Thermal Effect on the Instability of Annular Liquid Jet

The linear instability of an annular liquid jet with a radial temperature gradient in an inviscid gas steam is investigated theoretically. A physical model of an annular liquid jet with a radial temperature gradient is established, dimensionless governing equations and boundary conditions are given, and numerical solutions are obtained using the spectral collocation method. The correctness of the results is verified to a certain extent. The liquid surface tension coefficient is assumed to be a linear function of temperature. The effects of various dimensionless parameters (including the Marangoni number/Prandtl number, Reynolds number, temperature gradient, Weber number, gas-to-liquid density ratio and velocity ratio) on the instability of the annular liquid jet are discussed. A decreasing Weber number destabilizes the annular liquid jet when the Weber number is lower than a critical value. It is found that the effects of the Marangoni effect are related to the Weber number. The Marangoni effect enhances instability when the Weber number is small, while the Marangoni effect weakens instability when the Weber number is large. In addition, because the thermal effect is considered, a decreasing Reynolds number enhances the instability when the Weber number is lower than a critical value, which is similar to the results of a viscous liquid sheet with a temperature difference between two planar surfaces. Furthermore, the effects of other dimensionless parameters are also investigated.

Shape of an Annular Liquid Jet

Analytical and experimental studies have been done to determine the shape of a vertical, axisymmetric, annular liquid jet. From a balance of the surface, pressure, gravity, and inertia forces, a nonlinear, second-order, ordinary differential equation is obtained for the shape of the annular jet. This equation is solved numerically by the Runge-Kutta-Nystro¨m method. An annular jet either converges (closes), diverges, or maintains (theoretically) its original radius depending upon the magnitude of the difference between the inside and outside pressure. This corresponds to, in terms of a dimensionless pressure p, whether p is less than, greater than, or equal to 2. An experiment has been performed to verify the analytical solution. The jet velocity, inside pressure and other parameters have been varied to obtain different shapes of the jet, both closing and diverging. Good agreement with the analytical prediction is found.