Multi-objective optimization design method for gas-liquid mixed flow pump under multiple working conditions based on three-dimensional inverse problem

Abstract

The application discloses a multi-working condition and multi-target optimization design method for a gas-liquid mixed delivery pump based on a three-dimensional inverse problem, and aims at optimizing the design of the gas-liquid mixed delivery pump to improve the comprehensive performance of the pump. The load distribution of the impeller blade is selected as an optimization parameter, and the pump pressure rise, the efficiency and the gas volume fraction in the guide vane are selected as three performance parameters. The Euclidean distances d VP , d Vη and d Vβ of the original values and the expected values of the three performance parameters are calculated, the minimum value of the Euclidean distance is selected as an optimization target, an evolution algorithm is used for multi-target optimization, and the optimal solution of the optimization parameter is obtained. The external characteristics and the internal flow characteristics of the gas-liquid mixed delivery pump before and after optimization are compared, including the pressure load distribution on the pump impeller blade, the flow channel velocity flow line, the turbulent kinetic energy and the gas phase distribution. The external characteristics of the gas-liquid mixed delivery pump before and after optimization are verified through experiments, and it is further proved that the internal flow field of the pump after optimization is significantly improved, so that it is shown that the optimization process adopted in the design is feasible and effective.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of fluid machinery, in particular to a multi-working condition and multi-target optimization design method for a gas-liquid mixed delivery pump based on a three-dimensional inverse problem. BACKGROUND

[0002] The gas-liquid mixed delivery pump is a core equipment for deepwater oil and gas resource exploitation and long-distance transportation, and its safe operation and performance optimization are related to the development and utilization of deepwater oil and gas resources. However, due to the complex impeller flow passage structure and the rotation effect of the impeller, the pump is accompanied by complex flow phenomena such as secondary flow, tip leakage flow, wake flow and flow separation. These phenomena can cause a sharp drop in pump pressure rise, accompanied by strong pressure pulsation and vibration and other transient instability problems, thereby deteriorating the pumping capacity and conveying capacity of the pump and causing surge phenomenon. In particular, when the inlet gas volume fraction increases to a certain extent, the pumping of the gas-liquid mixed delivery pump is almost zero, or even negative pressure, which seriously affects the conveying performance of the pump. Therefore, in order to improve the energy performance and operation stability of the gas-liquid mixed delivery pump, scholars use geometric design and performance optimization to optimize the gas-liquid mixed delivery pump, but the selection of the above optimization working condition is usually single working condition, and the target selection is only performance parameters, and the comprehensive performance of the pump under multiple working conditions has not been considered, which is not conducive to the transportation of oil and gas resources under deepwater complex conditions. Therefore, the optimization problem of the impeller of the gas-liquid mixed delivery pump is a typical multi-working condition and multi-target optimization design problem. SUMMARY

[0003] The purpose of the present application is to provide a multi-working condition and multi-target optimization design method for a gas-liquid mixed delivery pump based on a three-dimensional inverse problem, which can improve the pump pressure rise and efficiency under multiple working conditions, and reduce the pump pressure rise, efficiency and gas volume fraction in the guide vane.

[0004] The technical solution adopted by the present application is: a multi-working condition and multi-target optimization design method for a gas-liquid mixed delivery pump based on a three-dimensional inverse problem, comprising the following steps:

[0005] Step 1: parameterizing design of the pump impeller based on the three-dimensional inverse problem design method, taking the impeller blade load distribution parameters as the optimization parameters, and determining the value range of the optimization parameters;

[0006] Step 2: optimal Latin hypercube sampling from the value range of the optimization parameters based on the DOE test design of the sensitivity analysis module to determine the sample space;

[0007] Step 3: Design multiple operating conditions, calculate the pump pressure rise, efficiency, and gas volume fraction in the guide vane for each sample in the sample space under each operating condition, set the expected values ​​for each of the three performance parameters, calculate the Euclidean distance between the performance parameter value and the expected value of each sample, and select the minimum Euclidean distance for each performance parameter as the optimization target.

[0008] Step 4: Based on the sample space of Step 2, construct an approximate model MOP using the MLS method, and use the model MOP to calculate the sensitivity of the samples corresponding to the optimization objective obtained in Step 3;

[0009] Step 5: Use an evolutionary algorithm to perform multi-objective optimization on the samples corresponding to the optimization target and their sensitivity. After multiple iterations, obtain the optimal solution for the optimization parameters.

[0010] The invention is further characterized by:

[0011] Step 1 is as follows:

[0012] Step 1.1, the impeller blade equation constructed based on the three-dimensional inverse problem design method is equation (1),

[0013]

[0014] In formula (1) The impeller blade load distribution includes controlling the load distribution at the blade hub and rim. Optimization parameters are selected based on the load distribution curves of the blade hub and rim, respectively. Simultaneously, the stacking angle, which determines the stacking position at the blade hub, is also considered. The accumulation angle at the blade rim accumulation position Also used as an optimization parameter;

[0015] Step 1.2: Using the selected optimization parameters as input variables, CFD software is used to perform numerical calculations on them to determine the value range of each input variable.

[0016] Step 1.1 The load distribution curves of the blade hub and the blade rim are constructed by fitting the blade hub curve and the blade rim curve with cubic spline curves respectively, obtaining the coordinates of the control points of each curve on the meridional XY plane, connecting the control points in sequence, and constructing the blade hub load curve and the blade rim load curve through cubic spline interpolation algorithm.

[0017] Step 1.1 Select the leading edge load y from the load distribution curve of the blade hub. hub The slope k of the straight line hub The x-coordinate of the point where the first parabola intersects the straight line. hub1 The x-coordinate of the point where the second parabola intersects the straight line.hub2 As an optimization parameter.

[0018] Step 1.1 Select the leading edge load y from the load distribution curve of the blade rim. shr The slope k of the straight line shr The x-coordinate of the point where the first parabola intersects the straight line. shr1 The x-coordinate of the point where the second parabola intersects the straight line. shr2 As an optimization parameter.

