Stabilizing effect of surrounding gas flow on a plane liquid sheet

The stability of a plane liquid sheet is studied experimentally and theoretically, with an emphasis on the effect of the surrounding gas. Co-blowing with a gas velocity of the same order of magnitude as the liquid velocity is studied, in order to quantify its effect on the stability of the sheet. Experimental results are obtained for a water sheet in air at Reynolds number Rel = 3000 and Weber number W e = 300, based on the half-thickness of the sheet at the inlet, water mean velocity at the inlet, the surface tension between water and air and water density and viscosity. The sheet is excited with different frequencies at the inlet and the growth of the waves in the streamwise direction is measured. The growth rate curves of the disturbances for all air flow velocities under study are found to be within 20 % of the values obtained from a local spatial stability analysis, where water and air viscosities are taken into account, while previous results from literature assuming inviscid air overpredict the most unstable wavelength with a factor 3 and the growth rate with a factor 2. The effect of the air flow on the stability of the sheet is scrutinized numerically and it is concluded that the predicted disturbance growth scales with (i) the absolute velocity difference between water and air (inviscid effect) and (ii) the square root of the shear from air on the water surface (viscous effect).

Oscillatory sensitivity patterns for global modes in wakes

Globally unstable wakes with co-flow at intermediate Reynolds numbers are studied, to quantify important spatial regions for the development and control of the global instability. One region of high structural sensitivity is found close to the inlet for all wakes, in agreement with previous findings for cylinder wakes. A second, elongated region of high structural sensitivity is seen downstream of the first one for unconfined wakes at Re = 400. When base flow modifications are considered, a spatially oscillating sensitivity pattern is found inside the downstream high structural sensitivity region. This implies that the same change in the base flow can either destabilize or stabilize the flow, depending on the exact position where it is applied. It is shown that the sensitivity pattern remains unchanged for different choices of streamwise boundary conditions and numerical resolution. Actual base flow modifications are applied in selected configurations, and the linear global modes recomputed. It is confirmed that the linear global eigenvalues move according to the predicted sensitivity pattern for small amplitude base flow modifications, for which the theory applies. We also look at the implications of a small control cylinder on the flow. Only the upstream high sensitivity region proves to be robust in terms of control, but one should be careful not to disturb the flow in the downstream high sensitivity region, in order to achieve control. The findings can have direct implications on the numerical resolution requirements for wakes at higher Reynolds numbers. Furthermore, they provide one more possible explanation to why confined wakes have a more narrow frequency spectrum than unconfined wakes.

Surface tension-induced global instability of planar jets and wakes

The effect of surface tension on global stability of co-flow jets and wakes at a moderate Reynolds number is studied. The linear temporal two-dimensional global modes are computed without approximations. All but one of the flow cases under study are globally stable without surface tension. It is found that surface tension can cause the flow to be globally unstable if the inlet shear (or equivalently, the inlet velocity ratio) is strong enough. For even stronger surface tension, the flow is re-stabilized. As long as there is no change of the most unstable mode, increasing surface tension decreases the oscillation frequency. Short waves appear in the high-shear region close to the nozzle, and their wavelength increases with increasing surface tension. The critical shear (the weakest inlet shear at which a global instability is found) gives rise to antisymmetric disturbances for the wakes and symmetric disturbances for the jets. However, at stronger shear, the opposite symmetry can be the most unstable one, in particular for wakes at high surface tension. The results show strong effects of surface tension that should be possible to reproduce experimentally as well as numerically.