Multi-objective optimization method for liquid-ring type combined pump

Abstract

Disclosed in the present invention is a multi-objective optimization method for a liquid-ring combined pump. By taking a head coefficient of a main centrifugal pump and the stress of an impeller as co

Description

The present disclosure belongs to the field of centrifugal pump design, and in particular relates to a multi-objective optimization method for a liquid-ring type combined pump. BACKGROUND Liquid-ring type combined pump is a self-priming pump, which is composed of a main centrifugal pump and a liquid-ring pump. It belongs to a special pump. The impeller of the main centrifugal pump and the liquid-ring impeller of the liquid-ring pump are coaxially arranged. The liquid-ring impeller of the liquid-ring pump is eccentrically placed with its annular pump cavity. When the liquid-ring impeller rotates, it will drive the liquid in the pump cavity to rotate at high rotational speed, forming a liquid-ring concentric with the pump cavity. On both axial sides of the liquid-ring impeller, there are crescent-shaped air chambers. One side serves as the low-pressure zone, where the crescent gradually expands as it rotates, while the other side is the high-pressure zone, where the crescent gradually contracts. The low-pressure zone acts as the suction area of the liquid-ring pump and is connected to the inlet of the main centrifugal pump at the front. The high-pressure zone, on the other hand, is the exhaust area of the liquid-ring pump, which vents gases to the outside atmosphere. When the liquid-ring type combined pump is turned on, the motor drives the liquid-ring impeller and the impeller to rotate at high speed. The liquid-ring pump evacuates the gases from within the main centrifugal pump and the inlet piping. There is a check valve at the outlet of the main centrifugal pump impeller. When the outlet pressure of the main centrifugal pump exceeds the spring pressure of the check valve, the check valve opens, completing the self-priming process of the liquid-ring type combined pump. The liquid-ring type combined pump boasts a simple structure, small size, and lightweight design, making it easy to install and maintain. It can adapt to various working environments and requirements, such as ground and high altitude, and has become one of the most ideal self-priming pump structures in aviation fuel systems. However, ensuring that the original performance parameters of the liquid-ring type combined pump remain unchanged while improving its selfpriming performance has become a new challenge. Therefore, there is an urgent need to propose a multi-objective optimization method for the liquid-ring type combined pump that considers both efficiency and self-priming performance. So far, there are no reports about multi-objective optimization methods for liquid-ring type combined pumps. SUMMARY Aiming at the shortcomings in the prior art, the present disclosure provides a multi-objective optimization method for the liquid-ring type combined pump, so as to reduce the weight of the combined pump and improve self-priming performance while satisfying the efficiency and blade strength of the combined pump. In order to achieve the above objectives, the following technical solutions are adopted: A multi-objective optimization method for liquid-ring type combined pumps is proposed. The liquid-ring type combined pump is a self-priming pump composed of a main centrifugal pump and a liquid-ring pump. The impeller of the main centrifugal pump and the liquid-ring impeller of the liquid-ring pump are coaxial. The multi-objective optimization method for liquid-ring type combined pumps includes the following steps: step 1: with a head coefficient and an impeller stress of the main centrifugal pump as constraints, a maximum hydraulic efficiency, a minimum impeller deformation and a lightest weight of the main centrifugal pump as optimum objectives, performing multi-objective optimization on the impeller of the main centrifugal pump in the liquid-ring type combined pump based on an intelligent optimization algorithm; step 2: based on optimization results of the main centrifugal pump, with self-priming time and shaft power of the liquid-ring pump as evaluation indicators, and main geometric parameters of the liquid-ring impeller, such as a blade number, a width, a blade outlet angle, an eccentricity and a hub inclination angle as test factors, establishing a regression model between the main geometric parameters of the liquid-ring impeller and the self-priming time and the shaft power of the liquidring pump is, to perform the multi-objective optimization