[0019] Step 3 specifically involves:

[0020] Step 3.1: Design multiple operating conditions. For any sample in the sample space, calculate its three performance parameters under each operating condition: pump pressure rise ΔP, efficiency η, and gas volume fraction β inside the guide vane, as shown in equation (2).

[0021]

[0022] Step 3.2, define the expected values ​​of the three performance parameters for each pump—pressure rise, efficiency, and gas volume fraction within the guide vane—as ΔP. O η O and β O Calculate the three performance parameters ΔP for each sample point. X η X and β X Its expected value ΔP O η O and β O The Euclidean distance d between them VP (ΔP X ,P O ),d Vη (Δη X ,η O ) and d Vβ (Δβ X ,β O As shown in equation (3),

[0023]

[0024] Step 3.3: Select the minimum Euclidean distance among each performance parameter in the sample and use it as the optimization objective, as shown in equation (4).

[0025]

[0026] The multiple operating conditions in step 3.1 are: three inlet gas content conditions at the optimal efficiency point, and two non-optimal efficiency point conditions at one inlet gas content condition, with the inlet gas content ranging from 5 to 25%.

[0027] The evolutionary algorithm in step 5 adopts a combined algorithm of a genetic algorithm and an evolutionary strategy.

[0028] The evolutionary algorithm in step 5 selects an initial population number of 32, an adaptability method of Pareto dominance, a selection sorting method of Pareto, a maximum generation number of 357, a crossover probability of 0.5 and a mutation probability of 0.7.

[0029] The present application has the following advantages:

[0030] 1. The present application designs the pump impeller by a three-dimensional inverse problem design method, which inversely deduces the geometric shape of the impeller from the expected performance, has the advantages of precisely meeting the performance requirement, shortening the design cycle, facilitating optimization and improvement and the like.

[0031] 2. The present application takes the load distribution parameter of the impeller blade as the optimization parameter, takes the pump pressure rise, efficiency and gas volume fraction in the guide vane as the optimization target, considers multiple working conditions, reduces the dimension of the high-dimensional objective function set in the optimization by the Euclidean distance method, determines the pump model with better performance by using the optimization algorithm for optimization on the basis of the establishment of the accurate approximate model, effectively improves the pressure rise value and efficiency of the pump model relative to before optimization, and reduces the pump pressure rise, efficiency and gas volume fraction in the guide vane. BRIEF DESCRIPTION OF DRAWINGS

[0032] Figure 1 is a load distribution diagram of the impeller blade of the present application, wherein is the blade load, m / m Max is the relative value of the meridian component of the blade surface streamline;

[0033] Figure 2 (a) is a sensitivity column chart of the optimization parameter to the target parameter d Vη of the embodiment 4 of the present application;

[0034] Figure 2 (b) is a sensitivity column chart of the optimization parameter to the target parameter d Vβ of the embodiment 4 of the present application;

[0035] Figure 2 (c) is a sensitivity column chart of the optimization parameter to the target parameter d VP of the embodiment 4 of the present application;

[0036] Figure 3 is an optimization flow chart of the evolutionary algorithm of the embodiment 5 of the present application;

[0037] Figure 4(a) is d Vη with d VP population distribution graph;

[0038] Figure 4 (b) is d Vβ with d VP population distribution graph;

[0039] Figure 4 (c) is d Vη with d Vβ population distribution graph;

[0040] Figure 5 is a comparison chart of impeller blade load distribution before and after optimization of embodiment 5 of the present application;

[0041] Figure 6 (a) is a comparison chart of impeller blade geometry before and after optimization of embodiment 5 of the present application, wherein red represents the optimized pump impeller blade and green represents the original pump impeller blade;

[0042] Figure 6 (b) is a comparison chart of impeller blade line type before and after optimization of embodiment 5 of the present application, wherein red represents the optimized pump blade and green represents the original pump blade;

[0043] Figure 7 (a) is a comparison chart of hub streamline direction pressure distribution of the impeller blade before and after optimization of embodiment 5 of the present application under the condition of IGVF = 15%, Q BEP

[0044] Figure 7 (b) is a comparison chart of Span direction pressure distribution of the impeller blade before and after optimization of embodiment 5 of the present application under the condition of IGVF = 15%, Q BEP

[0045] Figure 7 (c) is a comparison chart of shroud streamline direction pressure distribution of the impeller blade before and after optimization of embodiment 5 of the present application under the condition of IGVF = 15%, Q BEP

[0046] Figure 7 (d) is a comparison chart of hub streamline direction pressure distribution of the impeller blade before and after optimization of embodiment 5 of the present application under the condition of IGVF = 15%, 0.8Q BEP

[0047] Figure 7 ​​​​(e) is a comparison chart of pressure distribution in the hub flow direction of the impeller blade of Example 5 of the present application before and after optimization at the operating condition of IGVF = 15%, 0.8Q BEP (f) is a comparison chart of pressure distribution in the shroud flow direction of the impeller blade of Example 5 of the present application before and after optimization at the operating condition of IGVF = 15%, 0.8Q

[0048] Figure 7 (f) is a comparison chart of pressure distribution in the shroud flow direction of the impeller blade of Example 5 of the present application before and after optimization at the operating condition of IGVF = 15%, 0.8Q BEP (f) is a comparison chart of pressure distribution in the shroud flow direction of the impeller blade of Example 5 of the present application before and after optimization at the operating condition of IGVF = 15%, 0.8Q

[0049] Figure 7 (g) is a comparison chart of pressure distribution in the hub flow direction of the impeller blade of Example 5 of the present application before and after optimization at the operating condition of IGVF = 15%, 1.2Q BEP (g) is a comparison chart of pressure distribution in the hub flow direction of the impeller blade of Example 5 of the present application before and after optimization at the operating condition of IGVF = 15%, 1.2Q

