Ragnar Lárusson

PANS of Rudimentary Landing Gear

The paper presents results of simulations of the flow around rudimentary landing gear using an improved version of the Partially-Averaged Navier Stokes model (PANS z- f). The results are validated against time-averaged flow data such as pressure field and oil-film visualizations as well as quantities such as sound pressure level and surface pressure spectra that are relevant for aero acoustic noise generation. The results of PANS z- f are found to be in good agreement with the experimental data and observations. The PANS z- f presented here shows a clear advantage in the prediction of the flow compared with the reference LES simulation on an identical grid.

Linear Stability Analysis Using the Arnoldi Eigenmode Extraction Technique Applied to Separated Nozzle Flow

A linear stability analysis method, employing a linearized flow solver combined with the Arnoldi algorithm for eigenmode approximation, was applied to a separated supersonic flow inside an axially symmetric convergent-divergent nozzle. The eigenmodes were analyzed in terms of frequency, structure and damping. For the case demonstrated, four different types of axial modes and four different types of tangential modes were identified. Results show that the least damped axial modes displayed a relatively low frequency range, 60 Hz to 300 Hz. These modes showed a movement of the shock pattern inside the nozzle. The other mode types exhibited higher frequencies, strong shear layer interactions and acoustic waves. Additionally, the method revealed the presence of a continuous spectrum in the nozzle flow field.

Hybrid RANS-LES Simulation of Separated Nozzle Flow

Asymmetrical separation of a severely overexpanded supersonic nozzle flow can cause un- wanted lateral pressure forces, or side-loads, acting on the nozzle structure. Some empirical models for side-load estimation exist but provide only moderate accuracy. Computational Fluid Dynamics methods have improved in recent decades through advances in turbulence modeling and improvements in computing technology. Several past efforts have been made toward a more accurate side-load predictions through Computational Fluid Dynamics sim- ulations and and the current study aims to add to that knowledge base by exploring the capability of a Delayed Detached-Eddy Simulation employing the k−e turbulence model to simulate an overexpanded nozzle flow and provide a good side-load estimate. The results are promising with side-load levels comparable with experimental data although further development is needed.

Dynamic Mode Decomposition of a Separated Nozzle Flow with Transonic Resonance

Operating convergent–divergent nozzles at low pressure ratios can lead to flow separation. Certain nozzle contours are known to produce a discrete acoustical tone under such conditions that are believed to be generated by a phenomenon known as transonic resonance, which involves a standing pressure wave situated between the separation shock and the nozzle exit plane. This paper reports the findings of a dynamic mode decomposition analysis of a perturbed axisymmetric unsteady Reynolds-averaged Navier–Stokes simulation of a nozzle flow known to exhibit this phenomenon. Two cases of different pressure ratios were studied in depth. The results show that the two cases differ in the shape of the standing pressure wave. The lower pressure ratio produces a standing 3/4 pressure wave, whereas the higher pressure ratio produces a 1/4 wave. In both cases, dynamic mode decomposition modes that match the standing pressure wave shape were found to be the least damped and the most energetic modes of the modes produced by the dynamic mode decomposition algorithm. The frequency of the mode for the lower pressure ratio matched the experimentally observed transonic tone frequency extraordinarily well, whereas the higher pressure ratio case was in fair agreement. The dynamic mode decomposition algorithm captured the transonic frequency for five additional pressure ratios.

Investigation of supersonic jet flow using modal decomposition

Supersonic jet noise has been an important research topic for decades, both for its relevance within the aeronautical industry and for its scientific value. In the present study, the jet flow field produced by a slightly over expanded conical convergent-divergent nozzle was studied using modal decomposition. The nozzle exit Mach number is 1.58 at a nozzle pressure ratio of 4.0. The nozzle has an engine like geometry with a relatively sharp throat, creating an internal shock wave. Two different methods for modal decomposition were applied to the supersonic jet flow, namely Dynamic Mode Decomposition (DMD) and a method based on the Arnoldi algorithm. The DMD algorithm returns the eigenmodes of an approximate linear flow operator, which is constructed from the data set used in the algorithm. In the present study, the DMD algorithm was applied to observational data from a Large Eddy Simulation (LES) and 2D axisymmetric URANS simulation, respectively. The Arnoldi algorithm uses a 2D linearized flow solver to project the linear flow dynamics onto a reduced order Krylov subspace and computes the eigenmodes of that projection. Here, A steady state RANS solution of the jet flow was used as a reference state in the linear solver. The Results of the Arnoldi analysis for a azimuthal wavenumber m = 0 were directly compered with the DMD modes of a URANS simulations. It was found that both methods produce nearly identical modes in this case. The DMD modes of the LES data are comparable with the Arnoldi and URANS DMD modes in terms of frequency, acoustic radiation, and shock-cell movement. They were however, found to be significantly more damped. An additional Arnoldi analysis was performed with azimuthal wavenumber m = 1 and the resulting least damped mode had a frequency close to the experimentally observed screech frequency for the same nozzle geometry and operating condition. An animation of the evolution of the eigenmode reveals a feedback loop mechanisms that might contribute to the formation of screech tones.

Comparison of Eigenmode Extraction Techniques for Separated Nozzle Flows

Results of a previously published Arnoldi eigenmode analysis on a separated flow inside a convergent-divergent nozzle are compared with results obtained using a Dynamic Mode Decomposition (DMD) algorithm. The Arnoldi analysis employs a linearized flow solver and as a result, does not consider nonlinearity and turbulence. The DMD method is a snapshot- based approach, which approximates the Koopman modes of the nonlinear flow. In the present study the DMD algorithm has been applied to a data set from a two-dimensional URANS simulation of the separated nozzle flow. As such, it can take into account the full information of the nonlinear flow, including turbulence. The objective of this study is to investigate the effects of turbulence on the linear analysis. The results show that the Arnoldi and the DMD algorithms do in certain cases produce almost identical modes in terms of frequency, damping and structure. This indicates that even though the Arnoldi method needs an explicit linearization of the flow dynamics and excludes turbulence, it does reveal modes with discrete frequency that could be excited in the nonlinear flow with modeled turbulence.

Dynamic Mode Decomposition Applied to a Detached-Eddy Simulation of Separated Nozzle Flow

The paper presents results from a Dynamic Mode Decomposition (DMD) of data from a Detached Eddy Simulation (DES) of a separated flow inside a truncated ideal nozzle. Two cases of different pressure ratios were studied. Sparsity-Promoting algorithm along with computed optimal mode amplitudes were used to determine importance of individual modes. An ovalization mode (a mode with azimuthal wavenumber m = 2) was found for the lower pressure ratio and was linked to a peak in spectra from probe data. At the higher pressure ratio a helical mode (azimuthal wavenumber m = 1) was found and linked to a peak in spectra from probe data and the nozzle side-load spectrum. The paper shows the potential for using DMD for separated nozzle flows to identify im- portant periodic flow behavior but also underlines the challenges that the method faces, such as noise from resolved turbulence and difficulty identifying modes within the broad low-frequency-range of the side-load spectrum.