Design method for widening high-efficiency area of small-flow low-specific-speed multistage pump

Abstract

The invention belongs to the field of fluid machinery design, and particularly relates to a design method for widening an efficient area of a small-flow low-specific-speed multistage pump, which comprises the following steps of: S1, determining a flow amplification coefficient Kq, a specific-speed amplification coefficient Kns and a reference lift ratio Rb; s2, calculating a lift correction factor Fs based on the specific speed amplification coefficient Kns; s3, calculating a dynamic lift ratio R based on the lift correction factor Fs; s4, calculating a volute section design lift Hvo and a guide vane section design lift Hva based on the dynamic lift ratio R; s5, the design flow Qv of the guide vane section is calculated based on the rated flow Qr; and S6, designing a guide vane and a guide vane section impeller by taking the guide vane section design flow Qv and the guide vane section design lift Hva as basic parameters. The core contradiction of the design of the low-specific-speed multistage pump is solved, the efficiency of a rated point is guaranteed, meanwhile, the efficient area of the low-specific-speed multistage pump is widened, the working range of the multistage pump is widened, and the working stability of the multistage pump in a small-flow area is guaranteed.

Description

Technical Field

[0001] This invention belongs to the field of fluid machinery design, and in particular, it is a design method for expanding the high-efficiency range of multi-stage pumps with small flow rates and low specific speeds. Background Technology

[0002] With the rapid development of industry, low-flow-rate, low-specific-speed multistage pumps are core equipment in key areas such as mine emergency drainage systems, urban water supply networks, and chemical process transportation. They are often designed with low flow rate and high head characteristics to meet the needs of long-distance, low-velocity liquid transportation. However, traditional low-specific-speed multistage pumps have revealed three main technical bottlenecks in long-term engineering applications:

[0003] 1) Narrow high-efficiency zone, energy consumption out of control under varying operating conditions: The high-efficiency zone of traditional designs only covers ±30% of the rated flow. When the pumping station exceeds this range due to changes in operating conditions (such as peak / valley water supply, fluctuations in mine water inflow), the efficiency drops sharply. Taking a town water supply pumping station as an example, the efficiency decreases by more than 20% under varying operating conditions, resulting in an increase of 15%-20% in annual power consumption.

[0004] 2) Instability in the low-flow-rate range, leading to decreased reliability and lifespan: Currently, the mainstream design method for low-specific-speed multistage pumps is to increase the flow rate to improve their rated performance. However, this approach does not address the unique characteristics of low-specific-speed multistage pumps, such as large interstage losses and high energy buffering requirements at low flow rates. Due to the inherently steep head-flow curve of low-specific-speed pumps, increasing the flow rate often results in unstable flow conditions such as interstage vortices and backflow within the pump at low flow rates, causing a sharp drop in efficiency. In mine drainage scenarios, under low-flow conditions (e.g., 50% of rated flow), flow instability and significantly increased pressure pulsation occur, leading to excessive pump vibration (vibration velocity ≥7.1 mm / s, far exceeding the API 610 standard limit). This not only shortens the lifespan of vulnerable components such as mechanical seals and bearings but also poses safety risks due to unplanned shutdowns.

[0005] 3) Fluctuations in rated point efficiency, unrealized energy-saving potential: The traditional method of unifying the design parameters of guide vanes and volutes in low specific speed multistage pumps is limited by interstage losses and structural constraints, resulting in large fluctuations in rated point efficiency. Meanwhile, the discharge section volute of low specific speed pumps requires a large throat area to suppress vortices. However, conventional design methods often result in a smaller throat area, ultimately leading to generally low energy efficiency for low specific speed pumps. This fails to meet the assessment requirement of "pump group energy efficiency level ≥ 1" for key energy-consuming units, making energy-saving technological upgrades urgently needed.

[0006] Traditional multistage pump high-efficiency range expansion technologies often focus on optimizing a single aspect, making it difficult to simultaneously meet the requirements of "wide high-efficiency range, stable low flow rate, and optimal rated point." With the increasing number of application scenarios and industry demands, conventional design methods are ill-suited to the technical requirements of "multi-stage coordination and variable operating conditions" for low specific speed multistage centrifugal pumps. Ensuring rated point energy efficiency while expanding the high-efficiency range of low specific speed multistage pumps has become a key focus for the industry. Summary of the Invention

[0007] To overcome the shortcomings of the prior art, this invention proposes a design method for expanding the high-efficiency range of a low-flow-rate, low-specific-speed multistage pump. Through differentiated design of the guide vane section and volute section, the rated efficiency of the low-specific-speed multistage pump is maintained while expanding the high-efficiency range. The technical problem to be solved by this invention is achieved through the following technical solution:

