Method for improving hydraulic performance of multi-stage centrifugal pump and multi-stage centrifugal pump

Abstract

The invention belongs to the technical field of centrifugal pumps, and particularly relates to an optimal design method for hydraulic performance of a multi-stage centrifugal pump. Comprising the steps that the impeller theoretical lift HTi when the leakage effect is not considered is calculated; based on the calculated impeller theoretical lift HTi when the leakage effect is not considered, the inter-stage leakage rate q is calculated; based on the calculated inter-stage leakage rate q, the theoretical impeller lift HTii considering the inter-stage leakage effect is calculated; the impeller theoretical lift difference delta HT considering the inter-stage leakage effect is calculated on the basis of the impeller theoretical lift HTi without considering the leakage effect and the impeller theoretical lift HTii considering the inter-stage leakage effect, and then the design upper limit value b2ii for optimizing the outlet width of the impeller is calculated in a back-stepping mode on the basis of delta HT. Aiming at inter-stage leakage, the multi-stage centrifugal pump which is excellent in performance and stable in operation is obtained by starting from the impeller structure optimization direction and combining adjustment of inter-stage gaps.

Description

Technical Field

[0001] The invention belongs to the technical field of centrifugal pumps, and in particular relates to an optimization design method for the hydraulic performance of a multi-stage centrifugal pump. Background Art

[0002] The self-balancing high-pressure multistage pump is a new alternative product developed to solve the problems of the balance disc or balance drum mechanism of the traditional multistage pump, which is easy to wear during use, resulting in reduced work efficiency and short service life. It has symmetrically arranged impeller rotor components, and the axial forces generated by the symmetrical impellers at each stage offset each other. The remaining residual axial force is borne by the thrust bearing. It can achieve automatic balancing of the huge axial thrust in the pump cavity without using a balance disc structure, thus solving the problem caused by wear of the balancing device and improving the reliability and service life of the pump.

[0003] However, see Figure 6 and Figure 7 Taking the self-balancing high-pressure six-stage pump as an example, in practice, there will be an interstage gap between the sleeve a and the seal b of the pump main shaft, so that part of the medium flows from the sixth-stage impeller d to the third-stage impeller c through the interstage gap. Compared with the ideal state without interstage gap, the flow through the latter impellers increases, which makes the high efficiency point deviate from the rated working condition when the latter impellers work, and finally reduces the hydraulic performance of the whole machine. This situation is called the interstage leakage effect in this field, and it has become a technical bottleneck in this field.

[0004] In addition, due to the existence of the inter-stage leakage effect, the axial force of the impellers through which the inter-stage leakage flows will be smaller than that of the impellers without inter-stage leakage. Especially on the last-stage impeller, there will be a large residual axial force, which is not conducive to the stable operation of the pump and may even cause damage to the pump shaft system.

[0005] If the interstage gap is simply designed to be relatively small, it will cause easy contact and wear between the sleeve a and the seal b. It is urgent to propose a technical measure to solve the interstage leakage effect and thus improve the hydraulic performance of the pump. Summary of the invention

[0006] In view of the above technical problems, the present invention provides a method for improving the hydraulic performance of a multi-stage centrifugal pump. The present invention aims at inter-stage leakage, starts from the direction of impeller structure optimization, and combines the adjustment of the inter-stage gap to obtain a multi-stage centrifugal pump with excellent performance and stable operation.

[0007] The technical solution of the present invention is: a method for improving the hydraulic performance of a multi-stage centrifugal pump, the multi-stage centrifugal pump comprising a plurality of impellers symmetrically arranged on a main shaft, comprising the following steps:

[0008] 1) Calculate the theoretical impeller head H without considering the leakage effect Ti ;

[0009] 2) Based on the theoretical impeller head H calculated in step 1) without considering the leakage effect Ti , calculate the interstage leakage q;

[0010] 3) Based on the interstage leakage q calculated in step 2), calculate the theoretical impeller head H considering the interstage leakage effect Tii ;

[0011] 4) Based on the theoretical impeller head H without considering the leakage effect Ti and the theoretical impeller head H considering the interstage leakage effect Tii , calculate the theoretical impeller head difference ΔH considering the interstage leakage effect T , the ΔH T =H Ti -H Tii , then based on the ΔH T , reversely calculate the upper limit value b of the optimized impeller outlet width design 2ii , and select b 2i is the design lower limit, the b 2i is the initial value of the impeller outlet width before optimization;

