Nektar++ is an open-source framework that provides a flexible, high-performance and scalable platform for the development of solvers for partial differential equations using the high-order spectral/$hp$ element method. In particular, Nektar++ aims to overcome the complex implementation challenges that are often associated with high-order methods, thereby allowing them to be more readily used in a wide range of application areas. In this paper, we present the algorithmic, implementation and application developments associated with our Nektar++ version 5.0 release. We describe some of the key software and performance developments, including our strategies on parallel I/O, on in situ processing, the use of collective operations for exploiting current and emerging hardware, and interfaces to enable multi-solver coupling. Furthermore, we provide details on a newly developed Python interface that enables a more rapid introduction for new users unfamiliar with spectral/$hp$ element methods, C++ and/or Nektar++. This release also incorporates a number of numerical method developments - in particular: the method of moving frames, which provides an additional approach for the simulation of equations on embedded curvilinear manifolds and domains; a means of handling spatially variable polynomial order; and a novel technique for quasi-3D simulations to permit spatially-varying perturbations to the geometry in the homogeneous direction. Finally, we demonstrate the new application-level features provided in this release, namely: a facility for generating high-order curvilinear meshes called NekMesh; a novel new AcousticSolver for aeroacoustic problems; our development of a 'thick' strip model for the modelling of fluid-structure interaction problems in the context of vortex-induced vibrations. We conclude by commenting some directions for future code development and expansion.

In modern aeroengines, combustion noise has become a significant source to the overall noise, particularly at approach conditions. This requires further advances in understanding and predicting combustion noise of turbulent flames. This is the aim of the present study, where a hybrid computational fluid dynamics/computational aeroacoustics approach is applied on a generic premixed and pressurized combustor to assess its accuracy for combustion noise predictions. The hybrid approach consists of Reynolds-averaged Navier-Stokes (RANS) or largeeddy simulations (LES) mean flow and frequency-domain simulations based on linearized Navier-Stokes equations that are fed by combustion noise source terms. The latter are obtained from both the application of a statistical noise model on the RANS simulations and a postprocessing of incompressible LES, in a first step. The acoustic simulation results are compared with experimental pressure measurements conducted by the Centre National de la Recherche Scientifique. Very good agreement is found over the entire frequency range if the LES source model is applied. Sensitivity studies with respect to feeding lines, mean flowfield, and mesh were performed. The resulting comparisons of the linearized Navier-Stokes equation simulations based on the RANS and LES flowfields revealed that the combustion noise spectrum is mainly governed by the heat release spectrum but not by the aerodynamic combustor flowfield. However, this issue needs further investigation.

The reduction of pollution and noise emissions of modern aero engines represents a key concept to meet the requirements of the future air traffic. This requires an improvement in the understanding of combustion noise and its sources, as well as the development of accurate predictive tools. This is the major goal of the current study where the LOTAN network solver and a hybrid CFD/CAA approach are applied on a generic pre-mixed and pressurized combustor to evaluate their capabilities for combustion noise predictions. LOTAN solves the linearized Euler equations (LEE) whereas the hybrid approach consists of RANS mean flow and frequency-domain simulations based on linearized Navier-Stokes equations (LNSE). Both solvers are fed in turn by three different combustion noise source terms which are obtained from the application of a statistical noise model on the RANS simulations and a postprocessing of an incompressible and compressible LES. In this way the influence of the source model and acoustic solver is identified. The numerical results are compared with experimental data. In general good agreement with the experiment is found for both the LOTAN and LNSE solvers. The LES source models deliver better results than the statistical noise model with respect to the amplitude and shape of the heat release spectrum. Beyond this it is demonstrated that the phase relation of the source term does not affect the noise spectrum. Finally, a second simulation based on the inhomogeneous Helmholtz equation indicates the minor importance of the aerodynamic mean flow on the broadband noise spectrum.

