Effect of Buoyancy on the Instability of Light Jets and Plumes

Abstract

The linear global stability of light jets and plumes is analyzed to examine the role of buoyancy on the dynamics of the flow by varying the Froude number under low Mach number approximation. In this study, buoyancy is generated due to the heating of fluid injected at the inlet (thermal plume). The results also closely describe the dynamics of an isothermal light jet at the corresponding density ratio, $\rho _{\infty }/\rho _{j}$, where $\rho _{j}$ and $\rho _{\infty }$ are the jet and ambient density respectively. The analysis is limited to a thermal plume which has a density ratio $\rho _{\infty }/\rho _{j} = 7$ corresponding to the value for pure helium injected into air. At large Froude number (or small Richardson number), the dynamics of the flow are shown to be determined by the baroclinic torque resulting in the Kelvin Helmholtz instability as in the case of hot jets. However, as the Froude number is lowered, the dominant growth rate and Strouhal number increase monotonically and the dynamics become strongly buoyancy dependent. The variation of Strouhal number with Richardson number (or Froude number) resulting from the global instability is found to match closely with the experimental and DNS investigations on helium jets injected into air.