Large through-flow pump water pressure oscillation amplitude prediction method based on virtual target point matrix

Abstract

The application discloses a large-scale tubular pump water pressure oscillation amplitude prediction method based on a virtual target point matrix, and belongs to the technical field of large-scale low-lift water transfer projects. The method is as follows: the related characteristic parameters of a large-scale tubular pump device are determined, and the characteristic time sequence coordinates of a guide vane inlet section observed from the guide vane inlet direction are defined; the virtual time sequence target point matrix, the virtual wheel disc target point matrix and the radial extension function are calculated based on the characteristic parameters and the characteristic coordinates of the concerned points; and the water pressure oscillation amplitude of the guide vane inlet is calculated based on the obtained radial extension function. For a given large-scale tubular pump device, the water pressure oscillation amplitude at any concerned position of the guide vane inlet section can be quickly and accurately estimated by the application, which is simple, efficient and solves the problem that the existing method cannot accurately predict the water pressure oscillation amplitude of a large-scale tubular pump device under large-scale and multi-time sequence conditions, thereby providing reliable technical support for the quantitative evaluation of the hydraulic stability of the large-scale tubular pump device.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of large low-lift water transfer projects, and particularly relates to a large tubular pump water pressure oscillation amplitude prediction method based on a virtual target point matrix. BACKGROUND

[0002] The large tubular pump device is a large-flow and low-lift pump type frequently used in the field of large low-lift water transfer projects, and has a large device size and a diameter of an impeller that can exceed 3 m. The impeller has a low rotating speed, and is usually around 125 r / min. Under the coupling effect of such a large size and low rotating speed, the gravity effect of the large tubular pump device with a horizontal structure is particularly prominent, and there is always a constant pressure difference disturbance along the gravity direction, so that severe water pressure oscillation is easily induced at an inlet of a guide vane. However, since field testing of the prototype of the large tubular pump device is difficult to carry out, at present, quantitative evaluation of the water pressure oscillation amplitude can only rely on the traditional similarity principle, and the water pressure oscillation amplitude is calculated according to experimental or numerical simulation results of a device model according to the principle of hydraulic consistency. However, due to the influence of the significant gravity effect, it has been observed in actual operation that the water pressure oscillation amplitude at the inlet of the guide vane of the prototype of the large tubular pump device presents a strong non-symmetrical distribution feature that is completely different from that of the device model, and the feature also produces complex changes with changes in the device size and the time sequence position of the guide vane, thereby causing difficulties in rapid and accurate evaluation of the water pressure oscillation amplitude of the large tubular pump device. However, up to now, there has been no report on a high-efficiency prediction method for the water pressure oscillation amplitude of the large tubular pump device at home and abroad.

[0003] Therefore, in order to solve the problem that the water pressure oscillation amplitude of the large tubular pump device under large-scale and multi-time sequence conditions is difficult to accurately predict, the present application gives a practical high-efficiency prediction method for the water pressure oscillation amplitude on the basis of in-depth analysis of the water pressure oscillation characteristics at the inlet of the guide vane of the large tubular pump device, thereby providing reliable technical support for quantitative evaluation of the hydraulic stability of the large tubular pump device. SUMMARY

[0004] The present application provides a large tubular pump water pressure oscillation amplitude prediction method based on a virtual target point matrix, and aims to solve the problem that the existing method is difficult to accurately predict the water pressure oscillation amplitude of the large tubular pump device under large-scale and multi-time sequence conditions, so that for a given large tubular pump device, the water pressure oscillation amplitude at any concerned position of a guide vane inlet section can be rapidly and accurately estimated, thereby providing technical support for quantitative evaluation of the hydraulic stability of the large tubular pump device. The method comprises the following steps:

[0005] Step 1: defining relevant characteristic parameters of the large tubular pump device, including an impeller diameter D, a number of guide vanes Z, and a rated head H;

[0006] Step 2: Define the characteristic time coordinate λ, the circumferential coordinate θ and the radial coordinate s of the guide vane inlet section of the large tubular pump device respectively when viewed from the guide vane inlet direction;

[0007] Step 3: Introduce the start-up matrixes [P1]~[P5] and calculate the virtual time target point matrix [A] to represent the virtual time state of the guide vane of the large tubular pump device;

[0008] Step 4: Calculate the virtual wheel disc target point matrix [B] using the virtual time target point matrix [A] to represent the virtual wheel disc state of the guide vane inlet of the large tubular pump device;

