Dec 19, 2018

**Abstract: **Flowmeters are usually designed for stable working conditions. When the operating conditions are unstable, the measurement accuracy will be greatly affected. For the unsteady operation conditions, the factors affecting the measurement of the orifice plate type steam flowmeter were analyzed. By calculating the calculation formula under stable measurement conditions, the calculation formula under non-steady-state conditions is obtained, and the mass balance calibration is performed experimentally. The results show that when the actual operating conditions deviate from the design parameters, the expansion coefficient of steam will deviate from the design value, which will affect the measurement results. The modified **flowmeter** can be applied to steam measurement under unsteady conditions, and the calculation accuracy is obviously improved.

**Introduction**

Water vapor is an important medium used in industrial production. Many steam flow meters and analysts have studied the accurate measurement of steam flow and accumulated some experience. The most commonly used steam flow meters are differential pressure flow meters and vortex flow meters with steam density compensation. The steam density compensation generally adopts the method of steam pressure and temperature compensation, which are respectively implemented by a pressure transmitter and a temperature transmitter installed on the pipeline. Generally, industrial steam flow measurement is used for steady-state measurement, and the working state changes little. The design state of the flowmeter is slightly different from the actual use state. If the flowmeter is selected and installed in a correct and reasonable manner, and temperature and pressure compensation is performed, Basically can meet the measurement requirements.

However, for the experimental process using steam, in many cases it is required to work under different working conditions, the working state span is large, and transient measurement is often required. For example: When the entire mass release process of steam is released in a large-scale state of a scaled-down nuclear power plant, the flow requirement may vary from 1 to 100 t / h. This large-scale steam flow measurement will be supplied separately through several branches when it is realized, but it can only be provided by a limited size branch. It is difficult to meet the steam flow measurement under the condition that the steam flow parameters change at any time. Based on the basic calculation formula of **the orifice plate flowmeter**, this paper analyzes the influence of each parameter in the formula on the variable state flow measurement, and combines the experimental data to obtain the steam flow measurement formula that can adapt to the variable working condition parameters, and improve the steam flow in the unstable state. Measurement accuracy under conditions.

1 Orifice plate mass flowmeter calculation formula

1.1 theoretical calculation formula

The theoretical basis of the **differential pressure flowmeter** is the Bernoulli equation and the flow continuity equation. When the fluid flows through the throttling device, part of the pressure energy is converted into kinetic energy, and a **differential pressure** signal is generated. The differential pressure value is proportional to the square of the flow rate. The mathematical model for the mass flow rate of the **orifice plate type differential pressure flowmeter **is:

Q is mass flow, kg / s; C is the outflow coefficient; β is the ratio of pore diameter to pipe diameter (d / D); d is the equivalent pore diameter of the orifice, m; ε is the coefficient of steam expansion; D is the design pipe diameter, m; ΔP is the **flowmeter pressure difference**, Pa; ρ is the vapor density, kg / m3.

The maximum flow rate can be calculated by the following formula:

Where: subscript d represents the design value.

1.2 Simplified calculation formula

Usually, when the **flowmeter manufacturer** designs, the design flow value will be given according to the design working condition and structural parameters. In the process of use, the measurement signal obtained by the measurement and the temperature and pressure compensation parameters are compared and calculated to obtain the actual flow value, as shown in the following formula. Show:

Where: T is the steam temperature, K; P is the steam pressure, MPa; no subscript P, T is the actual value, subscript d is the design value.

When the actual parameters and design parameters change little, the steam flow calculation formula is:

2 Measurement influencing factors analysis

There are many factors affecting the measurement results of **the mass flowmeter**, including the orifice plate structure, the pressure take-up form and the hole position, the flowmeter installation, the working medium, the accuracy of the differential pressure gauge, and the fluid physical property parameters corresponding to the working state. This paper focuses on several factors that may cause differences in steady-state and non-steady-state measurement states, such as outflow coefficient, expansion coefficient, steam temperature, pressure, and flow.

