Two Dimensional Analysis and Optimization of Hybrid MDCD-TENO Schemes

In this article, a quasi-linear semi-discrete analysis of shock capturing schemes in two dimensional wavenumber space is proposed. Using the dispersion relation of the two dimensional advection and linearized Euler equations, the spectral properties of a spatial scheme can be quantified in two dimensional wavenumber space. A hybrid scheme (HYB-MDCD-TENO6) which combines the merits of the minimum dispersion and controllable dissipation (MDCD) scheme with the targeted essentially non-oscillatory (TENO) scheme was developed and tested. Using the two dimensional analysis framework, the scheme was spectrally optimized in such a way that the linear part of the scheme can be separately optimized for its dispersion and dissipation properties. In order to compare its performance against existing schemes, the proposed scheme as well as the baseline schemes were tested against a series of benchmark test cases. It was found that the HYB-MDCD-TENO6 scheme provides similar or better resolution as compared to the baseline TENO6 schemes for the same grid size.

Design and optimization of acoustic liners with a shear grazing flow: OPAL software platform applications

In the context of noise reduction in diverse applications where a shear grazing flow is present (i.e., engine nacelle, jet pump, landing gear), improved acoustic liner solutions are being sought. This is particularly true in the low-frequency regime, where space constraints currently limit the efficiency of classic liner technology. To perform the required multi-objective optimization of complex meta-surface liner candidates, a software platform called OPAL was developed. Its first goal is to allow the user to assemble a large panel of parallel/serial assembly of unit acoustic elements, including the recent concept of LEONAR materials. Then, the physical properties of this liner can be optimized, relatively to given weighted objectives (noise reduction, total size of the sample, weight), for a given configuration. Alternatively, properties such as the different impedances of liner unit surfaces can be optimized. To accelerate the process, different nested levels of optimization are considered, from 0D analytical coarse designs in order to reduce the parameter space, up to 2D plan or axisymmetric high-order Discontinuous Galerkin resolution of the Linearized Euler Equations. The presentation will focus on the different aspects of liner design considered in OPAL, and present an application on different samples made for a small scale aeroacoustic bench.

Design and optimization of acoustic liners with a shear grazing flow: OPAL software platform description

In the context of aircraft noise reduction in varied applications where a cold or hot shear grazing flow is present (i.e., engine nacelle, combustion chamber, jet pump, landing gear), improved acoustic liner solutions are being sought. This is particularly true in the low-frequency regime, where space constraints limit the efficiency of conventional liner technology. Therefore, liner design must take into account the dimensional and phenomenological characteristics of constituent materials, assembly specifications and industrial requirements involving multiphysical phenomena. To perform the single/multi-objective optimization of complex meta-surface liner candidates, a software platform coined OPAL (OPtimisation of Acoustic Liners) was developed. Its first goal is to allow the user to assemble a large panel of parallel/serial elementary acoustic layers along a given duct. Then, the physical properties of this liner can be optimized, relatively to weighted objectives, for a given flow and frequency range: impedance target, maximum absorption coefficient or transmission loss with a total sample size and weight... The presentation will focus on the different elementary bricks and assembly of a problem (from 0D analytical coarse designs in order to reduce the parameter space, up to 2D plan or axisymmetric high-order Discontinuous Galerkin simulations of the Linearized Euler Equations).

Isentropic Formulation of the Linearized Euler Equations For Perfectly Premixed Combustion Systems

The linearized Euler equations (LEE) provide an accurate — yet computationally efficient — description of propagation and damping of acoustic waves in geometrically complex, non-uniform reactive mean flows like those found in gas turbine combustion chambers. However, direct application of the LEE to perfectly premixed combustors with highly turbulent flows overestimates entropy waves as the LEE solution inherently contains coupled acoustic, vortical and entropy modes. In the present work, the LEE are decomposed into isentropic and non-isentropic parts ultimately obtaining a simplified set of isentropic LEE, in which only acoustic and vortical modes propagate. In the isentropic LEE, only continuity and momentum equations need to be solved. The energy equation is replaced by the isentropic relation between acoustic pressure and density. From the decomposition, the unsteady heat release term, which acts as a source in the energy equation, naturally arises as a source in the continuity equation. This way, the thermoacoustic coupling is still preserved in the isentropic formulation. The derived isentropic set of equations is first tested with a one-dimensional benchmark configuration consisting of a mean flow temperature jump, non-uniform mean flow velocity and unsteady heat release sources. Solutions of the non-isentropic and isentropic set of LEE are compared and the avoidance of entropy waves proved. Finally, isentropic LEE are used for reproducing the frequency of the self-excited first transversal mode of a lab-scale swirl-stabilized premixed combustor. Furthermore, isentropic and non-isentropic LEE solutions are compared. The non-isentropic LEE yield too high levels of entropy at the combustor exit that may explain the increased damping rate of the non-isentropic LEE solution compared to the isentropic LEE solution. This shows the relevance of isentropic LEE for correctly predicting thermoacoustic stability limits at high frequencies in relevant industrial applications.

