CN113202787A - Numerical simulation prediction method for necessary cavitation allowance of volute type centrifugal pump - Google Patents

Numerical simulation prediction method for necessary cavitation allowance of volute type centrifugal pump Download PDF

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CN113202787A
CN113202787A CN202110630105.5A CN202110630105A CN113202787A CN 113202787 A CN113202787 A CN 113202787A CN 202110630105 A CN202110630105 A CN 202110630105A CN 113202787 A CN113202787 A CN 113202787A
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blade
pressure value
area
inlet
value
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CN113202787B (en
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周佩剑
王浩
牟介刚
蒋登辉
罗会灿
沈盟淞
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China Jiliang University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D15/00—Control, e.g. regulation, of pumps, pumping installations or systems
    • F04D15/0088—Testing machines
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00—Details, component parts, or accessories
    • F04D29/40—Casings; Connections of working fluid
    • F04D29/42—Casings; Connections of working fluid for radial or helico-centrifugal pumps
    • F04D29/426—Casings; Connections of working fluid for radial or helico-centrifugal pumps especially adapted for liquid pumps
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00—Details, component parts, or accessories
    • F04D29/66—Combating cavitation, whirls, noise, vibration or the like; Balancing
    • F04D29/669—Combating cavitation, whirls, noise, vibration or the like; Balancing especially adapted for liquid pumps
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Structures Of Non-Positive Displacement Pumps (AREA)
  • Control Of Non-Positive-Displacement Pumps (AREA)

Abstract

本发明公开了一种蜗壳式离心泵必需汽蚀余量数值模拟预测方法。本发明主要步骤包括：建模，导出流体域；在CFX中进行网格划分；设置参考气压为0Pa并对模型进行不加空化模型，定常计算；通过后处理选择合适的叶片的吸力面对其作压力值作面积积分得到面均压力值；加上空化模型，设置参考气压值；重新计算，根据结果扬程是否满足条件来重新设置新的参考气压值至扬程下降3%的点。本发明可大大节约计算时间，提高计算效率，同时采取更改参考气压值的方法来计算泵的必需汽蚀余量。一般情况下只需不高于五次计算便可以得到泵的必需汽蚀余量值。

Figure 202110630105

The invention discloses a numerical simulation prediction method for the necessary NPSH of a volute type centrifugal pump. The main steps of the invention include: modeling, exporting the fluid domain; meshing in CFX; setting the reference air pressure to 0Pa and performing constant calculation without adding a cavitation model to the model; selecting a suitable suction face of the blade through post-processing The pressure value is integrated into the area to obtain the surface average pressure value; the cavitation model is added to set the reference air pressure value; the recalculation is performed, and the new reference air pressure value is reset to the point where the head drops by 3% according to whether the result lift meets the conditions. The invention can greatly save the calculation time, improve the calculation efficiency, and adopt the method of changing the reference air pressure value to calculate the necessary NPSH of the pump. In general, no more than five calculations are required to obtain the necessary NPSH value for the pump.