[0008] A design method for expanding the high-efficiency range of a low-flow-rate, low-specific-speed multistage pump includes the following steps:

[0009] S1: Determine the flow amplification factor K based on the rated flow rate Qr using the first value selection rule. q According to the original design, the specific speed n of the pump section s The value of the specific speed amplification factor K is determined by the second value selection rule. ns The reference head ratio R is determined by the third value selection rule. b ;

[0010] S2: Based on the specific speed amplification factor K ns Calculate the head correction factor F s Head correction factor F s The calculation method is as follows:

[0011] F s =1+0.01×(K) ns -1.3);

[0012] S3: Based on head correction factor F s The dynamic head ratio R is calculated as follows:

[0013] R = R b ×F s ;

[0014] S4: Calculate the design head H of the volute section based on the dynamic head ratio R. vo and the guide vane section design head H va The design head of the volute section is H. vo The calculation method is as follows:

[0015]

[0016] Where H is the total design head;

[0017] N1 is the guide vane stage number;

[0018] N2 is the volute series;

[0019] Guide vane section design head H va The calculation method is as follows:

[0020] H va =H vo ×R;

[0021] S5: Based on rated flow rate Q r Calculate the design flow rate Q of the guide vane section v The design flow rate Q of the guide vane section v The calculation method is as follows:

[0022] Q v =Q r ×K q ;

[0023] S6: Flow rate Q is designed based on the guide vane section. v Guide vane section design head H va Design the guide vanes and guide vane section impeller based on the basic parameters;

[0024] S7: Based on the original design pump section specific speed n s Calculate the throat area correction factor K a throat area correction factor K a The calculation method is as follows:

[0025] When n s <30:K a =1.1 - 0.001 × (30 - n) s );

[0026] When 30≤n s <50:K a =1.1 - 0.001 × (n s -30);

[0027] When 50≤n s <80:K a =1.025;

[0028] S8: Based on the throat area correction factor K a Calculate the corrected throat area A vo Correct the throat area A vo The calculation method is as follows:

[0029] A vo =A v ×K a ;

[0030] Among them, A v The throat area of ​​the volute segment is calculated using the velocity coefficient method or analytical method.

[0031] S9: At rated flow rate Q r 1. Design head H of the volute section vo and corrected throat area A vo Based on the basic parameters, design the volute and the corresponding impeller.

[0032] Furthermore, the first value selection rule is based on existing empirical parameters and combined with the principles of vortex suppression and flow buffering in small flow pumps, at the rated flow rate Q. r =3-30m 3 Within the range of / h, the data was finally obtained after combining empirical coefficients, statistical analysis of CFD calculations for multiple low specific speed pump types, and a large number of experimental results.

[0033] Furthermore, the second value selection rule, based on the design method of low specific speed pump outlet separation control, is based on the original design pump section specific speed n. s The data is derived from CFD calculations of multiple impeller design cases within the range of 23-80, and through extensive comparative experiments.

[0034] Furthermore, the third value selection rule is based on the fundamental principle of head loss when pumps are connected in series, and a large amount of statistical data was obtained from the pressure loss when multiple groups of pumps with different low specific speeds are connected in series.

[0035] Specifically, the original design pump section specific speed n s The calculation method is as follows:

[0036]

[0037] Where Qr is the rated flow rate;

[0038] n is the rated speed;

[0039] H r The calculation method for the design head of the original single-stage pump section is as follows:

[0040]

[0041] Where H is the total design head;

[0042] N1 is the guide vane stage number;

[0043] N2 is the volute series.

[0044] Specifically, the guide vane and guide vane section impeller are designed, including the throat height, inlet angle, diffusion angle, inlet width and outlet height of the guide vane, and the inlet angle, outlet angle, outlet width and outlet diameter of the guide vane section impeller.

[0045] Specifically, the design of the volute and the corresponding impeller includes the throat area of ​​the volute, the inlet angle, outlet angle, outlet width, and outlet diameter of the impeller in the volute section.

[0046] The beneficial effects of this invention are as follows:

[0047] 1. This invention solves the core contradiction in the design of low specific speed multistage pumps, namely, the inability to simultaneously satisfy rated point efficiency, low flow rate stability, and high-efficiency range. While ensuring rated point efficiency, this invention broadens the high-efficiency range of low specific speed multistage pumps, increases the operating range of the multistage pump, and guarantees the operational stability of the multistage pump in the low flow rate region.

