Disks with two different dimensions were used to clarify the differences in final vortex structures generated by the change in disk acceleration time. The experiment results and calculated results of vortex structures match when the disk thickness is 20 mm and the Reynolds number is 5000 - 15000. Also, they match when the disk thickness is 30 mm with a Reynolds number from 3000 - 5000 and 9000 - 20000. Even when the size of the disk and the Reynolds number are the same, the final vortex structures can be different due to differences in the disk acceleration time.
The flow brought about by a rotating object within a container is often seen in fluid machines which provide/get energy to fluids via the rotation of vaned wheels such as centrifugal pumps and turbines. Many related studies have been conducted by Bödewadt et al. [
Rotating flows can be found in fluid machinery and chemical reactors and they are examined to improve their performance [
In research conducted thus far, rotating disks of different shapes are used to change the gap within cylindrical containers and experiments have been conducted in respect of the impact that the gap in the radial direction has on the disk rotor in the container and, as a result, from the difference in disk dimensions, fluid movement phases that changes with each disk have been confirmed. Hence, in this study, experiments have been conducted to clarify the edge effect using disks with different dimensions by focusing on the edge effect. The transition scenario for the complex flow and the geometric effect changing the acceleration time has not been well clarified. The purpose of this study is to clarify the vortex structure by changing disk acceleration time.
is the flow between the fixed disk and the rotating disk, is such that the space in the container with rotating disk is symmetrical, the disk joining part has the same diameter as the rotating axis of 20.0 mm. The material of the disk is duralumin and the whole thing is coated with matte black. The dimensions of the rotating disk fixed in the container are as follows. Disk: Radius r = 127.0 mm, thickness hd = 30.0 mm.
The experiment devices used were an acrylic casing (Sanwa Kiki manufacturing) Xenon slit light source (500W, KS2000-30, Katou Mitsuken), an inverter (Mitsubishi Electrics), a control box (Sanwa Kiki manufacturing), a digital tachometer (Mitsubishi Electrics), and the main part of the experimental device, which was attached to them. Filming utilized a digital video camera (SONY HDR- CX560V) which has an effective pixel count of 6,140,000 (16:9) and, in this research, the filming was done with an average bit rate of 28 Mbps with a resolution 1920 × 1080 pixels and framerate of 60 fps. The recorded image can be digitally processed via a computer. A slit light source was placed right next to the cylindrical container so that the irradiation position would be horizontal and the experiment device was placed in a dark room to avoid light from the outside. Moreover, to achieve the desired number of rotations, the motor rotation was controlled with an inverter and the setting of the disk acceleration time was conducted with a MELSOFT series GX Works II (Mitsubishi Electrics) and the number of rotations of the axis was confirmed using a digital tachometer.
The test fluid uses Newton liquid in which distilled water and glycerin are mixed together well at specified mass ratios. This research used the ratio 3:2 of water to glycerin in the test fluid. To obtain the kinetic viscosity ν, a specific gravity meter (Nihon Keiryoki Kogyo K. K) was used. Moreover, viscosity μ was measured used an SV type viscosity meter (SV-10 KK A & D).
The three-dimensional flow inside the container is visualized on a two-di- mensional plane using aluminum powder. The visualization using aluminum powder is done by mixing aluminum powder, which has been put into a sieve with a lattice width of 20 μm, with the test fluid. The amount of aluminum powder mixed in is 0.1 g for 2.5 l of test fluid. Moreover, to prevent aluminum powder from floating due to surface tension of the test fluid at this point, 1 - 2 droplets of household neutral detergent are mixed in.
The Reynolds number
On this occasion, two types of disks −20 mm and 30 mm―are used. Moreover, disk acceleration times are 1 s and 30 s with a Reynolds number from 3000 - 20000 at 1000 intervals. It is thought that there are 4 types of vortex structures appearing in the gaps between the axes. The four types are polygonal, ring, positive progressing spiral, and negative progressing spiral.
In past experiments, it was impossible to set the Reynolds number within a stipulated time. In this experiment, the disk acceleration time was changed using a control box and MELSOFT series GX Works II (Mitsubishi Electrics).
An example of the change in the disk acceleration time is shown in
Moreover, in the actual experiment, to obtain the desired Reynolds number Re, the required rotational velocity was derived from viscosity and specific gravity. The final rotational velocity of the disk is set in respect of this derived result.