Figure 202110630105

Description

Numerical simulation prediction method for necessary cavitation allowance of volute type centrifugal pump
Technical Field
The invention relates to a novel centrifugal pump cavitation numerical calculation method, in particular to a numerical simulation prediction method for the necessary cavitation allowance of a volute type centrifugal pump.
Background
The cavitation margin is an important parameter of the pump, and refers to the surplus energy per unit weight of liquid at the pumping inlet in excess of the vaporization pressure, which reflects the cavitation performance of the pump. The smaller the pump cavitation margin, the stronger the cavitation resistance. According to the size of the cavitation allowance, the allowable height of the pump installation can be determined, and the method has important significance in practical engineering application. The pump cavitation performance directly influences whether the pump can operate as expected or not, which is related to the state of the whole system, and once cavitation calculation is inaccurate, the imaginable result can be caused. In the actual industry, a series of measures are taken to reduce the cavitation margin, and if an accurate and satisfactory value of the cavitation margin is not obtained, the performance of the pump is seriously reduced, and even the operation of the pump is interrupted. Therefore, it is important for the pump industry to be able to quickly and accurately obtain the size of the pump cavitation margin.
However, the conventional methods include a CFD simulation method and an experimental measurement method, where CFD is equivalent to a "virtual" experiment performed on a computer to simulate the actual fluid flow condition, and the experimental measurement cost is relatively high, so that the CFD simulation is usually used to obtain the cavitation margin of the pump. Now, the cavitation allowance when the head is reduced by 3% is generally taken as the necessary cavitation allowance of the pump, namely NPSHR。
The CFD is adopted to simulate the process of obtaining the necessary cavitation allowance, the existing method mostly sets the total pressure of the outlet to gradually reduce, and the simulation is carried out for a plurality of times until the total pressure value of the outlet reduces the lift by 3 percent. Because the lift is gradually reduced and then rapidly reduced along with the total pressure of the outlet in the reducing process, the lift reduction near a point of 3% can be obtained only by carrying out the process for many times, even more than ten times, in most cases, the method has low efficiency, consumes a large amount of time and resources, and ensures the precision of a specific simulation result difficultly.
Disclosure of Invention
In order to solve the problem of low efficiency in the process of obtaining the cavitation allowance according to the traditional CFD simulation method, the invention adopts a reference air pressure value and utilizes the reference air pressure value to calculate the cavitation allowance.
The invention specifically comprises the following steps:
the method comprises the following steps: establishing a fluid domain
Modeling a volute type centrifugal pump, and setting an initial position between the edge of a blade and a partition tongue;
connecting the top point of the partition tongue with the center of the blade inlet circle, connecting all the top points of the blades with the center of the blade inlet circle, ensuring that the minimum included angle between the connecting line of the top point of the partition tongue and the center of the blade inlet circle and the connecting line of the top point of the blades and the center of the blade inlet circle is between 1 and 5 degrees, and exporting the fluid domain file.
Step two: mesh partitioning
And carrying out grid division on the exported fluid domain file, carrying out grid refinement on the blade and the inlet and outlet areas, dividing out fine boundary layer grids, and carrying out quality improvement on all the grids.
Step three: constant calculation without adding cavitation model
Importing the grid file obtained in the step two into a software CFX, setting an initial reference air pressure value to be 0 under the condition of not adding a cavitation model, setting outlet static pressure according to rated lift, carrying out constant calculation to obtain a result file, and recording the lift H at the moment0And calculates the head H' that needs to be reduced to 3% while copying a result file for later use.
Step four: calculating the face pressure balance value of the selected blade
Carrying out post-processing on the result file obtained in the step three, observing the internal pressure distribution condition, and finding out the blade for integral; satisfy 1.2D on the blade for integrationin～0.75DoutThe area of the suction surface is integrated with the pressure area to obtain the surface pressure equalizing value PaWherein D isinIs the diameter of the inlet of the blade, DoutIs the vane exit diameter.
