Thread Content
In the previous issue, we mainly discussed what laminar flow principle and thermal principle gas mass flow meters and controllers are, as well as in which fields they are applied Next, we will mainly discuss the principles of two types of gas mass flow meters; in this session, we will start with the principle of thermal gas mass flow meters. https://pic4.zhimg.com/80/v2-bd4f201c4390b861ec5e69abcc31468f_1440w.jpg Image 1: The degree of coolness provided by a fan is related to its wind strength. 1. What is the principle behind thermal cooling? To answer this question, we need some basic knowledge; let’s learn it together. Let’s first look at the thermal principle. As shown in Figure 1, when it’s hot in summer and we use fans, we notice that these fans have different speed settings. When the fan is not turned on, it’s hottest; as the speed setting and wind force increase, we feel that the heat in our bodies dissipates more quickly, so our body temperature gradually drops, allowing us to experience a pleasant coolness. This feeling of coolness has a certain relationship with wind speed. Generally speaking, the stronger the wind, the cooler it feels. If we can quantify this degree of coolness, we can use it to represent different wind speeds, thereby determining the corresponding flow rate. Actually, this is the basic principle behind thermal flow meters: the flow rate of the fluid corresponds to the fan’s wind speed or its setting. Our skin, on the other hand, acts as a highly sensitive temperature sensor. By balancing the readings from these temperature sensors with the body’s own heat output, we can determine both the wind speed and the corresponding flow rate. The above explanation was given in plain language, and some readers might not be satisfied with it. Call this street-side science popularization, but can you be a bit more professional? This really isn’t a challenge for me; to write this chapter well and live up to the expectations of my readers, I’ve put in quite a lot of effort. Dear readers, please follow me as we continue reading. https://pic3.zhimg.com/80/v2-6b4a7c2e4309fc2d3b4e9eea452be96a_1440w.jpg Figure 2: Basic principle of thermal mass flow meters based on convective heat transfer. Thermal mass flow meters, also known as TMFs (Thermal Mass Flowmeters), are designed based on the principle of convective heat transfer, as shown in Figure 2. Its metal probe contains a temperature sensor based on a thermistor, which is used to measure the temperature of the probe. The probe also contains a heater, which is used to heat the probe so as to create a temperature difference with the fluid; this temperature difference is the basis for convective heat transfer. A metal probe placed in a fluid exchanges heat with the outside environment through three mechanisms: the convective heat transfer between the probe and the gas (usually heat loss), the thermal conduction from the probe to the wires and mounting structures (also usually heat loss), and the radiative heat transfer from the probe to the surrounding space (also usually heat loss). These three heat transfer methods can, at thermal equilibrium, achieve an energy balance with the amount of heat applied. Therefore, we have the following equation: (Equation 1) Here, it represents the heating power applied to the metal probe. Clearly, if the amount of heat applied exceeds the amount of heat dissipated, the temperature of the metal probe will rise; conversely, if the amount of heat applied is less than the amount of heat dissipated, the temperature of the metal probe will decrease. If they are exactly equal, the temperature of the metal probe remains unchanged. The temperature of the metal probe is measured by a built-in thermistor temperature sensor. 2. What are the main mathematical and physical principles involved in thermal mass flow meters? Next, we will further analyze the three basic mechanisms of heat dissipation and their relationship with flow rate measurement. The convective heat transfer between the probe and the gas being measured is something we need; we want this proportion to be as high as possible within the total heat transfer. It would be ideal if it could approach 100% entirely, and this is what is constantly pursued in engineering design. Of course, the closer it gets to 100%, the greater the difficulty involved. The heat conduction caused by the installation structure of the metal probe and the wires is the main source of error in thermal mass flow meters. The larger the proportion of heat conduction and dissipation, the greater the error introduced. Since the heat transfer rate cannot be determined accurately under different operating conditions, it cannot be completely eliminated during the correction process. To minimize the errors caused by low thermal conductivity, the best approach is to reduce the proportion of thermal conduction in the total heat transfer amount; in engineering terms, this is a process that continuously approaches 0. Similarly, the closer it is, the harder it is to achieve. As for the (heat exchange amount radiated by the probe into the external space), which represents spatial radiation, it spreads in all directions; therefore, it also constitutes a source of error in flow measurement and needs to be eliminated as much as possible. Fortunately, since the temperature of the heating block is not yet too high for radiation to occur, in error analysis it produces smaller errors than those caused by heat conduction; these errors can generally be neglected in engineering applications. From the above analysis, it can be seen that the main factor affecting the accuracy of thermal mass flow meters is the convective heat transfer, and the error term is. The