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

Abstract

The invention provides a decomposition representation and optimization design method for hydraulic radial force of a centrifugal pump impeller, and aims to help a designer to deeply understand composition characteristics of the hydraulic radial force of the impeller and carry out targeted optimization. The method comprises the steps that a centrifugal pump three-dimensional hydraulic model is drawn, grids are divided, a computational fluid mechanics model is established, and transient simulation calculation is conducted; recording time-varying data of liquid pressure borne by the reference blade in two orthogonal radial directions, and performing trigonometric function fitting based on a least square method; the representation of the liquid pressure borne by other blades is obtained through time translation; the hydraulic radial force of the impeller is decomposed into the vector sum of the liquid pressure borne by the blades. On the basis, the optimization design method takes the representation result of the liquid pressure borne by the reference blade as an optimization object, and the reduction of the hydraulic radial force is realized by adjusting the blade structure. According to the decomposition representation and optimization design method, the composition of the hydraulic radial force of the impeller can be more clearly understood, and the design optimization effect is improved.

Description

Technical Field

[0001] The invention relates to the technical field of centrifugal pumps, and in particular to a method for decomposing and optimizing the hydraulic radial force of a centrifugal pump impeller. Background Art

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

[0003] The current known technical solutions usually use computational fluid dynamics methods to predict the flow field in the pump during the transient rotation of the impeller and the time-varying curve of the impeller hydraulic radial force induced by the unsteady flow field, relying on multiple rounds of iterations of "impeller structure design-computational fluid dynamics prediction" until a lower-level impeller hydraulic radial force design solution is obtained. In these known technical solutions, the entire impeller is usually regarded as a whole, and there is a lack of research on the composition characteristics of the impeller hydraulic radial force, so it is difficult to analyze the root cause of the impeller hydraulic radial force in a targeted and in-depth manner and perform more targeted design optimization.

[0004] Therefore, it is urgent to adopt new ideas to study the composition characteristics of the hydraulic radial force of the centrifugal pump impeller and develop corresponding optimization design methods. Summary of the invention

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

[0006] To achieve the above object, the present invention provides, on one hand, a method for decomposing and expressing the hydraulic radial force of a centrifugal pump impeller, wherein the impeller is provided with an even number of periodically symmetrical blades, and is characterized in that the method comprises the following steps:

[0007] Step S1, drawing a three-dimensional hydraulic model of a centrifugal pump including an impeller area and a water outlet chamber, selecting a blade on the impeller as a reference blade and numbering it as 1, and numbering the remaining blades from 2 to N in sequence according to the rotation direction of the impeller, where N is the total number of blades;

[0008] Step S2: Based on the hydraulic model obtained in Step S1, divide the grid, establish a computational fluid dynamics model, and conduct transient simulation calculations under the working conditions required for the research to obtain the transient changes in the flow field;

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

[0010] Step S4: For the time-varying data obtained in Step S3, perform trigonometric function fitting based on the least squares method, and express the liquid pressure received by the reference blade in the first radial direction and the second radial direction as F 1X and F 1Y :

[0011]

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

[0013] ω = 2π / T (3)

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

[0015] Step S5: For any blade, denote its number as i, then express the liquid pressure received by it in the first radial direction and the second radial direction as F iX and F iY :

[0016]

[0017] Regard S 1X (t) and S 1Y (t) as periodic original signals with a period of T. The above S 1X [t - T(i - 1) / N] and S 1Y [t - T(i - 1) / N] respectively represent the signals obtained by shifting 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;

[0018] Step S6: Decompose and represent the hydraulic radial forces on the impeller in the first radial direction and the second radial direction under the working conditions to be studied respectively as and where F iX and F iY are the liquid pressures on the blade numbered i obtained in Step S5 in the first radial direction and the second radial direction respectively.

[0019] Optionally, in the computational fluid dynamics model in Step S2 of the above method for decomposing and representing the hydraulic radial force of the centrifugal pump impeller, the impeller region is set as a rotating moving mesh, and the rotation frequency is the rotation frequency of the impeller.

