Gas-liquid multiphase pump multi-working-condition multi-objective optimization design method based on three-dimensional inverse problem

Abstract

The invention discloses a gas-liquid multiphase pump multi-working-condition multi-target optimization design method based on a three-dimensional inverse problem, which aims at carrying out optimization design on a gas-liquid multiphase pump so as to improve the comprehensive performance of the pump, selects the load distribution of an impeller blade as an optimization parameter, selects three performance parameters, namely pump pressure rise, efficiency and the volume fraction of gas in a guide vane as target parameters, and aims at solving the problem of multi-working-condition multi-target optimization design of the gas-liquid multiphase pump. And calculating Euclidean distances dVP, dV eta and dV beta between original values and expected values of the three performance parameters, selecting the minimum Euclidean distance as an optimization target, and performing multi-target optimization by adopting an evolutionary algorithm to obtain an optimal solution of the optimized parameters. According to the method, the external characteristics and the internal flow characteristics of the gas-liquid multiphase pump before and after optimization are compared, the external characteristics comprise pressure load distribution on pump impeller blades, flow channel speed streamlines, turbulence energy and gas phase distribution, the external characteristics of the gas-liquid multiphase pump before and after optimization are verified through tests, and it is further verified that a flow field in the pump is remarkably improved after optimization, so that the performance of the gas-liquid multiphase pump is improved. Therefore, the optimization process adopted by the design is feasible and effective.

Description

Technical Field

[0001] The present invention relates to the technical field of fluid machinery, and in particular to a multi-operating-condition and multi-objective optimization design method for a gas-liquid mixed transmission pump based on a three-dimensional inverse problem. Background Art

[0002] The gas-liquid mixed flow pump is the core equipment for deepwater oil and gas resource exploitation and long-distance transportation. 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 channel structure and the rotation effect of the impeller, the gas-liquid mixed flow pump will be accompanied by complex flow phenomena such as secondary flow, blade tip leakage flow, wake flow and flow separation. These phenomena will cause the pressure rise of the pump to drop sharply, accompanied by transient instability problems such as strong pressure pulsation and vibration, which will further deteriorate the pump's boosting capacity and delivery capacity, and cause surge. In particular, when the inlet gas content increases to a certain extent, the boost of the gas-liquid mixed flow pump is almost zero, and even negative pressure occurs, which seriously affects the pump's delivery performance. Therefore, in order to improve the energy performance and operation stability of the gas-liquid mixed flow pump, scholars have optimized the gas-liquid mixed flow pump by using two means: geometric design and performance optimization. However, the selection of the above-mentioned optimization conditions is usually a single condition, and the target selection is only performance parameters. The comprehensive performance of the pump under multiple conditions has not been comprehensively considered, which is not conducive to the transportation of oil and gas resources in complex deepwater conditions. It can be seen that the optimization problem of the impeller of a gas-liquid mixed flow pump is a typical multi-condition and multi-objective optimization design problem. Summary of the invention

[0003] The purpose of the present invention is to provide a multi-operating condition and multi-objective optimization design method for a gas-liquid mixed flow pump based on a three-dimensional inverse problem. The gas-liquid mixed flow pump designed by this design method can improve the pump pressure rise and efficiency under various operating conditions, while reducing the pump pressure rise, efficiency and the gas volume fraction in the guide vane.

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

[0005] Step 1: Based on the three-dimensional inverse problem design method, the pump impeller is parametrically designed, the impeller blade load distribution parameter is used as the optimization parameter, and the value range of the optimization parameter is determined;

[0006] Step 2: Based on the DOE experimental design of the sensitivity analysis module, optimal Latin hypercube sampling is performed within the value range of the optimization parameter to determine the sample space;

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

[0008] Step 4: Based on the sample space of step 2, the MLS method is used to construct an approximate model MOP, and the model MOP is used to calculate the sensitivity of the sample corresponding to the optimization target obtained in step 3;

[0009] Step 5: Use evolutionary algorithm to perform multi-objective optimization on the samples corresponding to the optimization target and their sensitivity. After multiple iterative calculations, the optimal solution of the optimization parameters is obtained.

[0010] The present invention is also characterized in that:

[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 load distribution of the impeller blades includes controlling the load distribution of the blade hub and the rim. The optimization parameters are selected according to the load distribution curve of the blade hub and the load distribution curve of the rim. At the same time, the stacking angle that determines the stacking position of the blade hub is The stacking angle of the blade rim Also used as optimization parameter;

[0015] Step 1.2: Use the selected optimization parameters as input variables, use CFD software to calculate their values, and determine the value range of each input variable.

[0016] Step 1.1 The load distribution curve of the blade hub and the load distribution curve of the rim are constructed by fitting the blade hub curve and the blade rim curve respectively using cubic spline curves to obtain the coordinates of the control points of each curve on the meridian XY plane, connecting the control points in sequence, and constructing the blade hub load curve and the blade rim load curve through the 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 horizontal coordinate x of the intersection point of the first parabola and the straight line hub1 , the horizontal coordinate x of the intersection point of the second parabola and the straight linehub2 as optimization parameters.

[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 horizontal coordinate x of the intersection point of the first parabola and the straight line shr1 , the horizontal coordinate x of the intersection point of the second parabola and the straight line shr2 as optimization parameters.