Step five: determining reference air pressure value, adding cavitation model, and calculating verification result at constant time
The surface pressure equalizing value P obtained in the fourth stepaSubtracting the saturated vapor pressure PvAs a reference pressure value Pf. In the software CFX, a reference air pressure value is set, and the constant calculation is carried out to judge whether the lift value H in the simulation result reaches the point that the lift is reduced by 3%.
Step six: and (5) performing iterative calculation, and re-selecting the reference air pressure value according to the height H of the head in the result file to judge the result.
The invention has the beneficial effects that: according to the method, the next calculation is directly carried out according to the internal cavitation pressure value instead of blindly reducing the outlet pressure according to the reason of cavitation generation, so that the calculation time can be greatly saved, the calculation efficiency is improved, and meanwhile, the method for changing the reference pressure value is adopted to calculate the necessary cavitation allowance of the pump. Generally, the necessary cavitation balance value of the pump can be obtained by not more than five times of calculation.
Drawings
FIG. 1: the flow chart of the invention;
FIG. 2: selecting an angle by the blade;
FIG. 3: the extent of pressure zone a;
FIG. 4: an integration area;
FIG. 5: the NPSH-H curve obtained by the method of gradually reducing the total outlet pressure is compared with the NPSH-H curve obtained by the method.
Detailed Description
As shown in fig. 1, in order to achieve fast and accurate acquisition of the value of the cavitation margin, the present invention provides the following steps:
the method comprises the following steps: fluid domain establishment
Modeling is carried out on the volute type centrifugal pump, an initial position between the edge of the blade and the partition tongue is set, the top point of the partition tongue and the center of the inlet circle of the blade are connected, the top points of all the blades and the center of the inlet circle of the blade are connected, the minimum value of the included angle between the connecting line of the top point of the partition tongue and the center of the inlet circle of the blade and the connecting line of the top point of the blade and the center of the inlet circle of the blade is ensured to be between 1 and 5 degrees, and a fluid domain file is led out.
Step two: mesh partitioning
And carrying out grid division on the exported fluid domain file, carrying out grid refinement on the blade and the inlet and outlet areas, dividing out fine boundary layer grids, and carrying out quality improvement on all the grids.
Step three: constant calculation without adding cavitation model
And (4) importing the grid file obtained in the step two into a software CFX, setting an initial reference air pressure value as 0 under the condition of not adding a cavitation model, setting outlet static pressure according to rated lift, performing constant calculation to obtain a result file, recording the lift value at the moment, calculating the lift required to be reduced to 3%, and copying the result file for later use.
With a given flow value Q, the nominal head HNSetting is performed in software CFX:
static pressure P at outletmThe method comprises the following steps:
Pm＝(λHN+ε)ρg,λ∈(1.0～1.1),ε∈(10～20)
wherein rho is the density of the liquid, g is the acceleration of gravity, lambda is the lift coefficient, and epsilon is the reference amount of the lift
The mass flow rate at the inlet was set to: q
The inlet total pressure can be obtained through simulation treatment: pinAnd outlet total pressure: pout
According to the relationship between the pump head and the inlet-outlet pressure, the following conditions can be obtained: head H0＝(Pout-Pin)/ρg，H0The lift obtained without adding cavitation model. Lift H' at 3% drop: h' is 0.97H0
Step four: post-treatment
Post-processing the result file obtained in the third step, observing the internal pressure distribution condition, finding out the blade for integration, and satisfying 1.2D on the bladein～0.75DoutThe suction surface area is integrated with the pressure area to obtain the surface pressure equalizing value PaWhere D isinIs the diameter of the inlet of the blade, DoutIs the vane exit diameter.
The pressure distribution on the blade can be seen through a CFD post-processing blade pressure cloud chartConnecting the center O of the impeller inlet circle with the top point of the partition tongue to obtain a straight line l, and taking the center O of the impeller inlet circle as a rotation point to respectively rotate the straight line l by 1 degree and 5 degrees clockwise and anticlockwise respectively, and recording the straight line of 1 degree clockwise as l1And the straight line rotated clockwise by 5 degrees is denoted as l2And a line rotated counterclockwise by 1 DEG is denoted by l'1Line rotated counterclockwise by 5 DEG is denoted by l'2。