[0012] 5) According to the design upper limit value b of the optimized impeller outlet width calculated in step 4) 2ii To optimize the outlet width of the last few stages of impellers, let the optimized impeller outlet width be b 2n , where n is the number of times the impeller outlet width is optimized, when n=1, then b 2i 21 2ii , b 21 That is the impeller outlet width after the first adjustment. When n>1, b 2(n-1) 2n 2ii ;

[0013] 6) Adjust the interstage gap, and set the adjusted interstage gap to be δ m , where m is the number of interstage gap adjustments, m = 1, then 0.2 ≤ δ 1 ≤0.25, unit: mm, when m>1, then 0.2≤δ m ≤δ m-1 ;

[0014] 7) Verify the hydraulic performance of the adjusted water pump;

[0015] 7.1) Perform performance verification on the adjusted impeller outlet width;

[0016] If the head and axial force requirements are met, output b 2最终 , ​​​​

[0017] If the head and axial force requirements are not met, return to step 5);

[0018] 7.2) Perform performance verification on the adjusted interstage clearance;

[0019] If the efficiency requirement is met, output δ 最终 ,

[0020] If the efficiency requirement is not met, return to step 6).

[0021] Preferably, in step 1), the impeller theoretical head H without considering the leakage effect is Ti The calculation process:

[0022]

[0023]

[0024] Where:

[0025] V m2i is the impeller outlet axial velocity without considering the leakage effect, in meters per second;

[0026] Q is the rated flow rate at the impeller inlet, in cubic meters per second;

[0027] η v is the volumetric efficiency of the pump, estimated based on the specific speed;

[0028] D 2 is the outer diameter of the impeller without considering the leakage effect, in meters;

[0029] b 2i is the impeller outlet width without considering the leakage effect, in meters;

[0030] Ψ 2i The impeller outlet displacement coefficient without considering the leakage effect is 0.8 to 0.9;

[0031] n s is the specific speed of the pump, which is determined based on the design parameters of the pump;

[0032] H is the actual head of the pump, in meters;

[0033] n 1 is the impeller speed, in revolutions per minute;

[0034] U 2 is the impeller outlet peripheral speed without considering the leakage effect, in meters per second;

[0035] σ is the impeller outlet slip correction coefficient without considering the leakage effect, Z is the number of impeller blades;

[0036] β 2 is the blade outlet placement angle without considering the leakage effect, in degrees;

[0037] U 1 is the impeller inlet peripheral speed without considering the leakage effect, in meters per second;

[0038] D 1 is the impeller inlet diameter without considering the leakage effect, in meters;

[0039] V u1i V is the circumferential component of the absolute velocity at the impeller inlet without considering the leakage effect, in meters per second; u2i K is the circumferential component of the absolute velocity at the impeller outlet without considering the leakage effect, in meters per second; 1i is the coefficient related to the impeller inlet and pre-swirl without considering the leakage effect;

[0040] R 1 is the impeller inlet radius without considering the leakage effect, in meters;

[0041] m is the empirical coefficient, with a range of 0.055 to 0.08, where the larger value is taken for a larger specific speed;

[0042] g is the acceleration due to gravity, measured in square meters per second.

[0043] Preferably, in step 2), the calculation process of the inter-stage leakage q is

[0044]

[0045] Among them, H m =n 2 H Ti

[0046] F m =D h πδ

[0047] Where:

[0048] μ is the flow coefficient, and the corresponding flow coefficient can be calculated by looking up the data according to the form of the interstage sealing ring; F m is the flow cross-sectional area of ​​the sealing ring gap, in square meters;

[0049] g is the acceleration due to gravity, in square meters per second;

[0050] H m is the pressure drop across the interstage seal, in meters;

[0051] H Ti is the calculated theoretical head of the impeller without considering inter-stage leakage, in meters;

[0052] n 2 is the number of impellers through which the interstage leakage flow flows, in pieces;

[0053] δ is the seal ring gap, in meters;

[0054] D h is the interstage gap diameter, in meters.