reality is that even without any heat conduction losses, it’s still impossible to obtain an absolutely precise flow rate. Why? Since current science and technology are not yet advanced enough, the theoretical research on fluid heat transfer is incomplete, making it impossible to carry out accurate calculations; almost all mathematical formulas are semi-empirical. To understand why, let’s continue reading. According to Newton’s cooling law, we can express the convective heat transfer amount using the following formula: (Equation 2). Here, represents the convective heat transfer amount, is the convective heat transfer coefficient (this coefficient encompasses many factors, which will be explained in detail later), and is the temperature difference or average temperature difference between the incoming gas flow and the metal probe. Assuming no heat conduction losses and ignoring radiation losses, two terms are removed from Equation 1. By substituting Equation 2 into Equation 1, the following equation is obtained: (Equation 3) For the heating power of a metal probe heated by resistance, the following relationship holds: (Equation 4) Substituting Equation 4 into Equation 3 yields Equation 5, as follows: (Equation 5) Here, can be measured as current, can be measured as resistance, can be determined as the heat exchange area of the metal probe, and can be measured using a temperature sensor as the temperature difference. Then, if there is a fixed and precise relationship between the gas flow rate and the convective heat transfer coefficient, and if that relationship can be known with certainty, then the thermal mass flow meter will function successfully. Is there really such a relationship? In order to continue exploring the truth, and to avoid being ridiculed by all of you as peddlers of pseudo-science, we must conduct further in-depth research here. The content that follows requires some specialized knowledge, so I’ll try to explain it in as simple terms as possible. Based on the basic principles of heat transfer, the following formulas apply: Nusselt number (Formula 6), Prandt number (Formula 7), and Reynolds number (Formula 8). https://pic4.zhimg.com/80/v2-54aee12ebff39c542f4b2d2bdb76d477_1440w.jpg Figure 3: Schematic diagram of the Thomas flow meter. https://pic4.zhimg.com/80/v2-b88fd6d0aa475ac3f0a462789d0ead8b_1440w.jpg Figure 4: FCI thermal flow switch. These three are dimensionless parameters that are used as intermediate variables in calculating the heat transfer coefficient. Where is the thermal conductivity of the gas being measured ； The constant-pressure specific heat capacity of a gas ； For the dynamic viscosity of gases ； For gas density ； For gas flow rate ； It is the diameter of the metal probe. There is the following relationship among these three dimensionless parameters: (Equation 9) Equation 6 can be rewritten in another form as: (Equation 10) By substituting Equation 10 into Equation 5, the relationship between the heating amount and the convective heat transfer amount under ideal thermal equilibrium conditions can be obtained: (Equation 11) If is defined as the fluid temperature and is defined as the temperature of the outer surface of the metal probe, then the above equation can be rewritten as: (Equation 12) By substituting Equation 9 into Equation 12, the following relationship can be obtained: (Equation 13) The functional relationship in Equation 13 is empirical; different shapes of metal probes, different flow fields, and different gas substances all lead to changes in this functional relationship, so it is not fixed. At the same time, these parameters are all related to pressure, temperature, and the working medium. Therefore, the formulas in heat transfer are semi-empirical; a large amount of experimental data is required to make these formulas complete, and this task is so demanding that either performance or precision and scope of application must be sacrificed. It took over half a century abroad to develop thermal flowmeters (Thomas thermal flowmeters), starting in 1903, until FCI (FLUID COMPONENTS INTL) produced the first thermal mass flow switch (a flowmeter with low accuracy) in 1964. During the 1950s and 1960s, the United States and the Soviet Union engaged in a space race. There was a need for plasma thrusters for satellite development, and highly precise mass flow meters were required for ground tests of these engines. Scientists at NASA (National Aeronautics and Space Administration) developed a capillary thermal mass flow meter (as shown in Figure 5). This type of flow meter is suitable for measuring very small flow rates with high precision, and it is currently the mainstream product used in high-tech fields such as semiconductors, new materials, and aerospace. Vanputten first developed a flow sensor using silicon technology in 1974, and thereafter some research institutions abroad began working on the development of integrated thermal gas flow sensors (the principle is shown in Figure 7). Entering the 1990s, as microfabrication techniques based on semiconductor processes and microelectronics technology gradually matured, miniature flow sensors began to develop. They are primarily used in industries where price and size are important considerations, such as in the measurement of air intake in automotive engines (as shown in Figure 8). Over the past hundred years or so, foreign companies and research institutions have accumulated a large amount of data, which forms the basis for ensuring the accuracy of thermal flowmeters. Since significantly improving the performance of thermal mass flow meters requires massive amounts of data, existing thermal flow meters have already approached their engineering limits. Why do you say that? Let’s