Is selected to be located at1And l2Or l'1And l'2The connecting line between the tail end of the blade and the center O of the inlet circle of the impeller is marked as l3When there are a plurality of straight lines l3When it is, then use l3L is optimal when the included angle between l and l is 3 degrees3。
The suction surface of the selected blade meets 1.2Din～0.75DoutThe inner zone, i.e. the defined pressure zone range, is:
A＝∫sdt，t∈(1.2Din，0.75Dout)
t is 1.2D satisfied at the suction surface of the bladein～0.75DoutThe length of the inner area, s is 1.2D satisfied at the suction surface of the bladein～0.75DoutThe width of the inner zone; the maximum pressure value in the pressure region A is denoted as Pmax(ii) a Integrating the area of the area A to obtain the surface voltage-sharing value Pa：
Figure BDA0003103086260000031
Where A is the area of the region, AiIs an area element, phi is a zone pressure value, phiiIs the pressure element, and n is the division frequency.
Step five: determining reference air pressure value, adding cavitation model, and calculating verification result at constant time
The surface pressure equalizing value P obtained in the fourth stepaSubtracting the saturated vapor pressure PvAs a reference pressure value Pf. In the software CFX, a reference air pressure value is set, and the constant calculation is carried out to judge whether the lift value H in the simulation result reaches the point that the lift is reduced by 3%.
Setting the reference air pressure value as follows: pf＝Pa-Pv。
Step six: iterative calculation, re-selecting reference pressure value according to the height H of the head in the result file, and judging the result
1) When in use
Figure BDA0003103086260000041
When the current is over;
if H>0.97H0Taking the initial decrease Δ P00, decrease Δ P per iterationiAnd judging according to the finally obtained H, wherein i is the iteration number and is taken as:
Figure BDA0003103086260000042
considering the mechanism that the reduction amount of each iteration is too large to affect the subsequent calculation, after n iterations, the (n +1) th iteration is reduced by the amount deltaPn+1When the value is larger than a certain value, the value is halved to be used as the (n +1) th iteration reduction quantity delta Pn+1I.e. when
Figure BDA0003103086260000043
When it is taken
Figure BDA0003103086260000044
If H<0.97H0Taking the spare result file copied in the third step, and re-picking the result file based on the spare result file
Figure BDA0003103086260000045
I.e. setting a new reference air pressure value:
Figure BDA0003103086260000046
2) when in use
Figure BDA0003103086260000047
Then, the total inlet pressure P is obtained from the post-treatmentin*According to
Figure BDA0003103086260000048
From this, the necessary cavitation margin can be determined, where Pin*Is the total inlet pressure, vsFor pump inlet speed, NPSHrThe necessary cavitation margin.
The following description is given with reference to the accompanying drawings and specific examples:
taking a volute type centrifugal pump hydraulic model as an example, after modeling is completed by using three-dimensional modeling software, a CFD simulation technology is adopted to perform constant calculation of a non-cavitation model, a backup result file is calculated, a straight line connecting the circle center O of an impeller inlet circle and the top point of a baffle tongue is l, and blades positioned at +/-1-5 degrees on two sides of l are selected in post-processing, as shown in figure 2. With O as the center and the diameter of 0.75Dout、1.2DinTwo circles are drawn as boundary lines dividing the integration regions, as shown in fig. 3. For the blade meeting the conditions, the diameter of the center of circle at the edge of the blade is 0.75DoutAnd 1.2DinThe area integral of the suction surface is taken as the intersecting closed region, and the surface pressure equalizing value is obtained as shown in fig. 4. And (3) subtracting the saturated vapor pressure from the surface pressure value to serve as a reference air pressure value, adding a cavitation model for recalculation, judging whether the finally obtained lift value meets the condition, properly changing the reference air pressure value for recalculating the condition that the condition is not met, calculating all subsequent calculations on the basis of the previous step, and recalculating the first step on the basis of a backup result file for the condition that the lift is reduced too much.
Based on the graphs obtained by the traditional method and the method, as shown in fig. 5, the traditional method for reducing the outlet pressure calculates 10 times, the method calculates 5 times, but the results are similar, which shows that the method can be used as a numerical simulation prediction method for the necessary cavitation allowance of the volute type centrifugal pump.