on the liquid-ring impeller based on Genetic Algorithms; step 3: building a test bench for the liquid-ring type combined pump to experimentally verify feasibility of the multi-objective optimization method for the liquid-ring type combined pump; and step 4: taking thermodynamic effects, rotational motion, and geometric characteristics of the centrifugal pump into consideration, improving a Zwart-Gerber-Belamri cavitation model, known as a Z-G-B cavitation model, performing numerical calculations to analyze a cavitation flow inside the liquid-ring type combined pump before and after the multi-objective optimization, and analyzing cavitation characteristic curves, a cavitation volume fraction, and pressure pulsation characteristics of the liquid-ring type combined pump before and after the multi-objective optimization. Preferably, in the step 1, steps for multi-objective optimization of the main centrifugal pump impeller of the liquid-ring type combined pump are as follows: (1) the parametric modeling of the impeller of the main centrifugal pump in the liquid-ring type combined pump is achieved based on the five-point quartic Bezier curve, basing on ANSYS optiSLang, a multi-objective optimization design platform for the impeller of the main centrifugal pump in the liquid-ring type combined pump is established; (2) the multi-objective optimization mathematical model is constructed for the impeller of the main centrifugal pump in the liquid-ring type combined pump, the constructing of the model using the 10 blades angle control points and the 10 blades thickness control points from the five-point quartic Bezier curve as the design variables, the constraining of the model by the head coefficient and the impeller stress of the main centrifugal pump, the optimizing objectives including maximizing the hydraulic efficiency of the main centrifugal pump, minimizing the deformation of the impeller, and achieving the lightest weight; (3) the sample space for the multi-objective optimization design of the impeller of the main centrifugal pump in the liquid-ring type combined pump is generated using the optimal Latin hypercube sampling method; and (4) the global optimization solution with intelligent optimization algorithm is sought for the multi-objective optimization mathematical model of the impeller of the main centrifugal pump in the liquid-ring type combined pump, which leads to the acquisition of an optimal solution set for the impeller optimization. Preferably, the constraint on the head coefficient is that the fluctuation of the head coefficient ti) C of the main centrifugal pump is limited to within a range of 3%, that is —■—- X 100% <3% , where ip0 represents the head coefficient of the main centrifugal pump before optimization, tp(x) represents the head coefficient of the main centrifugal pump after optimization. Preferably, the constraint on the impeller stress is that the maximum stress <rmax experienced by the impeller of the main centrifugal pump after optimization is lower than or equal to the maximum stress Comax experienced by the impeller of the main centrifugal pump before optimization, that is amax <<TOmax- Preferably, the intelligent optimization algorithm is adaptive simulated annealing algorithm, or genetic algorithm, or ant colony algorithm, or particle swarm algorithm. Preferably, in the step 2, steps for multi-objective optimization of the liquid-ring impeller in the liquid-ring pump are as follows: (1) based on the optimization results of the main centrifugal pump, an orthogonal experiment is conducted on the liquid-ring impeller of the liquid-ring pump, using self-priming time and shaft power as evaluation indicators, the considering of the main geometric parameters of the liquid-ring impeller, including the blade number, the width, the outlet angle of the blades, the eccentricity, and the hub inclination angle, as the experimental factors, and the determining of the impact of each experimental factor on the evaluation indicators is achieved through the range analysis and the variance analysis; (2) using orthogonal polynomial regression analysis, a regression model is determined to establish the relationship between the main geometric parameters of the liquid-ring impeller and the self-priming time and shaft power of the liquid-ring pump; and (3) the regression model of self-priming time and shaft power was optimized by genetic algorithm, and the optimal structure of liquid-ring impeller was determined. Preferably, in the step 3, the steps to experimentally verify the feasibility of multi-objective optimization method for liquid-ring type combined pump are as follows: (1) a closed test