Gas-liquid mixed transportation vane pump collaborative optimization method based on vane thickness control

Abstract

The invention discloses a collaborative optimization method for a gas-liquid mixed transportation vane pump based on vane thickness control, and belongs to the technical field of gas-liquid mixed transportation. Comprising the following steps: presetting the efficiency and the gas-liquid distribution dispersion of the gas-liquid mixed transportation vane pump as optimization targets; the blade thickness distribution is controlled by adopting the blade front edge thickness, the blade tail edge thickness, the blade maximum thickness and the blade maximum thickness position of the impeller and the guide blade; determining a change space of blade thickness distribution control parameters, and constructing sample points of different blade thickness distributions; establishing a mixed medium transportation three-dimensional simulation model of the gas-liquid mixed transportation vane pump; a response surface method is adopted, and a response surface model with the blade thickness distribution curve control parameters as input and the efficiency and the gas-liquid distribution dispersion as output is constructed; and optimizing in the variation space of the blade thickness distribution control parameters by adopting a multi-target genetic algorithm to obtain the optimal thickness distribution control parameters. The operation efficiency of the mixed transportation vane pump can be effectively improved, and complex gas-liquid flow in the pump is improved.

Description

Technical Field

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

[0002] There are two main types of mixed flow pumps: volumetric and vane. Compared with the volumetric type, the vane type gas-liquid mixed flow vane pump has the advantages of small size, large delivery flow, low manufacturing precision requirements, low sensitivity to solid particles in the fluid medium, and easy use and maintenance. Therefore, the vane type gas-liquid mixed flow vane pump is more widely used. The vane type gas-liquid mixed flow vane pump can simultaneously transport two media with very different densities, but under the action of the high-speed rotation of the impeller, gas-liquid separation is easy to occur in the pump, which promotes flow separation and the formation of vortex, resulting in low efficiency of this type of pump, and the gas-liquid flow in the pump is very complex and difficult to control.

[0003] The combination of numerical calculation and optimization algorithm is usually used to improve the performance of the initial design pump, but the performance of the mixed pump and the conveying capacity of the mixed medium have not met the expected requirements. On the one hand, the previous optimization targets are usually performance indicators such as efficiency or head, without considering internal factors such as gas-liquid flow field; on the other hand, the optimization objects of related studies are only impellers or guide vanes, without considering the synergy between impellers and guide vanes. Therefore, a collaborative optimization method for gas-liquid mixed vane pump based on blade thickness control is needed, which takes into account the synergy between impellers and guide vanes, and optimizes both impellers and guide vanes at the same time to make up for the deficiency of focusing on the optimization design of a single component in the existing design method. Summary of the invention

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

[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 value of the impeller blade thickness TH1, the maximum value position of the impeller blade thickness L1, the leading edge thickness of the impeller blade LE1, the trailing edge thickness of the impeller blade TE1, the maximum value of the guide vane blade thickness TH2, the maximum value position of the guide vane blade thickness L2, the leading edge thickness of the guide vane blade LE2, and the trailing edge thickness of the guide vane blade 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 by 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 three-dimensional model design platform to complete the three-dimensional modeling of the impeller and guide vane at different sample points; where X≥13, and X is an odd number;

[0010] Step S6: establishing a three-dimensional simulation model of mixed medium transport of a gas-liquid mixed transport vane pump with the blade thickness distribution curve control parameters of the impeller and guide vanes of the gas-liquid mixed transport vane pump as input and the gas-liquid mixed transport 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 transport vane pump obtained in step S6, using simulation software, obtain the output results of the gas-liquid mixed transport 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 method is used to construct a response surface model with the blade thickness distribution curve control parameters of the impeller and guide vane of the gas-liquid mixed flow vane pump as input and the gas-liquid mixed flow 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 find the optimum 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 satisfies 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, 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 fraction at five blade heights of 0.1, 0.3, 0.5, 0.7, and 0.9, which is defined as formula (2):

[0019]

[0020] in:

[0021]

[0022] In the formula, n represents different leaf heights, 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 within a range of (0.8 to 1.2)TH 10 ; The range of the maximum value of the impeller blade thickness position L1 is (0.7~1.3)L 10 ; The range of the impeller blade leading edge thickness 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 guide vane thickness TH2 varies in the range of (0.8~1.2)TH 20 ; The range of the maximum thickness position of the guide vane L2 is (0.7~1.3)L 20 ; The range of the leading edge thickness LE2 of the guide vane 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=(3-5)D1 and an outlet pipe with a cross-sectional equivalent diameter of D2 and a length of L2=(5-10)D2.

