A collaborative optimization method for a gas-liquid mixed transmission vane pump based on blade thickness control

Abstract

The present invention discloses a collaborative optimization method for a gas-liquid mixed transport vane pump based on blade thickness control, which belongs to the field of gas-liquid mixed transport technology. The method comprises: presetting the efficiency and gas-liquid distribution discreteness of the gas-liquid mixed transport vane pump as optimization targets; using the leading edge thickness, trailing edge thickness, maximum blade thickness and maximum blade thickness position of the impeller and guide vane to control the blade thickness distribution; determining the variation space of the blade thickness distribution control parameters, and constructing sample points of different blade thickness distributions; establishing a three-dimensional simulation model for mixed medium transport of a gas-liquid mixed transport vane pump; adopting the response surface method to construct a response surface model with the blade thickness distribution curve control parameters as input and the efficiency and gas-liquid distribution discreteness as output; adopting a multi-objective genetic algorithm to find the optimal value in the variation space of the blade thickness distribution control parameters to obtain the optimal thickness distribution control parameters. The present invention can effectively improve the operating efficiency of the mixed transport vane pump and improve the complex gas-liquid flow in the pump.

Description

Technical Field

[0001] The present invention relates to the technical field of gas-liquid mixed transportation, and in particular to a collaborative optimization method for a gas-liquid mixed transportation vane pump based on blade thickness control. Background Art

[0002] There are two main types of mixed-flow pumps: positive displacement and vane. Compared to positive displacement pumps, vane pumps offer advantages such as smaller size, higher flow rates, lower manufacturing precision requirements, reduced sensitivity to solid particles in the fluid medium, and easier operation and maintenance. Therefore, they are more widely used. While they can simultaneously transport two media with significantly different densities, the high-speed rotation of the impeller can easily cause gas-liquid separation within the pump, leading to flow separation and the formation of vortices. This results in low pump efficiency and complex, difficult-to-control gas-liquid flow.

[0003] A method combining numerical calculations and optimization algorithms is often used to improve the performance of initially designed pumps, but currently, neither the performance of mixed-flow pumps nor the transport capacity of mixed media meet expectations. This is partly because previous optimization targets have typically focused on performance indicators such as efficiency or head, without considering intrinsic factors such as the gas-liquid flow field. Furthermore, related studies have focused on optimizing only the impeller or guide vanes, without considering the synergistic effect between the impeller and guide vanes. Therefore, a collaborative optimization method for a gas-liquid mixed-flow vane pump based on blade thickness control is needed. This method, which considers the synergistic effect between the impeller and guide vanes and simultaneously optimizes both, can address the shortcomings of existing design methods that focus on optimizing a single component. Summary of the Invention

[0004] The purpose of this invention is to propose a collaborative optimization method for a gas-liquid mixed transmission vane pump based on blade thickness control, including

[0005] Step S1: presetting the gas-liquid mixed transmission vane pump efficiency η and the gas-liquid distribution dispersion D as optimization targets;

[0006] Step S2: selecting the maximum impeller blade thickness TH1, the maximum impeller blade thickness position L1, the impeller blade leading edge thickness LE1, the impeller blade trailing edge thickness TE1, the maximum guide vane blade thickness TH2, the maximum guide vane blade thickness position L2, the guide vane blade leading edge thickness LE2, and the guide vane blade trailing edge thickness TE2 as blade thickness distribution control parameters, and determining their variation ranges;

[0007] Step S3: constructing N sample points of different blade thickness distribution curve control parameters using an experimental design method;

[0008] Step S4: Calculate the cubic interpolation polynomial ax of the blade thickness distribution curve function P(x) on (0, 1) 3 +bx 2+cx+d;

[0009] Step S5: Take X coordinate points on the blade thickness distribution curve function P(x) and import them into the 3D model design platform to complete the 3D modeling of the impeller and guide vanes at different sample points; where X ≥ 13 and X is an odd number;

[0010] Step S6: establishing a three-dimensional simulation model for mixed medium transport of a gas-liquid mixed vane pump, which uses the blade thickness distribution curve control parameters of the gas-liquid mixed vane pump impeller and guide vanes as input and uses the gas-liquid mixed vane pump efficiency η and the gas-liquid distribution dispersion D as output;

[0011] Step S7: Based on the three-dimensional simulation model of mixed medium transportation of the gas-liquid mixed transmission vane pump obtained in step S6, using simulation software, obtain output results of the gas-liquid mixed transmission vane pump efficiency η and gas-liquid distribution dispersion D;

