Method for efficiency optimization of two-stage centrifugal pump based on power distribution

Abstract

The present application relates to a kind of two-stage centrifugal pump efficiency optimization methods based on power distribution, including the minimum head distribution value of first-stage impeller according to the operating condition design parameter of two-stage centrifugal pump, the steps of calculating, using three-dimensional modeling software, the steps of establishing at least two three-dimensional models of two-stage impeller under different head ratio when the head distribution value of first-stage impeller is from 50% to the minimum head, using fluid calculation software to carry out numerical simulation of model, the steps of calculating the whole pump efficiency of each three-dimensional model and fitting each whole pump efficiency point corresponding to different distribution head of first-stage impeller in each three-dimensional model, obtain the graph to obtain the head corresponding, that is, obtain the optimal first-stage impeller outer diameter, and then realize the improvement of two-stage centrifugal pump efficiency.

Description

Technical Field

[0001] This invention relates to the field of efficiency optimization of two-stage centrifugal pumps. Background Technology

[0002] A centrifugal pump is a machine that converts the mechanical energy of a prime mover into the energy of a liquid, thereby increasing the potential energy, pressure energy, and kinetic energy of the liquid. The prime mover drives the impeller to rotate via the pump shaft, performing work on the liquid and increasing its energy.

[0003] When centrifugal pumps are required to achieve high head and high efficiency under low flow conditions, it is difficult to achieve the high efficiency design goal using a single-stage centrifugal pump design. Therefore, a multi-stage structure is needed. The existing two-stage centrifugal pump structure consists of two impellers connected in series via guide vanes.

[0004] Efficiency is one of the key performance indicators (KPIs) in centrifugal pump design, whether it's a single-stage or multi-stage pump. Currently, research on improving centrifugal pump efficiency mainly focuses on the structural optimization design of single-stage pumps. Furthermore, in two-stage centrifugal pumps, power losses at the guide vanes can lead to reduced efficiency. Conventional methods to reduce guide vane power loss also involve optimizing the guide vane structure, such as changing the number of blades, blade height, and wrap angle. While optimizing the pump's structure to improve efficiency is a feasible approach, it doesn't consider the power distribution between the two impeller stages from a system perspective to improve overall pump efficiency. When the power distribution between the first and second stage impellers is unreasonable, the power loss at the guide vanes cannot be reduced, making it difficult to achieve the high-efficiency design goal of a two-stage centrifugal pump. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a power allocation-based efficiency optimization method for a two-stage centrifugal pump that rationally distributes power between the first-stage and second-stage impellers, thereby reducing guide vane power loss and achieving the high-efficiency design goal of the two-stage centrifugal pump.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: a method for optimizing the efficiency of a two-stage centrifugal pump based on power distribution, comprising the following steps:

[0007] Based on the operating design parameters of the two-stage centrifugal pump, calculate the minimum head distribution value H of the first-stage impeller. min The operating condition design parameters include the given head, flow rate, rotational speed, and maximum allowable radial dimension.

[0008] Using 3D modeling software, the head distribution values ​​of the first-stage impeller were established from 50% to the minimum head H. min At that time, at least two three-dimensional models of the two-stage impeller under different head ratios;

[0009] Fluid calculation software is used to perform numerical simulation of the three-dimensional model to obtain the overall pump efficiency η of each three-dimensional model.

[0010] By fitting the overall pump efficiency points corresponding to different head distributions of the first-stage impeller in each three-dimensional model, the H1-η curve is obtained.

[0011] If the H1-η curve in the fitted H1-η curve graph shows a hump, then the head corresponding to the point of maximum efficiency is taken as the head H1 allocated to the first stage impeller.

[0012] If the H1-η curve in the fitted graph does not show a hump, then the minimum head distribution value H of the first-stage impeller is set to... min The head H1 is allocated to the first-stage impeller;

[0013] The head H1 corresponds to the optimal first-stage impeller outer diameter. This resulted in an improvement in the efficiency of the two-stage centrifugal pump.

