Calibration

5.5.1

Introduction

In this study, a new way of calibration is introduced to resolve the questions and uncertainties that resulted from the investigations of Harris (2013) since, as mentioned before, it was difficult to draw definitive conclusions from his mea- surements. We refer to this new technique as the rotating–arm (RA) calibration method and it is presented in Section 5.5.3.

In the calibration of hot–film process, the most commonly used relationship between the velocityU∗ and the voltage readingE from the hot–film is knows as

E2 =A+BU∗n. (5.1) Although this equation can be applied to a hot–film in water in principle, Wu and Bose (1993) reported that an extended King’s law, of the form of

E2 =A+BU∗n+CU∗2n, (5.2) can lead to an increase in accuracy over the simple King’s law itself at low ve- locities. This improvement was also confirmed as a part of this study and thus the calibration curves obtained from extended King’s law equation are used in the current study for changing the raw voltage measurements into velocity mag- nitudes.

Here, the calibration constants A, B, C and the exponentn are obtained by a least–squares curve fitting to the calibration data. Bruun (1995) reported that the exponential valuen depends on the probe type, the calibration method, and the velocity range.

5.5.2

Calibration Against von K´arm´an Flow

The method of calibrating the hot–wire probe directly over a smooth ro- tating disk surface by means of the von K´arm´an flow was first introduced by Ling- wood (1996) and then used in other studies, such as Imayama et al. (2012). This calibration technique will, hereinafter, be referred to as LK–calibration. It has already been revealed that this calibration technique is appropriate for the air– based rotating disk facilities as some of the previous results of Lingwood (1996) show a very good agreement with the velocity profiles obtained from the simi- larity solution of von K´arm´an (1921); refer to Section 2.2 for the corresponding figures. Therefore, it was thought that it is worth employing the same calibration method in our water–based rotating–disk experiments as well. The procedure for the LK–calibration is as follows.

The only known velocity for the rotating–disk flow is the rotational velocity of the disk Ω∗ itself and thus the velocity of the fluid v∗ = Ω∗r∗ at a particular radial position r∗ on the surface of the disk. Obviously, the flow velocity on the surface of the disk cannot be measured practically but the mean velocity profiles can be calculated by the similarity solution derived by von K´arm´an (1921). It is assumed that the actual mean velocities within the boundary layer are those predicted by the similarity solution and thus, in this method, the hot–film probes are calibrated against these theoretically predicted velocities.

For the rotating–disk flow in air–based facilities, the similarity solution accurately predicts the boundary–layer flow over the rotating disk, however, for the water–based facilities the boundary–layer flow has already been modified due to the finite size of the facility and thus the similarity solution does not exactly represent the real flow over the disk any longer. Nevertheless, the LK–calibration was reproduced in the current study for comparison with our newly proposed rotating–arm calibration method which will be introduced in Section 5.5.3.

To conduct the LK–calibration, the hot–film probe is positioned parallel to the disk surface and aligned in the flow direction correspondingly to measure the azimuthal component of the velocity. This is the dominant velocity component amongst the other two (radial and axial) in terms of their magnitude. The radial location of the probe can be adjusted by means of the 2–axis traverse system and its height over the surface of the disk can be changed precisely by the vertical vernier scale. Changing the location of the hot–film probe in both radial and axial directions leads to a calibration velocity range of 0 ≤ U ≤ 0.363 m/s. The maximum velocity is defined as the maximum value that can be practically measured in the boundary–layer over the rotating disk while keeping the flow in the laminar region. This is important because the reference velocities are predicted by the similarity solution which is only valid in the laminar–flow region. Velocity profiles obtained by this method is compared with the ones produced by rotating–arm calibration method in Section 6.1.

5.5.3

Rotating–Arm Calibration Method

The basic idea of this new technique is that the rotational speed of the shaft on which the arm is mounted is known and thus the probe can be tra- versed/rotated in still water with known velocities by means of this arm which holds the hot–film probe. The description and the procedure for the rotating–arm calibration method are provided as follows.

Figure 5.8: A sketch of the rotating–arm calibration method.

A simple device was manufactured particularly for this purpose. It consists of an aluminium bar (the rotating arm) with a probe support at one end and a pivot at the other end as illustrated in Figure 5.8. The pivot is secured on the support disk which is located on top of the shaft. The shaft is rotated with the motor and the angular frequency of the motor, f∗, can be controlled with a computer–based speed control unit. The rotational velocity Ω∗ can be obtained by Ω∗ = 2πf∗ and also measured directly from the shaft by means of a mechanical tachometer to check the reliability of the motor. It was found that the angular frequency of the motor is in the maximum error margin of±1%. The linear velocity of the probe U∗ in stationary water is calculated by U∗ = Ω∗l∗.

Here, l∗ represents the length of the rotating arm from the pivot (the axis of the rotation) to the probe support that holds the probe. The connection between the rotating arm and the pivot is made by screws and thus the length of the arm l∗

is adjustable. The electrical connection between the probe and the anemometer is made by a rotary slip–ring. The slip–ring is produced by Mercotac Inc and demonstrated in Figure 5.9. The connection through the slip–ring assembly is a standard technology to transfer electric signals between rotating and non–rotating systems without the requirement of cables. Although a mentor from the TSI company suggested that calibration through a slip–ring would not be possible, we tried it and managed to obtain accurate results due to the fact that the resistance of the slip–ring is less than 1 mΩ and it has extremely low electrical noise.

Figure 5.9: Slip–ring MERCOTAC Inc.

The motor is operated in the frequency range of 0≤f∗ ≤0.3183 Hz which provides the rotational velocity range of 0 ≤ Ω∗ ≤ 2 rad/s. The length of the rotating arm is fixed at l∗ = 0.3 m which leads to the linear velocity range of 0 ≤ U∗ ≤ 0.6 m/s. This particular length of the rotating arm is the maximum value that can be chosen because in this case the required velocity range can be obtained with smaller angular velocities. This is important for keeping the disturbances minimum in the stagnant medium created by the rotation of the probe itself. The radius of the stationary annular shroud (cf. Figure 5.8) is

0.113 m which protects the stagnant medium from the wakes formed by the rotation of the support disk and the shaft. Therefore, when the arm length l∗ is equal to 0.3 m, the probe is located at the middle of two stationary walls – water tank (R∗ = 0.5 m) and annular shroud (R∗ ∼= 0.1 m) – and considered not to be affected by the wakes which may be reflected from these walls. In this manner the only disturbance in stagnant water resulted from the rotation of the probe itself and this effect is minimized by stopping the rotation of the arm after each set of voltage measurement at a known corresponding velocity and leaving water to be stagnant again before the next set.

While the probe is being rotated with various constant velocities, the hot– film output voltages obtained from the constant temperature anemometer are transferred to a PC using a 16 bit DAQ card. The input range of this card is from −10 V to +10 V with a sampling rate capability of 100 kilo-samples per second. The sampling frequency during the calibration is 1 kHz and this leads to a time resolution of 0.001 s. This calibration technique, hereinafter, will be referred to as RA–calibration.