AF泡沫泵泵內(nèi)水力流量揚(yáng)程損失
    葉片泵其中包括抽送磨蝕性固液混合物泵的理論揚(yáng)程，可以利用試驗(yàn)方法根據(jù)專門平衡試驗(yàn)結(jié)果(首先C.C魯?shù)履蜓芯吭囼?yàn)方法，而中.A.鮑格尼茨卡婭進(jìn)行了泵的試驗(yàn))確定。
    為了求出平衡試驗(yàn)時(shí)的理論揚(yáng)程，可以采用下列方法。
    根據(jù)預(yù)先試驗(yàn)結(jié)果，考慮圓盤摩擦損失，確定消耗在機(jī)械損失方面的功率，測(cè)量通過葉輪入口密封溢流的液體數(shù)量q，并估算泄漏功率損失，此后測(cè)量泵的功率和與流量有關(guān)的泵產(chǎn)生的揚(yáng)程。
    流過葉輪的液體數(shù)量等于泵的流量和溢流量q之和。傳給流經(jīng)葉輪液體的功率，即水力功率Now等于水泵功率與消耗在機(jī)械損失(考慮圓盤摩擦)和容積損失(由試驗(yàn)預(yù)先確定)方面功率之差。于是，傳給流經(jīng)葉輪單位重量液體的功，即泵的理論揚(yáng)程為

以給定的精度可以測(cè)量泵的流量和功率，因此確定泵理論揚(yáng)程的方法是普遍采用的。知道泵不同流量時(shí)的理論揚(yáng)程，根據(jù)歐拉方程式，就可以計(jì)算葉輪出口切向速度c2u。

應(yīng)該注意，利用所述方法以足夠的精度可以以求出接近或者大于最佳流量時(shí)的理論揚(yáng)程。其理由如下，在小于最佳流量時(shí)，關(guān)系N/Q+q，因而理論揚(yáng)程與值Q+q有關(guān)，開

始迅速增加，并且變?yōu)榉蔷€性關(guān)系(圖3-2-9)。應(yīng)注意，在零流量時(shí)，形式上流過葉輪流量只等于泄漏值q，與流量Q相比其值很小，可見泵功率具有最終值。因此，由上述方法可以得到確定的理論楊程和根據(jù)其值計(jì)算的葉輪出口速度環(huán)量是相當(dāng)大的。同時(shí)理論揚(yáng)程不是流量的線性函數(shù)。
    

但是，根據(jù)旋轉(zhuǎn)環(huán)列葉柵理論，葉輪產(chǎn)生的理論揚(yáng)程是流量的線性函數(shù)，因此在平衡試驗(yàn)時(shí)得到的表證最佳和大流量狀態(tài)時(shí)關(guān)系Ht=f（Q）線性部分的直線，一般可以外推到低流量區(qū)(直線Hr.cam)
    如果外推法得到的理論揚(yáng)程(Ht.1cm) 乘以對(duì)應(yīng)值(Q+q)和pg，那么所求出的水力功率將明顯低于泵的測(cè)量功率(考慮消耗在機(jī)械損失方面的功率)。水力功率之差——試驗(yàn)法得到的值和上述方法的計(jì)算值之差，稱為制動(dòng)功率。在小流量時(shí)，制動(dòng)功率急劇增大。泵零流量對(duì)應(yīng)于那種所有水力功率完全全變?yōu)橹苿?dòng)功率的狀態(tài)。

 制動(dòng)功率的發(fā)生可以用葉輪和壓水室之間出現(xiàn)液體體封閉環(huán)流來解釋，即液體以葉輪傳給儲(chǔ)備能量流進(jìn)壓水室。這部分液體從壓水室返回葉輪，但已具有對(duì)應(yīng)于壓水室內(nèi)的儲(chǔ)備能量。這個(gè)過程與功的附加消耗有關(guān)，這部分功不是用于提高液體揚(yáng)程上面，而是轉(zhuǎn)化為損失。