[0020] Optionally, in the computational fluid dynamics model in Step S2 of the above method for decomposing and representing the hydraulic radial force of the centrifugal pump impeller, the rotation frequency of the impeller region is constant.

[0021] Optionally, in the computational fluid dynamics model in Step S2 of the above method for decomposing and representing the hydraulic radial force of the centrifugal pump impeller, it includes inlet and outlet boundary conditions, and a constant liquid inlet flow rate is set through one of them.

[0022] Optionally, in the transient simulation calculation in Step S2 of the above method for decomposing and representing the hydraulic radial force of the centrifugal pump impeller, there is a constant time step that is not greater than 1% of the impeller rotation period.

[0023] Optionally, in the above method for decomposing and representing the hydraulic radial force of the centrifugal pump impeller, one impeller rotation period for data recording in Step S3 is a complete impeller rotation period after the transient simulation calculation converges.

[0024] Optionally, in the above method for decomposing and representing the hydraulic radial force of the centrifugal pump impeller, the liquid pressures on the reference blade in the first radial direction and the second radial direction at a certain moment in Step S3 are respectively the integrals of the components of the liquid pressure on the surface of the reference blade in the first radial direction and the second radial direction over the blade surface area.

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

[0026] On the other hand, the present invention provides an optimization design method applying the above method for decomposing and representing the hydraulic radial force of the centrifugal pump impeller. This method is to use the representation results F 1X and F 1YTaking the optimization object, the blade structure design 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 representation results F 1X and F 1Y of the liquid pressures received by the reference blade in the first radial direction and the second radial direction are taken as the optimization object, including achieving any one or all of the following two goals through optimization design:

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

[0029]

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

[0031] The beneficial effects of the present invention will be introduced below in conjunction with the principle of the technical solution:

[0032] It is necessary to combine the knowledge of centrifugal pumps and fluid mechanics to understand the technical principle of this solution.

[0033] The impeller of a centrifugal pump usually consists of several blades and a hub for placing the blades. The impellers of some structural forms also include covers. The number of blades on the impeller of a centrifugal pump is usually even. This is because even-numbered blades are easier to achieve static balance and dynamic balance during the manufacturing process, are more stable during operation, can reduce the generation of eddy currents compared with odd-numbered blades, reduce resistance and improve efficiency; at the same time, even-numbered blades can reduce the vibration and noise of the blades, making the operation of the pump more stable and reliable.

[0034] The hydraulic radial force of the centrifugal pump impeller originates from the integral of the liquid pressure received at each part of the impeller surface over the surface area. Force is a vector. According to the principle of translation and decomposition of forces, the hydraulic radial force received by the entire impeller can be decomposed into the vector sum of the hydraulic radial forces received by each component of the impeller, and the hydraulic radial force received by any component can be decomposed into two components in the first radial direction and the second radial direction that are orthogonal to each other.

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

[0036] First, decompose the overall hydraulic radial force on the impeller into the hydraulic radial forces on all blades and the hydraulic radial forces on other parts except the blades. It is found that the hydraulic radial forces on the blades account for the vast majority of the overall hydraulic radial force on the impeller. Therefore, the hydraulic radial forces on all blades can be approximately regarded as the overall hydraulic radial force on the impeller.

[0037] Second, the curves of the hydraulic radial forces on each blade changing with time are all periodic curves, and the period size is equal to the impeller rotation period T.

[0038] Third, arbitrarily select a certain blade as the reference blade, and according to the rotation direction, let the next blade of the reference blade be the adjacent blade. Then, the curve of the hydraulic radial force on the adjacent blade changing with time lags behind the curve of the hydraulic radial force on the reference blade by exactly T / N in time: that is, by translating the curve of the hydraulic radial force on the adjacent blade changing with time in the direction of decreasing the time axis by T / N, it can completely coincide with the curve of the hydraulic radial force on the reference blade changing with time. Here, T and N are the impeller rotation period and the total number of blades respectively.

