渣浆泵特性曲线图的绘制

              第一节泵的统计资料
一、统计方法
  在泵制造业中，为了从给定参数初步确定过流部件的主要尺寸，或者相反，为了从泵过流部分的主要参数估算泵的最佳参数，都采用统计分析方法。
  根据对泵抽送均质液体试验结果的统计整理的分类方法，是C.C.鲁德涅夫提出来的。渣浆泵的结构特点不允许将抽送清水时泵的统计资料用于渣浆泵的计算，因此，根据已有的试验资料，对渣浆泵资料统计整理，在这里与C.C鲁德涅夫提出的统计方法一样，采用单位直径D.=O作为特征无因次参数(式中，Q和n为泵的最佳流量和转速)。
  应该注意，离心泵(包括渣浆泵)的统计资料是根据对最佳工作状态资料进行统计整理得到的。因此下列一些关系也只是对这种状态是正确的。
  用于渣浆泵上的统计方法，不仅在定量(无因次系数值)方面，而且在定性方面都不同于普通用途泵的方法。如果对于抽送清水的泵，根据给定参数(流量，扬程，转速或者比转速)可以单值地确定过流部分的重要特征尺寸，那么对于抽送磨蚀性固液混合物的泵，这些参数可以对应不同尺寸过流部分的工作部件，与所要求的固体颗粒大小有关。这些颗粒应该自由地通过泵内。此外，统计方法不可能用来确定渣浆泵过流部分要素的所有尺寸。例如，如果对抽送清水的泵，叶轮出口宽度b2是n,和D。的单值函数，那么对于渣浆泵，不可能根据统计资料来确定这个尺寸。
二、叶轮出口直径及算例
  根据对试验资料进行统计整理，可以计算叶轮出口直径D2.采用下列方法求出叶轮相对直径D2/D,与比转速n,的关系。
  确定泵最佳流量时的扬程
  因为给定工作状态时液流叶轮出口处切向分速度c2u=kuu2(式中，ku为比例系数)，所以得到

设计泵时的原始数据是流量、扬程和叶轮转速，因此，泵的比转速和单位直径常常是已知的。
    在设计抽送磨蚀性固液混合物的泵时，固体颗粒大小，即过流断面最小尺寸也是给定的。
    因为在给定的流量，扬程和转速的情况下，叶轮直径与叶轮出口宽度b2、叶片数z、出口角风有关，所以过流断面尺寸对系数k2值有重要影响。系数k2决定泵的主要尺寸，即叶轮直径D2。

抽送磨蚀性固液混合物泵的叶轮一般这样设计，即最小过流断面处于叶轮入口的叶片之间(在平面图上),主要由叶片数来确定。由此，可以认为叶片数是流道断面尺寸最有代表性指标，即泵的过流断面尺寸。一定尺寸的固体颗粒可以自由地通过这个断面。
    泵的水力效率和系数k2取决于叶轮下列一些参数:宽度，叶片数，叶片入口角和出口角。但是，对泵的数据进行统计整理时，最有代表性的指标是叶片数。除此之外，泵的水力效率还取决于压水室的尺寸和形式。比转速可以估算出计算断面的尺寸和压水室内的水力损失，总之可以估算出泵的水力效率。根据所述理由，采用下列方法对泵的试验数据统计整理:
(1)所有泵分为三组，取决于过流断面的尺寸，即取决于叶片数: z=4, z=3,z=2.
(2)在每组范围内，以一定近似程度采用水力效率只是比转速的函数，以比转速n,为函数对关系_Xn/3进行统计整理。

在每组范围内，按照三组泵的数据进行统计整理，可以得到关系D Xn?0=f(n,)是线性近似的，因为线性相关系数为0.85~-0.9,同时回归方程式具在下列形式:
对于叶轮为两枚叶片的泵(当 n,=70~210时)
对于叶轮为三枚叶片的泵(当n,=75~200时)

      叶轮门口圆周速度u2=D:n/60,于是 

或者

对于叶轮为四枚叶片的泵

或者

利用所得到的粗选叶轮直径关系式，可以进行计算，误差为2.5%。

此外，叶轮出口直径根据文献188中的公式可以计算，对于三枚叶片的叶轮

对于四枚叶片的叶轮

这两个公式虽然结构上有所简化，但是在确定叶轮直径D2时精度比式（3-4-1）~式（3-4-3）的计算结果要低。

现在列举一例，利用给定的泵的最佳参数选择叶轮直径：Q=3000m3/h，H=40m，n=600r/min，对于两枚叶片、三枚叶片和四枚叶片的叶轮进行计算。

泵的比转速为ns为

单位直接Dq为

利用式（3-4-1）~（3-4-3），可以求出叶轮出口直径。这时，对于两枚叶片的叶轮

由此得到，对于三枚叶片的叶轮

由此得到，对于四枚叶片的叶轮

三、叶轮其他参数

叶轮叶片数增加，将导致叶轮直径D2减小，但是这时叶片之间流道过流断面（在进

口处)同时也减小。

叶轮出口宽度要根据所要求的过道断面尺寸来选择，因此在抽送渣浆泵厂家固液混合物泵中，它不是比转速ns的函数，这种情况与抽送清水的泵中的情况一样。
    叶轮入口直径D。是单位直径Dq的函数
式中K。——叶轮入口直径系数。
    系数K。在本篇第二章第六节中已经进行了论证。

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.