[0048] 2. This invention introduces a dynamic head ratio R (R = H) va / H vo By quantifying the head distribution between the volute and the guide vanes, both high efficiency at the guide vane's rated point and high performance through H vo Controlling the design pressure of the volute casing avoids performance degradation caused by excessive differences between the two, creating space for adjusting the throat area. This overcomes the problems of low specific speed multistage pumps often being designed for high flow rates, which leads to increased vortex intensification and losses in the guide vane section at low flow rates; and the problems of controlling the throat area of ​​the volute casing to stabilize performance in low flow rates, which can cause excessive suppression of the guide vane rating point by the resistance of the volute casing section, resulting in efficiency losses.

[0049] 3. This invention establishes a calculation method for the piecewise mapping of the specific speed-throat area correction coefficient. By statistically analyzing multiple sets of low specific speed impeller-volute combination design results, the piecewise values ​​of the throat area correction coefficient are determined, achieving precise matching of "throat area-vortex suppression" at low specific speeds. This overcomes the problems of traditional empirical formulas failing to adapt the throat area of ​​low specific speed pumps to multiple specific speed scenarios, and the design results often being too small, leading to a sudden increase in pressure pulsation in the low flow rate region. Conversely, excessive adjustment of the throat area results in excessive efficiency loss in the low flow rate region.

[0050] 4. The design methods of the guide vane section and the volute section of the present invention are different. The guide vane section is designed with increased flow rate to be responsible for high-efficiency conversion at the rated point, while the volute section is designed with rated flow rate to ensure stability in the low flow rate range. This provides a valuable reference for the design of volute-guide vane at different specific speeds.

[0051] 5. The design method of this invention covers small flow rates (3m³ / h). 3 / h-30m 3 Low specific speed range (20-80) / h. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of the axial projection of the guide vane section and the volute section according to an embodiment of the present invention;

[0053] Figure 2 A schematic diagram of the axial projection of the guide vane section and volute section in the prior art;

[0054] Figure 3 This is a schematic diagram of the guide vane section of the present invention;

[0055] Figure 4 This is a schematic diagram of the volute segment of the present invention;

[0056] Figure 5 The graph shows a comparison of the performance curves of the three design methods.

[0057] Explanation of reference numerals in the attached figures:

[0058] 1-Guide vane, 2-Guide vane section impeller, 3-Volume, 4-Volume section impeller, I-Increased flow rate design method, II-Design method of the present invention, III-Rated flow rate design method. Detailed Implementation

[0059] A design method for expanding the high-efficiency range of a low-flow-rate, low-specific-speed multistage pump includes the following steps:

[0060] S1: Determine the flow amplification factor K based on the rated flow rate Qr using the first value selection rule. q According to the original design, the specific speed n of the pump section s The value of the specific speed amplification factor K is determined by the second value selection rule. ns The reference head ratio R is determined by the third value selection rule. b .

[0061] S2: Based on the specific speed amplification factor K ns Calculate the head correction factor F s Head correction factor F s The calculation method is as follows:

[0062] F s =1+0.01×(K) ns -1.3).

[0063] S3: Based on head correction factor F s The dynamic head ratio R is calculated as follows:

[0064] R = R b ×F s .

[0065] This invention introduces a dynamic head ratio R (R = H) va / H vo By quantifying the head distribution between the volute and the guide vanes, both high efficiency at the guide vane's rated point and high performance through H voControlling the design pressure of the volute casing avoids performance degradation caused by excessive differences between the two, creating space for adjusting the throat area. This overcomes the problems of low specific speed multistage pumps often being designed for high flow rates, which leads to increased vortex intensification and losses in the guide vane section at low flow rates; and the problems of controlling the throat area of ​​the volute casing to stabilize performance in low flow rates, which can cause excessive suppression of the guide vane rating point by the resistance of the volute casing section, resulting in efficiency losses.

[0066] S4: Calculate the design head H of the volute section based on the dynamic head ratio R. vo and the guide vane section design head H va The design head of the volute section is H. vo The calculation method is as follows:

[0067]

[0068] Where H is the total design head;

[0069] N1 is the guide vane stage number;

[0070] N2 is the volute series;

[0071] Guide vane section design head H va The calculation method is as follows:

[0072] H va =H vo ×R.

[0073] S5: Based on rated flow rate Q r Calculate the design flow rate Q of the guide vane section v The design flow rate Q of the guide vane section v The calculation method is as follows:

[0074] Q v =Q r ×K q .

[0075] S6: Flow rate Q is designed based on the guide vane section. v Guide vane section design head H va Based on the basic parameters, design the guide vanes and the impeller section of the guide vanes.