[0039] Fourth, the curves of the hydraulic radial forces on each blade changing with time can all be fitted into sine function curves with a high goodness of fit. Among them: the angular frequencies of each sine function are all the angular frequency of impeller rotation, the amplitudes and constant terms of each sine function are equal, and the initial phases of the sine functions corresponding to each blade decrease by 2π / N in turn with the order of rotation of the corresponding blade. That is, arbitrarily select a certain blade as the reference blade, and according to the rotation direction, let the next blade of the reference blade be the adjacent blade. Then, the initial phase of the sine function corresponding to the adjacent blade lags behind the initial phase of the sine function corresponding to the reference blade by 2π / N. Here, π and N are the pi and the total number of blades respectively.

[0040] Based on the above scientific laws, the technical solution of the present invention is designed. For the convenience of description, arbitrarily select a blade on the impeller as the reference blade and number it as 1, and number the remaining blades as 2 to N in turn according to the impeller rotation direction, where N is the total number of blades; denote the two mutually orthogonal radial directions of the impeller, namely the first radial direction and the second radial direction, as the X and Y directions respectively. Obtain the internal flow field of the pump and the time-varying situation of the hydraulic radial forces on each blade through transient computational fluid dynamics simulation.

[0041] First, approximately regard the overall hydraulic radial force of the impeller as the vector sum of the hydraulic radial forces on all blades, and orthogonally decompose the hydraulic radial force. Then, under the working conditions to be studied and optimized, the hydraulic radial forces on the impeller in the first radial direction and the second radial direction can be respectively decomposed and expressed as and where F iX and F iYare the liquid pressures on the blade numbered i in the first radial direction and the second radial direction respectively.

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

[0043]

[0044] The above a 1X , b 1X and a 1Y , b 1Y are all parameter values obtained by trigonometric function fitting; S 1X (t) and S 1Y (t) are both fitting residuals, and the two are respectively the differences between the original values and the trigonometric function fitting values of the liquid pressures on the reference blade in the X and Y directions at each moment; t is time, and ω is the angular frequency:

[0045] ω = 2π / T (3)

[0046] The above T is the impeller rotation period, and π is the pi.

[0047] In other words, the time-varying curve of the liquid pressure on the reference blade in a certain direction can be regarded as the superposition of a trigonometric function curve with a clear analytical expression and a residual curve without a clear analytical expression, where a 1X and a 1Y are the amplitudes obtained by trigonometric function fitting, and are the initial phases obtained by trigonometric function fitting, b 1X and b 1Y are the constant terms obtained by trigonometric function fitting

[0048] Thirdly, for other blades, it is only necessary to perform time translation based on the representation method of the reference blade. For the blade numbered i, the liquid pressures it receives in the X and Y directions are respectively expressed as F iX and F iY :

[0049]

[0050] Regarding S 1X (t) and S 1Y (t) as periodic original signals with a period of T, the above S 1X [t - T(i - 1) / N] and S 1Y[t - T(i - 1) / N] respectively represent the signals obtained by shifting the original signals S 1X (t) and S 1Y (t) by a time interval of T(i - 1) / N in the increasing direction of the time axis t.

[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. Among them, the initial phase in the trigonometric function fitting result lags by 2π(i - 1) / N based on the reference blade, and the residual curve lags by a time interval of T(i - 1) / N based on the reference blade.

[0052] Finally, based on the above decomposition representation method, the composition characteristics of the impeller hydraulic radial force can be understood more deeply, and the blade structure can be optimized more pertinently to reduce the impeller hydraulic radial force. In particular, according to the mathematical principle, sin(x) = sin(x + 2π) and sin(x) = -sin(x + π). Generally speaking, the blades on a centrifugal pump impeller are all periodically symmetric even-numbered blades. Then, for any blade, there must be another blade corresponding to it one by one. According to the expressions of the liquid pressure on both of them in the X and Y directions, it can be found that: the sine part of the trigonometric function curve in the time-varying curves of their liquid pressures can be exactly offset, leaving only the constant term. Therefore, in the optimization design process, there is no need to pay attention to the amplitude of the trigonometric function after fitting, but only to pay attention to the constant term part and the residual curve.

