Decomposition expression and optimization design method of hydraulic radial force of centrifugal pump impeller

Abstract

The application provides a decomposition expression and optimization design method of hydraulic radial force of a centrifugal pump impeller, aiming to help designers to deeply understand the composition characteristics of the hydraulic radial force of the impeller and to carry out targeted optimization. The method comprises the following steps: drawing a three-dimensional hydraulic model of the centrifugal pump, dividing the grid and establishing a computational fluid dynamics model, and carrying out transient simulation calculation; recording the time-varying data of the liquid pressure on the reference blade in two orthogonal radial directions, and carrying out trigonometric function fitting based on the least square method; obtaining the expression of the liquid pressure on other blades by time translation; and decomposing the hydraulic radial force of the impeller into the vector sum of the liquid pressure on each blade. Based on this, the optimization design method takes the expression result of the liquid pressure on the reference blade as the optimization object, and realizes the reduction of the hydraulic radial force by adjusting the blade structure. The decomposition expression and optimization design method of the application help to more clearly understand the composition of the hydraulic radial force of the impeller and improve the design optimization effect.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of centrifugal pumps, in particular to a method for decomposing and representing hydraulic radial force of a centrifugal pump impeller and optimizing design. BACKGROUND

[0002] Centrifugal pumps are the most widely used pumps, mainly used for liquid conveying and pressure boosting. The working principle of a centrifugal pump is that an impeller fixed on a main shaft rotates with the main shaft, liquid is axially sucked from the center of the impeller, and after work is done by the blades, the liquid is radially thrown out to the water outlet chamber and output. Therefore, during the operation of the centrifugal pump, the impeller is subjected to the action of hydraulic radial force caused by the liquid pressure. The size and fluctuation of the hydraulic radial force acting on the impeller are closely related to the deflection of the main shaft, vibration and noise, so a large number of scientific researchers and engineering and technical personnel are very concerned about how to suppress or reduce the hydraulic radial force acting on the impeller as much as possible.

[0003] The current known technical solutions usually use computational fluid dynamics method to predict the pump internal flow field during the transient rotation process of the impeller and the time-varying curve of the hydraulic radial force of the impeller induced by the unsteady flow field, rely on multiple iterations of "impeller structure design-computational fluid dynamics prediction", and until a lower level of hydraulic radial force design scheme of the impeller is obtained. In these known technical solutions, the entire impeller is usually regarded as a whole, and the constitutive characteristics of the hydraulic radial force of the impeller are not studied, so it is difficult to analyze the root cause of the hydraulic radial force of the impeller in depth and to carry out more targeted design optimization.

[0004] Therefore, it is urgent to study the constitutive characteristics of the hydraulic radial force of the centrifugal pump impeller and develop a corresponding optimization design method by using new ideas. SUMMARY

[0005] The main purpose of the present application is to provide a method for decomposing and representing hydraulic radial force of a centrifugal pump impeller and optimizing design, which can help designers to more deeply and clearly understand the constitutive characteristics of the hydraulic radial force of the impeller and to carry out more targeted design optimization work.

[0006] To achieve the above-mentioned purpose, the present application provides a method for decomposing and representing hydraulic radial force of a centrifugal pump impeller, wherein the impeller is provided with an even number of blades which are periodically symmetrical, and the method comprises the following steps:

[0007] Step S1, a three-dimensional hydraulic model of the centrifugal pump including the impeller region and the water outlet chamber is drawn, an optional blade on the impeller is taken as a reference blade and numbered as 1, and the remaining blades are numbered as 2 to N in turn according to the rotation direction of the impeller, wherein N is the total number of blades;

[0008] Step S2, based on the hydraulic model obtained in step S1, divide the grid, establish the computational fluid dynamics model, carry out transient simulation calculation under the working condition of the required research to obtain the flow field transient change situation;

[0009] Step S3, in the calculation process of step S2, respectively record the time-varying data of the liquid pressure suffered by the reference blade in the first radial direction and the second radial direction within one impeller rotation period, wherein the first radial direction and the second radial direction are two mutually orthogonal radial directions of the impeller;

[0010] Step S4, based on the least square method, triangular function fitting is carried out on the time-varying data obtained in step S3, and the liquid pressure suffered by the reference blade in the first radial direction and the second radial direction is represented as F 1X and F 1Y :

[0011]

[0012] The above a 1X , b 1X and a 1Y , b 1Y are parameter values obtained by triangular function fitting; S 1X (t) and S 1Y (t) are fitting residuals, which are the differences between the original values and the triangular function fitting values of the liquid pressure suffered by the reference blade in the first radial direction and the second radial direction at each time; t is time, and ω is angular frequency:

