbulent velocity fi eld may be presented in terms of two parameters—the scale and the intensity of turbulence. The intensity was defi ned as the square root of the turbulent kinetic energy, which essentially gives a root-mean-square velocity fl uctuation U’ . Three length scales were defi ned: the integral scale l0 , which characterizes the large eddies; the Taylor microscale λ , which is obtained from the rate of strain; and the Kolmogorov microscale lk , which typifi es the smallest dissipative eddies. These length scales and the intensity can be combined to form not one, but three turbulent Reynolds numbers: , . From the relationship between l0 , λ , and lk previously derived it isfound that . There is now suffi cient information to relate the Damkohler number Da and the length ratios l0 / δL , lk / δL and l0 / lk to a nondimensional velocity ratio U’ / SL and the three turbulence Reynolds numbers. The complex relationships are given in 图 10‑5 and are very informative. The right-hand side of the fi gure has R λ >100 and ensures the length-scale separation that is characteristic of high Reynolds number behavior. The largest Damkohler numbers are found in the bottom right corner of the fi gure. Using this graph and the relationship it contains, one can now address the question of whether and under what conditions a laminar fl ame can exist in a turbulent fl ow. From solutions of the laminar fl ame equations in an imposed shear fl ow, Klimov [50] and Williams [51] showed that a conventional propagating fl ame may exist only if the stretch factor K2 is less than a critical value of unity. Modeling the area change term in the stretch expression as and recalling that one can defi ne the Karlovitz number for stretch in turbulent fl ames as But as shown earlier so that MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.30) The turbulent Karlovitz number is defined as MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.31) that is , the characteristic time ratio of the laminar flame to that of the Kolmogorov scale. From (10.31) we have (10.6) and MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.32) The heavy line in 图 10‑5 indicates the conditions δL = lk. Below and to the right of this line, the Klimov–Williams criterion is satisfi ed and wrinkled laminar fl ames may occur. The fi gure shows that this region includes both large and small values of turbulence Reynolds numbers and velocity ratios ( U’ / SL ) both greater and less than 1, but predominantly large Da. Above and to the left of the criterion line is the region in which lk<δL . According to the Klimov–Williams criterion, the turbulent velocity gradients in this region, or perhaps in a region defi ned with respect to any of the characteristic lengths, are suffi ciently intense that they may destroy a laminar fl ame. The fi gure shows U≥SL in this region and Da is predominantly small. At the highest Reynolds numbers the region is entered only for very intense turbulence, U≥ SL . The region has been considered a distributed reaction zone in which reactants and products are somewhat uniformly dispersed throughout the fl ame front. Reactions are still fast everywhere, so that unburned mixture near the burned gas side of the fl ame is completely burned before it leaves what would be considered the fl ame front. An instantaneous temperature measurement in this fl ame would yield a normal probability density function—more importantly, one that is not bimodal. 图 10‑6 Regime diagram for premixed turbulent combustion (Peters 2000). 注意图中为对数坐标。对应于Re = 1的直线实际上是log(u’/sL) = -log(l0/δL) + 0, 即Re = u’l0/(sLδL) = 100 =1 In defining KaL we have referenced the flame thickness to the Kolmogorov scale. A more refined indication of the presence of chemical reactivity within a Kolmogorov eddy is to reference the reaction zone thickness, δR, to lk. Since δR ∼ δL/Ze, we can then define a Karlovitz number based on δR as MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.33) Figure 11.3.1 plots log(u’/sL) versus log(l0/δL) for the three relations(10.33) , with the specific transition values Rel = KaL = KaR = 1 and a typical Ze = 10. These transition boundaries have slopes of−1, 1/3 , and 1/3 .Aboundary for U’/SL = 1 is also indicated. These four boundaries identify five burning regimes, with the following characteristics.