[0050] Figure 7 (g) is a comparison chart of pressure distribution in the hub flow direction of the impeller blade of Example 5 of the present application before and after optimization at the operating condition of IGVF = 15%, 1.2Q BEP (g) is a comparison chart of pressure distribution in the hub flow direction of the impeller blade of Example 5 of the present application before and after optimization at the operating condition of IGVF = 15%, 1.2Q

[0051] Figure 7 (g) is a comparison chart of pressure distribution in the hub flow direction of the impeller blade of Example 5 of the present application before and after optimization at the operating condition of IGVF = 15%, 1.2Q BEP (g) is a comparison chart of pressure distribution in the hub flow direction of the impeller blade of Example 5 of the present application before and after optimization at the operating condition of IGVF = 15%, 1.2Q

[0052] Figure 7 (j) is a comparison chart of pressure distribution in the hub flow direction of the impeller blade of Example 5 of the present application before and after optimization at the operating condition of IGVF = 5%, Q BEP (j) is a comparison chart of pressure distribution in the hub flow direction of the impeller blade of Example 5 of the present application before and after optimization at the operating condition of IGVF = 5%, Q

[0053] Figure 7 (j) is a comparison chart of pressure distribution in the hub flow direction of the impeller blade of Example 5 of the present application before and after optimization at the operating condition of IGVF = 5%, Q BEP (j) is a comparison chart of pressure distribution in the hub flow direction of the impeller blade of Example 5 of the present application before and after optimization at the operating condition of IGVF = 5%, Q

[0054] Figure 7 (j) is a comparison chart of pressure distribution in the hub flow direction of the impeller blade of Example 5 of the present application before and after optimization at the operating condition of IGVF = 5%, Q BEP (j) is a comparison chart of pressure distribution in the hub flow direction of the impeller blade of Example 5 of the present application before and after optimization at the operating condition of IGVF = 5%, Q

[0055] Figure 7(m) represents the condition IGVF = 25% in Embodiment 5 of the present invention, Q BEP The image shows a comparison of the pressure distribution along the streamline of the impeller blade hub before and after optimization, where the dashed line represents the original pump and the solid line represents the optimized pump.

[0056] Figure 7 (n) represents the condition IGVF = 25% and Q in Embodiment 5 of the present invention. BEP The image shows a comparison of the pressure distribution along the impeller blade height span before and after optimization, where the dashed line represents the original pump and the solid line represents the optimized pump.

[0057] Figure 8 (o) is the condition IGVF = 25% in Embodiment 5 of the present invention, Q BEP The image shows a comparison of the pressure distribution along the shroud streamline of the impeller blade rim before and after optimization. The dashed line represents the original pump, and the solid line represents the optimized pump.

[0058] Figure 8 (a) is Example 5 of the present invention under operating conditions IGVF = 15%, Q BEP At the same time, optimize the velocity streamlines and turbulent kinetic energy and the pressure distribution on the blade surface at the top of the front impeller and guide vane flow channel half-blade;

[0059] Figure 8 (b) is the embodiment of the present invention under operating conditions IGVF = 15%, Q BEP At the same time, the optimized velocity streamlines and turbulent kinetic energy and blade surface pressure distribution at the top of the half-blade of the impeller and guide vane flow channel are shown.

[0060] Figure 8 (c) is the result of Embodiment 5 of the present invention under operating conditions of IGVF = 15% and 0.8Q. BEP At the same time, optimize the velocity streamlines and turbulent kinetic energy and the pressure distribution on the blade surface at the top of the front impeller and guide vane flow channel half-blade;

[0061] Figure 8 (d) is the result of Embodiment 5 of the present invention under operating conditions of IGVF = 15% and 0.8Q. BEP At the same time, the optimized velocity streamlines and turbulent kinetic energy and blade surface pressure distribution at the top of the half-blade of the impeller and guide vane flow channel are shown.

[0062] Figure 8 (e) is the result of Embodiment 5 of the present invention under operating conditions of IGVF = 15% and 1.2Q. BEP At the same time, optimize the velocity streamlines and turbulent kinetic energy and the pressure distribution on the blade surface at the top of the front impeller and guide vane flow channel half-blade;

[0063] Figure 8 (f) is the result of Embodiment 5 of the present invention under operating conditions of IGVF = 15% and 1.2Q. BEPAt the same time, the optimized velocity streamlines and turbulent kinetic energy and blade surface pressure distribution at the top of the half-blade of the impeller and guide vane flow channel are shown.

[0064] Figure 8 (g) is the condition IGVF = 5% in Embodiment 5 of the present invention, Q BEP At the same time, optimize the velocity streamlines and turbulent kinetic energy and the pressure distribution on the blade surface at the top of the front impeller and guide vane flow channel half-blade;

[0065] Figure 8 (h) is the condition IGVF = 5% in Embodiment 5 of the present invention, Q BEP At the same time, the optimized velocity streamlines and turbulent kinetic energy and blade surface pressure distribution at the top of the half-blade of the impeller and guide vane flow channel are shown.

[0066] Figure 8 (i) is the condition IGVF = 25% in Embodiment 5 of the present invention, Q BEP At the same time, optimize the velocity streamlines and turbulent kinetic energy and the pressure distribution on the blade surface at the top of the front impeller and guide vane flow channel half-blade;

[0067] Figure 8 (j) is the condition of IGVF = 25% and Q in Embodiment 5 of the present invention. BEP At the same time, the optimized velocity streamlines and turbulent kinetic energy and blade surface pressure distribution at the top of the half-blade of the impeller and guide vane flow channel are shown.