[0013] ω=2π / T (3)

[0014] The above T is the impeller rotation period, and π is the circular ratio;

[0015] Step S5, for any blade, its number is recorded as i, then the liquid pressure suffered by the blade in the first radial direction and the second radial direction is represented as F iX and F iY :

[0016]

[0017] S 1X (t) and S 1Y (t) are regarded as periodic original signals with T as the period, and the above S 1X [t-T(i-1) / N] and S 1Y [t-T(i-1) / N] respectively represent the signals obtained by moving the original signals S 1X (t) and S 1Y (t) in the increasing direction of time axis t by T(i-1) / N time interval respectively;

[0018] Step S6, the hydraulic radial force of the impeller in the required research condition in the first radial direction and the second radial direction is respectively decomposed and expressed as and Wherein F iX and F iY are the liquid pressure of the blade numbered i in the first radial direction and the second radial direction obtained in step S5.

[0019] Optionally, in the above decomposition and expression method of the hydraulic radial force of the centrifugal pump impeller, in the computational fluid dynamics model in step S2, the impeller region is set as a rotating dynamic grid, and the rotating frequency is the rotating frequency of the impeller.

[0020] Optionally, in the above decomposition and expression method of the hydraulic radial force of the centrifugal pump impeller, in the computational fluid dynamics model in step S2, the rotating frequency of the impeller region is constant.

[0021] Optionally, in the above decomposition and expression method of the hydraulic radial force of the centrifugal pump impeller, in the computational fluid dynamics model in step S2, the inlet and outlet boundary conditions are included, and a constant liquid inflow is set through one of the two.

[0022] Optionally, in the above decomposition and expression method of the hydraulic radial force of the centrifugal pump impeller, the time step of the transient simulation calculation in step S2 is constant, and is not greater than 1% of the rotating period of the impeller.

[0023] Optionally, in the above decomposition and expression method of the hydraulic radial force of the centrifugal pump impeller, one rotating period of the impeller for which the data is recorded in step S3 is a complete rotating period of the impeller after the transient simulation calculation reaches convergence.

[0024] Optionally, in the above decomposition and expression method of the hydraulic radial force of the centrifugal pump impeller, the liquid pressure of the reference blade in the first radial direction and the second radial direction at a certain time in step S3 is respectively the integral of the component of the liquid pressure on the surface of the reference blade in the first radial direction and the second radial direction to the surface area of the blade at the time.

[0025] Optionally, in the above decomposition and expression method of the hydraulic radial force of the centrifugal pump impeller, the fitting residual S 1X (t) and S 1Y (t) are both periodic signals with a period of T.

[0026] Another aspect of the present application provides an optimization design method using the above decomposition and expression method of the hydraulic radial force of the centrifugal pump impeller, which is, using the expression results F 1X and F 1YFor optimization, the blade structure is adjusted by means of transient simulation calculation of computational fluid dynamics to obtain an optimal blade structure design scheme.

[0027] Optionally, in the above optimization design method, the expression F 1X and F 1Y For optimization, the following two objectives are achieved by means of optimization design, including achieving any one or all of the following objectives:

[0028] Objective 1: Obtain the minimum value of one or more of the following parameters: fitting parameter b 1X , fitting parameter b 1Y , parameter

[0029]

[0030] Objective 2: Reduce the absolute value of fitting residual S 1X (t) and / or fitting residual S 1Y (t) in all or part of the time period.

[0031] The beneficial effects of the technical solutions of the present application will be introduced below in combination with the principles of the technical solutions:

[0032] The technical principles of the present application need to be understood in combination with the knowledge of centrifugal pumps and fluid mechanics.

[0033] The impeller of a centrifugal pump is usually composed of a plurality of blades and a hub for placing the blades, and the impeller of some structural forms further includes a cover plate. The number of blades on the impeller of a centrifugal pump is usually even, because even-numbered blades are easier to achieve static and dynamic balance during the manufacturing process, are more stable during operation, can reduce the generation of vortex, reduce resistance and improve efficiency compared with odd-numbered blades; at the same time, even-numbered blades can reduce the vibration and noise of the blades, so that the pump operates more smoothly and reliably.

[0034] The hydraulic radial force of a centrifugal pump impeller originates from the integration of the liquid pressure on the surface area of the impeller surface. Force is a vector, and according to the principles of translation and decomposition of force, the hydraulic radial force on the whole impeller can be decomposed into the vector sum of the hydraulic radial forces on each component of the impeller, and the hydraulic radial force on any component can be decomposed into two components in mutually orthogonal first and second radial directions.