Claims (4)

1.一种蜗壳式离心泵必需汽蚀余量数值模拟预测方法，其特征在于，具体包括以下步骤：1. a necessary NPSH numerical simulation prediction method for a volute type centrifugal pump, is characterized in that, specifically comprises the following steps: 步骤一：建立流体域Step 1: Create a Fluid Domain 对蜗壳式离心泵进行建模，设置叶片边缘与隔舌之间的初始位置；Model the volute centrifugal pump and set the initial position between the blade edge and the separator tongue; 连接隔舌顶点与叶片进口圆圆心，连接所有叶片顶点与叶片进口圆圆心，确保隔舌顶点与叶片进口圆圆心的连线和叶片顶点与叶片进口圆圆心的连线夹角最小值位于1°～5°之间，并导出流体域文件；Connect the apex of the tongue and the center of the blade inlet circle, connect all the vertices of the blade and the center of the inlet circle of the blade, and ensure that the minimum value of the angle between the apex of the tongue and the center of the inlet circle of the blade and the connection line between the apex of the blade and the center of the inlet circle of the blade is 1° ～5°, and export the fluid domain file; 步骤二：网格划分Step 2: Meshing 对导出的流体域文件进行网格划分，叶片、进出口区域进行网格的细化，划分出精细的边界层网格，并对所有的网格进行质量提升；Mesh the exported fluid domain file, refine the mesh of the blade, inlet and outlet areas, divide the fine boundary layer mesh, and improve the quality of all meshes; 步骤三：不加空化模型，定常计算Step 3: No cavitation model, steady calculation 对步骤二得到的网格文件，导入软件CFX中，在不加空化模型下，初始参考气压值设置为0，根据额定扬程设置出口静压，定常计算，得到一份结果文件，记录此时扬程H0，并计算需要降到3％的扬程H’，同时复制一份结果文件留作备用；Import the grid file obtained in step 2 into the software CFX, without adding the cavitation model, set the initial reference air pressure value to 0, set the outlet static pressure according to the rated head, perform constant calculation, and obtain a result file, record this time. Head H 0 , and calculate the head H' that needs to be reduced to 3%, and copy a result file for backup; 步骤四：计算选定叶片的面均压力值Step 4: Calculate the surface average pressure value of the selected blade 对于步骤三得到结果文件进行后处理，观察内部的压力分布情况，并找出作积分的叶片；对作积分的叶片上满足1.2Din～0.75Dout的吸力面区域作压力面积积分，得到面均压力值Pa，其中Din为叶片进口直径，Dout为叶片出口直径；Perform post-processing on the result file obtained in step 3, observe the internal pressure distribution, and find the blade for integration; perform pressure area integration on the suction surface area of the blade for integration that satisfies 1.2D in ~ 0.75D out , and obtain the surface Average pressure value P a , where D in is the blade inlet diameter, and D out is the blade outlet diameter; 步骤五：确定参考气压值，添加空化模型，定常计算验证结果Step 5: Determine the reference air pressure value, add a cavitation model, and verify the results by regular calculation 以步骤四中取得的面均压力值Pa减去饱和蒸气压Pv作为参考气压值Pf；在软件CFX中，设置参考气压值，定常计算来判断仿真结果中的扬程值H是否达到了扬程下降3％的点；Take the surface average pressure value P a obtained in the step 4 minus the saturated vapor pressure P v as the reference air pressure value P f ; in the software CFX, set the reference air pressure value, and calculate regularly to determine whether the lift value H in the simulation result has reached the The point at which the head drops by 3%; 步骤六：迭代计算，根据结果文件中扬程H大小，重新选取参考气压值，判断结果，具体是：Step 6: Iterative calculation, according to the size of the head H in the result file, re-select the reference air pressure value, and judge the result, specifically: 1)当
Figure FDA0003103086250000011
时，1) When
Figure FDA0003103086250000011
hour, ①若H>0.97H0，取初始减小量ΔP0＝0，每次迭代减小量ΔPi根据最后得到的H判断，这里i为迭代次数，取为:①If H>0.97H 0 , take the initial reduction ΔP 0 =0, and the reduction ΔP i for each iteration is judged according to the final H obtained, where i is the number of iterations, and is taken as:
Figure FDA0003103086250000012
Figure FDA0003103086250000012
 ②若H<0.97H0，采取步骤三中复制的备用结果文件，在此基础上重新拾取
Figure FDA0003103086250000013
即设置新的参考气压值：②If H<0.97H 0 , take the backup result file copied in step 3, and pick it up again on this basis
Figure FDA0003103086250000013
That is, to set a new reference air pressure value:
Figure FDA0003103086250000021
Figure FDA0003103086250000021
 2)当
Figure FDA0003103086250000022
时，从后处理中得到进口总压Pin*，根据
Figure FDA0003103086250000023