bench for the liquid-ring type combined pump is built, the test bench being capable of simulating the performance and the cavitation tests of the pump under both the ground and the high-altitude conditions, the aim of the test bench being to capture the key parameters such as the flow rate, the head, the efficiency, the power, the net positive suction head (NPSHr), and the pulsating pressure of the liquid-ring type combined pump; (2) the using of an electronic scale is employed for the measuring of the weight of the impeller of the main centrifugal pump in the liquid-ring type combined pump, the comparing and analyzing of the weight of the impeller of the main centrifugal pump before and after the optimization being performed; (3) the measuring of the head, the efficiency, the power, the outlet pulsating pressure, and the self-priming time of the liquid-ring type combined pump under the rated flow rate is achieved experimentally, the measuring of the net positive suction head (NPSHr) of the liquid-ring type combined pump under the rated flow rate being performed by the vacuum pump, the analyzing of the head coefficient, the efficiency, the power, the average outlet pulsating pressure, the net positive suction head (NPSHr), and the self-priming time of the liquid-ring type combined pump before and after the optimization under the rated flow being conducted in order to verify the feasibility of the multi-objective optimization method of the liquid-ring type combined pump; Preferably, in the step 4, the steps to improved Z-G-B model are as follows: (1) taking into account the rotational motion and geometric characteristics of the centrifugal pump, a formula for calculating the bubble diameter Rb is proposed, the formula being Rb = o.ooisc ,pin a-i / 3 wherejn f is the coefficient of constant term, which is obtained by fitting the visualization test data of centrifugal pump, z the blade number of the main centrifugal pump impeller, k is the turbulent kinetic energy, pi is the liquid phase density, n is the rotational speed of the liquidring type combination pump; (2) considering thermodynamic effect, improving Z-G-B cavitation model, the improved Z-G-B cavitation model of evaporation source term m+ expression and condensation source term ni~ expression is: = q 3(V-Op)pp , 12 Pv-P PlCpl'l~ai(T<x>~T'K (p<p ) evap Rb Pl PvLev' / t J 1 m - Gcond Rb ) (P>PV) wherein Cevap is the evaporation coefficient; av is the volume fraction of the vapor phase; pv is the density of the gas phase; Pv is the pressure in the bubble (assumed to be the saturated vapor pressure at the temperature of the operating medium in the pump); P is the liquid pressure around the bubble; Cpi is the specific heat at constant pressure of the liquid phase; at is the thermal diffusion of liquid; ai=XilpiCpr, fa is the thermal conductivity of the liquid phase; t is any time; is the far-field temperature; T is the temperature at any time t, Lev is the latent heat of vaporization; Coond is the condensation coefficient; (3) the parameters of physical properties in the improved Z-G-B cavitation model are fitted as a function of temperature by the least square method; and (4) the embedding of the improved Z-G-B cavitation model into the CFX is achieved by using the CFX expression language, the fitting of the thermal conductivity zv, the specific heat capacity at the constant pressure Cpv, and other parameters that were not comprised in the formula and also varied with the temperature being done as the temperature functions, and the inputting of these into the corresponding positions of the CFX pre-processing being performed. The present disclosure has the following advantages. (1) The present disclosure provides a multi-objective optimization method for the liquid-ring type combination pump, which realizes meeting the efficiency and blade strength, reduces the weight of the liquid-ring type combination pump and improves its self-priming performance. (2) The Z-G-B cavitation model developed in the present disclosure, which considers the thermodynamic effect, and the rotational motion and geometric characteristics of the centrifugal pump, improves the calculation accuracy of the cavitation flow in the liquid-ring type combined pump. