AF固體物在葉輪內(nèi)產(chǎn)生的附加水力損失
一、葉輪流道內(nèi)顆粒動(dòng)態(tài)平衡方程
    當(dāng)固液混合物在旋轉(zhuǎn)流道內(nèi)運(yùn)動(dòng)時(shí)，其尺寸大于臨界尺的顆粒發(fā)生明顯分離。較小的顆粒參與紊動(dòng)混合，它們的存在不影響水力損失。
    

那些正新多與東動(dòng)混合過(guò)程且不沿容與液休在葉輪流道內(nèi)流線重合  :的軌線運(yùn)動(dòng)的顆粒下面確定消耗在固體顆粒相對(duì)載流體運(yùn)動(dòng)方面的功。首先研究混合物流動(dòng)中單一固體顆粒在葉片之間流道內(nèi)的相對(duì)運(yùn)動(dòng)，這種運(yùn)動(dòng)是穩(wěn)定運(yùn)動(dòng)。將作用在顆粒上的力投影到相對(duì)運(yùn)動(dòng)軌線切線方向上。

固體顆粒體積和密度分別用qt和pr表示，顆粒沿著相對(duì)軌線的速度為wt。寫(xiě)出固體顆粒動(dòng)態(tài)平衡方程式，即

在此式中，左邊是考慮視在質(zhì)量的固體顆粒慣性力在相對(duì)速度方向上的投影，右邊是離心力、壓力梯度作用下所產(chǎn)生的力和顆粒在相對(duì)流體運(yùn)動(dòng)時(shí)迎面阻力所產(chǎn)生的力之和。
    因?yàn)檠芯抗腆w顆粒沿著其軌線的運(yùn)動(dòng)，所以，wrdt=ds,dwr/dt=dScosg/2=dR (式中，ds為固體顆粒軌線微小長(zhǎng)度)。
    于是，顆粒動(dòng)態(tài)平衡方程式可以寫(xiě)為
    在參數(shù)從葉輪入口到葉輪出口的變化范圍內(nèi)，對(duì)上式積分后得到
    固體顆粒在葉輪出口和入口處的相對(duì)速度;
    固體顆粒沿著相對(duì)軌線運(yùn)動(dòng)時(shí)迎面阻力所做的功用OT表示，于是就得到
    這部分功決定水力損失，其損失與固體顆粒沿著各自軌線(不與液體流線重合)運(yùn)動(dòng)而不參與紊動(dòng)混合過(guò)程有關(guān)。在所得到的公式中壓力降(pr- P!)用其表達(dá)式代替
    克服迎面阻力所消耗的功為
二、葉輪內(nèi)的總損失
    固液混合物在葉輪內(nèi)流動(dòng)時(shí)總損失hx是泵抽送載流體時(shí)葉輪內(nèi)的損失hn和由于重新參與紊動(dòng)混合的固體顆粒相對(duì)運(yùn)動(dòng)而產(chǎn)生的附加損失Ohx之和，因此，hk=hxo+Ohr。
    繼續(xù)與混合物起運(yùn)動(dòng)的且參與紊動(dòng)混合的顆粒體積濃度用P1表示，而顆粒尺寸大于臨界尺寸且沿著本身軌線運(yùn)動(dòng)的顆粒體積濃度用P2表示，固體顆粒在混合物中總體積濃度為: P=P1+P2。
    在葉輪流道內(nèi)沿著各自軌線運(yùn)動(dòng)且單位時(shí)間內(nèi)通過(guò)葉輪的顆粒數(shù)量等于P2Qr/qT (式中，Qr為泵的流量)。單位時(shí)間相應(yīng)地消耗的功等于P:QraT/gr.
    克服不參與紊動(dòng)混合的固體顆粒迎面阻力所做的功與輸送固液混合物單位重量所做的

功比值，即為葉輪附加水頭損失，這種損失與載流體內(nèi)存在的且與葉輪流道內(nèi)流體相對(duì)運(yùn)動(dòng)的固體顆粒有關(guān)。因此，得到。
利用式(3-5-7),，可以得到下式

從式（3-5-8）中可以得出下列結(jié)論：

(1) 懸浮物的級(jí)配在確定水頭水力損失時(shí)起到重要作用。當(dāng)懸浮物由大于臨界顆粒的顆粒組成時(shí)，即P,=0時(shí)，級(jí)配不影響附加水頭損失，這種損失與混合物中存在固體顆粒有關(guān)。
    (2)當(dāng)泵的揚(yáng)程增加時(shí)，即(u3 - uf)/2z項(xiàng)增大時(shí)，葉輪中附加水頭損失增大。