[0035] The applicant has found the following four rules in previous scientific research:

[0036] First, the hydraulic radial force of the impeller as a whole is decomposed into the hydraulic radial force of all the blades and the hydraulic radial force of other parts except the blades, and it is found that the hydraulic radial force of the blades accounts for a large proportion of the hydraulic radial force of the impeller as a whole, so the hydraulic radial force of all the blades can be approximately regarded as the hydraulic radial force of the impeller as a whole;

[0037] Second, the curve of the hydraulic radial force of each blade changing with time is a periodic curve, and the period size is equal to the rotation period T of the impeller;

[0038] Third, an optional blade is recorded as a reference blade, and the next blade of the reference blade in the rotation direction is an adjacent blade, and the curve of the hydraulic radial force of the adjacent blade changing with time is just T / N behind the curve of the hydraulic radial force of the reference blade changing with time in time, that is, the curve of the hydraulic radial force of the adjacent blade changing with time can be completely coincided with the curve of the hydraulic radial force of the reference blade changing with time after the curve of the hydraulic radial force of the adjacent blade changing with time is translated in the direction of reducing the time axis by T / N, and the above T and N are respectively the rotation period of the impeller and the total number of blades;

[0039] Fourth, the curve of the hydraulic radial force of each blade changing with time can be fitted into a sinusoidal function curve with a high fitting degree, wherein the angular frequency of each sinusoidal function is the angular frequency of the rotation of the impeller, the amplitude and the constant term of each sinusoidal function are equal, and the initial phase of the corresponding sinusoidal function of each blade is sequentially reduced by 2π / N in the direction of rotation of the corresponding blade, that is, an optional blade is recorded as a reference blade, and the next blade of the reference blade in the rotation direction is an adjacent blade, and the initial phase of the corresponding sinusoidal function of the adjacent blade is 2π / N behind the initial phase of the corresponding sinusoidal function of the reference blade, and the above π and N are respectively the circular constant and the total number of blades.

[0040] Based on the above scientific laws, the technical scheme of the present application is designed. For convenience of description, an optional blade on the impeller is selected as a reference blade and numbered as 1, and the remaining blades are sequentially numbered as 2 to N in the direction of rotation of the impeller, wherein N is the total number of blades; two mutually orthogonal radial directions of the impeller, i.e. the first radial direction and the second radial direction, are recorded as X and Y directions respectively. The time-varying hydraulic radial force of each blade in the pump is obtained through transient computational fluid dynamics simulation.

[0041] First, the hydraulic radial force of the impeller as a whole is approximately regarded as the vector sum of the hydraulic radial forces of all the blades, and the hydraulic radial force is orthogonally decomposed, so that the hydraulic radial forces of the impeller in the first radial direction and the second radial direction under the working condition to be researched and optimized designed are respectively represented as and wherein F iX and F iYThese represent the liquid pressures experienced by the blade numbered i in the first and second radial directions, respectively.

[0042] Secondly, it is only necessary to obtain the time-varying data of the liquid pressure on the reference blade in the X and Y directions and perform trigonometric function fitting based on the least squares method to orthogonally decompose the liquid pressure on it into F. 1X and F 1Y :

[0043]

[0044] a above 1X , b 1X and a 1Y , b 1Y All are parameter values ​​obtained by fitting trigonometric functions; S 1X (t) and S 1Y (t) represents the fitting residuals, which are the differences between the original values ​​and the trigonometric function fitted values ​​of the liquid pressure on the reference blade in the X and Y directions at each time point; t is time, and ω is the angular frequency.

[0045] ω=2π / T (3)

[0046] T represents the impeller rotation period, and π represents pi.

[0047] In other words, the time-varying curve of the liquid pressure in a certain direction experienced by the reference blade can be regarded as the superposition of a trigonometric function curve with a definite analytical expression and a residual curve without a definite analytical expression, where a 1X and a 1Y The amplitude is obtained by fitting a trigonometric function. and The initial phase is obtained by fitting trigonometric functions, b 1X and b 1Y The constant term obtained by fitting trigonometric functions

[0048] Furthermore, for other blades, it is only necessary to perform a time shift based on the reference blade representation method. For the blade numbered i, the liquid pressure it experiences in the X and Y directions is expressed as F, respectively. iX and F iY :

[0049]

[0050] S 1X (t) and S 1Y (t) is considered as a periodic original signal with a period of T, and the above S 1X [tT(i-1) / N] and S 1Yrespectively, represent the signal S 1X (t) and S 1Y (t) respectively, represent the signal S

[0051] In other words, the time-varying curve of the liquid pressure on the blade numbered i in a certain direction can also be regarded as the superposition of a trigonometric function curve and a residual curve, where the initial phase in the trigonometric function fitting result is delayed by 2π(i-1) / N based on the reference blade, and the residual curve is delayed by a time interval of T(i-1) / N based on the reference blade.

