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Design optimization of adaptive systems requires a robust analysis method that can accommodate various changes in design and boundary conditions. In this work, physics-informed neural networks (PINNs) are used to approximate solutions to differential equations across a range of problem parameter values. This mesh-free method simply requires residual evaluation at sampling points within the analysis domain and along boundaries, and the training process does not require any reference problem to be solved through conventional solution methods. The trained model can be used to predict the solution field, conduct parameter space analysis and design optimization. Using automatic differentiation, the design objective and their derivatives can be computed as a post process for a gradient-based design optimization. The method is demonstrated in a 1D heat transfer problem governed by the steady-state heat equation. Use of the PINN model for design optimization is illustrated in a problem of finding a material transition location to minimize temperature at a specified location. The PINN model that does not include problem parameters as input can be trained to within 0.05% error. PINN models that involve problem parameters as inputs are more difficult to train, especially when the input-to-output relationship is complex.

A machine learning algorithm that performs multifidelity domain decomposition is introduced. While the design of complex systems can be facilitated by numerical simulations, the determination of appropriate physics couplings and levels of model fidelity can be challenging. The proposed method automatically divides the computational domain into subregions and assigns required fidelity level, using a small number of high fidelity simulations to generate training data and low fidelity solutions as input data. Unsupervised and supervised machine learning algorithms are used to correlate features from low fidelity solutions to fidelity assignment. The effectiveness of the method is demonstrated in a problem of viscous fluid flow around a cylinder at Re ≈ 20. Ling et al. built physics-informed invariance and symmetry properties into machine learning models and demonstrated improved model generalizability. Along these lines, we avoid using problem dependent features such as coordinates of sample points, object geometry or flow conditions as explicit inputs to the machine learning model. Use of pointwise flow features generates large data sets from only one or two high fidelity simulations, and the fidelity predictor model achieved 99.5% accuracy at training points. The trained model was shown to be capable of predicting a fidelity map for a problem with an altered cylinder radius. A significant improvement in the prediction performance was seen when inputs are expanded to include multiscale features that incorporate neighborhood information.

Wave propagation in ducts is a rich topic that is important to consider in the design of turbomachinery components for aero-engine applications. In order to describe how the waves propagate inside a duct, an eigenmode decomposition of the equations modeling the fluid problem can be performed. The resulting eigenmodes may be used to construct nonreflecting boundary conditions, to investigate flow physics, or for post-processing numerical simulations to track the evolution of modal content through a computational domain. In the present work, an open-source Python tool, called noisyduck, was developed to compute eigenmode decompositions of the linearized Euler equations that model linear wave propagation in a duct with constant cross-section. The numerical method is verified against analytical solutions and reported results from the literature for uniform axial flow and swirling flow in an annulus. The noisyduck tool is made available as a public resource with the intent of reducing duplicated research efforts, and clarifying equation sets and formulations with respect to the literature in the area of eigenmode decompositions for problems in duct acoustics.

Applying a nonreflecting formulation of a boundary condition or blade row interface is sometimes of paramount importance for obtaining an accurate prediction of turbomachinery blade flutter or tonal noise, just to name a few examples. Although the theoretical foundations for these type of boundary conditions have existed for several decades, nonreflecting boundary conditions still remain an area of active research. Today, much focus appears to be put towards obtaining more generic, higher-order and numerically stable formulations. In this work, a quasi-three-dimensional nonreflecting formulation based on the exact, nonreflecting boundary condition for a single frequency and azimuthal wave number developed by Giles is presented. The proposed formulation is applicable without modifications to both steady and unsteady simulations. An implementation strategy which is consistent for both a boundary condition and blade row interface is also presented. This implementation strategy does also partly address the stability problems often encountered when the type of formulation considered in the presented work is used together with a pseudo-time integration approach for converging the flow residual. Results from a set of two-dimensional validation cases are also presented to verify the formulation.

The Harmonic Balance method is well suited for analyzing unsteadiness in turbomachinery flows comprised of a few dominant frequencies. A harmonic condition is imposed on the temporal derivatives through a Fourier transform operation. The solution is then reinterpreted as a time-domain problem, where several instances of time (lying within the largest period) are solved for simultaneously with the enforcement of the time-harmonic condition providing coupling between time instances. A discontinuous Galerkin discretization is used together with overset grids to provide higher-order spatial accuracy and flexibility in representing complex geometry. In this work, the discontinuous Galerkin infrastructure is extended for unsteady problems with a Harmonic Balance method and a Diagonally Implicit Runge-Kutta time-integrator. Verification results are presented for both time integration approaches in addition to results for a turbine blade with unsteadiness driven by a prescribed unsteady inlet boundary condition. Comparisons of results from the Harmonic Balance and Diagonally Implicit Runge-Kutta approaches are very close, with some small discrepancies that require further investigation. Significantly, rapid convergence from the Newton solver is obtained for the Harmonic Balance approach applied to the Euler equations for the turbine blade problem. Solutions converged by 8–10 orders of magnitude are obtained in between 5 and 16 Newton steps.

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.

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.

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.

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.

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.

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.