Stability of annular liquid sheets
Abstract
Linear and nonlinear stability analyses are used to study the growth of disturbances on an annular liquid sheet under various conditions in this thesis. Stability of an inviscid swirling annular liquid sheet, in the presence of gas phases inside and outside the sheet and moving with unequal gas velocities, is investigated using linear stability analysis. It is found that for a given flow situation, not all non-axisymmetric modes are evanescent as previous researchers found. In addition, an increase in axial Weber number causes an increase, both in the number of circumferential modes that are unstable and their corresponding growth rates. Also, an increase in Weber number increases the axial wavenumber at which maximum disturbance growth takes place. However, in the absence of swirl, the circumferential mode with the maximum growth rate, remains at n = 0. Swirl in the liquid phase causes the mode with the maximum growth rate to occur at circumferential mode, n $>$ 0. At low swirl Weber number, it stabilizes the annular sheet by causing the most destructive axial wavenumber and the corresponding growth rate to decrease. At high swirl Weber number, it causes the circumferential instability modes to dominate and under critical conditions where the action of the swirl and axial destabilizing forces are equal, the annular sheet is unstable to three-dimensional waves. The nonlinear behavior of the annular liquid sheet is studied using approximate one-dimensional equations derived by a thin sheet approximation. The model is validated by comparing the predictions against the exact linear analysis. Model predictions demonstrate that the disturbance amplitude is an important factor in the stability behavior. An increase in the sheet thickness causes the growth rate to increase. It is also observed that if the annular liquid sheet is nonstationary, disturbances that are linearly stable could become unstable and cause the sheet break up, if the amplitude of disturbances is not infinitesimal.
Degree
Ph.D.
Advisors
Bajaj, Purdue University.
Subject Area
Mechanical engineering|Aerospace materials|Fluid dynamics|Gases
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.