Method for determining morphology of vertical free outflow gas-liquid interface of large-diameter pressure water delivery system

Abstract

The invention discloses a method for determining the morphology of a vertical free outflow gas-liquid interface of a large-diameter pressure water delivery system, and belongs to the technical field of flow calculation of large-diameter pressure water delivery systems. Comprising the following steps: determining characteristic parameters describing vertical free outflow; establishing a coordinate system on the circular section of the vertical free outflow outlet; an appearance extreme value coefficient phi is introduced, and the maximum join height Hmax of a gas-liquid interface of large-diameter vertical free outflow is calculated; an appearance distribution coefficient delta y is introduced, and the distribution rule of the gas-liquid interface water height is determined; calculating the change of the water level rise along with y on the cross section of the vertical free outflow outlet x = 0 by using the appearance extreme value coefficient phi and the appearance distribution coefficient delta y; calculating the change of the water level along with x when y is equal to y0 on the cross section; and a diffusion flow factor a and a water-up flow factor b are introduced to calculate the internal flow characteristic hf of the vertical free outflow. The method can quickly and accurately estimate the appearance and the internal flow characteristics of the water-gas interface of the outlet section, and is simple, convenient and efficient.

Description

Technical Field

[0001] The present invention relates to the technical field of flow calculation of large-caliber pressurized water delivery systems, and in particular to a method for determining the morphology of a vertical free outflow gas-liquid interface of a large-caliber pressurized water delivery system. Background Art

[0002] Vertical free outflow is a special outflow structure used in large-diameter pressurized water delivery systems. It has the characteristics of large pipe diameter and large flow rate, and its gas-liquid interface morphology is complex and changeable. The morphology of the gas-liquid interface is crucial to the analysis of transient flow in pressurized water delivery systems. There is no calculation method for the morphology of the gas-liquid interface of vertical free outflow in large-diameter pressurized water delivery systems at home and abroad. To solve this problem, the present invention proposes a calculation method to determine the morphology of the gas-liquid interface of vertical free outflow in large-diameter pressurized water delivery systems, thereby providing reliable technical support for the transient flow analysis of large-diameter water delivery systems. Summary of the invention

[0003] The purpose of the present invention is to provide a method for determining the morphology of the gas-liquid interface of a vertical free outflow of a large-caliber pressurized water delivery system, comprising the following steps:

[0004] Step 1: Determine the characteristic parameters describing the vertical free outflow;

[0005] Step 2: On the circular cross section of the vertical free outflow outlet, establish a coordinate system with the center of the circle as the origin and the intersection of the longitudinal section and the outlet cross section as the reference;

[0006] Step 3: Introduce the shape extreme value coefficient φ and calculate the maximum height H of the gas-liquid interface of the large-diameter vertical free outflow max ;

[0007] Step 4: Introduce the shape distribution coefficient Δy to determine the distribution law of the gas-liquid interface height;

[0008] Step 5: Using the shape extreme value coefficient φ and the shape distribution coefficient Δy, calculate the change of the water surface height on the vertical free outflow outlet x=0 section with y;

[0009] Step 6: Calculate the change of water surface height with x on the section y=y0;

[0010] Step 7: Introduce the diffusion flow factor a and the Yonggao flow factor b to calculate the internal flow characteristics h of the vertical free outflow f .

[0011] The characteristic parameters in step 1 include the inlet diameter D0, the outlet diameter D1, and the flow rate Q of the water delivery system.

[0012] The maximum height H of the gas-liquid interface in step 3 max The calculation formula is as follows:

[0013]

[0014] Where Q is the flow rate of the water delivery system; g is the acceleration due to gravity.

[0015] In step 5, the function of the water surface height at the vertical free outflow outlet x=0 section as a function of y is:

[0016]

[0017] Among them, H x＝0 (y) is the change of vertical free outflow Yong high water level with y when x = 0; H max It is the maximum high water level of vertical free outflow.

[0018] In step 6, the function of the water surface height changing with x is:

[0019]

[0020] in, H is the change of vertical free outflow Yong high water level with x when y=y0; x＝0 It is the maximum high water level of the section.

[0021] The internal flow characteristics h of the vertical free outflow in step 7 f The calculation formula is as follows:

[0022]

[0023] Where Q is the flow rate of the water delivery system; g is the acceleration of gravity; and D0 is the inlet diameter.