[0055] Preferably, the impeller theoretical head H considering the interstage leakage effect is Tii The calculation process:

[0056]

[0057]

[0058] Where:

[0059] V m2ii The impeller outlet axial velocity considering the interstage leakage effect is in meters per second;

[0060] Q is the rated flow rate at the impeller inlet, in cubic meters per second;

[0061] q is the interstage leakage flow rate, in cubic meters per second;

[0062] η v is the volumetric efficiency of the impeller without considering leakage;

[0063] D 2 is the outer diameter of the impeller without considering the leakage effect, in meters;

[0064] b 2i is the impeller outlet width without considering the leakage effect, in meters;

[0065] Ψ 2i The impeller outlet displacement coefficient without considering the leakage effect is 0.8 to 0.9;

[0066] U 2 is the impeller outlet peripheral speed without considering the leakage effect, in meters per second;

[0067] n 1 is the impeller speed, in revolutions per minute;

[0068] σ ii is the impeller outlet slip correction factor without considering the interstage leakage effect, β 2 is the blade outlet placement angle without considering the interstage leakage effect, in degrees;

[0069] U 1is the impeller inlet peripheral speed without considering the leakage effect, in meters per second;

[0070] D 1 is the impeller inlet diameter without considering the leakage effect, in meters;

[0071] K 1ii The coefficient related to the impeller inlet and pre-swirl is considered to take into account the inter-stage leakage effect;

[0072] R 1 is the impeller inlet radius without considering the leakage effect, in meters;

[0073] m is the empirical coefficient, ranging from 0.055 to 0.08, where the larger value is taken for a larger specific speed;

[0074] V u1ii The circumferential component of the absolute velocity at the impeller inlet to take into account the interstage leakage effect, in meters per second;

[0075] V u2ii The circumferential component of the absolute velocity at the impeller outlet to take into account the interstage leakage effect, in meters per second;

[0076] g is the acceleration due to gravity, measured in square meters per second.

[0077] Preferably, in step 4), the impeller theoretical head difference ΔH considering the interstage leakage effect is T＝ H Ti -H Tii , reversely calculate the upper limit b of the optimized impeller outlet width 2ii The calculation process:

[0078]

[0079] Simplifying, we get:

[0080]

[0081] Combined with V m2i The upper limit b of the impeller outlet width after optimization can be calculated. 2ii :

[0082]

[0083] Where:

[0084] ψ 2ii The impeller blade outlet crowding coefficient is taken as 0.8 to 0.9 to consider the interstage leakage effect;

[0085] b 2ii is the calculated upper limit of the optimized impeller outlet width, in meters.

[0086] Preferably, in step 5), the adjusted impeller outlet width is set to b 2n , n is the number of times the impeller outlet width is adjusted, when n=1, then b 2n＝ (b 2i +b 2ii ) / 2, when n>1, then b 2n＝ (b 2i +b 2(n-1) ) / 2.

[0087] Preferably, in step 7), CFD software is used to perform performance verification.

[0088] Also provided is a multi-stage centrifugal pump prepared by the multi-stage centrifugal pump hydraulic performance improvement method.

[0089] Compared with the prior art, the present invention has the following beneficial effects:

[0090] The present invention aims at the form of annular interstage seal, takes the impeller component without considering the interstage leakage effect as the initial model, optimizes the design of the impeller component taking the interstage leakage effect into consideration, appropriately increases the outlet widths of several stages of impellers through which the interstage leakage flow flows, and simultaneously selects a suitable interstage gap to reduce the interstage leakage amount, thereby ultimately improving the hydraulic performance of the entire machine.

[0091] The invention patent obtains a universal hydraulic optimization method for multi-stage centrifugal pumps that takes into account the inter-stage leakage effect. The impeller designed using this method not only makes up for the lack of hydraulic performance, but also offsets part of the residual axial force, thereby better ensuring its efficient and stable operation at the operating point. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 is a flow chart of the present invention,

[0093] Figure 2 is a complete machine assembly diagram in an embodiment of the present invention,

[0094] Figure 3 is a schematic diagram of the three-dimensional structure of the sixth-stage impeller in an embodiment of the present invention,

[0095] Figure 4 is a schematic diagram of the optimized position of the sixth-stage impeller in an embodiment of the present invention,

[0096] Figure 5 is a graph of operating characteristics before and after optimization in an embodiment of the present invention,

[0097] Figure 6 This is a schematic diagram of the medium flow direction in the pump when inter-stage leakage is not considered.

[0098] Figure 7 It is a schematic diagram of the flow direction of the interstage leakage medium.