[0019] Step 3 is as follows:

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

[0021]

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

[0023]

[0024] Step 3.3, select the minimum Euclidean distance of each performance parameter in the sample and use it as the optimization target, as shown in formula (4):

[0025]

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

[0027] In step 5, the evolutionary algorithm adopts a combination algorithm of genetic algorithm and evolution strategy.

[0028] In step 5, the evolutionary algorithm selects the initial population size as 32, the fitness method as Pareto-dominated, the selection sorting method as Pareto, the maximum number of generations as 357, the crossover probability as 0.5, and the mutation probability as 0.7.

[0029] The beneficial effects of the present invention are:

[0030] 1. The present invention performs parameterized design of pump impellers through a three-dimensional inverse problem design method. The three-dimensional inverse problem design starts from the desired performance and reversely derives the geometric shape of the impeller. It has the advantages of accurately meeting performance requirements, shortening the design cycle, and facilitating optimization and improvement. The use of this design method can quickly modify and optimize the impeller design, and can quickly generate an impeller design that meets the performance requirements, reducing the process of repeated trials and modifications in traditional design methods.

[0031] 2. The present invention takes the impeller blade load distribution parameters as optimization parameters, and the pump pressure rise, efficiency and gas volume fraction in the guide vane as optimization targets, considers various working conditions, and reduces the dimension of the high-dimensional objective function set in the optimization through the Euclidean distance method. On the basis of establishing an accurate approximate model, an optimization algorithm is used to find the optimal solution and determine a pump model with better performance. The pressure rise value and efficiency of the pump model are effectively improved compared to before optimization, while the pump pressure rise, efficiency and gas volume fraction in the guide vane are reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is the load distribution diagram of the impeller blades of the present invention, 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 the optimization parameter of Example 4 of the present invention for the target parameter d Vη Sensitivity histogram;

[0034] Figure 2 (b) is the optimization parameter of Example 4 of the present invention for the target parameter d Vβ Sensitivity histogram;

[0035] Figure 2 (c) is the optimization parameter of Example 4 of the present invention for the target parameter d VP Sensitivity histogram;

[0036] Figure 3 This is the flow chart of the evolutionary algorithm optimization in Example 5 of the present invention;

[0037] Figure 4(a) is d in Example 5 of the present invention Vη With d VP Population distribution map;

[0038] Figure 4 (b) is d in Example 5 of the present invention Vβ With d VP Population distribution map;

[0039] Figure 4 (c) is d in Example 5 of the present invention Vη With d Vβ Population distribution map;

[0040] Figure 5 is a comparison diagram of impeller blade load distribution before and after optimization of Example 5 of the present invention;

[0041] Figure 6 (a) is a geometric comparison diagram of impeller blades before and after optimization in Example 5 of the present invention, wherein red represents the optimized pump impeller blades and green represents the original pump impeller blades;

[0042] Figure 6 (b) is a comparison diagram of the impeller blade line shapes before and after optimization in Example 5 of the present invention, where red represents the optimized pump blades and green represents the original pump blades;

[0043] Figure 7 (a) is the working condition of Example 5 of the present invention under the condition of IGVF=15%, Q BEP Comparison of pressure distribution in the streamline direction of the impeller blade hub before and after optimization, where the dotted line represents the original pump and the solid line represents the optimized pump;

[0044] Figure 7 (b) is the working condition of Example 5 of the present invention under the condition of IGVF=15%, Q BEP Comparison of pressure distribution in the direction of impeller blade height Span before and after optimization, where the dotted line represents the original pump and the solid line represents the optimized pump;

[0045] Figure 7 (c) is the working condition of Example 5 of the present invention under the condition of IGVF=15%, Q BEP Comparison of pressure distribution in the direction of the impeller blade rim shroud streamline before and after optimization, where the dotted line represents the original pump and the solid line represents the optimized pump;

[0046] Figure 7 (d) is the working condition of Example 5 of the present invention under IGVF=15%, 0.8Q BEP Comparison of pressure distribution in the streamline direction of the impeller blade hub before and after optimization, where the dotted line represents the original pump and the solid line represents the optimized pump;

[0047] Figure 7(e) is the working condition of Example 5 of the present invention under IGVF=15%, 0.8Q BEP Comparison of pressure distribution in the direction of impeller blade height Span before and after optimization, where the dotted line represents the original pump and the solid line represents the optimized pump;

[0048] Figure 7 (f) is the working condition of Example 5 of the present invention under IGVF=15%, 0.8Q BEP Comparison of pressure distribution in the direction of the impeller blade rim shroud streamline before and after optimization, where the dotted line represents the original pump and the solid line represents the optimized pump;

[0049] Figure 7 (g) is the working condition of Example 5 of the present invention under IGVF=15%, 1.2Q BEP Comparison of pressure distribution in the streamline direction of the impeller blade hub before and after optimization, where the dotted line represents the original pump and the solid line represents the optimized pump;

[0050] Figure 7 (h) is the working condition of Example 5 of the present invention under IGVF=15%, 1.2Q BEP Comparison of pressure distribution in the direction of impeller blade height Span before and after optimization, where the dotted line represents the original pump and the solid line represents the optimized pump;

[0051] Figure 7 (i) is the working condition of Example 5 of the present invention under IGVF=15%, 1.2Q BEP Comparison of pressure distribution in the direction of the impeller blade rim shroud streamline before and after optimization, where the dotted line represents the original pump and the solid line represents the optimized pump;