[0052] Finally, based on the above decomposition expression method, the constitutive characteristics of the hydraulic radial force of the impeller can be better understood, and the optimization design of the blade structure can be more targeted to achieve the reduction of the hydraulic radial force of the impeller. In particular, according to the mathematical principle, sin(x)=sin(x+2π) and sin(x)=-sin(x+π). Generally speaking, the blades on the centrifugal pump impeller are periodic and symmetrical, and there are an even number of blades. Therefore, for any blade, there is another corresponding blade. According to the expression of the liquid pressure on the two blades in the X and Y directions, it can be found that the sine part of the trigonometric function curve in the time-varying curve of the liquid pressure on the two blades can be exactly offset, leaving only the constant term. Therefore, during the optimization design process, we do not need to pay attention to the amplitude of the fitted trigonometric function, but only need to pay attention to the constant term and the residual curve.

[0053] In order to better understand, the X-direction hydraulic radial force of a certain 6-blade impeller is taken as an example for illustration.

[0054] The time-varying data of the liquid pressure on the reference blade numbered 1 in the X direction is fitted by a trigonometric function and expressed as F 1X :

[0055]

[0056] Then, the time-varying data of the liquid pressure on the other blades numbered 2 to 6 in the X direction can be rewritten directly according to the expression method of F 1X :

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] Because sin(x) = -sin(x-pi), we have:

[0063]

[0064] Therefore, in the optimization design process aiming at hydraulic radial force suppression, the focus should not be on the whole impeller's unsteady flow field and overall hydraulic radial force, but should be on the hydraulic radial force of a single blade and its nearby flow field. As for a single blade, even if the part of its time-varying curve of hydraulic radial force fitted into a trigonometric function has a high amplitude, it does not need to be considered due to the existence of the offset effect, but the constant term in the trigonometric function fitting result and the residual curve need to be focused on.

[0065] Therefore, the technical scheme of the present application breaks the conventional technical thinking in the field based on the latest scientific research findings, and through the decomposition representation of the hydraulic radial force of the centrifugal pump impeller, it can help designers more clearly understand the constitutive characteristics of the hydraulic radial force of the impeller, so as to more targetedly perform the design optimization work aiming at hydraulic radial force suppression. BRIEF DESCRIPTION OF DRAWINGS

[0066] Figure 1 The figure is a flow chart of the decomposition representation method of the hydraulic radial force of the centrifugal pump impeller in the embodiment of the present application.

[0067] Figure 2 The figure is a three-dimensional schematic diagram of the hydraulic model of the centrifugal pump in the embodiment of the present application.

[0068] Figure 3 The figure is a two-dimensional schematic diagram of the middle section of the three-dimensional diagram in a certain direction. Figure 2 The figure is a two-dimensional schematic diagram of the middle section of the three-dimensional diagram in a certain direction.

[0069] Figure 4 The figure is a time-varying curve of the X-direction hydraulic radial force of the impeller under a certain working condition of the centrifugal pump in the embodiment of the present application.

[0070] Figure 5 The figure is a time-varying curve of the Y-direction hydraulic radial force of the impeller under a certain working condition of the centrifugal pump in the embodiment of the present application.

[0071] Figure 6 The figure is a time-varying curve of the X-direction hydraulic radial force of each blade under a certain working condition of the centrifugal pump in the embodiment of the present application.

[0072] Figure 7 The figure is a time-varying curve of the Y-direction hydraulic radial force of each blade under a certain working condition of the centrifugal pump in the embodiment of the present application.

[0073] Figure 8The triangular function fitting part curve of the time-varying curve of the hydraulic radial force of each blade in the X direction of the centrifugal pump under a certain working condition in the embodiment of the application.

[0074] Figure 9 The triangular function fitting part curve of the time-varying curve of the hydraulic radial force of each blade in the Y direction of the centrifugal pump under a certain working condition in the embodiment of the application.

[0075] Figure 10 The fitting residual part curve of the time-varying curve of the hydraulic radial force of each blade in the X direction of the centrifugal pump under a certain working condition in the embodiment of the application.

[0076] Figure 11 The fitting residual part curve of the time-varying curve of the hydraulic radial force of each blade in the Y direction of the centrifugal pump under a certain working condition in the embodiment of the application.

