A fitting extrapolation method for static characteristic curve of direct-acting gas pressure regulator

Abstract

The present application belongs to the technical field of pressure regulator, and particularly relates to a fitting extrapolation method for static characteristic curve of direct-acting gas pressure regulator. The process mainly comprises: performing flow coefficient experiment of maximum opening of the pressure regulator to obtain flow coefficient and critical pressure difference ratio; selecting several small and medium flow points to perform static characteristic experiment of the pressure regulator, comparing the relationship between pressure difference ratio and critical pressure difference ratio, and converting the measured flow into critical flow; performing linear fitting on the critical flow and outlet pressure data, and selecting a fitting function with fitting degree greater than 0.95; bringing the target flow of the extrapolated flow region into the fitting function to obtain extrapolated outlet pressure data, drawing an extrapolated curve, and splicing the measured curve and the extrapolated curve to obtain a complete static characteristic curve. The method can reliably extrapolate the static characteristic curve to the required flow through fitting processing on the small flow measured data, so as to achieve the purpose of completing the static characteristic test of the pressure regulator and reduce the pressure and flow requirements of the test system.

Description

Technical Field

[0001] This invention belongs to the field of pressure regulator technology, specifically relating to a method for fitting and extrapolating the static characteristic curve of a direct-acting gas pressure regulator. Background Technology

[0002] Direct-acting gas pressure regulators play a role in regulating and stabilizing downstream gas pressure in municipal gas transmission and distribution systems. They are relatively simple in structure, low in cost, and the most widely used gas pressure regulators. Their static characteristic curve reflects the relationship between downstream gas consumption and gas pressure changes. Gas pressure that is too high or too low will affect the gas safety of downstream gas users. Before installing and using the pressure regulator, its static characteristic curve needs to be determined through testing.

[0003] In the static characteristic testing of certain pressure regulators with large diameters and high pressures, the lack of large flow rate data is due to limitations in the test site and energy storage capacity, thus limiting the practical measurement range of actual flow testing methods. Therefore, it is necessary to establish a reasonable method for predicting static characteristic curves, which, based on fitting partial measured data, reliably extrapolate the static characteristic curves to the required flow rates. Summary of the Invention

[0004] The purpose of this invention is to provide a fitting extrapolation method for the static characteristic curve of a direct-acting gas pressure regulator. This method can reliably extrapolate the static characteristic curve to the required flow rate by fitting and processing measured data at low flow rates, thereby achieving the purpose of completing the static characteristic test of the pressure regulator and reducing the pressure and flow requirements of the test system.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for fitting and extrapolating the static characteristic curve of a direct-acting gas pressure regulator, characterized by comprising the following steps:

[0007] (1) Conduct flow coefficient experiments at the maximum opening of the pressure regulator to obtain the maximum flow coefficient C and the critical pressure difference ratio Xt;

[0008] (2) The pressure regulator is set to an inlet pressure of P1s and an atmospheric pressure of Pa. Within the experimental flow range, v flow points are uniformly selected for static characteristic experiments, and the measured flow rate Q is obtained for each point. n Inlet pressure P1 n Export pressure P2 n And calculate their respective pressure differential ratios X. n， Where n = 1, 2, ..., v;

[0009] (3) Compare X n The relationship with Xt, when X n When Xt < Xt, calculate the expansion coefficient Y. n The measured flow rate Qn Converted to critical flow rate Qt n When X n When ≥Xt, directly use the measured flow rate Q n Converted to critical flow rate Qt n ;

[0010] (4) Regarding the critical flow rate Qt n and export pressure P2 n Perform linear fitting to obtain the fitted function;

[0011] (5) Select w target flow points Qj within the extrapolated flow area, where j=1,2,...,w. Calculate the extrapolated outlet pressure based on the fitting function obtained in step (4), and plot the extrapolation curve.

[0012] ⑹ Plot the measured curves and combine the measured curves with the extrapolated curves to obtain the static characteristic curve of the regulator with complete flow rate.

[0013] Additional technical features of the fitting extrapolation method for the static characteristic curve of the aforementioned direct-acting gas pressure regulator also include:

[0014] —In step (1), the determination process of the maximum flow coefficient C and the critical pressure difference ratio Xt is as follows:

[0015] ① Record the atmospheric pressure Pa, and uniformly select y points P1 for the inlet pressure. m Where m = 1, 2, ..., y, the flow rates Qc are measured respectively. m Under the condition of maximum regulator opening, the outlet pressure is P2. m =0; then, the pressure difference ratio X m =(P1 m -P2 m ) / (P1 m +Pa); Y m ×C=4.31Qc m / [(P1 m +Pa)×√X m ], where √ represents the square root;

[0016] ②X m x and y coordinates m ×C is the ordinate, and a linear equation is used to fit the curve, forming a fitted line.