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a flowchart of a multi-objective optimization method for liquid-ring type combined pump; FIG. 2 is calculation model of flow field for a liquid-ring type combined pump in an embodiment; FIG. 3 is the control points for the impeller profile of the main centrifugal pump in the liquidring type combined pump in an embodiment; FIG. 4 is the initialization state diagram for the self-priming calculation of the liquid-ring combined pump in an embodiment; FIG. 5 is schematic diagram of a closed test bench for the liquid-ring type combined pump in an embodiment; and FIG. 6 is cavitation characteristic curves of the liquid-ring type combined pump before and after optimization under rated flow rate in an embodiment. In the drawings: 1-Liquid-ring type combination pump, 2-Separator, 3-Controller, 4-Valve 1, 5-Vacuum pump, 6-Valve 2, 7-Flow meter, 8-Electric regulating valve, 9-Thermometer, 1 O-Level gauge, 11-Outlet pressure sensor, 12-Outlet pressure pulsation sensor. DETAILED DESCRIPTION OF THE EMBODIMENTS The present disclosure will be further described below in conjunction with the drawings and specific embodiments, but the protection scope of the present disclosure is not limited thereto. Embodiment 1 A multi-objective optimization method for a liquid-ring type combined pump is characterized by the fact that the liquid-ring type combined pump is a self-primmg pump composed of a main centrifugal pump and a liquid-ring pump. The impeller of the main centrifugal pump and the liquidring impeller of the liquid-ring pump are coaxial. In this embodiment, calculation model of flow field for a liquid-ring type combined pump is shown in FIG. 2. The multi-objective optimization method for the liquid-ring type combined pump includes the following steps: 1 Multi-objective optimization of impeller of main centrifugal pump for the liquid-ring type combined pump (1) Parametric modeling of the impeller of the main centrifugal pump in the liquid-ring type combined pump is achieved based on the five-point quartic Bezier curve. And based on ANSYS optiSLang, a multi-objective optimization design platform for the impeller of the main centrifugal pump in the liquid-ring type combined pump is established. (2) A multi-objective optimization mathematical model is constructed for the impeller of the main centrifugal pump in the liquid-ring type combined pump. This model uses 10 blades angle control points (shown in TABLE 1) and 10 blades thickness control points (shown in TABLE 2) from the five-point quartic Bezier curve as design variables (shown in FIG. 3). The constraints of the model are the head coefficient and the impeller stress of the main centrifugal pump. The optimization objectives are to maximize the hydraulic efficiency of the main centrifugal pump, minimize the deformation of the impeller, and achieve the lightest weight. TABLE 1 Parameters of blades angle control points Angle control point SAI SA2 SA3 SA4 SA5 Value / 0 174.94 145.88 123.04 100.83 87.69 Lower limit 169.44 140.88 118.04 95.83 82.69 Upper limit 179.44 150.88 128.04 105.83 92.69 Angle control point HAI HA2 HA3 HA4 HA5 Value / 0 172.54 146.01 132.07 105.82 77.18 Lower limit 167.54 141.01 127.07 100.82 72.18 Upper limit 177.54 151.01 137.07 110.82 79.18 TABLE 2 Parameters of blades thickness control points Thickness control point STI ST2 ST3 ST4 ST5 Value / mm 1.451 1.584 1.491 1.533 1.597 Lower limit 1.351 1.484 1.391 1.433 1.497 Upper limit 1.551 1.685 1.591 1.633 1.697 Thickness control point HT1 HT2 UTT nlj HT4 HT5 Value / mm 1.911 1.956 1.897 1.837 1.889 Lower limit 1.811 1.856 1.797 1.737 1.789 Upper limit 2.011 2.056 1.997 1.937 1.989 The constraint on the head coefficient is that the fluctuation of the head coefficient of the main centrifugal pump is limited to within a range of 3%, that is —;.............— x 100% <3% , where Wo ip0 represents the head coefficient of the main centrifugal pump before optimization, iXx) represents the head coefficient of the main centrifugal pump after optimization. The constraint on the impeller stress is that the maximum stress omax experienced by the impeller of the main centrifugal pump after optimization is lower than or equal to the maximum stress o0max experienced by the impeller of the main centrifugal pump before optimization, that is amax — max' (3) A sample space for the multi-objective optimization design of the impeller of the main centrifugal pump in the liquid-ring type combined pump is generated using the optimal Latin hypercube sampling method. (4) A global optimization solution with intelligent optimization algorithm is sought for the multiobjective optimization mathematical model of the impeller of the main centrifugal pump in the liquid-ring type combined pump, which leads to the acquisition of an optimal solution set for the impeller optimization. TABLES 3 and 4 present a comparison of the angle control point parameters and thickness control point parameters before and after optimization, respectively. TABLE 5 provides a comparison of the performance of the main centrifugal