[0014] Furthermore, the calculation of the minimum head distribution value H of the first-stage impeller... min The steps are as follows:

[0015] The maximum radial dimension D of the impeller allowed by the entire pump yx And based on the minimum head H of the first stage impeller min With the impeller's maximum permissible radial dimension D yx The relationship between flow rate Q and rotational speed n is expressed as (10), and the minimum head distribution value H of the first-stage impeller is calculated. min ,

[0016]

[0017] Among them, H 总 The total head distribution of the two-stage centrifugal pump impellers was determined; the minimum head distribution value H of the first-stage impeller was obtained. min .

[0018] Furthermore, the step of establishing at least two three-dimensional models of different two-stage impellers under different head ratios specifically includes:

[0019] 21) The total head H 总 The head distribution is evenly distributed between the two stages of the centrifugal pump, starting with the first stage impeller accounting for 50% of the total head. The head distribution is gradually reduced by 1% each time, until the minimum head distribution value H for the first stage impeller is reached. min ;

[0020] 22) Calculate the outer diameters of the first-stage impeller and the secondary impeller respectively when the head of the first-stage impeller decreases by 1% using formula (7):

[0021]

[0022] In the formula, D2 is the impeller outer diameter in meters (m), and Q is the flow rate of each impeller stage in a two-stage centrifugal pump in cubic meters per second (m³). 3 / s, n is the rotational speed of each impeller of the two-stage centrifugal pump, in r / min, H is H1 or H2, where H1 is the head allocated to the first-stage impeller and H2 is the head allocated to the second-stage impeller, both in m.

[0023] 23) Based on the calculation results of steps 21) and 22), establish a table of the outer diameter of the first or second stage impeller obtained by the head distribution calculation, and use three-dimensional modeling software to establish at least two three-dimensional models of the first stage impeller and the second stage impeller under different heads.

[0024] Furthermore, after obtaining the overall pump efficiency η of each three-dimensional model, a correspondence table is established between the overall pump efficiency η of each shown three-dimensional model and the head H1 of the first-stage impeller.

[0025] Furthermore, the H1-η curve is a curve obtained by using the first-stage impeller distribution head as the horizontal axis and the efficiency corresponding to the first-stage impeller distribution head as the vertical axis.

[0026] Furthermore, the 3D modeling software used is CAD, UG, or CFturbo, and the fluid calculation software used is Fluent or PumpLinx.

[0027] The beneficial effects of this invention are as follows: This invention provides a method for efficiency allocation and optimization of a two-stage centrifugal pump. This invention proposes that when designing a two-stage centrifugal pump, it is necessary to find the optimal outer diameter of the first-stage impeller that maximizes efficiency, thereby achieving power allocation, reducing power loss at the guide vanes of the two-stage centrifugal pump, and thus increasing the efficiency of the two-stage centrifugal pump. It also serves as a technical supplement to existing methods that increase overall pump efficiency by optimizing the guide vane structure. Attached Figure Description

[0028] Figure 1 This is a diagram illustrating the power distribution steps of the present invention;

[0029] Figure 2 The minimum head distribution value H in this invention min The diagram showing the values ​​of the head H1 distributed to the first-stage impeller when the efficiency is maximized to the left;

[0030] Figure 3 The minimum head distribution value H in this invention min A diagram showing the values ​​of the head H1 distributed to the first-stage impeller at the point of maximum efficiency;

[0031] Figure 4 This is a schematic diagram of the three-dimensional modeling structure of Scheme 1 of the present invention;

[0032] Figure 5 This is the H1-η curve in the calculation example of this invention. Detailed Implementation

[0033] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0034] Existing methods for reducing power loss in two-stage centrifugal pump guide vanes optimize the vane structure, but they do not consider the overall pump efficiency from a global perspective, taking into account the impact of power distribution between the first-stage and second-stage impellers. Therefore, this invention proposes a method for efficiency distribution and optimization in two-stage centrifugal pumps. In designing a two-stage centrifugal pump, the inventors discovered through calculations that reducing the outer diameter of the first-stage impeller and decreasing its head can reduce power loss in the guide vanes. The calculation process includes:

[0035] The power loss expression of the guide vane is shown in equation (1):

[0036] p v =γhq (1)

[0037] In the formula:

[0038] —Pressure drop across the guide vanes;

[0039] —Leakage on both sides of the guide vane;

[0040] The pressure drop across the guide vane is expressed as shown in equation (2):

[0041]

[0042] In the formula:

[0043] —That is, the head from the inlet of the first-stage impeller to the outlet of the guide vane, in meters;

[0044] —Head of the first stage impeller, in meters;

[0045] —Circumferential velocity at the exit of the first-stage impeller, m / s;

[0046] —Circumferential velocity of the first-stage impeller hub, m / s.