[0077] The parts in the figure: 1-impeller area, 2-discharge chamber, 3-suction section, 4-inlet pipe, 5-outlet pipe, 6-inlet, 7-outlet, 8-blade. DETAILED DESCRIPTION

[0078] The application will be further described below in combination with the drawings and embodiments.

[0079] As shown in the drawings, Figure 1 The application provides a method for decomposing the hydraulic radial force of an impeller of a centrifugal pump, the impeller being provided with an even number of blades 8 that are periodically symmetrical, characterized in that the method comprises the following steps:

[0080] Step S1, as shown in the drawings, Figure 2 and Figure 3 a three-dimensional hydraulic model of the centrifugal pump including the impeller area 1 and the discharge chamber 2 is drawn, and one blade 8 on the impeller is optionally taken as a reference blade and numbered 1, and the remaining blades 8 are sequentially numbered 2 to N according to the rotation direction of the impeller, wherein N is the total number of blades;

[0081] Step S2, based on the hydraulic model obtained in step S1, a grid is divided, a computational fluid dynamics model is established, and transient simulation calculation under the working condition required for the study is carried out to obtain the transient variation of the flow field;

[0082] Step S3, during the calculation process of step S2, the time-varying data of the liquid pressure on the reference blade in the first radial direction and the second radial direction within one rotation period of the impeller are recorded, respectively, wherein the first radial direction and the second radial direction are two mutually orthogonal radial directions of the impeller.

[0083] Specifically, a three-dimensional X-Y-Z rectangular coordinate system can be established, and the Z axis represents the axial direction of the impeller, and the X and Y axes represent the first radial direction and the second radial direction, respectively.

[0084] Please refer to Figures 3 to 11The following steps are understood:

[0085] Step S4, based on the least square method, trigonometric function fitting is performed on the time-varying data obtained in step S3, and the liquid pressure on the reference blade in the first radial direction and the second radial direction is represented as F 1X and F 1Y :

[0086]

[0087] a 1X , b 1X and a 1Y , b 1Y are parameter values obtained by trigonometric function fitting; S 1X (t) and S 1Y (t) are fitting residuals, which are the differences between the original values and the trigonometric function fitting values of the liquid pressure on the reference blade in the first radial direction and the second radial direction at each time, respectively; t is time, and ω is angular frequency:

[0088] ω = 2π / T (3)

[0089] where T is the impeller rotation period, and π is the circular constant;

[0090] Step S5, for any blade 8, denoted as i, the liquid pressure on it in the first radial direction and the second radial direction is represented as F iX and F iY :

[0091]

[0092] S 1X (t) and S 1Y (t) are regarded as periodic original signals with T as the period, where S 1X [t-T(i-1) / N] and S 1Y [t-T(i-1) / N] represent, respectively, the signals obtained by moving the original signals S 1X (t) and S 1Y (t) in the increasing direction of the time axis t by a time interval of T(i-1) / N;

[0093] Step S6, the hydraulic radial forces on the impeller in the first radial direction and the second radial direction under the working condition to be studied are respectively decomposed and represented as and where F iX and F iY are the liquid pressures on the blade 8 numbered i in the first radial direction and the second radial direction obtained in step S5.

[0094] Preferably, in the above method for decomposing and representing the hydraulic radial force of the impeller of a centrifugal pump, in the computational fluid dynamics model in step S2, the impeller region 1 is set as a rotating dynamic mesh, and the rotating frequency is the rotating frequency of the impeller.

[0095] Preferably, in the above method for decomposing and representing the hydraulic radial force of the impeller of a centrifugal pump, in the computational fluid dynamics model in step S2, the rotating frequency of the impeller region 1 is constant.

[0096] Preferably, in the above method for decomposing and representing the hydraulic radial force of the impeller of a centrifugal pump, in the computational fluid dynamics model in step S2, the inlet and outlet boundary conditions are included, and a constant liquid inflow is set by one of the two.

[0097] In one embodiment, the inlet boundary condition is set as a velocity inlet with constant velocity at each mesh node, and the velocity value is converted from the volume flow rate by dividing the inlet cross-sectional area; and the outlet boundary condition is a pressure outlet condition with zero gauge pressure.

[0098] Preferably, in the above method for decomposing and representing the hydraulic radial force of the impeller of a centrifugal pump, the time step in the transient simulation calculation in step S2 is constant, and is not greater than 1% of the rotating period of the impeller.

[0099] In one embodiment, the time step is the time required for the impeller to rotate 1°.

[0100] Preferably, in the above method for decomposing and representing the hydraulic radial force of the impeller of a centrifugal pump, one impeller rotating period for data recording in step S3 is one complete impeller rotating period after the transient simulation calculation reaches convergence.

