CN110617238B - Optimization design method of centrifugal pump impeller - Google Patents
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Abstract
The invention relates to the field of hydraulic optimization of centrifugal pumps. The method can more accurately and quickly determine the optimal working condition point of the centrifugal pump impeller under the common constraint of the vortex structure and the entropy product to obtain the corresponding impeller design parameters, so that the impeller has better hydraulic performance and better stability. The technical scheme is as follows: an optimal design method of a centrifugal pump impeller is characterized by comprising the following steps: the method comprises the following steps: 1) firstly, specifically determining a group of parameters to be optimized according to design requirements and design experience; 2) modeling and grid division; 3) CFX simulation verification; 4) extracting a vortex core structure; 5) analyzing the entropy yield; 6) efficient point matching; 7) and optimizing the design parameters of the impeller by adopting a simulated annealing optimization algorithm.
Description
Technical Field
The invention relates to the field of hydraulic optimization of centrifugal pumps, in particular to an optimization design method for an impeller of a centrifugal pump.
Background
At present, centrifugal pumps are the most widely used pump type in the pump industry, and the usage amount of the centrifugal pumps accounts for about 70% of the whole pump industry. The viscous action of the fluid in the centrifugal pump and the special geometric structure of the centrifugal pump determine that the actual flow inside the centrifugal pump is three-dimensional, viscous and abnormal, and in addition, the action of various factors such as the fluid flowing around the flow vanes and rotating at high speed inevitably forms various unstable flows, which mainly comprise: the unsteady factors of the centrifugal pump include the common occurrence and obvious action of the unsteady factors such as the flow shedding, the backflow, the secondary flow, the wake flow and various vortexes, so that the flow field inside the centrifugal pump presents strong and complex unsteady flow characteristics. At the design operating point, although the centrifugal pump keeps high operation efficiency, the existence of unsteady flow characteristics can also lead to poor operation stability and high vibration noise of the centrifugal pump. The impeller is the most important overflowing part and acting part in the centrifugal pump, the design quality of the impeller directly influences the operation efficiency and the operation stability of the pump, and further influences the design targets of vibration, noise and the like of the pump, so that the impeller of the pump is of great significance in optimization design.
For the hydraulic design of centrifugal pump impellers, three major problems mainly need to be solved: (1) the efficiency is improved; (2) performance is improved; (3) and the operation stability of the pump is enhanced. The invention patent with the application number of 201110202524.5, 7/20/2011 discloses an optimal design method for an impeller of an anti-cavitation centrifugal pump, which is used for designing an optimal design method for the impeller for improving cavitation erosion performance by constructing optimization parameters and adopting an NSGA-II genetic algorithm as an optimization tool, and the method does not consider factors influencing the running stability of the impeller and the like. The key point is to fully know the internal fluid motion state of the centrifugal pump to ensure safe, stable and efficient operation of the centrifugal pump, wherein separation flow and vortex motion are the most common flow phenomena, and the hydraulic fluctuation can generate pressure pulsation on the centrifugal pump to influence the operation stability of the centrifugal pump. Therefore, on the premise of fully considering the efficiency of the impeller and the pressure pulsation factor, an impeller optimization design method is provided to improve the hydraulic performance and stability of the centrifugal pump.
Disclosure of Invention
The invention aims to overcome the defects of the background technology and provides an optimal design method of a centrifugal pump impeller, which can more accurately and quickly determine the optimal working condition point of the centrifugal pump impeller under the common constraint of a vortex structure and an entropy product to obtain corresponding impeller design parameters, so that the impeller has better hydraulic performance and better stability.