[0047] The leakage at both ends of the guide vane is gap leakage. Due to the gap at the guide vane sealing ring, the pressure at both ends of the gap is different. Therefore, some of the high-pressure liquid at the guide vane outlet leaks through the gap at the guide vane sealing ring to the low-pressure side between the first-stage impeller and the guide vane. The expression for the leakage amount is shown in equation (3):

[0048]

[0049] In the formula:

[0050] —The cross-sectional area of ​​the flow path between the guide vanes and the first-stage impeller;

[0051] —Pressure drop across the guide vanes;

[0052] —The width of the flow cross section between the guide vanes and the first-stage impeller;

[0053] —Flow coefficient.

[0054] Substituting equations (2) and (3) into equation (1), the interstage power loss can be derived as follows:

[0055]

[0056] In the formula:

[0057] This represents the pressurization value of the liquid passing through the guide vanes, and it depends only on the guide vane structure. When the structure of the interstage guide vanes remains unchanged, it is a constant.

[0058] When the outer diameter of the first stage impeller is D 21 Reduce ΔD 21 The change in power loss Δp v As shown in equation (4):

[0059]

[0060] In the formula:

[0061] (1) The specific gravity, flow coefficient, gravitational acceleration, width of the flow section between the guide vane and the first impeller, and pressure increase of the liquid working medium passing through the guide vane are all constants greater than 0.

[0062] (2) Since the circumferential speed is minimum at the impeller hub, the right side of the equation is:

[0063]

[0064] Therefore, in equation (4), the change in power loss at the guide vane on the left side of the equation is negative, that is, the outer diameter D of the first-stage impeller is reduced. 21 It can reduce the power loss of the guide vanes.

[0065] To reduce power loss in the guide vanes, the outer diameter D of the first-stage impeller needs to be reduced. 21 The head of the first-stage impeller should be reduced during the design process for the following reasons:

[0066] (1) When designing impeller structural parameters, the formula for calculating the outer diameter of the impeller is:

[0067]

[0068] Since the flow rate and speed of each impeller in a two-stage centrifugal pump are the same, the greater the specific speed of the first-stage impeller, the greater the outer diameter D of the first-stage impeller. 21 The smaller.

[0069] (2) Specific speed n s The calculation formula is shown in equation (6):

[0070]

[0071] Since the liquid flow rate Q and rotational speed n are the same for each stage of the two-stage centrifugal pump, the specific speed of each stage of the two-stage centrifugal pump depends only on the head allocated to each stage of the impeller.

[0072] Substituting equation (6) into equation (5), we can derive the formula for calculating the impeller's outer diameter D2:

[0073]

[0074] As shown in the above formula, reducing the head H1 of the first-stage impeller will reduce the outer diameter D of the first-stage impeller. 21 This reduces the power loss p of the guide vanes. v Decrease.

[0075] The output power of a pump is the effective energy gained by the liquid output from the pump per unit time within the pump. The calculation formula is shown in equation (8):

[0076] N=γQH (8)

[0077] Since the liquid flow rate Q and specific gravity γ are the same after passing through the first and second stage impellers, the output power of each impeller in a two-stage centrifugal pump is only related to its respective distributed head H1 and H2, while the total distributed head H of the two-stage centrifugal pump impellers is... 总 It remains unchanged, as shown in equation (9):

[0078] H = H1 + H2 (9)

[0079] In summary: After reducing the head H1 distributed to the first-stage impeller, the outer diameter D of the first-stage impeller... 21 Reduce the power loss p of the guide vane v As the power is reduced, the power distribution between the two-stage impellers, N1 and N2, changes.