[0099] In the figure, 1 is the first-stage impeller, 2 is the second-stage impeller, 3 is the third-stage impeller, 4 is the fourth-stage impeller, 5 is the fifth-stage impeller, 6 is the sixth-stage impeller, 6.1 is the impeller outlet width, 7 is the pump inlet, and 8 is the pump outlet;

[0100] a is the shaft sleeve, b is the seal, c is the third-stage impeller, and d is the sixth-stage impeller;

[0101] Figure 5 In the figure, the horizontal axis is the ratio of the actual operating flow rate of the multistage pump to the flow rate at the rated operating point;

[0102] Figure 6 In the figure, the arrows represent the flow direction of the medium;

[0103] Figure 7 In the figure, the arrows represent the flow direction of the medium leaking between stages. DETAILED DESCRIPTION

[0104] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only 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 creative work are within the scope of protection of the present invention.

[0105] See also Figure 1 The present invention provides a method for optimizing the performance of a multi-stage centrifugal pump, comprising the following steps:

[0106] 1) Calculate the theoretical impeller head H without considering the leakage effect Ti ;

[0107] In step 1), the theoretical impeller head H without considering the leakage effect Ti The calculation process:

[0108] 1.1) First, find the impeller outlet axial velocity.

[0109]

[0110] in:

[0111] Where:

[0112] V m2i is the impeller outlet axial velocity without considering the leakage effect, in meters per second;

[0113] Q is the rated flow rate at the impeller inlet, in cubic meters per second;

[0114] η v is the volumetric efficiency of the pump, estimated based on the specific speed;

[0115] D 2 is the outer diameter of the impeller without considering the leakage effect, in meters;

[0116] b 2i is the impeller outlet width without considering the leakage effect, in meters;

[0117] Ψ 2i The impeller outlet displacement coefficient without considering the leakage effect is 0.8 to 0.9;

[0118] 1.2) Calculate the circumferential component of the absolute velocity at the impeller inlet without considering the leakage effect, in meters per second;

[0119]

[0120] Where: σ is the impeller outlet slip correction coefficient without considering the leakage effect, Z is the number of impeller blades;

[0121] U 2 is the impeller outlet circumferential speed without considering the leakage effect, in meters per second, where n 1 is the impeller speed, in revolutions per minute;

[0122] β 2 is the blade outlet placement angle without considering the leakage effect, in degrees;

[0123] 1.3) Calculate the circumferential component of the absolute velocity at the impeller inlet without considering the leakage effect, in meters per second;

[0124]

[0125] Where: k 1i is the coefficient related to the impeller inlet and pre-swirl without considering the leakage effect; R 1 is the impeller inlet radius without considering the leakage effect, in meters;

[0126] in Where m is the empirical coefficient, and its value range is 0.055 to 0.08, where the larger value is taken for the larger specific speed;

[0127] 1.4) Finally, calculate the theoretical impeller head H without considering the leakage effect. Ti ,

[0128]

[0129] Where: g is the acceleration due to gravity, in square meters per second;

[0130] Among them U 1is the impeller inlet peripheral speed without considering the leakage effect, in meters per second;

[0131] Where D 1 is the impeller inlet diameter without considering the leakage effect, in meters.

[0132] The purpose of calculating Hti is to make a comparison with the theoretical head of the impeller when there is inter-stage leakage flow. In addition, calculating the theoretical head of the impeller can facilitate the subsequent calculation of the inter-stage leakage flow.

[0133] 2) Based on the H calculated in step 1) Ti , calculate the interstage leakage q;

[0134] In step 2), the calculation process of the interstage leakage q is as follows:

[0135]

[0136] Among them, H m =n 2 H Ti , F m =D h πδ,

[0137] Where: n 2 is the number of impellers through which the interstage leakage flow flows, in pieces;

[0138] D h is the interstage gap diameter, in meters;

[0139] δ is the seal ring gap, in meters;

[0140] μ is the flow coefficient, and the corresponding flow coefficient can be calculated by looking up the data according to the form of the interstage sealing ring;

[0141] F m is the flow cross-sectional area of ​​the sealing ring gap, in square meters;

[0142] g is the acceleration due to gravity, in square meters per second;

[0143] H m It is the head generated by the pressure drop at both ends of the interstage seal, in meters;

[0144] H m It represents the theoretical head generated by the work done by the impellers of the last few stages through which the interstage leakage flow flows. It can be used to represent the head generated by the pressure drop at both ends of the interstage seal.