[0068] Figure 9 (k) is a diagram showing the pressure change on the impeller blade surface in Embodiment 5 of the present invention;

[0069] Figure 9 (l) is a diagram showing the velocity streamline and turbulent kinetic energy changes at the top of the guide vane channel half-blade in Embodiment 5 of the present invention;

[0070] Figure 9 (a) is the gas phase distribution diagram in the flow channel before optimization in Embodiment 5 of the present invention under the operating conditions of IGVF=15% and QBEP;

[0071] Figure 9 (b) is the optimized gas phase distribution diagram in the flow channel of Embodiment 5 of the present invention under the operating conditions of IGVF=15% and QBEP;

[0072] Figure 9 (c) is the gas phase distribution diagram in the flow channel before optimization in Embodiment 5 of the present invention under the operating conditions of IGVF = 15% and 0.8QBEP;

[0073] Figure 9 (d) is the optimized gas phase distribution diagram in the flow channel of Embodiment 5 of the present invention under the operating conditions of IGVF = 15% and 0.8QBEP;

[0074] Figure 9(e) is the gas phase distribution diagram in the flow channel before optimization in Embodiment 5 of the present invention under the operating conditions of IGVF = 15% and 1.2QBEP;

[0075] Figure 9 (f) is the optimized gas phase distribution diagram in the flow channel of Embodiment 5 of the present invention under the operating conditions of IGVF = 15% and 1.2QBEP;

[0076] Figure 9 (g) is the gas phase distribution diagram in the flow channel before optimization in Embodiment 5 of the present invention under the operating conditions of IGVF=5% and QBEP;

[0077] Figure 9 (h) is the optimized gas phase distribution diagram in the flow channel of Embodiment 5 of the present invention under the operating conditions of IGVF=5% and QBEP;

[0078] Figure 9 (i) is the gas phase distribution diagram in the flow channel before optimization in Embodiment 5 of the present invention under the operating conditions of IGVF=25% and QBEP;

[0079] Figure 10 (j) is the optimized gas phase distribution diagram in the flow channel of Embodiment 5 of the present invention under the operating conditions of IGVF=25% and QBEP;

[0080] Figure 10 (k) is a diagram indicating the magnitude of gas phase pressure in the flow channel in Embodiment 5 of the present invention;

[0081] Figure 11 (a) is a comparison curve of the head performance of the gas-liquid mixed transport pump in pure water condition between Embodiment 6 of the present invention and the comparative example.

[0082] Figure 1 (b) is a comparison graph of the efficiency performance curves of the gas-liquid mixed transport pump in pure water condition between Embodiment 6 of the present invention and the comparative example.

[0083] Figure 1 This is a comparison chart of the pressure rise curves under the gas-liquid two-phase operating condition in Embodiment 6 of the present invention. Detailed Implementation

[0084] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0085] This invention discloses a multi-condition, multi-objective optimization design method for gas-liquid mixed transport pumps based on a three-dimensional inverse problem, specifically including the following steps:

[0086] Step 1: Parametric design of the pump impeller based on the three-dimensional inverse problem design method, using the impeller blade load distribution parameters as optimization parameters;

[0087] Step 1.1: Construct the impeller blade equation based on the three-dimensional inverse problem design method, as shown in equation (1):

[0088]

[0089] In formula (1), p + p - These represent the pressure values ​​on the pressure and suction surfaces of the blades, respectively; ρ is the liquid density; BN is the number of blades; The average relative velocity of the blades; The meridional component of the average relative velocity of the blades can be derived from... calculate; This represents the meridional component of the relative velocity of the blade pressure surface; The meridional component of the relative velocity between the blade's suction surfaces; The circumferential component of the average absolute velocity; Let be the velocity torque; m be the meridional component of the streamline along the blade surface. The above equation shows that the pressure difference between the pressure and suction surfaces of the blade can be controlled by adjusting the partial derivative of the velocity torque along the meridional streamline. The load distribution of the blades is adjusted accordingly. In other words, controlling the load distribution of the blades can indirectly control the work capacity of the blades. Based on this principle, the load distribution of the impeller blades is parametrically designed.

[0090] The impeller blade load distribution includes the load distributions controlling the blade hub and shroud respectively. Cubic spline curves are used to fit the hub and shroud curves respectively, obtaining the coordinates of the control points Q0, Q1, Q2, and Q3 on the meridional XY plane. The control points Q0 to Q3 are then connected sequentially, and a cubic spline interpolation algorithm is used to construct the hub load curve and the shroud load curve, as shown below. Figure 2 As shown, the load distribution curves of both the blade hub and shroud include two parabolic segments and one straight line segment. Therefore, both load distribution curves require four parameters for control, namely the hub leading edge load y. hub Shroud leading edge load y shr The slope k of the hub line hub The slope k of the Shroud line shr The x-coordinate of the point where the parabola and the straight line intersect in the first segment of the hub. hub1 The x-coordinate of the point where the first parabola and the straight line intersect is shroud. shr1 The x-coordinate of the point where the parabola and the straight line intersect in the second segment of the hub. hub2 And the x-coordinate of the point where the second parabola and the straight line intersect in Shroud's second segment. shr2 The above eight parameters are used as optimization parameters. In addition, the hub stacking angle determines the blade stacking position. and rim overlap angle It was also selected as an optimization parameter. The accumulation angle of a pump usually refers to the change in the wrap angle of the blade trailing edge from the hub to the rim. When viewed from the impeller outlet direction, the accumulation angle is positive when the inclination direction of the trailing edge at the rim is opposite to the impeller rotation direction, and negative when the inclination direction is opposite to the impeller rotation direction. The accumulation angle is 0 when the position of the trailing edge at the hub is the same as the position at the rim.

[0091] 1.2 Select the above 10 optimization parameters as input variables. The 10 optimization parameters are as follows: y hub y shr k hub k shr x hub1 x shr1 x hub2 x shr2 , and CFD software is used to calculate the values ​​of the input variables and determine the range of values ​​for each input variable.

[0092] Step 2: Based on the sensitivity analysis module, the DOE experimental design performs optimal Latin hypercube sampling from the range of optimized parameter values ​​to determine the sample space;

[0093] Step 2.1: Use the DOE experimental design in the sensitivity analysis module to select samples from the range of values ​​for each input variable;

[0094] Step 2.2: Use the optimal Latin hypercube sampling method to sample from the selected sample and determine the sample space.