[0009] Step 5: Calculate the radial variation function C(s) using the virtual wheel disc target point matrix [B] to represent the radial variation characteristics of the water pressure oscillation amplitude of the large tubular pump device;

[0010] Step 6: When the water pressure oscillation amplitude of the large tubular pump device needs to be evaluated, first input the characteristic time coordinate λ of the point of interest, and then obtain the required virtual time target point matrix [A] and virtual wheel disc target point matrix [B] according to Steps 3 and 4; then input the circumferential coordinate θ of the point of interest, and then obtain the required radial variation function C(s) according to Step 5; finally, input the radial coordinate s of the point of interest, and predict the water pressure oscillation amplitude △P of the point of interest.

[0011] Step 2 is as follows:

[0012] On the annular section of the guide vane inlet of the large tubular pump device, take the shaft center as the coordinate origin, take the positive top position as the circumferential starting point, take the clockwise direction as the positive direction of the circumferential direction when viewed from the guide vane inlet direction, and mark the circumferential coordinate as θ accordingly; take the direction from the hub to the rim as the positive direction of the radial direction, and mark the radial coordinate as s accordingly, which is equal to the ratio of the distance from any point in the annular section to the hub to the distance from the rim to the hub, so s=0 at the hub and s=1 at the rim; start from the circumferential starting point θ=0, set 13 virtual wheel disc target points at intervals of π / 6 along the positive direction, and mark them as θ1~θ13 in turn; start from the circumferential starting point θ=0, set 5 virtual time target points at intervals of π / 2Z along the positive direction, and mark them as λ1~λ5 in turn, and mark the circumferential coordinate of the guide vane inlet edge on the positive direction side closest to the circumferential starting point as the characteristic time coordinate λ. 13

[0013] The calculation formula of the virtual time target point matrix [A] in Step 3 is as follows:

[0014]

[0015] In the formula, tanh(·) is the hyperbolic tangent function; ξ is an empirical constant; λ is the characteristic time coordinate; k is the outer target point count symbol; [P k ​is the start-up matrix corresponding to the outer target point count symbol k; λ k is the virtual timing target corresponding to the outer target point count symbol k; m is the inner target point count symbol; λ m is the virtual timing target corresponding to the inner target point count symbol m.

[0016] The calculation formula of the virtual roulette target matrix [B] in step 4 is as follows:

[0017] [B] = [A][s 3 s 2 s 1] T

[0018] In the formula, the superscript T represents the transpose operation of the matrix.

[0019] The calculation formula of the radial transformation function C(s) in step 5 is as follows:

[0020]

[0021] In the formula, ln(·) is the natural logarithm function; θ is the circumferential coordinate; INT(·) is the integer function; α and β are empirical constants; π is the circular constant; i is the outer target point count symbol; θ i is the virtual roulette target corresponding to the outer target point count symbol i; j is the inner target point count symbol; θ j is the virtual roulette target corresponding to the inner target point count symbol j; t is the interval discrimination number of the virtual roulette target.

[0022] The prediction formula of the water pressure oscillation amplitude △P in step 6 is as follows:

[0023]

[0024] In the formula, ρ is the water flow density; g is the gravitational acceleration; H is the rated head; D is the impeller diameter; γ and are empirical constants.

[0025] The start-up matrices [P1]~[P5] in step 3 are as follows:

[0026]

[0027]

[0028]

[0029]

[0030] The empirical constant ξ = 0.013.

[0031] The empirical constants β = 0.014 and α = 1.

[0032] empirical constant γ = 0.141,

[0033] The present application has the advantages of:

[0034] 1. The present application can quickly and accurately estimate the water pressure oscillation amplitude at any concerned position of the guide vane inlet section under the conditions of different device sizes and different guide vane timing positions of a given large tubular pump device, and the method is simple and efficient.