[0145] 3) Based on the q calculated in step 2), calculate the theoretical impeller head H considering the interstage leakage effect Tii ;

[0146] In step 3), the theoretical impeller head H considering the interstage leakage effect Tii The calculation process is as follows:

[0147] 3.1) First, calculate the impeller outlet axial velocity considering the interstage leakage effect, in meters per second;

[0148]

[0149] 3.2) Calculate the circumferential component of the absolute velocity at the impeller outlet considering the interstage leakage effect, in meters per second;

[0150]

[0151] Where:

[0152] 3.3) Calculate the circumferential component of the absolute velocity at the impeller inlet considering the interstage leakage effect, in meters per second;

[0153]

[0154] Where:

[0155] 3.4) Finally, find the theoretical head of the impeller considering the interstage leakage effect.

[0156]

[0157] Where: The parameters in each calculation formula are defined as follows:

[0158] V m2ii The impeller outlet axial velocity considering the interstage leakage effect is in meters per second;

[0159] Q is the rated flow rate at the impeller inlet, in cubic meters per second;

[0160] q is the interstage leakage flow rate, in cubic meters per second;

[0161] η v is the volumetric efficiency of the impeller without considering leakage;

[0162] D 2 is the outer diameter of the impeller without considering the leakage effect, in meters;

[0163] b 2i is the impeller outlet width without considering the leakage effect, in meters;

[0164] Ψ 2i The impeller outlet displacement coefficient without considering the leakage effect is 0.8 to 0.9;

[0165] U2 is the impeller outlet peripheral speed without considering the leakage effect, in meters per second;

[0166] n 1 is the impeller speed, in revolutions per minute;

[0167] σ ii is the impeller outlet slip correction factor without considering the interstage leakage effect,

[0168] β 2 is the blade outlet placement angle without considering the interstage leakage effect, in degrees;

[0169] U 1 is the impeller inlet peripheral speed without considering the leakage effect, in meters per second;

[0170] D 1 is the impeller inlet diameter without considering the leakage effect, in meters;

[0171] K 1ii The coefficient related to the impeller inlet and pre-swirl is considered to take into account the inter-stage leakage effect;

[0172] R 1 is the impeller inlet radius without considering the leakage effect, in meters;

[0173] m is the empirical coefficient, ranging from 0.055 to 0.08, where the larger value is taken for a larger specific speed;

[0174] V u1ii The circumferential component of the absolute velocity at the impeller inlet to take into account the interstage leakage effect, in meters per second;

[0175] V u2ii The circumferential component of the absolute velocity at the impeller outlet to take into account the interstage leakage effect, in meters per second;

[0176] g is the acceleration due to gravity, measured in square meters per second.

[0177] 4) Based on H Ti and H Tii , calculate the theoretical impeller head difference ΔH considering the interstage leakage effect T , ΔH T =H Ti -H Tii , and then based on ΔH T , reversely calculate the upper limit b of the optimized impeller outlet width 2ii , and select b 2i is the design lower limit, b 2i is the initial value of the impeller outlet width before optimization;

[0178] In step 4), according to the theoretical head difference ΔH of the impeller considering the interstage leakage effect T＝ H Ti -H Tii , reversely calculate the upper limit b of the optimized impeller outlet width 2ii The calculation process:

[0179]

[0180] Simplifying, we get:

[0181]

[0182] Combined with V m2i The upper limit b of the impeller outlet width after optimization can be calculated. 2ii :

[0183]

[0184]

[0185] Where:

[0186] ψ 2ii The impeller blade outlet crowding coefficient is taken as 0.8 to 0.9 to consider the interstage leakage effect;

[0187] b 2ii is the calculated upper limit of the optimized impeller outlet width, in meters.

[0188] 5) According to the b calculated in step 4) 2ii To optimize the outlet width of the last few stages of impellers, that is, the impeller after interstage leakage, the optimized impeller outlet width is set to b 2n , where n is the number of times the impeller outlet width is optimized, when n=1, then b 2i 21 2ii , b 21 That is the impeller outlet width after the first adjustment. When n>1, b 2(n-1) 2n 2ii Specifically, the median method can be used, assuming that the adjusted impeller outlet width is b 2n , n is the number of times the impeller outlet width is adjusted, when n=1, then b 2n =(b 2i +b 2ii ) / 2, when n>1, then b 2n =(b 2i +b 2(n-1) ) / 2.