[0095] Step 3: Design multiple operating conditions, calculate the pump pressure rise, efficiency, and three performance parameters (pump pressure rise, efficiency, and gas volume fraction in the guide vane) for each sample in the sample space under each operating condition, set the expected values ​​of these three performance parameters, calculate the Euclidean distance between the performance parameter values ​​of each sample and their expected values, and select the minimum Euclidean distance for each performance parameter as the optimization target.

[0096] Step 3.1: Design multiple operating conditions. For any sample in the sample space, calculate its three performance parameters under each operating condition: pump pressure rise ΔP, efficiency η, and gas volume fraction β inside the guide vane, as shown in equation (2).

[0097]

[0098] Wherein, X1, X2, X3, X4, and X5 are respectively working condition 1, working condition 2, working condition 3, working condition 4, and working condition 5;

[0099] Step 3.2, define the expected values ​​of the three performance parameters—pump pressure rise, efficiency, and gas volume fraction within the guide vane—as ΔP. O η O and βO Calculate the three performance parameters ΔP respectively. X η X and β X Its expected value ΔP O η O and β O The Euclidean distance d between them VP (ΔP X ,P O ),d Vη (Δη X ,η O ) and d Vβ (Δβ X ,β O As shown in equation (3),

[0100]

[0101] Step 3.3: Select the minimum Euclidean distance among each performance parameter in the sample and use it as the optimization objective, as shown in equation (4).

[0102]

[0103] Step 4: Based on the sample space of Step 2, construct an approximate model MOP using the MLS method, and use the model MOP to calculate the sensitivity of the samples corresponding to the optimization objective obtained in Step 3;

[0104] Step 4.1: Construct an approximate model MOP based on the sample space from Step 2 using the MLS method;

[0105] Step 4.2: Calculate the sensitivity of the sample corresponding to each optimization objective to the optimization objective itself using the approximate model MOP.

[0106] Step 5: Use an evolutionary algorithm to perform multi-objective optimization on the samples corresponding to the optimization target and their sensitivity. After multiple iterations, obtain the optimal solution for the optimization parameters.

[0107] By selecting a combination of GA and ES algorithms, and allowing for expansion between the two, multi-objective optimization is performed on the sensitivity of each objective parameter to obtain the optimal solution.

[0108] Example 1

[0109] Based on the blade equation (1) in the three-dimensional inverse problem design method, the load distribution of the impeller blade is parametrically designed. The load distribution parameters of the impeller blade are used as optimization parameters. The blade load distribution mainly controls the load distribution of the blade hub and shroud. Cubic spline curves are used to fit the blade hub curve and the blade shroud curve respectively to obtain the coordinates of the control points Q0, Q1, Q2, and Q3 on the meridional XY plane. The control points Q0 to Q3 are connected in sequence. The blade hub curve and the blade shroud curve are constructed by cubic spline interpolation algorithm, such as Figure 3 As shown, the load distribution curves of the blade hub and shroud mainly consist of two parabolic segments and one straight line segment. Therefore, both load distribution curves require four parameters for control, namely the leading edge load (y). hub and y shr ), the slope of the straight line (k) hub and k shr ), the x-coordinate of the point where the first parabola and the straight line intersect (x) hub1 and x shr1 ), and the x-coordinate of the intersection point of the second parabola and the straight line (x hub2 and x shr2 In addition, the stacking angle determines the location of blade stacking. and ) was also selected as an optimization parameter.

[0110] y hub y shr k hub k shr x hub1 x shr1 x hub2 x shr2 , and Ten optimization parameters were used as input variables. CFD software was used to calculate the values ​​of the ten input variables. The range of values ​​for the input variables was gradually changed and bad calculation points were eliminated. Finally, the range of values ​​for the input variables was determined to be -20% to 20%. Table 1 shows the upper and lower boundaries of each input variable.

[0111] Table 1 Input Variable Range

[0112]

[0113] Example 2

[0114] Based on Example 1, using the DOE experimental design with the sensitivity analysis module, 310 samples were selected within the range of values ​​of the input variables in step 1 to form the sample space U. XTable 2 shows the values ​​for the selected samples, with the first five and last five samples listed briefly to illustrate their characteristics.

[0115] Table 2 Selected Samples

[0116]

[0117] As shown in Table 2, the sample space U X The sample consists of 10 optimization parameters for the impeller blade load distribution during the optimization design of the gas-liquid mixed transport pump. Each optimization parameter varies within a range of values.

[0118] Example 3

[0119] Based on Example 2, five operating conditions were designed. The flow rate operating condition was selected by choosing the optimal efficiency point (Q) at a rotational speed of 3500 rpm. BEP The operating conditions and three nearby flow conditions are Q. BEP 0.8Q BEP 1.2Q BEP Q BEP The optimal efficiency point operating flow rate is used. The inlet gas content (IGVF) operating condition selection method is to select three inlet gas content (IGVF) conditions before and after the surge condition, i.e., IGVF = 5%, 15%, and 25%, where IGVF is the inlet gas content. Specifically, the five operating conditions are the three inlet gas content conditions (IGVF = 5%, 15%, and 25%) at the optimal efficiency point operating condition; Q BEP =78m 3 / h) and two non-optimal efficiency conditions under one inlet gas content condition (IGVF = 15%; 0.8Q) BEP 1.2Q BEP ).

[0120] For U in the sample space X For any sample in the formula, there are three performance parameters under each operating condition: pump pressure rise ΔP, efficiency η, and gas volume fraction β inside the guide vane, as shown in formula (5).

[0121]

[0122] The subscripts X1 to X5 represent 5 operating conditions, i.e., IGVF = 15%, Q BEP IGVF = 15%, 0.8Q BEP IGVF = 15%, 1.2Q BEP IGVF = 5%, Q BEP IGVF = 25%, Q BEP Where IGVF is the inlet gas content, and Q is the inlet gas content. BEP The flow rate is the optimal efficiency point.

[0123] Obtain the set of performance parameters ΔP of the pump model before optimization. X η X and β X And thereby define the expected performance parameter set ΔP. O η O and β O Each performance parameter has an original value corresponding to an expected value, and the original performance parameter can be adjusted as needed to ensure that the sample performance parameter does not exceed the expected performance parameter range. Table 3 shows the sample space U. X The original and expected performance parameters of a sample under 5 operating conditions.