[0035] 2. The present application solves the problem that the existing method cannot accurately predict the water pressure oscillation amplitude of a large tubular pump device under large-scale and multi-timing conditions, thereby providing reliable technical support for quantitative evaluation of the hydraulic stability of a large tubular pump device. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 The implementation flowchart of the prediction method of the water pressure oscillation amplitude of a large tubular pump device based on a virtual target point matrix provided by the present application;

[0037] Figure 2 The structure schematic diagram of the large tubular pump device of the present application;

[0038] Figure 3 The schematic diagram of the guide vane inlet section characteristic coordinates of the large tubular pump device from the guide vane inlet direction of the present application;

[0039] Figure 4 The guide vane inlet water pressure oscillation amplitude result comparison chart of a large tubular pump device with a impeller diameter of 2.4m under different prediction methods;

[0040] Figure 5 The guide vane inlet water pressure oscillation amplitude result comparison chart of a large tubular pump device with a impeller diameter of 4.2m under different prediction methods. DETAILED DESCRIPTION

[0041] The present application proposes a prediction method of the water pressure oscillation amplitude of a large tubular pump based on a virtual target point matrix, which will be further described below in combination with the drawings and specific embodiments.

[0042] Figure 1 The implementation flowchart of the prediction method of the water pressure oscillation amplitude of a large tubular pump device based on a virtual target point matrix provided by the present application; Figure 2 The structure schematic diagram of the large tubular pump device of the present application; the prediction method of the water pressure oscillation amplitude of a large tubular pump device based on a virtual target point matrix of the present embodiment is specifically implemented as follows:

[0043] Step 1: Determine the relevant characteristic parameters of the given large-scale axial flow pump device, including impeller diameter D = 2.4m, number of guide vanes Z = 7, and rated head H = 7.72m.

[0044] Step 2: Based on the given large-scale axial flow pump assembly, such as... Figure 3 As shown, on the annular cross-section of the guide vane inlet, with the axis center as the origin, the top position as the circumferential starting point, and the clockwise direction observed from the guide vane inlet as the positive circumferential direction, the circumferential coordinates are denoted as θ. The direction from the hub to the rim of the annular cross-section is taken as the positive radial direction, and the radial coordinates are denoted as s. The value of s is equal to the ratio of the distance from any point within the annular cross-section to the hub to the distance from the rim to the hub; therefore, s = 0 at the hub and s = 1 at the rim. Starting from the circumferential starting point θ = 0, 13 virtual wheel target points are set along the positive direction at intervals of π / 6 and sequentially denoted as θ1 to θ2. 13 Starting from the circumferential starting point θ = 0, five virtual timing target points are set along the positive direction with an interval of π / 2Z and are sequentially denoted as λ1 to λ5. The circumferential coordinate of the guide vane inlet side that is on the positive direction side and closest to the circumferential starting point is designated as the characteristic timing coordinate λ.

[0045] Step 3: Introduce the startup matrix [P1]~[P5]. Based on the given large-scale axial flow pump device, if the characteristic time-series coordinate of interest λ=0, calculate the virtual time-series target matrix [A] using the following formula:

[0046]

[0047] In the formula, tanh(·) is the hyperbolic tangent function; ξ is an empirical constant with a value of 0.013; λ is the characteristic time series coordinate; k is the outer target point count sign; [P k ] represents the activation matrix corresponding to the outer target counting symbol k; λ k For the outer target counting symbol k, the virtual time-series target symbol is k; for the inner target counting symbol m, the inner target counting symbol is m; for the inner target counting symbol m, the inner target counting symbol m is m. m The virtual time-series target corresponding to the inner target counting symbol m.

[0048] The startup matrices [P1] to [P5] are as follows:

[0049]

[0050]

[0051]

[0052]

[0053] Step 4: Using the aforementioned virtual time-series target matrix [A], calculate the virtual wheel target matrix [B] according to the following expression to characterize the virtual wheel state at the guide vane inlet of the large-scale axial flow pump device.

[0054]

[0055] In the formula, the superscript T represents the transpose operation of the matrix.

[0056] Step 5: Using the aforementioned virtual wheel target matrix [B], calculate the radial topological function C(s) according to the following expression to characterize the radial topological characteristics of the water pressure oscillation amplitude of the large-scale axial flow pump device.

[0057] If the circumferential coordinate of the point of interest is θ = π, the radial topology function C(s) can be calculated using the following formula:

[0058]

[0059] In the formula, ln(·) is the natural logarithm function; INT(·) is the floor function; α and β are empirical constants, with values ​​of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 ...

[0060] 0.014; π is the mathematical constant pi; i is the outer target point count symbol; θ i The outer target counting symbol i represents the virtual wheel target; j represents the inner target counting symbol; θ j t represents the virtual roulette target corresponding to the inner target counting symbol j; t represents the interval discrimination number of the virtual roulette target.

