。  

這兩種液流相加

，就形成第三個(gè)液流，它繞角速度為w的旋轉(zhuǎn)葉柵葉片流動(dòng)。所得到的液流流量等于兩個(gè)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(gè)相加液流是有勢(shì)的，因?yàn)橄嗉右毫魉俣确较蛟谌~片繞流時(shí)在葉型每上點(diǎn)是相同的(葉型切向)和葉片葉型磨削點(diǎn)就確定了流束與葉型的匯合點(diǎn)和方向

，所以分別引起相加液流中每一個(gè)液流的速度環(huán)量求和。

因此，葉柵出口所研究?jī)蓚€(gè)液流速度環(huán)量也相加

，對(duì)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(shí)所研究葉柵葉型流動(dòng)值s與液流是否被選擇為原始液流無(wú)關(guān)

，因?yàn)樵谌~器人口環(huán)量f、流量q和葉柵角速度給定時(shí)

，只可能是一個(gè)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(shí)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(duì)于一般情況來(lái)說(shuō)

， 葉柵特性k

、to和工不能確定

，只有在液體在葉輪內(nèi)流動(dòng)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.