Method for determining the protection range of the impeller chamber of a large tubular pump under cavitation oscillation conditions

Abstract

The present invention belongs to the technical field of hydraulic machinery engineering and provides a method for determining the protection range of the runner chamber under cavitation oscillation conditions of large-scale tubular pumps. The implementation process is as follows: first, a "life expansion curve" and a "life shrinkage curve" are introduced to respectively describe the growth and collapse processes of the cavitation zone under cavitation oscillation conditions of large-scale tubular pumps; then, based on the birth threshold and death threshold, the key peak nodes are gradually calculated; then, based on the protection threshold, the label values ​​of the upper and lower protection nodes are sequentially obtained; finally, the optimal protection range of the runner chamber is determined by combining the peak nodes and the label values ​​of the upper and lower protection nodes. The present invention provides for the first time an empirical estimation method that follows the laws of cavitation oscillation and realizes economical protection of the runner chamber. It can quickly and accurately predict the optimal circumferential protection range of the runner chamber, ensuring that large-scale tubular pumps have the necessary anti-cavitation capabilities while avoiding the additional economic losses caused by excessive protection across the entire range.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydraulic machinery engineering, and in particular relates to a method for determining the protection range of a runner chamber of a large-scale tubular pump under cavitation oscillation conditions. Background Art

[0002] In engineering, tubular pumps with impeller diameters exceeding 3 meters are referred to as "large tubular pumps." Large tubular pumps experience significant gravity effects during operation, manifesting as a hydrostatic pressure differential between the top and bottom of the impeller flow channel comparable to the pump head. This can easily induce cavitation oscillation, manifested as significant cavitation at the top of the impeller flow channel and none at the bottom. This cavitation zone evolves periodically as the impeller rotates. Under these unique cavitation oscillation conditions, the inner wall of the impeller chamber is subjected to periodic impact from the cavitation zones carried by each blade, which can easily cause cavitation damage and compromise the healthy operation of the tubular pump. Therefore, protection of the impeller chamber is essential. However, the optimal circumferential range for protection is currently unclear in engineering, as different areas experience varying degrees of cavitation impact. For example, the top of the flow channel should be prioritized for protection, while the bottom generally requires no protection. Excessive protection of the entire flow channel can incur significant economic costs. Summary of the Invention

[0003] (1) Technical issues to be resolved

[0004] The present invention aims to solve the problem of how large the circumferential range is to be most economical in protecting the inner wall of the impeller chamber under the impact of cavitation oscillation induced by gravity effect for a large-scale tubular pump with an impeller diameter exceeding 3m.

[0005] (2) Technical solution

[0006] The present invention provides a method for determining the protection range of the runner chamber of a large-scale tubular pump under cavitation oscillation conditions, and the implementation process includes the following steps:

[0007] Step 1: Given the “life expansion curve” V according to the following formula + , which is used to characterize the growth process of the cavitation zone under the cavitation oscillation conditions of large-scale tubular pumps. The specific expression is:

[0008]

[0009] Wherein, e is a natural constant, x is a node coordinate variable used to mark the circumferential position of the runner chamber, α1 is an upper limit value used to characterize the maximum cavitation degree of the cavitation zone growth process, α2 is the slope value, and α3 is the milestone point, which together determine the growth speed of the "life expansion curve";

[0010] Step 2: Given the “life shrinkage curve” V according to the following formula -, which is used to characterize the collapse process of the cavitation zone under the cavitation oscillation conditions of large-scale tubular pumps. The specific expression is:

[0011]

[0012] Wherein, e is a natural constant, x is a node coordinate variable used to mark the circumferential position of the runner chamber, α4 is an upper limit value used to characterize the maximum cavitation degree of the cavitation zone collapse process, α5 is the slope value, and α6 is the milestone point, which together determine the decay speed of the "life atrophy curve";

[0013] Step 3: Let V + Equal to the birth threshold δ B , reversely find the birth node is x = A; let V - Equal to the death threshold δ D , reversely solve the dead node to be x=B;

[0014] Step 4: Calculate the peak node value T according to the following formula, that is, determine the circumferential position where the cavitation in the runner chamber reaches the maximum destructive capacity. The specific expression is:

[0015]