2.1 Outflow coefficient

The outflow coefficient is mainly affected by the orifice structure, ie the pore ratio β and the Reynolds number. It is basically unchanged for a specific flow meter β. The relationship between the **orifice flow** coefficient and the Reynolds number is shown in Figure 1.

Fig.1 The variation of the outflow coefficient C with the Reynolds number Re

It can be seen from Fig. 1 that in low and medium Reynolds numbers, the C value varies with the Reynolds number, while in the high Reynolds number (greater than 10 000, turbulent region), the C value changes little. According to the factory report, the **flowmeter **designed in this paper can know that the actual working conditions are far greater than 10 000, so the experimental working conditions are basically in the turbulent flow zone, and the outflow coefficient changes little under different working conditions.

2.2 Expansion coefficient

The coefficient of expansion is a correction for the change in density of the outflow coefficient in the compressible fluid. For **orifice flowmeters**, since the **flowmeter **expansion is both axial and radial, it is currently calculated according to empirical formulas. According to ISO 5167, the three pressure-receiving methods of the orifice plate adopt the same formula of the expansion coefficient, which is suitable for mediums such as air, steam and natural gas, as shown in the following formula:

Where: β is the ratio of pore diameter to tube diameter, which is a structure-related parameter, which can be considered unchanged during normal use; k is a physical parameter, which is related to the working medium.

Therefore, the magnitude of the expansion coefficient is mainly affected by the pressure on the upstream and downstream of the orifice. When designing the maximum flow rate, the expansion coefficient is the corresponding value under the maximum flow rate. For example, at 0.8 MPa (gauge pressure), the flow coefficient is about 0. 88 or so. When the actual steam is discharged, if the upstream and downstream pressures are not in a stable state, the operating conditions deviate from the design condition, and the actual expansion coefficient does not match the design expansion coefficient, thereby affecting the flow measurement.

2.3 Working pressure, temperature impact

When the **steady-state flowmeter** is designed, the working pressure of the **flowmeter** is basically constant, and the corresponding expansion coefficient is given for the given working pressure and flow rate, and the working pressure will be larger when the transient test or the back pressure changes greatly. Variety. The values of the expansion coefficient at different temperatures and working pressures are shown in Table 1. In this paper, the experimental conditions may be gradually increased from 0 (gauge pressure) to about 1.0 MPa (variation with back pressure).

Table 1 Steam expansion coefficient values under different parameters

It can be seen from the values of the expansion coefficients given in Table 1 that the lower the operating temperature and pressure, the smaller the expansion coefficient at the same flow rate.

2.4 Traffic Impact

As shown in Table 1, at the same working pressure, the smaller the flow rate, the larger the corresponding expansion coefficient, which is closer to 1. In the case of unsteady transient measurements, the direct effect of temperature and pressure can be compensated by temperature and pressure values measured without affecting transient measurements. When it comes to steam working fluids, changes in temperature and pressure affect the effect of combined pressure and flow on the coefficient of expansion. Take steam 1.5 t/h as an example. When the working pressure is 0.1 MPa, it is 0.9523; at 0.2MPa, it is 0.9778. 0.5MPa.

When the flow rate is 2t/h, the expansion coefficient is 0. 9894. When the flow rate rises to 6t/h, the expansion coefficient drops to 0.906 3, which is about 10%. The experimental working pressure varied from 0 to 0.8 MPa throughout the experimental process. Calculating the mass flow rate with a fixed coefficient of expansion results in a calculation error of more than 10%.

