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渣漿泵的相似定律及比轉(zhuǎn)數(shù) 兩臺泵相似，嚴(yán)格的講必須滿足兩臺泵幾何相似，液流運(yùn)動相似和液流動力相似。
(1)幾何相似:即兩臺泵過流部件相似點(diǎn)的各角度相等，同名尺寸比值相等。即:
式中，注腳“p”為實(shí)型泵;“m”為模型泵;
L----任 意點(diǎn)的相應(yīng)線性尺寸。
(2)液體運(yùn)動相似:就是兩臺泵內(nèi)相應(yīng)點(diǎn)的液體流速方向相同，大小成同一比例。 即:
(3) 液體動力相似:就是作用在兩臺泵相應(yīng)點(diǎn)液體上的同名力(如慣性力、黏性力、重力)的比值相等。
實(shí)際上兩臺泵要同時(shí)滿足上述三個(gè)條件是困難的，在實(shí)際應(yīng)用時(shí)，常忽略了一些次要因素。由于泵中的流速較高，處于阻力平方區(qū)，所以通常在泵中不考慮動力相似。
離心泵的工況點(diǎn)是用它的性能參數(shù)表表示的，在相似工況下，兩臺相似泵有如下關(guān)系:即泵的流量Q相似定律，泵的揚(yáng)程H相似定律，泵的功率相似定律。
1.流量相似定律
泵的流量:根據(jù)式(2-13) 可用下式表示:
兩臺相似泵的流量關(guān)系可用下式表示:
由于兩臺泵相似，則有
由于在相似工況運(yùn)行，必然運(yùn)動相似。所以
故式(2-30)可寫為
這就是泵流量相似定律。
2.揚(yáng)程相似定律
由式(2-14)及式(2-25)，兩臺相似泵的揚(yáng)程關(guān)系可用下式表示:
由于兩臺泵運(yùn)動相似，必然滿足
代入上式(2-32)可得
這就是泵揚(yáng)程相似定律。
3.功率相似定律
由式(2-6)可得兩臺相似泵的功率關(guān)系式:
將式(2-31)， 式(2-33)及η=nn7.m代入式(2-34)得
這就是泵功率相似定律。
當(dāng)實(shí)型泵與模型泵的尺寸比例相差不太大時(shí)，為了簡化問題起見，認(rèn)為模型泵與實(shí)型泵的效率相等，即ηp = Twm，Tnp=7im，p=mm，于是可得:
式中，注腳“p”表示實(shí)型來，注腳“m表示模型泵。
利用以上相似定律，大型泵可以做成小的模型泵進(jìn)行試驗(yàn)，然后將模型泵的實(shí)驗(yàn)結(jié)果換算成實(shí)行泵的性能。但是當(dāng)兩尺寸相差很大時(shí)，誤差會較大，需參考有關(guān)資料來進(jìn)行修正。
當(dāng)同一 臺泵輸送同一種液體時(shí)在
則有
這就是泵的比例定律，在泵的調(diào)節(jié)中就用改變轉(zhuǎn)速來改變泵的性能，用式(2 - 39)、式(2-40)、式(2-41) 來計(jì)算改變轉(zhuǎn)速后泵的性能。在試驗(yàn)中，當(dāng)試驗(yàn)設(shè)備受到限制時(shí)，可用降速試驗(yàn)，然后用上式進(jìn)行換算泵的性能。
二、 泵的比轉(zhuǎn)數(shù)π。
1.比轉(zhuǎn)數(shù)n。的得出
相似工況下，由式(2-36) 及式(2-37)可得:
將式(2-42)兩端平方，式(2-43) 兩端立方，然后相除消去D，再開四次方可得到:
即兩臺相似的泵，將相應(yīng)的工況下的性能參數(shù)代入式(2 -44)，計(jì)算出來的數(shù)值是相同的，把這個(gè)數(shù)值稱為泵的比轉(zhuǎn)數(shù)nq:
ng就有這樣的性質(zhì)，對一系列幾何相似的泵，在相似的工況下ng值都相等，也即na相等，兩臺泵就幾何相似，ng 就是相似泵的相似準(zhǔn)則。
在我國為了使與水輪機(jī)的比轉(zhuǎn)數(shù)一致， 將上面公式乘以一個(gè)數(shù)3.65 ，則泵的比轉(zhuǎn)數(shù)n。為:
ns與ng本質(zhì)上沒有任何區(qū)別，只是數(shù)值上不同，我國長久以來已經(jīng)習(xí)慣使用n,，歐美國家常用ne,由于各國使用的單位不一致，所以同一臺泵算出來的比轉(zhuǎn)數(shù)值是不一樣的。
2.比轉(zhuǎn)數(shù)n、計(jì)算注意事項(xiàng)
(1)同一臺泵在不同工況下具有不同的n。值，作為相似準(zhǔn)則的n.是指對應(yīng)最高效率點(diǎn)工況(即設(shè)計(jì)工況)的n。值。
(2)雙吸泵比轉(zhuǎn)數(shù)的計(jì)算:因?yàn)楸绒D(zhuǎn)數(shù)是對葉輪而言的，雙吸泵實(shí)際是將兩個(gè)單吸葉輪背靠背的裝在一起并聯(lián)工作，所以雙吸泵的比轉(zhuǎn)數(shù)n。
(3)多級泵比轉(zhuǎn)數(shù)的計(jì)算:因?yàn)槎嗉壉孟喈?dāng)于將幾個(gè)單級泵的葉輪裝在一根軸上，串聯(lián)工作，所以多級泵的比轉(zhuǎn)數(shù)n,應(yīng)用單級揚(yáng)程來計(jì)算。
3. 比轉(zhuǎn)數(shù)n。的用處
(1)利用比轉(zhuǎn)數(shù)n.對葉輪進(jìn)行分類和分析性能變化狀況