[0016] Step 5: Let V + Equal to the protection threshold β, the mark value of the upper protection node x = M is obtained inversely, that is, the circumferential position where the cavitation in the runner chamber begins to have destructive power is determined; let V - Equal to the protection threshold β, the mark value of the protection node x = N is obtained inversely, which determines the circumferential position where the runner chamber cavitation finally loses its destructive ability;

[0017] Step 6: Establish a circumferential coordinate system, including defining the counterclockwise rotation direction of the impeller based on the inlet direction of the tubular pump, and defining the top point of the tubular pump runner chamber as the position of θ = 90° and the bottom point of the tubular pump runner chamber as the position of θ = 270°, with the direction of gravity as the reference;

[0018] Step 7: Calculate the circumferential coordinates θ of the upper protection node according to the following formula: + and the circumferential coordinates θ of the lower protection node - , according to the circumferential coordinate θ + and the circumferential coordinate θ - Determine the optimal protection range of the runner chamber in the circumferential interval [θ + ,θ - ]Inside;

[0019]

[0020] In the method for determining the protection range of the runner chamber under the cavitation oscillation condition of a large-scale tubular pump provided by the present invention, in step 1, the life expansion curve V+ The values ​​of parameters α1, α2, and α3 in the expression are: α1 = 0.9902, α2 = -44.9196, and α3 = 1.5461.

[0021] Regarding the method for determining the protection range of the runner chamber under the cavitation oscillation condition of a large-scale tubular pump provided by the present invention, in step 2, the life atrophy curve V - The values ​​of parameters α4, α5, and α6 in the expression are: α4 = 0.9608, α5 = 182.5196, and α6 = 1.9537.

[0022] For the method for determining the protection range of the runner chamber under the cavitation oscillation condition of a large-scale tubular pump provided by the present invention, in step 3, the values ​​of the birth threshold and the death threshold are δ B =δ D =0.0012.

[0023] Regarding the method for determining the protection range of the impeller chamber of a large-scale tubular pump under cavitation oscillation conditions provided by the present invention, in step 5, the protection threshold β is set to 0.5.

[0024] (3) Compared with the prior art, the beneficial effects of the present invention

[0025] The present invention proposes a method for determining the protection range of the impeller chamber of a large-scale tubular pump under cavitation oscillation conditions. The method has the advantages of providing, for the first time, an empirical estimation method that follows the law of cavitation oscillation and realizes economical protection of the impeller chamber. The method is applicable to large-scale tubular pumps with impeller diameters exceeding 3 meters, and can quickly and accurately predict the optimal circumferential protection range of the impeller chamber. The method can ensure that the large-scale tubular pump has the necessary anti-cavitation ability, and can avoid the additional economic losses caused by excessive protection in the full range, thereby providing technical guidance for reasonably ensuring the anti-cavitation ability of large-scale tubular pumps. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments.

[0027] Figure 1 Schematic diagram of the circumferential coordinate system in step 6 of the present invention.

[0028] Figure 2 The diagram shows the circumferential protection range of the impeller chamber of a large-scale tubular pump with an impeller diameter of 4.2 m determined according to the determination method provided by the present invention, and a comparison diagram thereof with the measured value.

[0029] Figure 3 This is a flow chart for implementing the method for determining the protection range of the impeller chamber of a large-scale tubular pump under cavitation oscillation conditions provided by the present invention. DETAILED DESCRIPTION

[0030] In order to make the purpose, technical solutions and advantages of the implementation of the present invention clearer, the relevant technical solutions will be described in more detail below with reference to the accompanying drawings. In the accompanying drawings, the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work and without departing from the essence and spirit taught by the present invention are within the scope of protection of the present invention.

