# Simplified Calibration Method for Constant-Temperature Hot-Wire Anemometry
## 2 Measuring Technique, Equipment, and Data Reduction
### Hot-Wire Anemometry  
A standard single hot-wire probe, which was made of Tungsten (KANOMAX Inc., Suita city, Osaka, Japan, 0251R-T5), was employed for the wind tunnel experiment. The probe consists of a wire, which was 2 mm long with a diameter of 5 \(\upmu\)m and two prongs, which were 7 mm long.  
The output signal from the hot-wire probe was converted to a voltage by an A/D converter (KANOMAX Inc., constant temperature hot-wire anemometer: CTA). The voltage data was recorded by a data recorder (A&D Inc., Tokyo, Japan, RM-1100) at a sampling rate of 20 kHz. At each probe position, the output voltage data was recorded for a duration of 5 s.  
Figure 2 presents a schematic diagram of the measurement system with hot-wire equipment and the measurement locations on the flat-plate test model. The measurement locations were changed by changing the probe position. The vertical probe position (i.e., \(z\)-position) from the wall surface was varied from 1 to 20 mm by an electrically controlled traversing system. The \(x\) and \(y\) positions were fixed: \(x=600\) mm (\(x/x_{chord}=2/3\)) and \(y=-20\) mm (\(y/y_{width}=-0.031\)). A total of 25 measurement locations in the vertical direction was realized by changing the \(z\) position of the probe. The vertical position of the probe was changed starting from \(z=1.0\) to 10 mm, which corresponds to the periphery of the upper edge of the boundary layer, with an increment of 0.5 mm. Then, the vertical probe position was increased with increments of 2 mm or 4 mm until it reached \(z=20\) mm, expecting that the change in the velocity profile in the vertical direction at those heights would be small since the flow in this area is freestream. When reached at \(z=20\) mm, the probe position was changed in the opposite direction (i.e., in the order of decreasing height) in order to check for hysteresis of the detected signal and temperature dependence of the signal.  
The probe's soundness was confirmed at each measurement by measuring the resistance of the probe. The resistances measured before and after the testing were both around 4.0 \(\Omega\), and therefore no damage to the probe was seen. In general, an output signal detected by a tungsten-made hot-wire probe may involve a time decay under a long-duration measurement that involves a large temperature variation in the flow. It should be noted that slight time decays with temperature dependence in the output signal, which will be described in Section 2.3, were obtained during the wind tunnel experiments. However, the time decay of the output signal will also be converted to the flow velocity properly by the calibration method with the temperature correction, which will be described in detail in Section 3. The probe was also varied at each measurement.  
The wire of the hot-wire probe was placed perpendicular to the flow and the probe orientation to the flow was fixed. The probe stem was also normal to the wall surface. With this configuration, the streamwise component of the flow was considered to be detected. Therefore, the measured velocity was considered as the \(U\) velocity. More details of the hot-wire anemometry applied to the same flowfield is available in [PERSON] et al. [10].  
Figure 2: Schematic diagram of hot-wire anemometry setup and measurement locations.