Cooled Vortex Street Generated by Cooling a Cylinder at Low Reynolds Number: Effects of Reynolds Number Difference on Cooled Wake and Cooled Vortex Street

Abstract

First, the dominant action in the cooled wakes in mercury and water at the Reynolds number Re = 22 and 44 is discussed. Next, the cooled wake at Re = 22 is numerically simulated and is compared with the previous results at Re = 44. Finally, effects of Re on the cooled wake and the cooled vortex street are elucidated, and are found to be extremely powerful as follows.

• 1. The dominant action can be determined at different fluids and different Re. Here, the vorticity and the temperature are relating with each other.

• a. “Table of diffusion intensity order” is invented. By obtaining and using this table, the dominant action can be determined automatically.

• b. The kinds of the dominant action are the advection and the diffusion in the vorticity and the temperature.

• c. In mercury and water at Re = 44 and 22, the dominant action is the vorticity diffusion at the low Re, the vorticity advection at the high Re, the temperature diffusion at the low Peclet number Pe, and the temperature advection at the high Pe.

• d. The dominant action in air at Re = 44 is between the dominant action in mercury and water at Re = 44. The dominant action in air at Re = 22 is the same as the dominant action in mercury at Re = 22.

• e. By using the dominant action, the wake variations and item 2 below, i.e., the characteristics of the cooled wake behavior, can be explained.

• 2. When Re is decreased, the following occurs and its cause is elucidated.

• f. In the cooled wake, the Karman vortex street does not occur, but the cooled vortex street with g below occurs.

• g. The vortex spiral size is not changed in mercury but is increased in water.

• h. The following is decreased in mercury but is increased in water. The range of the absolute Richardson number|Ri|generating the cooled vortex street, the spiral degree in the cooled vortex, the critical|Ri| for the symmetric wake onset, and the reciprocal of the temperature wake area.

Notes

Pr = 0.029 at mercury and Pr = 10.5 at water.

Mercury and water at Re = 44 are in [16].

Mercury and water at Re = 44 are in [16].

Pr = 0.72 at air.