pump before and after optimization. TABLE 3 Comparison of blades angle control points Angle control point SAI SA2 SA3 SA4 SA5 HAI HA2 HA3 HA4 HA5 Original model / ° 174.94 145.88 123.04 100.83 87.69 172.54 146.01 132.07 105.82 77.18 Optimal model / ° 170.92 145.15 124.64 100.73 82.35 178.21 148.21 122.69 108.26 77.72 TABLE 4 Comparison of blades thickness control points Thickness control point STI ST2 ST3 ST4 ST5 HT1 HT2 HT3 HT4 HT5 Original model / mm 1.451 1.584 1.491 1.533 1.597 1.911 1.956 1.897 1.837 1.889 Optimal 1.321 1.604 1.504 1.502 1.568 2.031 1.790 2.050 1.992 1.986 model / mm 3 1 3 8 2 5 1 1 7 6 TABLE 5 Comparison of the performance of the main centrifugal pump before and after optimization Performance parameter Head coefficient Hydraulic efficiency / % Impeller stress / MPa Impeller defonnation / mm Original model 0.657 60.52 125.09 0.177 Optimal model 0.651 64.92 87.87 0.1015 2 Multi-objective optimization of liquid-ring impeller of liquid-ring pump for the liquid-ring type combined pump (1) Based on the optimization results of the main centrifugal pump, an orthogonal experiment is conducted on the liquid-ring impeller of the liquid-ring pump, using self-priming time and shaft power as evaluation indicators. The main geometric parameters of the liquid-ring impeller, including the blade number, width, outlet angle of the blades, eccentricity, and hub angle, are considered as experimental factors. To ensure the accuracy of the calculation results, a monitoring surface is set at the outlet of the main centrifugal pump to monitor the outlet gas content. The self-priming process is considered complete when the gas content at the outlet of the main centrifugal pump is less than 0.2%. FIG. 4 gives the initialization state diagram for the self-priming calculation of the liquid-ring combined pump in an embodiment. Based on the range analysis and variance analysis, the influence of various test factors on the self-priming time is ranked as follows: blade number >width >eccentricity >outlet angle of the blades >hub inclination angle. For the influence on shaft power based on range analysis, the ranking is: width >eccentricity >blade number >outlet angle of the blades >hub inclination angle. However, the ranking for the influence on shaft power is: width >outlet angle of the blades >blade number >eccentricity >hub inclination angle. It can be seen from this that the hub inclination angle is a secondary influencing factor for both self-priming time and shaft power. Therefore, only blade number, width, outlet angle of the blades, and eccentricity are considered in subsequent studies. (2) Using orthogonal polynomial regression analysis, a regression model is determined to establish the relationship between blade number of the liquid-ring impeller, width of the liquid-ring impeller, outlet angle of the blades of the liquid-ring impeller, eccentricity of the liquid-ring impeller and the self-priming time and shaft power of the liquid-ring pump. (3) The regression model of self-priming time and shaft power was optimized by genetic algorithm, and the optimal structure of liquid-ring impeller was determined. The optimal structural parameters of the liquid ring wheel are as follows: blade number of the liquid-ring impeller is 10, width of the liquid-ring impeller is 19.1 mm, outlet angle of the blades of the liquid-ring impeller is 155°, and eccentricity of the liquid-ring impeller is 3.6 mm. The results of numerical calculations show that under rated flow rate, the self-priming time of the optimized liquid-ring type combined pump is reduced by 0.20 s compared to the original pump, and the shaft power of the optimized liquid-ring type combined pump is also reduced by 1.57 kW. The feasibility of multi-objective optimization method for liquid-ring type combined pump is verified by experiments (1) A closed test bench for the liquid-ring type combined pump (shown in FIG. 5) is built, which could simulate the performance and cavitation tests of the pump under both ground and high-altitude conditions. This test bench aims to capture key parameters such as flow rate, head, efficiency, power, net positive suction head (NPSHr), and pulsating pressure of the liquid-ring type combined pump. (2) Using an electronic scale, the weight of the impeller of the main centrifugal pump in the liquid-ring type combined pump is measured. And the weight of impeller of main centrifugal pump before and after optimization is compared and analyzed. The results show that the weights of the main centrifugal pump impeller before and after optimization are 131.24 g and 123.79 g, respectively. (3) The head, efficiency, power, outlet