[0124] Table 3 Original performance parameters and expected performance parameters

[0125]

[0126] Calculate the three performance parameter sets ΔP respectively. X η X and β X The Euclidean distances between each original performance parameter and its expected performance parameter in the set of expected performance parameters are shown in Equation (6). The Euclidean distances between the three performance parameters are d0, ... VP (ΔP X ,ΔP O ),d Vη (Δη X ,Δη O ) and d Vβ (Δβ X ,Δβ O The Euclidean distances of the three performance parameters form a set d. VP (ΔP X ,ΔP O ),d Vη (Δη X ,Δη O ) and d Vβ (Δβ X ,Δβ O ),

[0127]

[0128] Find the three sets of Euclidean distances d respectively. VP (ΔP X ,ΔP O ),d Vη (Δη X ,Δη O ) and d Vβ (Δβ X ,Δβ OThe minimum value in the sample space U is used as the optimization objective. Data dimensionality reduction is achieved using the Euclidean distance method, ensuring that there are only three optimization objective parameters regardless of the number of operating points. The final mathematical model for the gas-liquid mixed-transfer pump optimization design adopted in this invention is shown in equation (4). Therefore, the high-dimensional multi-objective optimization problem of the gas-liquid mixed-transfer pump can be transformed into: finding the minimum value in the sample space U. X The internal set of three performance parameters ΔP X η X and β X With the set of three expected parameters ΔP O η O and β O The distance d between VP (ΔP X ,ΔP O ),d Vη (Δη X ,Δη O ) and d Vβ (Δβ X ,Δβ O The three smallest samples.

[0129] Example 4

[0130] Based on Example 3, and using the samples in Table 2, an approximate model MOP (Multi-Objective Programming Model) is constructed using the MLS method.

[0131] The variance contribution of each optimization parameter in the three samples was calculated using the approximate model MOP, and the sensitivity of each optimization parameter (design variable) to the optimization target parameter was obtained, as shown in Table 4.

[0132] Table 4. Sensitivity of design variables to each target parameter

[0133]

[0134] As shown in Table 4, each optimization parameter has different sensitivities to different target parameters. For example, the Euclidean distance d has almost no effect on the target parameter efficiency. Vη The optimization parameters are the x-coordinates of the intersection points of the first parabolic segment and the straight line segment of the hub load distribution. hub1 and the slope k of the straight line segment hub ; Euclidean distance d of the gas volume fraction inside the guide vane as a target parameter Vβ The optimization parameters with minimal impact are the rim load distribution and the leading edge load y. shr The x-coordinate of the intersection point of the first parabolic segment and the straight segment of the wheel flange load distribution is... shr1 The slope k of the straight segment of the hub load distribution hub Calculate the variance contribution of the optimization parameters. Figure 4 A bar chart is used to illustrate the influence of each optimization parameter on the objective parameter, where the Euclidean distance d for the objective parameter efficiency is shown.Vη The four most influential optimization parameters are the stacking angle at the impeller hub. Accumulation angle at the impeller rim The slope k of the straight segment of the rim load distribution shr The x-coordinate of the intersection point of the parabola and the straight line segment of the hub load distribution is... hub2 The target parameter is the Euclidean distance d of the gas volume fraction inside the guide vane. Vβ The four most influential optimization parameters are the stacking angle at the impeller hub. The slope k of the straight segment of the rim load distribution shr The angle of accumulation at the impeller rim The x-coordinate of the intersection point of the parabola and the straight line segment of the hub load distribution is... hub2 Furthermore, the slope k of the straight segment of the rim load distribution shr The x-coordinate of the intersection point of the second parabolic segment and the straight line segment of the hub load distribution is... hub2 The x-coordinate of the intersection point of the parabola and the straight line segment in the second segment of the wheel flange load distribution is... shr2 and the stacking angle at the impeller hub Euclidean distance d for the target parameter pump pressure rise VP The impact is the greatest.

[0135] Example 5

[0136] Building upon Example 4, an evolutionary algorithm (EAs) is employed to optimize the gas-liquid mixing pump design. The optimization parameters and their sensitivities from the three samples corresponding to the minimum Euclidean distance are used as inputs to the evolutionary algorithm. EAs have three variants: Genetic Algorithm (GA), Evolutionary Strategy (ES), and Evolutionary Programming. This invention uses a combination of GA and ES, allowing for expansion between the two. The optimization process is as follows: Figure 5 As shown.

[0137] The performance of evolutionary algorithms in solving optimization designs depends on the choice of initial population, crossover probability, and mutation probability. Too small a population size results in poor performance or even no feasible solution, while too large a population increases computational cost and slows convergence. A high crossover probability easily eliminates high-fitness individuals, while a low probability causes the search to stagnate and the algorithm to fail to converge. A low mutation probability prevents the generation of new individuals, while a high mutation probability makes the algorithm a random search, leading to long processing times. For multi-objective optimization, it is necessary to find solutions close to the Pareto optimum or diverse solutions representing the entire Pareto front to find the optimal point of the optimization design. This invention selects an initial population size of 32, uses Pareto as the fitness method, selects Pareto as the sorting method, has a maximum number of generations of 357, and sets the crossover probability and mutation probability to 0.5 and 0.7, respectively.

[0138] After optimization, a Pareto front solution set will be generated. Figure 6The distribution of the optimized population across three two-dimensional objective spaces is shown. Most individuals in the optimized population outperform the original individuals, confirming the effectiveness of the multi-objective evolutionary algorithm in optimization design. However, the Pareto front solutions for the two-dimensional population distributions corresponding to each pair of objectives exhibit inconsistent performance of the objective parameters. Therefore, a comprehensive consideration is needed to select the final optimized solution. Table 5 compares the optimized solution selected in this invention with the optimized parameter values ​​of the original model before optimization.