The technical scheme provided by the invention is as follows:
an optimal design method of a centrifugal pump impeller is characterized by comprising the following steps: the method comprises the following steps:
1) firstly, according to design requirements, a group of parameters to be optimized is specifically determined according to design experience: width of impeller inlet b1Impeller exit width b2Blade inlet angle beta1Blade exit angle beta2The number of blades z, this set of parameters to be optimized gives the constraints below. Other impeller parameters are used as design constants;
the constraint range of the parameters to be optimized is as follows:
in the above formula:
Km1-the impeller inlet axial surface coefficient,
ns-the specific speed of rotation of the pump,
Fr-a flow rate of the fluid,
h-the lift is set as the height of the pump,
n-the rotating speed of the impeller,
g-acceleration of gravity;
when the design parameters of the centrifugal pump impeller are optimized in the step, the distribution condition of the energy loss inside the centrifugal pump in the step 4) can be analyzed, so that a main area of the energy loss of the impeller is obtained, and a reference is provided for the adjustment of the design parameters of the impeller corresponding to the low-efficiency area of the impeller, so that the pertinence of the optimization of the design parameters is improved, and the verification times and the workload of the design parameters are reduced.
2) Modeling and meshing: modeling the calculation domain of the centrifugal pump impeller under a determined coordinate system (shown in figure 2) by using three-dimensional modeling software according to the parameters of the centrifugal pump impeller; utilizing ANSYS ICEM software to perform meshing on the three-dimensional model;
3) and (3) CFX simulation verification: the grid is led into CFX software, transient numerical simulation calculation of the centrifugal pump impeller under the full-flow working condition is carried out under given boundary conditions (including inlet pressure, outlet flow, wall surface and dynamic and static interface setting and impeller rotating speed), and the result can be automatically generated by the software; carrying out post-processing on the numerical simulation result to obtain a flow-lift and flow-efficiency performance curve of the centrifugal pump; comparing whether the lift and the efficiency under the drawn grid meet the design requirements or not according to the performance curve, and if the design requirements are not met, repeating the step 2) to divide the grid of the three-dimensional model again until the grid meeting the design requirements is obtained;
4) extracting a vortex core structure: based on the simulation result obtained in the step 3), extracting the vortex core structure in the calculation domain based on a Q method to obtain the data of the vortex core strength changing along with the flow, wherein the Q value represents the strength relation between the fluid infinitesimal rotation and the deformation;
5) entropy production analysis: based on the grid obtained in the step 3), calculating the distribution condition of the internal energy loss of the centrifugal pump according to the speed distribution of the CFD calculation result according to the formulas (1.1), (1.2) and (1.3); then carrying out volume integration on the formulas (1.2) and (1.3) in an impeller region by using a formula (1.4) to obtain the total entropy yield of the impeller;
in the above formula
Spro，t-total entropy production rate per unit volume of impeller,
Spro，d′-a rate of impeller pulsation entropy production per unit volume,
t-the temperature of the fluid, and,
p-the density of the fluid,
-a turbulent dissipation ratio of the fluid,
u, v, w-velocity components of the fluid in the direction X, Y, Z respectively,
representing the time-average velocity value, u ', v ', w ' representing the pulsation velocity value;
6) efficient point matching: carrying out non-dimensionalization on the data obtained in the step 4) and the step 5), and importing the data into data processing software for drawing to obtain a curve of the total entropy of the impeller and the vortex core strength changing along with the flow; wherein the non-dimensional flow corresponding to the minimum vortex core strength is Fr1The dimensionless flow corresponding to the minimum total entropy yield of the impeller is Fr2；
7) Optimizing design parameters of the impeller by adopting a simulated annealing optimization algorithm to ensure that the dimensionless flow corresponding to the minimum vortex core strength and the dimensionless flow corresponding to the minimum impeller total entropy yield are both F'rAnd F'r＝Fr1＝Fr2At this point, the optimum design parameters for the impeller are found to be 1.
In the step 4), the step of extracting the vortex structure by using the Q method comprises the following steps:
the above equation is simplified to the following Q-values in cartesian coordinates:
wherein, the Q method defines the area where Q > 0 as the area where the vortex tube is; the deformation rate tensor and the vorticity in the above formula are calculated by editing a CEL expression in POST-processing software CFD-POST according to a numerical simulation result. Setting a threshold value, and extracting Fr＝FrdThe infinitesimal iso-surface of (A) determines the vortex morphology, wherein FrdTo design the flow rate. After the Q value is determined, in CFD-POST, a vorticity isosurface under the Q value is made, the vorticity coefficient is adopted for coloring, then the strength of the vortex core is quantitatively calculated by software, and data are recorded.