Elimination of Numerical Damping in the Stability Analysis of Noncompact Thermoacoustic Systems With Linearized Euler Equations

The hybrid computational fluid dynamics/computational aeroacoustics (CFD/CAA) approach represents an effective method to assess the stability of noncompact thermoacoustic systems. This paper summarizes the state-of-the-art of this method, which is currently applied for the stability prediction of a lab-scale configuration of a perfectly premixed, swirl-stabilized gas turbine combustion chamber at the Thermodynamics institute of the Technical University of Munich. Specifically, 80 operational points, for which experimentally observed stability information is readily available, are numerically investigated concerning their susceptibility to develop thermoacoustically unstable oscillations at the first transversal eigenmode of the combustor. Three contributions are considered in this work: (1) flame driving due the deformation and displacement of the flame, (2) visco-thermal losses in the acoustic boundary layer and (3) damping due to acoustically induced vortex shedding. The analysis is based on eigenfrequency computations of the Linearized Euler Equations with the stabilized finite element method (sFEM). One main advancement presented in this study is the elimination of the nonphysical impact of artificial diffusion schemes, which is necessary to produce numerically stable solutions, but falsifies the computed stability results.

Calculation of the Thermoacoustic Stability of a Main Stage Thrust Chamber Demonstrator

The stability behavior of a virtual thrust chamber demonstrator with low injection pressure loss is studied numerically. The approach relies on an eigenvalue analysis of the Linearized Euler Equations. An updated form of the stability prediction procedure is outlined, addressing mean flow and flame response calculations. The acoustics of the isolated oxidizer dome are discussed as well as the complete system incorporating dome and combustion chamber. The coupling between both components is realized via a scattering matrix representing the injectors. A flame transfer function is applied to determine the damping rates. Thereby it is found that the procedure for the extraction of the flame transfer function from the CFD solution has a significant impact on the stability predictions.

90 Years of Galbrun’s Equation: An Unusual Formulation for Aeroacoustics and Hydroacoustics in Terms of the Lagrangian Displacement

The field of aeroacoustics has gained much attention since the well-known acoustic analogies were first published in the 1950s. In parallel, the continuous growth of computational resources has enabled researchers and engineers to investigate phenomena involving flow-induced noise or sound propagation effects related to arbitrary velocity fields. To describe the latter mentioned physical processes, Galbrun utilized a mixed Eulerian–Lagrangian framework to describe perturbations of the underlying fluid dynamics. While less known compared to the more common linearized Euler equations, Galbrun’s equation provides an original framework. Since its publication in 1931, a number of scholars have further developed the approach first proposed by Galbrun. This paper provides a review of the existing literature dedicated to the use of Galbrun’s equation by highlighting possible advantages of the underlying theory as well as difficulties when utilizing numerical methods for solving problems in time or frequency domain. Furthermore, this work intents to serve as a companion for researchers interested in the field of aeroacoustics and hydroacoustics associated with Galbrun’s equation.

Elimination of Numerical Damping in the Stability Analysis of Non-Compact Thermoacoustic Systems With Linearized Euler Equations

The hybrid Computational Fluid Dynamics/Computational AeroAcoustics (CFD/CAA) approach represents an effective method to assess the stability of non-compact thermoacoustic systems. This paper summarizes the state-of-the-art of this method, which is currently applied for the stability prediction of a lab-scale configuration of a perfectly-premixed, swirl-stabilized gas turbine combustion chamber at the Thermodynamics institute of the Technical University of Munich. Specifically, 80 operational points, for which experimentally observed stability information is readily available, are numerically investigated concerning their susceptibility to develop thermoacoustically unstable oscillations at the first transversal eigenmode of the combustor. Three contributions are considered in this work: (1) flame driving due the deformation and displacement of the flame, (2) visco-thermal losses in the acoustic boundary layer and (3) damping due to acoustically induced vortex shedding. The analysis is based on eigenfrequency computations of the Linearized Euler Equations with the stabilized Finite Element Method (sFEM). One main advancement presented in this study is the elimination of the non-physical impact of artificial diffusion schemes, which is necessary to produce numerically stable solutions, but falsifies the computed stability results.

Towards an Acoustic Simulation of a Water Drop Impacting in a Water Pool

The sound which is produced when a water drop impacts into a water pool is a prominent example for acoustics produced by multiphase flow. In this work the feasibility of numerical methods for simulating this challenging test case is evaluated. First the multiphase flow needs to produce the correct physical mechanisms, e.g. the bubble entrapment. For this an in-house block-structured finite-volume solver with the volume-of-fluid method is used. For the curvature computation a standard finite difference method within the continuum surface force model is employed, including some necessary improvements. A high resolution in space and time is essential and therefore the method is parallelized by domain decomposition. The acoustic part is simulated with the linearized Euler equations which are valid in each phase but need to be adapted in the interface region. The results are compared with numerical and experimental data. It is shown, that the methods are suitable for simple test cases. A coupled drop impact test case corresponds with equivalent experiments until the drop detachment. The acoustic pressure shows a significant rise in the vicinity of the bubble detachment within both phases. However, an oscillation of the cavity bottom can not be observed in the multiphase neither in the acoustic outputs of the airborne signal.