[0061] Step 6: When it is necessary to evaluate the water pressure oscillation amplitude of a large-scale axial flow pump device, first input the characteristic time-series coordinate λ of the point of interest, and obtain the required virtual time-series target matrix [A] and virtual wheel target matrix [B] according to Step 3 and Step 4; then input the circumferential coordinate θ of the point of interest, and obtain the required radial topology function C(s) according to Step 5.

[0062] Given a large-scale axial flow pump device, if the radial coordinate of the point of interest is s = 0.5, the water pressure oscillation amplitude ΔP at the point of interest can be predicted using the following formula:

[0063]

[0064] In the formula, ρ is the water flow density, with units of kg / m³. 3 g is the acceleration due to gravity, with units of m / s². 2 H is the rated head, in meters; D is the impeller diameter, in meters; γ, These are empirical constants, with values ​​of 0.141 and 0.422, respectively.

[0065] According to the calculation method in the above embodiment, when the impeller diameter D = 2.4m, the number of guide vanes Z = 7, the rated head H = 7.72m, the water pressure oscillation amplitude ΔP at the circumferential coordinate θ = 0, π / 6, π / 3, π / 2, 2π / 3, 5π / 6, π, 7π / 6, 4π / 3, 3π / 2, 10π / 3, 11π / 3, 2π, respectively, the characteristic time sequence coordinate λ = 0, the radial coordinate s = 0.5, the variation diagram of the water pressure oscillation amplitude with the circumferential coordinate under the condition is drawn, and the calculation results of the high-precision numerical simulation method verified by experiments and the calculation results of the existing prediction method based on the principle of hydraulic consistency are compared, as shown in FIG. 1. Figure 4 If the impeller diameter D = 4.2m, the rated head H = 7.83m, and the remaining conditions remain the same as above, the variation diagram of the water pressure oscillation amplitude with the circumferential coordinate under the condition is drawn, and the calculation results of the high-precision numerical simulation method verified by experiments and the calculation results of the existing prediction method based on the principle of hydraulic consistency are compared, as shown in FIG. 2. Figure 5

[0066] It can be seen from the analysis that the existing prediction method is usually based on the principle of hydraulic consistency, and the water pressure oscillation amplitude ΔP / ρgH at the same relative position in the original model is considered to be equal according to the experimental or numerical simulation results of the device model, so that the water pressure oscillation amplitude of the device prototype is greatly underestimated, and the precision requirement of engineering calculation cannot be met, which may increase the instability risk of the device prototype. The high-precision numerical simulation method can accurately predict the water pressure oscillation amplitude of the guide vane inlet of the large tubular pump device, but the implementation process is complex and the calculation efficiency is low, which cannot meet the efficient demand of engineering calculation. In comparison, the prediction method of the present application has a simple implementation process and high calculation efficiency, and the water pressure oscillation amplitude obtained by using the method is very close to the high-precision actual result, and the relative error at most positions is controlled within 5%, the prediction accuracy is obviously better than the calculation result of the existing prediction method, and the high-efficient and precise demand of engineering calculation can be met.

[0067] In summary, for a given large tubular pump device, the prediction method of the present application can quickly and accurately estimate the water pressure oscillation amplitude at any concerned position of the guide vane inlet cross section, which is simple and efficient, and can solve the problem that the existing method cannot accurately predict the water pressure oscillation amplitude of the large tubular pump device under the condition of large scale and multiple time sequences, thereby providing reliable technical support for the quantitative evaluation of the hydraulic stability of the large tubular pump device.​