[0101] In one embodiment, the total duration of the transient simulation calculation is 6 impeller rotating periods, and the last complete impeller rotating period is used for data recording.

[0102] Preferably, in the above method for decomposing and representing the hydraulic radial force of the impeller of a centrifugal pump, the liquid pressure on the reference blade in the first radial direction and the second radial direction at a certain time in step S3 is the integral of the component of the liquid pressure on the surface of the reference blade in the first radial direction and the second radial direction at that time, respectively, with respect to the surface area of the blade.

[0103] Preferably, in the above method for decomposing and representing the hydraulic radial force of the impeller of a centrifugal pump, the fitting residual S 1X (t) and S 1Y (t) are both periodic signals with a period of T, the rotating period of the impeller.

[0104] Another aspect of the present invention provides an optimization design method applying the above-described decomposition representation method of the hydraulic radial force of a centrifugal pump impeller. This method involves using the expression result F of the liquid pressure experienced by the reference blade in the first and second radial directions. 1X and F 1Y To optimize the design, computational fluid dynamics transient simulation is used to adjust the blade structure design to obtain the optimal blade structure design scheme.

[0105] Preferably, in the above-described optimized design method, the result F, representing the liquid pressure experienced by the reference blade in the first and second radial directions, is used. 1X and F 1Y To optimize an object, this includes achieving one or both of the following two objectives through optimized design:

[0106] Objective 1: To obtain the minimum value of one or more of the following parameters: fitting parameter b 1X Fitting parameter b 1Y ,parameter

[0107]

[0108] Objective 2: Reduce the fitting residual S 1X (t) and / or fitting residual S 1Y (t) is the absolute value over all or part of the time period.

[0109] Example

[0110] In a more specific embodiment: Please refer to Figures 1 to 11 Understand this embodiment.

[0111] In this embodiment, the centrifugal pump impeller has 6 blades 8, with a flow rate of 16.2 m³ / s. 3 The working conditions studied were 2900 r / min and 2 h. Figure 1 A flowchart of the impeller hydraulic radial force decomposition representation method is given. Figure 2 This is a three-dimensional schematic diagram of the hydraulic model of the centrifugal pump. Figure 3 for Figure 2 A two-dimensional schematic diagram of the mid-section of a three-dimensional image in a certain direction, and Figure 3 The phase of the impeller is the initial moment in the transient calculation. The impeller rotation period T = 60 / 2900 ≈ 0.0207s, and the angular frequency ω = 2π / T ≈ 303.5s. -1 The time step for computational fluid dynamics transient calculations is 1 / 120 of the impeller rotation period.

[0112] Figure 3 A rectangular coordinate system was set up, with the X and Y directions being the first and second radial directions of the impeller, respectively, and arrows indicating the impeller's rotation direction.

[0113] Figure 4 and Figure 5 The figures show the time-varying curves of the impeller hydraulic radial force in the X and Y directions of the centrifugal pump under the studied operating conditions. Figure 6 and Figure 7 These are the time-varying curves of the hydraulic radial forces of each blade in the X and Y directions of the centrifugal pump under the studied operating conditions. Figure 6 The curve resulting from the superposition of the various curves and Figure 4 The middle curve is very similar, Figure 7 The curve resulting from the superposition of the various curves and Figure 5 The curves in the middle are very similar.

[0114] right Figure 6 The time-varying curve corresponding to blade No. 1, fitted with a trigonometric function expression, is as follows:

[0115] Goodness of fit R 2 A value >0.95 indicates a very good fit.

[0116] right Figure 7 The time-varying curve corresponding to blade No. 1, fitted with a trigonometric function expression, is as follows:

[0117] Goodness of fit R 2 A value >0.95 indicates a very good fit.

[0118] Based on the fitting results and residuals of blade 1, the fitting results and residuals of blades 2 through 6 can be rewritten. For example, the time-varying curve of the hydraulic radial force in the X direction of blade 2 can be fitted with the following trigonometric function expression:

[0119]

[0120] Therefore, the trigonometric function fitting curves of the time-varying hydraulic radial force of each blade in the X and Y directions of the centrifugal pump under the studied operating conditions are obtained, as shown in the figures below. Figure 8 and Figure 9 .

[0121] Furthermore, the residual curves of the time-varying hydraulic radial force curves of each blade in the X and Y directions of the centrifugal pump under the studied operating conditions were obtained, as shown in the figures below. Figure 10 and Figure 11 .

[0122] observe Figure 4 and Figure 5 It can be seen that, without decomposition, the time-varying curve of the impeller hydraulic radial force is quite complex and no clear pattern can be found.

