Abstract This paper introduces a new type of differential pressure device that integrates the advantages of the metering performance of the classic Venturi tube, the annular orifice plate and the wear-resistant orifice plate—the inner Venturi tube. The structure, measurement principle, technical performance, applicable range, method for determining the expansibility coefficient and the mechanism of the excellent metering performance of the inner Venturi tube are briefly discussed. At the same time, the wide application and good development prospects of this differential pressure device are expected to replace the traditional differential pressure devices such as orifice plates. Keywords Venturi tube differential pressure flow meter 1. Introduction Differential pressure flow meters, as a traditional metering method, have a development history of nearly 100 years. Today, it is still the most widely used industrial online flow measurement instrument. The throttling elements used in differential pressure flow meters are mainly standard orifice plates, nozzles and Venturi tubes [1]. Given the various defects in the technical performance of these throttling devices, in order to meet the needs of actual industrial measurement, people have successively invented several modified throttling devices based on orifice plates and nozzles, such as annular orifice plates, conical inlet orifice plates, quarter-circle orifice plates (nozzles), wear-resistant orifice plates [2], wedge flow meters, and V-Cone conical flow meters. These modified throttling devices can make up for some deficiencies in the technical performance of standard throttling devices under certain specific measurement conditions, but their use is very limited and their measurement accuracy is also low. The American V-Cone flow meter is a modified throttling device with relatively good performance, but the problem of unstable discharge coefficient caused by "sharp edge erosion" has not been completely solved. The patented technology product developed by Dalian Sonica Electronics Co., Ltd. - the inner Venturi tube - is a modified Venturi tube that is a special-shaped Venturi tube that is a modification of the traditional Venturi tube. It integrates the advantages of annular orifice plates, wear-resistant orifice plates and Venturi tubes. Its technical performance is better than that of orifice plates, nozzles and classic Venturi tubes, and also better than other existing modified throttling devices. The internal Venturi flow meter is a new generation of differential pressure flow measurement instrument with unique performance, and it has achieved good results in industrial metrology trials. 2. Structure and Measurement Principle 2.1 The internal Venturi tube consists of a circular measuring tube 1 and a special-shaped core 2 placed inside the measuring tube (see Figures 1 and 2). The special-shaped core is a rotating body coaxial with the measuring tube. Its generatrix is ​​the axial section of the wall of a classic truncated Venturi tube with an imaginary infinitely thin wall. That is, the radial outer surface of the rotating body consists of three parts: a front conical surface 6, a middle cylindrical surface 7, and a rear conical surface 8. The special-shaped core is positioned by its support shafts 9 and 10 and support rings 3 and 4 coaxial with the measuring tube, and is clamped and fixed by a braking component (for small-diameter products, there is no front support shaft; only the rear shaft is used for positioning and fixing by the rear support ring). The support ring consists of an inner ring, an outer ring, and 3-4 support ribs connecting the inner and outer rings. A pressure tap 5 (or a remote flange pressure tap) is installed at a specific location on the measuring tube wall. Both ends of the measuring tube are standard flanges for connection to the on-site process piping. 2.2 In terms of basic measurement principle, the internal Venturi tube and the classic Venturi tube, and other traditional differential pressure flow meters, have the same measurement principle. Both are flow measurement methods based on the law of conservation of energy—Bernoulli's equation and the flow continuity equation. The basic direct measurement quantity is still the differential pressure before and after the throttling device. As shown above, a different diameter annular cavity (annular gap) is formed between the outer surface of the special core and the inner surface of the measuring tube. The axial flow surface variation law of the annular cavity is similar to that of the classic Venturi tube. This makes the flow bundle change and throttling process when the fluid flows through the internal Venturi tube basically the same as that when the fluid flows through the classic Venturi tube. 3 Metering Performance 3.1 The metering performance of the internal Venturi tube and the comparison of the standard orifice plate, nozzle, and classic Venturi tube are shown in Table 1, a summary table of throttling device performance. 3.2 Technical Characteristics of Internal Venturi Tubes Compared with standard throttling devices such as orifice plates and various modified throttling devices, the technical characteristics of internal venturi tubes are mainly reflected in the following aspects: ① Good measurement stability. During the measurement process, the discharge coefficient can remain constant for a long time, which is a unique advantage not possessed by any other throttling device. ② Strong adaptability to the measured medium. It can measure various liquids, gases and steam, including clean fluids and fluids containing solid particles, low-pressure high-flow-rate gases, high-humidity gases, and other various dirty fluids. ③ Wide measurement range (range ratio). When the range ratio is greater than 10:1, or even 15:1 or 25:1, the linearity of the discharge coefficient can still be lower than 0.4% within the Reynolds number range commonly used in industrial measurements (no secondary meter software correction is required). Please refer to Figure 3 for the measured discharge coefficient distribution of some products of the NV2118 internal venturi tube flowmeter. ④ Wide applicable Reynolds number range. The lower limit of the applicable Reynolds number is lower than that of standard throttling devices, especially much lower than that of the standard classic venturi tube. ⑤ Short straight pipe section requirement. The required straight pipe section length is even shorter than that of a classic Venturi tube. For the same type of upstream flow obstruction, the shortest required straight pipe section length is only about 1/8 of that of an orifice plate, thus effectively avoiding or reducing the additional measurement uncertainty of the measurement system. ⑥ Low pressure loss, approximately 1/3 to 1/5 of that of an orifice plate. 