多相流基础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（简介）,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:,空泡份额的计算,Lahey给出了各种不同空泡份额分布情况下的变化，如图所示,空泡份额的计算,除了分布参数（Distribution Parameter）和平均漂移速度（Averaged Drift Velocity）外，其它所有项均是可测量的，故对一些流型，漂移速度已有关联，分布参数也进行了确定。 一旦分布参数和漂移速度的值已经确定，那么确定各种气液流率下空泡份额就简单了，只需将 变一下形，就可得到：,表中给出了合理的分布参数和漂移速度值，可用来求得空泡份额。值得注意的是，对于环状流给出的这些值仅是粗略近似的，因为环状流是一种分离流动，其漂移速度通常不是常数。然而，只要两相混合物的速度远大于漂移速度，给出的值仍能大致满足同向环状流动。还要注意的是，除分母上所用密度不同外， 与 形式上一样。这也反映了同属弥散流动的泡状流与雾状流之间的某些共性。,空泡份额的计算,注意，由于漂移和分布参数的选择依赖于空泡份额，所以有时需要采用迭代的方法。这通常很简单就可以做到的，而且有时在实际中并不是总是必要的。 另外要注意的是，若漂移速度相对总的体积流密度为小，那么空泡份额由下式粗略地给出,这样，我们可以看到，即使没有局部滑移，空泡份额 与运动学静态空泡份额 仍是有差异的。此差异是由于空泡份额（浓度）和速度分布的存在而造成的。空泡份额与速度两者之间的相互作用影响（即表达为分布参数）由分布参数C0的定义式给出。由前表可以看到，对于简单的绝热流动，C0大致在1.25以下变化。所以，空泡份额常常是比运动学静态空泡份额小约20%30%。这是由于空泡总是趋于集中在高速区，这样可以被优先带走。（应当注意，在有传