[0139] Table 5 Comparison of optimization parameter values ​​before and after optimization

[0140]

[0141] The performance of the optimized pump was verified by numerical calculations and experimental tests. The performance differences before and after optimization were compared to find the correlation between changes in geometric parameters and performance improvement. Figure 7 This paper presents a comparison of the impeller blade load distribution before and after optimization of a gas-liquid mixed-transfer pump. After optimization, the impeller blade load distribution parameters are as follows: hub load distribution and leading edge load y. hub Slope k of the straight segment of the rim load distribution shr The x-coordinate of the intersection point of the parabola and the straight line segment of the hub load distribution is... hub2 The changes are significant; the load distribution on the blades increases in the first half and decreases in the second half, which will affect the geometric changes of the gas-liquid mixing pump. Figure 8 The geometric characteristics of the impeller blades of the gas-liquid mixed-transfer pump before and after optimization were compared. After optimization, the leading edge of the pump impeller blades moved in the opposite direction of impeller rotation, while the trailing edge moved in the same direction. The blade length became shorter, the wrap angle smaller, and the inlet and outlet installation angles and deflection changed. The load distribution of the optimized blades in the first half (m / m) Max <0.5) The load increases and decreases in the second half. The change in the load distribution of the impeller blades will affect the geometric change of the gas-liquid mixing pump.

[0142] The optimized geometry of the gas-liquid mixed-transfer pump improves the pump's pressure rise and efficiency while reducing the pressure rise, efficiency, and gas volume fraction within the guide vanes. The target parameters for the optimized pump are d... VP =0.24, d Vη =0.17 and d Vβ =0.26, representing reductions of 25.67%, 19.05%, and 7.14% respectively compared to the original values, demonstrating a significant performance improvement. Table 6 presents the optimized pump performance parameters and their changes relative to the original values ​​under five operating conditions.

[0143] Table 6 Comparison of performance parameter values ​​before and after optimization

[0144]

[0145] The optimized pump showed improved pressure rise and efficiency under all five operating conditions, while the gas volume fraction inside the guide vanes decreased, achieving optimal efficiency at the point of lowest efficiency (Q). BEP Under the condition of IGVF = 15% and 1.2 times the optimal efficiency point (1.2(Q) BEP Under IGVF = 15% (maximum pressure rise and efficiency improvement) and the optimal efficiency point operating condition (Q BEP The performance parameters under the following conditions showed significant improvement: IGVF = 25% (the largest decrease in gas volume fraction inside the guide vane).

[0146] Further analysis of the reasons for the performance improvement is as follows:

[0147] Impact of pressure distribution: To analyze the reasons for the performance improvement of the gas-liquid mixing pump before and after optimization, Figure 9 The pressure distribution of the pump impeller blades before and after optimization was compared under five operating conditions. The green dashed line represents the original pump, and the blue solid line represents the optimized pump. The dimensionless pressure coefficient Cp is used, as shown in Equation (7).

[0148]

[0149] In the formula, p is the pressure on the impeller blades; U Ds1 ρ is the circumferential velocity at the impeller inlet rim. m This represents the density of the gas-liquid mixture. Compared to the pressure surface of the pump impeller blades before optimization, the pressure surface of the pump impeller blades after optimization has been increased. At the same time, the pressure difference between the pressure surface and the suction surface has also been increased, which increases the impeller's work capacity and helps to improve the pump's boosting capacity.

[0150] Effects of flow field changes: The pressure distribution on the impeller blades of a gas-liquid mixed-transfer pump may be affected by changes in the internal flow field. Figure 10 The velocity streamlines and turbulent kinetic energy distribution in the pump impeller and guide vane flow channels, as well as the pressure distribution on the blades, were compared before and after optimization under five operating conditions. The changes in the pump impeller blades after optimization improved the flow structure in the flow channel, reduced secondary flow phenomena (including the distribution and range of secondary flow), reduced turbulent kinetic energy, and effectively improved the pump performance.

[0151] Influence of gas phase distribution: The geometry of the impeller blades in a gas-liquid mixing pump affects the gas phase distribution within the flow channel. Figure 11 The gas phase distribution inside the pump before and after optimization was compared under different operating conditions. After optimization, the impeller of the pump prevented or reduced the accumulation of gas pockets or gas masses in the flow channel, and the gas masses on the impeller rim inlet side and hub outlet side were reduced or even disappeared.

[0152] Example 6

[0153] The single-stage gas-liquid mixing pump, whose main parameters are shown in Table 7 below, was optimized using the method of this invention. A prototype model was created based on the three-dimensional geometric model of the impeller of the optimized pump. The initial pump model mainly includes an inlet pipe, impeller, guide vanes, and outlet pipe. The number of blades in the impeller and guide vanes are 4 and 7, respectively, and the lengths of the inlet pipe and outlet pipe are 4 times and 6 times the impeller inlet rim diameter, respectively.

[0154] Table 7 Main Parameters of Gas-Liquid Mixed Transport Pump

[0155]

[0156] Comparative Example

[0157] The unoptimized single-stage gas-liquid mixing pump from Example 6 was used.

[0158] This invention constructs a visual test rig for a gas-liquid mixed-transport pump based on the gas-liquid two-phase integrated test system of the State Key Laboratory of Eco-water Conservancy in Arid Areas of Northwest China. With other components remaining unchanged, external characteristic tests, visualization tests, and pressure pulsation tests were conducted under different operating conditions using the model sample from Example 6 and the pump impeller of the comparative example.

[0159] ​ The external characteristic parameters of the pump before and after optimization were compared under pure water conditions. Compared with the unoptimized pump, the head of the optimized pump was improved in almost all four speed conditions, while the head was relatively lower under high flow conditions. Overall, the slope of the head curve changed. Furthermore, under all four speed conditions, the head of the optimized pump was improved in all conditions except for high flow conditions, and the efficiency was also improved under high flow conditions.

