Numerical Simulations of Lobed Mixer Flow Fields

The applicability of a three-dimensional, steady, compressible, unstructured-mesh, viscous, Navier-Stokes solver and a two-dimensional, unsteady, slender-body approximation was studied for the investigation of lobed mixer flow fields. The viscous flow solver was evaluated for its ability to calculate the shed streamwise circulation, its subsequent downstream evolution and the thrust. The effects of the type of grid generation, boundary layer grid density, turbulence model and smoothing scheme were examined. Structured-based meshes for lobed mixer geometries had severely skewed elements that resulted in vorticity that was unsupported by physical laws. This was overcome by using fully unstructured grids. Approximately 6 boundary layer elements were required to capture the boundary layer over the lobes for attached flows: if separation occurred, more elements were necessary. Replacing the standard k-e turbulence model with the turbulent diffusivity of a shear-layer had no impact on the parameters of interest. In general, the viscous Navier-Stokes solver was best suited for examining the flow over the lobes. Downstream of the trailing edge, the circulation could not be evaluated with confidence. However, from a sensitivity analysis, it was found that the scalar mixedness could still be evaluated to within 20%. Having established the validity of the Navier-Stokes solver, it was used to study the viscous effects in lobed mixers. Lobes with penetration angles from 22" to 45* were examined. As the lobe penetration angle was increased, the trailing edge circulation deviated from a simple one-dimensional model because of increased boundary layer blockage and separation. Extending this model using an effective penetration angle and height gave predictions of the shed streamwise circulation that corresponded to the computed ones to within 5%. There was no benefit, in terms of the trailing streamwise circulation, of increasing the penetration angle above 30* because of increased boundary layer blockage and separation. The losses associated with the lobed mixer increased with the penetration angle and were dominated by mixing losses. The scalar mixedness, interface length and streamwise vorticity were compared between the three-dimensional solver and slender-body approximation to determine the latter's range of applicability. It was found that the slender-body approximation was valid outside the range given by dimensional analysis of the governing Navier-Stokes equations. Slender-body theory held for flows with non-dimensional shed streamwise circulations of up to =1 and AU / U 5 0.3. The approximation was less valid for a stream-to-stream density ratio of 0.5. Thesis Supervisor: Ian A. Waitz Professor of Aeronautics and Astronautics