外文翻譯 --流體力學混合在單螺桿擠出機

1、<p><b>　　中文3685字</b></p><p>　　附件一：外文資料翻譯譯文</p><p>　　流體力學混合在單螺桿擠出機</p><p>　　Ravlndran Chella和Julio M. Ottlno*</p><p>　　Massachusetts州Amherst，Massachuset

2、ts大學，化學工程系 01003卷</p><p><b>　　矩形空腔流</b></p><p>　　圖5為一個序列的一個接口，已進行二維矩形腔流拉伸步驟，在長度增長的界面，L(t）伴隨著條紋厚度減少而減少，它被定義為相鄰的接口之間的平均垂直距離，因此L(t)s(t)常數(shù)，Biggs和Middleman(1974b)使用一個簡化的標記和細胞（MAC）技術(Harlo

3、w和Amsden，1970)來追蹤該接口的位置。然而，他們只考慮水平接口以及他們認為小拉伸比率的情況。</p><p>　　圖5對兩個相鄰的垂直拉伸的流體層之間的接口在二維矩形腔流的步驟順序示意圖</p><p>　　在一個典型的數(shù)值模擬中，變形及連續(xù)線拉伸（或表面）是使用有限數(shù)量的粒子模擬。對于幅度的一個或兩個數(shù)量級的相對伸展的線變形，包含所述線路分離的單個顆粒，定義并不清晰，對每一個粒

4、子的初始濃度（每單位長度的粒子數(shù)量）會有一段時間在這幾乎不可能重建。（如果粒子流混亂，這個問題會急劇變得嚴重。）當進行線路中的示蹤粒子模擬時，相同的問題會出現(xiàn)在實驗工作中，另一方面，該線路不能過于集中，因為它不是被動接口，如果線路是可溶性示蹤劑模擬，問題將會擴散。一般來說，這似乎很難遵循傳統(tǒng)的跟蹤方法或實驗的或相對較高的拉伸比拉伸，數(shù)值誤差可能會使它不可能實現(xiàn)可逆性預期規(guī)則運動(Khakhar等人,1984),界面的長度變化的關系可以用

5、有限的材料進行拉伸計算</p><p><b>　　(11)</b></p><p>　　該組包含該接口的差分線元件的初始取向的需要被指定，對于垂直界面（垂直于移動板塊）=(0,l)和水平界面（平行移動板塊）= (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計算是相對簡單的。這里使用的方法可以進行計算任意大的拉伸比，為了能夠運用公式11，一種光腔流場

6、的數(shù)學描述是有必要的，在這種情況下，參與關于瞬態(tài)問題利用穩(wěn)態(tài)速度分布的誤差比較小，例如穩(wěn)態(tài)操作條件下迅速達到正常操作條件（Bigg 和 Middleman,1974b Erwin 和 Moktharian，1981），由公式1可以得出這一流程最簡單的說明。</p><p>　　圖6比較簡化為矩形空腔流獲得使用SFT（- - -）和公式12得到 W / H = 15</p><p>　　然而

7、，使用公式1和公式11結合以確定L(t)的值，在方向和變形經(jīng)過由材料元件移動到其互補的位置變化假設是必要的。但是，計算表明，混合實現(xiàn)假定取向的變化是非常敏感的方向，因此需要開發(fā)一個流場的數(shù)學描述，并不需要這樣任意假設。在n - s方程的數(shù)值解這個流場(公式l，公式2)是可能的，它似乎并不需要計算拉伸比率或更高的基于當前的跟蹤技術，此外，一個半解析處理允許對不同參數(shù)的影響更易于可理解。因此，在附錄中，Kantorovich Galerki

8、n方法(Kantorovich and Krylov, 1964) 被用來獲得一個近似的解析解的穩(wěn)態(tài)，蠕變流動腔流方程。根據(jù)公式A.8，A.15和A.22</p><p>　　在公式A.22中,,和的作用僅僅被定義為腔的長寬比。</p><p>　　雖然這些方程滿足邊界條件下速度的平均移動量，但僅在使用它們計算流線時相對準確，對于復雜的縱橫比，與那些得到更準確的數(shù)值方法(Pan 和 Acr

9、ivos, 1967)；以及坐標的最大和最小坐標重合幾乎完全與SFT的相應互補值的位置（圖6），這些方程就不適用了。</p><p>　　通過最初垂直接口，使用公式11 和 公式12，計算相對拉伸為兩個不同方面比率在圖 7 中表示。在特有的循環(huán)時間，縱橫比對界面的相對拉伸只有很小的影響。關于單調遞增的均值曲線的振蕩周期值約等于,振蕩周期可以由圖8得出，當拉伸率(= d L(t)/ dt)時，作圖的接口特定速率準確