[0053] For better understanding, take the hydraulic radial force in the X direction of a 6-blade impeller as an example for illustration.

[0054] Perform trigonometric function fitting on the time-varying data of the liquid pressure on the reference blade numbered 1 in the X direction and represent it as F 1X :

[0055]

[0056] Then, for the time-varying data of the liquid pressure on the other blades numbered 2 to 6 in the X direction, without recording and calculating the fitting through the simulation process, it can be directly rewritten according to the representation method of F 1X :

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] Since sin(x) = -sin(x - π), thus:

[0063]

[0064] Therefore, in the optimization design process aiming at suppressing the hydraulic radial force, there is no need to focus on the unsteady flow field of the whole impeller and the overall hydraulic radial force. Instead, attention should be paid to the hydraulic radial force on a single blade and the flow field near it. Looking at a single blade, even if the part of the time-varying curve of its hydraulic radial force after fitting into a trigonometric function has a high amplitude, actually due to the cancellation effect, it does not need to be considered. Instead, attention should be paid to the constant term in the trigonometric function fitting result and the residual curve.

[0065] Therefore, based on the latest scientific research findings, the technical solution of the present invention breaks the conventional technical thinking in this field. Through the decomposition representation of the hydraulic radial force of the centrifugal pump impeller, it can help designers understand the composition characteristics of the impeller hydraulic radial force more deeply and clearly, so as to carry out the design optimization work for suppressing the hydraulic radial force more pertinently. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 It is a flowchart of the method for decomposing and representing the hydraulic radial force of the centrifugal pump impeller in the embodiment of the present invention.

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

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

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

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

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

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

[0073] Figure 8It is a trigonometric function fitting curve of the time-varying curve of the hydraulic radial force of each blade in the X direction under a certain working condition of the centrifugal pump in an embodiment of the present invention.

[0074] Figure 9 It is a trigonometric function fitting curve of the time-varying curve of the hydraulic radial force of each blade in the Y direction under a certain working condition of the centrifugal pump in an embodiment of the present invention.

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

[0076] Figure 11 It is a fitting residual curve of the time-varying curve of the hydraulic radial force of each blade in the Y direction under a certain working condition of the centrifugal pump in an embodiment of the present invention.

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

[0078] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0079] like Figure 1 As shown, the present invention provides a method for decomposing and expressing the hydraulic radial force of a centrifugal pump impeller, wherein the impeller is provided with an even number of blades 8 that are periodically symmetrical, and is characterized in that it comprises the following steps:

[0080] Step S1: Figure 2 and Figure 3 As shown, a three-dimensional hydraulic model of a centrifugal pump including an impeller area 1 and a water outlet chamber 2 is drawn, and a blade 8 on the impeller is selected as a reference blade and numbered as 1, and the remaining blades 8 are numbered from 2 to N in sequence according to the impeller rotation direction, where N is the total number of blades;

[0081] Step S2: based on the hydraulic model obtained in step S1, divide the grid, establish a computational fluid dynamics model, and carry out transient simulation calculations under the working conditions to be studied to obtain the transient changes of the flow field;

[0082] In the calculation process of step S3 and 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 cycle 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 XYZ rectangular coordinate system can be established, and the Z axis represents the impeller axial direction, and the X and Y axes represent the first radial direction and the second radial direction respectively;

[0084] Please refer to Figures 3 to 11Understand the subsequent steps:

[0085] Step S4: For the time-varying data obtained in step S3, perform trigonometric function fitting based on the least squares method, and express the liquid pressures on the reference blade in the first radial direction and the second radial direction as F 1X and F 1Y :

[0086]

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

[0088] ω = 2π / T (3)

[0089] where T is the impeller rotation period and π is the pi;

[0090] Step S5: For any blade 8, denote its number as i, then express the liquid pressures on it in the first radial direction and the second radial direction as F iX and F iY :

[0091]

[0092] Regard S 1X (t) and S 1Y (t) as periodic original signals with a period of T. The above S 1X [t - T(i - 1) / N] and S 1Y [t - T(i - 1) / N] respectively represent the signals obtained by shifting 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: Decompose and express the hydraulic radial forces on the impeller in the first radial direction and the second radial direction under the working conditions to be studied as and where F iX and F iY are respectively the liquid pressures on blade 8 numbered i obtained in step S5 in the first radial direction and the second radial direction.