二、液體在泵內(nèi)的流動(dòng)條件

    下面研究液體在泵葉輪內(nèi)的流動(dòng)條件，在這種條件下可能出現(xiàn)液體在葉輪和壓水室之間交換。當(dāng)泵流量足以使葉輪出口斷面由流動(dòng)液體完全充滿時(shí)，就可以保證葉片葉型無脫流的繞流，根據(jù)葉柵流體動(dòng)力學(xué)理論，理論揚(yáng)程與泵流量的關(guān)系是線性的。
    在小流量時(shí)，勢(shì)流速度下降，葉片葉型沖角增大，產(chǎn)生附加在葉片背面上的部分液流制動(dòng)。在這些情況下，已不能將葉輪葉片繞流看做無脫流運(yùn)動(dòng)。這時(shí)理論揚(yáng)程與泵流量之間的關(guān)系可能是非線性的。因此在泵小流量狀態(tài)時(shí)采用的理論揚(yáng)程與流量之間線性規(guī)律外推方法，不能認(rèn)為有充分的根據(jù)。
    在本章第一節(jié)，根據(jù)斯托多拉方法得到了有限時(shí)片教時(shí)理論揚(yáng)程H的公式，存在很大脫流區(qū)將導(dǎo)致考慮脫流區(qū)[式(3-2 8和不考慮股流區(qū)[式(3-2-7)時(shí)確定的葉輪出口絕對(duì)速度的切向分速度C2o 有明顯區(qū)別。

比較考慮和不考慮脫流區(qū)時(shí)C表達(dá)式指出，根據(jù)斯托多拉方法對(duì)有限片數(shù)的修正公式

在推導(dǎo)關(guān)系式(3-2-12)時(shí)，曾采用沿著直線EA發(fā)生液流脫流,但是實(shí)際上沿著直線DA發(fā)生。
圖3-2-10上用直線近似地代替葉柵的曲線。

直線ae平行于葉片并將葉片節(jié)距分為兩個(gè)線段

是液流脫流表面在葉片之間空間的投影。假定，在交點(diǎn)e由直線de和ae形成的夾角為o，由曲線de等分。因?yàn)榱骶€的法線是繞流角的等分線，所以直線Oc (點(diǎn)O是法線與渦漩流線的交點(diǎn)，這點(diǎn)在圖3-2-7上是點(diǎn)B)方向不變，而直線Oe占據(jù)O‘e位置。在三角形Tee中,角度分別等于:A (頂角C);

在這種情況下，應(yīng)根據(jù)三角形O‘ce面積(參閱圖3-2- 10)，確定沿封閉線ABC(圖3-2-7)的環(huán)量。為了求出這個(gè)面積，從點(diǎn)c向平分線eO’作垂直線(直線cO),以定近似程度用三角形 O‘ce面積代替三角形O’ec 的面積。在三角形O‘0c 中，角O”cO等于。根據(jù)上述計(jì)算，渣漿泵葉輪中，角號(hào)在3*~8”之間變化，所以三角形0’o“c面積比三角形Oec總面積小10%.在這種情況下，決定沿封閉線ABC (參閱圖3-2-7)環(huán)量時(shí)，應(yīng)該采用(-Az),而不是p角，式中Ah=號(hào).因此在式(3-2-12) 中，必須用(B一AB)角代替&角。
現(xiàn)在求日角與葉輪出口液流參數(shù)一排擠系數(shù)業(yè) 和B角之間的關(guān)系。如果從點(diǎn)。作直線db延長(zhǎng)線的垂線，那么從三角形deh和ach得到

在采用抽送固液混合物的泵葉輪上，a在0.7~1.5范圍內(nèi)變化，這對(duì)修正角的影響很小(對(duì)于上述a值，B變化為士1°，這與a=1時(shí)其值相比)。當(dāng)a=1時(shí)，a等于w對(duì)于tano表達(dá)式。AF泡沫泵

Hydraulic Flow Head Loss in AF Foam Pump

The vane pump includes the theoretical head of the pump for pumping abrasive solid-liquid mixtures. The test method can be used to determine the pump according to the special equilibrium test results (first C.C. Rudenev research test method, and then C.A. Baughnitskaya carried out the pump test).

In order to obtain the theoretical head of equilibrium test, the following methods can be used.

According to the pre-test results, considering the disc friction loss, the power consumed in the mechanical loss is determined, the quantity Q of liquid overflowing through the impeller inlet seal is measured, and the leakage power loss is estimated. Thereafter, the power of the pump and the head of the pump related to the flow rate are measured.

The amount of liquid flowing through the impeller is equal to the sum of the flow rate and the overflow Q of the pump. The power transmitted to the fluid flowing through the impeller is equal to the difference between pump power and power consumed in terms of mechanical loss (considering disc friction) and volume loss (determined in advance by test). Thus, the theoretical lift of the pump is the work that is transmitted to the liquid per unit weight flowing through the impeller.