比轉(zhuǎn)數(shù)ns的大小與時(shí)輪形狀和泵性能曲線形狀有密切關(guān)系，如表2-3所示。比轉(zhuǎn)數(shù)ns越小，D2/D0值越大，葉輪流道相對地越細(xì)長，葉片為圓柱規(guī)葉片不扭曲；Q-H曲線比較平坦: Q-P曲線隨流量Q增大功率P上升得比較快: Q-η曲線高效區(qū)比較寬，但最高效率m比較低。
隨比轉(zhuǎn)數(shù)n。逐漸增大，D2/D。 值變小，葉輪流道越來越寬，葉片進(jìn)口處開始變扭曲;Q- H曲線也越來越陡;當(dāng)n。 大到一定值時(shí)葉輪出口邊就傾斜了，成了混流泵，葉片從進(jìn)口到出口都變成扭曲;Q -H曲線開始出現(xiàn)s形曲線; Q-P曲線隨流量Q增大功率P上升得比較慢，當(dāng)n。大到一定值時(shí)功率P隨流量Q的增大不再增大或稍有下降。Q一η曲線高效區(qū)變窄，但最高效率增高，在n。 = 120 時(shí)能得到最好的效率值，當(dāng)n。> 180后，隨n。增加，最高效率7m反而有所降低。 渣漿泵
Similarity law of pump
The two pumps are similar. Strictly speaking, the geometry of the two pumps must be similar, the movement of the liquid flow is similar and the power of the liquid flow is similar.
(1) geometric similarity: that is to say, the angles of the similar parts of the two pumps are equal, and the size ratio of the same name is equal. Namely:
In the formula, "P" is the solid pump; "m" is the model pump;
L - corresponding linear dimension of any point.
(2) similar liquid movement: that is, the flow velocity direction of the corresponding points in the two pumps is the same, and the size is in the same proportion. Namely:
(3) liquid dynamic similarity: it means that the ratio of the same name force (such as inertia force, viscosity force and gravity) acting on the corresponding point liquid of two pumps is equal.
In fact, it is difficult for two pumps to meet the above three conditions at the same time. In practical application, some secondary factors are often ignored. Due to the high flow rate in the pump, which is in the resistance square area, the dynamic similarity is usually not considered in the pump.
The working point of centrifugal pump is expressed by its performance parameter table. Under similar working conditions, two similar pumps have the following relations: the flow Q similar law of pump, the head h similar law of pump, and the power similar law of pump.
1. Flow similarity law
Pump flow: according to formula (2-13), it can be expressed as follows:
The flow relationship of two similar pumps can be expressed as follows:
Since the two pumps are similar, there are
Because it operates under similar working conditions, it will inevitably move in the same way. therefore
Therefore, formula (2-30) can be written as
This is the law of pump flow similarity.