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

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

[0096] Preferably, in the method for decomposing and representing the hydraulic radial force of the centrifugal pump impeller, the computational fluid dynamics model in step S2 includes inlet and outlet boundary conditions, and a constant liquid inlet flow rate is set through one of them.

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

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

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

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

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

[0102] Preferably, in the method for decomposing and representing the hydraulic radial force of the centrifugal pump impeller, the liquid pressures on the reference blade in the first radial direction and the second radial direction at a certain moment in step S3 are respectively the integrals of the components of the liquid pressure on the surface of the reference blade in the first radial direction and the second radial direction over the blade surface area.

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

[0104] On the other hand, the present invention provides an optimization design method applying the decomposition representation method of the hydraulic radial force of the centrifugal pump impeller. The method is as follows: taking the representation results F 1X and F 1Y of the liquid pressures received by the reference blade in the first radial direction and the second radial direction as the optimization objects, and adjusting the blade structure design by means of transient simulation calculation of computational fluid dynamics to obtain an optimal blade structure design scheme.

[0105] Preferably, in the above optimization design method, taking the representation results F 1X and F 1Y of the liquid pressures received by the reference blade in the first radial direction and the second radial direction as the optimization objects, it includes achieving any one or all of the following two objectives through optimization design:

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

[0107]

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

[0109] Embodiment

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

[0111] In this embodiment, the impeller of the centrifugal pump has 6 blades 8, and the flow rate of 16.2 m 3 / h and the rotational speed of 2900 r / min are the working conditions under study. Figure 1 The flow chart of the decomposition representation method of the impeller hydraulic radial force is given. Figure 2 It is a three-dimensional schematic diagram of the hydraulic model of the centrifugal pump. Figure 3 It is Figure 2 a two-dimensional schematic diagram of the middle section of the three-dimensional diagram in Figure 3 a certain direction, and the phase where the impeller is located in -1 is the initial moment in the transient calculation. The impeller rotation period T = 60 / 2900 ≈ 0.0207 s, and the angular frequency ω = 2π / T ≈ 303.5 s

[0112] Figure 3 A rectangular coordinate system is established in

[0113] Figure 4 and Figure 5 are the time-varying curves of the impeller hydraulic radial forces in the X and Y directions of the centrifugal pump under the studied operating conditions, respectively. Figure 6 and Figure 7 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, respectively. The curve obtained by superimposing the curves in Figure 6 is very similar to the curve in Figure 4 ; the curve obtained by superimposing the curves in Figure 7 is very similar to the curve in Figure 5 .

[0114] For Figure 6 the time-varying curve corresponding to the No. 1 blade in

[0115] the fitting goodness of fit R 2 > 0.95, indicating that the fitting effect is very good.

[0116] For Figure 7 the time-varying curve corresponding to the No. 1 blade in

[0117] the fitting goodness of fit R 2 > 0.95, indicating that the fitting effect is very good.

[0118] According to the fitting results and residuals of the No. 1 blade, the fitting results and residuals of the No. 2 to No. 6 blades can be rewritten. For example, for the time-varying curve of the hydraulic radial force of the No. 2 blade in the X direction, the trigonometric function expression obtained by fitting is:

[0119]

[0120] Thus, the partial curves of the trigonometric function fitting of 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 are shown in Figure 8 and Figure 9 .

[0121] Furthermore, the partial curves of the residuals of 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 are shown in Figure 10 and Figure 11 .

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

[0123] Then observing Figure 6 andFigure 7 It can be seen that the curves of the hydraulic radial forces on each blade 8 varying with time are all periodic curves, and the period size is equal to the impeller rotation period T; arbitrarily select a certain blade 8 as the reference blade, and according to the rotation direction, let the next blade 8 of this reference blade be the adjacent blade. Then, the curve of the hydraulic radial force on the adjacent blade varying with time lags behind the curve of the hydraulic radial force on the reference blade by exactly T / N in time.