[0123] Next, observe Figure 6 andFigure 7 It can be seen that the curve of the hydraulic radial force experienced by each blade 8 with time is a periodic curve, and the period is equal to the rotation period T of the impeller; optionally, a certain blade 8 is taken as a reference blade, and the next blade 8 of the reference blade in the rotation direction is taken as a neighboring blade, then the curve of the hydraulic radial force experienced by the neighboring blade with time is just T / N behind the curve of the hydraulic radial force experienced by the reference blade with time.

[0124] However, simply decomposing the time-varying curve of the hydraulic radial force of the impeller into the superposition of the time-varying curves of the hydraulic radial force of each blade, by comparing Figure 4 and Figure 6 or Figure 5 and Figure 7 It can be found that the fluctuation amplitude of the time-varying curve of the hydraulic radial force of each blade is significantly greater than the time-varying curve of the hydraulic radial force of the impeller, so the amount of effective information obtained is less.

[0125] Further observation Figure 8 and Figure 9 It can be seen that the curve of the hydraulic radial force experienced by each blade 8 with time can be fitted as a sinusoidal function curve with a high fitting degree, wherein: the angular frequency of each sinusoidal function is the angular frequency of the rotation of the impeller, the amplitude and constant term of each sinusoidal function are equal, and the initial phase of the corresponding sinusoidal function of each blade 8 decreases by 2π / N in the direction of rotation in turn, that is, optionally, a certain blade 8 is taken as a reference blade, and the next blade 8 of the reference blade in the rotation direction is taken as a neighboring blade, then the initial phase of the corresponding sinusoidal function of the neighboring blade is 2π / N behind the initial phase of the corresponding sinusoidal function of the reference blade, and the above π and N are the circular constant and the total number of blades respectively.

[0126] In addition, the sinusoidal part of the sinusoidal function curve of the No. 1 blade and the No. 4 blade, the No. 2 blade and the No. 5 blade, and the No. 3 blade and the No. 6 blade can be mutually offset to retain the constant term. Therefore, in the optimization design process targeting the hydraulic radial force suppression, the focus should not be on the non-steady flow field of the entire impeller and the overall hydraulic radial force, but should be focused on the hydraulic radial force experienced by a single blade 8 and the flow field near it. As for a single blade 8, even if the part of the time-varying curve of the hydraulic radial force fitted into a trigonometric function has a high amplitude, in fact, due to the offset effect, it does not need to be considered, but the constant term in the trigonometric function fitting result and the residual curve need to be focused on.

[0127] Further, from Figure 10 and Figure 11It can be seen that the residual curves of the hydraulic radial force borne by each blade 8 with time change have similar rules: the residual part curve in the time-varying curve of the liquid pressure in a certain direction borne by the blade numbered i lags behind the 1st reference blade by a time interval of T(i-1) / N. Therefore, the residual curve of the 1st blade can be used to infer the residual curves of the other blades 8 according to the time shift mode and the periodic principle.

[0128] According to the decomposition expression results of the centrifugal pump impeller hydraulic radial force, subsequent optimization design is carried out, that is, the expression results of the liquid pressure borne by the 1st blade in the X and Y directions F 1X and F 1Y are taken as the optimization objects, and the blade structure design is adjusted by means of the transient simulation calculation of computational fluid dynamics to obtain the optimal blade structure design scheme.

[0129] Specifically, in this embodiment, the installation angle and wrap angle and other structure design parameters of the blade 8 are adjusted to obtain the fitting parameter b 1X and the minimum value of the fitting parameter b 1Y is taken as the optimization target to carry out the optimization design work.

[0130] In this embodiment, based on the latest scientific research findings, the conventional technical thinking in the field is broken, and through the decomposition expression of the centrifugal pump impeller hydraulic radial force, the designer can more clearly understand the constitutive characteristics of the impeller hydraulic radial force, so as to more targetedly carry out the design optimization work for the hydraulic radial force suppression.