2. Law of head similarity
From equations (2-14) and (2-25), the head relationship of two similar pumps can be expressed as follows:
Because the two pumps have similar movement, it is necessary to meet
Substitute the above formula (2-32) to get
This is the law of pump head similarity.
3. Power similarity law
The power relationship of two similar pumps can be obtained from equation (2-6):
By substituting equation (2-31), equation (2-33) and η = nn7. M into equation (2-34), we can get
This is the law of pump power similarity.
When the size ratio of the real pump and the model pump is not too large, in order to simplify the problem, it is considered that the efficiency of the model pump and the real pump is equal, that is, η P = TWM, TNP = 7im, P = mm, so we can get:
In the formula, "P" means real type, and "m" means model pump.
Using the above similarity law, large pump can be made into small model pump for test, and then the experimental results of model pump can be converted into the performance of pump. However, when there is a large difference between the two dimensions, the error will be large, so it is necessary to refer to the relevant information for correction.
When the same pump delivers the same liquid
Then there are
This is the proportional law of the pump. In the regulation of the pump, change the speed to change the performance of the pump. Use formula (2-39), formula (2-40) and formula (2-41) to calculate the performance of the pump after changing the speed. In the test, when the test equipment is limited, the speed reduction test can be used, and then the above formula can be used to convert the performance of the pump.
2. Specific speed π of pump.
1. Specific speed n. Draw
Under similar working conditions, formula (2-36) and formula (2-37) can be used to obtain:
Square the two ends of formula (2-42) and cube the two ends of formula (2-43), then divide and eliminate D, and then open the fourth power to get:
That is to say, for two similar pumps, the performance parameters under corresponding working conditions are substituted into equation (2-44), and the calculated value is the same, which is called the specific speed of pump NQ:
Ng has such a property. For a series of pumps with similar geometry, under similar working conditions, ng values are equal, that is, Na is equal. Two pumps are geometrically similar, and ng is the similarity criterion of similar pumps.
In our country, in order to make the specific speed consistent with the turbine, multiply the above formula by a number of 3.65, then the specific speed of the pump n. For:
In essence, there is no difference between ns and ng, but the numerical value is different. China has been used to use n for a long time. European and American countries often use ne. Because the units used in different countries are different, the specific rotation calculated by the same pump is different.
2. Specific speed n. precautions for calculation
(1) the same pump has different N under different working conditions. Value, as the similarity criterion, N. refers to n corresponding to the highest efficiency point condition (i.e. design condition). Value.
(2) calculation of the specific speed of double suction pump: because the specific speed is for the impeller, the double suction pump actually installs two single suction impellers back-to-back and works in parallel, so the specific speed of the double suction pump is n.
(3) calculation of specific speed of multistage pump: because multistage pump is equivalent to installing several impellers of single-stage pump on a shaft and working in series, the specific speed of multistage pump n shall be calculated by single-stage head.
3. Specific speed n. Usefulness
(1) use specific speed n. classify impeller and analyze performance change
The specific speed ns is closely related to the shape of the time wheel and the shape of the pump performance curve, as shown in table 2-3. The smaller the specific speed ns is, the larger the D2 / d0 value is, the more slender the impeller passage is, and the blade is cylindrical gauge blade without distortion; the Q-H curve is relatively flat; the Q-P curve rises faster with the increase of flow Q; the efficient area of q-η curve is wider, but the highest efficiency m is lower.
With specific revolution n. Gradually increased, D2 / d The smaller the value, the wider the impeller channel, the more twisted the blade inlet; the steeper the Q-H curve; when n When it reaches a certain value, the outlet edge of the impeller inclines and becomes a mixed flow pump, and the blades become twisted from the inlet to the outlet; the Q-H curve begins to show a S-shaped curve; the Q-P curve increases slowly with the flow Q, and the power P increases slowly when n. At a certain value, the power P will not increase or decrease slightly with the increase of flow Q. The efficient region of q-η curve narrowed, but the highest efficiency increased at n =The best efficiency value can be obtained at 120, when n. >After 180, with n. However, the highest efficiency of 7 m decreased Slurry pump
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