Research on V Cone Flowmeter

In recent years, with the continuous advancement of electronic technology and computer technology, flow measurement instruments have begun to develop in the direction of integration and intelligence. Among them, the smart flow meter is a kind of intelligent flow measurement instrument which is widely used. It measures the flow signal from different types of flow transmitters, supplemented by the temperature and pressure obtained by the temperature transmitter and the pressure transmitter. Compensation signal, real-time flow compensation for different fluids according to different algorithms, so as to achieve measurement, accumulation, display and output of fluid volume flow or mass flow. In addition to these basic functions, the current flow totalizer also has additional functions such as recording, communication, and printing, and it has certain fault diagnosis and self-recovery capabilities.

The intelligent V-cone flowmeter is developed on the basis of the “V” type inner cone throttling device. Simultaneous detection of temperature, differential pressure, absolute pressure signals, real-time temperature and pressure compensation for flow. In the traffic algorithm, floating point numbers are used for calculations, and at the same time, the fast square root algorithm based on the Newton iteration method is used to perform floating point calculations.

1 V cone flowmeter working principle and temperature and pressure compensation

1.1 Working Principle of Intelligent V Cone Flowmeter

The intelligent V-cone flowmeter is mainly composed of a sensor part and a conversion part, wherein the sensor part includes a “V” throttling device, a temperature sensor, a pressure sensor, etc. The conversion part includes an acquisition circuit, an SD16_A, a liquid crystal display circuit, and the like.

1.1.1 Traffic Measurement

The V-cone flowmeter utilizes a V-shaped pointed cone that is coaxially installed in the pipe to throttle the fluid gradually to the inner side wall of the pipe. The flow is measured by measuring the differential pressure before and after the V-shaped inner cone. The V-cone throttling device includes a conical body mounted in the measuring tube and a corresponding pressure tap. The measuring tube is pre-precision machined and produces differential pressure across the pointed cone. The differential high pressure (positive pressure) is the static pressure p1 measured at the pressure inlet of the pipe wall before the upstream fluid shrinks, and the low pressure (negative pressure) is at the downstream end face of the cone, in the central axis of the cone. Take the pressure p2 at the pressure hole as shown in the figure. The tip of the cone flows towards the cone, with a sharp, acute angle between the cone and its trailing surface. The edge of this commissure face provides a smooth transition before the fluid enters the downstream low pressure zone, eventually allowing the fluid to flow through the annular gap between the cone and the pipe.

Figure 1 V cone flowmeter working principle diagram

The calculation of the flow is derived from the Bernoulli equation. The conclusion is that the flow in the flow tube is proportional to the square root of the differential pressure before and after the “V” throttling element, and the volumetric flow rate is calculated as follows:

(1)

Where: qm is the volume flow value, kg/s; c is the outflow coefficient; ε is the coefficient of expansion; β is the equivalent diameter ratio; d is the equivalent opening diameter; ρ is the density of the fluid, g/m3; Δp For the differential pressure value, ΔP = P1 - P2Pa.

1.1.2 Outflow coefficient C

According to ISO 4006, the outflow coefficient of throttling flowmeter is defined as the ratio of incompressible fluid flow to actual flow and theoretical flow (in the case of compressible fluid, the ratio is equal to the outflow coefficient multiplied by the coefficient of expansion); for V cone flow Because there is no standard document, it must be measured with an incompressible fluid. The following is a calibration device designed to calibrate the outflow coefficient in the experiment, as shown in Figure 2.

Figure 2 Outlet coefficient calibration device

The volumetric cylinder measures the actual volumetric flow and the V-cone flowmeter measures the theoretical flow rate. For each V-cone flowmeter, the outflow coefficient C used in the flow formula is obtained by flow calibration. The typical value range for C is 0.75 to 0.85.

1.1.3 V-cone flowmeter gas expansion coefficient

If the measured medium is a gas or vapor, the Bernoulli's equation must be corrected using the gas expansion coefficient ε. This is because the change in the gas density ρ caused by the pressure change at both ends of the throttle does not apply to the liquid. The coefficient of expansion ε is 1 for liquids and ε <1 for gases and steam. According to the expansion coefficient of the gas defined in ISO 4006:

(2)

(3)

Where C is the previously calibrated outflow coefficient.

Although there is no standard document available at present, due to the limited conditions available, the expansion coefficient cannot be calibrated with a device such as an outflow coefficient. So here I use the conclusions of three doctors from NEL Laboratories and McCrometer in an international traffic conference in 2001. The basic idea is: According to ISO 5167, C·ε and Δp/(k· P1) is regarded as a linear relationship. Using gas as a medium test, the product of C and ε is obtained, and then the coefficient of expansion can be obtained by removing the outflow coefficient. In this topic, there is no direct reference to their fitting formulas. Instead, they use the formula fitted out by Prof. Xu Ying of Tianjin University. The fitting formula is as follows:

(4)

In the formula: β is the equivalent diameter ratio; ΔP is the differential pressure value, Pa; K is the isentropic index, the air isentropic index is 1; P1 is the static pressure value, Pa.

1.2 Temperature and pressure compensation

When measuring gas mass flow under working conditions, due to the influence of temperature and pressure, it will deviate from the ideal working state, resulting in a large deviation of the measurement results. Therefore, in the measurement of steam mass flow must be supplemented with temperature and pressure compensation.

1.2.1 Temperature and pressure compensation of superheated steam mass flow

There are two options for compensation for superheated steam in the Smart V cone flow. One option is to look up table difference method. Since the density of superheated steam is a binary function of pressure P and temperature T, its density table is large, and the storage of this density table requires a large storage space. In addition, the interpolation of binary functions is not simple. Therefore, although the look-up table method can achieve high compensation accuracy, it is not favored by people. Another alternative is formula compensation.

The following density compensation formula can be used:

(5)

Where: T is the temperature of superheated steam, °C; p is the absolute pressure of superheated steam, MPa; a = 0.00471; b = 10.97; c = 1.0336; d = 1.32 x 10-5; e = 0.0097.

Figure 3 Temperature and pressure compensation for superheated steam mass flow

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