A hybrid compressible-incompressible numerical method for moving drops
Improving the modeling of the momentum transfer between drops and gas in sprays is of importance in practical combustion systems. In this work, a numerical method is developed to study transient internal and external flow fields of deforming drops moving in a gas. The liquid phase is modeled as an incompressible fluid while the gas phase is modeled as a compressible fluid. A second-order total-variation-diminishing (TVD) scheme for the convective terms, and a second-order central difference approximation for the viscous terms are employed. The interface separating the two phases is tracked in time by employing an unstructured grid with triangular elements for the two phases, which conforms to the deforming interface at all instants of time. A finite-volume discretization of the strong conservative form of the governing equations is solved for both phases. An implicit iterative procedure is employed to simultaneously solve the gas and liquid phase equations together with the interface boundary conditions. ^ The accuracy of the gas phase solution is assessed through computations of several test problems. The computed results are in adequate agreement with analytical solutions, and with experimental and numerical results from prior work. Prior to computing drops, the transient drag of a decelerating solid sphere is computed and results compared with published results. The agreement is within 4.6%. Computed frequencies of oscillating drops are compared with analytical values, and found to agree within 1.6%. ^ Application of the numerical method to compute moving drops shows that increasing the Weber number results in greater drop deformation and ultimately shear breakup. Oblate deformation leads to increased drag and prolate to reduced drag relative to a solid sphere. Increasing Ohnesorge number results in slower and lesser deformation, and reduced drag. ^
Major Professor: John Abraham, Purdue University.
Engineering, Mechanical|Physics, Fluid and Plasma