[0076] S7: Based on the original design pump section specific speed n s Calculate the throat area correction factor K a throat area correction factor K a The calculation method is as follows:

[0077] When n s <30:K a =1.1 - 0.001 × (30 - n) s );

[0078] When 30≤n s<50:K a =1.1 - 0.001 × (n s -30);

[0079] When 50≤n s <80:K a =1.025.

[0080] This invention establishes a calculation method for the piecewise mapping of the specific speed-throat area correction coefficient. By statistically analyzing multiple sets of low specific speed impeller-volute combination design results, the piecewise values ​​of the throat area correction coefficient are determined, achieving precise matching of "throat area-vortex suppression" at low specific speeds. This overcomes the problems of traditional empirical formulas for designing the throat area of ​​low specific speed pumps, which cannot adapt to multiple specific speed scenarios, and the design results are mostly too small, leading to a sudden increase in pressure pulsation in the low flow rate region. On the other hand, excessive adjustment of the throat area results in excessive efficiency loss in the low flow rate region.

[0081] S8: Based on the throat area correction factor K a Calculate the corrected throat area A vo Correct the throat area A vo The calculation method is as follows:

[0082] A vo =A v ×K a ;

[0083] Among them, A v The throat area of ​​the volute segment is calculated using the velocity coefficient method or analytical method.

[0084] S9: At rated flow rate Q r 1. Design head H of the volute section vo and corrected throat area A vo Based on the basic parameters, design the volute and the corresponding impeller.

[0085] The design method of this invention covers small flow rates (3m). 3 / h-30m 3 The design parameters of low specific speed multistage pumps can be quickly determined within the low specific speed (20-80) range.

[0086] The first value selection rule of this invention is based on existing empirical parameters and combines the principles of vortex suppression and flow buffering of small flow pumps, at the rated flow rate Q. r =3-30m 3 Within the range of / h, the data obtained after combining empirical coefficients and statistically analyzing CFD calculations and numerous experimental results of multiple low specific speed pump types is presented in tabular form in this embodiment. See Table 1 for details.

[0087] Table 1

[0088]

[0089] It should be noted that the existing empirical parameters and coefficients mentioned in the first value selection rule are flow amplification reference coefficients obtained by fitting multiple excellent low specific speed hydraulic models before 1997, as compiled in "Theory and Design of Low Specific Speed ​​Centrifugal Pumps" (Yuan Shouqi. Theory and Design of Low Specific Speed ​​Centrifugal Pumps [M]. Machinery Industry Press, 1997.). This is combined with newly developed and optimized models from the past 10 years that have been widely used in the industry, with flow rates ranging from 4-40 m³ / h. 3 The results of CFD calculations and experiments on 40 excellent low-flow-rate and low-specific-speed hydraulic models were obtained by second-order fitting correction.

[0090] The second value selection rule is based on the design method of low specific speed pump outlet separation control, where the specific speed n of the original designed pump section is... s Within the range of 23-80, the data obtained from CFD calculations of multiple impeller design cases and extensive comparative experiments are presented in tabular form in this embodiment. See Table 2 for details.

[0091] Table 2

[0092]

[0093] To avoid the risk of head loss caused by excessive head distribution differences, the third value rule is based on the basic principle of head loss when pumps are connected in series. A large amount of statistical data was obtained from the pressure loss of multiple groups of pumps with different low specific speeds when they are connected in series. The data in this embodiment is presented in tabular form, see Table 3 for details.

[0094] Table 3

[0095]

[0096] Original design pump section specific speed n s The calculation method is as follows:

[0097]

[0098] Where Qr is the rated flow rate;

[0099] n is the rated speed;

[0100] H r The calculation method for the design head of the original single-stage pump section is as follows:

[0101]

[0102] Where H is the total design head;

[0103] N1 is the guide vane stage number;

[0104] N2 is the volute series.

[0105] Design the guide vanes and guide vane section impeller, including the throat height, inlet angle, diffusion angle, inlet width and outlet height of the guide vanes, and the inlet angle, outlet angle, outlet width and outlet diameter of the guide vane section impeller.

[0106] Design the volute and corresponding impeller, including the throat area of ​​the volute, the inlet angle, outlet angle, outlet width, and outlet diameter of the impeller section in the volute.

[0107] The guide vanes and volutes can be designed using existing theoretical formulas, such as those in "Modern Pump Theory and Design". However, by using the values ​​derived from this invention as basic parameters, we can design dimensions that differ from those obtained by ordinary design methods, and the hydraulic performance will also be different.

