外文翻译 --流体力学混合在单螺杆挤出机.doc

毕业设计（论文）外文资料翻译中文3685字附件一：外文资料翻译译文流体力学混合在单螺杆挤出机Ravlndran Chella和Julio M. Ottlno*Massachusetts州Amherst，Massachusetts大学，化学工程系 01003卷矩形空腔流图5为一个序列的一个接口，已进行二维矩形腔流拉伸步骤，在长度增长的界面，L(t）伴随着条纹厚度减少而减少，它被定义为相邻的接口之间的平均垂直距离，因此L(t)s(t)常数，Biggs和Middleman(1974b)使用一个简化的标记和细胞（MAC）技术(Harlow和Amsden，1970)来追踪该接口的位置。然而，他们只考虑水平接口以及他们认为小拉伸比率的情况。图5对两个相邻的垂直拉伸的流体层之间的接口在二维矩形腔流的步骤顺序示意图在一个典型的数值模拟中，变形及连续线拉伸（或表面）是使用有限数量的粒子模拟。对于幅度的一个或两个数量级的相对伸展的线变形，包含所述线路分离的单个颗粒，定义并不清晰，对每一个粒子的初始浓度（每单位长度的粒子数量）会有一段时间在这几乎不可能重建。（如果粒子流混乱，这个问题会急剧变得严重。）当进行线路中的示踪粒子模拟时，相同的问题会出现在实验工作中，另一方面，该线路不能过于集中，因为它不是被动接口，如果线路是可溶性示踪剂模拟，问题将会扩散。一般来说，这似乎很难遵循传统的跟踪方法或实验的或相对较高的拉伸比拉伸，数值误差可能会使它不可能实现可逆性预期规则运动(Khakhar等人,1984),界面的长度变化的关系可以用有限的材料进行拉伸计算 (11)该组包含该接口的差分线元件的初始取向的需要被指定，对于垂直界面（垂直于移动板块）=(0,l)和水平界面（平行移动板块）= (l,0)，以及所有的行元素，由于它是在初始配置，所以用公式11计算是相对简单的。这里使用的方法可以进行计算任意大的拉伸比，为了能够运用公式11，一种光腔流场的数学描述是有必要的，在这种情况下，参与关于瞬态问题利用稳态速度分布的误差比较小，例如稳态操作条件下迅速达到正常操作条件（Bigg 和 Middleman,1974b Erwin 和 Moktharian，1981），由公式1可以得出这一流程最简单的说明。图6比较简化为矩形空腔流获得使用SFT（- - -）和公式12得到 W / H = 15然而，使用公式1和公式11结合以确定L(t)的值，在方向和变形经过由材料元件移动到其互补的位置变化假设是必要的。但是，计算表明，混合实现假定取向的变化是非常敏感的方向，因此需要开发一个流场的数学描述，并不需要这样任意假设。在n - s方程的数值解这个流场(公式l，公式2)是可能的，它似乎并不需要计算拉伸比率或更高的基于当前的跟踪技术，此外，一个半解析处理允许对不同参数的影响更易于可理解。因此，在附录中，Kantorovich Galerkin方法(Kantorovich and Krylov, 1964) 被用来获得一个近似的解析解的稳态，蠕变流动腔流方程。根据公式A.8，A.15和A.22 在公式A.22中,和的作用仅仅被定义为腔的长宽比。虽然这些方程满足边界条件下速度的平均移动量，但仅在使用它们计算流线时相对准确，对于复杂的纵横比，与那些得到更准确的数值方法(Pan 和 Acrivos, 1967)；以及坐标的最大和最小坐标重合几乎完全与SFT的相应互补值的位置（图6），这些方程就不适用了。通过最初垂直接口，使用公式11 和 公式12，计算相对拉伸为两个不同方面比率在图 7 中表示。在特有的循环时间，纵横比对界面的相对拉伸只有很小的影响。关于单调递增的均值曲线的振荡周期值约等于,振荡周期可以由图8得出，当拉伸率(= d L(t)/ dt)时，作图的接口特定速率准确显示了相同特征的振荡，这样的振荡特征需要重新定位（图3b）。图7接口的矩形腔流函数的计算与速度场由公式12得出，最初垂直界面（垂直于移动板） 除以腔成体积相等的通道纵横比的相对拉伸图8 无因次的特定接口的拉伸率在矩形空腔流(W / H = 15，最初垂直界面)图9 相对拉伸中矩形腔流接口的初始方向的影响（W/H = 15）对单一的接口长度影响初始方向如图 9 所示，该混合程度的初始取向可通过图9中工件的坐标表现。研究发现，每一种情况下计算出的界面面积的实际值对初始取向的依赖性非常小，在图8中可以查找原因，一个最初垂直界面区域（垂直于流线）和一个最初水平界面区域（几乎平行流简化）之间存在巨大差异，极大实现越来越多的最初垂直界面缩小成为水平对齐。同时发现混合相对等于甚至大于位移的初始位置，接口相对的界面区域可以认为是近似关系图10变化在沿矩形空腔流动的流线行进的差分材料元件的标高（a）和方位（b）所示可以由公式12计算出速度(F是正常材料平面之间的角度和轴)图11比较的界面拉伸矩形空腔流预测了SFT(- - -)，预测使用的流场比值12()，（W / H = 15,最初垂直界面） (13)而在挤出机混合分析中速度计算可以由等式12得出，这并不包括另外概念上的问题，这与SFT的计算量相比明显增加了，因此，确定流体元件的取向变化与该流场获得的信息是否可以被纳入使用SFT结果准确混合计算是有用的，图10中，表示典型的时间差分线元的取向变化的关系，也表示在图中的上面部分是元素相应的坐标（图10a），虚线表示最大值和最小值的位置。 图表明这里本身能够快速建立坐标，可以忽略材料元件的初始位置或方向，因此，当围绕轴方向旋转到界面区域时，相关因素旋转接近。SFT的研究与假设是边界旋转近，通过材料元素混合的预测是否有用，现在得到验证。图12腔纵横比对拉伸与使用SFT预测矩形方腔流的初始垂直界面的影响使用SFT计算初始垂直界面的变形与使用图11中12式相比，旋转流体元素在空间旋转，两条曲线的数值有较好的一致性，然而，使用SFT得到的振荡周期是使用公式12得到结果的三倍以上，这与再分配时的值大概一致 (由Shearer（1973）定义，以从腔体的一侧完全置换流体的其它部分所需要的时间)使用SFT计算 (14)使用这两种不同的流场的初始垂直界面混合预测之间的公式，即使在图11所示的比较大的拉伸比也适用，这似乎很奇怪，因为SFT预测水平的接口不变形以及接口的很大一部分是近于水平拉伸比。然而，对于有限次的界面是从来没有完全意义上的水平，SFT中预测一个小而有限的拓展与公式12的结果一致。预测弱混合的实现使用公式12得到纵横比，采用SFT确认（图12），SFT中相关要素按回转，由此可见，通过公式12可以计算出复制的矩形腔流混合的主要特点，从而，在三维空间中使用挤出流是有利的，因为它相对公式12简单了。由于缺少实验数据，实验数据的理论预测比较难，可行性实验数据不完整（例如 Bigg 和Middleman,1974b) 两者都是因为不确定二维流动是否在实验装置中实现和并不是大多数据在有利的情况下测得（较大的纵横比）。但是，综合实验程序正在进行中（Chien, 1984）。从空腔流得到的结论在挤出机中的应用应谨慎，但应注意的是，流速在整个挤出机中的横截面的分布可防止确切坐标中的矩形腔和轴向距离沿着所述挤出机连续时间之间转化，另外，从拓扑的角度来看，如果我们考虑两种流体混合，说A和B最初在腔流水平层状，然后在侧壁的两条接触线，最后存在于整个运动，然而，挤出机最初充满，随后A和B作为参考，相邻的水平层将有明显区分，没有接触线，当在垂直界面时将会出现类似情况。 图13通过挤出机的流场中的引入相邻的水平层的两种液体混合产生的层状结构的示意图图14迹线在挤出机通道材料元素 从以上讨论中可以很明显得出，该方法在用于分析三维挤出流量的二维空腔流混合是可能的没有准确的扩展，但是近似关系的可能性有待继续探讨。分析单螺杆挤出机的混合关于在挤出机中混合方法的分析主要与用于所述螺旋环形混合器类似，修改是必要的，但是，通过公式12算出的速度场，得出一个完全的分析方法是不可能的，由在流体元件迹线的总数不连续可排除SFT 。图13是挤出机中通道的两种液体的混合示意图，截面切割和轴向切割显示由混合作用所产生的层状结构。