[0080] However, the outer diameter D of the first stage impeller 21 There are two reasons why it cannot be infinitely small:

[0081] (1) To make the outer diameter D of the first stage impeller 21If the head H1 of the primary impeller is reduced, it is known from equation (9) that the head H2 of the secondary impeller outer diameter will increase accordingly. As shown in equation (7), the outer diameter of the secondary impeller will thus increase. If it is too large, it will exceed the allowable radial dimension D of the entire pump. yx ;

[0082] (2) When the head H2 distributed by the outer diameter of the secondary impeller is increased, it can be seen from equation (7) that the specific speed n of the secondary impeller is increased. s Decrease when the specific speed n s When the head-flow curve of the secondary impeller is small, a hump is likely to appear, that is, a hump appears in the efficiency curve H1-η of the two-stage centrifugal pump.

[0083] Therefore, the method to improve the efficiency of a two-stage centrifugal pump by achieving appropriate power distribution between the two stages aims to find an optimal first-stage impeller outer diameter, denoted as the optimal first-stage impeller outer diameter. The outer diameter must meet the following three constraints:

[0084] (1) The outer diameter of the first-stage impeller should be as small as possible;

[0085] (2) The outer diameter of the secondary impeller is smaller than the allowable radial dimension D of the entire pump. yx ;

[0086] (3) The outer diameter of the secondary impeller cannot make the specific speed n of the secondary impeller... s If the value is too small, try to avoid the appearance of a hump on the H1-η curve.

[0087] To achieve the above objectives, the present invention provides the following specific embodiments:

[0088] Example 1: A method for optimizing the efficiency of a two-stage centrifugal pump based on power allocation, comprising the following steps:

[0089] S1: Based on the operating design parameters of the two-stage centrifugal pump, calculate the minimum head distribution value H of the first-stage impeller. min The operating condition design parameters include the given head, flow rate, rotational speed, and maximum allowable radial dimension.

[0090] Calculate the minimum head distribution value H of the first stage impeller. min The steps are as follows:

[0091] The maximum radial dimension D of the impeller allowed by the entire pump yx And based on the minimum head H of the first stage impeller min With the impeller's maximum permissible radial dimension D yx The relationship between flow rate Q and rotational speed n is expressed as (10), and the minimum head distribution value H of the first-stage impeller is calculated. min ,

[0092]

[0093] Among them, H 总 The total head distribution of the two-stage centrifugal pump impellers was determined; the minimum head distribution value H of the first-stage impeller was obtained. min .

[0094] S2: Using 3D modeling software, such as CAD, UG, or CFturbo, establish the head distribution value of the first-stage impeller from 50% to the minimum head H. min At that time, at least two three-dimensional models of the two-stage impeller under different head ratios;

[0095] The specific steps for establishing at least two three-dimensional models of different two-stage impellers under different head ratios are as follows:

[0096] S21: Total head H 总 The head distribution is evenly distributed between the two stages of the centrifugal pump, starting with the first stage impeller accounting for 50% of the total head. The head distribution is gradually reduced by 1% each time, until the minimum head distribution value H for the first stage impeller is reached. min ;

[0097] S22: Calculate the outer diameters of the first and second stage impellers when the head of the first stage impeller decreases by 1% using formula (7):

[0098]

[0099] In the formula, D2 is the impeller outer diameter in meters (m), and Q is the flow rate of each impeller stage in a two-stage centrifugal pump in cubic meters per second (m³). 3 / s, n is the rotational speed of each impeller of the two-stage centrifugal pump, in r / min, H is H1 or H2, where H1 is the head allocated to the first-stage impeller and H2 is the head allocated to the second-stage impeller, both in m.

[0100] S23: Based on the calculation results of steps 21) and 22), establish a table of the outer diameter of the primary or secondary impeller obtained by the head distribution calculation, and use 3D modeling software to establish at least two 3D models of the primary and secondary impellers under different heads.

[0101] S3: Using fluid calculation software, such as Fluent or PumpLinx, numerical simulation of the three-dimensional model is performed to obtain the overall pump efficiency η of each three-dimensional model; at the same time, a correspondence table is established between the overall pump efficiency η of each three-dimensional model and the head H1 of the first impeller.