10、顯示了相同特征的振蕩，這樣的振蕩特征需要重新定位（圖3b）。</p><p>　　圖7接口的矩形腔流函數(shù)的計算與速度場由公式12得出，最初垂直界面（垂直于移動板） 除以腔成體積相等的通道縱橫比的相對拉伸</p><p>　　圖8 無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)</p><p>　　圖9 相對拉伸中矩形腔流接口的初始方向的影

11、響（W/H = 15）</p><p>　　對單一的接口長度影響初始方向如圖 9 所示，該混合程度的初始取向可通過圖9中工件的坐標表現(xiàn)。研究發(fā)現(xiàn)，每一種情況下計算出的界面面積的實際值對初始取向的依賴性非常小，在圖8中可以查找原因，一個最初垂直界面區(qū)域（垂直于流線）和一個最初水平界面區(qū)域（幾乎平行流簡化）之間存在巨大差異，極大實現(xiàn)越來越多的最初垂直界面縮小成為水平對齊。同時發(fā)現(xiàn)混合相對等于甚至大于位移的初始位置，接

12、口相對的界面區(qū)域可以認為是近似關系</p><p>　　圖10變化在沿矩形空腔流動的流線行進的差分材料元件的標高（a）和方位（b）所示可以由公式12計算出速度(F是正常材料平面之間的角度和軸)</p><p>　　圖11比較的界面拉伸矩形空腔流預測了SFT(- - -)，預測使用的流場比值12(─)，（W / H = 15,最初垂直界面）</p><p><b

13、>　　(13)</b></p><p>　　而在擠出機混合分析中速度計算可以由等式12得出，這并不包括另外概念上的問題，這與SFT的計算量相比明顯增加了，因此，確定流體元件的取向變化與該流場獲得的信息是否可以被納入使用SFT結果準確混合計算是有用的，圖10中，表示典型的時間差分線元的取向變化的關系，也表示在圖中的上面部分是元素相應的坐標（圖10a），虛線表示最大值和最小值的位置。 圖表明這里本身

14、能夠快速建立坐標，可以忽略材料元件的初始位置或方向，因此，當圍繞軸方向旋轉到界面區(qū)域時，相關因素旋轉接近。SFT的研究與假設是邊界旋轉近，通過材料元素混合的預測是否有用，現(xiàn)在得到驗證。</p><p>　　圖12腔縱橫比對拉伸與使用SFT預測矩形方腔流的初始垂直界面的影響</p><p>　　使用SFT計算初始垂直界面的變形與使用圖11中12式相比，旋轉流體元素在空間旋轉，兩條曲線的數(shù)值有

15、較好的一致性，然而，使用SFT得到的振蕩周期是使用公式12得到結果的三倍以上，這與再分配時的值大概一致 (由Shearer（1973）定義，以從腔體的一側完全置換流體的其它部分所需要的時間)使用SFT計算 </p><p><b>　　(14)</b></p><p>　　使用這兩種不同的流場的初始垂直界面混合預測之間的公式，即使在圖11所示的比較大的拉伸比也適用，這

16、似乎很奇怪，因為SFT預測水平的接口不變形以及接口的很大一部分是近于水平拉伸比。然而，對于有限次的界面是從來沒有完全意義上的水平，SFT中預測一個小而有限的拓展與公式12的結果一致。</p><p>　　預測弱混合的實現(xiàn)使用公式12得到縱橫比，采用SFT確認（圖12），SFT中相關要素按回轉，由此可見，通過公式12可以計算出復制的矩形腔流混合的主要特點，從而，在三維空間中使用擠出流是有利的，因為它相對公式12簡單

17、了。</p><p>　　由于缺少實驗數(shù)據(jù)，實驗數(shù)據(jù)的理論預測比較難，可行性實驗數(shù)據(jù)不完整（例如 Bigg 和Middleman,1974b) 兩者都是因為不確定二維流動是否在實驗裝置中實現(xiàn)和并不是大多數(shù)據(jù)在有利的情況下測得（較大的縱橫比）。但是，綜合實驗程序正在進行中（Chien, 1984）。</p><p>　　從空腔流得到的結論在擠出機中的應用應謹慎，但應注意的是，流速在整個擠出機

18、中的橫截面的分布可防止確切坐標中的矩形腔和軸向距離沿著所述擠出機連續(xù)時間之間轉化，另外，從拓撲的角度來看，如果我們考慮兩種流體混合，說A和B最初在腔流水平層狀，然后在側壁的兩條接觸線，最后存在于整個運動，然而，擠出機最初充滿，隨后A和B作為參考，相鄰的水平層將有明顯區(qū)分，沒有接觸線，當在垂直界面時將會出現(xiàn)類似情況。 </p><p>　　圖13通過擠出機的流場中的引入相鄰的水平層的兩種液體混合產(chǎn)生的層狀結構的示意