[0017] When X m =0, then Y m =1, Y m ×C=C; when Y m =0.667, Y m If ×C = 0.667C, then Xt = X m .

[0018] —In step (2), the static characteristic experiment, the pressure difference ratio X n =(P1 n -P2 n ) / (P1 n +Pa).

[0019] —In step (3), when X n When Xt < Xt, the coefficient of thermal expansion Y n =1-X n / (3×Xt;when X n When Xt ≥ , the coefficient of thermal expansion Y n =0.667;

[0020] Then, the measured flow rate Q n Converted to critical flow rate Qt n The formula is Qt n =Y n ×P1s×Q n / (0.667×P1) n ).

[0021] —In step (4), the critical flow rate Qt n and export pressure P2 n To perform fitting, the function formula is:

[0022] Quadratic fitting function: P2 n =a+b×Qt n +c×Qt n 2 ;or

[0023] First-order fitting function: P2 n =a+b×Qt n。

[0024] —In step (4), ① when v≥5, then perform linear and quadratic function fitting respectively, and calculate the goodness of fit R. 2 , ;

[0025] in, The nth pressure value is calculated using the fitted function. To measure the outlet pressure P2 of v n The average value;

[0026] ② Determine the R-value of linear and quadratic functions. 2 If the value is greater than 0.95, select R. 2 The fitting function with an R-value greater than 0.95 is the final fitting function to be selected; if the R-values ​​of the linear and quadratic functions are... 2 Since all values ​​are greater than 0.95, a linear function is selected as the final fitting function.

[0027] —In step (5), ① the pressure regulator is assigned an inlet pressure of P1s and an outlet pressure of P2s to calculate the maximum flow rate Qmax:

[0028] That is: Qmax = 0.232 × Y × C × (P1s + Pa) × √Xt, where √ represents the square root;

[0029] First, calculate the pressure difference ratio X = (P1s - P2s) / (P1s + Pa).

[0030] When X≥Xt, the expansion coefficient Y=0.667; when X<Xt, the expansion coefficient Y=1-X / (3×Xt).

[0031] ② Compare the relationship between the voltage regulator's claimed maximum flow rate Qmax-P1s and the calculated maximum flow rate Qmax, and take the smaller of the two as the extrapolated maximum boundary flow rate Qm. The extrapolated flow rate region is the range from the extrapolated maximum boundary flow rate Qm to the measured flow rate Q in the static characteristic experiment. n The maximum value Q n The numerical range of max

[0032] Then the target flow Qj = Q n max+(Qm-Q n max) × j / w, where j = 1, 2, ..., w;

[0033] ③ Convert the target flow rate Qj into the extrapolated critical flow rate Qtj.

[0034] Qtj = Y × P1s × Qj / (0.667 × P1); where, P1 = P1s

[0035] The externalized outlet pressure p2j is calculated by finally selecting the fitting function;

[0036] ④ Perform linear fitting on the extrapolated critical flow rate Qtj and the extrapolated outlet pressure p2j to obtain the fitting function, and plot the extrapolation curve.

[0037] Compared with existing technologies, the fitting extrapolation method for the static characteristic curve of a direct-acting gas pressure regulator provided by this invention has the following advantages: First, a flow coefficient experiment is conducted to obtain the flow coefficient and critical pressure difference ratio. Then, static characteristic experiments are performed with several values ​​within a small to medium flow range to convert the measured flow rate into the critical flow rate. Based on this, a linear fit is performed between the critical flow rate and the outlet pressure. A fitting function with a fitting degree greater than 0.95 is selected to calculate the target flow point within the extrapolation region, deriving the extrapolation data and obtaining the extrapolation curve. Combining the measured data curve and the extrapolation data curve yields the complete static characteristic curve of the pressure regulator. This method reliably extrapolates the static characteristic curve to the required flow rate by fitting measured data at small flow rates, thereby achieving the purpose of completing the static characteristic test of the pressure regulator and reducing the pressure and flow requirements of the test system. Attached Figure Description

[0038] Figure 1 This is a flowchart of the fitting and extrapolation method for the static characteristic curve of the direct-acting gas pressure regulator of the present invention;

[0039] Figure 2 These are experimental data for the flow coefficient.