[0102] S4: Fit the overall pump efficiency points corresponding to different distribution heads of the first-stage impeller in each three-dimensional model to obtain the H1-η curve. The H1-η curve is a curve obtained with the distribution head of the first-stage impeller as the horizontal axis and the efficiency corresponding to the distribution head of the first-stage impeller as the vertical axis.

[0103] If the H1-η curve in the fitted H1-η curve graph shows a hump, then the head corresponding to the point of maximum efficiency is taken as the head H1 allocated to the first stage impeller.

[0104] If the H1-η curve in the fitted graph does not show a hump, then the minimum head distribution value H of the first-stage impeller is set to... min The head H1 is allocated to the first-stage impeller;

[0105] The head H1 corresponds to the optimal first-stage impeller outer diameter. This resulted in an improvement in the efficiency of the two-stage centrifugal pump.

[0106] like Figure 1 As shown, since the optimal first-stage impeller outer diameter is directly sought... The present invention is quite challenging, therefore it first addresses the maximum allowable radial dimension D of the impeller for the entire pump. yx The minimum head distribution value H of the first-stage impeller is calculated. min Secondly, the same head is allocated to both impeller stages. The outer diameters and other operating parameters of the two impeller stages are calculated. After modeling the two-stage centrifugal pump using 3D modeling software, the overall pump efficiency is obtained using fluid dynamics software. Then, the head allocated to the first-stage impeller is gradually reduced until the minimum head allocation value H for the first-stage impeller is reached. min Repeating the above steps yields a series of efficiencies for two-stage centrifugal pumps, i.e., H1-η curves corresponding to the efficiency of the two-stage centrifugal pump and the head of the first-stage impeller. Based on this method, when designing a two-stage centrifugal pump, the optimal head distribution of the first-stage impeller can be obtained through the H1-η curve. and optimal first-stage impeller outer diameter Based on the above design concept and steps, a suitable power distribution between the two impellers can be achieved, which can maximize the efficiency of the two-stage centrifugal pump at the system level.

[0107] Calculation example of this invention:

[0108] Step 1: Based on the operating design parameters of the two-stage centrifugal pump in Table 1, calculate the minimum head distribution value H of the first-stage impeller. min :

[0109] Table 1. Operating Design Parameters of Two-Stage Centrifugal Pumps

[0110]

[0111] Substituting equation (9) into equation (7), we can derive the minimum allowable head H of the first-stage impeller. min With the impeller's maximum permissible radial dimension D yx The relationship between flow rate Q and rotational speed n is expressed as equation (10):

[0112]

[0113] The calculation yielded the following:

[0114]

[0115] Step 2: Assign different head to the two-stage impellers, design different impeller outer diameter schemes, and build models using 3D modeling software:

[0116] The total design head H 总 The head allocation is proportionally distributed to the first-stage impeller, starting at 50% and gradually decreasing by 1% each time, until the minimum head allocation value H for the first-stage impeller is reached. min The outer diameters of the first / secondary impellers, as shown in Table 2, were obtained from the head distribution calculation.

[0117] Table 2 shows the outer diameters of the first / secondary impellers calculated from the head distribution.

[0118]

[0119] Using the nine sets of primary / secondary impeller outer diameters in Table 2, three-dimensional models of schemes 1-9 were created using the 3D modeling software CFturbo, as follows: Figure 4 The three-dimensional model of the two-stage pump in Scheme 1 is shown. Schemes 2 to 9 are similarly modeled using CFturbo.

[0120] Step 3: Based on the 3D model established in Step 2, PumpLinx was used to numerically simulate different schemes, and the overall pump efficiency corresponding to the nine schemes was obtained. The data is shown in Table 3.

[0121] Table 3 Efficiency of different schemes

[0122]

[0123]

[0124] Using the first-stage impeller head H1 as the abscissa and the corresponding overall pump efficiency η as the ordinate, the H1-η curve is obtained by fitting the curve as shown in Figure 1. Figure 5 As shown, the curve has two cases:

[0125] 1) such as Figure 2As shown, if the H1-η curve shows a hump, the head corresponding to the point of maximum efficiency is taken as the head H1 allocated to the first stage impeller.