由此可以求出必需汽蚀余量，其中Pin*为进口总压，vs为泵进口速度，NPSHr为必需汽蚀余量，ρ为液体密度，g为重力加速度。2) When
Figure FDA0003103086250000022
, the total inlet pressure P in* is obtained from the post-processing, according to
Figure FDA0003103086250000023
From this, the necessary NPSH can be obtained, where P in* is the total inlet pressure, v s is the pump inlet speed, NPSH r is the necessary NPSH, ρ is the liquid density, and g is the acceleration of gravity. 2.根据权利要求1所述的一种蜗壳式离心泵必需汽蚀余量数值模拟预测方法，其特征在于，其特征在于：步骤三具体是：2. the necessary NPSH numerical simulation prediction method of a kind of volute type centrifugal pump according to claim 1, is characterized in that, it is characterized in that: step 3 is specifically: 通过给定的流量值Q，额定扬程HN，在软件CFX中进行设置出口静压以及进口的质量流量；Through the given flow value Q and the rated head H N , the outlet static pressure and the inlet mass flow are set in the software CFX; 根据泵扬程与进出口压力关系计算不加空化模型下的扬程值。Calculate the head value without the cavitation model according to the relationship between the pump head and the inlet and outlet pressure. 3.根据权利要求1所述的一种蜗壳式离心泵必需汽蚀余量数值模拟预测方法，其特征在于，其特征在于：步骤四具体是：3. the necessary NPSH numerical simulation prediction method of a kind of volute type centrifugal pump according to claim 1, is characterized in that, it is characterized in that: step 4 is specifically: 通过CFD后处理叶片压力云图，可得出叶片上的压力分布；The pressure distribution on the blade can be obtained by post-processing the blade pressure cloud map by CFD; 设连接叶轮进口圆圆心O与隔舌顶点为直线l，以叶轮进口圆圆心O为旋转点将直线l分别顺时针和逆时针旋转1°和5°；其中顺时针旋转1°的直线记为l1，顺时针旋转5°的直线记为l2，逆时针旋转1°的直线记为l’1，逆时针旋转5°的直线记为l’2，选取位于l1和l2或l’1和l’2之间的叶片，该叶片即为作积分的叶片；Assume that the line l connecting the center O of the inlet circle of the impeller and the vertex of the separation tongue is a straight line l, and the line l is rotated clockwise and counterclockwise by 1° and 5° respectively with the center O of the impeller inlet circle as the rotation point; the straight line rotated 1° clockwise is recorded as l 1 , the straight line rotated 5° clockwise is recorded as l 2 , the straight line rotated by 1° counterclockwise is recorded as l' 1 , the straight line rotated by 5° counterclockwise is recorded as l' 2 , choose between l 1 and l 2 or l The blade between ' 1 and l' 2 , the blade is the integral blade; 在叶片吸力面处取满足1.2Din～0.75Dout内的区域，即确定的压力区域范围为：At the suction surface of the blade, take the area within 1.2D in ~ 0.75D out , that is, the determined pressure area range is: A＝∫sdt，t∈(1.2Din，0.75Dout)A=∫sdt, t∈(1.2D in , 0.75D out ) t为叶片吸力面处满足1.2Din～0.75Dout内的区域长度，s为叶片吸力面处满足1.2Din～0.75Dout内的区域宽度；t is the length of the area at the suction surface of the blade that satisfies the range of 1.2D in to 0.75D out , and s is the width of the area at the suction surface of the blade that meets the range of 1.2D in to 0.75D out ; 对区域A作面积积分得到面均压力值Pa：The area average pressure value Pa is obtained by integrating the area A :
Figure FDA0003103086250000024
Figure FDA0003103086250000024
 这里A为区域面积，Ai为面积元，φ为区域压力值，φi为压力元，n为分割次数。Here A is the area of the area, A i is the area element, φ is the area pressure value, φ i is the pressure element, and n is the number of divisions. 4.根据权利要求3所述的一种蜗壳式离心泵必需汽蚀余量数值模拟预测方法，其特征在于，其特征在于：步骤六中鉴于每次迭代减小量过大会影响后续计算的机理，当迭代n次后，第(n+1)次迭代减小量ΔPn+1大于一定值时，对其取半作为第(n+1)次迭代减小量ΔPn+1，即当
Figure FDA0003103086250000031
时，取
Figure FDA0003103086250000032
Pmax为吸力面区域上的最大压力值。4. a kind of volute type centrifugal pump necessary NPSH numerical simulation prediction method according to claim 3 is characterized in that: it is characterized in that: in step 6, in view of that each iteration reduction is too large to affect subsequent calculation Mechanism, when the (n+1)th iteration reduction ΔP n+1 is greater than a certain value after n iterations, take half of it as the (n+1)th iteration reduction ΔP n+1 , namely when
Figure FDA0003103086250000031
when, take
Figure FDA0003103086250000032
P max is the maximum pressure value on the suction surface area.
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