Hydrodynamic stability of shear flows : Jet in crossflow, particle laden planar and swirling jets
Jet in crossflow is a flow scenario that involves momentum exchange of a round jet injected into a crossflow. This flow configuration has industrial importance because of its application in gas turbine combustors which requires mixing of hot combustion products with cold air bled from the compressor to achieve the required temperature profile at the exit of the combustion chamber. Baseflow model proposed by Kelly and Alves (2008) is considered to study the near field of the jet with a thin shear layer and a weak crossflow. Linear stability calculations for the direct injection jet (leading order free jet) shows that the axi-symmetric mode m=0 is more unstable than m=1. The effect of addition of a weak crossflow is studied. The crossflow to jet velocity ratio is small, the eigenspectra for weak crossflow cases are different in that, at small wavenumbers the zero crossflow eigenmodes has a sightly higher growth rate compared to the weak crossflow cases. We find that addition of weak crossflow results in the most amplified mode that is predominantly axi-symmetric (m=0) while higher helical modes both even and odd are present but with smaller magnitude. As the velocity ratio is increased, the contribution of axi-symmetric modes to the most unstable mode decreases and helical disturbances (both lower and higher helical modes) shows contribution which possibly explains why the smoke visualizations of Fric and Roshko showed the near field of the jet (in presence of crossflow) are dominated by distorted vortex rings. Spatiotemporal analysis of a constant density zero crossflow jet at Re=800 is found to be convectively unstable. Particle laden flows are commonly seen in many industrial applications such as fluidized beds in process industry, air laden with abrasive particles in abrasive machining and particle laden plumes in chemical industries. In the present work, we perform local analysis of a particle laden planar jet in the dilute suspension regime. Unladen parallel planar jets have been extensive studied using normal modes and is shown to have two unstable modes namely sinuous and varicose modes. Sinuous modes are found to be more unstable compared to the varicose modes. In the present study, we investigate the effect of particles on the stability of planar jets. Addition of particles at low Stokes numbers (St) (fine particles) results in higher growth rates than that of the unladen jet. In the intermediate Stokes number regime, addition of particles have a stabilizing effect on both the sinuous and the varicose modes. Interestingly for St~10, the unstable varicose mode is completely damped. Increasing the Stokes number by increasing the particle size, both sinuous and varicose modes show increasing growth rates, while increasing density ratio has a stabilizing effect on the flow. For non uniform particle loading, additional modes apart from the sinuous and varicose modes are observed. These modes suggests occurrence of compositional instability with an increased particle accumulation in the shear layer that is an order of magnitude higher compared to that of the sinuous and varicose modes. Linear stability of annular swirling jet laden with particles in a swirl-stabilized combustor is considered. Eigenspectra of the particle laden jet for low, intermediate and large Stokes numbers with uniform particle concentration shows three unstable modes (centre, sinuous and varicose modes) and a new set of neutrally stable modes which are absent in the unladen jet eigenspectrum. As Stokes number is increased, the growth rates of the centre and shear layer modes reduces compared to that of the unladen swirling jet. Magnitude of the velocity eigenmodes peaks in the vortex core and reduces radially outward. Variation in the particle concentration occurs mostly in the vortex core and almost none in the shear layer indicating that particles migrate from the centreline to the vortex core. But as the swirl number is increased further, it is seen that although the fluid velocities peak in the vortex core, the particle velocities peak in the shear layer. The increase in swirl number results in the particle concentration magnitude peaking in the shear layer and not in the vortex core. The effect of increase in backflow parameter is to increase the growth rate of the centre mode. Sinuous and varicose modes also have reduced growth rates at intermediate Stokes numbers. As the backflow parameter is increased, the growth rate of sinuous and varicose modes increases. The increase in baseflow azimuthal vorticity leads to increase in the net generation rate of vorticity fluctuations from rearrangement of base flow vorticity by velocity disturbances, unsteady vortex stretching due to base flow velocity gradients. We look at the effect of non uniformity of the particle concentration in the base flow. It is found that when the peak of the concentration profile lies within the vortex core, the centre modes are stable. Sinuous and varicose modes remain unstable for regardless of where the peak is located, although the growth rates are smaller than the unladen flow. Ring modes remain stable as in the case of unladen flow and uniform concentration. Recent studies on the unladen flow by Manoharan and weakly non linear calculations by Manoharan et al on a turbulent single phase annular swirling jet indicate that m=1 mode causes precessing vortex core (PVC) oscillations. The radial, azimuthal velocities and particle concentration fields for the present calculation at St=1, suggests that the effect of addition of particles is to reduce the growth rate of the fluctuations, thus reducing the PVC oscillations.