[0040] Figure 3 These are measured data for static characteristics;

[0041] Figure 4 The measured flow rate with static characteristics is converted into critical flow rate data;

[0042] Figure 5 These are the curves of the first-order and second-order fitting functions;

[0043] Figure 6 To fit the extrapolated data;

[0044] Figure 7 This is the complete static characteristic curve resulting from the combination of the measured curve and the extrapolated curve. Detailed Implementation

[0045] The following detailed description, in conjunction with embodiments and accompanying drawings, explains the process and working principle of a fitting extrapolation method for the static characteristic curve of a direct-acting gas pressure regulator provided by the present invention.

[0046] To facilitate understanding of the technical solution provided in this application, the relevant content of the technical solution is explained.

[0047] For a typical direct-acting gas pressure regulator, its working principle is to obtain the outlet pressure signal of the regulator through a signal tube, and use the force balance of regulating elements such as springs, diaphragms, and valve discs to change the airflow area between the valve disc and the valve port, thereby achieving the purpose of stabilizing the gas outlet pressure. When the fluid inside the regulator is in a critical flow state (or choked flow), the fluid center velocity at the regulator valve port reaches the speed of sound, and the average velocity is a constant value. At this time, the flow rate is proportional to the flow area of ​​the valve port.

[0048] When the pressure regulator is working, the internal fluid velocity is above 20 m / s, and the fluid is in a turbulent state. Based on the force balance analysis of the valve disc, the dynamic pressure of the flow field on the valve disc is linearly related to the square of the flow velocity. For internal pressure tapping regulators, the downstream pressure obtained by the signal tube is affected by its location. Overall, the fitting function of outlet pressure and flow rate includes a quadratic term of flow rate. Because the spring compression changes when the flow area changes, the spring force is linearly related to the flow area of ​​the valve port. Therefore, the fitting function of outlet pressure and flow rate includes a linear term of flow rate. Due to the relatively constant forces such as valve disc gravity, fluid static pressure, and spring preload pressure, the fitting function of outlet pressure and flow rate includes a constant term. In particular, when the fluid influence on the actuating element is small, the outlet pressure can be simplified to a linear function of flow rate.

[0049] The flow coefficient and static characteristic test device of the pressure regulator in this embodiment is designed according to GB 27790 "Urban Gas Pressure Regulator". The pressure regulator under test is a direct-acting pressure regulator with a nominal diameter of DN50. The test process is applicable to GB / T17213.2—2017 and GB / T 17213.9—2005 standards.

[0050] like Figure 1 As shown, the method process is as follows:

[0051] Step 1: Remove the main spring of the pressure regulator and adjust the valve port of the pressure regulator to the maximum by mechanical fastening. At this time, the outlet pressure p2 is 0 and the fluid in the pressure regulator is in a subcritical flow state. Select 5 equally spaced inlet pressures.

[0052] Since the inlet pressure range is selected for testing under subcritical flow conditions, the required flow reserve is minimal. Generally, the critical pressure difference ratio of the regulator is 0.6~0.7, which means that when the outlet pressure p2 is 0, the inlet pressure p1 is approximately less than 120 kPa to ensure that it is in a subcritical state.

[0053] The flow rate Qc, inlet pressure p1, and atmospheric pressure pa were measured and recorded respectively. The pressure difference ratio x and the product of the expansion coefficient Y and the flow coefficient C were calculated according to formulas (1) and (2). The experimental data obtained are as follows: Figure 2 As shown:

[0054] (1)

[0055] (2)

[0056] Note: The formula is from GB / T 17213.2—2017 "Industrial process control valves - Part 2-1: Calculation formula for fluid flow rate under installation conditions".

[0057] Step 2: Using X as the x-axis and YC as the y-axis, fit the curve with a linear equation to form a fitted line;

[0058] When X=0, then Y=1, YC=C; when Y=0.667, YC=0.667C, then the critical pressure difference ratio Xt=X. That is, when the horizontal axis X=0, the vertical axis YC=C=22.71; at the vertical axis YC=15.15, the horizontal axis X=Xt=0.7074 is read.

[0059] Note: The determination method is derived from GB / T 17213.9—2005 "Industrial process control valves - Part 2-3: Flow capacity test procedures";

[0060] Step 3: The pressure regulator is set to an inlet pressure of 100 kPa and an atmospheric pressure of 102 kPa. Within the experimental flow range (generally less than 50% of the maximum claimed flow), six flow points are uniformly selected for static characteristic experiments. The measured flow rate Q, inlet pressure P1, and outlet pressure P2 are obtained respectively. The pressure difference ratio X is calculated using formula (1). The obtained measured data are as follows: Figure 3 As shown;

[0061] Step 4: By comparison, the pressure difference ratio X < critical pressure difference ratio (0.7074), the gas flow in the regulator is in a subcritical flow state.

