Onset of inertia- and buoyancy-driven vortex flow

The understanding of the critical condition for the appearance of the inertia- and buoyancy-driven vortex rolls in the chamber is of fundamental interest in the fluid flow study. Here we investigate the onset of the inertia-driven rolls by visualizating the flow in the processing chamber at various jet Reynolds numbers for an unheated disk (Ra=0). Note that the lowest jet flow rate which can be accurately resolved in the

present experimental apparatus is 0.1 slpm. Even at this small Q_j the primary inertia-driven roll is already seen in the chamber for all H with the jet issued from the small injection pipe (D_j=10.0 mm). For the large injection pipe (D_j=22.1 mm) the critical Rej for the onset of the primary inertia-driven roll is somewhat higher and thus can be located here. The present data are summarized in Table 3.1 for the onset of the primary and secondary inertia-driven rolls at various jet-to-disk separation distances.

The results suggest that as the jet Reynolds number exceeds certain low level the primary inertia-driven roll appears. The secondary inertia-driven roll is initiated at somewhat higher jet Reynolds numbers (Table 3.1). Some inertia-driven rolls at slightly supercritical Rej are shown in Fig. 3.3 for the jet-to-disk separation distance fixed at 20.0 mm. The results manifest that the primary inertia-driven roll is much smaller and weaker for the large injection pipe (Figs. 3.3 (c) & (d)). More specifically, for D_j=10.0 and 22.1 mm the primary inertia-driven roll respectively appears at Rej=13.6 and 15. Note that at the low Rej near the critical level the roll is relatively small and appears near the exit of the injection pipe (Figs. 3.3 (a) & (d)). It should be mentioned that for an unheated disk an outer roll also appears in the duct (Figs. 3.3 (a)

& (b)). This roll is formed by the deflection of the wall-jet flow along the disk by the chamber side. At a higher Rej this outer roll is smaller and weaker (Fig. 3.3(b)) due to the radial thickening of the boundary layer flow along the disk and the deflection of the flow at the chamber side is milder. It has nothing to do with buoyancy effect since Ra=0. Besides, the onset conditions of the tertiary inertia-driven roll are also given in the table. It is of interest to note that at a smaller jet-to-disk separation distance the primary inertia-driven roll is induced at a slightly higher jet Reynolds number, as evident from comparing the results in Figs. 3.4 and 3.5.

The results summarized in Table 3.1 indicate that at given D_j the critical jet Reynolds numbers for the onset of the primary, secondary and tertiary inertia-driven

rolls increase when the jet-to-disk separation distance is reduced from 20.0 mm to 10.0 mm. However, it is of interest to note that the critical Rej does not experience any change when H is reduced from 30.0 to 20.0 mm for the primary and tertiary rolls.

The increase of the critical Rej at decreasing H is conjectured to mainly result from the more significant retarding of the jet by the disk at a smaller H, which in turn yields a higher viscous damping effect on the impinging jet and a higher Rej is needed to induce the flow recirculations.

As we continue to increase the jet Reynolds number slightly beyond the critical Re_j for the onset of the tertiary roll, the flow in the processing chamber does not reach any steady state at long time. Instead, the flow becomes time dependent and experiences a transition from steady to unsteady states. Obviously, this transition is driven by the jet inertia since ΔT=0 and no buoyancy-driven rolls appear. The present data for the inertia driven steady-to-unsteady transition are summarized in Table 3.2 for Dj=10.0 mm. The results indicate that the critical Rej for this flow transition increases when the jet-to-disk separation distance is shortened, similar to those for the onset of the inertia-driven rolls. It is of interest to note that the critical Rej for this steady-unsteady transition increases with Ra at given H. The above results suggest that the time-dependent flow induced by the jet inertia can be stabilized by increasing the Rayleigh number Ra at H≦20.0 mm. However, for H=30.0 mm an opposite trend is noted. This is due to the fact that at the longest H (=30.0 mm) tested here the radial extent of the buoyancy-driven roll is so large and it directly contacts with the primary inertia-driven roll. As Rej gradually increases, both the primary inertia-driven and buoyancy-driven rolls squeeze each other resulting in time-dependent flow.

When the disk is heated, our flow visualization further shows that for given Dj, ΔT and H the buoyancy-driven roll begins to appear in the region near the heated disk edge as Rej is below certain critical level for a given Ra. This critical condition is

considered to be reached as long as we can barely see the buoyancy-driven roll in the video films recording the images of the vortex rolls. This is exemplified in Fig. 3.6.

Moreover, Table 3.3 summarizes the critical condition for the onset of the buoyancy-driven roll based on the present data. The data indicate that for given Dj and H the critical Re_j for the onset of the buoyancy driven roll is higher for a higher Gr. It should be mentioned that how the onset condition of the buoyancy roll is affected by the jet-to-disk separation distance is reflected in the Grashof number since Gr is proportional to H³. Note that the critical buoyancy-to-inertia ratio Gr/Rej2

for the onset of the buoyancy roll is nearly constant for a given D_j, irrespective of the jet-to-disk separation distance. For Dj=10.0 and 22.1 mm the critical ratio Gr/Rej2

is nearly equal to 0.0045 and 0.021, respectively. It is also noted that the onset of the buoyancy-driven roll occurs when the wall-jet flow in the radial direction is reversed by the upward buoyancy associated with the heated disk and hence the onset should be mainly determined by the local flow condition characterized by the local Reynolds number of the wall-jet flow Re_w and the Grashof number Gr. Besides, the onset is most likely to take place near the outer edge of the disk. Therefore, the onset condition is expected to depend primarily on the local buoyancy-to-inertia ratio Gr/Rew2

. The data given in Table 3.3 do show that the buoyancy roll begins to appear when the local buoyancy-to-inertia ratio at the edge of the disk Gr/Re_we² is around 33.0 with the deviations within the experimental uncertainty for all Dj and H considered.