scholarly journals On The Mesh Divergence Of Inviscid Adjoint Solutions

2021 ◽  
Author(s):  
C. Lozano ◽  
J. Ponsin
Keyword(s):  
Adjoint Solutions

scholarly journals Adjoint-based parametric sensitivity analysis for swirling M-flames

2018 ◽  
Vol 859 ◽  
pp. 516-542 ◽  
Author(s):  
Calum S. Skene ◽  
Peter J. Schmid
Keyword(s):  
Sensitivity Analysis ◽  
Frequency Response ◽  
Stokes Equations ◽  
Numerical Study ◽  
Computational Cost ◽  
Base Flow ◽  
Sensitivity Analyses ◽  
Perturbation Expansions ◽  
Mean Flow ◽  
Adjoint Solutions

A linear numerical study is conducted to quantify the effect of swirl on the response behaviour of premixed lean flames to general harmonic excitation in the inlet, upstream of combustion. This study considers axisymmetric M-flames and is based on the linearised compressible Navier–Stokes equations augmented by a simple one-step irreversible chemical reaction. Optimal frequency response gains for both axisymmetric and non-axisymmetric perturbations are computed via a direct–adjoint methodology and singular value decompositions. The high-dimensional parameter space, containing perturbation and base-flow parameters, is explored by taking advantage of generic sensitivity information gained from the adjoint solutions. This information is then tailored to specific parametric sensitivities by first-order perturbation expansions of the singular triplets about the respective parameters. Valuable flow information, at a negligible computational cost, is gained by simple weighted scalar products between direct and adjoint solutions. We find that for non-swirling flows, a mode with azimuthal wavenumber $m=2$ is the most efficiently driven structure. The structural mechanism underlying the optimal gains is shown to be the Orr mechanism for $m=0$ and a blend of Orr and other mechanisms, such as lift-up, for other azimuthal wavenumbers. Further to this, velocity and pressure perturbations are shown to make up the optimal input and output showing that the thermoacoustic mechanism is crucial in large energy amplifications. For $m=0$ these velocity perturbations are mainly longitudinal, but for higher wavenumbers azimuthal velocity fluctuations become prominent, especially in the non-swirling case. Sensitivity analyses are carried out with respect to the Mach number, Reynolds number and swirl number, and the accuracy of parametric gradients of the frequency response curve is assessed. The sensitivity analysis reveals that increases in Reynolds and Mach numbers yield higher gains, through a decrease in temperature diffusion. A rise in mean-flow swirl is shown to diminish the gain, with increased damping for higher azimuthal wavenumbers. This leads to a reordering of the most effectively amplified mode, with the axisymmetric ($m=0$) mode becoming the dominant structure at moderate swirl numbers.

Interpretation of Adjoint Solutions for Turbomachinery Flows

AIAA Journal ◽  
2013 ◽  
Vol 51 (7) ◽  
pp. 1733-1744 ◽  
Author(s):  
Andre C. Marta ◽  
Sriram Shankaran ◽  
Qiqi Wang ◽  
Prem Venugopal
Keyword(s):  
Adjoint Solutions

Dispersion in Nonlinear Plates: Amplitude Dependent Lamb Waves

2016 ◽  
Author(s):  
Pawel Packo ◽  
Michael J. Leamy
Keyword(s):  
Lamb Wave ◽  
Lamb Waves ◽  
Wave Dispersion ◽  
Inner Product ◽  
Solvability Conditions ◽  
Higher Harmonic Generation ◽  
Wave Technique ◽  
Lamb Wave Propagation ◽  
Higher Order Dispersion ◽  
Adjoint Solutions

This paper presents results from a perturbation-based analysis approach, and accompanying numerical validation, for calculating amplitude-dependent Lamb wave dispersion in nonlinear plates. Nonlinearities considered include those arising from geometric and material nonlinearities. Using a Lindstedt-Poincaré perturbation analysis, nonlinear dispersion relationships are presented in closed form using the partial wave technique. Solvability conditions, based on an operator formalism accompanied by inner product projections against adjoint solutions, yield higher-order dispersion approximations capturing amplitude-dependent Lamb wave propagation. Numerical simulations using a cellular automata approach verify the predicted dispersion shifts for an example nonlinear plate. The analysis and identification of amplitude-dependent, nonlinear Lamb wave dispersion complements recent research focusing on higher harmonic generation and internally resonant waves, which require precise frequency-wavenumber matching, including at large amplitudes.

scholarly journals Unsteady Adjoint of Pressure Loss for a Fundamental Transonic Turbine Vane

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Chaitanya Talnikar ◽  
Qiqi Wang ◽  
Gregory M. Laskowski
Keyword(s):  
Boundary Layer ◽  
Large Eddy Simulation ◽  
Adjoint Equations ◽  
High Fidelity ◽  
Trailing Edge ◽  
Eddy Simulation ◽  
Large Eddy ◽  
High Fidelity Simulations ◽  
Unsteady Adjoint ◽  
Adjoint Solutions

High-fidelity simulations, e.g., large eddy simulation (LES), are often needed for accurately predicting pressure losses due to wake mixing and boundary layer development in turbomachinery applications. An unsteady adjoint of high-fidelity simulations is useful for design optimization in such aerodynamic applications. In this paper, we present unsteady adjoint solutions using a large eddy simulation model for an inlet guide vane from von Karman Institute (VKI) using aerothermal objectives. The unsteady adjoint method is effective in capturing the gradient for a short time interval aerothermal objective, whereas the method provides diverging gradients for long time-averaged thermal objectives. As the boundary layer on the suction side near the trailing edge of the vane is turbulent, it poses a challenge for the adjoint solver. The chaotic dynamics cause the adjoint solution to diverge exponentially from the trailing edge region when solved backward in time. This results in the corruption of the sensitivities obtained from the adjoint solutions. An energy analysis of the unsteady compressible Navier–Stokes adjoint equations indicates that adding artificial viscosity to the adjoint equations can dissipate the adjoint energy while potentially maintaining the accuracy of the adjoint sensitivities. Analyzing the growth term of the adjoint energy provides a metric for identifying the regions in the flow where the adjoint term is diverging. Results for the vane obtained from simulations performed on the Titan supercomputer are demonstrated.

Sign in / Sign up

Export Citation Format

Share Document