[0052] Figure 7 (j) is the working condition of Example 5 of the present invention under the condition of IGVF=5%, Q BEP Comparison of pressure distribution in the streamline direction of the impeller blade hub before and after optimization, where the dotted line represents the original pump and the solid line represents the optimized pump;

[0053] Figure 7 (k) is the working condition of Example 5 of the present invention under the condition of IGVF=5%, Q BEP Comparison of pressure distribution in the direction of impeller blade height Span before and after optimization, where the dotted line represents the original pump and the solid line represents the optimized pump;

[0054] Figure 7 (l) is the working condition of Example 5 of the present invention under IGVF=5%, Q BEP Comparison of pressure distribution in the direction of the impeller blade rim shroud streamline before and after optimization, where the dotted line represents the original pump and the solid line represents the optimized pump;

[0055] Figure 7(m) is the working condition of Example 5 of the present invention under IGVF=25%, Q BEP Comparison of pressure distribution in the streamline direction of the impeller blade hub before and after optimization, where the dotted line represents the original pump and the solid line represents the optimized pump;

[0056] Figure 7 (n) is the working condition of Example 5 of the present invention under IGVF=25%, Q BEP Comparison of pressure distribution in the direction of impeller blade height Span before and after optimization, where the dotted line represents the original pump and the solid line represents the optimized pump;

[0057] Figure 7 (o) is the working condition of Example 5 of the present invention under IGVF=25%, Q BEP Comparison of pressure distribution in the direction of the impeller blade rim shroud streamline before and after optimization, where the dotted line represents the original pump and the solid line represents the optimized pump;

[0058] Figure 8 (a) is the working condition of Example 5 of the present invention under the condition of IGVF=15%, Q BEP When optimizing the velocity streamlines and turbulent kinetic energy at the height of the front impeller and guide vane flow passage half blade, as well as the pressure distribution diagram on the blade surface;

[0059] Figure 8 (b) is the working condition of Example 5 of the present invention under the condition of IGVF=15%, Q BEP When optimizing, the velocity streamlines and turbulent kinetic energy at the half-blade height of the impeller and guide vane flow passage and the pressure distribution diagram on the blade surface are;

[0060] Figure 8 (c) is the working condition of Example 5 of the present invention under IGVF=15%, 0.8Q BEP When optimizing the velocity streamlines and turbulent kinetic energy at the height of the front impeller and guide vane flow passage half blade, as well as the pressure distribution diagram on the blade surface;

[0061] Figure 8 (d) is the working condition of Example 5 of the present invention under IGVF=15%, 0.8Q BEP When optimizing, the velocity streamlines and turbulent kinetic energy at the half-blade height of the impeller and guide vane flow passage and the pressure distribution diagram on the blade surface are;

[0062] Figure 8 (e) is the working condition of Example 5 of the present invention under IGVF=15%, 1.2Q BEP When optimizing the velocity streamlines and turbulent kinetic energy at the height of the front impeller and guide vane flow passage half blade, as well as the pressure distribution diagram on the blade surface;

[0063] Figure 8 (f) is the working condition of Example 5 of the present invention under IGVF=15%, 1.2Q BEPWhen optimizing, the velocity streamlines and turbulent kinetic energy at the half-blade height of the impeller and guide vane flow passage and the pressure distribution diagram on the blade surface are;

[0064] Figure 8 (g) is the working condition of Example 5 of the present invention under the condition of IGVF=5%, Q BEP When optimizing the velocity streamlines and turbulent kinetic energy at the height of the front impeller and guide vane flow passage half blade, as well as the pressure distribution diagram on the blade surface;

[0065] Figure 8 (h) is the working condition of Example 5 of the present invention under IGVF=5%, Q BEP When optimizing, the velocity streamlines and turbulent kinetic energy at the half-blade height of the impeller and guide vane flow passage and the pressure distribution diagram on the blade surface are;

[0066] Figure 8 (i) is the working condition of Example 5 of the present invention under IGVF=25%, Q BEP When optimizing the velocity streamlines and turbulent kinetic energy at the height of the front impeller and guide vane flow passage half blade, as well as the pressure distribution diagram on the blade surface;

[0067] Figure 8 (j) is the working condition of Example 5 of the present invention under IGVF=25%, Q BEP When optimizing, the velocity streamlines and turbulent kinetic energy at the half-blade height of the impeller and guide vane flow passage and the pressure distribution diagram on the blade surface are;

[0068] Figure 8 (k) is a diagram indicating the pressure change on the surface of the impeller blades in Example 5 of the present invention;

[0069] Figure 8 (l) is a diagram indicating the change of velocity streamlines and turbulent kinetic energy at the height of the half-blade of the guide vane flow passage in Example 5 of the present invention;

[0070] Fig. 9 (a) is the gas phase distribution diagram in the flow channel before optimization in Example 5 of the present invention when IGVF=15% and QBEP;

[0071] Fig. 9 (b) is the gas phase distribution diagram in the flow channel after optimization in Example 5 of the present invention under the working condition of IGVF=15%, QBEP;

[0072] Fig. 9 (c) is the gas phase distribution diagram in the flow channel before optimization when IGVF=15% and QBEP=0.8 in Example 5 of the present invention;

[0073] Fig. 9 (d) is the gas phase distribution diagram in the flow channel after optimization in Example 5 of the present invention under the working condition of IGVF=15%, 0.8QBEP;

[0074] Fig. 9(e) is the gas phase distribution diagram in the flow channel before optimization when IGVF=15% and 1.2QBEP in Example 5 of the present invention;

