# Design of a Mass Air Flow Sensor Employing Additive Manufacturing and Standard Airfoil Geometry
## 4 Discussion  
As a general remark, based on the previously presented experimental findings, the adaptation of standard airfoil geometry to the housing design leads undoubtedly to an extensive increase in the measurement range of the final sensing device. Taking into consideration the findings of previous relative research work [12], but also the simulations presented in this paper, this increase is attributed mainly to the drastic reduction of the circulating flow inside the bypass pathway, especially near the sensing area, by appropriately shaping the flow profile at both inlet and outlet ports of the bypass pathway. Furthermore, we should note that the obtained experimental results are in agreement with those theoretically predicted by the performed simulations, since the recorded measurement range for both bypass topologies was significantly larger compared to the obtained range when the RTD element was placed directly on the housing's main inlet. In more detail, an increase of 33.3% and over 130% was measured for the High Velocity Bypass and Low Velocity Bypass topologies, respectively. Regarding the numerically estimated reduction in velocity over the sensing element for each topology (see previous section, Table 2), we should consider the following based on our findings. The convective heat flux of air over a surface can be expressed by the following equation:  
\[q=h_{c\_air}\cdot\Delta T \tag{2}\]  
where:  
\(q\) is the rate of heat flux perpendicular to a surface (W/m\({}^{2}\))  
\(h_{c\_air}\) is the convective heat transfer coefficient of air (W/m\({}^{2}\cdot\)K)  
\(\Delta T\) is the temperature difference between the air and surface (K). The convective heat transfer coefficient of air (\(h_{c\_air}\)) can be estimated though by the following empirical equation [28]:  
\[h_{c\_air}=12.12-1.16\ v+11.6\ v^{1/2} \tag{3}\]  
where \(v\) is the relative speed between the surface and air (m/s). Equation (3) is graphically presented at Figure 15 for velocity values from 0 to 17 m/s; we note that the value of the convective heat transfer coefficient (\(h_{c\_air}\)) increases negligibly for velocities exceeding 16 m/s, while for velocities exceeding 14 m/s, the increase is less than 2% (i.e., from 39.3 to 40 W/m\({}^{2}\cdot\)K). Thus, regardless of the topology employed in the developed sensor, even if we consider the Constant Temperature (CT) mode of operation, where the temperature difference (\(\Delta\)T) between the incoming air and the sensing element is maintained constant, saturation of the sensor's signal should be expected at an air velocity of 14 m/s, approximately. Figure 15: Convective heat transfer coefficient of air over a surface vs. velocity. Additionally, when the sensor is operating at Constant Current (CC) mode, as in the performed characterization, the sensing element's temperature declines considerably as the incoming flow (i.e., velocity) increases. Note that the maximum temperature decrease deduced from the experimental data presented was from 40 \({}^{\circ}\)C to 46 \({}^{\circ}\)C (Figures 11b, 12b and 13b), which corresponds to a decrease of 31.6% to 36.5% of the initial temperature. Therefore, we can safely conclude that saturation of the sensor's signal is expected at a significantly lower velocity of 14 m/s (which theoretically applies considering CT mode of operation) for all three topologies. Considering the velocity decrease factor, which is deduced from the performed CFD simulations for each bypass topology (see Table 2), we can estimate the air velocity over the sensing element for any of the specific inflow values tested. As already mentioned in the results section, saturation at the sensor's output signal was recorded for a flow rate of 4000 SLPM (280 kg/h), approximately, for the High Velocity Bypass topology employed.