(10.32) , and(10.2) , Laminar Flame Regime (Rel < 1): In this regime the turbulence intensity is weak and the turbulence scale is small. The flow is laminar and there is minimum extent of flame wrinkling. Wrinkled Flamelet Regime (Rel > 1, KaL < 1, u’/sL < 1): Since KaL < 1, the flame thickness is much smaller than theKolmogorov scale. As such, the fundamental flame element retains the laminar flame structure within the turbulent flow field, hence the name laminar flamelet. Since u’ can be interpreted as the turnover velocity of the large eddies, u’< sL implies that the flamelet surface is only slightly wrinkled as it passes through these eddies (图 10‑7a). 图 10‑7 (a) Weak flame-vortex interaction (u o < sL) resulting in a wrinkled flamelet. (b) Strong flame-vortex interaction (u o > sL) resulting in a corrugated flamelet. (c) Strong flamevortex interaction with the smaller eddies penetrating into and broadening the preheat zone of the flame (Peters 2000). Corrugated Flamelet Regime: Since KaL < 1, the flame element still retains its laminar flame structure. However, since u’> sL, the flamelet becomes highly convoluted upon traversing the eddy 图 10‑7b), with the extent of distortion being of the same order as the size of the eddy and folding of the flamelet is expected. The characteristic eddy size that separates the behaviors of wrinkled and corrugated flames can be assessed by equating the turnover velocity with the laminar flame speed. By calling this eddy size as the Gibson scale, lG, and from the general relation (10.6) , we have It is reasonable to expect that folding of the flamelet can lead to pockets of unburned and burned mixtures. The unburned pocket will burn out by itself as the enclosing flame propagates inward, provided it does not extinguish due to curvatureinduced stretch effects. The burned pocket, however, will grow as the enclosing flame propagates outward. Such a growth will be limited by the continuous interaction with eddies of size lG, indicating that there is a preference for the formation of burned pockets of size lG. Reaction-Sheet Regime: The lower boundary of this regime, KaL = 1, implies lk ≈ δL from Eq.图 10‑7(10.30) . Thus in this regime, although the flame still behaves as a flamelet for the large eddies, the smaller eddies can now penetrate into the preheat zone of the flame structure and thereby enhance the heat and mass transfer rates. The flame is broadened as a consequence ( GOTOBUTTON ZEqnNum712506 \* MERGEFORMAT c). The reaction sheet, being thinner than the Kolmogorov scale, δR < lK, is however only wrinkled, with its structure unaffected by the eddy motion. Well-Stirred Reactor Regime: In this regime the Kolmogorov eddies are smaller than the reaction zone thickness and as such can penetrate into the reaction zone structure. This facilitates diffusion, and, hence, heat transfer rate to the preheat zone, leading to a precipitous drop in the flame temperature and consequently extinction of the flame. The entire flow now behaves like a well-stirred reactor, without any distinct local structure. The above classification of regimes of combustion modes is based mostly on comparison of characteristic length and time scales. The boundaries, however, can be significantly modified by considering additional physics. For example, the discussion on wrinkling and corrugation was conducted without considering the significant change in density across the flame. In reality, since the normal flow velocity is greatly increased due to thermal expansion, while the tangential velocity is continuous across the flame, the original vortex structure can be substantially modified downstream of the flame. Thus the efficiency of rolling up a flame by a vortex could be smaller than anticipated. In view of these considerations, the various boundaries shown in图 10‑6, except that of Rel = 1, should be viewed as only tentative, pending further study. 10.2.3. 湍流火焰传播速度 As has been shown, the mass consumption rate per unit area in premixed laminar fl ames is simply ρ SL , where ρ is the unburned gas mixture density. Correspondingly, for power plants operating under turbulent conditions, a similar consumption rate is specifi ed as ρ ST , where ST is the turbulent burning velocity. The mass consumption rate of a given mixture varies with the state of turbulence created in the combustor. Explicit expressions for a turbulent burning velocity ST will be developed, and these expressions will show that various turbulent fi elds increase ST to values much larger than SL . However, increasing turbulence levels beyond a certain value increases ST very little, if at all, and may lead to quenching of the fl ame。 