In the step 6), the total entropy yield of the impeller is subjected to dimensionless treatment, wherein the numerical value of the entropy yield of each impeller is divided by the minimum value of the entropy yield of the impeller; carrying out non-dimensionalization treatment on the strength of the vortex core, namely dividing the numerical value of the strength of each vortex core by the minimum value of the strength of the vortex core; the flow is subjected to non-dimensionalization treatment by dividing the numerical value of each flow by the design flow Frd。
The invention has the beneficial effects that:
1) the method reflects the change condition of the efficiency of the impeller by analyzing the entropy yield value inside the impeller; describing the change of the pressure pulsation by numerically processing the vortex core intensity; the impeller is optimally designed through the combination of entropy yield and vortex core strength, namely, the impeller is optimally designed by simultaneously considering the efficiency of the impeller and pressure pulsation, so that the impeller can be ensured to have better operating efficiency and operating stability.
2) The method adopts the Q method to extract the surface area of the vortex structure of the main vortex core area in the impeller of the centrifugal pump, and digitizes the vortex structure, thereby being beneficial to vividly understanding the change of pressure pulsation and providing a basis for the optimization of the impeller.
3) By adopting an energy entropy method and according to the distribution condition of energy loss in the centrifugal pump, the main area of energy loss of the impeller can be analyzed, and the reference is provided for adjusting the design parameters of the impeller corresponding to the low-efficiency area of the impeller.
4) Based on the Q method and the energy entropy theory combined constraint, the efficient working condition point of the centrifugal pump impeller is optimized and determined, so that the optimized centrifugal pump impeller parameters can be obtained more efficiently, and the optimization is more accurate and efficient than the traditional impeller.
5) The design parameters of the centrifugal pump impeller are optimally designed by adopting a simulated annealing algorithm, so that the optimal design parameters of the impeller can be more accurately and quickly obtained.
Drawings
Fig. 1 is a flow chart of an optimal design method of an impeller of a centrifugal pump according to the present invention.
Fig. 2 is a schematic view of the inlet and outlet angles of the impeller of the initial centrifugal pump.
Fig. 3 is a view from a-a of fig. 2 (which is a schematic view of the width of the inlet and outlet of the impeller of the initial centrifugal pump).
FIG. 4 is a grid diagram of the optimized centrifugal pump impeller.
FIG. 5 is a graph of total entropy yield and vortex core strength as a function of flow rate for an impeller of a centrifugal pump according to an embodiment of the present invention under initial parameters.
FIG. 6 is a graph of total entropy yield and vortex core strength as a function of flow for an impeller of a centrifugal pump according to an embodiment of the present invention under optimum design parameters.
Detailed Description
The following further description is made with reference to the embodiments shown in the drawings.
The method for optimally designing the centrifugal pump impeller shown in FIG. 1 is carried out according to the following steps:
1) firstly, according to design requirements, a group of parameters to be optimized is specifically determined according to design experience: width of impeller inlet b1Impeller exit width b2Blade inlet angle beta1Blade exit angle beta2The number of blades z (angles and port widths are indicated in fig. 2 and 3)) This set of parameters that need to be optimized and the constraint ranges given below. Other impeller parameters are used as design constants;
the design parameters of the centrifugal pump impeller to be optimized are constrained as follows:
in the above formula:
Km1-the impeller inlet axial surface coefficient,
ns-the specific speed of rotation of the pump,
Fr-a flow rate of the fluid,
h-the lift is set as the height of the pump,
n-the rotating speed of the impeller,
g-acceleration of gravity;
when the design parameters of the centrifugal pump impeller are optimized in the step, the distribution condition of the energy loss inside the centrifugal pump in the step 4) can be analyzed, so that a main area of the energy loss of the impeller is obtained, and a reference is provided for the adjustment of the design parameters of the impeller corresponding to the low-efficiency area of the impeller, so that the pertinence of the optimization of the design parameters is improved, and the verification times and the workload of the design parameters are reduced.