Claims

1. A method of decomposition representation of the hydraulic radial forces of a centrifugal pump impeller, said impeller being provided with an even number of blades (8) of periodic symmetry, characterized in that, The method comprises the following steps: Step S1, drawing a three-dimensional hydraulic model of a centrifugal pump including an impeller area (1) and a water outlet chamber (2), optionally taking one blade (8) on the impeller as a reference blade and numbering it as 1, and numbering the remaining blades (8) as 2 to N in sequence according to the rotation direction of the impeller, wherein N is the total number of blades; Step S2, based on the hydraulic model obtained in step S1, dividing the grid, establishing a computational fluid dynamics model, and carrying out transient simulation calculation under the required research working condition to obtain the transient change of the flow field; In the calculation process of step S2, the time-varying data of the liquid pressure on the reference blade in the first radial direction and the second radial direction within one impeller rotation period are recorded respectively, wherein the first radial direction and the second radial direction are two mutually orthogonal radial directions of the impeller; Step S4, based on the least square method, trigonometric function fitting is performed on the time-varying data obtained in step S3, and the liquid pressure borne by the reference blade in the first radial direction and the second radial direction is respectively represented as F 1X and F 1Y : a 1X , b 1X and a 1Y , b 1Y are the parameter values obtained by fitting the trigonometric functions; S 1X (t) and S 1Y (t) are the fitting residuals, which are the differences between the original values and the fitting values of the liquid pressure on the first and second radial directions of the reference blade at each time; t is the time, and ω is the angular frequency. ω = 2π / T (3) wherein T is the impeller rotation period, and π is the circular constant; Step S5, for any blade (8), let its number be i, then the liquid pressure on it in the first and second radial directions are denoted as F iX and F iY : S 1X (t) and S 1Y (t) are regarded as periodic original signals with T as a period, the above S 1X [t-T(i-1) / N] and S 1Y [t-T(i-1) / N] respectively represent signals obtained by moving the original signals S 1X (t) and S 1Y (t) in the increasing direction of the time axis t by a time interval of T(i-1) / N respectively; Step S6, the hydraulic radial force of the impeller under the required research condition in the first radial direction and the second radial direction is respectively decomposed and expressed as and Wherein F iX and F iY are the liquid pressure of the blade (8) numbered i obtained in step S5 in the first radial direction and the second radial direction respectively.

2. The method of claim 1, wherein the hydraulic radial force of the centrifugal pump impeller is decomposed into a component in the tangential direction and a component in the radial direction. In the computational fluid dynamics model in step S2, the impeller area (1) is set as a rotating dynamic grid, and the rotation frequency is the rotation frequency of the impeller.

3. The method of claim 1 or 2, wherein In the computational fluid dynamics model in step S2, the rotation frequency of the impeller area (1) is constant.

4. The method of claim 1, wherein the hydraulic radial force of the centrifugal pump impeller is decomposed into a component in the radial direction and a component in the tangential direction. In the computational fluid dynamics model in step S2, the inlet and outlet boundary conditions are included, and a constant liquid inflow is set through one of the two.

5. The method of claim 1, wherein the hydraulic radial force of the centrifugal pump impeller is decomposed into a component in the tangential direction and a component in the radial direction. The transient simulation calculation in step S2 has a constant time step that is not greater than 1% of the impeller rotation period.

6. The method of claim 1, wherein the hydraulic radial force of the centrifugal pump impeller is decomposed into a component in the radial direction and a component in the tangential direction. The impeller rotation period for which data recording is performed in step S3 is one complete impeller rotation period after the transient simulation calculation reaches convergence.

7. The method of claim 1, wherein the hydraulic radial force of the centrifugal pump impeller is decomposed into a component in the direction of the rotational axis of the impeller and a component in the direction perpendicular to the rotational axis of the impeller. The liquid pressure on the reference blade in the first radial direction and the second radial direction at a certain time in step S3 is the integral of the component of the liquid pressure on the surface of the reference blade in the first radial direction and the second radial direction at that time with respect to the surface area of the blade.

8. The method of claim 1, wherein the hydraulic radial force of the centrifugal pump impeller is decomposed into a component in the radial direction and a component in the tangential direction. The fitting residual S in the step S4 1X (t) and S 1Y (t) are periodic signals with a period T of rotation of the impeller.

9. An optimization design method using the decomposition representation method of the hydraulic radial force of the impeller of the centrifugal pump according to any one of claims 1 to 8, characterized in that, the representation result F of the liquid pressure on the reference blade in the first radial direction and the second radial direction 1X and F 1Y For the optimization object, the adjustment of the blade structure design is performed by means of the transient simulation calculation of computational fluid dynamics to obtain the optimal blade structure design scheme.

10. The method of optimizing design of claim 9, wherein, the representation F of the liquid pressure on the reference blade in the first and second radial directions 1X and F 1Y To optimize the object, including by optimizing the design to achieve either or both of the following two objectives: Objective 1 : Achieve a minimum of one or more of the following parameters: fitted parameter b 1X , fitted parameter b 1Y , parameter Objective 2: Reduce the fitting residual S 1X (t) and / or the fitting residual S 1Y The absolute value of (t) over all or part of the time period.

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