Claims

1. A method for predicting the amplitude of water pressure oscillation in a large-scale axial-flow pump based on a virtual target matrix, characterized in that, Includes the following steps: Step 1: Determine the relevant characteristic parameters of the large-scale axial flow pump unit, including impeller diameter D, number of guide vanes Z, and rated head H; Step 2: Define the characteristic temporal coordinates λ, circumferential coordinates θ, and radial coordinates s of the guide vane inlet section of the large axial flow pump device as viewed from the guide vane inlet direction; Step 3: Introduce the start-up matrix [P1]~[P5] and calculate the virtual timing target matrix [A] to characterize the virtual timing state of the guide vanes of the large-scale axial flow pump device; Step 4: Calculate the virtual wheel target matrix [B] using the virtual time-series target matrix [A] to characterize the virtual wheel state at the guide vane inlet of the large-scale axial flow pump device; Step 5: Calculate the radial topological function C(s) using the virtual wheel target matrix [B] to characterize the radial topological characteristics of the water pressure oscillation amplitude of the large-scale axial flow pump device; The formula for calculating the radial topology function C(s) in step 5 is as follows: ， In the formula, ln(·) is the natural logarithm function; θ is the circumferential coordinate; INT(·) is the floor function; α and β are empirical constants; π is pi; i is the outer target point count symbol; θ i θ represents the virtual wheel target corresponding to the outer target counting symbol i; j represents the inner target counting symbol; θ j is the virtual roulette target point corresponding to the inner target point counting symbol j; t is the interval discrimination number of the virtual roulette target point; Step 6: When it is necessary to evaluate the water pressure oscillation amplitude of a large-scale axial flow pump device, first input the characteristic time-series coordinates λ of the point of interest, and obtain the required virtual time-series target matrix [A] and virtual wheel target matrix [B] according to Step 3 and Step 4; then input the circumferential coordinates θ of the point of interest, and obtain the required radial topology function C(s) according to Step 5; finally input the radial coordinates s of the point of interest to predict the water pressure oscillation amplitude ΔP of the point of interest. The prediction formula for the water pressure oscillation amplitude ΔP in step 6 is as follows: ， In the formula, ρ is the water flow density; g is the gravitational acceleration; H is the rated head; D is the impeller diameter; and γ and φ are empirical constants.

2. The method for predicting the water pressure oscillation amplitude of a large-scale axial-flow pump based on a virtual target matrix according to claim 1, characterized in that, Step 2 is described in detail below: On the annular cross section of the guide vane inlet of a large axial flow pump device, the axis is taken as the origin of the coordinate system, the top position is taken as the starting point of the circumferential direction, and the clockwise direction observed from the guide vane inlet is taken as the positive direction of the circumferential direction. Based on this, the circumferential coordinate is marked as θ. Taking the direction from the hub to the rim of the annular cross-section as the positive radial direction, and denoting the radial coordinates as s, the value of which is equal to the ratio of the distance from any point within the annular cross-section to the hub to the distance from the rim to the hub. Therefore, s=0 at the hub and s=1 at the rim. Starting from the circumferential starting point θ=0, 13 virtual wheel target points are set along the positive direction at intervals of π / 6 and are sequentially denoted as θ1~θ2. 13 Starting from the circumferential starting point θ=0, five virtual timing target points are set along the positive direction with an interval of π / 2Z and are denoted as λ1~λ5. The circumferential coordinate of the guide vane inlet side that is on the positive direction side and closest to the circumferential starting point is designated as the characteristic timing coordinate λ.

3. The method for predicting the water pressure oscillation amplitude of a large-scale axial-flow pump based on a virtual target matrix according to claim 1, characterized in that, The formula for calculating the virtual temporal target matrix [A] in step 3 is as follows: ， In the formula, tanh(·) is the hyperbolic tangent function; ξ is an empirical constant; λ is the characteristic time series coordinate; k is the outer target point count sign; [P k ] represents the activation matrix corresponding to the outer target counting symbol k; λ k For the outer target counting symbol k, the virtual time-series target symbol is k; for the inner target counting symbol m, the inner target counting symbol is m; for the inner target counting symbol m, the inner target counting symbol m is m. m The virtual time-series target corresponding to the inner target counting symbol m.

4. The method for predicting the water pressure oscillation amplitude of a large-scale axial-flow pump based on a virtual target matrix according to claim 1, characterized in that, The formula for calculating the virtual roulette target matrix [B] in step 4 is as follows: ， In the formula, the superscript T represents the transpose operation of the matrix.

5. The method for predicting the water pressure oscillation amplitude of a large-scale axial-flow pump based on a virtual target matrix according to claim 1, characterized in that, The activation matrices [P1] to [P5] in step 3 are specifically as follows: ， ， ， 。 6. The method for predicting the water pressure oscillation amplitude of a large-scale axial-flow pump based on a virtual target matrix according to claim 3, characterized in that, The empirical constant ξ = 0.

013.

7. The method for predicting the water pressure oscillation amplitude of a large-scale axial-flow pump based on a virtual target matrix according to claim 1, characterized in that, The empirical constants are β=0.014 and α=1.

8. The method for predicting the water pressure oscillation amplitude of a large-scale axial-flow pump based on a virtual target matrix according to claim 1, characterized in that, The empirical constants are γ = 0.141 and φ = 0.422.

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