[0012] Step S8: Based on the sample points of step S3 and the output results of step S7, a response surface methodology is used to construct a response surface model with the blade thickness distribution curve control parameters of the impeller and guide vanes of the gas-liquid mixed vane pump as input and the gas-liquid mixed vane pump efficiency η and the gas-liquid distribution dispersion D as output;

[0013] Step S9: Based on the response surface model obtained in step S8, a multi-objective optimization algorithm is used to search for the optimal solution in the sample space to obtain a non-inferior solution set of the blade thickness distribution curve control parameters that enables the gas-liquid mixed transmission vane pump to operate efficiently;

[0014] Step S10: Use the non-inferior solution set of step S9 as a new sample point, repeat steps S4 to S7, and verify the accuracy of the non-inferior solution set; if the verification result meets the expectations, determine the blade thickness distribution curve control parameter combination that meets the efficient operation of the gas-liquid mixed transmission vane pump and the uniform distribution of gas and liquid in the pump as the final solution; if the verification result does not meet the expectations, perform a global sensitivity analysis on the blade thickness distribution control parameters, select the control parameters that have a great impact on the optimization target and expand their variation range, and repeat steps S1 to S10 until the verification result meets the expected requirements.

[0015] The efficiency η of the gas-liquid mixed transmission vane pump in step S1 is defined as formula (1):

[0016]

[0017] Where Q, M, ω, and ρ are the total volume flow rate, torque, rotational angular velocity, and mixture density, respectively;

[0018] The gas-liquid distribution dispersion D is the average value of the sum of the standard deviations of the gas volume fractions at the five blade heights of 0.1, 0.3, 0.5, 0.7, and 0.9, and is defined as formula (2):

[0019]

[0020] in:

[0021]

[0022] In the formula, n represents different leaf height surfaces, a g is the gas volume fraction, is the average gas volume fraction, A n is the corresponding leaf height area.

[0023] The maximum value of the impeller blade thickness TH1 in step S2 varies from (0.8 to 1.2) TH 10 The range of the maximum thickness position L1 of the impeller blade is (0.7~1.3)L 10 The range of the thickness of the leading edge of the impeller blade LE1 is (0.8~1.2)LE 10 The range of the thickness of the trailing edge of the impeller blade TE1 is (0.8~1.2)TE 10 The maximum thickness of the guide vane TH2 varies from (0.8 to 1.2)TH 20 The range of the maximum thickness of the guide vane position L2 is (0.7~1.3)L 20 The range of the thickness of the leading edge of the guide vane LE2 is (0.8~1.2)LE 20 The range of the thickness of the trailing edge of the guide vane TE2 is (0.8~1.2)TE 20 .

[0024] The three-dimensional simulation model of mixed medium transportation of the gas-liquid mixed transmission vane pump also includes an inlet pipe with a cross-sectional equivalent diameter of D1 and a length of L1 = (3 to 5) D1 and an outlet pipe with a cross-sectional equivalent diameter of D2 and a length of L2 = (5 to 10) D2.

[0025] In step S3 , N=k(m+2)(m+1) / 2, where m represents the number of blade thickness distribution control parameters, k is the expansion coefficient, and k≥1.1.

[0026] The selection of the X coordinate points in step S5 is as follows:

[0027] (0, P(0)), (L i , P(L i ))、(1,P(1))、 Where Z is a positive integer, i=1 or 2, 1 represents the impeller, and 2 represents the guide vane.

[0028] The beneficial effects of the present invention are:

[0029] The present invention uses the leading edge thickness, trailing edge thickness, maximum blade thickness, and location of maximum blade thickness of the impeller and guide vanes to precisely control blade thickness distribution. This approach simultaneously considers external factors such as mixed-flow pump performance and internal factors such as the gas-liquid flow field within the pump, significantly enhancing optimization reliability. Furthermore, the present invention effectively improves the operating efficiency of mixed-flow blades and enhances gas-liquid flow within the pump. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 Schematic diagram of the process of the collaborative optimization method of the gas-liquid mixed transmission vane pump based on blade thickness control of the present invention;

[0031] Figure 2(a) shows the impeller blade thickness distribution curve P(x);

[0032] Figure 2(b) shows the guide vane thickness distribution curve P(x);

[0033] Figure 3 It is a three-dimensional simulation model diagram of the present invention;

[0034] Figure 4 This is the optimization result diagram of the Pareto front;

[0035] Figure 5 (a) (b) are the distribution cloud diagrams of gas volume fraction in the impeller and guide vane of the mixed flow pump before and after optimization, respectively;

[0036] Figure 6 Schematic diagram of the method for generating the blade thickness distribution curve P(x). DETAILED DESCRIPTION

[0037] The present invention proposes a collaborative optimization method for a gas-liquid mixed transmission vane pump based on blade thickness control, which is further described below with reference to the accompanying drawings and specific embodiments.