[0108] Centrifugal pumps have many design parameters. This invention only lists the parts that have a significant impact on hydraulic performance. All of the listed parts need to be designed in order to achieve the beneficial effects of this invention. If the pump design is completed by designing only a few parts of the guide vane or a few parts of the volute, the beneficial effects of this invention will not be achieved.

[0109] The following practical example illustrates the design method of this invention.

[0110] Rated flow rate Q r =6m 3 / h, total head H = 234m, single-stage head H r =19.5m, rotational speed n=2950rpm, guide vane stage N1=10, volute stage N2=2.

[0111] Calculate the specific speed n of the original design pump section s :

[0112]

[0113] The original design stipulated that both the volute section and the guide vane section were designed for the same flow rate and the same head, i.e., a total of 12 pump stages, with an average head of 234m, and each stage designed for a flow rate of 6m³ / h. 3 / h, the single-stage head is designed to be 234 / 12=19.5m.

[0114] S1: Determine the flow amplification factor K by referring to Table 1. q =1.69;

[0115] Determine the specific speed amplification factor K from Table 2. a s = 1.28;

[0116] Determine the reference head ratio R from Table 3. b =1.1.

[0117] S2: Based on the specific speed amplification factor K nsCalculate the head correction factor F s :

[0118] F s =1+0.01×(K) ns -1.3)=1+0.01×(1.28-1.3)=0.9998.

[0119] S3: Based on head correction factor F s Calculate the dynamic head ratio R:

[0120] R = R b ×F s =1.09978.

[0121] S4: Calculate the design head H of the volute section based on the dynamic head ratio R. vo Guide vane section design head H va :

[0122]

[0123] H va =H vo ×R=18×1.09978≈19.8m.

[0124] S5: Based on rated flow rate Q r Calculate the design flow rate Q of the guide vane section v :

[0125] Q v =Q r ×K q =6 × 1.69 = 10.14m 3 / h.

[0126] S6: Flow rate Q is designed based on the guide vane section. v Guide vane section design head H va Based on the basic parameters, design the guide vanes and the impeller section of the guide vanes.

[0127] Pump performance is affected by a variety of parameters, not just one. Most parameters are designed based on the two fundamental parameters of flow rate and head, thus yielding Q. v =10.14 and H va After the value is 19.8, all design parameters that require reference flow rate or head must be considered based on these two values.

[0128] Based on "Modern Pump Flow and Design", the following design is performed:

[0129] 1. Guide vane section impeller outer diameter D2:

[0130]

[0131] Where, kD2 This is a correction factor;

[0132] n s1 For Q v and H va Specific speed of the lower guide vane section;

[0133] The calculated impeller outer diameter D2 is 125.1 mm. It can be rounded up or finely adjusted according to the structure. After fine adjustment, D2 is 128 mm.

[0134] 2. Impeller outlet width b2:

[0135]

[0136] Where, k b2 This is a correction factor;

[0137] The calculated impeller outlet width b2 is 5.79 mm, which is rounded down to 6 mm.

[0138] 3. Impeller inlet angle β1:

[0139] Theoretically calculate the axial surface velocity at the inlet edge of each streamline, and calculate the flow angle according to the formula:

[0140] ;

[0142] Among them, v m1i and u 1i These are the axial velocity and circumferential velocity of the inlet edge of the i-th streamline, respectively;

[0143] After calculating the flow angle, add the angle of attack (3°-15°) to obtain the inlet angle at the starting point of each streamline on the inlet side. It is worth mentioning that, since the flow rate and head of the guide vane section are increased, in order to reduce inlet impact and avoid excessive deviation of the high-efficiency zone, the inlet angle of attack can be selected as a small value (0°-11°).

[0144] The impeller inlet angle β1 is found to be 18°.

[0145] 4. The commonly used blade exit angle β2 ranges from 16° to 30°.

[0146] The following factors should be considered when selecting β2: For low specific speed pumps, selecting a larger β2 angle to increase the head can reduce D2, thereby reducing disc friction losses and improving pump efficiency. However, increasing the β2 angle reduces the hydraulic efficiency in the pressure chamber at the same flow rate and causes impact losses in the pump volute flow channel at low flow rates. To obtain a good pump characteristic curve and pump performance, an excessively large β2 angle should not be selected. It is worth mentioning that, since this example uses an increased flow rate method to design the guide vane section impeller, the outlet width b2 is increased compared to the normal design, resulting in an increased head. Therefore, a smaller value can be selected to stabilize the outlet liquid flow.

[0147] The guide vane section pump is a low specific speed pump, and the blade outlet angle β2 is calculated to be 18°.