[0124] However, simply decomposing the time-varying curve of the impeller hydraulic radial force into the superposition of the time-varying curves of the hydraulic radial forces on 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 on each blade is significantly greater than that of the time-varying curve of the impeller hydraulic radial force. Therefore, the amount of effective information obtained is less.

[0125] Further observation of Figure 8 and Figure 9 shows that the curves of the hydraulic radial forces on each blade 8 varying with time can all be fitted into sine function curves with a high goodness of fit. Among them: the angular frequencies of each sine function are all the angular frequency of impeller rotation, the amplitudes and constant terms of each sine function are equal, and the initial phases of the sine functions corresponding to each blade 8 decrease by 2π / N in turn with the sequence of rotation of the corresponding blades. That is, arbitrarily select a certain blade 8 as the reference blade, and according to the rotation direction, let the next blade 8 of this reference blade be the adjacent blade. Then, the initial phase of the sine function corresponding to the adjacent blade lags behind the initial phase of the sine function corresponding to the reference blade by 2π / N. Here, π and N are the pi and the total number of blades respectively.

[0126] In addition, the sine parts of the sine function curves of blade No. 1 and blade No. 4, blade No. 2 and blade No. 5, and blade No. 3 and blade No. 6 can cancel each other out while retaining the constant terms. Thus, in the optimization design process aiming at hydraulic radial force suppression, there is no need to focus on the unsteady flow field of the entire impeller and the overall hydraulic radial force, but should focus on the hydraulic radial force on a single blade 8 and the flow field near it. And for a single blade 8, even if the part of its time-varying curve of the hydraulic radial force after being fitted into a trigonometric function has a very high amplitude, actually due to the cancellation effect, it is not necessary to consider it either. Instead, it is necessary to pay attention to the constant term and the residual curve in the trigonometric function fitting result.

[0127] Furthermore, from Figure 10 and Figure 11It can be seen that the residual curves of the hydraulic radial forces on each blade 8 changing with time have a similar pattern: the residual part curve in the time-varying curve of the liquid pressure on the blade 8 numbered i in a certain direction lags behind the 1st reference blade by a time interval of T(i - 1) / N. Therefore, based on the residual curve of the 1st blade, according to the time shift method and the periodic principle, the residual curves of other blades 8 can be deduced.

[0128] Based on the above decomposition representation results of the hydraulic radial force of the centrifugal pump impeller, the subsequent optimization design is carried out, that is, taking the representation results F 1X and F 1Y of the liquid pressures on the 1st blade in the X and Y directions as the optimization objects, and adjusting the blade structure design by means of transient simulation calculation of computational fluid dynamics to obtain the optimal blade structure design scheme.

[0129] Specifically, in this embodiment, by adjusting the structural design parameters such as the installation angle and the wrap angle of the blade 8, the minimum values of the fitting parameters b 1X and the fitting parameter b 1Y are taken as the optimization objectives to carry out the optimization design work.

[0130] In this embodiment, based on the latest scientific research findings, the conventional technical thinking in this field is broken. Through the decomposition representation of the hydraulic radial force of the centrifugal pump impeller, it can help designers more deeply and clearly understand the composition characteristics of the hydraulic radial force of the impeller, so as to more pertinently carry out the design optimization work for suppressing the hydraulic radial force.