[0024] The calculation formula of the shape extreme value coefficient φ is as follows:

[0025]

[0026] Among them, D1 is the outlet diameter and D0 is the inlet diameter.

[0027] The calculation formula of the shape distribution coefficient Δy is as follows:

[0028]

[0029] Among them, Δy is the gas-liquid interface shape distribution coefficient; Q is the flow rate of the water delivery system; D0 is the inlet diameter; D1 is the outlet diameter; g is the gravitational acceleration.

[0030] The calculation formula of diffusion flow factor a is as follows:

[0031] a=8.148(D1 / D0) -5.362 +0.734

[0032] The calculation formula of Yonggao flow factor b is as follows:

[0033]

[0034] Among them, D0 is the inlet diameter; D1 is the outlet diameter.

[0035] The beneficial effects of the present invention are:

[0036] 1. For a given large-caliber pressurized water delivery system with vertical free outflow, the present invention can quickly and accurately calculate the gas-liquid interface appearance and internal flow characteristics of the outlet section under different geometric conditions and flow conditions. The method is simple and efficient.

[0037] 2. The present invention solves the problem that it is difficult to obtain the morphology of the vertical free outflow gas-liquid interface of such large-diameter pressurized water delivery systems, thereby providing reliable technical support for the transient flow analysis of large-diameter water delivery systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is a flow chart of a method for determining the gas-liquid interface morphology of vertical free outflow in a large-caliber pressurized water delivery system;

[0039] Figure 2 It is a longitudinal section view of a vertical free outflow system of a large-caliber pressurized water delivery system of the present invention;

[0040] Figure 3 A schematic diagram of coordinates for defining outlet cross-sectional features of a large-caliber vertical free outflow system of the present invention as viewed from the outlet top view;

[0041] Figure 4 The inlet diameter of the vertical free flow is D0 = 9.1m, the outlet diameter is D1 = 15m, and the flow rate of the water delivery system is Q = 150m 3 Schematic diagram of the gas-liquid interface shape at the x=0 section of / s;

[0042] Figure 5 The inlet diameter of the vertical free flow is D0 = 9.1m, the outlet diameter is D1 = 15m, and the flow rate of the water delivery system is Q = 150m 3 Schematic diagram of the gas-liquid interface shape at the cross section y=0.752m of / s;

[0043] Figure 6 This is a comparison chart of the prediction results of internal flow characteristic values ​​changing with flow rate under different calculation methods for vertical free outflow with inlet diameter D0=9.1m and outlet diameter D1=15m. DETAILED DESCRIPTION

[0044] The present invention provides a method for determining the morphology of the gas-liquid interface of the vertical free outflow of a large-caliber pressurized water delivery system. The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0045] Figure 1 The flow chart of the method for determining the gas-liquid interface morphology of the vertical free outflow of a large-caliber pressurized water delivery system is shown in FIG. In this embodiment, the method specifically includes the following steps:

[0046] Step 1: For example, for a large-caliber pressurized water delivery system with vertical free outflow, determine the characteristic parameters describing the vertical free outflow, with inlet diameter D0 = 9.1m, outlet diameter D1 = 15m, and water delivery system flow rate Q = 150m 3 / s.

[0047] like Figure 2 As shown in the figure, the vertical free flow has the following structural features: (1) its longitudinal section changes gradually in a trumpet-like manner according to a fixed rule; (2) its own vertical free flow gradual widening structure is connected to a vertical straight pipe upstream; (3) after passing through the vertical gradual widening structure, its free outflow reaches a horizontal infinite position.

[0048] The trumpet-shaped widening law of the vertical free outflow longitudinal section is obtained by the following method: on the longitudinal section, the elevation difference between the inlet and outlet of the vertical free outflow is (D1-D0) / 2; with the inlet elevation line and the perpendicular point from the outlet outer edge to the line as the center, an arc with a radius of (D1-D0) / 2 is drawn that intersects the inlet and outlet points.

[0049] Step 2: On the circular cross section of the vertical free flow outlet, with the center of the circle as the origin and the intersection of the longitudinal section and the outlet section as the reference, establish a coordinate system. The longitudinal section direction is the y-axis, and the direction rotated 90° clockwise along the y-axis is the x-axis, which is used to characterize the gas-liquid interface morphology during vertical free flow. The coordinate system is as follows: Figure 3 shown.