19、圖</p><p>　　圖14跡線在擠出機通道材料元素 </p><p>　　從以上討論中可以很明顯得出，該方法在用于分析三維擠出流量的二維空腔流混合是可能的沒有準確的擴展，但是近似關系的可能性有待繼續(xù)探討。</p><p>　　分析單螺桿擠出機的混合</p><p>　　關于在擠出機中混合方法的分析主要與用于所述螺旋環(huán)形混合器類似，修改是必

20、要的，但是，通過公式12算出的速度場，得出一個完全的分析方法是不可能的，由在流體元件跡線的總數(shù)不連續(xù)可排除SFT 。</p><p>　　圖13是擠出機中通道的兩種液體的混合示意圖，截面切割和軸向切割顯示由混合作用所產(chǎn)生的層狀結構。至于螺旋環(huán)形混合器，和 s用作最大混合度的局部措施，混合參數(shù)和分部在任一通道截面對應流場的不均勻性中，并在進料面上條紋的方向及厚度分布，對于許多應用來說在第一個片刻來描述這些分布應該是

21、足夠了。</p><p>　　力矩軸向配置和橫截面的混合參數(shù)分布的裝置文件可以如下確定（圖14所示）：（1）許多不同材料的平面確定在進料平面，每個對應界面區(qū)域中的原料的位置和方向。選擇平面的數(shù)量應足夠大，從而這個變量計算分布的影響可以忽略不計；當然，實際數(shù)字依賴所取得的結果；在實踐中，200-300因素被認為足夠條紋厚度幅度下降三個數(shù)量級。注意RTD被發(fā)現(xiàn)對混合參數(shù)分布到所選材料的元素不敏感。（2）公式2用于所述

22、流場的數(shù)學描述來計算這些材料每個平面的拉伸過程。（3）均值和所述混合參數(shù)分布的情況由幾個軸向位置確定，這種方法是非常通用的，并且可以被應用到其它混合器中去。</p><p>　　對于連續(xù)流動系統(tǒng)的宏觀混合效率是由下列關系式確定（Ottino等人，1981）</p><p><b>　　(15)</b></p><p>　　在更詳細的計算中，檢查

23、上混合綁定是很有意義的，通過設置公式15中右側的eff(z) = 1獲得。通常情況下，定義在上部混合預測值顯著高于大多數(shù)實際混合流量（Ottino和Macosko，1980；Ottino，1983），但考慮到估計模型參數(shù)對混合模型參數(shù)的影響，計算綁定上混合模型參數(shù)對于SFT特別簡單。</p><p><b>　　(16)</b></p><p>　　取函數(shù){N}和含有

24、，的函數(shù)以及L/H函數(shù)的比例常數(shù)的平均值（需要考慮其上的平均停留時間的影響）。因此，由公式16來看，影響混合的相關參數(shù)為{N}，，，和L/H。W / H的影響只能間接地通過移動流體單元的垂直坐標變化。</p><p>　　在此基礎上，當上限值增大時，混合的可能性將被增大，然后由公式16得出，混合參數(shù)方程可通過：（1）保持L / H和不變，增加；（2）保持和不變，增加L/H；（3）保持L/H和不變，當>時，增

25、加；當<時，減小，可由以下方程得出</p><p><b>　　(17)</b></p><p><b>　　和</b></p><p>　　以及（4）H L/H 和保持不變，減少H。</p><p>　　這些結論與定性實驗結果相一致（Maddock，1959；Sheridan， 1975），

26、在下一節(jié)中將使用更完美的分析方法進行測試。</p><p>　　附件二：外文資料原文</p><p>　　Fluid Mechanics of Mixing in a Single-Screw Extruder</p><p>　　Ravlndran Chella and Julio M. Ottlno* </p><p>　　Departm

27、ent of Chemical Engineering, University of Massachusetts, </p><p>　　Amherst, Massachusetts 0 1003</p><p>　　Rectangular Cavity Flow </p><p>　　Figure 5 is a diagram of a sequence of s

28、teps 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 a

29、s 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 tra

30、ck the position of t</p><p>　　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.</p>

31、;<p>　　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

32、 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 beyon

33、d which it becomes nearly impossible to reconstruct the line. (This proble</p><p><b>　　(11)</b></p><p>　　The set of initial orientations of the differential line elements comprising

34、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 o

35、f 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 mathematica</p><p

36、>　　Figure6. Comparison of streamlines for rectangular cavity flow obtained using the SFT (- - -) and eq 12 for W/H = 15.</p><p>　　However, in using eq 1 in conjunction with eq 11 to determine L(t), assump

