A wake from an elliptic cylinder with fixed separation points is analyzed numerically, and is clarified as follows : An isothermal Karman vortex street never occurs at Re<36, but a cooled Karman vortex street is generated by cooling a progressive wavy wake at 26≤ Re<36, where Re is the Reynolds number. The cooled Karman vortex street can be generated at smaller value of the absolute Richardson number in an elliptic cylinder wake than a circular cylinder wake. By cooling the Karman vortex street, a suppressed flow Is generated. Both the Karman vortex street and the suppressed flow have a double structure combined the motions due to both negative buoyancy and the forced flow. The dominant motion is due to the forced now at the Karman vortex street, and due to negative buoyancy for the suppressed flow. At the boundary between the Karman vortex street and the suppressed now, the dominant motion is exchanged, and the wake frequency and the mean Nusselt number decrease abruptly.
Investigations in the present paper have been made theoretically on a breakdown and a development of the Karman vortex street in both positively and negatively buoyant wakes. Unsteady numerical solutions are obtained by means of time-dependent numerical analysis. To verify the validity. of the results of numerical analysis, results of flow visualization were compared with numerical solutions. The following results were obtained.1. The natural convection from the cylinder has a remarkable influence on the Karman vortex street.2. In the positively buoyant wake above a heated horizontal cylinder, the Karman vortex street breaks down.3. In the negatively buoyant wake, the Karman vortex street develops.
A positively buoyant wake from a circular cylinder at the Reynolds number 800∿940 is measured, discussed and found as follows : By heating an isothermal wake, turbulent energy and turbulent vorticity in the isothermal turbulent wake are conserved in the buoyant wake, and this buoyant wake certainly becomes a double structure combined non linearly with two kinds of large-scaled coherent motions, i.e. one is the vortex street motion and the other the plume swaying motion with extremely different frequencies each other. That is, the buoyant wake is a turbulent flow with a triple structure of free turbulence, vortex motion and swaying motion. Structural instability with abrupt change occurs certainly due to unbalance between two kinds of large scaled motions.
Spectrum of the plume in a stably stratified ambient was elucidated to have gradients -9/2 and -8.0 at laminar state, and -5/3 and -3.0 at turbulent state, in addition the frequency band of the turbulence was higher than that of the swaying motion. By employing the above results, flow regimes, i.e. laminar, transitional, and turbulent, at any location can be determined. By plotting flow regimes on visualization photos, retransitional and relaminar phenomena are specified. Stable stratification generates turbulence, suppresses turbulence, and leads to reverse transition and relaminarization, which do not occur in the plume in an unstratified ambient, thus characterizing the plume in a stratified ambient. The Grashof number for the beginning of transition is approximated as Grs=9.15×105{Q[W/m]}1.62. Critical heat rate Q for the beginning of either the transitional or turbulent regime is Qs[W/m]=1.30-2.75 or Qe[W/m]=5.10-8.73.
By analyzing numerically a buoyant flow in stably stratified air in an enclosure, a thermal cylinder was found and the cross-over phenomenon (CO) was elucidated as follows: A plume occurred time-averagedly from a line heat source and its height was suppressed by stratification. To transport heat upwards from the plume front, an isothermal line was divided near the front and a thermal cylinder was generated. The time-averaged temperature decreased upwards in the plume, and the temperature at the front became lower than that in environment. Thus, the time-averaged cross-over occurred. In the region where thermal cylinders were rising intermittently above the front, the convective heat was transported by thermal cylinders and the conductive heat were transported from above and both side. As a result, the time-averaged temperature of the buoyant flow increased upwards and approached the environment temperature.
The cooled wake in mercury, air, or water at the Reynolds number 44 is analyzed numerically. Effects of fluid kinds on the time-dependence and the cylinder surface values in the cooled wake and the cooled vortex street are elucidated as follows: (1) The streamfunction oscillates with the constant amplitude in both the Karman vortex street in any fluid and the cooled vortex street in mercury and air, but oscillates with the amplitude pluraling in both the transitional process to the cooled vortex street in any fluid and the cooled vortex street in water. (2) The oscillation type in the cooled vortex street depends on the Prandtl number Pr. The oscillation has the constant amplitude at the low and moderate Pr as mercury and air, but, has the amplitude pluraling at the high Pr as water. (3) The distribution and the time-dependence of the local and mean coefficients of wall shear stress c_f, C_f and the local and mean Nusselt numbers Nu, Nu_m are elucidated in the cooled wake in mercury, air and water. (4) In the cooled wake in any fluid, the negative buoyancy makes the Strouhal number St, mean coefficient of wall shear stress C_f, mean Nusselt number Nu_m, and vortex speed U_v small, and the amplitude of wake oscillation large. The cooled vortex street in any fluid oscillates with the frequency less than the Karman vortex street. (5) The St number in any kind of fluid and the C_f and Nu_m numbers in air are decreased suddenly in the transitional process. The decrease behavior of St is different among fluid kinds. (6) The sudden change is an unstable-like phenomenon, and the transitional region with the sudden change is the unstable-like state. The streamfunction oscillation has the amplitude pluraling in the unstable-like state, and has the constant amplitude in the stable-like state.
A thermal plume above a heated square on the earth ground in stably stratified air was formulated as a three-dimensional, time-dependent motion of the fluid with variable density and property, the Coriolis force, and the pressure as weight of air column. A direct numerical simulation (DNS) methodology was obtained. Computed results of plumes with and without the Coriolis force in neutrally or stably stratified air were shown, and three-dimensionality and time-dependency in those plumes were elucidated. The computed results were validated as follows : Features and differences between plumes without the Coriolis force in neutrally stratified air from the square and a point source were validated as reasonable. In stably stratified air, the computed plume without the Coriolis force showed the cross-over phenomenon and the time-dependent temperature with the constant maximum value, and agreed qualitatively with those of a plane plume. The computed plume with the Coriolis force in neutrally or stably stratified air was physically reasonable.
The breakdown phenomenon of the Karman vortex street is made clear from the viewpoints of flow visualizations by the smoke-wire method, power spectra, and the Strouhal number. In the positively buoyant wake behind both a heated horizontal circular cylinder and a heated horizontal triangular one, the Karman vortex street breaks down due to the natural convection. By adding the natural convection to the neutrally buoyant wake, the Strouhal number increases gradually, and then decreases abruptly. In the wake with large Froude number, the swaying motion of the natural convection plume occurs because the natural convection effect is rather dominant. As causes of the breakdown, an acceleration of velocity in the wake is more dominant than a shift of the separation points.