The viscosity of the test fluid is taken to be μ(mPa・s), specific gravity s and the number of disk rotations, N(rpm). The representative velocity is taken to be V(m/s), representative length r(m), and kinetic viscosity, ν(m2/s).
The required number of rotations was derived from the following equation.
The numerically calculated values for vortex structure when the disk acceleration time is 1 s are compared against the experimental results. Below,
shows the numerically calculated results. This figure plots the Reynolds number on the vertical axis and the thickness of the disk on the horizontal axis. ts represents the disk acceleration time and h the thickness of the disk. Furthermore, the polygonal vortex, ring vortex, and negatively progressing spiral vortex are abbreviated as P, R, and S-, respectively.
The structure of the vortex appearing in the radial gaps is shown below.
Disk vortex structures expected to appear are shown in
Next, a ring vortex appears at a Reynolds number of 3000 when the disk thickness is 20 mm. A polygonal vortex appears at a Reynolds number of 4000 - 20000. A ring vortex appears at a Reynolds number of 3000 - 5000 when the disk
thickness is 30 mm. A negatively progressing wave spiral vortex appears at a Reynolds number of 6000 - 20000. Furthermore, the vortex structures of polygonal vortex and negatively progressing spiral vortex are abbreviated as P and S-, respectively.
The vortex structures that appeared when the disk thickness was 20.0 mm and 30.0 mm with a disk acceleration time of 1 s and 30 s are shown in
Different results were shown in the table when the disk thickness was 30 mm when the Reynolds number was 7000 - 10000. Furthermore, vortex structures which could not be clearly determined visually or as a polygon, ring, negatively progressing spiral―as p, r, s- were marked as undeterminable.
The vortex structure was filmed across the r-θ cross-section. Part of the still images is shown from Figures 6-8.
20mm | disk acceleration time ts (s) | 30 mm | disk acceleration time ts (s) | ||
---|---|---|---|---|---|
Reynolds number | 1 | 30 | Reynolds number | 1 | 30 |
3000 | nontypable | nontypable | 3000 | nontypable | nontypable |
4000 | 4000 | ||||
5000 | p | 5000 | |||
6000 | 6000 | p or r | |||
7000 | p | 7000 | p | r | |
8000 | 8000 | p or s- | |||
9000 | 9000 | s- | |||
10,000 | 10,000 | ||||
11,000 | 11,000 | nontypable | |||
12,000 | 12,000 | ||||
13,000 | 13,000 | s- | |||
14,000 | 14,000 | ||||
15,000 | p or s- | 15,000 | |||
16,000 | p or s- | 16,000 | |||
17,000 | 17,000 | ||||
18,000 | 18,000 | ||||
19,000 | 19,000 | ||||
20,000 | 20,000 |
polygonal vortex. Similarly,
Results comparing the final vortex structures obtained by experiment and by numerical calculation results discretized using the difference method with the three-dimensional unsteady compressible Navier-Stokes equation are shown in
From the table, it can be said that the numerically calculated results and experiment results match when the disk thickness is 20 mm with a Reynolds number of 5000 - 1500 and when the disk thickness is 30 mm with a Reynolds number of 9000 - 20000.
Disks with two different dimensions were used to clarify the differences in final vortex structures generated by the change in disk acceleration time and the following results were obtained based on visualization experiments and analysis results.
1) The experiment results and calculated results of vortex structures match when the disk thickness is 20 mm and the Reynolds number is 5000 - 15000. Also, they match when the disk thickness is 30 mm with a Reynolds number from
Disk acceleration time ts (S) | Disk thickness hd (mm) | Reynolds number | Experimental result | Calculated result |
---|---|---|---|---|
1 | 20 | 5000 - 15,000 | p | p |
16000 - 20,000 | s- | |||
30 | 3000 - 5000 | r | r | |
6000 | r or p | s- | ||
7000 | p | |||
8000 | p or s- | |||
9000 - 20,000 | s- |
3000 - 5000 and 9000 - 20000.
2) Even when the size of the disk and the Reynolds number are the same, the final vortex structures can be different due to differences in the disk acceleration time.
This research was supported by the research grant from the Nitto Foundation. We appreciate good comments from reviewers.
Furukawa, H., Wada, A. and Watanabe, T. (2017) Experimental Study of Clarification of Vortex Structure by Changing Disk Acceleration Time. World Journal of Mechanics, 7, 185- 194. https://doi.org/10.4236/wjm.2017.78017