pulsating pressure and self-priming time of the liquidring type combined pump under rated flow rate are experimentally measured, and the net positive suction head (NPSHr) of the liquid-ring type combined pump under rated flow rate is measured by vacuum pump. At the same time, the head coefficient, efficiency, power, average outlet pulsating pressure, net positive suction head (NPSHr) and self-priming time of the liquid-ring type combined pump before and after optimization under rated flow were analyzed. TABLE 6 shows the performance comparison of the liquid-ring combined type pump before and after optimization. It can be seen that the efficiency of the liquid-ring type combined pump has increased by 2.55 percentage points, the power has decreased by 5.26%, the average value of outlet pulsation pressure has decreased by 4.29%, NPSHr has decreased by 9.59%, and the self-priming time has decreased by 6.52%. Therefore, the multi-objective optimization method for the liquid-ring type combined pump proposed in the present disclosure patent is feasible. TABLE 6 Performance comparison of the liquid-ring type combined pump before and after optimization Performance parameter Head coefficient Efficiency / % Power / kW Average value of outlet pulsation pressure / kPa NPSHr / m Self-priming time / s Original model 0.653 51.42 7.04 378.19 2.71 4.6 Optimal model 0.649 53.97 6.67 361.94 2.45 4.3 4 The Z-G-B cavitation model is improved, and the cavitation flow in the liquid-ring type combined pump before and after optimization is compared (1) Taking into account the rotational motion and geometric characteristics of the centrifugal pump, a formula for calculating the bubble diameter Rb is proposed. Rh = _£2£l££_f_£22—>-i / 3. 1 1 &1 1 D zmax(l,Vfc) ^36002^ Where C is the coefficient of constant term, which is obtained by fitting the visualization test data of centrifugal pump, z the blade number of the main centrifugal pump impeller, k is the turbulent kinetic energy, pi is the liquid phase density, n is the rotational speed of the liquid-ring type combination pump. (2) Considering thermodynamic effect, improving Z-G-B cavitation model, the improved Z-G-B cavitation model of evaporation source term m+ expression and condensation source term m~ expression is: 30-MPi, , f2P„-P PlCpi^CT^-T) m -cevap Rb 3 ) (R<rv) m~ = Qond ( Pv) Rb -y 3 pi pvLev\[t where CeVaP is the evaporation coefficient; av is the volume fraction of the vapor phase; pv is the density of the gas phase; Pv is the pressure in the bubble (assumed to be the saturated vapor pressure at the temperature of the operating medium m the pump); P is the liquid pressure around the bubble; Cpi is the specific heat at constant pressure of the liquid phase, ai is the thermal diffusion of liquid, ai=kilpiCpi', hi is the thermal conductivity of the liquid phase; t is any time; Tm is the far-field temperature; T is the temperature at any time / ; Lev is the latent heat of vaporization; Coond is the condensation coefficient. (3) The parameters of physical properties in the improved Z-G-B cavitation model are fitted as a function of temperature by the least square method. (4) The improved Z-G-B cavitation model was embedded into CFX by CFX expression language. The thermal conductivity 2V, specific heat capacity at constant pressure Cpv and other parameters that were not included in the formula and also varied with temperature were fitted as temperature functions and input into the corresponding positions of CFX pre-processing. (5) Cavitation flows inside the liquid-ring type combined pump before and after optimization are numerically simulated based on the improved Z-G-B cavitation model. And the cavitation characteristic curves, the cavitation volume fraction, and the pressure pulsation characteristics of the pump before and after optimization are analyzed. FIG. 6 shows cavitation characteristic curves of the liquid-ring type combined pump before and after optimization under rated flow rate. It can be seen that the critical cavitation coefficient of the optimization scheme has decreased by 15.18%. Therefore, the cavitation inside the optimized liquidring type combined pump has been suppressed to some extent. The content described in the embodiments of this specification is merely an enumeration of the forms of realizing the inventive concept. The scope of protection of the present disclosure should not be deemed to be limited to the specific forms described in the embodiments. The scope of protection of the present disclosure also includes equivalent technical means that can be conceived by those skilled in the art based on the inventive concept of the present disclosure.