[0148] 5. Guide vane inlet width b3:

[0149] b3 = b2 + (2 ~ 5);

[0150] The inlet width of the guide vane is calculated to be b3 = 10 mm.

[0151] 6. Guide vane inlet angle α3:

[0152] tanα3=(1.1~1.3)tanα′2;

[0153]

[0154] Among them, v m The axial velocity at the impeller outlet;

[0155] v u2 The circumferential velocity component at the impeller outlet;

[0156] The inlet angle of the guide vane was calculated to be α3 = 7°.

[0157] 7. Guide vane throat height a3:

[0158]

[0159] Where z is the number of guide vane blades, in this example z = 4;

[0160] V3 is the throat velocity; in this example, V3 = 9.3 m / s.

[0161] b3 is the guide vane inlet width;

[0162] The calculated throat height of the guide vane is a3 = 7.57 mm, which is rounded down to 7.6 mm.

[0163] 8. Guide vane outlet height a4:

[0164]

[0165] Where V4 is the exit velocity, in this example V4 = 4.65 m / s;

[0166] The calculated guide vane exit height a4 is 12.3 mm, which is rounded down to 12 mm.

[0167] 9. Guide vane diffusion angle:

[0168]

[0169] Where F3 = 76mm2 F4 = 180mm 2 ;

[0170] The guide vane performance is controlled by the exit height and throat height. Once these two are determined, the diffusion angle can only be calculated after drawing the diffusion section length. In this example, after drawing the guide vane, the diffusion section length L = 30.1 mm was measured, and the calculated diffusion angle is 10.1°.

[0171] S7: 30≤n s <50:K a =1.1 - 0.001 × (n s -30);

[0172] Obtain the throat area correction factor K a =1.0826.

[0173] S8: Calculate the corrected throat area A vo :

[0174] A vo =A v ×K a =184.8 × 1.0826 = 200.06 mm 2 .

[0175] It should be noted that taking a slightly larger value for the throat area of ​​the volute is not harmful. Therefore, the corrected throat area can be fine-tuned or rounded as needed. In this example, the corrected throat area A is... vo =200mm 2 .

[0176] S9: At rated flow rate Q r 1. Design head H of the volute section vo and corrected throat area A vo Based on the basic parameters, design the volute and the corresponding impeller.

[0177] Based on "Modern Pump Theory and Design", the following design was created:

[0178] 1. Outer diameter D2 of the volute section impeller:

[0179]

[0180] Where, k D2 This is a correction factor;

[0181] n s2 For Q r and H vo Specific speed of the lower volute section;

[0182] The calculated outer diameter of the impeller in the volute section is D2 = 118.8 mm, which is rounded down to D2 = 120 mm.

[0183] 2. Impeller outlet width b2 in the volute section:

[0184]

[0185] Where kb2 is the correction factor;

[0186] The calculated impeller outlet width of the volute section is b2 = 4.1 mm, which is rounded down to 5 mm.

[0187] 3. Inlet angle β1 of the volute section impeller:

[0188] Theoretically calculate the axial surface velocity at the inlet edge of each streamline, and calculate the flow angle according to the formula:

[0189]

[0190] Among them, v m1i Let be the axial velocity of the inlet side of the i-th streamline of the impeller in the volute section;

[0191] u 1i Let be the circumferential velocity of the inlet edge of the i-th streamline of the impeller in the volute section;

[0192] After calculating the flow angle, add the angle of attack (3°-15°) to obtain the inlet angle at the starting point of each streamline on the inlet side. It is worth mentioning that, since the flow rate and head of the guide vane section are increased, in order to reduce inlet impact and avoid excessive deviation of the high-efficiency zone, the inlet angle of attack can be selected as a small value (0°-11°).

[0193] The impeller inlet angle β1 of the volute section is found to be 20°.

[0194] 4. The volute section impeller is a low specific speed impeller, and the blade exit angle β2 is calculated to be 19°.

[0195] The final axial projections of the guide vane section and volute section are shown in the figure. Figure 1 As shown, the design methods of the guide vane section and the volute section of the present invention are different. The guide vane section utilizes an increased flow rate design to be responsible for high-efficiency conversion at the rated point, while the volute section utilizes a rated flow rate design to ensure stability in the low flow rate range.

[0196] Multistage pumps consist of guide vane sections and volute sections. Generally, the flow sequence within the pump is: suction - impeller - guide vane - impeller - volute - discharge. Current designs employ a single design method for the entire pump section (volute and guide vane sections), either using the rated flow rate method or the increased flow rate method. See [reference needed]. Figure 2 As shown, Figure 2 This is a schematic diagram of the axial projection of the guide vane section and the volute section obtained using a single design method.