[0189] 6) Adjust the interstage gap, and set the adjusted interstage gap to be δ m ​​​​, where m is the number of interstage gap adjustments, m = 1, then 0.2 ≤ δ 1 ≤0.25, unit: mm, when m>1, then 0.2≤δ m ≤δ m-1 ;

[0190] 7) Use CFD software to verify the performance of the redesigned machine. The goal after optimization is: the head and efficiency of the machine are higher than the initial model under the conditions of small flow, rated flow and large flow, and the axial force is smaller than the initial model;

[0191] If the head and axial force requirements are not met, readjust the impeller outlet width; increasing the impeller outlet width can increase the head and reduce the axial force;

[0192] If the efficiency requirement is not met, the interstage gap δ is readjusted; the reduction of the gap mainly improves the efficiency and reduces the axial force to a certain extent;

[0193] Continuously iterate and optimize until the head, efficiency and axial force can meet the requirements.

[0194] It should be noted that after the impeller outlet width changes, the front cover arc radius and inlet radius of the impeller will also change. When the impeller outlet width is known, the latter two can be inferred. This is a conventional technology and can be calculated based on the impeller design software. The specific calculation method will not be repeated here.

[0195] For multi-stage self-balancing centrifugal pumps with interstage leakage effect, interstage leakage will increase the working flow of the impellers in the latter stages, resulting in a decrease in the head of the impellers in the latter stages, and at the same time, the axial force of the impellers in the latter stages is significantly smaller than that of the former stages, especially the last stage; due to the interstage leakage, the volumetric efficiency of the pump is greatly reduced, which is the reason for the low efficiency of the whole machine. Therefore, if you want to increase the head and reduce the axial force, you can optimize the parameters of the impellers in the stages with interstage leakage flow, and if you want to improve the efficiency of the whole machine, you can reduce the interstage leakage.

[0196] Example

[0197] See also Figure 2 In this embodiment, a six-stage self-balancing high-pressure multistage centrifugal pump prepared by the above-mentioned multistage centrifugal pump hydraulic performance improvement method is provided, and its interstage seal is an annular seal, which is the interstage leakage point, and the main parameters are as follows:

[0198] Rated flow rate Q = 115.68m^3 / h

[0199] Pump speed n = 4240 rpm

[0200] Pump specific speed n s =47

[0201] First stage impeller outer diameter D 2 =315mm

[0202] First stage impeller inlet diameter D 1 =150mm

[0203] First stage impeller outlet diameter b 2 =10mm

[0204] The outer diameters D of the first stage impeller 1, the second stage impeller 2, the third stage impeller 3, the fourth stage impeller 4, the fifth stage impeller 5 and the sixth stage impeller 6 2 =315mm

[0205] The inlet diameters D of the first-stage impeller 1, the second-stage impeller 2, the third-stage impeller 3, the fourth-stage impeller 4, the fifth-stage impeller 5 and the sixth-stage impeller 6 1 =145mm

[0206] The outlet diameters b of the first-stage impeller 1, the second-stage impeller 2, the third-stage impeller 3, the fourth-stage impeller 4, the fifth-stage impeller 5 and the sixth-stage impeller 6 2 =10mm

[0207] Initial model interstage seal ring width δ=0.25mm

[0208] Initial model interstage seal ring diameter D h =135mm

[0209] Initial model interstage seal length L = 240 mm

[0210] The pump inlet and outlet diameters are both 148mm

[0211] From the previous formula, the theoretical head of the impeller without considering the interstage leakage effect can be calculated as:

[0212] H Ti =311.48m

[0213] The interstage leakage calculated from the theoretical head is:

[0214] q=10.2366m 3 / h

[0215] From the inter-stage leakage, the theoretical head of the impeller considering the inter-stage leakage effect can be obtained as:

[0216] H Tii =303.31m

[0217] Combining this with the previous calculation formula, we can get:

[0218] v mi -v mii =0.366m / s

[0219] Combined with the calculation formula of axial velocity and the impeller outlet width b without considering the interstage leakage effect 2i = 10mm, the upper limit of the optimized impeller outlet width can be calculated as: b 2ii =12mm

[0220] Therefore, the optimal range of the impeller outlet width parameter value is determined as follows: 10mm<b 2 <12mm

[0221] The optimization range of the interstage gap width parameter value is: 0.2mm≤δ≤0.25mm

[0222] See also Figure 3 and Figure 4 After multiple iterations of analysis, the optimized fourth, fifth and sixth stage impeller outlet widths of 4.1 were finally selected. 2最终 =11.5mm

