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The purpose of this study is to investigate experimentally the effects of orbital motion on the velocity field of boundary layer flow over a rotating disk. The characteristics of velocity field at a fixed orbital angular section measured by a hot-wire anemometer show that the structure of the 3-dimensional boundary layer flow is deformed elliptically and displaced in a certain direction that is not in the orbital radial direction, but the direction of deformation depends on the combination of orbital and rotational directions. For coincide orbital and rotational directions, there are regions where the intensity of low-frequency disturbances increases rapidly in a certain central region (laminar region under pure rotation). The transient vortices, which form streaks on the coating film, are considered to be destroyed by low-frequency disturbances. However, for opposite orbital and rotational directions, the low-frequency disturbances are not observed in any section. As the adding orbital speed increases, the intensity of velocity fluctuations in the turbulence region becomes larger in the expected except in a certain region. This location of the region also depends on the direction of deformation or the combination of orbital and rotational directions.

Flow fields over rotating disks appear in the context of spin-coating manufacture of semiconductors. Many studies have been accomplished both theoretical [

In our earlier work, we found that the laminar region narrows and the transition point moves inward on the disk, regardless of the direction of rotation as the applied orbital rotating speed increases [

The objective of this study is to investigate this velocity field using a larger disk than in the previous study. The effects of the velocity field in the turbulence region, the deformation of boundary layer structure, and the characteristics of disturbances are presented based on measurements obtained using a hot-wire anemometer.

The experimental apparatus consists of a rotating disk mounted on an orbital rotation base (_{o} is 50 mm (=R/3). The counterclockwise direction is taken as positive direction for both rotation and revolution (i.e., orbital movement). The angular speeds of rotation and revolution are controlled independently. Experimental trials were performed at a rotational velocity N of +3000 rpm and orbital speeds N_{o} in the range of −500 rpm ≤ N_{o} ≤ +500 rpm stationary.

Two distinct coordinate systems are used. In the fixed coordinate system, the origin O_{o} is the center of the orbit, and the radial distance from O_{o} is denoted r_{o}. In the moving coordinate system, the origin O is the center of disk. The coordinates of the two systems are denoted r, θ, and z for the distance in the radial direction, the angle in the circumferential direction, and distance in the axial direction, respectively. As indicated in _{o} and the disk center O is on line AB in the fixed coordinate system, directions OA (q = 180˚), OB (q = 0˚), OC (q = 90˚), and OD (q = 270˚) in the radial direction will be denoted by r_{A}, r_{B}, r_{C}, and r_{D}, respectively.

The velocity field of the boundary layer flow on the disk is measured with a single hot-wire anemometer at a fixed angular position using a timing-mark laser sensor. The hot-wire is positioned parallel to the disk surface and aligned normal

to the rotation. Hence the tangential (i.e., circumferential) velocity v_{θ} is measured. The velocity data of 250 points are sampled at all radial position on the disk, and the mean tangential velocity V_{θ} is calculated. An analog-to-digital converter is triggered by a timing pulse signal from the orbital base; this ensures that the center of each time record represents the same orbital angular position. The velocities at 1024 points are sampled at every trigger signal for at most 750 orbital revolutions at a sampling frequency of 100 kHz (low-pass filter: 12 kHz).

The radial boundary layer is measured at a height z = 0.65 mm from the disk’s surface (so that z/δ = 3.0). Here δ is the thickness of the boundary layer in the pure-rotation case defined as δ = (ν/ω)^{1/2} (ν: kinematic viscosity of air, ω: angular velocity of a rotation disk).

_{θ}) at a given orbital angular position, where the orbit center O_{o} is on the measurement section AOB (_{θ} in the OC direction (r_{c} direction) and OB direction (r_{B} direction) are defined as positive.