[0038] Figure 1 The figure is a flow chart of the collaborative optimization method of the gas-liquid mixed transmission vane pump based on blade thickness control of the present invention; the method specifically includes the following steps:

[0039] S1: The optimization objectives are the pump efficiency under two-phase operation (IGVF = 10%) and the dispersion D of the gas distribution within the impeller and guide vane flow field. A higher efficiency η for a gas-liquid mixed flow vane pump reduces the energy loss. A lower dispersion D of the gas distribution within the impeller and guide vane flow field indicates a more uniform gas distribution within the pump, which in turn improves the gas-liquid flow state within the pump and makes it more suitable for gas-liquid two-phase flow.

[0040] The efficiency η of the gas-liquid mixed transmission vane pump is defined as:

[0041]

[0042] Where Q, M, ω, and ρ are the total volume flow rate, torque, rotational angular velocity, and mixture density, respectively;

[0043] The gas-liquid distribution dispersion D is the average value of the sum of the standard deviations of the gas volume fractions at the five blade heights of 0.1, 0.3, 0.5, 0.7, and 0.9, and is defined as:

[0044]

[0045] in:

[0046]

[0047] In the formula, n represents different leaf height surfaces, a g is the gas volume fraction, is the average gas volume fraction, A n is the corresponding leaf height area.

[0048] S2: Select the leading edge thickness LE of the impeller and guide vane i , blade trailing edge thickness TE i , maximum blade thickness TH i and the maximum thickness position of the blade L i is the blade thickness distribution control parameter and its variation range, where LE i0 TE i0 , TH i0 and L i0 is the initial value, and i=1 or 2, 1 represents the impeller, and 2 represents the guide vane.

[0049] Table 1 Variation range of thickness control parameters

[0050]

[0051] S3: Based on Table 1, a Latin Hypercube Experimental Design (LDE) method was used to construct N = k(m+2)(m+1) / 2 sample points with different blade thickness distribution control parameters, where m represents the number of blade thickness distribution control parameters, k is the expansion coefficient, and k ≥ 1.1. Here, N = 1.333 × (8+2) × (8+1) / 2 = 60 sample points:

[0052] Table 2 Sample points

[0053]

[0054]

[0055] S4: Based on the 60 sample points in Table 2, use computer program A to calculate the cubic interpolation polynomial P(x) of the blade thickness distribution curve function P(x) on (0, 1) = ax 3+bx 2 +cx+d; Figure 6 Schematic diagram of the method for generating the blade thickness distribution curve P(x).

[0056] The axial position of the blade is normalized, the normalized position of the leading edge of the blade is 0, and the normalized position of the trailing edge of the blade is 1; based on the normalized position of the blade and the control parameters of the blade thickness distribution curve, the three coordinates on the blade thickness distribution curve function P(x) are determined: (0, LE i )、(L im , TH i )、(1,TE i ), where (L i , TH i ) is the extreme point, so P'(L i )=0; Use computer program A to calculate the coefficients a, b, c, d that satisfy equations (1) to (4), and the blade thickness distribution curve function P(x)=ax can be obtained quickly and accurately. 3 +bx 2 +cx+d; Figure 2(a) is the impeller blade thickness distribution curve P(x); Figure 2(b) is the guide vane blade thickness distribution curve P(x);

[0057] eqn(1)=a*x1 3 +b*x1 2 +c*x1+d–y1=0

[0058] eqn(2)=a*x2 3 +b*x2 2 +c*x²+d–y²=0

[0059] eqn(3)=a*x3 3 +b*x3 2 +c*x3+d–y3=0

[0060] eqn(4)=3*a*x2 2 +2bx2+cx2–y2_prime=0

[0061] Where: (x1, y1), (x2, y2), (x3, y3) and (x2, y2_prime) correspond to (0, LE i )、(L i , TH i )、(1,TE i ) and (L i , P'(L i )).