Now it is important to stress that, whereas the laminar fl ame speed is a unique thermochemical property of a fuel–oxidizer mixture ratio, a turbulent fl ame speed is a function not only of the fuel–oxidizer mixture ratio, but also of the fl ow characteristics and experimental confi guration. Thus, one encounters great diffi culty in correlating the experimental data of various investigators. In a sense, there is no fl ame speed in a turbulent stream. Essentially, as a fl ow fi eld is made turbulent for a given experimental confi guration, the mass consumption rate (and hence the rate of energy release) of the fuel–oxidizer mixture increases. Therefore, some researchers have found it convenient to defi ne a turbulent fl ame speed ST as the mean mass fl ux per unit area (in a coordinate system fi xed to the time-averaged motion of the fl ame) divided by the unburned gas density ρ0 . The area chosen is the smoothed surface of the time-averaged fl ame zone. However, this zone is thick and curved; thus the choice of an area near the unburned gas edge can give quite a different result than one in which a fl ame position is taken in the center or the burned gas side of the bushy fl ame. Therefore, a great deal of uncertainty is associated with the various experimental values of ST reported. Nevertheless, defi nite trends have been reported. These trends can be summarized as follows: 1. ST is always greater than SL . This trend would be expected once the increased area of the turbulent fl ame allows greater total mass consumption. 2. ST increases with increasing intensity of turbulence ahead of the fl ame. Many have found the relationship to be approximately linear. (This point will be discussed later.) 3. Some experiments show ST to be insensitive to the scale of the approach fl ow turbulence. 4. In open fl ames, the variation of ST with composition is generally much the same as for SL , and ST has a well-defi ned maximum close to stoichiometric. Thus, many report turbulent fl ame speed data as the ratio of ST / SL . 5. Very large values of ST may be observed in ducted burners at high approach fl ow velocities. Under these conditions, ST increases in proportion to the approach fl ow velocities, but is insensitive to approach fl ow turbulence and composition. It is believed that these effects result from the dominant infl uence of turbulence generated within the stabilized fl ame by the large velocity gradients. The defi nition of the fl ame speed as the mass fl ux through the fl ame per unit area of the fl ame divided by the unburned gas density ρ0 is useful for turbulent nonstationary and oblique fl ames as well. Diffi culty arises with this defi nition of ST because the time-averaged turbulent fl ame is bushy (thick) and there is a large difference between the area on the unburned gas side of the fl ame and that on the burned gas side. Nevertheless, many experimental data points are reported as ST. Experimental determination of turbulent burning velocities have adopted four major techniques, namely the Bunsen flame, the rod-stabilized flame, the stagnation or counterflow flame, and the expanding spherical flame. The first three methods involve stationary flames, with turbulence generated upstream by the use of screens, grids, or perforated plates. For the Bunsen and rod-stabilized flames, the turbulence decays as the flow approaches the flame and the true “upstream” turbulence intensity needs to be specified. For the stagnation flow, the adverse pressure gradient in the streamwise direction tends to retard the decay such that with judicious selection of a global strain rate, fairly constant turbulence intensity can be maintained. For the rod-stabilized flame, additional turbulence can also be generated in the form of the vortices produced as the flow passes over the rod. Because of the globally stationary nature of these three flames, these are also the configurations through which the turbulent flame structure is measured and studied. For the expanding spherical flame, turbulence is generated by several fans oppositely located within the combustion bomb. 图 10‑8Experimental turbulent burning velocity as function of turbulence intensity and pressure, for φ = 0.9 methane–air mixtures (Kobayashi et al. 1996). 