渣浆泵叶轮流道内的脱流
一、叶轮内的脱流
    在大多数抽送均质液体的叶片泵内，液流在远离最佳况时与叶轮叶片流线型表面脱流。如抽送磨蚀性固液混合物的叶轮内，由于叶片数少和在叶片之间流道和轴向断面流道相当宽，不仅在小流量状态，而且在最佳状态，甚至在大流量状态，都能观察到这种现象。

在全苏水力机械科学研究所对FpY160/31.5型泵叶轮试验时，根据专门确定试样磨损形貌确认了液流脱流区形成。由非金属建筑材料科学研究所利用高速摄影机对rpY型泵抽送不同粒径级配的固液混合物时拍照，也确定了这种现象。

I. H.乌达洛夫在莫斯科矿冶学院利用高速摄影机进行了一批试验，确定了最佳状态和小流量状态时具有不同形状叶片的试验叶轮中脱流区边界。

对涂色水流拍摄照片得出这样的结果，即在最佳状态或者接近最佳状态时脱流区形态与一般叶片叶轮在小流量状态(0. 54Qam和0.375Qaum)时脱流区形态相似。
二、叶轮出口排挤系数的修正
  现在研究渣浆泵叶轮内脱流的条件，即根据叶轮和液流的参数考虑脱流区存在来估算叶轮出口排挤系数V2值。  
  首先求修正值，即存在脱流区时必须将其记在确定液流在叶轮出口处切向分速度的示意图上。保持斯托多拉和麦捷里提出的基本假设。并采用下列补充假定：

站出，

      (1)脱流从时片背面开始发生，在叶轮出口液流被排挤。这时液流在叶轮出口断面面积(考虑叶片厚度和可能的脱流)为

（2）在决定叶轮出口叶片间空间内流量的流束相对运动时，保持与无排挤时相同的方向，即限定脱硫区的表面平行于叶片移动（在图3-2-7上虚线EA）。

由涡漩引起的沿着叶轮出口边液流的速度环量

假定表面AB和BC垂直于由涡漩引起的流线，并且是顶角A和C的等分线，点B是液体在叶片间空间范围内旋转中心。用直线三角形面积代替曲线三角形ABC的面积，

式中t2——叶片节距；

    R2——叶轮半径；

     Z——叶轮叶片数。

于是液体沿着叶轮出口边平均速度为

式中u2——叶轮出口圆周速度。

用c2m代表不考虑脱流和叶片厚度所引起的排挤时液体在叶轮出口径向分速度

当存在液流拖流和考虑叶片有限厚度时，叶轮出口径向分速度等于。

从叶轮出口速度三角形可以得到考虑有限叶片数和由脱流和叶片有限厚度引起的排挤时叶轮出口液流切向分速度值为

当转速和流量都恒定时，等式左边具有最小值，即在排挤系数W:一定时叶轮出口切向分速度具有最大值。假定在给定的条件下，叶轮流道内形成不同强度的脱流。作为假定，采用在供给能量最大条件下，即在切向分速度cxa增加最大时，液流在叶轮内可能产生稳定脱流。
    因而，在叶轮内形成稳定脱流条件是

对于流量Q修正值，比较借助高速摄影机对3K一6型试验泵试验泵透明叶轮拍照得到的试验资料(HI.H. 乌达洛夫资料)与式(3-2-9) ~式(3-2-11)计算结果。根据乌达洛夫资料，在下列特性叶轮内，在流量Q= 0.0078m2/s时观察不到脱流区: D.-0.26m, b,=0.016m, 4:=19. 8m/s, B-=15，z=4, 9=0.76. 在所研究情况下，根据式(3-2-10)得到

于是对应无脱流叶片绕流的最小流量为

即采用计算方法确定Qo的误差为4%左右。

在低比转速挖泥泵上，在特殊情况下采用流道式叶轮。在这些叶轮出口液流排挤远大于叶片式叶轮，即。明显低于叶片式叶轮。流道轮内脱流区大小取决于非工作流道空间的相对尺寸;如果其尺寸大于可能脱流区尺寸，那么就不产生脱流。这种叶轮排挤系数可以根据式(3-2-9)确定，但必须预先根据叶轮几何尺寸计算出o.如果根据公式得到的w2大于w2那么这就表明在给定工况下叶轮道之间没有脱流，如果由式（3-2-9）确定的w2小与w0，那么w2小与1，并且在流道式叶轮内产生脱流。在w0值如此很小时，即在几何排挤很大时，脱流区尺寸明显要小于叶片式叶轮。

在推导式(3-2-9)时，没有引人工作状态方面的限制，因此公式可以在所有状态下下应用。根据流量变化一倍以上的很大范围内系数w2计算值(3-2-9)和试验值(乌达落夫资料)的比较，可以得到满意的一致性，因此在确定理论扬程时，可以利用式(3-2-9)估算对应泵特性曲线工作部分的所有状态下叶轮流道内脱流区尺寸。渣浆泵

De-flow in impeller runner of slurry pump

I. De-flow in impeller

In most vane pumps pumping homogeneous liquids, the flow is separated from the streamlined surface of the impeller blade when it is far from the optimum condition. For example, in the impeller pumping abrasive solid-liquid mixture, this phenomenon can be observed not only in the small flow state, but also in the optimum state, even in the large flow state, because of the small number of blades and the relatively wide flow passage between blades and the axial section.

