# Research on Liquid Flow Measurement Method Based on Heat Transfer Method

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## Abstract

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^{3}/d, the flow in this range is proportional to the electrical signal, and the relative error of measurement is within ±5.8%. According to the analysis of the experimental results, the thermal flowmeter has a simple mechanical structure and no redundant moving parts, which can prolong its service life when used on site. When considering industrial applications, the error may be greater than the laboratory error.

## 1. Introduction

^{3}/d, and the measurement error of this thermal flowmeter is smaller than the standard value under the condition of ultra-high water cut. When the water cut is above 90%, the measurement error is within 8%, and when the water cut is about 80%, the error is within 25.9%. It can be seen that the error increases as the water cut decreases. Jeong, U. [17] proposed to use PMPF to obtain liquid sodium flow in a wide temperature range. A non-stationary method was adopted for the calibration of the probe given the liquid sodium temperature range of 150–415 °C. A relationship between the measured voltage signal and the flow rate was obtained successfully. One of the main problems in reference [18] is how to determine the water density in the calibration facility under actual conditions or reference actual conditions and derive approximate functions describing the temperature characteristics of water density, which are applicable to uncertainty analysis. Doh, I. [19] proposed a miniaturized thermal flowmeter consisting of a silicon substrate, a platinum heater layer on a silicon dioxide thin membrane, and a polymer microchannel to provide accurate flow-rate measurement. The present thermal flowmeter is fabricated by the micromachining and micromolding process and exhibits sensitivity, linearity, and uncertainty of 0.722 mW/(g/h), 98.7%, and (2.36 ± 0.80)%, respectively, in the flow-rate range of 0.5–2.5 g/h when the flowmeter is operated in the constant temperature mode with the channel width of 0.5 mm. The measurement range of the flow rate can be easily adjusted by changing the cross-sectional microchannel dimension. The present miniaturized thermal flowmeter shows a high potential for infusion-pump calibration in clinical settings. Yang, Y. et al. [20] developed a constant power thermal flowmeter for liquid phase flow and used Matlab numerical simulation software to analyze the relationship between the measurement results of a thermal flowmeter and oil–water two-phase flow under different water holdup conditions. The results show that the output voltage of the thermal flowmeter decreases monotonously with the increase of water holdup at the same flow rate, so the flow measurement of the thermal flowmeter must be corrected in combination with the water cut.

_{2}. The experimental results show that the temperature difference when the flow is lower ΔT is higher; the higher the added power, the higher the overall curve.

## 2. Study on Measuring Mechanism of Thermal Flowmeter

#### 2.1. Mechanical Structure Design of Flowmeter

#### 2.2. Constant Voltage Heating

_{c}to the total resistance. Figure 2 shows the constant voltage heating mode. R

_{1}is a power resistor with constant resistance, and R is a PT20 platinum resistor with variable resistance. Throughout the experiment, R

_{w}is a measurable variable.

_{0}is the resistance value of PT20 at 0 °C, and a and b are proportional coefficients. The coefficient b has a small order of magnitude. In this paper, ignoring the higher order term of b, we can get:

_{w}at both ends of the platinum resistance during fluid dynamics can be expressed as:

_{w}in Formula (5) changes with T, and other parameters are known or measurable. So, the differential form of U

_{w}and T in formula (5) can be expressed as:

_{w}is no longer linear with temperature T.

#### 2.3. Constant Current Heating

_{w}in Formula (9) changes with T, and other parameters are known or measurable. So, the differential form of U

_{w}and T in Formula (10) can be expressed as follows:

_{w}at both ends of the platinum resistance always keep a linear relationship with the temperature T of the platinum resistance, where R

_{w}can be measured. This linear relationship is conducive to subsequent experimental calibration and measurement, etc.

#### 2.4. Constant Power Heating

_{w}in Formula (13) changes with T, and other parameters are known or measurable. So, the differential form of U

_{w}and T in Formula (14) can be expressed as follows:

_{w}at both ends of the platinum resistance and temperature T is not linear with time, and the current and voltage at both ends of the platinum resistance change with time at the same time.

_{w}at both ends of the platinum resistance and temperature T with time synchronization can only be obtained by constant current heating. The temperature of the speed measuring probe is linear with the size of the flow rate, so it can be known that U

_{w}at both ends of the platinum resistance is proportional to the flow rate. Compared with the constant power heating method in reference [15], the constant current heating method in this paper improves the linearity and resolution.

## 3. Discussion on Power Factor of Constant Current Heating

^{2}/°C; A is the surface area of the heating probe, m

^{2}; t

_{h}, t

_{e}represents the temperature of the heating probe and the temperature of the background where the fluid is located, °C. The surface area of the heating probe can be expressed as (16), where l is the probe length, m, and d is the probe diameter, m.