[0126] 2) such as Figure 3 As shown, if the H1-η curve does not show a hump, then the minimum allowable head H of the first-stage impeller will be set to... min The head H1 is allocated to the first-stage impeller;

[0127] Step 4: As Figure 5 As shown in the figure, the two-stage centrifugal pump has the highest efficiency when the head distribution of the first-stage impeller is 4.7m, and the corresponding outer diameter of the first-stage impeller is 58.5mm.

[0128] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing the efficiency of a two-stage centrifugal pump based on power allocation, characterized in that, Includes the following steps: Based on the operating design parameters of the two-stage centrifugal pump, calculate the minimum head distribution value of the first-stage impeller. The operating condition design parameters include the given head, flow rate, rotational speed, and maximum allowable radial dimension. Using 3D modeling software, the head distribution values ​​of the first-stage impeller were established from 50% to the minimum head. At that time, at least two three-dimensional models of the two-stage impeller under different head ratios are required. The specific steps are as follows: 21) Total head The head distribution is evenly distributed between the two impellers of the centrifugal pump, starting with the first-stage impeller accounting for 50% of the total head. The head distribution is gradually reduced by 1% each time, until the minimum head distribution value for the first-stage impeller is reached. ; 22) Calculate the outer diameters of the first-stage impeller and the secondary impeller respectively when the head of the first-stage impeller decreases by 1% using formula (7): （7） ； In the formula The impeller outer diameter is in meters (m). This refers to the flow rate of each impeller stage in a two-stage centrifugal pump, expressed in m³ / s. 3 / s, This refers to the rotational speed of each impeller in a two-stage centrifugal pump, expressed in r / min. yes or The aforementioned The head allocated to the first stage impeller, The head allocated to the secondary impeller, in meters (m); 23) Based on the calculation results of steps 21) and 22), establish a table of the outer diameter of the first or second stage impeller obtained by the head distribution calculation, and use three-dimensional modeling software to establish at least two three-dimensional models of the first stage impeller and the second stage impeller under different heads; Fluid dynamics calculation software was used to perform numerical simulations based on the aforementioned three-dimensional models, thereby obtaining the overall pump efficiency for each three-dimensional model. ; By fitting the three-dimensional models to the overall pump efficiency points corresponding to different head distributions of the first-stage impeller, we obtain... Line graph; If the fitting result Curve graph If the curve shows a hump, the head corresponding to the point of maximum efficiency is taken as the head allocated to the first-stage impeller. ; If the fitting result Curve graph If the curve does not show a hump, then the minimum head distribution value of the first-stage impeller will be... The head distributed by the first-stage impeller ; The head This corresponds to obtaining the optimal first-stage impeller outer diameter. This resulted in an improvement in the efficiency of the two-stage centrifugal pump.

2. The method for optimizing the efficiency of a two-stage centrifugal pump based on power distribution as described in claim 1, characterized in that, The calculation of the minimum head distribution value of the first-stage impeller. The steps are as follows: Maximum impeller radial dimension allowed by the entire pump And based on the minimum head of the first-stage impeller With the impeller's maximum permissible radial dimension ,flow and rotational speed The relationship expression (10) is used to calculate the minimum head distribution value of the first-stage impeller. , （10） in, The total head distribution for the two-stage centrifugal pump impellers was determined; the minimum head distribution value for the first-stage impeller was obtained. .

3. The method for optimizing the efficiency of a two-stage centrifugal pump based on power distribution as described in claim 1, characterized in that, The overall pump efficiency of each three-dimensional model is obtained. Then, the overall pump efficiency corresponding to each of the shown 3D models is established. Distribute head with the first stage impeller The corresponding table.

4. The method for optimizing the efficiency of a two-stage centrifugal pump based on power distribution as described in claim 1, characterized in that, The aforementioned The curve is a graph with the first-stage impeller head distribution on the horizontal axis and the efficiency corresponding to the first-stage impeller head distribution on the vertical axis.

5. The method for optimizing the efficiency of a two-stage centrifugal pump based on power distribution as described in any one of claims 1-4, characterized in that, The 3D modeling software used is CAD, UG, or CFturbo, and the fluid calculation software used is Fluent or PumpLinx.

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