[0223] Select the optimized interstage gap width δ 最终 =0.2mm

[0224] The optimized model is subjected to CFD numerical analysis, and its external characteristic curve and impeller axial force curve are obtained as follows: Figure 5 , analysis shows that the hydraulic performance of the optimized pump is better than the initial model under small flow, rated and large flow conditions; at the rated operating point, the head is 2.2% higher than the initial one, the efficiency is 0.3% higher than the initial one, and the axial force is 10% less than the initial one; at the operating point of 0.8 times the rated flow rate, the head is 0.2% higher than the initial one, the efficiency is 0.6% higher than the initial one, and the axial force is 16% less than the initial one; at the operating point of 1.2 times the rated flow rate, the head is 3.5% higher than the initial one, the efficiency is 0.33% higher than the initial one, and the axial force is 10.2% less than the initial one.

[0225] The present invention aims to increase the head, reduce the axial force and improve the efficiency. The interstage seal is in the form of an annular seal. The pump flow components are optimized and designed by considering the interstage leakage to make them better adapt to variable flow conditions, thereby achieving the purpose of improving hydraulic performance.

[0226] The above is a description of the present invention with reference to specific embodiments, but the present invention is not limited to the specific embodiments.

Claims

1. A method for improving the hydraulic performance of a multi-stage centrifugal pump, the multi-stage centrifugal pump comprising a plurality of impellers symmetrically arranged on a main shaft, characterized in that: The following steps are involved: 1) Calculate the theoretical impeller head H without considering the leakage effect Ti ; 2) Based on the theoretical impeller head H calculated in step 1) without considering the leakage effect Ti , calculate the interstage leakage q; 3) Based on the interstage leakage q calculated in step 2), calculate the theoretical impeller head H considering the interstage leakage effect Tii ; 4) Based on the theoretical impeller head H without considering the leakage effect Ti and the theoretical impeller head H considering the interstage leakage effect Tii , calculate the theoretical impeller head difference ΔH considering the interstage leakage effect T , the ΔH T =H Ti -H Tii , then based on the ΔH T , reversely calculate the upper limit value b of the optimized impeller outlet width design 2ii , and select b 2i is the design lower limit, the b 2i is the initial value of the impeller outlet width before optimization; 5) According to the design upper limit value b of the optimized impeller outlet width calculated in step 4) 2ii To optimize the outlet width of the last few stages of impellers, let the optimized impeller outlet width be b 2n , where n is the number of times the impeller outlet width is optimized, when n=1, then b 2i 21 2ii , b 21 That is the impeller outlet width after the first adjustment. When n>1, b 2(n-1) 2n 2ii ;​​​​ 6) Adjust the interstage gap, and set the adjusted interstage gap to be δ m , where m is the number of interstage clearance adjustments, m=1, then 0.2≤δ1≤0.25, unit: mm, when m>1, then 0.2≤δ m ≤δ m-1 ; 7) Verify the hydraulic performance of the adjusted water pump; 7.1) Perform performance verification on the adjusted impeller outlet width; If the head and axial force requirements are met, output b 2最终 , If the head and axial force requirements are not met, return to step 5); 7.2) Perform performance verification on the adjusted interstage clearance; If the efficiency requirement is met, output δ 最终 , If the efficiency requirement is not met, return to step 6).

2. A method for improving the hydraulic performance of a multi-stage centrifugal pump according to claim 1, characterized in that: In step 1), the impeller theoretical head H without considering the leakage effect Ti The calculation process: Where: V m2i is the axial velocity of the impeller outlet without considering the leakage effect, in meters per second; Q is the rated flow rate at the impeller inlet, in cubic meters per second; η v is the volumetric efficiency of the pump, estimated based on the specific speed; D2 is the outer diameter of the impeller without considering the leakage effect, in meters; b 2i is the impeller outlet width without considering the leakage effect, in meters; Ψ 2i is the impeller outlet displacement coefficient without considering the leakage effect, which is 0.8 to 0.9; n s is the specific speed of the pump, which is determined based on the design parameters of the pump; H is the actual head of the pump, in meters; n1 is the impeller speed, in revolutions per minute; U2 is the circumferential velocity of the impeller outlet without considering the leakage effect, in meters per second; σ is the slip correction coefficient of the impeller outlet without considering the leakage effect, Z is the number of impeller blades; β2 is the blade outlet placement angle without considering the leakage effect, in degrees; U1 is the impeller inlet peripheral speed without considering the leakage effect, in meters per second; D1 is the impeller inlet diameter without considering the leakage effect, in meters; V u1i is the circumferential component of the absolute velocity at the impeller inlet without considering the leakage effect, in meters per second; V u2i is the circumferential component of the absolute velocity at the impeller outlet without considering the leakage effect, in meters per second; K 1i is the coefficient related to the impeller inlet and pre-swirl without considering the leakage effect; R1 is the impeller inlet radius without considering the leakage effect, in meters; m is the empirical coefficient, with a range of 0.055 to 0.08, where the larger value is taken for a larger specific speed; g is the acceleration due to gravity, measured in square meters per second.