2) Modeling and meshing: modeling a calculation domain of the centrifugal pump impeller under a determined coordinate system (shown in figure 2; the Y axis of the coordinate system is vertical to the paper surface and faces outwards) by using three-dimensional modeling software according to basic parameters of the centrifugal pump impeller; the three-dimensional model is gridded using ANSYS ICEM software.
3) And (3) CFX simulation verification: and (3) introducing the grids into CFX software, and performing transient numerical simulation calculation on the centrifugal pump impeller under the full-flow working condition under the given boundary conditions including inlet pressure, outlet flow, wall surface and dynamic and static interface settings and impeller rotating speed, wherein the results are automatically generated by the software. Then carrying out post-processing on the numerical simulation result to obtain performance curves of the centrifugal pump, such as flow-lift, flow-efficiency and the like; comparing whether the lift and the efficiency under the drawn grid meet the design requirements or not according to the performance curve, and if the design requirements are not met, repeating the step 2) to perform grid division on the three-dimensional model again until the grid division meeting the design requirements is obtained;
4) vortex structure extraction: based on the simulation result obtained in the step 3), vortex structure extraction is carried out in a calculation domain based on a Q method to obtain data of vortex core strength changing along with flow, so as to realize numerical processing of the vortex core strength and visually describe the change of pressure pulsation; wherein, the Q value represents the strength relation between the rotation and deformation of the fluid infinitesimal;
the method for extracting the vortex structure comprises the following specific steps: determining the Q value according to the formulas (1.5), (1.6) and (1.7):
the above equation is simplified to the following Q-values in cartesian coordinates:
wherein, the Q method defines the area where Q > 0 as the area where the vortex tube is; the deformation rate tensor and the vorticity in the above formula are calculated by editing a CEL expression in POST-processing software CFD-POST according to a numerical simulation result. Setting a threshold value, and extracting Fr＝FrdThe infinitesimal iso-surface of (A) determines the vortex morphology, wherein FrdTo design the flow rate. After the Q value is determined, in CFD-POST, a vorticity isosurface under the Q value is made, the vorticity coefficient is adopted for coloring, then the strength of the vortex core is quantitatively calculated by software, and data are recorded.
5) Entropy production analysis: based on the grid obtained in the step 3), calculating the distribution condition of the internal energy loss of the centrifugal pump according to the speed distribution of the CFD calculation result according to the formulas (1.1), (1.2) and (1.3) based on the energy entropy theory; the total entropy yield of the impeller is then obtained from equation (1.4) to reflect the variation in impeller efficiency.
In the above formula
Spro，t-total entropy production rate per unit volume of impeller,
Spro，d′-a rate of impeller pulsation entropy production per unit volume,
t-the temperature of the fluid, and,
p-the density of the fluid,
-a turbulent dissipation ratio of the fluid,
u, v, w-velocity components of the fluid in the direction X, Y, Z respectively,
representing the time-average velocity value, u ', v ', w ' representing the pulsation velocity value;
6) efficient point matching: carrying out non-dimensionalization on the data obtained in the step 4) and the step 5), and introducing the data into data processing software for drawing to obtain curves of the total entropy yield and the vortex core strength of the impeller along with the change of flow; wherein the non-dimensional flow corresponding to the minimum vortex core strength is Fr1The dimensionless flow corresponding to the minimum total entropy yield of the impeller is Fr2；
In the step, the total entropy productivity of the impeller is subjected to dimensionless treatment, and the numerical value of the entropy productivity of each impeller is divided by the minimum value of the entropy productivity of the impellerA value; carrying out non-dimensionalization treatment on the strength of the vortex core, namely dividing the numerical value of the strength of each vortex core by the minimum value of the strength of the vortex core; the flow is subjected to non-dimensionalization treatment by dividing the numerical value of each flow by the design flow Frd。
7) Optimizing design parameters of the impeller by adopting a simulated annealing optimization algorithm to ensure that the dimensionless flow corresponding to the minimum vortex core strength and the dimensionless flow corresponding to the minimum entropy yield are both F'r(F′rTo design the flow FrdDimensionless flow obtained after dimensionless treatment, hence F'r1), i.e. F'r＝Fr1＝Fr2At this point, the optimum design parameters for the impeller are found to be 1.