When the impeller of FpY160/31.5 pump was tested by Quansu Institute of Hydraulic and Mechanical Sciences, the formation of liquid flow stripping zone was confirmed according to the wear morphology of specimens. The phenomenon was also determined by the use of high-speed camera by the Institute of Nonmetallic Building Materials Science when pumping solid-liquid mixtures of different particle sizes by rpY pump.

I. H. Udalov carried out a series of experiments at Moscow Institute of Mining and Metallurgy using high-speed cameras to determine the boundary of the detachment zone in the test impeller with different shape blades under the optimal and small flow conditions.

Photographs taken of the color-coated flow show that the shape of the stripping zone is similar to that of the general impeller blade in the small flow state (0.54Qam and 0.375Qaum).

2. Correction of extrusion coefficient at impeller outlet

Now, the condition of flow separation in the impeller of slurry pump is studied, that is, the extrusion coefficient V2 of the impeller outlet is estimated by considering the existence of flow separation zone according to the parameters of impeller and fluid flow.

Firstly, the corrected value must be recorded in the diagram of determining the tangential velocity of the liquid flow at the outlet of the impeller when there is a detachment zone. Keep the basic assumptions put forward by Stodora and McGerry. The following supplementary assumptions are adopted:

Stand out.

(1) De-flow begins at the back of the time sheet and is squeezed out at the outlet of the impeller. At this time, the area of the liquid flow at the outlet section of the impeller (considering the thickness of the blade and possible de-flow) is as follows

(2) When determining the relative motion of the flow beam in the space between the blades at the impeller outlet, the direction is the same as that without squeezing, i.e., the surface of the desulfurization zone is parallel to the blade movement (dashed EA in Fig. 3-2-7).

Velocity circulation of liquid flow along the outlet of impeller caused by vortices

Assuming that the surface AB and BC are perpendicular to the streamline caused by the eddy and are equal to the apex angle A and C, point B is the center of rotation of the liquid in the space between the blades. The area of curve triangle ABC is replaced by the area of straight triangle.

T2 - blade pitch;

R2 - impeller radius;

Z - Number of impeller blades.

So the average velocity of the liquid along the outlet of the impeller is zero.

U2 - the circumferential velocity of impeller outlet.

C2m is used to represent the radial partial velocity of liquid at the outlet of impeller when the extrusion caused by no consideration of the deflux and blade thickness is taken into account.

The radial partial velocity of the impeller outlet is equal to that of the impeller outlet when there is a liquid drag and the finite thickness of the blade is taken into account.

From the triangle of impeller outlet velocity, the tangential velocity values of fluid flow at impeller outlet can be obtained considering the number of finite blades and the displacement caused by the defLOW and the finite thickness of blades.

When the rotational speed and flow rate are constant, the left side of the equation has the minimum value, that is, the tangential velocity of impeller outlet has the maximum value when the extrusion coefficient W: is constant. It is assumed that under given conditions, different strength of the flow passage of the impeller will be formed. As a hypothesis, under the condition of maximum energy supply, that is, when the tangential velocity CXA increases to the maximum, the steady flow may occur in the impeller.

Therefore, the conditions for the formation of stable flow separation in the impeller are as follows:

For the flow Q correction value, the experimental data (HI. H. Udalov data) and the calculation results of formula (3-2-9) ~formula (3-2-11) obtained by high-speed camera photographing the transparent impeller of the 3K-6 test pump are compared. According to Udalov's data, no bleeding zone can be observed in the following characteristic impellers at flow Q= 0.0078 m2/s: D. -0.26m, b, = 0.016m, 4:= 19.8m/s, B-= 15, z = 4, 9= 0.76. Under the studied conditions, the bleeding zone can be obtained by formula (3-2-10).

So the minimum flow rate corresponding to the flow around the blade without detachment is as follows

That is to say, the error of Qo determined by calculation method is about 4%.

In the low specific speed dredging pump, the flow passage impeller is used under special circumstances. At the outlet of these impellers, the flow displacement is much larger than that of vane impellers. It is obviously lower than the vane impeller. The size of the stripping zone in the runner wheel depends on the relative size of the Non-Runner space; if the size of the stripping zone is larger than the size of the possible stripping zone, no stripping will occur. The extrusion coefficient of this impeller can be determined by formula (3-2-9), but it must be calculated in advance according to the geometric size of impeller. If the w_2 obtained by formula is larger than w_2, this indicates that there is no flow separation between the impeller passages under given working conditions. If w_2 determined by formula (3-2-9) is smaller than w_0, w_2 is smaller than 1, and in the flow passage impeller. Desulfurization occurs. When the W0 value is so small, that is to say, when the geometrical extrusion is very large, the size of the exit zone is obviously smaller than that of the vane impeller.

When deriving formula (3-2-9), there is no restriction on the working state of the introducer, so the formula can be applied in all states. Comparing the calculated value of coefficient W2 (3-2-9) with the experimental value (Udalov data) in a wide range with more than twice the flow rate variation, the satisfactory consistency can be obtained. Therefore, when determining the theoretical head, the size of the detachment zone in the impeller runner under all conditions corresponding to the working part of the pump characteristic curve can be estimated by formula (3-2-9).