[0031] See Figure 1-3 The method for determining the protection range of the runner chamber of a large-scale tubular pump under cavitation oscillation conditions provided by the present invention is implemented as follows:

[0032] Step 1: Given the “life expansion curve” V according to the following formula + , which is used to characterize the growth process of the cavitation zone under the cavitation oscillation conditions of large-scale tubular pumps. The specific expression is:

[0033]

[0034] Wherein, e is a natural constant, x is a node coordinate variable used to mark the circumferential position of the runner chamber, α1 is an upper limit value used to characterize the maximum cavitation degree of the cavitation zone growth process, α2 is the slope value, and α3 is the milestone point, which together determine the growth speed of the "life expansion curve";

[0035] Step 2: Given the “life shrinkage curve” V according to the following formula - , which is used to characterize the collapse process of the cavitation zone under the cavitation oscillation conditions of large-scale tubular pumps. The specific expression is:

[0036]

[0037] Wherein, e is a natural constant, x is a node coordinate variable used to mark the circumferential position of the runner chamber, α4 is an upper limit value used to characterize the maximum cavitation degree of the cavitation zone collapse process, α5 is the slope value, and α6 is the milestone point, which together determine the decay speed of the "life atrophy curve";

[0038] Step 3: Let V + Equal to the birth threshold δ B , reversely find the birth node is x = A; let V - Equal to the death threshold δ D , reversely solve the dead node to be x=B;

[0039] Step 4: Calculate the peak node value T according to the following formula, that is, determine the circumferential position where the cavitation in the runner chamber reaches the maximum destructive capacity. The specific expression is:

[0040]

[0041] Step 5: Let V + Equal to the protection threshold β, the mark value of the upper protection node x = M is obtained inversely, which determines the circumferential position where the cavitation in the runner chamber begins to have destructive power; let V - Equal to the protection threshold β, the mark value of the protection node x = N is obtained by reverse calculation, that is, the circumferential position where the runner chamber cavitation finally loses its destructive ability is determined;

[0042] Step 6: Establish a circumferential coordinate system, including defining the impeller as counterclockwise rotating with the inlet direction of the tubular pump as the reference, and defining the top point of the tubular pump runner chamber as the position of θ = 90° and the bottom point of the tubular pump runner chamber as the position of θ = 270° with the direction of gravity as the reference;

[0043] Step 7: Calculate the circumferential coordinates θ of the upper protection node according to the following formula: + and the circumferential coordinates of the lower protection node θ - , according to the circumferential coordinate θ + and the circumferential coordinate θ - Determine the optimal protection range of the runner chamber in [θ + ,θ - ], calculate the circumferential coordinate θ of the upper protection node + and the circumferential coordinates θ of the lower protection node - The specific expression is:

[0044]

[0045] In the above embodiment, the lifeline includes a life expansion curve and a life contraction curve.

[0046] In this example, the life expansion curve V in step 1 + The values ​​of parameters α1, α2, and α3 in the expression are: α1 = 0.9902, α2 = -44.9196, and α3 = 1.5461.

[0047] In this example, the life shrinkage curve V in step 2 - The values ​​of parameters α4, α5, and α6 in the expression are: α4 = 0.9608, α5 = 182.5196, and α6 = 1.9537.

[0048] In this example, the birth threshold and death threshold in step 3 are set to δ B =δ D =0.0012.

[0049] In this example, in step 5, the protection threshold β is set to 0.5.

[0050] The following takes a large tubular pump with an impeller diameter of 4.2m as an example to explain in detail the method for determining the protection range of the impeller chamber under cavitation oscillation conditions of the large tubular pump.

[0051] First, the birth node A is calculated as:

[0052]

[0053] The dead node B is calculated as:

[0054]

[0055] Then the peak node T is calculated as:

[0056]

[0057] Then calculate the mark value M of the upper protection node as:

[0058]

[0059] Then calculate the mark value N of the next protection node:

[0060]

[0061] Finally, the circumferential coordinate θ of the upper protection node is calculated + for:

[0062] θ + =[1-4(TM)]·90°≈1.48°

[0063] Calculate the circumferential coordinate θ of the lower protection node - for:

[0064] θ - =[1+4(NT)]·90°≈147.89°

[0065] From the circumferential coordinates of the lower protection node and the upper protection node obtained by the above calculation, it can be seen that the optimal protection range of the runner chamber is within the circumferential range of 1.48° to 147.89° (the circumferential coordinate system is shown in the attached figure). Figure 1 As shown). Actual observations show that for a large tubular pump with an impeller diameter of 4.2 m, with the gravity direction as a reference, during the cavitation growth process from the bottom to the top of the impeller, the + ≈3°, the cavitation zone reaches a semi-vaporized state, that is, the vapor volume fraction is about to exceed 50%. In engineering, this is considered to be the starting point for entering the cavitation protection zone. In the process of cavitation collapse from the top to the bottom of the impeller, at θ -When the angle is ≈145°, the cavitation zone reaches a semi-vaporized state, that is, the volume fraction of the vapor phase is about to be less than 50%. In engineering, this is considered to be the end point for exiting the cavitation protection zone. Obviously, the estimation results of this patent are in good agreement with the actual observation results, and the optimal circumferential protection range of the runner chamber can be predicted quickly and accurately. In contrast, traditional engineering experience cannot infer this accurate economic range, and can only take irrational measures such as semi-circular protection of the top of the runner chamber or overall full circumferential protection. For large-scale cross-flow pumps with huge sizes, this will significantly increase the protection cost. In summary, this patent provides for the first time an empirical estimation method that follows the law of cavitation oscillation and realizes economical protection of the runner chamber. It can quickly and accurately predict the optimal circumferential protection range of the runner chamber, which can not only ensure that large-scale cross-flow pumps have the necessary anti-cavitation ability, but also avoid the additional economic losses caused by excessive protection in the entire range.

[0066] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the protection scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for determining the protection range of the runner chamber of a large-scale tubular pump under cavitation oscillation conditions, characterized in that: The method comprises the following steps: Step 1: Given the "life expansion curve" V according to the following formula + , which is used to characterize the growth process of the cavitation zone under the cavitation oscillation conditions of large-scale tubular pumps. The specific expression is: Where, e is a natural constant, x is a node coordinate variable used to mark the circumferential position of the runner chamber, α1 is the upper limit value, α2 is the slope value, and α3 is the mileage point; Step 2: Given the "life shrinkage curve" V according to the following formula - , which is used to characterize the collapse process of the cavitation zone under the cavitation oscillation conditions of large-scale tubular pumps. The specific expression is: Where, e is a natural constant, x is a node coordinate variable used to mark the circumferential position of the runner chamber, α4 is the upper limit value, α5 is the slope value, and α6 is the mileage point; Step 3: Let V + Equal to the birth threshold δ B , reversely find the birth node is x = A; let V - Equal to the death threshold δ D , reversely solve the dead node to be x=B; Step 4: Calculate the value T of the Dingsheng node according to the following formula. The specific expression is: Step 5: Let V + Equal to the protection threshold β, the mark value x of the protection node is obtained inversely, and V - Equal to the protection threshold β, the mark value of the protected node x = N is obtained inversely; Step 6: Establish a circumferential coordinate system, including defining the counterclockwise rotation direction of the impeller based on the inlet direction of the tubular pump, and defining the top point of the tubular pump runner chamber as the position of θ = 90° and the bottom point of the tubular pump runner chamber as the position of θ = 270°, with the direction of gravity as the reference; Step 7: Calculate the circumferential coordinates θ of the upper protection node according to the following formula: + and the circumferential coordinates θ of the lower protection node - , according to the circumferential coordinate θ + and the circumferential coordinate θ - Determine the optimal protection range of the runner chamber in [θ + ,θ - ] in the circumferential range, the specific expression is:

2. The method for determining the protection range of the runner chamber of a large-scale tubular pump under cavitation oscillation conditions according to claim 1 is characterized in that: In step 1, the life expansion curve V + The values ​​of parameters α1, α2, and α3 in the expression are: α1 = 0.9902, α2 = -44.9196, and α3 = 1.5461.

3. The method for determining the protection range of the runner chamber of a large-scale tubular pump under cavitation oscillation conditions according to claim 1 is characterized in that: In step 2, the life shrinkage curve V - The values ​​of parameters α4, α5, and α6 in the expression are: α4 = 0.9608, α5 = 182.5196, and α6 = 1.9537.

4. The method for determining the protection range of the runner chamber of a large-scale tubular pump under cavitation oscillation conditions according to claim 1 is characterized in that: In step 3, the birth threshold and death threshold are set to δ B =δ D =0.0012.

5. The method for determining the protection range of the runner chamber of a large-scale tubular pump under cavitation oscillation conditions according to claim 1 is characterized in that: In step 5, the protection threshold β is set to 0.5.

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