[0050] Step 3: Introduce the shape extreme value coefficient φ and calculate the maximum height H of the gas-liquid interface of large-diameter vertical free outflow according to the following expression: max .

[0051]

[0052] Where Q is the flow rate of the water delivery system; g is the acceleration of gravity; φ is the extreme value coefficient of the shape, which is obtained according to the following formula:

[0053]

[0054] Among them, D1 is the outlet diameter and D0 is the inlet diameter.

[0055] Step 4: Introduce the shape distribution coefficient Δy to determine the distribution law of the gas-liquid interface height:

[0056]

[0057] Among them, Δy is the gas-liquid interface shape distribution coefficient; Q is the system flow rate; D0 is the vertical free flow inlet diameter; D1 is the vertical free flow outlet diameter; g is the gravitational acceleration.

[0058] Step 5: Based on the given large-diameter pressurized water supply system vertical free outflow system, use the shape distribution coefficient Δy to calculate the change of water surface height on the vertical free outflow outlet x=0 section with y according to the following expression.

[0059]

[0060] Among them, H x＝0 (y) is the change of vertical free outflow Yong high water level with y when x = 0; H max is the maximum vertical free outflow height; Δy is the shape distribution coefficient. The height of the water surface at section x=0 changes as follows: Figure 4 As shown. Take y = [-17.5, -10, 0, 0.75, 10, 17.5], the corresponding height is H x＝0 =[0.02,0.25,0.99,1.01,0.35,0.03].

[0061] Step 6: Based on the given vertical free outflow system, use H x＝0 (y), the change of water surface height with x at section y=y0 is calculated according to the following expression.

[0062]

[0063] in, H is the change of vertical free outflow Yong high water level with x when y=y0; x＝0 It is the maximum high water level of the section.

[0064] When y=[-17.5,-10,0,0.752,10,17.5], H x＝0 =[0.02, 0.25, 0.99, 1.01, 0.35, 0.03], the corresponding expression of the cross-sectional water surface height change is:

[0065]

[0066] The water surface height changes at section y = 0.752m are as follows Figure 5 shown.

[0067] Step 7: According to the given vertical free outflow system, introduce the diffusion flow factor a and the Yonggao flow factor b to calculate the internal flow characteristics h of the vertical free outflow. f .

[0068] The diffusion flow factor a is obtained according to the following formula:

[0069] a=8.148(D1 / D0) -5.362 +0.734=1.29

[0070] The diffusion flow factor b is obtained according to the following formula:

[0071]

[0072] Internal flow characteristics f for:

[0073]

[0074] Where Q is the system flow rate; D0 is the vertical free flow inlet diameter; D1 is the vertical free flow outlet diameter; g is the gravitational acceleration; H max is the maximum water level of vertical free outflow; π is pi.

[0075] If the inlet diameter D0 of the vertical free flow device is 9.1 m and the outlet diameter D1 is 15 m, which is consistent with the above conditions, the change of internal flow characteristics under different flow rates is calculated and compared with the experimental results and the predicted results calculated based on the empirical formula. Figure 6 shown.

[0076] From the analysis of the image, it can be seen that the existing method for predicting the internal flow characteristics of large-diameter vertical free outflow is derived from the empirical formula of the gradually widening tube of non-vertical free outflow, and does not take into account the influence of the gas-liquid interface morphology of the vertical free outflow. Therefore, it greatly underestimates the internal flow characteristic value of the vertical free outflow, cannot meet the accuracy requirements of engineering calculations, and increases the risk of engineering operation. Although the laboratory measurement and numerical test methods can relatively accurately predict the morphology of the gas-liquid interface through the similarity law, the implementation process is complicated and the efficiency is low, which cannot meet the high-efficiency requirements of engineering calculations. In contrast, the method for determining the gas-liquid interface morphology of the present invention has a simple implementation process and high calculation efficiency. The internal flow characteristics obtained by this method are very close to the high-precision empirical results. The relative error at most positions is controlled within 3%. The prediction accuracy is significantly better than the results calculated by the existing empirical formula, and can simultaneously meet the high-efficiency and accuracy requirements of engineering calculations.