Example (b): the basic design parameters of a group of centrifugal pump impellers are empirically given as initial design parameters, and other parameters are constant values. The initial design parameters are shown in table 1.
TABLE 1
According to the initial design parameters, the specific implementation operation is carried out according to the following steps.
1. Establishing a specific three-dimensional model of the impeller by using three-dimensional modeling software SolidWorks and parameters in table 1, as shown in FIG. 2;
2. the model is subjected to grid division, the total number of grid nodes is 2556414, and the grid distribution is shown in fig. 4 (the case of optimal design parameters). And the boundary conditions shown in Table 2 are given for numerical simulation calculation;
TABLE 2
In the step, grid verification is required, namely, whether the lift and the efficiency obtained by comparison and calculation meet the design requirements or not is compared, if the lift and the efficiency do not meet the requirements, the grid is modified until the lift and the efficiency meet the design requirements;
3. after the grid meets the requirements, the grid quality is proved to be appropriate, the accuracy of the calculation result is reliable, and the extraction of the vortex core structure is carried out at the moment. Namely, the Q method is used to obtain the data of the vortex core intensity varying with the flow rate, the calculated vortex core intensity is 0.28756 at the flow rate, and then the flow rate is changed to continue the calculation. Finally obtaining a curve 2 shown in figure 5 after dimensionless processing;
4. according to the numerical simulation result obtained in the step 2, obtaining the relationship of the total entropy yield of the impeller along with the change of the flow according to the formulas (1.1), (1.2), (1.3) and (1.4), such as a curve 1 shown in fig. 5;
5. the flow rate corresponding to the minimum vortex core intensity on curve 1 in FIG. 5 is set as Fr1The flow value corresponding to the minimum value of the total entropy yield of the impeller on the curve 2 is set as Fr2. At this time, the dimensionless flow rate corresponding to the minimum vortex core intensity is Fr1When the total entropy production of the impeller is minimum, the corresponding dimensionless flow is Fr20.76. At this time Fr2＞Fr1Therefore, parameter optimization is required.
6. Optimizing design parameters of the impeller by adopting a simulated annealing optimization algorithm and a simulated annealing optimization algorithm to ensure that dimensionless flow corresponding to the minimum vortex core strength and dimensionless flow corresponding to the minimum entropy yield are both F'r，F′r＝Fr1＝Fr2At this point, the optimum design parameters for the impeller are found to be 1.
After the centrifugal pump impeller is subjected to multiple times of optimization of design parameters (steps 1-6 above), the optimal design parameters (shown in table 3) are finally obtained, and a vortex core strength-flow curve and an impeller total entropy yield-flow curve of the centrifugal pump impeller are drawn again (see fig. 5), wherein at this time, the dimensionless flow corresponding to the minimum vortex core strength and the dimensionless flow corresponding to the minimum entropy yield both reach F'r，F′r＝Fr1＝Fr2The design parameter can be determined as the optimal design parameter of the impeller, namely 1.