Claims

1. A multi-objective optimization method for a liquid-ring type combined pump, characterized in that the liquid-ring type combined pump is a self-priming pump composed of a main centrifugal pump and a liquid-ring pump, an impeller of the main centrifugal pump and a liquid-ring impeller of the liquid-ring pump are coaxial, and the multi-objective optimization method for the liquid-ring type combined pump comprises the following steps:step 1: with a head coefficient and an impeller stress of the main centrifugal pump as constraints, a maximum hydraulic efficiency, a minimum impeller deformation and a lightest weight of the main centrifugal pump as optimum objectives, performing multi-objective optimization on the impeller of the main centrifugal pump in the liquid-ring type combined pump based on an intelligent optimization algorithm;step 2: based on optimization results of the main centrifugal pump, with self-priming time and shaft power of the liquid-ring pump as evaluation indicators, and main geometric parameters of the liquid-ring impeller, such as a blade number, a width, a blade outlet angle, an eccentricity and a hub inclination angle as test factors, establishing a regression model between the main geometric parameters of the liquid-ring impeller, and the self-priming time and the shaft power of the liquidring pump, to perform the multi-objective optimization on the liquid-ring impeller based on Genetic Algorithms;step 3: building a test bench for the liquid-ring type combined pump to experimentally verify feasibility of the multi-objective optimization method for the liquid-ring type combined pump; andstep 4: taking thermodynamic effects, rotational motion, and geometric characteristics of the centrifugal pump into consideration, improving a Zwart-Gerber-Belamri cavitation model, known as a Z-G-B cavitation model, performing numerical calculations to analyze a cavitation flow inside the liquid-ring type combined pump before and after the multi-objective optimization, and analyzing cavitation characteristic curves, a cavitation volume fraction, and pressure pulsation characteristicsof the liquid-ring type combined pump before and after the multi-objective optimization.

2. The multi-objective optimization method for the liquid-ring type combined pump according to claim 1, characterized in that in the step 1, steps for the multi-objective optimization of the impeller of the main centrifugal pump are as follows:(1) parametric modeling of the impeller of the main centrifugal pump in the liquid-ring type combined pump is achieved based on five-point quartic Bezier curve, and based on ANSYS optiSLang, a multi-objective optimization design platform for the impeller of the main centrifugal pump in the liquid-ring type combined pump is established;(2) a multi-objective optimization mathematical model is constructed for the impeller of the main centrifugal pump in the liquid-ring type combined pump, the constructing of the model using the 10 blades angle control points and the 10 blades thickness control points from the five-point quartic Bezier curve as the design variables, the constraining of the model by the head coefficient and the impeller stress of the main centrifugal pump, the optimizing objectives including maximizing the hydraulic efficiency of the main centrifugal pump, minimizing the deformation of the impeller, and achieving the lightest weight;(3) a sample space for the multi-objective optimization design of the impeller of the main centrifugal pump in the liquid-ring type combined pump is generated using an optimal Latin hypercube sampling method; and(4) a global optimization solution with intelligent optimization algorithm is sought for the multiobjective optimization mathematical model of the impeller of the main centrifugal pump in the liquid-ring type combined pump, leading to acquisition of an optimal solution set for the impeller optimization.

3. The multi-objective optimization method for the liquid-ring type combined pump according to claim 1 or 2, characterized in that the constraint on the head coefficient is that the fluctuation of the head coefficient of the main centrifugal pump is limited to within a range of 3%, that is—■—- x 100% <3%, wherein i / >0 represents the head coefficient of the main centrifugal pumpbefore optimization, represents the head coefficient of the main centrifugal pump after optimization.

4. The multi-objective optimization method for the liquid-ring type combined pump according to claim 1 or 2, characterized in that the constraint on the impeller stress is that the maximum stress ^max experienced by the impeller of the main centrifugal pump after optimization is lower than or equal to the maximum stress aOmax experienced by the impeller of the main centrifugal pump before optimization, that is amax <&Omax.

5. The multi-objective optimization method for the liquid-ring type combined pump according to claim 1 or 2, characterized in that the intelligent optimization algorithm is an adaptive simulated annealing algorithm, or a genetic algorithm, or an ant colony algorithm, or a particle swarm algorithm.