3. A method for improving the hydraulic performance of a multi-stage centrifugal pump according to claim 2, characterized in that: In step 2), the calculation process of the inter-stage leakage q is Among them, H m =n2H Ti F m =D h pd Where: μ is the flow coefficient, and the corresponding flow coefficient can be calculated by looking up the data according to the form of the interstage sealing ring; F m is the flow cross-sectional area of ​​the sealing ring gap, in square meters; g is the acceleration due to gravity, in square meters per second; H m is the pressure drop across the interstage seal, in meters; H Ti is the calculated theoretical head of the impeller without considering inter-stage leakage, in meters; n2 is the number of impellers through which the interstage leakage flow flows, in units; δ is the seal ring gap, in meters; D h is the interstage gap diameter, in meters.

4. A method for improving the hydraulic performance of a multi-stage centrifugal pump according to claim 3, characterized in that: In step 3), the impeller theoretical head H considering the interstage leakage effect Tii The calculation process: Where: V m2ii The impeller outlet axial velocity considering the interstage leakage effect is in meters per second; Q is the rated flow rate at the impeller inlet, in cubic meters per second; q is the interstage leakage flow rate, in cubic meters per second; η v is the volumetric efficiency of the impeller without considering leakage; D2 is the outer diameter of the impeller without considering the leakage effect, in meters; b 2i is the impeller outlet width without considering the leakage effect, in meters; Ψ 2i The impeller outlet displacement coefficient without considering the leakage effect is 0.8 to 0.9; U2 is the impeller outlet peripheral speed without considering the leakage effect, in meters per second; n1 is the impeller speed, in revolutions per minute; σ ii is the impeller outlet slip correction factor without considering the interstage leakage effect, β2 is the blade outlet placement angle without considering the interstage leakage effect, in degrees; U1 is the impeller inlet peripheral speed without considering the leakage effect, in meters per second; D1 is the impeller inlet diameter without considering the leakage effect, in meters; K 1ii The coefficient related to the impeller inlet and pre-swirl is considered to take into account the inter-stage leakage effect; R1 is the impeller inlet radius without considering the leakage effect, in meters; m is the empirical coefficient, ranging from 0.055 to 0.08, where the larger value is taken for a larger specific speed; V u1ii The circumferential component of the absolute velocity at the impeller inlet to take into account the interstage leakage effect, in meters per second; V u2ii The circumferential component of the absolute velocity at the impeller outlet to take into account the interstage leakage effect, in meters per second; g is the acceleration due to gravity, measured in square meters per second.

5. A method for improving the hydraulic performance of a multi-stage centrifugal pump according to claim 4, characterized in that: In step 4), the impeller theoretical head difference ΔH considering the interstage leakage effect is T =H Ti -H Tii , reversely calculate the upper limit b of the optimized impeller outlet width 2ii The calculation process: Simplifying, we get: Combined with V m2i The upper limit b of the impeller outlet width after optimization can be calculated. 2ii : Where: ψ 2ii The impeller blade outlet crowding coefficient is taken as 0.8 to 0.9 to consider the inter-stage leakage effect.

6. A method for improving the hydraulic performance of a multi-stage centrifugal pump according to claim 1, characterized in that: In step 5), the adjusted impeller outlet width is set to b 2n , n is the number of times the impeller outlet width is adjusted, when n=1, then b 2n =(b 2i +b 2ii ) / 2, when n>1, then b 2n =(b 2i +b 2(n-1) ) / 2.

7. The method for improving the hydraulic performance of a multi-stage centrifugal pump according to claim 1 is characterized by: In step 7), performance verification is performed using CFD software.

8. A multi-stage centrifugal pump prepared by using the method for improving the hydraulic performance of a multi-stage centrifugal pump as described in any one of claims 1 to 7.

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