[0025] 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.

[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 thickness and maximum thickness position of the impeller and the guide vane to control the thickness distribution of the blade, thereby achieving precise control of the thickness distribution of the blade; while taking into account external factors such as the performance of the mixed pump and internal factors such as the gas-liquid flow field in the pump as targets, the reliability of optimization is greatly improved. In addition, the present invention can also effectively improve the operating efficiency of the mixed pump blades and improve the gas-liquid flow in the pump. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It 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;

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

[0032] Figure 2(b) is the guide vane blade 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) and (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 will be further described below in conjunction with 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 comprises the following steps:

[0039] S1: The optimization target is to select the pump efficiency under two-phase working condition (IGVF = 10%) and the distribution dispersion D of the gas in the impeller and guide vane flow field for optimization design. The higher the efficiency η of the gas-liquid mixed vane pump, the smaller the proportion of energy loss; and the smaller the gas distribution dispersion D in the impeller and guide vane flow field, the more uniform the gas distribution in the pump, indicating that the gas-liquid flow state in the pump is better, and it is more suitable for conveying 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, 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 heights, 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: According to Table 1, Latin hypercube experimental design method is used to construct N = k (m + 2) (m + 1) / 2 sample points of different blade thickness distribution curve 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; by using computer program A to calculate coefficients a, b, c, d satisfying equations (1)~(4), 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 three-dimensional model design platform to complete the three-dimensional modeling of the impeller and guide vane 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 selection of the X coordinate points is 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 of 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 a cross-sectional equivalent diameter of D1 and a length of L1 = (3~5)D1 and an outlet pipe with a cross-sectional equivalent 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 transport vane pump, the output results of the efficiency and gas-liquid distribution discreteness of the gas-liquid mixed transport vane pump are obtained by using simulation software.

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

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

[0068] S10: A model with the best comprehensive performance is selected from the Pareto solution set and verified by CFD calculation. Figure 4 This is the optimization result diagram of the Pareto front. From the calculation results, it can be seen 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 in 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 sides 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 the guide vane, 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 in that: 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 value of the impeller blade thickness TH1, the maximum value position of the impeller blade thickness L1, the leading edge thickness of the impeller blade LE1, the trailing edge thickness of the impeller blade TE1, the maximum value of the guide vane blade thickness TH2, the maximum value position of the guide vane blade thickness L2, the leading edge thickness of the guide vane blade LE2, and the trailing edge thickness of the guide vane blade 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 by 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 three-dimensional model design platform to complete the three-dimensional modeling of the impeller and guide vane at different sample points; where X≥13, and X is an odd number; Step S6: establishing a three-dimensional simulation model of mixed medium transport of a gas-liquid mixed transport vane pump with the blade thickness distribution curve control parameters of the impeller and guide vanes of the gas-liquid mixed transport vane pump as input and the gas-liquid mixed transport 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 transport vane pump obtained in step S6, using simulation software, obtain the output results of the gas-liquid mixed transport 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 method is used to construct a response surface model with the blade thickness distribution curve control parameters of the impeller and guide vane of the gas-liquid mixed flow vane pump as input and the gas-liquid mixed flow 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 find the optimum 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 satisfies 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 of 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 transport vane pump in step S1 is defined as formula (1): Where Q, M, ω and ρ are the total volume flow, 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 fraction at five blade heights of 0.1, 0.3, 0.5, 0.7, and 0.9, which is defined as formula (2): in: In the formula, n represents different leaf heights, 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 value of the impeller blade thickness position L1 is (0.7~1.3)L 10 ; The range of the impeller blade leading edge thickness 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 guide vane thickness TH2 varies in the range of (0.8~1.2)TH 20 ; The range of the maximum thickness position of the guide vane L2 is (0.7~1.3)L 20 ; The range of the leading edge thickness 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 transmission vane pump also includes an inlet pipe with a cross-sectional equivalent diameter of D1 and a length of L1=(3-5)D1 and an outlet pipe with a cross-sectional equivalent diameter of D2 and a length of L2=(5-10)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 is 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.

Images