4 Performance Mechanism Analysis 4.1 The erosion of the sharp edge of the throttling device throat, the fouling of the throttling device, and the narrow range ratio are the fundamental reasons why the discharge coefficient of orifice plates and other throttling devices cannot remain constant during use. The internal Venturi tube has no sharp edge at the throttling part and no fouling conditions, and has a very wide range ratio, so the discharge coefficient can remain constant for a long time during use. 4.2 The combination of the internal core and measuring tube in the internal Venturi tube forms a conical contraction section between the inlet conical surface and the inner circle of the measuring tube. This conical contraction section has a flow adjustment (or rectification, mixing) effect similar to, but stronger than, that of the conical contraction section at the inlet of the classic Venturi tube. The mechanism of the flow adjustment effect of the conical contraction section is as follows: As the fluid flows forward in the Venturi tube cavity, with the gradual reduction of the flow cross section, not only does the flow velocity gradually increase and the pressure gradually decrease, but the fluid with lower velocity flowing near the tube wall and the fluid with higher velocity flowing near the tube axis form a "mixed flow". This makes the original large velocity distribution gradient smaller and smaller, and corrects the asymmetrical velocity distribution such as deflection and rotation that occurs before the fluid flows into the cavity due to the flow obstruction of the upstream pipe. Thus, the uniform velocity distribution required by the differential pressure instrument is obtained at the throat of the throttling device. The flow adjustment effect described above is similar to that of the classic Venturi tube, but the adjustment force (flow equalization effect) of the internal Venturi tube is greater and more effective. This is because, when fluid flows through a classic Venturi tube, the contraction creates a force that pushes the fluid from the tube wall towards the tube axis, while when fluid flows through an internal Venturi tube, the contraction creates a force that pushes the fluid from the tube axis towards the surrounding tube walls, forcing flow splitting. Therefore, the internal Venturi tube is stronger than the classic Venturi tube in both flattening the velocity distribution gradient and "correcting" non-axisymmetric flow. It is this effective flow adjustment function that makes the discharge coefficient of the internal Venturi tube far less sensitive to changes in the flow Reynolds number Re and the throttling diameter ratio β than traditional throttling devices such as orifice plates and nozzles. As a result, the discharge coefficient of the internal Venturi tube can maintain good linearity over a wide range of Reynolds numbers (range ratios). The flow adjustment effect of the conical contraction section described above is also an important reason why the required straight pipe length for internal Venturi tube installation can be much lower than that for orifice plates. 4.3 An annular flow gap is formed between the outer surface of the inner core of the internal Venturi tube and the inner surface of the measuring tube. This geometric feature of the throttling part is similar to that of the annular orifice plate. The research experiment of NEL in the UK shows that during the measurement process, not only will solid particles in the fluid and liquid droplets in the gas not accumulate in the throttling part, but the annular flow gap formed between the annular orifice plate and the pipe has a strong anti-interference ability against upstream flow interference. The test data provided by NEL shows that under severe rotating flow, when the standard orifice plate discharge coefficient changes by 25%, the annular orifice plate discharge coefficient changes by less than 1% [4]. It can be said that the reason why the internal Venturi tube has low requirements for the upstream straight pipe section is mainly because the annular flow gap has a good flow adjustment function. 4.4 There is no sharp edge at the throat of the throttling part of the internal Venturi tube. The angle between the cylindrical surface of the core and its front and rear conical surfaces is an obtuse angle greater than 120º. This structural form is similar to the "sharp edge passivation treatment" technology proposed by Soviet scholars for wear-resistant orifice plates, which involves chamfering the sharp right-angled edge of the standard orifice plate inlet. The stable discharge coefficient of wear-resistant orifice plates is widely recognized in the flow measurement industry. In fact, internal Venturi tubes are better than wear-resistant orifice plates in terms of discharge coefficient stability because wear-resistant orifice plates only solve the "sharp edge erosion" problem, while another important reason for changes in the discharge coefficient—the "fouling" problem of the orifice plate—still exists. Only the internal Venturi tube structure simultaneously solves both the "sharp edge erosion" problem of the orifice plate and the "fouling" problem of the throttling element. 