The relationship between thermal flowmeters and pressure and temperature

To answer the original poster’s question, we first need to understand the measurement principle of thermal mass flow meters. The mathematical model of the thermal mass flow meter is as follows: H = Cp * m * ΔT; m = H / (Cp * ΔT); Qm = K * ΔP / (Cp * ΔT). Qm: Gas mass flow rate; K: Meter constant; ΔP: Compensated electrical power; Cp: Specific heat capacity at constant pressure; ΔT: Temperature difference between the two probes. The flow sensor consists of two thermal resistors: one is the reference probe, and the other is the heating probe. As gas flows past the heating probe, it carries away some of the heat, causing the probe to cool down; the amount of heat lost is proportional to the mass flow rate. By keeping the temperature difference between the heating probe and the reference probe at a constant value, the heating current required for detection is determined, thereby yielding the corresponding mass flow rate. This working principle is what we refer to as the constant temperature difference principle. Currently, most thermal sensors worldwide are produced based on the principle of temperature difference. Through mathematical models, we can see that the flow rate is inversely proportional to the specific heat capacity of the measured medium, and directly proportional to the amount of electrical power used for heating. In other words, the greater the electrical power, the greater the mass. If the medium under test is constant, then its specific heat capacity at constant pressure is also constant; we can consider this specific heat capacity as a constant value. However, we all know that the specific heat capacity at constant pressure is not a constant value. The concept of specific heat at constant pressure refers to the amount of energy required to raise the temperature by one degree when the pressure remains constant; in other words, it is the ability to absorb heat. The heat absorption capacity of each medium varies at different temperatures. Please refer to the following chart: Specific heat capacity at constant pressure cp/(kJ/kg·K) Name Molecular formula Temperature/°C –40 10 60 110 160 260 360 460 760 1200 Hydrogen H2 14.83 14.29 14.11 14.09 14.18 14.43 14.67 14.84 15.02 16.25 Oxygen O2 0.9378 0.9169 0.9169 0.9253 0.9420 0.9797 1.013 1.043 1.097 1.147 Nitrogen N2 1.089 1.043 1.026 1.026 1.034 1.059 1.089 1.118 1.172 1.252 Ammonia NH3 2.005 2.043 2.114 2.186 2.303 2.508 2.700 2.881 3.329 3.869 Carbon monoxide CO 1.084 1.043 1.029 1.030 1.038 1.068 1.101 1.130 1.189 1.264 Carbon dioxide CO2 0.7997 0.8289 0.8709 0.9043 0.9546 1.030 1.097 1.147 1.243 1.340 Sulfur dioxide SO2 0.5862 0.6071 0.6322 0.6573 0.6908 0.7411 0.7787 0.8122 0.8541 0.8960 Hydrogen sulfide H2S 0.9839 0.9797 0.9964 1.013 1.051 1.118 1.176 1.235 1.361 1.524 Methane CH4 2.077 2.189 2.336 2.466 2.675 3.031 3.383 3.689 4.568 5.355 Ethane C2H6 1.465 1.692 1.913 2.081 2.336 2.721 3.077 3.395 4.153 4.823 Propane C3H8 1.344 1.603 1.846 2.026 2.290 2.684 3.031 3.337 4.036 4.652 n-Butane C4H10 1.361 1.612 1.846 2.022 2.282 2.663 3.002 3.295 3.965 4.555 n-Pentane C5H12 1.352 1.603 1.838 2.009 2.265 2.646 2.977 3.266 3.923 4.492 n-Hexane C6H14 1.339 1.591 1.825 2.001 2.257 2.633 2.960 3.249 3.889 4.455 n-Heptane C7H16 1.336 1.587 1.821 1.993 2.248 2.625 2.952 3.232 3.869 4.425 n-Octane C8H18 1.336 1.583 1.817 1.993 2.244 2.617 2.943 3.224 3.852 4.400 n-Nonane C9H20 1.331 1.583 1.817 1.989 2.240 2.613 2.935 3.215 3.839 4.384 n-Decane C10H22 1.331 1.578 1.813 1.985 2.236 2.608 2.931 3.207 3.831 4.371 Cyclopentane C5H10 0.7913 1.105 1.800 1.578 1.863 2.273 2.629 2.935 3.630 4.199 Methylcyclopentane C6H12 0.9295 1.231 1.499 1.687 1.964 2.361 2.705 3.002 3.663 4.216 Ethylcyclopentane C7H14 0.9504 1.256 1.528 1.721 1.997 2.399 2.738 3.035 3.689 4.442 Cyclohexane C6H12 0.8499 1.181 1.469 1.679 1.976 2.412 2.784 3.107 3.831 4.371 Methylcyclohexane C7H14 0.9797 1.294 1.578 1.679 2.072 2.491 2.851 3.161 3.848 4.371 Ethylcyclohexane C8H16 1.026 1.336 1.612 1.813 2.098 2.512 2.868 3.169 3.839 4.358 Ethylene C2H4 1.298 1.495 1.687 1.829 2.043 2.357 2.633 2.872 3.416 3.919 Propylene C3H6 1.256 1.461 1.658 1.805 2.026 2.353 2.642 2.897 3.479 3.998 1-Butene C4H8 1.231 1.461 1.679 1.838 2.068 2.412 2.709 2.968 3.546 4.065 1-Pentene C5H10 1.269 1.499 1.712 1.871 2.106 2.449 2.747 3.006 3.588 4.099 1-Hexene C6H12 1.277 1.507 1.725 1.884 2.123 2.466 2.767 3.031 3.613 4.124 From the above chart, it is clear that under certain conditions, the variation in specific heat capacity at constant pressure is very small. However, when there are significant temperature changes, the specific heat capacity also changes considerably; this change has an impact on measurements. For different media, the rate of change of their specific heat at constant pressure also varies with different temperature changes. SIERRA, the American company that was among the first in the world to develop thermal-based products, has conducted research on the impact of temperature and pressure changes on flow meters, and provides very detailed specifications for the technical characteristics of its products. As indicated in the 620S product manual regarding the effects of temperature and pressure: Temperature coefficient: ±0.02% of the reading per 0°F within a range of ±500°F under the conditions specified by the user. Under the conditions specified by the user, the range is from ±500F to 1000F, with a reading accuracy of ±0.03% per 0F. Within ±25°C under user-specified conditions, it is ±0.04% of the reading per °C. Under the conditions specified by the user, the range is from ±25°C to 50°C, with a reading accuracy of ±0.06% per °C. Pressure coefficient: 0.02% per psi (air); consult the manufacturer for other gases. Domestic products have not undergone any in-depth research in this area; therefore, the effects of changes in temperature and pressure on flow meters are not mentioned in the brochures of such products. This is why we place particular emphasis on true-flow calibration for thermal applications (especially the measurement of other gases besides air). If the calibration is not carried out according to the actual process conditions on site, the performance of the flow meter will not be optimal, and the likelihood of problems arising is high. None of the thermal flow meters produced domestically has been calibrated for actual flow rates. When used with air, this isn’t a major issue; however, when used with other gases, problems are likely to occur. And once a problem arises, it’s really difficult to resolve; whether the gauge is replaced or not, it won’t eliminate the problem at its root. This is why high-quality products abroad place such emphasis on real-flow calibration, with specific heat at constant pressure being a key factor.