6. The multi-objective optimization method for the liquid-ring type combined pump according to claim 1, characterized in that steps for the multi-objective optimization of the liquid-ring impeller in the liquid-ring pump in the step 2 are as follows:(1) based on the optimization results of the main centrifugal pump, an orthogonal experiment is conducted on the liquid-ring impeller of the liquid-ring pump, using self-priming time and shaft power as evaluation indicators, the considering of the main geometric parameters of the liquid-ring impeller, including the blade number, the width, the outlet angle of the blades, the eccentricity, and the hub inclination angle, as the experimental factors, and the determining of the impact of each experimental factor on the evaluation indicators is achieved through the range analysis and the variance analysis;(2) using orthogonal polynomial regression analysis, a regression model is determined to establish the relationship between the main geometric parameters of the liquid-ring impeller and the self-priming time and shaft power of the liquid-ring pump; and(3) the regression model of self-priming time and shaft power was optimized by genetic algorithm, and the optimal structure of liquid-ring impeller was determined.

7. The multi-objective optimization method for the liquid-ring type combined pump accordingto claim 1, characterized in that steps to experimentally verify the feasibility of multi-objective optimization method for liquid-ring type combined pump in the step 3 are as follows:(1) a closed test bench for the liquid-ring type combined pump is built, the test bench being capable of simulating the performance and the cavitation tests of the pump under both the ground and the high-altitude conditions, the aim of the test bench being to capture the key parameters such as the flow rate, the head, the efficiency, the power, the net positive suction head (NPSHr), and the pulsating pressure of the liquid-ring type combined pump;(2) the using of an electronic scale is employed for the measuring of the weight of the impeller of the main centrifugal pump in the liquid-ring type combined pump, the comparing and analyzing of the weight of the impeller of the main centrifugal pump before and after the optimization being performed; and(3) the measuring of the head, the efficiency, the power, the outlet pulsating pressure, and the self-priming time of the liquid-ring type combined pump under the rated flow rate is achieved experimentally, the measuring of the net positive suction head (NPSHr) of the liquid-ring type combined pump under the rated flow rate being performed by the vacuum pump, the analyzing of the head coefficient, the efficiency, the power, the average outlet pulsating pressure, the net positive suction head (NPSHr), and the self-priming time of the liquid-ring type combined pump before and after the optimization under the rated flow being conducted in order to verify the feasibility of the multi-objective optimization method of the liquid-ring type combined pump.

8. The multi-objective optimization method for the liquid-ring type combined pump according to claim 1, characterized in that steps to improve the Z-G-B model in the step 4 are as follows:(1) taking into account the rotational motion and geometric characteristics of the centrifugal pump, a formula for calculating the bubble diameter Rb is proposed, the formula being Rb = 0.0018C ,pLn a-i / 3 wherein q js coefficient of constant term, which is obtained by fitting the zmax(l,Vfc) ^36002^ ’ >J &visualization test data of centrifugal pump, z the blade number of the main centrifugal pump impeller, k is the turbulent kinetic energy, pi is the liquid phase density, n is the rotational speed of the liquid-ring type combination pump;(2) considering thermodynamic effect, improving Z-G-B cavitation model, the improved Z-G-B cavitation model of evaporation source term m+ expression and condensation source termexpression are:m+ = Cevap ( _ PicPi^(T^~T)y (p<p )P Rb Si 3 Pl pvLev4t J y - >m~ = Ccond ( (p>p )COnd Rb \l3 Pt pvLev4t J V ’wherein Qvap is the evaporation coefficient; av is the volume fraction of the vapor phase; pv is the density of the gas phase; Pv is the pressure in the bubble (assumed to be the saturated vapor pressure at the temperature of the operating medium in the pump); P is the liquid pressure around the bubble; Cpi is the specific heat at constant pressure of the liquid phase; ai is the thermal diffusion of liquid; ai=^ilpiCpi\ 2 / is the thermal conductivity of the liquid phase; t is any time; T® is the far-field temperature; T is the temperature at any time l. Lev is the latent heat of vaporization; Ccond is the condensation coefficient;(3) the parameters of physical properties in the improved Z-G-B cavitation model are fitted as a function of temperature by the least square method; and(4) the embedding of the improved Z-G-B cavitation model into the CFX is achieved by using the CFX expression language, the fitting of the thermal conductivity Av, the specific heat capacity at the constant pressure Cpv, and other parameters that were not comprised in the formula and also varied with the temperature being done as the temperature functions, and the inputting of these into the corresponding positions of the CFX pre-processing being performed.

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