[0160] ​ The pressure rise (ΔP) of the pump before and after optimization was compared under three speeds: 900 rpm, 1200 rpm, and 1500 rpm, for gas-liquid two-phase operation (flow rate conditions were the optimal efficiency points at the corresponding speeds). Overall, the optimized pump showed a general improvement in pressure rise under different speed conditions, with the most significant improvement observed at higher inlet gas content (IGVF ≥ 15%). This reduced surge and facilitated stable operation under high inlet gas content, further validating the applicability of the optimization scheme to gas-liquid mixed-phase pumps.

[0161] In summary, as demonstrated by the above embodiments, after multi-objective optimization of the gas-liquid mixed-transfer pump using the optimization process of this design, the three performance parameters of the pump have been effectively improved compared to before optimization. By comparing the pressure load distribution on the pump impeller blades, the flow channel velocity streamlines, turbulent kinetic energy, and gas phase distribution before and after optimization, it is further confirmed that the flow field inside the pump has been significantly improved after optimization. This indicates that the optimization process adopted in this invention is feasible and effective.

Claims

1. A multi-operating condition and multi-objective optimization design method for gas-liquid mixed delivery pumps based on three-dimensional inverse problems, characterized in that, The method comprises the following steps: Step 1: parameterizing design of a pump impeller based on a three-dimensional inverse problem design method, taking a blade load distribution parameter of the impeller as an optimization parameter, and determining a value range of the optimization parameter; The step 1 is specifically: Step 1.1, the impeller blade equation constructed based on the three-dimensional inverse problem design method is formula (1), （1）， wherein p + , p – are the pressure values on the pressure and suction side of the blade, respectively; ρ is the liquid density; BN is the number of blades; is the average relative velocity of the blade; is the meridional component of the average relative velocity of the blade, calculated from ; is the meridional component of the relative velocity on the pressure side of the blade; is the meridional component of the relative velocity on the suction side of the blade; is the circumferential component of the average absolute velocity; is the velocity moment; m is the meridional component of the blade surface streamline; In formula (1) is a blade load distribution of the impeller, the blade load distribution of the impeller including a load distribution of a blade hub and a load distribution of a blade shroud, the optimization parameters being selected according to a load distribution curve of the blade hub and a load distribution curve of the blade shroud, respectively, while an overlap angle determining an overlap position of the blade hub φ hub and an overlap position of the blade shroud φ shr are also optimization parameters; Step 1.2, taking the selected optimization parameter as an input variable, performing numerical calculation by using a CFD software, and determining a value range of each input variable; Step 2: performing optimal Latin hypercube sampling from the value range of the optimization parameter based on a sensitivity analysis module DOE test design, and determining a sample space; Step 3: designing multiple working conditions, respectively calculating pump pressure rise, efficiency and gas volume fraction in a guide vane of each sample in the sample space under each working condition, setting an expected value of the three performance parameters respectively, calculating Euclidean distances between performance parameter values of each sample and the expected values, and respectively selecting minimum values of the Euclidean distances of each performance parameter as optimization targets; Step 4: based on the sample space of step 2, constructing an approximate model MOP by using an MLS method, and calculating sensitivities of samples corresponding to the optimization targets obtained in step 3 by using the model MOP; Step 5: performing multi-objective optimization on the samples corresponding to the optimization targets and the sensitivities by using an evolutionary algorithm, and obtaining an optimal solution of the optimization parameter through multiple iteration calculations.

2. The method according to claim 1, wherein, The load distribution curve of the blade hub and the load distribution curve of the rim are constructed by using a cubic spline curve to fit the blade hub curve and the blade rim curve respectively, obtaining coordinates of control points of each curve on a meridian plane XY, and connecting the control points in sequence to construct the load curves of the blade hub and the blade rim by using a cubic spline interpolation algorithm.

3. The multi-working condition and multi-objective optimization design method of the gas-liquid mixed delivery pump based on three-dimensional inverse problems according to claim 1 or 2, characterized in that, the leading edge load of the load distribution curve of the blade hub described in step 1.1 y hub the slope of the straight line k hub the abscissa of the intersection point of the first parabolic segment and the straight line x hub1 the abscissa of the intersection point of the second parabolic segment and the straight line x hub2 as optimization parameters.

4. The method according to claim 3, characterized in that, the load distribution curve of the blade of step 1.1 is selected for the leading edge load y shr the slope of the straight line k shr the abscissa of the intersection of the first parabolic segment and the straight line x shr1 the abscissa of the intersection of the second parabolic segment and the straight line x shr2 as optimization parameters.

5. The method according to claim 4, wherein, The step 3 is specifically: Step 3.1, design multiple operating conditions, for any sample in the sample space, calculate its pump pressure rise Δpump under each operating condition P , efficiency η and gas volume fraction in the guide vane β three performance parameters, as shown in equation (2), （2）； Step 3.2, define the expected values of the three performance parameters, pressure rise, efficiency and gas volume fraction in the guide vane, respectively as Δ P O , η O and β O , respectively calculate the Euclidean distance between the three performance parameters Δ P X , η X and β X and their expected values Δ P O , η O and β O , respectively, as shown in equation (3) d VP (Δ P X , P O ), d Vη (Δ η X , η O ) and d Vβ (Δ β X , β O ), respectively. （3）； Step 3.3, respectively selecting minimum values of the Euclidean distances of each performance parameter in the sample as optimization targets, as shown in formula (4), （4）。 6. The method according to claim 5, wherein, The multiple working conditions of step 3.1 are three inlet gas rate working conditions at the best efficiency point and two non-best efficiency point working conditions at one inlet gas rate, and the range of the inlet gas rate is 5-25%.

7. The method according to claim 1, wherein, The evolutionary algorithm in step 5 is a combination algorithm of a genetic algorithm and an evolutionary strategy.

8. The method according to claim 7, characterized in that, In step 5, the evolutionary algorithm selects an initial population number of 32, an adaptability method of Pareto dominance, a sorting method of Pareto, a maximum number of generations of 357, a crossover probability of 0.5, and a mutation probability of 0.7.

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