(3)應(yīng)該注意，公式右邊括號(hào)中第二項(xiàng)和第三項(xiàng)比第一項(xiàng)小得多，因此在泵的流量變化時(shí)葉輪中附加水頭損失變化很小。
    (4)在抽送懸浮物時(shí)，當(dāng)所有顆粒小于臨界顆粒時(shí)，即P:=P時(shí)，就不存在附加損失，這時(shí)可以將混合物看做均質(zhì)液體。AF泡沫泵

Additional Hydraulic Loss Caused by AF Solid in Impeller

I. Dynamic Balance Equation of Particles in Impeller Channel

When the solid-liquid mixture moves in the rotating channel, the particles whose size is larger than the critical ruler are separated obviously. Smaller particles participate in turbulent mixing, and their presence does not affect hydraulic loss.

The mixing process of Zhengxin is mostly Eastward-Moving and does not coincide with the flow line in the impeller passage along the volume and liquid rest: the work consumed by the solid particles relative to the fluid-carrying motion is determined under the particles moving along the trajectory. Firstly, the relative motion of a single solid particle in the flow passage between blades is studied, which is a stable motion. The force acting on the particles is projected to the tangent direction of the relative trajectory.

The volume and density of solid particles are expressed by QT and PR respectively. The velocity of particles along the relative trajectory is wt. Write out the dynamic equilibrium equation of solid particles, i.e.

In this formula, the projection of inertia force of solid particles in relative velocity direction is considered on the left side, and the sum of forces produced by centrifugal force, pressure gradient and the force produced by the head-on resistance of particles in relative fluid motion is considered on the right side.

Because the motion of solid particles along their trajectories is studied, wrdt = ds, DWR / dt = dScosg / 2 = dR (in formula, DS is the small length of solid particle trajectories).

Thus, the particle dynamic equilibrium equation can be written as

In the range of parameters from impeller inlet to impeller outlet, the upper integral is obtained.

Relative velocity of solid particles at impeller outlet and inlet;

The functional OT representation of the head-on drag of solid particles moving along relative trajectories is obtained.

This part of the work determines the hydraulic loss, which is related to the solid particles moving along their respective trajectories (not coinciding with the liquid streamlines) and not participating in the turbulent mixing process. In the obtained formula, the pressure drop (pr-P!) is replaced by its expression.

Work consumed to overcome head-on resistance

2. Total loss in impeller

The total loss of HX of solid-liquid mixture flowing in impeller is the sum of the loss of HN in impeller when pumping fluid and the additional loss of Ohx caused by the relative motion of solid particles re-participating in turbulent mixing. Therefore, HK = HXO + Ohr.

The volume concentration of particles which continue to move with the mixture and participate in turbulent mixing is expressed by P1, while the volume concentration of particles whose size is larger than the critical size and moves along its own trajectory is expressed by P2, and the total volume concentration of solid particles in the mixture is P=P1+P2.

The number of particles passing through the impeller in a unit time is equal to P2Qr/qT (in this case, Qr is the flow rate of the pump). The corresponding work consumed per unit time is equal to P:QraT/gr.

Work done to overcome the head-on resistance of solid particles that do not participate in turbulent mixing and to transport solid-liquid mixtures per unit weight

The ratio of work is the additional head loss of impeller, which is related to the solid particles existing in the carrier fluid and the relative motion of the fluid in the impeller channel. So, get it.

By using formula (3-5-7), the following formula can be obtained.

The following conclusions can be drawn from formula (3-5-8):

(1) The gradation of suspended solids plays an important role in determining head hydraulic loss. When suspended solids are composed of particles larger than critical particles, i.e. P, = 0, the gradation does not affect the additional head loss, which is related to the presence of solid particles in the mixture.

(2) When the pump head increases, i.e. (u3-uf)/2z term increases, the additional head loss in impeller increases.

(3) It should be noted that the second and third terms in the brackets on the right side of the formula are much smaller than the first term, so the additional head loss in the impeller changes little when the flow rate of the pump changes.

(4) When the suspended solids are pumped, when all the particles are smaller than the critical particles, i.e. P:=P, there is no additional loss. At this time, the mixture can be regarded as homogeneous liquid.