至于螺旋环形混合器，和 s用作最大混合度的局部措施，混合参数和分部在任一通道截面对应流场的不均匀性中，并在进料面上条纹的方向及厚度分布，对于许多应用来说在第一个片刻来描述这些分布应该是足够了。力矩轴向配置和横截面的混合参数分布的装置文件可以如下确定（图14所示）：（1）许多不同材料的平面确定在进料平面，每个对应界面区域中的原料的位置和方向。选择平面的数量应足够大，从而这个变量计算分布的影响可以忽略不计；当然，实际数字依赖所取得的结果；在实践中，200-300因素被认为足够条纹厚度幅度下降三个数量级。注意RTD被发现对混合参数分布到所选材料的元素不敏感。（2）公式2用于所述流场的数学描述来计算这些材料每个平面的拉伸过程。（3）均值和所述混合参数分布的情况由几个轴向位置确定，这种方法是非常通用的，并且可以被应用到其它混合器中去。对于连续流动系统的宏观混合效率是由下列关系式确定（Ottino等人，1981） (15)在更详细的计算中，检查上混合绑定是很有意义的，通过设置公式15中右侧的eff(z) = 1获得。通常情况下，定义在上部混合预测值显著高于大多数实际混合流量（Ottino和Macosko，1980；Ottino，1983），但考虑到估计模型参数对混合模型参数的影响，计算绑定上混合模型参数对于SFT特别简单。 (16)取函数N和含有，的函数以及L/H函数的比例常数的平均值（需要考虑其上的平均停留时间的影响）。因此，由公式16来看，影响混合的相关参数为N，和L/H。W / H的影响只能间接地通过移动流体单元的垂直坐标变化。在此基础上，当上限值增大时，混合的可能性将被增大，然后由公式16得出，混合参数方程可通过：（1）保持L / H和不变，增加；（2）保持和不变，增加L/H；（3）保持L/H和不变，当时，增加；当时，减小，可由以下方程得出 (17)和 以及（4）H L/H 和保持不变，减少H。这些结论与定性实验结果相一致（Maddock，1959；Sheridan， 1975），在下一节中将使用更完美的分析方法进行测试。附件二：外文资料原文Fluid Mechanics of Mixing in a Single-Screw ExtruderRavlndran Chella and Julio M. Ottlno* Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 0 1003Rectangular Cavity Flow Figure 5 is a diagram of a sequence of steps in the stretching of an interface that has been subjected to two-dimensional rectangular cavity flow. The increase in length of the interface, L(t), is accompanied by a decrease in the striation thickness, defined as the average perpendicular distance between neighboring interfaces, so that for long times L(t)s(t)constant. Biggs and Middleman (1974b) used a simplified Marker-and-Cell (MAC) technique (Harlow and Amsden, 1970) to track the position of the interface. However, they only considered the case where the interface was horizontal, and they assumed small stretch ratios. Figure5. Schematic diagram of sequence of steps in the stretching of an interface between two adjacent vertical fluid layers in two dimensional rectangular cavity flow.In a typical numerical simulation, the deformation and stretching of continuous lines (or surfaces) is modeled using a finite number of particles. For a relative stretch of one or two orders of magnitude as the line deforms the individual particles comprising the line separate, making the line less clearly defined. For every initial concentration of particles (number of particles per unit length) there will be a time beyond which it becomes nearly impossible to reconstruct the line. (This problem is magnified dramatically if the flow is chaotic.) An identical problem arises in experimental work when a line is simulated in terms of tracer particles. On the other hand, the line cannot be too concentrated as it would not behave as a passive interface. If the line is simulated in terms of a soluble tracer, the problem is diffusion. In general, it appears to be extremely difficult to follow stretching by conventional tracking techniques and/or experiments for relative stretch ratios of orderor higher. Numerical errors might make it impossible to achieve the reversibility expected from regular motions (Khakhar et al, 1984). The change in length of the interface may be calculated using the relation for the stretching of a finite material line (11)The set of initial orientations of the differential line elements comprising the interface need to be specified. For a vertical interface (perpendicular to the moving plate) = (0,l), and for a horizontal interface (parallel to the moving plate) = (l,0), for all the line elements. The evaluation of the integral in eq 11 is relatively simple as it is over the