[0197] Compared with the prior art, the two seem to have little difference in overall shape, but their dimensions are completely different, which leads to different effects on pump performance. The former, namely the present invention, has achieved unexpected results: while ensuring the rated point efficiency, it has broadened the high-efficiency range of the low specific speed multistage pump, increased the working range of the multistage pump, and ensured the working stability of the multistage pump in the low flow range.

[0198] Combination Figures 3 to 5 As shown in the figure, I represents the increased flow design method, II represents the design method of the present invention, and III represents the rated flow design method. I and III are existing design methods.

[0199] from Figure 3 As can be seen, compared with the rated flow design method, the present invention widens the flow channel in the guide vane section, which has a stronger fluid medium passing capacity and improves the efficiency at the rated point.

[0200] from Figure 4 As can be seen, compared with the rated flow design method, the present invention, after throat area correction, widens the throat width in the volute section, making the fluid medium flow more stable, thereby ensuring the efficiency in the small flow range.

[0201] from Figure 5 As can be seen, the performance curve of the low specific speed multistage pump (guide vane section + volute section working together) designed using the increased flow rate design method is cfi. It can be seen that if both the guide vane section and the volute section are designed using the increased flow rate method, although the rated point f meets the energy-saving evaluation value requirements, its high-efficiency zone has a small coverage area on the low flow rate side, and the efficiency drops rapidly, resulting in a relatively severe bias towards certain operating conditions, which is not conducive to operation under multiple operating conditions.

[0202] The performance curve of the low specific speed multistage pump designed using the rated flow design method is denoted as adg. It can be seen that although the high-efficiency region is wider on the low flow side, the rated point d does not meet the energy-saving evaluation value requirements.

[0203] The performance curve of the low specific speed multistage pump designed using this invention is beh. It can be seen that the high-efficiency range of the whole machine covers a wider range on the low flow side. The main reason is that the volute stage is designed according to the rated flow, and after the dynamic head ratio is adjusted, the specific speed of the volute stage is higher. It is easier to achieve the purpose of widening the high-efficiency range in the design, so the operation is more stable.

[0204] Meanwhile, the rated point e met the rated energy efficiency requirements, mainly because the design of the guide vane section improved the overall energy efficiency of the machine at the rated point.

[0205] It should be noted that the head of the guide vane section designed in this invention is slightly higher than that of the volute section, which may cause local head loss. To this end, it is possible to reduce the loss by optimizing the hydraulic structure of the guide vane blades. For example, by optimizing the outlet angle of the guide vane blades or using three-dimensional twisted blades, the additional head loss can be controlled within 6%, and the overall performance is still better than that of the traditional design.

[0206] In the GB19762-2025 centrifugal pump energy efficiency standard requirements, the rated flow rate Q r =6m 3 / h, total head H = 234m, single-stage head H r Under the design parameters of 19.5m, n=2950rpm, N1=10 guide vane stages, and N2=2 volute stages, the secondary energy efficiency requirement for a multistage clean water centrifugal pump is 47.15%.

[0207] Numerical calculations were performed on the multistage centrifugal pumps designed using the three different design methods. The results are shown in Table 4. Efficiency I represents the efficiency of the increased flow design method, efficiency II represents the efficiency of the present invention, and efficiency III represents the efficiency of the rated flow design method.

[0208] Table 4

[0209]

[0210] As shown in Table 4, within the range of 0.6Q to 0.9Q, efficiency II is higher than efficiency I, meaning that this invention ensures higher efficiency in the low-flow-rate range. In the low-flow-rate region (the area less than 1.0Q), if 90% of the level 2 energy efficiency is taken as the limit value for the high-efficiency region (approximately 42.4%), it can be estimated by interpolation that the high-efficiency region for efficiency I is approximately after 0.84Q, and the high-efficiency region for efficiency II is approximately after 0.81Q, meaning that this invention broadens the high-efficiency region.

[0211] At the rated point (i.e., at 1.0Q), efficiency III is 46.8%, which does not meet the level 2 energy efficiency requirement; efficiency II is 47.55%, which meets the level 2 energy efficiency requirement, meaning that this invention can meet the needs of most users; efficiency I is 48.32%, which is higher, but considering the low flow range, from 1.0Q to 0.8Q, efficiency I decreases by 15.3%, while efficiency II only decreases by 11.4%. Therefore, this invention is more effective.

