AF泡沫泵抽送清水時工作原理

第一節(jié) 旋轉(zhuǎn)環(huán)列葉柵流體動力學(xué)
一、泵的理論揚(yáng)程
   泵的理論揚(yáng)程Ht是葉輪傳給單位重量流體的能量。因此，理論揚(yáng)程等于泵的揚(yáng)程H和水力損失hw之和，即Hr=H+hw.為了確定它與哪些參數(shù)有關(guān)，下面研究流體在葉片泵葉輪內(nèi)流動示意圖(圖3-2-1).繪出限定通過葉輪葉片液流的控制表面(用波紋線表示)。液體壓力垂直地作用在葉片前有效截面AB和A’B’上和葉片后有效截面CD和C’D‘上，這部分液體相對葉輪旋轉(zhuǎn)軸不產(chǎn)生力矩。與液體黏性有關(guān)的切應(yīng)力沿著截面作用，但是它所引起的力矩與泵軸上的扭矩相比很小，可以忽略。
   沿著壁面BD和B’D‘作用摩擦力，因此相對葉輪旋轉(zhuǎn)軸產(chǎn)生摩擦力矩Mr.沿著表面AC和A’C‘,在葉柵固定處發(fā)生應(yīng)力，相對葉輪軸的合成力矩等于泵軸上的扭矩M,。
   當(dāng)流體對葉輪工作葉片繞流時，產(chǎn)生流體動力，其力矩M=M, Mm， 于是單位時間內(nèi)傳給流經(jīng)泵內(nèi)液體的功率為
N= Mw

式中w——泵軸角速度。
   假定泵的流量為Q,液體密度為p.于是單位時間內(nèi)傳給流經(jīng)泵內(nèi)液體的功率為
Nτ= HrpgQ
因為研究的是理想化的液體流動圖，所以不考慮泄漏量q。
現(xiàn)在可以確定理論揚(yáng)程為

Hr=Mw
Qpg
   上面清楚了作用在葉輪葉片上流體動力力矩與液流哪些運(yùn)動參數(shù)有關(guān)。為此將動力矩方程式(歐拉方程式)應(yīng)用于所討論的系統(tǒng)上。

在流入葉片前的有效截面上,研究單位時間內(nèi)穿過有效截面的單元面積df的液體質(zhì)量pdQ.這時液流圓周分速度等于Cu,而旋轉(zhuǎn)軸到所研究面積的徑向距離為RgR (下標(biāo)1和2分別表示葉輪入口和出口處的參數(shù))。

在所研究液流截面之間液流動量矩的變化量等于葉輪葉片上流體動力矩， 即為
    首先研究時片數(shù)無限多的特殊情況，當(dāng)葉輪前后有效截而所有點上速度矩為常數(shù)時，即

    因為液流速度環(huán)量，在葉輪前為r，葉輪后為，所以葉輪葉片上流體動力矩

這個表達(dá)式在葉片泵工作過程理論中起到重要作用，因為它將液流在兩個控制截面(葉輪前后)上的平均運(yùn)動學(xué)參數(shù)與理論揚(yáng)程聯(lián)系起來。
    在一般情況下，當(dāng)液流在葉輪葉片前后截面所有點上速度矩不能采用為常數(shù)時，可以利用它們的平均值。于是
    

為了估算給定泵軸角速度、葉輪入口速度環(huán)量和流量時理論揚(yáng)程，必須確定葉輪出口速度環(huán)量。為此研究下列液體流經(jīng)離心泵葉輪的理想化示意圖。
(1)液體流經(jīng)由徑向配置的圓柱流線葉型組成的離心泵葉輪，葉型由兩側(cè)的平面限定(圖3-2-2)，這個系統(tǒng)稱為平面徑向葉柵。
    假定葉柵寬度用b表示，通過葉柵液體流量用Q表示，得到流過葉柵單位寬度液體流量為
            q=Q/b

假定液體在垂直其軸線的所有平面上的流動是運(yùn)動學(xué)相同的，這樣，在研究液體對葉型繞流時，可以認(rèn)為這種運(yùn)動為平面運(yùn)動。  