[0077] In summary, for a given large-diameter pressurized water delivery system with vertical free outflow, the method of the present invention can quickly and accurately estimate the shape of the water-gas interface at the outlet section and its internal flow characteristics. It is simple and efficient, and can solve the problem that the gas-liquid interface morphology is difficult to obtain in existing methods, thereby providing reliable technical support for the transient flow analysis of large-diameter water delivery systems.

Claims

1. A method for determining the morphology of the gas-liquid interface in vertical free outflow of a large-caliber pressurized water delivery system, characterized in that: The steps include: Step 1: Determine the characteristic parameters describing the vertical free outflow; Step 2: On the circular cross section of the vertical free outflow outlet, establish a coordinate system with the center of the circle as the origin and the intersection of the longitudinal section and the outlet cross section as the reference; Step 3: Introduce the shape extreme value coefficient φ and calculate the maximum height H of the gas-liquid interface of large-diameter vertical free outflow max ; Step 4: Introduce the shape distribution coefficient Δy to determine the distribution law of the gas-liquid interface height; Step 5: Using the shape extreme value coefficient φ and the shape distribution coefficient Δy, calculate the change of the water surface height on the vertical free outflow outlet x=0 section with y; Step 6: Calculate the change of water surface height with x on the section y=y0; Step 7: Introduce the diffusion flow factor a and the Yonggao flow factor b to calculate the internal flow characteristics h of the vertical free outflow f .

2. According to the method for determining the morphology of the vertical free outflow gas-liquid interface of a large-caliber pressurized water delivery system in claim 1, it is characterized in that: The characteristic parameters in step 1 include the inlet diameter D0, the outlet diameter D1, and the flow rate Q of the water delivery system.

3. According to the method for determining the gas-liquid interface morphology of vertical free outflow of a large-caliber pressurized water delivery system in claim 1, it is characterized in that: In step 3, the maximum height H of the gas-liquid interface max The calculation formula is as follows: Where Q is the flow rate of the water delivery system; g is the acceleration due to gravity.

4. The method for determining the gas-liquid interface morphology of vertical free outflow of a large-caliber pressurized water delivery system according to claim 1 is characterized in that: In the step 5, the function of the water surface height on the vertical free outflow outlet x=0 section as a function of y is: Among them, H x＝0 (y) is the change of vertical free outflow Yong high water level with y when x = 0; H max It is the maximum high water level of vertical free outflow.

5. According to the method for determining the morphology of the vertical free outflow gas-liquid interface of a large-caliber pressurized water delivery system in claim 1, it is characterized in that: The function of the water surface height changing with x in step 6 is: in, H is the change of vertical free outflow Yong high water level with x when y=y0; x＝0 It is the maximum high water level of the section.

6. The method for determining the gas-liquid interface morphology of vertical free outflow of a large-caliber pressurized water delivery system according to claim 1 is characterized in that: The internal flow characteristics h of the vertical free outflow in step 7 f The calculation formula is as follows: Where Q is the flow rate of the water delivery system; g is the acceleration of gravity; and D0 is the inlet diameter.

7. The method for determining the gas-liquid interface morphology of vertical free outflow of a large-caliber pressurized water delivery system according to claim 1 or 3, characterized in that: The calculation formula of the shape extreme value coefficient φ is as follows: Among them, D1 is the outlet diameter and D0 is the inlet diameter.

8. The method for determining the gas-liquid interface morphology of vertical free outflow of a large-caliber pressurized water delivery system according to claim 1 or 4, characterized in that: The calculation formula of the shape distribution coefficient Δy is as follows: Among them, Δy is the gas-liquid interface shape distribution coefficient; Q is the flow rate of the water delivery system; D0 is the inlet diameter; D1 is the outlet diameter; g is the gravitational acceleration.

9. The method for determining the gas-liquid interface morphology of vertical free outflow of a large-caliber pressurized water delivery system according to claim 1 or 6, characterized in that: The calculation formula of diffusion flow factor a is as follows: a=8.148(D1 / D0) -5.362 +0.734 The calculation formula of Yonggao flow factor b is as follows: Among them, D0 is the inlet diameter; D1 is the outlet diameter.

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