[0075] Fig. 9 (f) is a gas phase distribution diagram in the flow channel after optimization in Example 5 of the present invention under the working condition of IGVF=15%, 1.2QBEP;

[0076] Fig. 9 (g) is the gas phase distribution diagram in the flow channel before optimization in Example 5 of the present invention when IGVF=5% and QBEP;

[0077] Fig. 9 (h) is the gas phase distribution diagram in the flow channel after optimization in Example 5 of the present invention under the working condition of IGVF=5%, QBEP;

[0078] Fig. 9 (i) is the gas phase distribution diagram in the flow channel before optimization in Example 5 of the present invention when IGVF=25% and QBEP;

[0079] Fig. 9 (j) is the gas phase distribution diagram in the flow channel after optimization in Example 5 of the present invention under the working condition IGVF=25%, QBEP;

[0080] Fig. 9 (k) is a diagram indicating the gas pressure in the flow channel of Example 5 of the present invention;

[0081] Fig.10 (a) is a comparison diagram of the lift performance curves of the gas-liquid mixed delivery pump under pure water conditions of Example 6 of the present invention and the comparative example;

[0082] Fig.10 (b) is a comparison diagram of the efficiency performance curves of the gas-liquid mixed delivery pump under pure water conditions of Example 6 of the present invention and the comparative example;

[0083] Fig.11 It is a comparison diagram of the pressure rise curves of the gas-liquid two-phase working condition in Example 6 of the present invention. DETAILED DESCRIPTION

[0084] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0085] The present invention discloses a multi-operating-condition and multi-objective optimization design method for a gas-liquid mixed delivery pump based on a three-dimensional inverse problem, which specifically comprises the following steps:

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

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

[0088]

[0089] In formula (1), p + , p - are the pressure values ​​on the pressure and suction surfaces of the blades, respectively; ρ is the liquid density; BN is the number of blades; is the average relative speed of the blade; is the meridional component of the average relative velocity of the blade, which can be obtained by calculate; is the meridional component of the relative velocity on the blade pressure surface; is the meridional component of the relative velocity of the blade suction surface; is the circular component of the mean absolute velocity; is the velocity moment; m is the meridian component of the blade surface streamline. The above formula shows that the pressure difference between the pressure surface and the suction surface of the blade can be controlled by controlling the partial differential of the velocity moment along the meridian streamline. That is to say, the blade load distribution is adjusted, that is to say, controlling the blade load distribution can indirectly control the working capacity of the blade. Based on this principle, the impeller blade load distribution is parameterized.

[0090] The impeller blade load distribution includes the load distribution of the blade hub and the blade shroud. The blade hub curve and the blade shroud curve are fitted by cubic spline curves to obtain the coordinates of the control points Q0, Q1, Q2, and Q3 of each curve on the meridian XY plane. The control points Q0 to Q3 are connected in sequence, and the blade hub load curve and the blade shroud load curve are constructed by the cubic spline interpolation algorithm. Figure 1 As shown in Figure 2, the load distribution curves of the hub and shroud of the blade both include two parabolas and one straight line. Therefore, both load distribution curves require four parameters to 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 、hubThe horizontal coordinate x of the intersection point of the first parabola and the straight line hub1 , shroud the horizontal coordinate x of the intersection point of the first parabola and the straight line shr1 、hubThe horizontal coordinate x of the intersection point of the second parabola and the straight line hub2 And the horizontal coordinate x of the intersection point of the second parabola and the straight line of shroud shr2 , the above 8 parameters are used as optimization parameters. In addition, the hub stacking angle that determines the blade stacking position and flange overlap angle The stack angle of the 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, when the inclination direction of the trailing edge at the rim is opposite to the impeller rotation direction, the stack angle is positive, otherwise it is negative. When the trailing edge position at the hub is the same as the position at the rim, the stack angle is 0.

[0091] 1.2 Select the above 10 optimization parameters as input variables. The specific 10 optimization parameters are: y hub ,y shr , k hub , k shr 、x hub1 、x shr1 、x hub2 、x shr2 , and Use CFD software to calculate the numerical value of the input variables and determine the value range of each input variable.

[0092] Step 2: Based on the DOE experimental design of the sensitivity analysis module, optimal Latin hypercube sampling is performed within the value range of the optimization parameter to determine the sample space;

[0093] Step 2.1, use the DOE experimental design of the sensitivity analysis module to select samples from the value range of each input variable;

[0094] Step 2.2, use the optimal Latin hypercube sampling method to sample from the selected samples and determine the sample space.

[0095] Step 3: Design multiple working conditions, calculate the three performance parameters of pump pressure rise, efficiency and gas volume fraction in the guide vane for each sample in the sample space under each working condition, set the expected values ​​of the three performance parameters, calculate the Euclidean distance between the performance parameter value of each sample and its expected value, select the minimum Euclidean distance in each performance parameter, and use them as optimization targets respectively;

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

[0097]

[0098] Among them, X1, X2, X3, X4, and X5 are working conditions 1, working conditions 2, working conditions 3, working conditions 4, and working conditions 5 respectively;

[0099] Step 3.2: define the expected values ​​of the three performance parameters of pump pressure rise, efficiency and gas volume fraction in 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 VP (ΔP X ,P O ), d Vη (Δη X ,η O ) and d Vβ (Δβ X ,β O ), as shown in formula (3),

[0100]

[0101] Step 3.3, select the minimum Euclidean distance of each performance parameter in the sample and use it as the optimization target, as shown in formula (4):

[0102]

[0103] Step 4: Based on the sample space of step 2, the MLS method is used to construct an approximate model MOP, and the model MOP is used to calculate the sensitivity of the sample corresponding to the optimization target obtained in step 3;

[0104] Step 4.1, construct the approximate model MOP using the MLS method based on the sample space in step 2;

[0105] Step 4.2, calculate the sensitivity of the samples corresponding to each optimization target to the optimization target itself through the approximate model MOP.