3 Flow meter measurement correction program

According to the above analysis, for the **steam mass flowmeter**, the main error of the **current flowmeter **measurement mainly comes from the deviation of the expansion coefficient. The commonly used formula for calculating the water vapor expansion coefficient ε is:

Where: P1 and P2 are the pressures at the upstream pressure of the flowmeter and the lowest point of the downstream pressure. Trying to use the differential pressure signal collected by the flowmeter as the differential pressure of (P1 - P2), the ε value change is very small, which is close to 1, which is quite different from the ε given by the flowmeter design calculation. From the definition of pressure, P2 is the pressure value of the flow velocity downstream of the orifice plate and the lowest pressure point, which is different from the pressure obtained by the **flowmeter**. Here, based on the ε provided by the flowmeter design, the relationship between P2 and the flowmeter differential pressure signal is fitted by the ε value under different conditions provided by the design. The results are as follows:

4 Analysis and comparison of experimental systems and experimental results

4. 1 experimental system

The system diagram used in the steam flow meter is shown in Figure 2. In Figure 2, the steam enters the tank after passing through the **orifice mass flow meter**. The outer surface of the tank has annular ventilation, which can be used to cool the tank. The temperature and pressure compensation measuring points are arranged before and after the flow meter, and the real-time measurement results of the flow meter are collected and summarized. When the steam enters the tank, it will raise the pressure inside the tank and will condense in the tank. The condensed heat will be taken away by the outside of the tank. After the steam entering the tank is completely cooled, the condensed water can be drained from the lower outlet and weighed, and the weighing result is compared with the real-time measurement result of the flowmeter to verify the measurement accuracy of the** mass flowmeter.** During the experiment, as the steam enters the tank, the steam in the tank is difficult to completely condense in time, and the pressure will gradually increase, which will cause the steam state near the upstream flow meter to change accordingly, that is, the working state of the **flowmeter **is compared with the design value. Constantly changing, this change will gradually increase as the steam flow increases.

Figure 2 Steam mass flowmeter measurement system diagram

4.2 Comparative analysis of experimental results

The parameters measured during the steam flow are obtained through experiments, and the general formula and the modified formula are used for corresponding calculation and processing to obtain the required data. Figure 3 shows the relationship between the coefficient of expansion and expansion before and after correction.

Figure 3 Steam expansion coefficient as a function of time

It can be seen from Fig. 3 that the coefficient of expansion gradually increases with time, and the working state of the **flowmeter r**emains stable after 6000 s, and the expansion coefficient remains basically unchanged. Comparing the expansion coefficient before and after the correction, the corrected expansion coefficient is significantly smaller than before the correction, and is closer to the value in Table 1. The results of the correction of the expansion coefficient can be substituted into the corresponding steam mass flow calculation in equation (1). The results are shown in Fig. 4. After a short period of growth, the mass flow remained basically stable with little change. Compared with the gradual reduction process of the expansion coefficient, the mass flow difference before and after the correction remains stable and rising throughout the process. The time value of the steam mass flow value in Fig. 4 is time-integrated to obtain the total steam input quality under the corresponding conditions. After the experiment is completed, after cooling, the total mass of the condensed water obtained by the weighing device is collected by the weighing device at the lower end of the experimental shell, and the mass flow before and after the correction is evaluated by comparing the difference between the two. The quantity of the automated flow meter is measured, Volume 36, Issue 9, September 2015 The accuracy of the measurement. The results are shown in Table 2, experiment number 1 is the quality result statistics shown in Figure 4, and numbers 2 and 3 are the other two test results. The mass balance results show that the modified **mass flowmeter** formula can significantly improve the measurement accuracy.

Figure 4 Steam mass flow versus time

Table 2 Summary of steam mass balance

5 Conclusion

According to the working environment of the **mass flowmeter **whose working state changes, the possible influencing factors are analyzed, and the flowmeter correction calculation formula suitable for the unsteady state is obtained according to the different steady-state design results. The conclusions are as follows: (1) When the actual operating conditions When the deviation from the design conditions, the measurement accuracy of the mass flow meter will decrease; (2) When the steam mass flow rate is measured, the coefficient of expansion of the steam has a great influence on the measurement result; (3) the mass balance result indicates the corrected quality. The flow meter can be applied to steam measurement under variable working conditions, and the calculation accuracy is obviously improved.