initial configuration. The approach used here can be carried out to arbitrarily large stretch ratios. In order to apply eq 11, a mathematical description of the cavity flow field is needed. The error involved in the use of a steady-state velocity profile for an essentially transient problem is relatively small in this case, as steady-state operating conditions are rapidly attained under normal operating conditions (Bigg and Middleman, 1974b; Erwin and Moktharian, 1981). The simplest such description for this flow is that given by eq 1. Figure6. Comparison of streamlines for rectangular cavity flow obtained using the SFT (- - -) and eq 12 for W/H = 15.However, in using eq 1 in conjunction with eq 11 to determine L(t), assumptions are necessary regarding the changes in orientation and deformation undergone by a material element in moving to its complementary location. However, computations indicate that the mixing achieved is extremely sensitive to the assumed change in orientation at the flights. It is therefore desirable to develop a mathematical description of the flow field that does not entail such arbitrary assumptions. While a numerical solution to the Navier-Stokes equations for this flow field (eq A.l,2)is possible, it does not seem feasible to compute stretch ratios of order or higher based on current tracking techniques. Additionally, a semianalytical treatment allows for easier visualization of the effect of different parameters. Hence, in the Appendix,the Kantorovich-Galerkin method (Kantorovich and Krylov, 1964) is used to obtain an approximate analytical steady-state, creeping flow solution to the cavity flow equations. From eq A.8, A.15, and A.22 where,andare functions only of the cavity aspect ratio, defined in eq A.22. Even though these equations satisfy the boundary condition on the velocity at the moving plate only in the mean the streamlines calculated using them are in good agreement, for large aspect ratios, with those obtained by more accurate numerical methods (Pan and Acrivos, 1967); also,the maximum and minimumcoordinates of the streamlines coincide almost exactly with the location of the corresponding complementary plants of the SFT (Figure 6). The relative stretch experienced by an initially vertical interface, calculated using eq 11 and 12, is shown in Figure 7 for two different aspects ratios. The aspect ratio has only a small influence on the relative stretch of the interface; the period of oscillation of the curves about a monotonically increasing mean value is approximately equal to , a characteristic recirculation time.The periodic oscillation can be seen more clearly in Figure 8, where the specific rate of stretching of the interface a(= d In L(t)/dt) plotted vs. time shows the same characteristic oscillation. Thus the cavity flow has weak reorientation (Figure 3b).Figure7. Relative stretch of interface in rectangular cavity flow as a function of the channel aspect ratio, calculated with the velocity field of eq 12, for an initially vertical interface (perpendicular to the moving plate) dividing cavity into equal volumes.Figure8. Nondimensionalized specific rate of stretching of interface in rectangular cavity flow (W/H = 15, initially vertical interface).Figure9. Influence of initial orientation on relative stretch of interface in rectangular cavity flow (W/H = 15) The influence of the initial orientation of the interface on the normalized interface