[0106] Step 5: Use evolutionary algorithm to perform multi-objective optimization on the samples corresponding to the optimization target and their sensitivity. After multiple iterative calculations, the optimal solution of the optimization parameters is obtained.

[0107] A combination algorithm of GA and ES is selected, and expansion between the two is allowed. The sensitivity of each target parameter is optimized by multi-objective optimization to obtain the optimal solution.

[0108] Example 1

[0109] Based on the blade equation (1) in the three-dimensional inverse problem design method, the impeller blade load distribution is parametrically designed. The impeller blade load distribution parameters are used as optimization parameters. The blade load distribution mainly controls the load distribution of the blade hub and the blade shroud. The blade hub curve and the blade shroud curve are fitted with cubic spline curves to obtain the coordinates of the control points Q0, Q1, Q2, and Q3 of each curve on the meridian XY plane. The control points Q0 to Q3 are connected in sequence, and the blade hub curve and the blade shroud curve are constructed by the cubic spline interpolation algorithm. Figure 1 As shown in the figure, the load distribution curves of the hub and shroud of the blade mainly include two parabolas and one straight line. Therefore, both load distribution curves require four parameters to control, namely, the leading edge load (y hub and shr ), the slope of the straight line (k hub and k shr ), the horizontal coordinate of the intersection point of the first parabola and the straight line (x hub1 and x shr1 ), and the horizontal coordinate (x hub2 and x shr2 In addition, the stacking angle ( and ) is also selected as an optimization parameter.

[0110] y hub ,y shr , k hub , k shr 、x hub1 、x shr1 、x hub2 、x shr2 , and A total of 10 optimization parameters are used as input variables. CFD software is used to calculate the values ​​of the 10 input variables, gradually changing the value range of the input variables and excluding the bad points. Finally, the value range of the input variables is determined to be -20% to 20%. Table 1 gives the upper and lower boundaries of each input variable.

[0111] Table 1 Input variable range

[0112]

[0113] Example 2

[0114] Based on Example 1, the DOE experimental design using the sensitivity analysis module uses the optimal Latin hypercube sampling method to select 310 samples within the value range of the input variable in step 1 to form a sample space U XTable 2 gives the values ​​of the selected samples. The table simply lists the first five samples and the last five samples to reflect their sample characteristics.

[0115] Table 2 Selected samples

[0116]

[0117] From Table 2, we can see that the sample space U X The samples in the figure are 10 optimization parameters for the impeller blade load distribution during the optimization design of a gas-liquid mixed flow pump, and each optimization parameter varies within a range of values.

[0118] Example 3

[0119] Based on Example 2, five working conditions were designed, among which the flow condition selection method was to select the best efficiency point (Q BEP ) condition and the three nearby flow conditions, namely Q BEP , 0.8Q BEP , 1.2Q BEP , where Q BEP is the flow rate at the best efficiency point. The inlet gas content rate condition selection method is to select three inlet gas content rate (IGVF) conditions before and after the surge condition, namely IGVF = 5%, 15%, 25%, where IGVF is the inlet gas content rate. The five conditions are specifically the three inlet gas content rate conditions at the best efficiency point condition (IGVF = 5%, 15%, 25%; Q BEP =78m 3 / h) and two non-optimal efficiency point conditions (IGVF = 15%; 0.8Q BEP , 1.2Q BEP ).

[0120] For the sample space U X Any sample in has three performance parameters under each working condition, namely, pump pressure rise ΔP, efficiency η and gas volume fraction β in the guide vane, as shown in formula (5).

[0121]

[0122] The subscripts X1 to X5 represent five working conditions, namely, IGVF = 15%, Q BEP IGVF=15%,0.8Q BEP IGVF=15%,1.2Q BEP IGVF=5%,Q BEP IGVF=25%,Q BEP IGVF is the inlet gas fraction, Q BEP It is the flow rate at the best efficiency point.

[0123] Get the performance parameter set ΔP of the pump model before optimization X , η X and β X , and define the expected performance parameter set ΔP O , η O and β O The original value of each performance parameter corresponds 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 gives the sample space U X The original and expected performance parameters of a sample under five operating conditions.

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

[0125]

[0126] Calculate the three performance parameter sets ΔP separately X , η X and β X The Euclidean distance between each original performance parameter and its expected performance parameter in the expected performance parameter set is shown in formula (6). The Euclidean distances of the three performance parameters are d 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 three Euclidean distance sets d respectively VP (ΔP X ,ΔP O ), d Vη (Δη X ,Δη O ) and d Vβ (Δβ X ,Δβ O) and takes it as the optimization target. Data dimension reduction is achieved by the Euclidean distance method. No matter how many operating points there are, there are only three optimization target parameters. The mathematical model for the optimization design of the gas-liquid mixed flow pump adopted by the present invention is finally shown in formula (4). Therefore, the high-dimensional multi-objective optimization problem of the gas-liquid mixed flow pump can be converted to: Find the sample space U X The three performance parameters set ΔP X , η X and β X With three expected parameter sets ΔP O , η O and β O The distance between VP (ΔP X ,ΔP O ), d Vη (Δη X ,Δη O ) and d Vβ (Δβ X ,Δβ O ) minimum 3 samples.