[0062] Step 5: Calculate the expansion coefficient Y at the measured point using formula (3), and convert the measured flow rate Q to the critical flow rate Qt using formula (4).

[0063] The method for calculating the expansion coefficient Y at the measured points is as follows:

[0064] (3)

[0065] Convert the measured flow rate Q to the critical flow rate Qt:

[0066] (4)

[0067] Where p1 is the measured inlet pressure and p1s is the specified inlet pressure of 100 kPa. In particular, when in critical flow, Y = 0.667.

[0068] Experimental data such as Figure 4 As shown;

[0069] Step 6: Fit the critical flow rate Qt and outlet pressure P2 using quadratic and linear functions respectively.

[0070] Furthermore, the method for selecting the fitting function is as follows:

[0071] Under the same inlet pressure, the outlet pressure is fitted using a quadratic function of the flow rate (5). In particular, when the fluid influence on the actuating element is small, it can be simplified to a linear function (6).

[0072] (5)

[0073] (6)

[0074] Since the number of possible values ​​v > 5, the data are fitted with linear and quadratic functions respectively. In the quadratic function (5), a is 5.016 and b is -1.265 × 10. -3 c is taken as 0.579×10 -6 In the linear function (6), a takes the value of 5.005 and b takes the value of -1.048×10. -3 ;

[0075] Then draw the curve as shown. Figure 5 As shown.

[0076] Step 7: The evaluation index for the fitting function is the goodness of fit R. 2 The goodness of fit R is calculated using formula (7). 2 ；

[0077] in, The nth pressure value is calculated using the fitted function. The average value of the measured outlet pressure is v=6.

[0078] Then, calculate the goodness-of-fit R of the quadratic function respectively. 2 =0.979, goodness of fit of the linear function R 2 =0.977, both are greater than 0.95, so a linear function is selected as the final fitting function.

[0079] Step 8: Based on the flow coefficient C calculated in Step 2, when the specified inlet pressure P1s is 0.1 MPa and the specified outlet pressure P2s is 5 kPa, calculate the maximum flow rate Qmax of the pressure regulator using formula (8) = 697.3 m³ / s. 3 / h.

[0080] Q max =0.232YC(P1s +P a )√X t （8）

[0081] First, the pressure difference ratio X = (P1s-P2s) / (P1s+Pa) is calculated using formula (1).

[0082] When X ≥ Xt, the expansion coefficient Y = 0.667;

[0083] When X < Xt, the expansion coefficient Y = 1 - X / (3 × Xt) is obtained by formula (3).

[0084] Step 9: The company claims a maximum flow rate of 500 m³ / s. 3 / h, the maximum measured flow rate in step 3 was 318.41m³ / h. 3 / h, then it is between 320 and 500m 3 Within the range of / h, select 6 target flow points Qj at the same interval, and calculate the extrapolated data points based on the final fitting function obtained in step 7.

[0085] First, the target flow rate Qj is converted into the extrapolated critical flow rate Qtj using formula (4).

[0086] Qtj = Y × P1s × Qj / (0.667 × P1); where, P1 = P1s

[0087] Y is obtained through formula (3), Y = 1 - X / (3 × Xt);

[0088] X is obtained through formula (1), X = (P1s - P2s) / (P1s + Pa)

[0089] The extrapolated critical flow rate Qtj is used to calculate the extrapolated outlet pressure p2j through the final fitting function obtained in step 7. Specific extrapolated data are as follows: Figure 6 As shown;

[0090] Step 10: Plot the measured curve based on the measured data obtained in Step 3, and combine the measured curve with the extrapolated curve to obtain the completed static characteristic curve of the voltage regulator, such as... Figure 7 As shown.