_{μ}), Prandtl number (P

_{r}), and Reynolds number (R

_{e}) are introduced in this paper to express the functional relationship between heating power and fluid heat transfer. The expression is as follows:

_{f}is the thermal conductivity of the fluid, W/m/°C; η is the dynamic viscosity of the fluid, $Pa\xb7s$; C

_{p}is the specific heat capacity of fluid at constant pressure; ρ is the fluid density, kg/m

^{3}; v is the fluid velocity, m/s; and D is the diameter of fluid pipe, m. When the measured fluid fills the pipe, the interference of natural convection is ignored. At this time, the heat E of the forced convection heat transfer zone of the thermal probe obtained from the simultaneous Formulas (15)–(17) can be expressed as follows:

_{u}can be expressed as follows:

_{e}in Formula (21) will change with the change of flow velocity, and it is reasonable to take 0.4 as m after many experiments. The simultaneous Formulas (16)–(21) can get the expression of heat E in the convection zone:

_{c}and B

_{c}instead of the parameters in Formula (22).

## 4. Experimental Analysis and Discussion

#### 4.1. Introduction to Experimental Environment

#### 4.2. Analysis of Experimental Results

^{3}/d is calibrated. The flow less than 0.5 m

^{3}/d will generate vortices, which will make the measurement inaccurate. Therefore, the calibrated flow starts from more than 0.5 m

^{3}/d. The calibrated model is used to detect the relationship between flow and voltage. Figure 6 shows the linear relationship curve between flow and voltage. It can be seen from Figure 6 that the voltage decreases gradually with the increase of flow. The linearity of the yellow area in Figure 6 is better, and the flow range is 0.5–15 m

^{3}/d. The linearity of the green area is poor, and the flow range is 15–25 m

^{3}/d. Therefore, Formula (28) can be used to express the range of 0.5–15 m

^{3}/d, and the determination coefficient of fitting is 0.995, and the fitting degree is high.

^{3}/d can be fitted by polynomial, the determination coefficient of fitting is 0.9991, and the fitting degree is high. The fitting function can be expressed by Formula (29).

^{3}/d, the power factor no longer changes significantly. The change of the power factor is the same as the trend of the residual power of the heat source and is also related to the selection of m value in Formula (21). When m = 0.4, the linearity of flow and voltage between 0.5–15 m

^{3}/d is good. It can be seen from the above analysis that when the flow rate is below 15 m

^{3}/d, the linearity between the flow rate and the voltage value at both ends of the platinum resistance is better. Since the thermal probe selected in this paper is commercial on the market, the specifications and parameters of the thermal probe shown cannot be changed. According to the experimental test results, when the flow rate exceeds 15 m

^{3}/d, the sensitivity of the thermal probe to the flow rate has reached the saturation state. When the flow rate continues to increase, the sensitivity of the thermal probe becomes poor and the resistance value no longer changes, so the heating power basically remains unchanged.

^{3}/d is within ±5.8%. Because this experiment is tested in a good environment, the relative error is within the acceptable range. However, the actual working conditions will be affected by pipeline friction, fluid salinity, fluid flow pattern, gas, and impurities, and the error will be greater than that of the laboratory. Figure 11 shows the relative error between the measured value and the model calculation value.

## 5. Conclusions

^{3}/d, and the linearity of flow and voltage is better, so it can be used as the measurement standard of industrial unidirectional fluid. The experimental analysis shows that the relative error of the experiment is ±5.8%. The constant current heating method used in this paper has better linearity and higher resolution than the constant power method in reference [15], which can improve the flow measurement range. This is a major innovation of this paper. The conclusion of this experiment can provide a reliable basis for the flow measurement of ultra-high water cut wells in the oilfield and also lay a foundation for the total flow measurement of multiphase flow.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**Experimental environment. (

**a**) Schematic diagram of experimental circulation system. (

**b**) Construction chart of experimental circulation system.

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**MDPI and ACS Style**

Qin, H.; Dang, R.; Dang, B.
Research on Liquid Flow Measurement Method Based on Heat Transfer Method. *Water* **2023**, *15*, 1052.
https://doi.org/10.3390/w15061052

**AMA Style**

Qin H, Dang R, Dang B.
Research on Liquid Flow Measurement Method Based on Heat Transfer Method. *Water*. 2023; 15(6):1052.
https://doi.org/10.3390/w15061052

**Chicago/Turabian Style**

Qin, Hongwei, Ruirong Dang, and Bo Dang.
2023. "Research on Liquid Flow Measurement Method Based on Heat Transfer Method" *Water* 15, no. 6: 1052.
https://doi.org/10.3390/w15061052