[0062] S5: Take X coordinate points on the blade thickness distribution curve function P(x) and import them into the 3D model design platform to complete the 3D modeling of the impeller and guide vanes at different sample points; where X ≥ 13 and X is an odd number. Figure 3 This is a three-dimensional simulation model diagram of the present invention. The X coordinate points are selected as follows:

[0063] (0, P(0)), (L i , P(L i ))、(1,P(1))、 Where Z is a positive integer, i=1 or 2, 1 represents the impeller, and 2 represents the guide vane.

[0064] S6: Establish a three-dimensional simulation model for mixed medium transportation of a gas-liquid mixed vane pump with the blade thickness distribution curve control parameters of the impeller and guide vanes of the gas-liquid mixed vane pump as input and the efficiency η and gas-liquid distribution dispersion D of the gas-liquid mixed vane pump as output. This model also includes an inlet pipe with an equivalent cross-sectional diameter of D1 and a length of L1 = (3~5)D1 and an outlet pipe with an equivalent cross-sectional diameter of D2 and a length of L2 = (5~10)D2.

[0065] S7: Based on the obtained three-dimensional simulation model of mixed medium transportation of the gas-liquid mixed transmission vane pump, the output results of the efficiency and gas-liquid distribution discreteness of the gas-liquid mixed transmission vane pump are obtained by using simulation software.

[0066] S8: Based on the obtained sample points and their corresponding output results, the response surface methodology is used to construct a response surface model with the blade thickness distribution curve control parameters of the impeller and guide vanes of the gas-liquid mixed vane pump as input and the efficiency and gas-liquid distribution discreteness of the gas-liquid mixed vane pump as output.

[0067] S9: Based on the response surface model with the blade thickness distribution curve control parameters of the gas-liquid mixed vane pump impeller and guide vane as input and the efficiency and gas-liquid distribution dispersion of the gas-liquid mixed vane pump as output, the NSGA-Ⅱ multi-objective optimization algorithm was used to find the optimal solution in the sample space. The population size and genetic generation were both set to 100, the crossover probability was 0.9, the crossover distribution index was 10, and the variation distribution index was 20. A total of 10,000 gas-liquid mixed vane pump models were calculated during the optimization calculation process.

[0068] S10: A model with the best overall performance is selected from the Pareto solution set and verified by CFD calculations. Figure 4 The optimization result diagram of the Pareto front is shown in the figure. The calculation results show that the efficiency of the mixed flow pump after optimization has been greatly improved, which is 1.06 times that before optimization. Figure 5(a) (b) are the distribution cloud diagrams of the gas volume fraction in the impeller and guide vanes of the mixed flow pump before and after optimization (span = 0.5). Gas aggregation occurred near the suction surface of the impeller blades before and after optimization. This is because the density of the gas is relatively small, and the pressure difference between the front and back of the impeller blades causes the acceleration of the gas per unit volume to be relatively large, which in turn causes the gas to gather on the suction surface of the blades. However, the degree and range of gas aggregation in the original impeller and guide vanes are very large, while the degree and range of gas aggregation in the optimized impeller and guide vanes are very small, with only a small amount of gas gathering near the suction surface of the impeller outlet blades. At the same time, the degree of gas aggregation in the guide vanes after optimization is greatly reduced, making the flow smoother.

[0069] It can be seen that after completing the multi-objective collaborative optimization design considering the thickness of the impeller and guide vanes, the gas-liquid mixed transportation capacity of the mixed pump was significantly improved.