图 10‑8shows typical data of the measured turbulent burning velocity, sT/sL, as a function of u o/sL for constant pressure. It is seen that, with increasing turbulence intensity, sT/sL monotonically increases with increasing turbulence intensity, though with a gradually decreasing slope. This is known as the bending effect. Various expressions have been derived and proposed for the turbulent burning velocity, mostly phenomenological in nature. We discuss in the following some of these expressions. Reaction Sheet versus Flamelet Descriptions: Damk¨ ohler first recognized that, depending on whether the turbulence scale is smaller or larger than the laminar flame thickness, the turbulent flame propagation modes are fundamentally different, as are the situations corresponding to the reaction sheet and wrinkled flamelet regimes. Specifically, when the turbulence scale is smaller than the laminar flame thickness, the turbulent eddies simply modify the transport process between the reaction sheet and the unburned gas. Thus analogous to the laminar flame result of SL ∼ D1/2, we can express the turbulent burning velocity as MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.34) where D and DT are the molecular and turbulent diffusivities respectively. Consequently, MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.35) Furthermore, since DT ∼ νT ∼ u’l0, while D ∼ ν, we have MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.36) When the turbulence scale is larger than the flame thickness, we are in the laminar flamelet regime. Wrinkling of the flame increases its surface area, and hence its total burning rate, such that a turbulent burning velocity can be defined according to (图 10‑9) MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.37) where AT is the total surface area of the wrinkled laminar flame and Athe area of the approach flow. Thus the determination of sT is reduced to an evaluation of the area ratio AT/A.于The following descriptions are all based on this concept. 图 10‑9Definition of the turbulent burning velocity for wrinkled flamelets (Peters 2000). Vector Description: To relate the flame geometry to the flow dynamics, from the flame geometry triangle in Figure 11.3.5 we have MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.38) 图 10‑10Vector diagram showing the triangle derivation of the turbulent burning velocity (Williams 1985). For the triangle on flow dynamics, the velocity component normal to the flame surface is SL while that tangential to it is u’, which represents the influence of stretch exerted by the turbulent eddy along the flame surface. Thus MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.39) Then MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.40) In the limits of weak and strong turbulence, Eq. (10.40) respectively becomes MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.41) and MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.42) which show quadratic and linear variations respectively. In particular, in the strong turbulence limit Eq. (10.42) is simply MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.43) which shows that the laminar flamelet loses its influence in that the flame surface is passively convected by the turbulent eddies. The turbulent burning rate is then just given by the turbulence intensity. This linear behavior at high turbulence intensities, however, is contrary to the observed bending effect shown in 图 10‑8. Fractal Description: The simple, triangle description allows only one scale of wrinkling. Since turbulence has a cascade of scales, it is reasonable to expect that surface wrinkling should also exhibit a range of scales. To determine the area of the rough surface of a wrinkled flame, the concept of statistical geometry known as fractals has been applied (Gouldin 1987). Fractals are geometrical objects such as curves, surfaces, volumes, and higher-dimensional bodies that have rugged boundaries and obey certain self-similarity behavior. Measurements of turbulent flows and turbulent flames have shown that D varies between 2.31 and 2.36. Using these values in the above equation shows that the exponent 3(D− 2) ≈ 1 such that sT ≈ u o, the high turbulent intensity limit of the vector description given by Eq.(10.43) . Dynamic Evolution Description: In this formulation we consider the evolution of a flame surface as it is entrained by a turbulent flow. The surface will have its area stretched as it moves through the flow. Thus in the Lagrangian frame, the evolution of the flame surface area Acan be described by the turbulent analogue of the laminar flame stretch equation (10.2.25), The final result is which shows the proper bending behavior as u’/sL increases. Renormalization Theories: Recognizing that processes occurring in turbulent flows involve wide spectra of spatial-temporal scales, renormalization methods have been applied to the evaluation of various turbulent properties such as the turbulent transport coefficients. The basic concept is the successive averaging over gradually increasing scales. Sivashinsky (1988), following Yakhot (1988), developed a cascade renormalization theory of turbulent burning