Claims

1. A method for decomposing and expressing the hydraulic radial force of a centrifugal pump impeller, wherein the impeller is provided with an even number of blades (8) that are periodically symmetrical, characterized in that: The following steps are involved: Step S1, drawing a three-dimensional hydraulic model of a centrifugal pump including an impeller region (1) and a water outlet chamber (2), selecting a blade (8) on the impeller as a reference blade and numbering it as 1, and numbering the remaining blades (8) from 2 to N in sequence according to the impeller rotation direction, wherein N is the total number of blades; Step S2: based on the hydraulic model obtained in step S1, divide the grid, establish a computational fluid dynamics model, and carry out transient simulation calculations under the working conditions to be studied to obtain the transient changes of the flow field; In the calculation process of step S3 and 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 cycle are recorded respectively, wherein the first radial direction and the second radial direction are two mutually orthogonal radial directions of the impeller; Step S4: Perform trigonometric function fitting on the time-varying data obtained in step S3 based on the least square method, and express the liquid pressure on the reference blade in the first radial direction and the second radial direction as F 1X and F 1Y : a above 1X , b 1X and a 1Y , b 1Y All are parameter values ​​obtained by trigonometric function fitting; S 1X (t) and S 1Y (t) are the fitting residuals, and the two are the differences between the original values ​​of the liquid pressure on the reference blade in the first radial direction and the second radial direction at each moment and the trigonometric function fitting value; t is time, and ω is angular frequency: ω=2π / T(3) In the above, T is the impeller rotation period, and π is the circumference of a circle; Step S5: For any blade (8), let its number be i, and the liquid pressure on it in the first radial direction and the second radial direction are respectively expressed as F iX and F iY : S 1X (t) and S 1Y (t) is regarded as a periodic original signal with a period of T. 1X [tT(i-1) / N] and S 1Y [tT(i-1) / N] respectively represents the original signal S 1X (t) and S 1Y (t) The signal obtained after moving in the increasing direction of the time axis t by a time interval of T(i-1) / N; Step S6: Decompose the hydraulic radial forces on the impeller in the first radial direction and the second radial direction under the working conditions to be studied into and where F iX and F iY The liquid pressures on the blade (8) numbered i in the first radial direction and the second radial direction obtained in step S5 respectively.

2. The method for decomposing and expressing the hydraulic radial force of a centrifugal pump impeller according to claim 1, characterized in that: In the computational fluid dynamics model in step S2, the impeller region (1) is set as a rotating dynamic grid, and the rotation frequency is the rotation frequency of the impeller.

3. The method for decomposing and expressing the hydraulic radial force of a centrifugal pump impeller according to claim 1 or 2, characterized in that: In the computational fluid dynamics model in step S2, the rotation frequency of the impeller region (1) is constant.

4. The method for decomposing and expressing the hydraulic radial force of a centrifugal pump impeller according to claim 1, characterized in that: The computational fluid dynamics model in step S2 includes inlet and outlet boundary conditions, and a constant liquid inlet flow rate is set by one of the inlet and outlet boundary conditions.

5. The method for decomposing and expressing the hydraulic radial force of a centrifugal pump impeller according to claim 1, characterized in that: The transient simulation calculation in step S2 has a constant time step that is no greater than 1% of the impeller rotation period.

6. The method for decomposing and expressing the hydraulic radial force of a centrifugal pump impeller according to claim 1, characterized in that: One impeller rotation cycle for which data is recorded in step S3 is a complete impeller rotation cycle after the transient simulation calculation reaches convergence.

7. The method for decomposing and expressing the hydraulic radial force of a centrifugal pump impeller according to claim 1, characterized in that: The liquid pressure on the reference blade in the first radial direction and the second radial direction at a certain moment in step S3 is respectively the integral of the components of the liquid pressure on the reference blade surface in the first radial direction and the second radial direction at that moment over the blade surface area.

8. The method for decomposing and expressing the hydraulic radial force of a centrifugal pump impeller according to claim 1, characterized in that: The fitting residual S in step S4 1X (t) and S 1Y (t) are all periodic signals with the impeller rotation period T as the period.

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

10. The optimization design method according to claim 9, characterized in that: The result F of expressing the liquid pressure on the reference blade in the first radial direction and the second radial direction 1X and F 1Y The optimization object includes achieving any or all of the following two goals through optimization design: Objective 1: Get the minimum value of one or more of the following parameters: Fitting parameter b 1X , fitting parameter b 1Y ,parameter Objective 2: Reduce the fitting residual S 1X (t) and / or the fitting residual S 1Y (t) Absolute value over all or part of the time period.

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