多相流基礎(chǔ)chapter5-driftfluxmodel.ppt

Chapter five Drift flux model （第五章漂移流模型）,A type of separated flow model especially aimed at the relative motion of the phases, developed by G.B. Wallis. It is most applicable to bubbly flow and plug flow. It is not particularly relevant to annular flow because it has two characteristic velocities in one phase (liquid film velocity and liquid drop velocity),Introduction（簡(jiǎn)介）,Development of the model,slip velocity:,then:,The definition of drift flux (the gas relative to the liquid):,Definition of drift velocities:,where:,The drift velocities are the difference between the actual velocity and the average velocity.,The drift flux is the volumetric flux of a component relative to the surface moving at the average velocity.,The drift flux of the gas is:,Because we have:,We can obtain:,Similarly we have:,Attentions: From former equations, we can find the two drift flux of gas and liquid are equal and opposite. Commonly only drift flux of gas is used. In upwards flow with upward velocity, the drift flux of gas is positive. For homogeneous flow, because it is a flow with zero slip velocity, the drift flux of gas is equal to zero.,For steady-state one-dimensional flow, force balance can be written for the liquid in the absence of wall shear stress:,The physical importance of the drift flux,For gas:,Then we obtain:,Tip: In the absence of wall shear, F is a function only of the void fraction, physical properties.,It can also be written as:,Tip: Both the drift flux jgl and the slip velocity us are functions only of and of the physical properties of the system.,Example: bubbly flow,For bubbly flow, Whalley(1987) proposed one equation:,Where ub is the rising velocity of a single isolated bubble, because we have,Finally we obtained:,Drift flux vs void fraction,Because us is always a finite non-zero quantity, then,as,and,as,Drift flux vs void fraction,Drift flux can also be written as:,as,and,as,Then,is linear in,Tip:,Solution for void fraction for co-current upflow,The former two graphs can be combined as the right composite graph. It represents co-current upflows because both superficial velocities are positive. Increasing the gas velocity leads to an increase in the void fraction. Increasing the liquid velocity leads to a decrease in the void fraction.,The graph represents the liquid flows up and the gas flows down. There is no solution because the situation is not physically possible.,The graph represents the liquid flows down and the gas flows down. There is a solution.,For line “a”, corresponding to a small downward liquid velocity, there are two solutions (normally the one at lower void fraction is actually obtained). For line “b”, it represents a limit to the counter-current flow (This limit is known as flooding, a more general description of flooding will be given in Chapter 6),The graph represents the liquid flows down and the gas flows up. This situation is more complicated. For line “c”, corresponding to a large downward liquid velocity, there is no solution.,For flooding the superficial velocities are:,At “A”,so,and,;,At “B”,so,;,Example: plug flow,The rising velocity of a plug up in a tube of diameter d is given as (see whalley 1987):,Then the drift velocity of the gas relative to the mean fluid is:,If we use the result that the plug actually responds to the center-line velocity greater than the mean velocity, then we have:,Then the corresponding drift flux is:,Substituting from:,Then we have:,For the particular case of zero liquid flow (Vl=0),and,A general equation for the void fraction is:,Correlations due to profile effects:,The void fraction could be written as:,Since:,Then we have:,For bubbly flow, we have:,and,Considering:,Then we obtain:,Zuber and Findlay introducing a distribution parameter C0:,Zuber and Findlay suggested that for vertical upflow:,Where C0=1.13; For bubbly flow they suggested that:,This equation indicates the drift velocity is dependent only upon the physical properties and not upon the void fraction. Although it does not obey the condition that jgl0 as 1, it gives good results in the low-void-fraction region (0.3).,For bubbly flow, ugj is equivalent to the rise velocity ub, then:,For low-pressure air-water flow this expression has a value of 0.23m/s, it is very near the experimental result for equivalent diameters in the range 1mm to 10mm; For steam-water flow the value of the bubble rise velocity changes only slowly with pressure, at least in the range 1bar to 100bar. Near the critical point ub falls rapidly because 0 and g/ l 1.,Bubble rise velocity for various pressures of steam-water flow:,空泡份額的計(jì)算,Lahey給出了各種不同空泡份額分布情況下的變化，如圖所示,空泡份額的計(jì)算,除了分布參數(shù)（Distribution Parameter）和平均漂移速度（Averaged Drift Velocity）外，其它所有項(xiàng)均是可測(cè)量的，故對(duì)一些流型，漂移速度已有關(guān)聯(lián)，分布參數(shù)也進(jìn)行了確定。 一旦分布參數(shù)和漂移速度的值已經(jīng)確定，那么確定各種氣液流率下空泡份額就簡(jiǎn)單了，只需將 變一下形，就可得到：,表中給出了合理的分布參數(shù)和漂移速度值，可用來(lái)求得空泡份額。值得注意的是，對(duì)于環(huán)狀流給出的這些值僅是粗略近似的，因?yàn)榄h(huán)狀流是一種分離流動(dòng)，其漂移速度通常不是常數(shù)。然而，只要兩相混合物的速度遠(yuǎn)大于漂移速度，給出的值仍能大致滿足同向環(huán)狀流動(dòng)。還要注意的是，除分母上所用密度不同外， 與 形式上一樣。這也反映了同屬?gòu)浬⒘鲃?dòng)的泡狀流與霧狀流之間的某些共性。,空泡份額的計(jì)算,注意，由于漂移和分布參數(shù)的選擇依賴(lài)于空泡份額，所以有時(shí)需要采用迭代的方法。這通常很簡(jiǎn)單就可以做到的，而且有時(shí)在實(shí)際中并不是總是必要的。 另外要注意的是，若漂移速度相對(duì)總的體積流密度為小，那么空泡份額由下式粗略地給出,這樣，我們可以看到，即使沒(méi)有局部滑移，空泡份額 與運(yùn)動(dòng)學(xué)靜態(tài)空泡份額 仍是有差異的。此差異是由于空泡份額（濃度）和速度分布的存在而造成的?？张莘蓊~與速度兩者之間的相互作用影響（即表達(dá)為分布參數(shù)）由分布參數(shù)C0的定義式給出。由前表可以看到，對(duì)于簡(jiǎn)單的絕熱流動(dòng)，C0大致在1.25以下變化。所以，空泡份額常常是比運(yùn)動(dòng)學(xué)靜態(tài)空泡份額小約20%30%。這是由于空泡總是趨于集中在高速區(qū)，這樣可以被優(yōu)先帶走。（應(yīng)當(dāng)注意，在有傳