(2)流經(jīng)葉輪的液流為勢流，這就可以利用勢流多連通域的特性，如果繞每個葉片葉型的速度環(huán)量等于ra，那么葉柵出口處速度環(huán)量為

實際上，真實液體在葉輪中流動時，沿著葉片表面和壁面形成邊界層。因此可能產(chǎn)生脫流，出現(xiàn)反向流動，生成由液流帶走的自由渦漩。但是，現(xiàn)代葉輪結(jié)構(gòu)保證最大限度地降低水力損失，因此可以認(rèn)為至少在泵最佳工況時脫流和渦漩形成是不大的，所起的作是次要的。由于壁面和葉片長度不大，邊界厚度可以忽略。因此液流可以采取為勢流。
    (3)葉片葉型端部磨削，根據(jù)恰普雷金假設(shè)可以認(rèn)為，在葉型繞流時，流束匯合總具在葉型磨削點處形成。
    (4)在流量q和葉柵前環(huán)量r’給定時，葉柵后環(huán)量值只能是唯一的。
    在研究對平行配置葉型系統(tǒng)中單獨葉型繞流時，假定在葉型前一定距離上液流是平面平行流動，在平面葉柵或者單獨葉型后一定距離上液流均勻流動，并且再變?yōu)槠矫嫫叫辛鲃印?/span>
    研究環(huán)列葉柵，不只隔離處在葉輪入口前的泵元件，而且隔離排水設(shè)備，即不考慮它們對葉柵工作的影響。假定在葉柵入口前，液流徑向分速度由強(qiáng)度為q的源來確定，而圓周速度分量則由環(huán)量I‘來確定.
    在葉柵后定距離上，液流均勻流動。同時徑向分速度由與葉柵前相同強(qiáng)度的源來確定，而圓周速度分量則由位于葉柵出口處的速度環(huán)量I“來確定。下面確定固定葉柵和移動葉柵時速度環(huán)量I”與流量和速度環(huán)量r’之間的聯(lián)系。先研究兩種液流對固定葉柵無脫流的繞流。第一種液流用流量q,葉柵入口速度環(huán)量I:和出口環(huán)量T”表征，第二種液流分別用流量q2，環(huán)量T2和I”表征。環(huán)量T和流量q1變化a倍，這將導(dǎo)致液流中所有速度變化a倍，因而葉柵出口速度環(huán)量廠”變化a倍。同時流線保持其以前的形狀。對于第二種液流，葉柵入口流量和速度環(huán)量變化b倍，這將導(dǎo)致葉柵出口速度環(huán)量變化b倍。
液體速度方向，直接沿著葉柵流線型葉型，將與葉片葉型相切。除此之外，對于任意葉片磨削點繞流的情況，就確定了流束與葉型的匯合點。
    將兩種所研究的液流合成，其速度分別增大到a和b倍。因為在葉片表面上，第一種和第二種液流速度方向為切向，即其方向在流線型葉型任意點均重合，在液流合成時，沿著葉片葉型的速度值相加。因為流束與葉型的匯合點被確定，沿著葉片葉型的速度環(huán)量也相加;因為兩個液流具有速度勢;因而葉柵出口速度環(huán)量相加.
    所得到的總液流對葉柵葉型繞流，并且具有下列特性。流經(jīng)葉柵的液體流量等于流量之和: q=aq1 +bqz (流出強(qiáng)度等于流量之和)。因為葉柵前液流圓周速度方向與葉柵入口圓周相切，因此葉柵入口速度環(huán)量I等于合成液流環(huán)量之和，即I=aI1 +bI2.葉柵出口速度環(huán)量為I“=aI” +bI“2.根據(jù)所得到的等式消除任意值a和b，可以求出已知葉柵葉片繞流的任意可能的液流之I”、I‘ 和q之間的關(guān)系式如下

如上所述，在T和q值給定時，f值是唯的。因此，對于給定葉柵

  繼續(xù)研究液體在旋轉(zhuǎn)葉柵內(nèi)的流動。假定繞葉柵液流絕對運(yùn)動具有速度勢。因為不同流線在不同瞬時將通過旋轉(zhuǎn)葉柵范圍內(nèi)確定的固定點，因此所研究的液流是非穩(wěn)定流動。在無脫流繞流時，直接沿著葉片葉型運(yùn)動的液體質(zhì)點將有兩個速度分量一圓周速度u,等于葉片葉型在同一點的圓周速度，和相對速度w,其方向與葉片葉型相切。在葉片葉型每一點的圓周速度u與葉輪角速度w有關(guān)，相對速度與流過葉柵的液體流量有關(guān)。
   應(yīng)該注意，在流量變化一樣和葉柵入口速度環(huán)量相同時，液流沿著移動和固定葉柵葉片葉型相對速度變化是相等的。