move on. 3. What is the data volume trap of thermal principle gas mass flow meters? We will first introduce a relatively classic empirical formula based on the Nusselt number. In 1946, Cransham obtained an empirical formula for heat transfer that could be used within a limited range, by fitting experimental data through numerous experiments; it is given as follows: (Equation 14). By substituting Equation 14 into Equation 13, we obtain the following equation: (Equation 15). Equation 15 is called a semi-empirical formula because the coefficients in it (0.42, 0.2, 0.57, 0.33, 0.5) were determined through experimental fitting rather than through theoretical derivation. Therefore, its scope of use must be limited; this is what I mentioned earlier – either the scope of application needs to be reduced or the precision needs to be lowered. Since flowmeters themselves require high precision, the applicable range of the above formula is very narrow; it can be said to be unsuitable for calculating the flow rate of thermal flowmeters, serving only as a guide. Therefore, to achieve high precision, a large number of experiments must be conducted in order to find a flowmeter that meets the precision requirements under specific conditions. If the scope of application is to be expanded, the number of experiments must be increased exponentially or even by orders of magnitude. Next, let’s take a look at the factors that can affect traffic accuracy. They are respectively: 1 different flow rates (or velocities), 2 different inlet temperatures, 3 different inlet pressures, 4 different probe temperature differences, 5 different ambient temperatures, 6 different pipe diameters, 7 different probe shapes, 8 different probe materials, 9 different gas types, 10 different probe installation configurations, and so on. Why “etc.”? Because if higher precision is required, many factors that were previously less important must be taken into account, which leads to a sharp increase in the number of items that need to be tested. For now, let’s ignore the secondary factors and focus on these 10 main factors. Assuming we treat each factor as a variable and test each variation 10 times (which is already very few), then using the most basic single-variable testing method in physical experiments, we would need 10 billion experiments to cover the entire test range. Even if we adopt a replication approach (the physical structure of the flow meter remains completely unchanged; this is just a hypothesis, and it often involves patent infringement), and we eliminate those four factors, we would still need at least 1 million experiments to explore this reduced test domain. Moreover, the prerequisite is that each test variable undergo only 10 variations, and such variations clearly cannot achieve the 1% measurement accuracy we desire. If the number of test variations for each variable is increased to 20, then even in a reduced version of the test domain, the total number of tests required after traversal still has to increase significantly to 64 million. Therefore, the accuracy of thermal mass flow meters is based on a large amount of experimental data, particularly reliable experimental data and data from practical engineering applications; this is what constitutes the \"data volume trap\" of thermal principle-based gas mass flow meters. It should be emphasized that if one wishes to significantly improve the performance of thermal flowmeters, it is necessary to modify factors such as the design structure and material of the probe, as well as the temperature; in such cases, all experimental data must be re-collected in order to update the database. In other words, the physical structure of the thermal flow meter corresponds one-to-one with the database. This is also why the upgrading of thermal flowmeters is very slow, often taking more than a decade. By analyzing the situation, it is easy to see why it took half a century for significant development and progress in thermal flowmeters abroad; this was due to limitations in the level of fundamental research. Without breakthroughs in basic principles, such a status quo cannot be fundamentally changed. Based on principle analysis, it has become extremely difficult to further improve the performance and accuracy of thermal mass flow meters; it is almost impossible due to time and cost constraints. To achieve comprehensive breakthroughs in this field domestically, without a database available, substantial investment and a long period of data accumulation are required; it is conservatively estimated that the number of tests needed for such an experimental database will be on the order of 1 billion times. 3. How can we understand the essence of heat transfer from the perspective of molecular motion? The core of a thermal flow meter is heat transfer. According to existing theories, heat transfer essentially involves the absorption of heat by gas molecules colliding with a solid wall within a thin layer adjacent to that wall (in essence, it is an increase in the average kinetic energy of the molecules, which is the process of heat conduction in gases). The temperature gradient within this thin layer is very large; we generally refer to this layer of gas molecules as the temperature boundary layer. The process by which these thin layers of gas molecules transfer heat to the main flow region through molecular collisions is known as the \"mass transfer\" process (the greater the gradient in the velocity boundary layer, the thinner the thermal boundary layer, and the faster the convective heat transfer rate). The thickness of the temperature boundary layer and the temperature distribution are closely influenced by the flow boundary layer (a thin layer in which the flow