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渣漿泵特性曲線圖的繪制

              第一節泵的統計資料
一、統計方法
  在泵制造業中，為了從給定參數初步確定過流部件的主要尺寸，或者相反，為了從泵過流部分的主要參數估算泵的最佳參數，都采用統計分析方法。
  根據對泵抽送均質液體試驗結果的統計整理的分類方法，是C.C.魯德涅夫提出來的。渣漿泵的結構特點不允許將抽送清水時泵的統計資料用于渣漿泵的計算，因此，根據已有的試驗資料，對渣漿泵資料統計整理，在這里與C.C魯德涅夫提出的統計方法一樣，采用單位直徑D.=O作為特征無因次參數(式中，Q和n為泵的最佳流量和轉速)。
  應該注意，離心泵(包括渣漿泵)的統計資料是根據對最佳工作狀態資料進行統計整理得到的。因此下列一些關系也只是對這種狀態是正確的。
  用于渣漿泵上的統計方法，不僅在定量(無因次系數值)方面，而且在定性方面都不同于普通用途泵的方法。如果對于抽送清水的泵，根據給定參數(流量，揚程，轉速或者比轉速)可以單值地確定過流部分的重要特征尺寸，那么對于抽送磨蝕性固液混合物的泵，這些參數可以對應不同尺寸過流部分的工作部件，與所要求的固體顆粒大小有關。這些顆粒應該自由地通過泵內。此外，統計方法不可能用來確定渣漿泵過流部分要素的所有尺寸。例如，如果對抽送清水的泵，葉輪出口寬度b2是n,和D。的單值函數，那么對于渣漿泵，不可能根據統計資料來確定這個尺寸。
二、葉輪出口直徑及算例
  根據對試驗資料進行統計整理，可以計算葉輪出口直徑D2.采用下列方法求出葉輪相對直徑D2/D,與比轉速n,的關系。
  確定泵最佳流量時的揚程
  因為給定工作狀態時液流葉輪出口處切向分速度c2u=kuu2(式中，ku為比例系數)，所以得到

設計泵時的原始數據是流量、揚程和葉輪轉速，因此，泵的比轉速和單位直徑常常是已知的。
    在設計抽送磨蝕性固液混合物的泵時，固體顆粒大小，即過流斷面最小尺寸也是給定的。
    因為在給定的流量，揚程和轉速的情況下，葉輪直徑與葉輪出口寬度b2、葉片數z、出口角風有關，所以過流斷面尺寸對系數k2值有重要影響。系數k2決定泵的主要尺寸，即葉輪直徑D2。

抽送磨蝕性固液混合物泵的葉輪一般這樣設計，即最小過流斷面處于葉輪入口的葉片之間(在平面圖上),主要由葉片數來確定。由此，可以認為葉片數是流道斷面尺寸最有代表性指標，即泵的過流斷面尺寸。一定尺寸的固體顆?？梢宰杂傻赝ㄟ^這個斷面。
    泵的水力效率和系數k2取決于葉輪下列一些參數:寬度，葉片數，葉片入口角和出口角。但是，對泵的數據進行統計整理時，最有代表性的指標是葉片數。除此之外，泵的水力效率還取決于壓水室的尺寸和形式。比轉速可以估算出計算斷面的尺寸和壓水室內的水力損失，總之可以估算出泵的水力效率。根據所述理由，采用下列方法對泵的試驗數據統計整理:
(1)所有泵分為三組，取決于過流斷面的尺寸，即取決于葉片數: z=4, z=3,z=2.
(2)在每組范圍內，以一定近似程度采用水力效率只是比轉速的函數，以比轉速n,為函數對關系_Xn/3進行統計整理。

在每組范圍內，按照三組泵的數據進行統計整理，可以得到關系D Xn?0=f(n,)是線性近似的，因為線性相關系數為0.85~-0.9,同時回歸方程式具在下列形式:
對于葉輪為兩枚葉片的泵(當 n,=70~210時)
對于葉輪為三枚葉片的泵(當n,=75~200時)

      葉輪門口圓周速度u2=D:n/60,于是 

或者

對于葉輪為四枚葉片的泵

或者

利用所得到的粗選葉輪直徑關系式，可以進行計算，誤差為2.5%。

此外，葉輪出口直徑根據文獻188中的公式可以計算，對于三枚葉片的葉輪

對于四枚葉片的葉輪

這兩個公式雖然結構上有所簡化，但是在確定葉輪直徑D2時精度比式（3-4-1）~式（3-4-3）的計算結果要低。

現在列舉一例，利用給定的泵的最佳參數選擇葉輪直徑：Q=3000m3/h，H=40m，n=600r/min，對于兩枚葉片、三枚葉片和四枚葉片的葉輪進行計算。

泵的比轉速為ns為

單位直接Dq為

利用式（3-4-1）~（3-4-3），可以求出葉輪出口直徑。這時，對于兩枚葉片的葉輪

由此得到，對于三枚葉片的葉輪

由此得到，對于四枚葉片的葉輪

三、葉輪其他參數

葉輪葉片數增加，將導致葉輪直徑D2減小，但是這時葉片之間流道過流斷面（在進

口處)同時也減小。

葉輪出口寬度要根據所要求的過道斷面尺寸來選擇，因此在抽送渣漿泵廠家固液混合物泵中，它不是比轉速ns的函數，這種情況與抽送清水的泵中的情況一樣。
    葉輪入口直徑D。是單位直徑Dq的函數
式中K?！~輪入口直徑系數。
    系數K。在本篇第二章第六節中已經進行了論證。

Drawing Characteristic Curve of Slurry Pump

Section I Statistics of Pumps

I. Statistical methods

In the pump manufacturing industry, statistical analysis is used to determine the main dimensions of the flow passage components from the given parameters, or on the contrary, to estimate the optimal parameters of the pump from the main parameters of the flow passage parts.