    繞旋轉(zhuǎn)葉柵的液流和繞固定葉柵的液流相加，得到第二個液流，它繞角速度相同的旋轉(zhuǎn)葉柵流動。
  下面確定在具有角速度w,的旋轉(zhuǎn)葉冊時葉柵入口和出口的流量與速度環(huán)量之間的關(guān)系。令繞葉柵葉片的液流流量用q.，入口速度環(huán)量用r和出口速度用工”表示。
  在葉柵角速度為時，同樣液流的特性如下:流量q-qa/am.葉福人口速度環(huán)量

r.=r,w/w，葉柵出口速度環(huán)量I“,=Ia/a

下面研究繞同一葉柵葉片流動的液流，現(xiàn)在已是固定葉柵。這種液流的參數(shù)分別用9、r和I”表示。  

這兩種液流相加，就形成第三個液流，它繞角速度為w的旋轉(zhuǎn)葉柵葉片流動。所得到的液流流量等于兩個合成液流流量之和，即q=g-+g.而葉柵入口液流的速度環(huán)量f=r.+r. 

 兩個相加液流是有勢的，因為相加液流速度方向在葉片繞流時在葉型每上點是相同的(葉型切向)和葉片葉型磨削點就確定了流束與葉型的匯合點和方向，所以分別引起相加液流中每一個液流的速度環(huán)量求和。

因此，葉柵出口所研究兩個液流速度環(huán)量也相加，對于總的液流

根據(jù)已知液流特性可以求出因子s液流繞其以角速度w旋轉(zhuǎn)時所研究葉柵葉型流動值s與液流是否被選擇為原始液流無關(guān)，因為在葉器人口環(huán)量f、流量q和葉柵角速度給定時，只可能是一個確定的葉柵提出口速變環(huán)量值T.

即與流量呈線性關(guān)系。

環(huán)列旋轉(zhuǎn)葉棚理論是確定時片泵理論揚(yáng)程各種方法的基礎(chǔ)。式(3-2-6)在上述假定條件下是正確的。
    對于一般情況來說， 葉柵特性k、to和工不能確定，只有在液體在葉輪內(nèi)流動確定的條件下才可以求出。AF泡沫泵

Working principle of AF foam pump for pumping clean water

Section 1 Hydrodynamics of Rotating Annular Cascades

1. The theoretical head of the pump

The theoretical head ht of the pump is the energy transmitted by the impeller to the unit weight fluid. Therefore, the theoretical head is equal to the sum of pump head H and hydraulic loss hw, i.e. Hr=H+hw. In order to determine which parameters are related to it, the following study is made on the flow diagram of fluid in the impeller of vane pump (Figure 3-2-1). The control surface (expressed by corrugated lines) which restricts the flow through the impeller blade is drawn. The liquid pressure acts vertically on the effective sections AB and A'B'in front of the blade and CD and C'D' in the back of the blade. This part of the liquid produces no torque relative to the impeller rotating shaft. The shear stress related to the liquid viscosity acts along the cross section, but the torque caused by it is very small compared with the torque on the shaft of the pump and can be neglected.

Friction force acts along the wall BD and B'D', so the friction moment is produced relative to the impeller rotating shaft Mr. along the surface AC and A'C', stress occurs at the fixed position of the cascade, and the composite moment of the relative impeller shaft is equal to the torque M on the pump shaft.

When the fluid flows around the impeller blade, it generates hydrodynamic force, whose moment M = M, Mm, so the power transmitted to the liquid flowing through the pump in unit time is as follows:

N= Mw

W - pump shaft angular speed in type.

Assuming that the flow rate of the pump is Q and the density of the liquid is p, the power transmitted to the liquid flowing through the pump in unit time is 0.

N tau = HrpgQ

Because the ideal liquid flow diagram is studied, the leakage q is not considered.