[0129] Example 4

[0130] On the basis of Example 3, based on the samples in Table 2, the MLS method is used to construct an approximate model MOP (multi-objective programming model);

[0131] The variance contribution of each optimization parameter in the three samples was calculated by 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 target parameters

[0133]

[0134] From Table 4, we can see that each optimization parameter has different sensitivities to different target parameters. For example, the target parameter efficiency Euclidean distance d Vη The optimization parameter is the horizontal coordinate x of the intersection point of the first parabola and the straight line segment of the hub load distribution. hub1 and the slope k of the straight line segment hub ; Euclidean distance d for the target parameter gas volume fraction in the guide vane Vβ The optimization parameters with little influence are the rim load distribution and the leading edge load y shr , the horizontal coordinate x of the intersection point of the first parabola and the straight line segment of the wheel rim load distribution shr1 and the slope k of the hub load distribution straight line segment hub Compute the variance contribution of the optimized parameters. Figure 2 The influence of each optimization parameter on the target parameter is given by a bar graph, among which the Euclidean distance d of the target parameter efficiency isVη The top four optimization parameters with the greatest impact are the stacking angle at the impeller hub Stack angle at the impeller rim The slope k of the straight line segment of the wheel rim load distribution shr The horizontal coordinate x of the intersection point of the second parabola of the hub load distribution and the straight line segment hub2 ; and for the target parameter, the Euclidean distance d of the gas volume fraction in the guide vane Vβ The top four optimization parameters with the greatest impact are the stacking angle at the impeller hub The slope k of the straight line segment of the wheel rim load distribution shr , the stacking angle at the impeller rim The horizontal coordinate x of the intersection point of the second parabola of the hub load distribution and the straight line segment hub2 In addition, the slope k of the straight line segment of the wheel rim load distribution is shr , the horizontal coordinate x of the intersection point of the second parabola of hub load distribution and the straight line segment hub2 , the horizontal coordinate x of the intersection point of the second parabola of the wheel rim load distribution and the straight line segment shr2 and the stacking angle at the impeller hub Euclidean distance d of pump pressure rise to target parameter VP The greatest impact.

[0135] Example 5

[0136] On the basis of Example 4, an evolutionary algorithm (EAs) is used to optimize the design of the gas-liquid mixed transmission pump, and the optimization parameters and their sensitivities in the three samples corresponding to the minimum Euclidean distance are used as the input of the evolutionary algorithm. EAs has three variants: genetic algorithm (GA), evolutionary strategy (ES) and evolutionary programming. The present invention adopts the combined application of GA and ES, and allows expansion between the two. The optimization process is as follows: Figure 3 shown.

[0137] The performance of the evolutionary algorithm in solving the optimization design depends on the selection of the initial population, crossover probability and mutation probability. If the population size is too small, the performance is poor or even there is no feasible solution. If it is too large, the amount of calculation will increase and the convergence speed will be slow. If the crossover probability is too large, it is easy to eliminate individuals with high fitness. If it is too small, the search will stagnate and the algorithm will not converge. If the mutation probability is low, new individuals cannot be generated. If it is high, the algorithm will become a random search and take a long time. For multi-objective optimization, it is necessary to find a diversified solution close to the Pareto optimal solution or representing the entire Pareto frontier to find the optimal point of the optimization design. The present invention selects the initial population size as 32, the fitness method as Pareto-dominated, the selection sorting method as Pareto, the maximum number of generations as 357, and the crossover probability and mutation probability as 0.5 and 0.7 respectively.

[0138] After the optimization is completed, a Pareto frontier solution set will be formed. Figure 4The distribution of the optimized population in three two-dimensional target spaces is shown. The performance of most population individuals is better than that of the original individuals, which confirms the effectiveness of the multi-objective evolutionary algorithm in optimization design. However, in the Pareto frontier solution of the two-dimensional population distribution corresponding to each two objectives, the performance of the target parameters is uneven, and comprehensive consideration is required to select the final optimization solution. Table 5 shows the comparison between the optimization solution selected by the present invention and the optimization 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 is verified by numerical calculations and experimental tests, the performance difference of the pump before and after optimization is compared, and the correlation between the change of geometric parameters and performance improvement is found. Figure 5 The comparison of the impeller blade load distribution before and after the optimization of the gas-liquid mixed transmission pump is given. After optimization, the pump impeller blade load distribution parameters such as the hub load distribution leading edge load y hub , the slope k of the straight line segment of the wheel rim load distribution shr The horizontal coordinate x of the intersection point of the second parabola and the straight line segment of the hub load distribution hub2 The change is large, the load in the front half of the blade load distribution increases, and the load in the second half decreases, which will affect the geometric changes of the gas-liquid mixed flow pump. Figure 6 The geometric characteristics of the impeller blades of the gas-liquid mixed flow pump before and after optimization were compared. After optimization, the leading edge of the pump impeller blade moved in the opposite direction of the impeller rotation direction, the trailing edge moved in the direction of the impeller rotation direction, the blade length became shorter, the wrap angle became smaller, and the inlet and outlet placement angles and deflections changed. The load distribution of the front half of the blade after optimization (m / m Max <0.5) The load increases and decreases in the second half. The change in the load distribution on the impeller blades will affect the geometric changes of the gas-liquid mixed flow pump.