C. C. Rudenev proposed a classification method based on the statistical analysis of the results of homogeneous liquid pumping tests. The structural characteristics of slurry pump do not allow the statistical data of pump when pumping clean water to be used in slurry pump calculation. Therefore, according to the existing experimental data, the statistical data of slurry pump are sorted out. The unit diameter D. = O is used as the characteristic dimensionless parameter here as C.C. Rudenev's statistical method. Optimum flow rate and speed.

It should be noted that the statistics of centrifugal pumps (including slurry pumps) are based on the statistics of the best working conditions. So some of the following relationships are just right for this state.

Statistical methods used in slurry pumps are not only quantitative (dimensionless coefficient value), but also qualitative, which are different from those used in general purpose pumps. If the important characteristic dimensions of the overflow part can be determined singly according to the given parameters (flow rate, head, rotational speed or specific rotational speed) for pumping clean water, then for pumping abrasive solid-liquid mixture, these parameters can correspond to the working parts of the overflow part of different sizes and the required size of solid particles. Of These particles should pass freely through the pump. In addition, the statistical method can not be used to determine all dimensions of the flow passage elements of slurry pumps. For example, for pumps pumping clean water, the impeller outlet width B2 is n, and D. For slurry pumps, it is impossible to determine the size based on statistical data.

2. Impeller outlet diameter and calculation example

Based on the statistical analysis of the test data, the outlet diameter D2 of the impeller can be calculated. The relationship between the relative diameter D2/D of the impeller and the specific speed n can be obtained by the following methods.

Head for Determining Optimum Flow Rate of Pump

Because the tangential velocity c2u = kuu2 at the outlet of the impeller is obtained at a given working condition.

The original data of pump design are flow rate, head and impeller speed, so the specific speed and unit diameter of pump are often known.

When designing pumps for pumping abrasive solid-liquid mixtures, the size of solid particles, i.e. the minimum size of the cross section, is also given.

Because the diameter of impeller is related to outlet width b 2, blade number Z and outlet angular wind at given flow rate, head and speed, the size of cross-section has an important influence on coefficient K 2. The coefficient K2 determines the main size of the pump, namely the impeller diameter D2.

The impeller for pumping abrasive solid-liquid mixture pump is generally designed in this way, that is, the minimum cross-section is between the blades at the impeller entrance (in the plan), which is mainly determined by the number of blades. Therefore, it can be considered that the number of blades is the most representative index of the flow passage cross-section size, that is, the size of the flow passage cross-section of the pump. Solid particles of a certain size can pass through this section freely.

The hydraulic efficiency and coefficient K2 of the pump depend on the following parameters of the impeller: width, number of blades, blade inlet angle and outlet angle. However, the most representative index is the number of blades when the data of pumps are statistically sorted out. In addition, the hydraulic efficiency of the pump also depends on the size and form of the pressure chamber. Specific speed can be used to estimate the size of the calculated section and the hydraulic loss in the pressure chamber. In a word, the hydraulic efficiency of the pump can be estimated. According to the reasons mentioned above, the following methods are used to collect the test data of the pump.

(1) All pumps are divided into three groups, depending on the size of the cross section, i.e. the number of blades: z = 4, z = 3, z = 2.

(2) Within each group, hydraulic efficiency is only a function of specific speed to a certain approximation degree, and the relation _Xn/3 is statistically sorted out with specific speed n as a function.

In each range, according to the statistics of three groups of pumps, the relationship D Xn?0=f(n,) is linear approximation, because the linear correlation coefficient is 0.85-0.9, and the regression equation is in the following form:

For pumps with two blades with impellers (when n, = 70-210)

For pumps with three blades with impellers (when n, = 75-200)

The circumferential velocity of impeller door U2 = D:n/60, so

perhaps

Pumps with four blades in impeller

perhaps

By using the obtained formula of roughly selected impeller diameter, the calculation can be carried out with an error of 2.5%.

In addition, the outlet diameter of the impeller can be calculated according to the formula in document 188. For the impeller with three blades

For impellers with four blades

Although these two formulas are simplified in structure, the accuracy of determining impeller diameter D2 is lower than that of formula (3-4-1)~formula (3-4-3).

Now an example is given. The impeller diameter is chosen by using the optimal parameters of the given pump: Q = 3000m3/h, H = 40m, n = 600r/min. The impellers of two, three and four blades are calculated.

The specific speed of the pump is ns.

Unit direct Dq is

By using formula (3-4-1) ~ (3-4-3), the outlet diameter of impeller can be calculated. At this time, for two blades of impeller

Thus, for the impeller with three blades

Thus, for the impeller with four blades

3. Other parameters of impeller

Increasing the number of impeller blades will reduce the diameter of the impeller D2, but at this time the flow passage cross section between the blades (in)

The mouth area) also decreases.

The outlet width of impeller should be chosen according to the required cross-section size of passage, so it is not used in pumping solid-liquid mixture pump.