Regarding the second question raised by the original poster: the impact of humidity. It is clear that humidity has a significant impact on thermal flow meters, as the heat absorption capacity of humid gas differs greatly from that of dry gas. When the gas being measured contains water vapor, the direct consequence is severe deviations in the measurement values, and the magnitude of these deviations is related to the level of humidity. If the water content is high, it can severely damage the flow meter (as water vapor disrupts the temperature field, causing the electric heating wire to operate under overload conditions for extended periods, which increases the likelihood of damage to the probe). Therefore, thermal-type products are recommended for use in clean and dry gases; the presence of dust has little impact, and they can even be used in environments with some contaminants, though this will simply increase the frequency of maintenance.

Based on the equation Qm=K*ΔP/Cp*ΔT, it can be understood that pressure does not play a role in the calculation of flow rate; therefore, pressure factors need not be considered when calculating flow rate

As actually mentioned earlier, the measurement of thermal flow meters is related to the heat absorption capacity of each type of medium, and this heat absorption capacity is nothing other than the specific heat capacity of that medium. It is a physical quantity commonly used in thermodynamics, representing an object’s ability to absorb or release heat. The greater the specific heat capacity, the stronger an object’s ability to absorb or release heat. It refers to the amount of heat absorbed or released per unit mass of a substance when its temperature increases or decreases by one unit. The specific heat capacity of a substance depends on the process being carried out. In engineering applications, the three commonly used specific heats are constant-pressure specific heat Cp, constant-volume specific heat Cv, and specific heat at saturation. Specific heat at constant pressure, Cp: It is the amount of energy absorbed or released by a unit mass of a substance when its temperature rises or falls by 1°C or 1 K under constant pressure. This is the crux of the problem. The specific heat at constant pressure is defined under the condition that pressure remains unchanged; therefore, when the pressure changes, this specific heat at constant pressure no longer applies. However, the effect of pressure changes on specific heat capacity is minimal; therefore, we generally consider pressure changes to be negligible in thermal measurements. But this does not mean that pressure changes have no impact at all on thermal measurements. Taking the SIERRA thermal products in the United States as an example, the impact of one of their pressure parameters is expressed quantitatively to illustrate the effect of pressure changes: pressure coefficient: 0.02% per psi (for air); consult the manufacturer for other gases.

As actually mentioned earlier, the measurement of thermal flow meters is related to the heat absorption capacity of each type of medium, and this heat absorption capacity is nothing other than the specific heat capacity of that medium. It is a physical quantity commonly used in thermodynamics, representing an object’s ability to absorb or release heat. The greater the specific heat capacity, the stronger an object’s ability to absorb or release heat. It refers to the amount of heat absorbed or released per unit mass of a substance when its temperature increases or decreases by one unit. The specific heat capacity of a substance depends on the process being carried out. In engineering applications, the three commonly used specific heats are constant-pressure specific heat Cp, constant-volume specific heat Cv, and specific heat at saturation. Specific heat at constant pressure, Cp: It is the amount of energy absorbed or released by a unit mass of a substance when its temperature rises or falls by 1°C or 1 K under constant pressure. This is the crux of the problem. The specific heat at constant pressure is defined under the condition that pressure remains unchanged; therefore, when the pressure changes, this specific heat at constant pressure no longer applies. However, the effect of pressure changes on specific heat capacity is minimal; therefore, we generally consider pressure changes to be negligible in thermal measurements. But this does not mean that pressure changes have no impact at all on thermal measurements. Taking the SIERRA thermal products in the United States as an example, the impact of one of their pressure parameters is expressed quantitatively to illustrate the effect of pressure changes: pressure coefficient: 0.02% per psi (for air); consult the manufacturer for other gases.