velocities. In this approach, the continuous spectrum of a turbulent flow is first replaced by a cascade of eddies of widely separated scales.The relations obtained for these eddies are then extrapolated to the original continuous system. Figure 11.3.7 shows a conceptual representation of the successive averaging over flame wrinkles of progressively larger scales, leading to the derivation of a turbulent burning velocity at each scale of averaging until wrinkles of all scales are averaged with the corresponding identification of the final, global turbulent burning velocity. New research results It is known that certain turbulent flames propagate at more than 20 times the unstretched laminar flame speed [1,2]. There are two possible explanations: (1) flame stretch is expected to be the dominant mechanism if the flame remains in the thin flame regime (i.e., if the turbulent eddies are not able to enter and thicken the reaction zone). (2) Turbulent diffusion is expected to dominate in the thick flame regime; however, there is mounting evidence that reaction zones remain thin even at high turbulent intensities that approach extinction levels [4,5] 10.2.4. 湍流火焰的实验研究 邓克尔利用本生灯对丙烷-氧的预混合气燃烧火焰进行实验测定，给出不同雷诺数时湍流火焰传播速度的变化。 （a）当Re <2300时：ST /Sl = 1，为层流状态； （b）当2300 6000时：ST / Sl ( Re ，且 。式中A、B和a、b都是常数。由此可见，湍流火焰传播速度大于层流火焰传播速度，湍流火焰传播速度随湍流强度的增加而增加。邓克尔对实验结果做的理论解释认为湍流的作用使层流火焰前沿皱折。 博林杰和威廉姆斯: 进行实验测定验证邓、谢概念。得到的实验结果可用经验公式表示ST = 0.18SLd 0.26Re0.24。可以看出，湍流火焰传播速度ST 不仅与SL和Re成正比，而且还与管径d有关 10.2.5. Flamelet Modeling 10.3. 非预混湍流燃烧 Regimes of Combustion Modes As in premixed combustion, we shall discuss various combustion modes in nonpremixed turbulent combustion. The essential description should still be based on the characteristic time and length scales, although a nonpremixed flame does not have a propagation velocity and thus identifying a relevant characteristic time scale is not straightforward. Furthermore, the preheat zone of the nonpremixed flame is purely determined by the convective–diffusive transport caused by the turbulent flow field, and thus is little affected by the chemical reaction. In terms of the mixture fraction variable discussed in Chapters 5, 6, and 9, the transport layer thickness is expressed as MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.44) where χst = 2ν|∇Z|2 st is the scalar dissipation rate, defined in Eq. (9.4.15), evaluated at the stoichiometric mixture fraction. The characteristic time scale for transport is then given by MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.45) The flame Damk¨ ohler number, MACROBUTTON MTPlaceRef \* MERGEFORMAT (10.46) is an important parameter that represents the relative chemical strength of the flame. If DaL ≈ 1, then the residence time within the reaction zone is not long enough to sustain combustion, and thus the flame is prone to extinction. The above scaling argument can be approximately extended to turbulent combustion. In the spectrum of turbulent eddies, we expect that the Kolmogorov eddies have the shortest turnover time and are most effective in the transport process in the preheat zone. Mixture Fraction Modeling 11. 液体燃料燃烧 12. 固体燃料燃烧 13. 燃烧污染 14. 附录 14.1. 燃烧过程的热力学第一定律[9] 14.2. Misc 蒺藜 jílí 一年生草本植物,茎横生在地面上,开小黄花,果实也叫蒺藜,有刺,可以入药 像蒺藜的东西。如“铁蒺藜”,“蒺藜骨朵”:旧时一种兵器 参考文献 [1] 傅献彩、沈文霞、姚天扬、侯文华. 《物理化学》（第5版）高等教育出版社, 2005 [2] 〔英〕斯蒂芬·F·梅森，上海外国自然科学哲学著作编译组译，自然科学史，上海人民出版社：154-159 [3] 吴国盛，科学的历程，北京大学出版社，2002年 [4] Irvin Glassman, Richard A. Yetter. Combustion, 4th. edition, 2008, Elsevier Inc. [5] CHUNG K. LAW. COMBUSTION PHYSICS. Cambridge University Press, New York, 2006 [6] Margaret Robson Wright. An Introduction to Chemical Kinetics. John Wiley & Sons. 2004 [7] J. Warnatz, U. Maas, R.W. Dibble. Combustion: Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation. 4th Edition. Springer-Verlag Berlin Heidelberg, 2006 [8] Charles E., Baukal, Jr. Industrial Combustion Pollution and Control. Marcel Dekker, Inc., 2004 [9] Michael J. Moran, Howard N. Shapiro. Fundamentals of Engineering Thermodynamics. 5th Edition, John Wiley & Sons Ltd, 2006. Section 13.2. [10] R. Byron Bird, Warren E. Stewart, Edwin N. Lightfoot. Transport phenomena. 2nd edition. John Wiley & Sons, Inc. 2002 [11] Poling. The properties of gases and liquids. 5th edition. [12] Chien-Hsiung Tsai. The Asymmetric Behavior of Steady Laminar Flame Propagation in Ducts. Combustion Science and Technology, Volume 180, Issue 3 March 2008 , pages 533 - 545 � JOSE O. SINIBALDI, CHARLES J. MUELLER and JAMES F. DRISCOLL. LOCAL FLAME PROPAGATION SPEEDS ALONG WRINKLED, UNSTEADY, STRETCHED PREMIXED FLAMES. 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