TABLE 3
Claims (4)
1. An optimal design method of a centrifugal pump impeller is characterized by comprising the following steps: the method comprises the following steps:
1) firstly, according to design requirements, a group of parameters to be optimized is specifically determined according to design experience: width of impeller inlet b1Impeller exit width b2Blade inlet angle beta1Blade exit angle beta2The number z of the blades, the group of parameters needing to be optimized and the constraint range are given below, and other impeller parameters are used as design constants;
the constraint range of the parameters to be optimized is as follows:
30°＜β1＜40°
15°＜β2＜40°
in the above formula
Km1-the impeller inlet axial surface coefficient,
ns-the specific speed of rotation of the pump,
Fr-a flow rate of the fluid,
h-the lift is set as the height of the pump,
n-the rotating speed of the impeller,
g-acceleration of gravity;
2) modeling and meshing: modeling a calculation domain of the centrifugal pump impeller under the determined coordinate system by using three-dimensional modeling software according to parameters of the centrifugal pump impeller; utilizing ANSYS ICEM software to perform meshing on the three-dimensional model;
3) and (3) CFX simulation verification: importing the grids into CFX software, carrying out transient numerical simulation calculation on a centrifugal pump impeller under a full-flow working condition under a given boundary condition, and automatically generating a result by the software; carrying out post-processing on the numerical simulation result to obtain a flow-lift and flow-efficiency performance curve of the centrifugal pump; comparing whether the lift and the efficiency under the drawn grid meet the design requirements or not according to the performance curve, and if the design requirements are not met, repeating the step 2) to divide the grid of the three-dimensional model again until the grid meeting the design requirements is obtained;
4) extracting a vortex core structure: based on the simulation result obtained in the step 3), extracting the vortex core structure in the calculation domain based on a Q method to obtain the data of the vortex core strength changing along with the flow, wherein the Q value represents the strength relation between the fluid infinitesimal rotation and the deformation;
5) entropy production analysis: based on the grid obtained in the step 3), calculating the distribution condition of the internal energy loss of the centrifugal pump according to the speed distribution of the CFD calculation result according to the formulas (1.1), (1.2) and (1.3); then carrying out volume integration on the formulas (1.2) and (1.3) in an impeller region by using a formula (1.4) to obtain the total entropy yield of the impeller;
in the above formula
Spro，t-total entropy production rate per unit volume of impeller,
Spro，d′-a rate of impeller pulsation entropy production per unit volume,
t-the temperature of the fluid, and,
p-the density of the fluid,
-a turbulent dissipation ratio of the fluid,
u, v, w-velocity components of the fluid in the direction X, Y, Z respectively,
representing the time-average velocity value, u ', v ', w ' representing the pulsation velocity value;
6) efficient point matching: carrying out non-dimensionalization on the data obtained in the step 4) and the step 5), and introducing the data into data processing software for drawing to obtain curves of the total entropy yield and the vortex core strength of the impeller along with the change of flow; wherein the non-dimensional flow corresponding to the minimum vortex core strength is Fr1The dimensionless flow corresponding to the minimum total entropy yield of the impeller is Fr2；
7) Optimizing design parameters of the impeller by adopting a simulated annealing optimization algorithm to ensure that the dimensionless flow corresponding to the minimum vortex core strength and the dimensionless flow corresponding to the minimum impeller total entropy yield are both F'rAnd F'r＝Fr1＝Fr2At this point, the optimum design parameters for the impeller are found to be 1.
2. The optimum design method of a centrifugal pump impeller according to claim 1, characterized in that: in the step 4), the step of extracting the vortex structure by using the Q method comprises the following steps: determining the Q value according to the formulas (1.5), (1.6) and (1.7):
tensor of deformation ratio-
Vorticity-
Q value-
The above equation is simplified to the following Q-values in cartesian coordinates:
the Q method defines the area with Q > 0 as the area where the vortex tube is located, and the deformation rate tensor and the vorticity in the above formula are calculated by editing a CEL expression in POST-processing software CFD-POST according to a numerical simulation result; extraction of Fr＝FrdThe infinitesimal iso-surface of (A) determines the vortex morphology, wherein FrdTo design the flow rate; after the Q value is determined, in CFD-POST, a vorticity isosurface under the Q value is made, a vorticity intensity coefficient is adopted for coloring, then the strength of a vortex core is quantitatively calculated by software, and data are recorded.
3. The optimum design method of a centrifugal pump impeller according to claim 1, characterized in that: in the step 5), the total entropy yield of the impeller is subjected to dimensionless treatment, wherein the numerical value of the entropy yield of each impeller is divided by the minimum value of the entropy yield of the impeller; carrying out non-dimensionalization treatment on the strength of the vortex core, namely dividing the numerical value of the strength of each vortex core by the minimum value of the strength of the vortex core; the flow is subjected to non-dimensionalization treatment by dividing the numerical value of each flow by the design flow Frd。
4. The method for optimally designing an impeller of a centrifugal pump according to claim 1, wherein the method comprises the steps of: in the step 3), the boundary conditions comprise inlet pressure, outlet flow, wall surface and dynamic and static interface settings and impeller rotating speed.
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