length is shown in Figure 9. The apparent sensitivity of the mixing level to the initial orientation is an artifact of choice of coordinates in Figure 9. When the actual amount of interfacial area in each case is calculated, the dependence on the initial orientation is found to be very small. The reason for this can be seen in Figure 8, where the initial large differences between an initially vertical interface (almost perpendicular to the flow streamlines) and an initially horizontal interface (almost parallel to the flow streamlines), narrows considerably as more and more of the initially vertical interface becomes aligned horizontally. Also, mixing is found to be relatively insensitive even to large displacements in the initial location of the interface. The relative stretch of the interface can be approximated by the relationFigure10. Change in elevation (a) and orientation (b) of a differential material element in traveling along a streamline in rectangular cavity flow, calculated with the velocity field of eq 12 (F is the angle between the normal to the material plane and the axis).Figure11. Comparison of interface stretching in rectangular cavity flow predicted by the SFT (-) with that predicted using the flow field of eq 12 (),(W/H = 15, initially vertical interface). (13)While the use of the velocity field given by eq 12 in the analysis of mixing in the extruder involves no additional conceptual difficulty, the computational effort is considerably increased compared with the SFT. Hence it is useful to determine whether information obtained with this flow field regarding the change in orientation of the fluid elements near the flights can be incorporated into mixing calculations using the SFT with satisfactory results. Figure 10 shows a typical plot of the change in orientation of a differential line element with time. Also indicated, in the upper portion of the figure, are the corresponding coordinates of the element (Figure 10a), the dashed lines indicating the locations of the maximums and the minimums. The pattern shown here is found to quickly establish itself regardless of the initial location or orientation of the material element. Thus the material elements are rotated through nearly while reversing their flow direction near the boundaries. The usefulness of the SFT in making predictions of mixing with the material elements assumed to rotate through at the boundaries is now examined.Figure12. Influence of cavity aspect ratio on stretching of an initially vertical interface in rectangular cavity flow as predicted using the SFT. The deformation of an initially vertical interface calculated using the SFT, with the fluid elements rotated through at the flights, is compared to that calculated using eq 12, in Figure 11. Numerically the two curves are in good agreement; however, the period of the oscillation obtained using the SFT is more than three times that obtained using eq 12 and is approximately in agreement with the value of the redistribution time (defined by Shearer (1973) as the time required to displace fluid completely from one side of the cavity to the other) calculated using the SFT (14)The agreement between the mixing predictions for an initially vertical interface using these two different flow fields, even for the relatively large stretch ratios shown in Figure 11, seems rather surprising as the SFT predicts no deformation of a horizontal interface, and a