velocity changes sharply from the wall surface to the main flow region). In general, the faster the flow velocity, the greater the velocity gradient in the flow boundary layer; the thinner the temperature boundary layer, and the more intense the heat transfer. This is why we often experience that \"the faster the wind, the cooler it is\". This is the core of convective heat transfer in the entire thermal flow meter; since the knowledge involved is too complex, it will not be discussed in detail here. 4. What is the fundamental obstacle preventing an improvement in the response speed of thermal principle gas mass flow meters? The principle of a thermal mass flow meter is to calculate the mass flow rate of a fluid based on temperature and heat transfer. Among them, the temperature measurement by the temperature probe is the core key parameter. We know that in theory, the temperature measured by the temperature probe should match the conditions of the incoming flow in real time, but in practice this is often not the case. The main reason is that the temperature probe has mass, and thus possesses heat capacity; the energy balance of the entire probe actually follows this rule: the change in energy acquired by the temperature probe is equal to the difference between the heat exchanged through convection and the amount of heat applied. It can be expressed by the following formula: (Equation 16) Here, represents the change in energy of the probe’s temperature, and this change is what directly causes the variation in the probe’s temperature. It can be expressed by the following formula: (Equation 17) In this formula, represents the specific heat capacity of the probe material, represents the mass of the probe, and represents the change in the probe’s temperature. As we mentioned earlier, only the temperature measured when the temperature probe is in thermal equilibrium can be used for accurate flow rate calculations. In other words, when equals , the temperature of the probe remains unchanged at that time. Under this thermal equilibrium condition, the temperature measured by the temperature probe is the effective temperature required for flow rate calculation. The response time of a so-called thermal gas mass flow meter refers to the time interval from the change in flow rate until the change in temperature measured by the temperature probe approaches 0. From Equations 16 and 17, we can see that this holds under the assumption that the heating amount and convective heat transfer cannot change significantly due to various constraints (such as material and structural strength requirements), and that the specific heat capacities of the materials differ little. Changing the size of the probe can significantly reduce its mass and greatly improve the response speed of the temperature probe, thereby substantially increasing the response speed of the thermal mass flow meter. It should be noted that the quality of the temperature probe here refers not only to the quality of the temperature sensor itself, but also to the quality of the mounting or encapsulation structure that is in close contact with the temperature sensor. https://pic3.zhimg.com/80/v2-002e8342dfa69e635b6f0689947d58c2_1440w.jpg Figure 5: Schematic diagram of the capillary thermal mass flow meter. https://pic4.zhimg.com/80/v2-f0b35f6a681d8b72aa5e11358596abfb_1440w.jpg Figure 6: Capillary thermal mass flow meter. https://pic1.zhimg.com/80/v2-7a538f2bc9ce9745f05bcc6f5773c1ec_1440w.jpg Figure 7: Schematic diagram of the application of silicon-based thermal flow sensor chips. https://pic2.zhimg.com/80/v2-35de7ee307b6d8310865711fdde5eb0d_1440w.jpg Figure 8: Thermal sensors manufactured using silicon-based thermal sensor chips. Over the past century, considerable efforts have been made to reduce the size of thermal temperature probes. From the initial hot wires, to capillaries, and finally to semiconductor nanostructures, it can be said that we have almost reached the pinnacle of technology. Currently, hot wires are rarely used except in a few scientific experiments, as their strength is too low leading to easy damage, and they are also prone to contamination ； Currently, capillaries represent the mainstream approach for thermal mass flow meters for gases; they offer the best accuracy, repeatability, and response speed, especially when measuring very small gas flows. Currently, the size of capillaries is less than 1 millimeter, while the diameter of the heating wires (usually made of platinum) is less than 0.2 millimeters. Due to the requirements regarding structural and mechanical stability, these dimensions have reached their limit, and no significant progress has been made in the past 10 years. Thermal sensors based on semiconductor nanostructures (what is commonly referred to as thermal chip technology) are primarily used for measuring the air intake flow in automotive engines, among other applications where price and size are important considerations. Designing heat transfer structures from a microscale perspective does have its advantages; its response time is faster than that of capillary types, with a maximum response time of around 0.5 seconds (the maximum value for capillaries is around 1 second), which essentially represents its technical limit – no significant improvements have been seen in the past 10 years. Finally, I’ll leave a hint here regarding the response speed of mass flow meters based on the principle of laminar flow. The maximum response speed of laminar flow principle mass flow meters can exceed 1 millisecond (which is 1/1000th of a second). Therefore, their response speed is significantly higher than that of thermal mass flow meters. We will elaborate on the underlying principles in the next issue.