ON THE INFLUENCE OF THE MOMENTUM THICKNESS ON STREAMWISE JET INSTABILITIES

Different techniques have been employed through the years to predict hydrodynamic instabilities on high speed liquid jets. In this work, a local linear stability analysis (LSA) has been chosen to estimate streamwise wavelengths on the jet surface near the jet exit.  Data for 0.24 to 0.5 diameters downstream in a high speed water jet issuing into air, given by Reynolds number based momentum thickness between 240 and 600, for validation of the method.  

The hypothesis is: near the exit of the jet nozzle, for high speed liquid jets, the local velocity profile evolves based on the momentum thickness and, because of large inertia effects, the flow may be considered as inviscid for instability purposes. Therefore, the approach in this work is based on the Rayleigh equation and with the momentum thickness scaling, both non-dimensional and dimensional values of the most unstable wavelengths are obtained.

The key aspect of the  approach is the relevance of the momentum thickness as the scaling factor for calculation purposes on dimensional values of wavelengths.

Also, a hyperbolic tangent velocity profile is assumed for the Linear Stability Analysis based on the Rayleigh equation. Numerical restrictions and comparisons, using the Riccati transformation, are specified and described in detail to generalize this approach.

Results show that analytical estimates of the most unstable streamwise wavelengths are close to the experimental measurements published by Portillo et al. in 2011.  The agreement using this new approach is often within the experimental uncertainty.