Now we can confirm that the theoretical head is

Hr=Mw

Qpg

It is clear that the hydrodynamic moment acting on the impeller blade is related to the motion parameters of the fluid flow. For this reason, the dynamic moment equation (Euler equation) is applied to the system under discussion.

On the effective section before inflow into the blade, the liquid mass pdQ of unit area DF passing through the effective section in unit time is studied. At this time, the circumferential velocity of the liquid flow is equal to that of copper, and the radial distance from the rotating axis to the studied area is RgR (subscripts 1 and 2 represent the parameters at the inlet and outlet of the impeller, respectively).

The variation of fluid flow momentum between the studied fluid flow sections is equal to the hydrodynamic momentum on the impeller blade.

Firstly, the special case of infinite number of time slices is studied. When the impeller is effectively truncated before and after, and the velocity moment at all points is constant, that is to say

Because the fluid velocity circulation is r in front of the impeller and R behind the impeller, the hydrodynamic moment on the impeller blade

This expression plays an important role in the theory of working process of vane pump, because it links the average kinematics parameters of fluid flow on two control sections (front and back of impeller) with the theoretical head.

In general, when the velocity moments of fluid flow at all points of impeller blade cross section can not be used as constants, their average values can be used. Therefore

In order to estimate the theoretical head of a given pump shaft angular velocity, impeller inlet velocity circulation and flow rate, it is necessary to determine the impeller outlet velocity circulation. For this reason, the following ideal schematic diagram of liquid flowing through centrifugal pump impeller is studied.

(1) The centrifugal pump impeller is composed of a radially arranged cylindrical streamline blade. The blade profile is defined by the planes on both sides (Fig. 3-2-2). This system is called a planar radial cascade.

Assuming that the width of the cascade is expressed in B and the liquid flow through the cascade is expressed in Q, the liquid flow through the unit width of the cascade is obtained as follows.

Q=Q/b

It is assumed that the flow of liquid in all planes perpendicular to its axis is kinematically identical. Thus, when studying the flow of liquid around the blade, it can be considered as a planar motion.

(2) The fluid flow through the impeller is potential flow, which can make use of the characteristics of potential flow multi-connected region. If the velocity circulation around each blade is equal to ra, then the velocity circulation at the outlet of the cascade is equal to ra.

In fact, when the real liquid flows in the impeller, a boundary layer is formed along the blade surface and wall. Therefore, it is possible to produce deflow, reverse flow and free vortices carried away by liquid flow. However, the modern impeller structure guarantees the maximum reduction of hydraulic loss, so it can be considered that at least in the best working conditions of the pump, the formation of the flow and eddy is not large, the work is secondary. Because the length of the wall and blade is small, the boundary thickness can be neglected. So the liquid flow can be taken as potential flow.

(3) When the blade is grinded at the end of blade profile, according to the Chaplegin hypothesis, it can be concluded that when the blade is flowing around the blade profile, the convergence of flow beams is formed at the grinding point of the blade profile.

(4) When the flow rate Q and cascade front circulation R'are given, the cascade back circulation value can only be unique.

When studying the flow around a single blade in a parallel configuration blade system, it is assumed that the liquid flow is planar parallel at a certain distance before the blade profile and uniform at a certain distance after the planar cascade or the single blade profile, and then becomes planar parallel flow.

The annular cascade is not only isolated from the pump components in front of the impeller entrance, but also from the drainage equipment, i.e. without considering their influence on the cascade operation. It is assumed that before the cascade entrance, the radial partial velocity of the fluid flow is determined by the source with strength q, while the circumferential velocity component is determined by the circulation I'.

At a fixed distance behind the cascade, the flow is uniform. At the same time, the radial partial velocity is determined by the source with the same intensity as that in front of the cascade, while the circumferential velocity component is determined by the velocity circulation I located at the exit of the cascade. Next, the relationship between velocity circulation I"and flow rate and velocity circulation r" in fixed and moving cascades is determined. Firstly, the flow around a fixed cascade with two kinds of fluid flow without detachment is studied. The first flow is characterized by flow rate q, cascade inlet velocity circulation I: and outlet circulation T", and the second flow is characterized by flow rate q2, circulation T2 and I, respectively.