The use of a hybrid CFD-CAA method is becoming a standard approach for farfield jet noise prediction, due to its low computational cost compared with a direct compressible prediction. Hybrid CFD-CAA methods require the exchange of information between different codes. For 3D far-field propagation that relies on noise sources information, the amount of data that has to be sent can be enormous, since the size of the meshes is typically of the order of million of elements. Hence, the use of traditional file-based approaches to exchange the data between the codes is limited, as hundreds of terabytes for storing the noise sources can be reached and the scalability of the overall method is limited by the available I/O bandwidth. In this work, a coupling strategy is used in which all the necessary data is exchanged directly in memory by using an open-source library called CWIPI [1]. In addition, it includes an interpolation package that allows the use of different mesh topologies for different codes. The code used for the noise source calculation is a Large Eddy Simulations (LES) code that is use for industry design and academic research [2]. For the acoustic propagation, the solver used is APESolver, part of the high-order open-source code Nektar++ [3]. Encouraging results for combustion noise has been presented by Lackhove et al. [4] with a similar methodology.

Due to the reduction of fuel consumption and new global emission limits, especially for the pollutant emissions of NOx, improvements to lean combustion technologies in aeroengine combustors are unavoidable. Near to the lean limits, combustion tends to be unstable. A geometry related coupling between unsteady heat release and acoustic perturbations leads to thermoacoustic instabilities, which show an undesirable impact on pressure, velocity and heat release in the combustor Such instabilities occur when the unsteady heat release fluctuations are in phase with the acoustic pressure fluctuations. The. aim of this study is to find an industrially applicable, three-dimensional numerical model for the prediction of combustion noise, which can also provide insight in thermoacoustic instabilities and acoustic effects in a responsive environment in enclosed, technical combustion systems. The turbulent reacting flow in a realistic gas turbine combustor has been computed by means of Large Eddy Simulation coupled to a tabulated chemistry approach based on the Flamelet Generated Manifold ansatz. The reactive LES provides very well suited method to study the impact of unsteady heat release as a major source of acoustic noise in combustion. For the simultaneous treatment of the reacting flow and its acoustic features, a Computational Aero Acoustics (CAA) solver has been coupled with the LES solver following a hybrid approach. In this work the acoustic wave propagation is calculated by the Linearized Euler Equations (LEE). The interface between both codes is optimized for the realisation of an acoustic feedback loop in order to obtain a suitable representation of acoustically self-excited oscillations. To demonstrate the prediction capability of the hybrid LES/CAA approach, geometry-dependent thermoacoustic instabilities in a generic half-dump combustor, for which experimental data are available, are investigated. The numerical results are compared to measured pressure fluctuations under both thermoacoustically stable and unstable conditions.

Combustion noise has become a significant contributor to the overall noise emitted by modern aero-engines. This development is attributed to reduced noise sources in other components due to design improvements and the introduction of premixed combustors that burn more unsteadily and hence emit more noise. These next generation combustion systems are more prone to acoustic instabilities and thus require improved methods for the prediction of combustion noise. This paper presents a numerical approach which exploits the different scales prevalent in these combustion systems by computing the flow field and acoustics separately and coupling both simulations in real time. To demonstrate its capabilities, the methodology is successfully applied to a premixed and pressurized propane flame which was experimentally investigated by CNRS [1] and for which pressure measurement data are available. In the present numerical model, the separation of the physical phenomena facilitates the application of the most suitable numerical schemes and governing equations to both sets of problems. Due to the low Mach numbers governing typical combustors, the flow field can be adequately described by the incompressible Navier-Stokes equations. These are solved by an implicit finite volume flow solver which is supplemented by a tabulated chemistry approach to account for the combustion processes. For the acoustics, the three dimensional Acoustic Perturbation Equations (APE) are solved using a state of the art, low dispersion Discontinuous Galerkin CAA tool. Both codes are run in parallel and exchange fields on-line to maintain the highest possible temporal resolution and data transfer rates. The different natures of both phenomena require an elaborate coupling scheme that comprises temporal and spatial interpolation and filtering. Since the incompressible formulation of the flow solver allows for considerably larger time steps and the acoustics solver employs much simpler governing equations, the overall computational costs of this approach are up to 10 times lower than those of a compressible simulation with similar fidelity.