Claims

1. A method for fitting and extrapolating the static characteristic curve of a direct-acting gas pressure regulator, characterized in that, Includes the following steps: (1) Conduct flow coefficient experiments at the maximum opening of the pressure regulator to obtain the maximum flow coefficient C and the critical pressure difference ratio Xt; (2) The pressure regulator is set to an inlet pressure of P1s and an atmospheric pressure of Pa. Within the experimental flow range, v flow points are uniformly selected for static characteristic experiments, and the measured flow rate Q is obtained for each point. n Inlet pressure P1 n Export pressure P2 n And calculate their respective pressure differential ratios X. n， Where n = 1, 2, ..., v; (3) Compare X n The relationship with Xt, when X n When Xt < Xt, calculate the expansion coefficient Y. n The measured flow rate Q n Converted to critical flow rate Qt n When X n When ≥Xt, directly use the measured flow rate Q n Converted to critical flow rate Qt n ; (4) Regarding the critical flow rate Qt n and export pressure P2 n Perform linear fitting to obtain the fitted function; (5) Select w target flow points Qj within the extrapolated flow area, where j=1,2,...,w. Calculate the extrapolated outlet pressure based on the fitting function obtained in step (4), and plot the extrapolation curve. ⑹ Plot the measured curves and combine the measured curves with the extrapolated curves to obtain the complete static characteristic curve of the pressure regulator for the flow rate; In step (3), when X n When Xt < Xt, the coefficient of thermal expansion Y n =1-X n / (3×Xt;when X n When Xt ≥ , the coefficient of thermal expansion Y n =0.667; Then, the measured flow rate Q n Converted to critical flow rate Qt n The formula is Qt n =Y n ×P1s×Q n / (0.667×P1) n ); In step (4), the critical flow rate Qt n and export pressure P2 n To perform fitting, the function formula is: Quadratic fitting function: P2 n =a+b×Qt n +c×Qt n 2 ;or First-order fitting function: P2 n =a+b×Qt n; In step (4), ① when v≥5, then perform linear and quadratic function fitting respectively, and calculate the goodness of fit R. 2 , ; in, The nth pressure value is calculated using the fitted function. To measure the outlet pressure P2 of v n The average value; ② Determine the R-value of linear and quadratic functions. 2 If the value is greater than 0.95, select R. 2 The fitting function with an R-value greater than 0.95 is the final fitting function to be selected; if the R-values ​​of the linear and quadratic functions are... 2 If all values ​​are greater than 0.95, a linear function is selected as the final fitting function. In step (5), ① the pressure regulator is specified with inlet pressure P1s and outlet pressure P2s, and the maximum flow rate Qmax is calculated: That is: Qmax = 0.232 × Y × C × (P1s + Pa) × √Xt, where √ represents the square root; First, calculate the pressure difference ratio X = (P1s - P2s) / (P1s + Pa). When X≥Xt, the expansion coefficient Y=0.667; when X<Xt, the expansion coefficient Y=1-X / (3×Xt). ② Compare the relationship between the voltage regulator's claimed maximum flow rate Qmax-P1s and the calculated maximum flow rate Qmax, and take the smaller of the two as the extrapolated maximum boundary flow rate Qm. The extrapolated flow rate region is the range from the extrapolated maximum boundary flow rate Qm to the measured flow rate Q in the static characteristic experiment. n The maximum value Q in n The numerical range of max Then the target flow Qj = Q n max+(Qm-Q n max) × j / w, where j = 1, 2, ..., w; ③ Convert the target flow rate Qj into the extrapolated critical flow rate Qtj. Qtj = Y × P1s × Qj / (0.667 × P1); where, P1 = P1s The externalized outlet pressure p2j is calculated by finally selecting the fitting function; ④ Perform linear fitting on the extrapolated critical flow rate Qtj and the extrapolated outlet pressure p2j to obtain the fitting function, and plot the extrapolation curve.

2. The fitting and extrapolation method for the static characteristic curve of a direct-acting gas pressure regulator according to claim 1, characterized in that: In step (1), the determination process for the maximum flow coefficient C and the critical pressure difference ratio Xt is as follows: ① Record the atmospheric pressure Pa. Select y points P1m uniformly for the inlet pressure P1, where m = 1, 2, ..., y. Measure the flow rate Qc at each point. m Under the condition of maximum regulator opening, the outlet pressure is P2. m =0; Then, the pressure difference ratio X m =(P1 m -P2 m ) / (P1 m +Pa); Y m ×C=4.31Qc m / [(P1 m +Pa)×√X m ], Where √ represents the square root; ②X m x and y coordinates m ×C is the ordinate, and a linear equation is used to fit the curve, forming a fitted line. When X m =0, then Y m =1, Y m ×C=C; when Y m =0.667, Y m If ×C = 0.667C, then Xt = X m .

3. The fitting and extrapolation method for the static characteristic curve of a direct-acting gas pressure regulator according to claim 1 or 2, characterized in that: In step (2), the static characteristic experiment, the pressure difference ratio X n =(P1 n -P2 n ) / (P1 n +Pa).

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