The flow rate and power of the pump can be measured with a given accuracy, so the method of determining the theoretical head of the pump is widely used. According to Euler equation, the tangential velocity c2u at the impeller outlet can be calculated by knowing the theoretical head of the pump at different flow rates.

It should be noted that the theoretical head close to or greater than the optimal flow rate can be obtained with sufficient accuracy by using the method. The reasons are as follows: when the flow rate is less than the optimal flow rate, the relation N/Q+q, so the theoretical head is related to the value Q+q.

It increases rapidly and becomes a non-linear relationship (Fig. 3-2-9). It should be noted that at zero flow rate, the flow through impeller in form is only equal to leakage value q, which is very small compared with flow Q, so that the pump power has the final value. Therefore, the theoretical Yang Cheng determined by the above method and the calculated velocity circulation at the impeller outlet based on its value are quite large. At the same time, theoretical head is not a linear function of flow rate.

However, according to the theory of rotating annular cascade, the theoretical head generated by impeller is a linear function of flow rate, so the straight line of linear part of relation Ht=f(Q) can be extrapolated to low flow area (straight line Hr.cam) when the optimal and large flow state is proved by balance test.

If the theoretical head (Ht.1cm) obtained by the extrapolation method is multiplied by the corresponding values (Q+q) and pg, the hydraulic power obtained will be significantly lower than the measured power of the pump (considering the power consumed in terms of mechanical loss). The difference between the hydraulic power obtained by the test method and the calculated value by the above method is called braking power. When the flow rate is small, the braking power increases sharply. The zero flow rate of the pump corresponds to the state in which all hydraulic power is completely converted into braking power.

The occurrence of braking power can be explained by the closed circulation of liquid between impeller and water chamber, that is, the liquid flows into the water chamber with the reserve energy transferred from impeller. This part of the liquid returns to the impeller from the pressure chamber, but has the reserve energy corresponding to the pressure chamber. This process is related to the additional consumption of work, which is not used to improve the liquid lift, but is converted into loss.

2. Flow Conditions of Liquids in Pumps

The following studies the flow conditions of liquid in the pump impeller, under which the liquid may exchange between the impeller and the pressurized water chamber. When the flow rate of the pump is enough to make the outlet section of the impeller fully filled with flowing liquid, the flow around the blade can be guaranteed. According to cascade hydrodynamics theory, the relationship between theoretical head and pump flow rate is linear.

When the flow rate is small, the potential velocity decreases and the blade profile angle of attack increases, resulting in partial hydraulic braking attached to the back of the blade. In these cases, the flow around impeller blades can not be regarded as no-flow-out motion. At this time, the relationship between theoretical head and pump flow may be non-linear. Therefore, the method of extrapolating the linear law between theoretical head and flow rate can not be considered to have sufficient basis when the pump is in a small flow state.

In the first section of this chapter, according to Stodora's method, the formula of theoretical head H for finite-time slice teaching is obtained. The existence of large detachment zones will lead to a distinct difference in tangential velocity C2o of the impeller outlet absolute velocity when considering the detachment zone [Formula (3-28) and not considering the strand zone [Formula (3-2-7).

Comparing the C e­xpression with and without considering the stripping zone, it is pointed out that the modified formula of finite number of sheets is based on Stodora's method.

When deducing the relation (3-2-12), it was used to produce liquid flow off along the straight EA, but in fact along the straight DA.

The cascade curve is approximately replaced by a straight line on Fig. 3-2-10.

The straight line AE is parallel to the blade and divides the blade pitch into two segments

It is the projection of the surface of the liquid flow outflow in the space between the blades. It is assumed that at the intersection point e, the angle formed by the lines de and AE is o, and the curve De is equal to each other. Because the normal line of the streamline is the equipartite of the flow angle, the direction of the straight line Oc (point O is the intersection of the normal line and the eddy streamline, which is point B in Figure 3-2-7) remains unchanged, while the straight line O e occupies the position of O'e. In triangle Tee, the angles are equal to: A (top angle C), respectively.

In this case, the circulation of ABC along the closed line (Figure 3-2-7) should be determined according to the triangular O'ce area (see Figure 3-2-10). In order to find this area, the vertical line (straight line cO) is made from point C to bisector eO', and the triangle O'ce area is used to replace the triangle O'ec area to a certain degree of approximation. In triangle O'0c, angle O"cO equals. According to the above calculation, in the impeller of slurry pump, the horn changes between 3*~8, so the triangle 0'o "c area is 10% smaller than the triangle Oec area. In this case, it is decided to follow the closed line.