[0212] In summary, this invention solves the core contradiction in the design of low specific speed multistage pumps, namely, the inability to simultaneously satisfy rated point efficiency, low flow rate stability, and a wide high-efficiency range. While ensuring rated point efficiency, this invention broadens the high-efficiency range of low specific speed multistage pumps, increases the operating range of multistage pumps, and guarantees the operational stability of multistage pumps in the low flow rate region.

Claims

1. A design method for expanding the high-efficiency range of a multistage pump with low flow rate and low specific speed, characterized in that, Includes the following steps: S1: Based on rated flow rate Q r The value of K is determined by the first value selection rule to determine the flow amplification factor K. q According to the original design, the specific speed n of the pump section s The value of the specific speed amplification factor K is determined by the second value selection rule. ns The reference head ratio R is determined by the third value selection rule. b ; S2: Based on the specific speed amplification factor K ns Calculate the head correction factor F s The head correction factor F s The calculation method is as follows: F s =1+0.01×(K ns -1.3); S3: Based on head correction factor F s The dynamic head ratio R is calculated as follows: R=R b ×F s ; S4: Calculate the design head H of the volute section based on the dynamic head ratio R. vo and the guide vane section design head H va The volute section is designed to have a head H. vo The calculation method is as follows: Where H is the total design head; N1 is the guide vane stage number; N2 is the volute series; The guide vane section is designed to have a head H. va The calculation method is as follows: H va =H vo ×R; S5: Based on rated flow rate Q r Calculate the design flow rate Q of the guide vane section v The design flow rate Q of the guide vane section v The calculation method is as follows: Q v =Q r ×K q ; S6: Flow rate Q is designed based on the guide vane section. v Guide vane section design head H va Design the guide vanes and guide vane section impeller based on the basic parameters; S7: Based on the original design pump section specific speed n s Calculate the throat area correction factor K a The throat area correction coefficient K a The calculation method is as follows: When n s <30:K a =1.1 - 0.001 × (30 - n) s ); When 30≤n s <50:K a =1.1 - 0.001 × (n s -30); When 50≤n s <80:K a =1.025; S8: Based on the throat area correction factor K a Calculate the corrected throat area A vo The corrected throat area A vo The calculation method is as follows: A vo =A v ×K a ; Among them, A v The throat area of ​​the volute segment is calculated using the velocity coefficient method or analytical method. S9: At rated flow rate Q r 1. Design head H of the volute section vo and corrected throat area A vo Based on the basic parameters, design the volute and the corresponding impeller.

2. The design method for widening the high-efficiency range of a low-flow-rate, low-specific-speed multistage pump according to claim 1, characterized in that, The first value selection rule is based on existing empirical parameters and combined with the principles of vortex suppression and flow buffering of small flow pumps, at the rated flow rate Q r =3-30m 3 Within the range of / h, the data was finally obtained after combining empirical coefficients, statistical analysis of CFD calculations for multiple low specific speed pump types, and a large number of experimental results.

3. The design method for widening the high-efficiency range of a multi-stage pump with low flow rate and low specific speed according to claim 1, characterized in that, The second value selection rule is based on the design method of low specific speed pump outlet separation control, where the specific speed n of the original designed pump section is... s The data is derived from CFD calculations of multiple impeller design cases within the range of 23-80, and through extensive comparative experiments.

4. The design method for widening the high-efficiency range of a low-flow-rate, low-specific-speed multistage pump according to claim 1, characterized in that, The third value selection rule is based on the fundamental principle of head loss when pumps are connected in series, and is derived from a large amount of statistical data on pressure loss when multiple groups of pumps with different low specific speeds are connected in series.

5. The design method for widening the high-efficiency range of a low-flow-rate, low-specific-speed multistage pump according to claim 1, characterized in that, The original design pump section specific speed n s The calculation method is as follows: Among them, Q r Rated flow rate; n is the rated speed; H r The calculation method for the design head of the original single-stage pump section is as follows: Where H is the total design head; N1 is the guide vane stage number; N2 is the volute series.

6. The design method for widening the high-efficiency range of a low-flow-rate, low-specific-speed multistage pump according to claim 1, characterized in that, The design of the guide vane and guide vane section impeller includes the throat height, inlet angle, diffusion angle, inlet width and outlet height of the guide vane, and the inlet angle, outlet angle, outlet width and outlet diameter of the guide vane section impeller.

7. The design method for widening the high-efficiency range of a low-flow-rate, low-specific-speed multistage pump according to claim 1, characterized in that, The design of the volute and corresponding impeller includes the throat area of ​​the volute, the inlet angle, outlet angle, outlet width, and outlet diameter of the impeller section of the volute.

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