37、tions 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 sensi

38、tive 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</p>&l

39、t;p>　　where,,andare functions only of the cavity aspect ratio, defined in eq A.22. </p><p>　　Even though these equations satisfy the boundary condition on the velocity at the moving plate only in the mea

40、n 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 strea

41、mlines coincide almost exactly with the location of the corresponding complementary plants of the SFT (Figure 6). </p><p>　　The relative stretch experienced by an initially vertical interface, calculated usi

42、ng 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

43、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 int</p><p>　　

44、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 p

45、late) dividing cavity into equal volumes.</p><p>　　Figure8. Nondimensionalized specific rate of stretching of interface in rectangular cavity flow (W/H = 15, initially vertical interface).</p><p&g

46、t;　　Figure9. Influence of initial orientation on relative stretch of interface in rectangular cavity flow (W/H = 15) </p><p>　　The influence of the initial orientation of the interface on the normalized inte

47、rface 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 c

48、alculated, 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</p><p>

49、;　　Figure10. 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

50、the normal to the material plane and the axis).</p><p>　　Figure11. Comparison of interface stretching in rectangular cavity flow predicted by the SFT (----) with that predicted using the flow field of eq 12

51、(─),(W/H = 15, initially vertical interface).</p><p><b>　　(13)</b></p><p>　　While the use of the velocity field given by eq 12 in the analysis of mixing in the extruder involves no a

52、dditional 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 orienta

53、tion 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</p><p>　　Figure12. Influence of

54、cavity aspect ratio on stretching of an initially vertical interface in rectangular cavity flow as predicted using the SFT. </p><p>　　The deformation of an initially vertical interface calculated using the S

55、FT, 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 usi

56、ng 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 com</p>&

57、lt;p><b>　　(14)</b></p><p>　　The agreement between the mixing predictions for an initially vertical interface using these two different flow fields, even for the relatively large stretch ratios

58、 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 time

59、s the interface is never perfectly horizontal, and the SFT predicts a small but finite stretch in agreement with the</p><p>　　The weak dependence of the mixing achieved on the channel aspect ratio predicted

60、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 predicte

61、d 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.</p><p>　　Comparison of the theoretical predictions with e

62、xperimental 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 fl

63、ow 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).</p>

64、<p>　　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 tr

65、ansformation 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 horiz

66、ontally in the cavity flow, the two contact lines at the side wall are p</p><p>　　Figure13. Schematic diagram of lamellar structure generated by the extruder flow field in the mixing of two fluids introduced

67、 as adjacent horizontal layers.</p><p>　　Figure14. Pathline of material elements in extruder channel. </p><p>　　From the above arguments it is apparent that no rigorous extension of the approach

68、 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.</p><p>　　Analysis of Mixing

69、 in Single Screw Extruder</p><p>　　The 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 completel

70、y 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. </p><p>　　Figure 13 is a diagr

71、am 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 measur

72、es 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

73、the striations in the feed plane. For ma</p><p>　　Axial profiles of the means and moments of the cross- sectional mixing parameter distributions can be determined as follows (see Figure 14): (i) A number of

74、differential material planes are identified in the feed plane,the location and orientation of each corresponding to the position of the interfacial area in the feed. The number of planes chosen should be large enough tha

75、t the influence of this variable on the calculated distributions is negligible; the actual number, of course, depends on th</p><p>　　The macroscopic mixing efficiency for continuous flow systems is defined b

76、y the relation (Ottino et al., 1981)</p><p><b>　　(15)</b></p><p>　　Before resorting to more detailed calculations, it is instructive to examine the upper mixing bound, obtained by se

77、tting eff(z) = 1 on the right-hand side of eq 15. Typically, the upper mixing bound predicts values significantly higher than are achieved in most practical mixing flows (Ottino and Macosko, 1980; Ottino, 1983), but prov

78、ides an indication of the influence of model parameters on mixing. Computation of the upper mixing bound is particularly simple for the SFT.</p><p><b>　　(16)</b></p><p>　　The proport

79、ionality constant required for equality is a function of the feed orientations {N}, and of ,, and L/H (through their influence on the mean residence time). Thus from eq 16, the relevant parameters that influence mixing

80、are {N},,, and L/H. The influence of W/H arises only indirectly through the change in the vertical coordinate of the fluid elements at the flights. </p><p>　　On the basis that when the upper bound increases,

81、 there is a possibility of improved mixing, then from eq 16, mixing may be improved by: (i) increasingat constant L/H and; (ii)increasin- g L/H at constantand; (iii) increasingfor>, decreasingfor<, at constant L/H

82、and , where</p><p><b>　　(17)</b></p><p><b>　　and</b></p><p>　　and (iv) decreasing H at constant L/H and.</p><p>　　These conclusions are in agree