Under pure rotation, the velocity data at r/R ≤ 0.55 in any section accord with the theoretical values in laminar flow on a purely rotating disk given by von Karman [

In

From these velocity distributions, the point of V_{θ} = 0 moves towards r_{A} and r_{D}. It is found that the mean center of spiral flow is located in the AOD region (r-θ plane at 180˚ < θ < 270˚) and moves increasingly away from the origin of the disk as orbital speed increases. Additionally, both the transition points from the boundary layer flow to transient flow and then to turbulent flow, at the OA, OB, and OC sections, move radially inward with increasing V_{θ}. That is, the boundary transitions occur earlier. However, at the OD section, the transition points move radially outward along r_{D}. The structure of the 3-dimensional boundary layer flow is deformed elliptically and displaced to the D-side under orbital motion.

In

With increasing negative orbital speed, both transitions in boundary layer flow (laminar to transient and laminar to turbulent) are promoted earlier at the OB and OD sections; however, they are delayed at the OA and OC sections with increasing negative orbital speed. With N_{o} = −300 and −500 rpm, the laminar region expands and the laminar?transient transition is delayed, although it is remarkable that the mean velocity at the OA section significantly increases between the laminar region and the turbulence region. It is considered that the velocity on the surface of the disk along O to O_{o} is accelerated, and the thickness of the boundary layer along O_{o} to A increases because surface velocity decreases.

The radial distributions of the root mean squared (rms) values of the fluctuating tangential velocity at the same orbital angular position V_{θ}_{,rms} are shown in

In _{o} = +500 rpm, the fluctuation intensity becomes

larger in the central region where it is considered to be laminar flow (r/R ≤ 0.5) from the linear velocity profile (see _{θ} at r/R = 0.3 in this region and each section at N_{o} = −500 rpm are given in _{A}/R = 0.3 and r_{D}/R = 0.3 in the OA and OD sections. However, the velocities at r_{B}/R = 0.3 and r_{C}/R = 0.3 in the OB and OC sections have disturbances over long periods (low frequencies) and with large amplitudes. Consequently, it is found that the fluctuation intensity increases in this region (BOC). These low-frequency disturbances are no different from transient vortices, which cause velocity fluctuations with periods of around 12 degrees as shown at r/R = 0.65 (in the transition region) in the pure-rotation case in

The low-frequency disturbances are expected to be generated in this region, where the velocity changes most and the outward radial velocity component is maximum at around q = 45˚ by adding the orbital motion on the rotating disk. Therefore, the origin of the low-frequency disturbances is considered to be associated with the instability of the streamline curvature [_{D}/R = 0.80). A detailed investigation will be conducted on this aspect in future work. Also, as the orbital speed increases, the fluctuation intensity in the turbulence region becomes larger except at the OA section.

In

The effects of orbital motion on the velocity field of boundary layer flow over a rotating disk were investigated experimentally. The velocity field at a fixed orbital angular section measured by a hot-wire anemometer show shifts at the transition points and changes in velocity gradients in consequence of the orbital motion. We conclude that the structure of the 3-dimensional boundary layer flow is deformed elliptically and displaced in a certain direction that is not in the orbital radial direction. This displacement depends on the direction of rotation.

For coincide orbital and rotational directions, there are regions where the intensity of fluctuations in velocity increases rapidly, departing from the mean velocity profile in normally laminar regions. These disturbances are characterized by low frequency and high amplitude. The transient vortices, which form streaks on the coating of films, are considered to be destroyed by low-frequency disturbances. However, for opposite orbital and rotational directions, the low-fre- quency disturbances are not observed at any section.

Concerning the effects occurring in the turbulence region, the fluctuating intensity becomes larger as the orbital speed increases except in a certain region. These are observed irrespective of the direction of rotation. However, the expected location of the region also depends on the direction of rotation.

This study is supported by Tokyo Electron Kyushu Inc. Useful discussions with Mr. Kurishima, H. and Mr. Kudo, K. at Tokyo Electron Kyushu Inc. are appreciated.

Munekata, M., Utatsu, T., Yoshikawa, H. and Okumura, Y. (2017) Effects of Orbital Motion on the Velocity Field of Boundary Layer Flow over a Rotating Disk. Open Journal of Fluid Dynamics, 7, 169-177. https://doi.org/10.4236/ojfd.2017.72011