large portion of the interface is nearly horizontal at these large stretch ratios. However, for finite times the interface is never perfectly horizontal, and the SFT predicts a small but finite stretch in agreement with the predictions of eq 12. The weak dependence of the mixing achieved on the channel aspect ratio predicted using eq 12 is confirmed using the SFT (Figure 12). The SFT with the rotation of the material elements at the flights is thus seen to duplicate the principal features of mixing in the rectangular cavity flow as predicted using eq 12, and its use in the analysis of mixing in the three-dimensional extruder flow is favored over eq 12 because of its relative simplicity.Comparison of the theoretical predictions with experimental data is difficult because of a scarcity of experimental data. The available experimental data are incomplete (e.g., Bigg and Middleman, 1974b) both because of the uncertainity about whether two-dimensional flow was achieved in the experimental setup and because not many data were taken under conditions of interest here (large aspect ratios). However, a comprehensive experimental program is underway (Chien, 1984).The conclusions obtained from the cavity flow should be applied with care to extruders. It should be noted that the distribution of velocities across the extruder cross-section prevents an exact coordinate transformation between successive times in the rectangular cavity and axial distance along the extruder. Also, from a topological point of view, if we consider the mixing of two fluids, say A and B, initially layered horizontally in the cavity flow, the two contact lines at the side wall are present throughout the entire motion. However, an extruder filled initially with A and subsequently fed with A and B as adjacent horizontal layers would have A wetting and boundaries completely, with no contact lines. An analogous situation is obtained for a vertical interface. Figure13. Schematic diagram of lamellar structure generated by the extruder flow field in the mixing of two fluids introduced as adjacent horizontal layers.Figure14. Pathline of material elements in extruder channel. From the above arguments it is apparent that no rigorous extension of the approach used to analyze mixing for the two-dimensional cavity flow is possible to the three-dimensional extruder flow; however, the possibility of approximate relations will be explored.Analysis of Mixing in Single Screw ExtruderThe approach used to analyze mixing in the extruder is similar in principal to that used for the helical annular mixer; modifications are necessary, however, as a completely analytical approach is not possible using the velocity field given by eq 12 and is precluded for the SFT by the discontinuities in the fluid element pathlines at the flights. Figure 13 is a diagram of the mixing of two fluids in the extruder channel. Cross-sectional cuts and an axial cut display the layered structure generated by the mixing action. As for the helical annular mixer, and s are used as local measures of the state of mixedness. The distribut- ions of the mixing parameters andat any channel cross section correspond to the nonhomo- geneity of the flow field and to distributions in the orientations and thicknesses of the striations in the feed plane. For many applications it should be sufficient to characterize these distributions by their first few moments. Axial profiles of the me