Claims

1. A collaborative optimization method for a gas-liquid mixed transmission vane pump based on blade thickness control, characterized by: include Step S1: presetting the gas-liquid mixed transmission vane pump efficiency η and the gas-liquid distribution dispersion D as optimization targets; Step S2: selecting the maximum impeller blade thickness TH1, the maximum impeller blade thickness position L1, the impeller blade leading edge thickness LE1, the impeller blade trailing edge thickness TE1, the maximum guide vane blade thickness TH2, the maximum guide vane blade thickness position L2, the guide vane blade leading edge thickness LE2, and the guide vane blade trailing edge thickness TE2 as blade thickness distribution control parameters, and determining their variation ranges; Step S3: constructing N sample points of different blade thickness distribution curve control parameters using an experimental design method; Step S4: Calculate the cubic interpolation polynomial ax of the blade thickness distribution curve function P(x) on (0, 1) 3 +bx 2 +cx+d; Step S5: Take X coordinate points on the blade thickness distribution curve function P(x) and import them into the 3D model design platform to complete the 3D modeling of the impeller and guide vanes at different sample points; where X ≥ 13 and X is an odd number; Step S6: establishing a three-dimensional simulation model for mixed medium transport of a gas-liquid mixed vane pump, which uses the blade thickness distribution curve control parameters of the gas-liquid mixed vane pump impeller and guide vanes as input and uses the gas-liquid mixed vane pump efficiency η and the gas-liquid distribution dispersion D as output; Step S7: Based on the three-dimensional simulation model of mixed medium transportation of the gas-liquid mixed transmission vane pump obtained in step S6, using simulation software, obtain output results of the gas-liquid mixed transmission vane pump efficiency η and gas-liquid distribution dispersion D; Step S8: Based on the sample points of step S3 and the output results of step S7, a response surface methodology is used to construct a response surface model with the blade thickness distribution curve control parameters of the impeller and guide vanes of the gas-liquid mixed vane pump as input and the gas-liquid mixed vane pump efficiency η and the gas-liquid distribution dispersion D as output; Step S9: Based on the response surface model obtained in step S8, a multi-objective optimization algorithm is used to search for the optimal solution in the sample space to obtain a non-inferior solution set of the blade thickness distribution curve control parameters that enables the gas-liquid mixed transmission vane pump to operate efficiently; Step S10: Use the non-inferior solution set of step S9 as a new sample point, repeat steps S4 to S7, and verify the accuracy of the non-inferior solution set; if the verification result meets the expectations, determine the blade thickness distribution curve control parameter combination that meets the efficient operation of the gas-liquid mixed transmission vane pump and the uniform distribution of gas and liquid in the pump as the final solution; if the verification result does not meet the expectations, perform a global sensitivity analysis on the blade thickness distribution control parameters, select the control parameters that have a great impact on the optimization target and expand their variation range, and repeat steps S1 to S10 until the verification result meets the expected requirements.

2. The collaborative optimization method for a gas-liquid mixed transmission vane pump based on blade thickness control according to claim 1 is characterized in that: The efficiency η of the gas-liquid mixed transmission vane pump in step S1 is defined as formula (1): Where Q, M, ω, and ρ are the total volume flow rate, torque, rotational angular velocity, and mixture density, respectively; The gas-liquid distribution dispersion D is the average value of the sum of the standard deviations of the gas volume fractions at the five blade heights of 0.1, 0.3, 0.5, 0.7, and 0.9, and is defined as formula (2): in: In the formula, n represents different leaf height surfaces, a g is the gas volume fraction, is the average gas volume fraction, A n is the corresponding leaf height area.

3. The collaborative optimization method for a gas-liquid mixed transmission vane pump based on blade thickness control according to claim 1 is characterized in that: The maximum value TH1 of the impeller blade thickness in step S2 varies within a range of (0.8 to 1.2) TH 10 The range of the maximum thickness position L1 of the impeller blade is (0.7~1.3)L 10 The range of the thickness of the leading edge of the impeller blade LE1 is (0.8~1.2)LE 10 The range of the thickness of the trailing edge of the impeller blade TE1 is (0.8~1.2)TE 10 The maximum thickness of the guide vane TH2 varies from (0.8 to 1.2)TH 20 The range of the maximum thickness of the guide vane position L2 is (0.7~1.3)L 20 The range of the thickness of the leading edge of the guide vane LE2 is (0.8~1.2)LE 20 The range of the thickness of the trailing edge of the guide vane TE2 is (0.8~1.2)TE 20 .

4. The collaborative optimization method for a gas-liquid mixed transmission vane pump based on blade thickness control according to claim 1 is characterized in that: The three-dimensional simulation model of mixed medium transportation of the gas-liquid mixed vane pump also includes an inlet pipe with a cross-sectional equivalent diameter of D1 and a length of L1 = (3 to 5) D1 and an outlet pipe with a cross-sectional equivalent diameter of D2 and a length of L2 = (5 to 10) D2.

5. The collaborative optimization method for a gas-liquid mixed transmission vane pump based on blade thickness control according to claim 1 is characterized in that: In step S3, N=k(m+2)(m+1) / 2, wherein m represents the number of blade thickness distribution control parameters, k is the expansion coefficient, and k≥1.

1.

6. The collaborative optimization method for a gas-liquid mixed transmission vane pump based on blade thickness control according to claim 1, characterized in that: The selection of the X coordinate points in step S5 is as follows: (0, P(0)), (L i , P(L i ))、(1,P(1))、 Where Z is a positive integer, i=1 or 2, 1 represents the impeller, and 2 represents the guide vane.

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