4.5 The internal Venturi tube structure makes its fluid throttling process similar to that of a classic Venturi tube. When the fluid flows through the throttling section, there is no sudden contraction and diffusion. Although the pressure drop (differential pressure) necessary for measurement can be formed, there is no eddy current that easily causes energy loss, as seen in orifice plate throttling, resulting in less permanent pressure loss. 4.6 The internal Venturi tube exhibits strong resistance to media contamination, and its pressure tap is not easily clogged. This is due to two anti-clogging measures incorporated into the product's structure: first, a flow-blocking element is installed at the pressure tap to create a relatively high-pressure zone locally, reducing the accumulation of sludge-like particles and solid particulate matter in the fluid at the pressure tap; second, for media that are particularly prone to causing pressure tap clogging, a remote flange pressure tapping structure is adopted. 4.7 The internal Venturi tube is easier to manufacture than the classic Venturi tube. The geometric dimensions of the measuring tube and the core, as well as the positional tolerances between the core and the measuring tube, can be strictly controlled, even for larger diameter tubes. Its superior structural manufacturability and ease of precision manufacturing are crucial guarantees for the high measurement accuracy of the internal Venturi tube, and are also the main reason why it can be manufactured using different materials and adaptable to various measurement conditions. 5 Method for determining the expansibility coefficient As a differential pressure flow meter, the Venturi tube, like the standard orifice plate, nozzle and Venturi tube, must introduce an expansibility coefficient ε less than 1 in the flow calculation formula when measuring compressible fluids. GB/T2624 standard stipulates that the expansibility coefficient ε is calculated and gives two ε calculation formulas. One is the theoretical calculation formula for standard nozzle, Venturi nozzle and classic Venturi tube; the other is the empirical calculation formula for orifice plate. From the physical meaning of the expansibility coefficient, it can be seen that the type (structural form) of the throttling device determines its applicability to the above two calculation formulas. According to the "Flow Measurement Engineering Handbook" [3], for throttling devices with curved profiles and gradually decreasing flow cross sections (not sudden contraction), the actual minimum flow cross section when the fluid flows through such a throttling device is almost the same as the minimum flow cross section formed by the profile of the throttling device. The calculation method of the ε value of such throttling devices is applicable to the theoretical calculation formula. Clearly, the internal venturi tube is a gradually contracting throttling device, therefore the calculation method for the ε value also applies to the theoretical calculation formula. The correct deduction that the theoretical calculation formula applies to the ε value of the internal venturi tube has been verified by experiments conducted by the National Institute of Metrology of China and the Chengdu Natural Gas Flow Substation of the National Crude Oil Large Flow Metering Station on the same NV internal venturi tube. These experiments used both the measured outflow coefficient C with water and the product εC of the measured outflow coefficient and the expandability coefficient of natural gas. For DN50mm, β=0.55, and ΔP/P1=0.04, the outflow coefficient C=0.8177, εC=0.7967, the experimentally converted ε=0.9743, and the theoretically calculated ε=0.9746. The theoretically calculated ε value matches the experimentally converted value. 6. Application and Development Prospects The superior technical performance of the internal venturi tube will play a crucial role in solving the currently recognized challenges of metering large-flow, low-pressure, and high-humidity gases, as well as the metering challenges of dirty fluids such as coal gas and non-clean natural gas. For metering applications that currently still use traditional differential pressure instruments such as orifice plates but urgently need improved measurement accuracy and metering performance, the internal venturi tube will be an ideal replacement. When paired with a precision differential pressure transmitter and intelligent secondary instruments, the internal venturi tube can achieve long-term, stable, and accurate online metering, partially replacing high-priced flow meters such as vibratory mass flow meters and ultrasonic gas flow meters. Furthermore, the internal venturi tube also offers unique metering advantages in applications where long straight pipe sections are unavailable, and in metering applications involving special high-temperature, high-pressure, highly corrosive, and dirty media, as well as non-single-phase flow measurements. Since its development, the venturi tube product has been successfully tested for metering high-moisture natural gas, low-pressure dirty biogas, coke oven gas, coal gas, steam, hot water, and high-temperature heat transfer oil, and its practical application range is rapidly expanding. Currently, the accurate discharge coefficient of the venturi tube still requires actual flow calibration, which brings some inconvenience to its use. The venturi tube can be calibrated using a dry calibration method, which is technically feasible, but requires the establishment of corresponding industry or national technical standards. It is believed that with the widespread application of venturi tube flow meters, the dry calibration method will become a reality in the near future. 7. Conclusion: The venturi tube flow meter overcomes the metering drawbacks of traditional differential pressure instruments such as orifice plates while retaining its simple structure and reliable operation. As a new generation of differential pressure flow measurement instruments, the venturi tube brings new vitality to traditional differential pressure flow measurement technology, possessing wide applicability, and its promising development prospects are evident.