Nathan A. Wukie

A implicit, discontinuous Galerkin Chimera solver using automatic differentiation

The development of a fully-implicit, discontinuous Galerkin solver based on Chimera, overset grids is presented. Newton’s method is used as a nonlinear solver for governing equation sets, enabled by an intrinsic automatic differentiation capability that computes the linearization of the spatial scheme. A GMRES matrix-solver is used to solve the linear system along with a block-ILU0 preconditioner. Results include solutions of the Euler equations for subsonic flow over a smooth bump as well as over a circular cylinder. The convergence rates for spatial orders of accuracy for the solver match the analytical rates. Up to 4th-order accuracy is shown for 3rd-order polynomials (P3). Additionally, quadratic convergence is demonstrated for the nonlinear solver; verifying that the automatic differentiation capability was implemented successfully. Solutions converged in 7 or fewer iterations. Results are presented utilizing the Chimera overset grid capability, demonstrating that quadratic convergence is maintained with the Chimera grid interfaces.

Modeling and Simulation of Bleed Holes in the Presence of Shock Wave/Boundary Layer Interaction

Bleed simulation and modeling are studied for shock wave boundary layer interactions using computational simulations obtained with the OVERFLOW Navier-Stokes equation solver for a mixed compression inlet geometry studied experimentally by the U.S. Air Force Research Laboratory and a single hole unit problem. The AFRL test rig is simulated with bleed using the Slater model using expected test bleed rates. A test of a modified bleed configuration was also conducted with the intent of affecting flow quality by controlling corner separation. The single hole unit problem was simulated with variations in plenum exit pressure, upstream Reynolds number and plenum depth and compared with a hole-only analysis developed previously by the authors. A full simulation of the AFRL rig with a row of discrete cooling holes was also conducted to demonstrate an application of the technique. Results show that the flow quality at the aerodynamic interface plane can be affected positively by side wall bleed. They also show that Reynolds number has only a minor effect on bleed mass flow but does alter the main flow/bleed hole interaction. Both plenum depth and exit pressure affect both bleed mass flow and main flow/bleed hole interaction much more significantly.

Implementation of a Quasi-Three-Dimensional Nonreflecting Blade Row Interface for Steady and Unsteady Analysis of Axial Turbomachines

Higher order nonreflecting blade row interfaces are today widely used for performing both steady and unsteady simulations of the flow within axial turbomachines. In this paper, a quasi-three-dimensional nonreflecting interface based on the exact, two-dimensional nonreflecting boundary condition for a single frequency and azimuthal wave number developed by Giles is presented. The formulation has been implemented to work for both steady simulations as well as unsteady simulations employing the nonlinear Harmonic Balance method. The theory behind the construction of the nonreflecting interface is presented and details on the numerical implementation is also provided. The implementation is verified for two dimensional wave propagation along a straight cascade. It is shown that the interface correctly absorbs incoming waves, but also found that the chosen implementation strategy may be ill-posed. A simple solution to stabilize the implementation is therefore implemented, but future work should seek a more generic solution to this problem.

Software engineering for efficient development of flexible numerical software

Computational physics and numerical modeling require substantial levels of software development. Recently, there have been community efforts to incorporate good software engineering practices within the development of scientific computing applications. This paper further advocates for the use of good software engineering practices in science and engineering and presents some software engineering solutions, challenges, and lessons learned from recent development efforts on a framework for computational fluid dynamics.

Simulations and Models for Aspiration in a Supersonic Flow Using OVERFLOW

A SIGNIFICANT problem with supersonic inlets occurs when shock waves interact with the boundary layer. Separated flow can grow to encompass a significant portion of the inlet area in these regions. The inlet can unstart if this condition is not alleviated. The traditional approach to counteract this effect is to aspirate sections of the inlet using bleed holes with the goal of removing a portion of the flow, diminishing the size of the separated region, and reducing blockage. This bleed is expensive in terms of increased mechanical complexity, cost, weight, and drag but is still necessary to control bad flow behavior. For this reason, modeling/simulation of bleed is still a necessity for accurate numerical prediction of supersonic inlets [1,2]. Prior research on bleed includes both experimental [3–5] and computational studies. Computational studies generally fall under two categories. The first group resolves all regions of the bleed flow [6–10]. The second group of computational studies attempts tomodel regions of bleed using boundary conditions [11–18]. Because of the large number of discrete holes used in inlet bleed systems, modeling the “global” bleed effect through a boundary condition is often a muchmore practical method of accounting for bleedmass flow in full inlet simulations. A bleed boundary condition detailed by Slater [17] extended a previously developed boundary condition from Mayer and Paynter [11] by introducing a scaling to experimental sonic flow coefficient data that allows the local flow variables to be evaluated at thewall and eliminating the need to search for the edge of the boundary layer, as was the case in the bounary condition from Mayer and Paynter. Manavasi et al. [12] and Hamed et al. [16] used this boundary condition to study single holes and a small number of holes in series. The major focus of their work was the behavior of the solution downstream of the bleed hole and the interaction between bleed holes. They noted that Slater’s boundary condition provides a better match of downstream conditions if applied only to the physical region of the bleed hole itself, rather than in a distributed fashion over the bleed plate. In this work, mass aspirated from a supersonic flow through bleed holes is both simulated and modeled to better understand the flow physics and demonstrate effective and efficientmethods formodeling and simulating bleed hole systems when using the Chimera overset grid methodology.

Evaluation of a time-linearized Navier-Stokes method for booster tone noise analyses

A computational study of booster tone noise was performed using a linearized-unsteady Navier-Stokes solver in a proprietary computational fluid dynamics code. A model-scale fan rig geometry that was studied experimentally was chosen for this investigation to evaluate the ability of the linearized-unsteady methodology to predict booster tone noise. The predicted in-duct sound power levels were compared to sound power levels calculated from sideline traversing microphone data. The comparison indicates that the simulation is able to capture trends in booster tone noise along Approach, Cutback, and Sideline operating points and also the relative significance of the 1 and 2 booster harmonics.