[0142] The optimized geometric changes of the gas-liquid mixed pump improve the pump pressure rise and efficiency, while reducing the pump pressure rise, efficiency and gas volume fraction in the guide vane. The target parameters of the optimized pump are d VP =0.24, d Vη = 0.17 and d Vβ =0.26, which are 25.67%, 19.05% and 7.14% lower than the original values, respectively, and the performance improvement effect is obvious. Table 6 shows the performance parameter values ​​of the optimized pump under 5 working conditions and the changes in the performance parameter values ​​of the pump before optimization.

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

[0144]

[0145] After optimization, the pressure rise and efficiency of the pump are improved under the five working conditions, the gas volume fraction in the guide vane is reduced, and the optimal efficiency point (Q BEP ) IGVF = 15%, 1.2 times the best efficiency point condition (1.2 (Q BEP )) IGVF = 15% (maximum pressure rise and efficiency improvement) and the best efficiency point condition ((Q BEP )) under IGVF = 25% (the gas volume fraction in the guide vane decreases the most), the performance parameter values ​​of these three operating conditions are greatly improved.

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

[0147] Impact of pressure distribution: In order to analyze the reasons for the performance improvement of the gas-liquid mixed transmission pump before and after optimization, Figure 7 The pressure distribution of the pump impeller blades before and after optimization under five working conditions is compared, where the green dotted line represents the original pump and the blue solid line represents the optimized pump. The dimensionless pressure coefficient Cp is used, as shown in formula (7).

[0148]

[0149] Where p is the pressure on the impeller blades; U Ds1 is the circumferential velocity at the impeller inlet rim; ρ m is the density of the gas-liquid mixed phase. Compared with the pressure on the pressure surface of the pump impeller blades before optimization, the pressure on the pressure surface of the pump impeller blades after optimization has increased, and the pressure difference between the pressure surface and the suction surface has also increased, which increases the work capacity of the impeller and helps to improve the boosting capacity of the pump.

[0150] Influence of flow field changes: The pressure distribution on the impeller blades of the gas-liquid mixed flow pump may be affected by changes in the internal flow field. Figure 8 The velocity streamlines and turbulent kinetic energy distribution in the pump impeller and guide vane flow channel and the pressure distribution on the blades before and after optimization under five working conditions were compared. The changes in the pump impeller blades after optimization improved the flow structure in the flow channel, weakened the secondary flow phenomenon (including the distribution and range of the secondary flow), reduced the turbulent kinetic energy, and effectively improved the performance of the pump.

[0151] Influence of gas phase distribution: The geometric shape of the impeller blades of the gas-liquid mixed transmission pump affects the gas phase distribution in the flow channel. Fig. 9 The gas phase distribution inside the pump before and after optimization under different working conditions was compared. The impeller of the optimized pump prevented or reduced the accumulation of air pockets or air masses in the flow channel, and the air masses on the inlet side of the impeller rim and the outlet side of the hub were reduced or even disappeared.

[0152] Example 6

[0153] The single-stage gas-liquid mixed transmission pump with the main parameters of the initial model shown in Table 7 below was optimized by the method of the present invention, and a model sample was built according to the three-dimensional geometric model of the impeller of the optimized pump. The initial model of the pump mainly includes an inlet pipe, an impeller, a guide vane and an outlet pipe, wherein the number of impeller and guide vane blades are 4 and 7 respectively, and the length of the inlet pipe and the outlet pipe are 4 and 6 times the diameter of the impeller inlet rim respectively.

[0154] Table 7 Main parameters of gas-liquid mixed transmission pump

[0155]

[0156] Comparative Example

[0157] The unoptimized single-stage gas-liquid mixed transport pump in Example 6 was used.

[0158] The present invention builds a gas-liquid mixed pump visualization test bench based on the gas-liquid two-phase comprehensive test system of the Northwest Arid Area Ecological Water Conservancy State Key Laboratory. With other components unchanged, the model sample of Example 6 and the pump impeller of the comparative example are respectively used to carry out external characteristic tests, visualization tests and pressure pulsation tests under different working conditions.

[0159] Fig.10 The external characteristic parameters of the pumps before and after optimization under pure water conditions were compared. Compared with the pump before optimization, the head of the pump after optimization was basically improved under four speed conditions. The head under large flow conditions was relatively lower than that of the pump before optimization, and the slope of the head curve changed overall. In addition, under four speed conditions, the head of the pump after optimization was improved in all conditions except large flow conditions, and the efficiency was improved in large flow conditions.

[0160] Fig.11 The pressure rise values ​​(ΔP) of the pumps before and after optimization were compared under gas-liquid two-phase working conditions at three speeds of 900rpm, 1200rpm and 1500rpm (the flow conditions were all the best efficiency working points at the corresponding speeds). In general, the pressure rise values ​​of the pumps after optimization were basically improved under different speed conditions, and the pressure rise value was most significantly improved when the inlet gas content was high (IGVF ≥ 15%), which reduced the surge phenomenon and contributed to the stable operation under high inlet gas content, further verifying the applicability of the optimization scheme to gas-liquid mixed transmission pumps.

