Session L32: Immersed Boundary Methods

A sharp-interface method for computing the shock-induced evaporation rate of droplet

Shock-induced evaporation of droplets governs the rate of combustion and subsequent deposition of energy in scramjet engines, rocket motors, heterogenous explosions etc. Therefore, it is important to accurately predict the evaporation rate of the droplets during interaction with shock waves. In this work, a sharp-interface method is developed to calculate the evaporation rate of the droplets. The level-set method is used to track the liquid-gas interface. A robust ghost fluid method is developed to couple the flow fields of the liquid and the gaseous phase at the interface. A modified interfacial Riemann problem is solved at every point on the interface to account for the jump in the pressure and the normal velocity fields due to surface tension and evaporation. The tangential components of the velocity fields for the ghost fluid are obtained such that the jump in the stresses at the interface due to the Marangoni effect is respected. The current sharp-interface method is validated against analytical solutions of 1-D Riemann problems and experimental studies of shock interaction with water-column. Subsequently, simulations of shock-droplet interactions are performed to estimate the shock-induced evaporation rate of the droplets.   

Flapping dynamics of an inverted flag with different shapes in a uniform flow

The flapping motion of an inverted flag with different shapes in a uniform flow was simulated using an immersed boundary method. The shapes of the flag were distinguished by the shape ratio (S=W_T / W_L) defined as the ratio of the trailing edge width (W_T) to the leading edge width (W_L). To investigate the effects of the shape ratio on the dynamics of the inverted flag, the peak-to-peak amplitude (A/L) and the Strouhal number (St) were analyzed as a function of the bending rigidity (0.1 ≤ γ ≤ 0.3) and the shape ratio (0.5 ≤ S ≤ 2). The vortical structures behind the inverted flag were visualized by the Q-criterion to examine the vortex dynamics. The hydrodynamic forces exerted on the flag were explored to reveal the correlation between the kinematics of the inverted flag and the vortex formation during a flapping period. Finally, we estimated the strain energy (E_s) stored on the inverted flag and the conversion ratio (R) of the flow kinetic energy to the strain energy.   

Evaluation of temperature wall functions for large-eddy simulation over curvilinear geometries

Recently, a novel transport scheme combining a cut-cell finite volume method for scalars and a direct-forcing immersed boundary method for momentum has been implemented in the open-source, low-Mach LES solver called the Fire Dynamics Simulator (FDS).  This talk discusses the implementation and testing of heat transfer wall functions over curvilinear and non-grid-aligned geometries.  Nusselt number correlations are compared for forced and natural convection.   

An Immersed Boundary Projection Method for Dynamics of Rigid Bodies Interacting with Fluid Flows

The fast immersed boundary projection method using a nullspace approach and multi-domain far-field boundary conditions developed by Colonius and Taira (Comput. Methods Appl. Engrg., 2008) is further extended to simulate dynamics of rigid bodies interacting with fluid flows. Dynamics of rigid bodies is characterized by the velocity of the center of mass and the angular velocity about the center of mass, which are governed by the translational and rotational equations of motion involving boundary forces. By introducing the summation and distribution operators, equations of motion are coupled with the incompressible Navier-Stokes equations through the no-slip constraint and boundary forces. Boundary forces are regarded as Lagrange multipliers that enable the no-slip constraint to be implicitly determined to arbitrary precision without associated time-step restrictions. Through projections, the current method removes not only slip component of the velocity field but also components of rigid-body dynamics that do not satisfy equations of motion. Results from simulating an impulsively-rotated circular shell in a quiescent fluid are in good agreement with numerical solutions of the analytical model.