[0161] In summary, it can be seen from the above embodiments that after the optimization process of the present invention is used to carry out multi-objective optimization of the gas-liquid mixed flow pump, the three performance parameter values ​​of the pump are effectively improved compared with those before optimization. By comparing the pressure load distribution, flow channel velocity streamlines, turbulent kinetic energy and gas phase distribution on the pump impeller blades before and after optimization, it is further confirmed that the flow field in the pump is significantly improved after optimization, which shows that the optimization process adopted by the present invention is feasible and effective.

Claims

1. A multi-condition and multi-objective optimization design method for a gas-liquid mixed flow pump based on a three-dimensional inverse problem, characterized in that: The steps include: Step 1: Based on the three-dimensional inverse problem design method, the pump impeller is parametrically designed, the impeller blade load distribution parameter is used as the optimization parameter, and the value range of the optimization parameter is determined; Step 2: Based on the DOE experimental design of the sensitivity analysis module, optimal Latin hypercube sampling is performed within the value range of the optimization parameter to determine the sample space; Step 3: Design multiple working conditions, calculate the three performance parameters of pump pressure rise, efficiency and gas volume fraction in the guide vane for each sample in the sample space under each working condition, set the expected values ​​of the three performance parameters, calculate the Euclidean distance between the performance parameter value of each sample and its expected value, select the minimum Euclidean distance in each performance parameter, and use them as optimization targets respectively; Step 4: Based on the sample space of step 2, the MLS method is used to construct an approximate model MOP, and the model MOP is used to calculate the sensitivity of the sample corresponding to the optimization target obtained in step 3; Step 5: Use evolutionary algorithm to perform multi-objective optimization on the samples corresponding to the optimization target and their sensitivity. After multiple iterative calculations, the optimal solution of the optimization parameters is obtained.

2. The multi-condition and multi-objective optimization design method for a gas-liquid mixed flow pump based on a three-dimensional inverse problem according to claim 1 is characterized in that: The step 1 is specifically as follows: Step 1.1, the impeller blade equation constructed based on the three-dimensional inverse problem design method is equation (1), In formula (1) The load distribution of the impeller blades includes controlling the load distribution of the blade hub and the rim. The optimization parameters are selected according to the load distribution curve of the blade hub and the load distribution curve of the rim. At the same time, the stacking angle that determines the stacking position of the blade hub is The stacking angle of the blade rim Also used as optimization parameter; Step 1.2: Use the selected optimization parameters as input variables, use CFD software to calculate their values, and determine the value range of each input variable.

3. The multi-condition and multi-objective optimization design method for a gas-liquid mixed flow pump based on a three-dimensional inverse problem according to claim 2 is characterized in that: The load distribution curve of the blade hub and the load distribution curve of the rim described in step 1.1 are constructed by fitting the blade hub curve and the blade rim curve respectively using cubic spline curves to obtain the coordinates of the control points of each curve on the meridian XY plane, connecting the control points in sequence, and constructing the blade hub load curve and the blade rim load curve through the cubic spline interpolation algorithm.

4. The multi-condition and multi-objective optimization design method for a gas-liquid mixed flow pump based on a three-dimensional inverse problem according to claim 2 or 3, characterized in that: 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 horizontal coordinate x of the intersection point of the first parabola and the straight line hub1 , the horizontal coordinate x of the intersection point of the second parabola and the straight line hub2 as optimization parameters.

5. The multi-condition and multi-objective optimization design method for a gas-liquid mixed flow pump based on a three-dimensional inverse problem according to claim 2 or 3, characterized in that: 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 horizontal coordinate x of the intersection point of the first parabola and the straight line shr1 , the horizontal coordinate x of the intersection point of the second parabola and the straight line shr2 as optimization parameters.

6. The multi-condition and multi-objective optimization design method for a gas-liquid mixed flow pump based on a three-dimensional inverse problem according to claim 3 is characterized in that: The step 3 is specifically as follows: Step 3.1, design multiple working conditions. For any sample in the sample space, calculate the three performance parameters of pump pressure rise ΔP, efficiency η and gas volume fraction β in the guide vane under each working condition, as shown in formula (2): Step 3.2: define the expected values ​​of the three performance parameters of each pump, namely, pressure rise, efficiency and gas volume fraction in the guide vane, as ΔP O , η O and β O , calculate the three performance parameters ΔP of each sample point respectively X , η X and β X Its expected value ΔP O , η O and β O The Euclidean distance d between VP (ΔP X ,P O ), d Vη (Δη X ,η O ) and d Vβ (Δβ X ,β O ), as shown in formula (3), Step 3.3, select the minimum Euclidean distance of each performance parameter in the sample and use it as the optimization target, as shown in formula (4):

7. The multi-condition and multi-objective optimization design method for a gas-liquid mixed flow pump based on a three-dimensional inverse problem according to claim 6 is characterized in that: The multiple operating conditions of step 3.1 are: three inlet gas content operating conditions at the best efficiency point operating condition, and two non-best efficiency point operating conditions at one inlet gas content operating condition, and the inlet gas content ranges from 5-25%.

8. The multi-condition and multi-objective optimization design method for a gas-liquid mixed flow pump based on a three-dimensional inverse problem according to claim 1 is characterized in that: The evolutionary algorithm in step 5 adopts a combination algorithm of genetic algorithm and evolution strategy.

9. The multi-condition and multi-objective optimization design method for a gas-liquid mixed flow pump based on a three-dimensional inverse problem according to claim 8 is characterized in that: The evolutionary algorithm described in step 5 selects an initial population size of 32, a fitness method of Pareto-dominant, a selection 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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