Large eddy simulations of turbulent flows and aeroacoustics noise predictions using high-order methods

Large eddy simulation (LES) has received increased attention in industrial applications over the past few decades for challenging vortex-dominated turbulent flows. Direct numerical simulations (DNS) have also been used to study interesting flow physics at low to moderate Reynolds numbers. This is due to the advancements in computational algorithms and computing power of modern computers which paved the way for simulating more practical flow problems. In its 2030 vision, NASA has predicted that scale resolving simulations will be increasingly used for vortex-dominated turbulent flow simulations such as rotorcraft flows and turbomachinery flows in aircraft engines. Multiple international workshops on high-order CFD methods have conclusively demonstrated the advantage of high-order methods over 1st and 2nd order ones in accuracy/efficiency for such scale-resolving simulations due to their lower dispersion and dissipation errors. In this dissertation, we analyze the performance of high-order CFD methods for LES using Fourier analysis techniques. We also propose new ideas and approaches for studying the dispersion/dissipation of high-order multi-degree of freedom methods. In addition, we study aspects of mesh resolution requirements for DNS and LES of turbomachinery flows using the high-order flux reconstruction/correction procedure via reconstruction (FR/CPR) method. Finally, we offer an efficient implementation of the Ffowcs-Williams & Hawkings (FWH) acoustic analogy formulation in a hybrid framework with the FR/CPR method for jet noise predictions of supersonic jets

On adomian based numerical schemes for euler and navier-stokes equations, and application to aeroacoustic propagation

140 p.En esta tesis se ha desarrollado un nuevo método de integración en tiempo de tipo derivadas sucesivas (multiderivative), llamado ABS y basado en el algoritmo de Adomian. Su motivación radica en la reducción del coste de simulación para problemas en aeroacústica, muy costosos por su naturaleza transitoria y requisitos de alta precisión. El método ha sido satisfactoriamente empleado en ambas partes de un sistema híbrido, donde se distinguen la parte aerodinámica y la acústica.En la parte aerodinámica las ecuaciones de Navier-Stokes incompresibles son resueltas con unmétodo de proyección clásico. Sin embargo, la fase de predicción de velocidad ha sido modificadapara incluir el método ABS en combinación con dos métodos: una discretización espacial MAC devolúmenes finitos, y también con un método de alto orden basado en ADER. El método se ha validado respecto a los problemas (en 2D) de vórtices de Taylor-Green, y el desarrollo de vórticesde Karman en un cilindro cuadrado. La parte acústica resuelve la propagación de ondas descritaspor las ecuaciones linearizadas de Euler, empleando una discretización de Galerkin discontinua. El método se ha validado respecto a la ecuación de Burgers.El método ABS es sencillo de programar con una formulación recursiva. Los resultados demuestran que su sencillez junto con sus altas capacidades de adaptación lo convierten en un método fácilmente extensible a órdenes altos, a la vez que reduce el coste comparado con otros métodos clásicos

On Adomian Based Numerical Schemes for Euler and Navier-Stokes Equations, and Application to Aeroacoustic Propagation

In this thesis, an Adomian Based Scheme (ABS) for the compressible Navier-Stokes equations is constructed, resulting in a new multiderivative type scheme not found in the context of fluid dynamics. Moreover, this scheme is developed as a means to reduce the computational cost associated with aeroacoustic simulations, which are unsteady in nature with high-order requirements for the acoustic wave propagation. We start by constructing a set of governing equations for the hybrid computational aeroacoustics method, splitting the problem into two steps: acoustic source computation and wave propagation. The first step solves the incompressible Navier-Stokes equation using Chorin's projection method, which can be understood as a prediction-correction method. First, the velocity prediction is obtained solving the viscous Burgers' equation. Then, its divergence-free correction is performed using a pressure Poisson type projection. In the velocity prediction substep, Burgers' equation is solved using two ABS variants: a MAC type implementation, and a ``modern'' ADER method. The second step in the hybrid method, related to wave propagation, is solved combining ABS with the discontinuous Galerkin high-order approach. Described solvers are validated against several test cases: vortex shedding and Taylor-Green vortex problems for the first step, and a Gaussian wave propagation in the second case. Although ABS is a multiderivative type scheme, it is easily programmed with an elegant recursive formulation, even for the general Navier-Stokes equations. Results show that its simplicity combined with excellent adaptivity capabilities allows for a successful extension to very high-order accuracy at relatively low cost, obtaining considerable time savings in all test cases considered.Predoc Gobierno Vasc

On adomian based numerical schemes for euler and navier-stokes equations, and application to aeroacoustic propagation

140 p.En esta tesis se ha desarrollado un nuevo método de integración en tiempo de tipo derivadas sucesivas (multiderivative), llamado ABS y basado en el algoritmo de Adomian. Su motivación radica en la reducción del coste de simulación para problemas en aeroacústica, muy costosos por su naturaleza transitoria y requisitos de alta precisión. El método ha sido satisfactoriamente empleado en ambas partes de un sistema híbrido, donde se distinguen la parte aerodinámica y la acústica.En la parte aerodinámica las ecuaciones de Navier-Stokes incompresibles son resueltas con unmétodo de proyección clásico. Sin embargo, la fase de predicción de velocidad ha sido modificadapara incluir el método ABS en combinación con dos métodos: una discretización espacial MAC devolúmenes finitos, y también con un método de alto orden basado en ADER. El método se ha validado respecto a los problemas (en 2D) de vórtices de Taylor-Green, y el desarrollo de vórticesde Karman en un cilindro cuadrado. La parte acústica resuelve la propagación de ondas descritaspor las ecuaciones linearizadas de Euler, empleando una discretización de Galerkin discontinua. El método se ha validado respecto a la ecuación de Burgers.El método ABS es sencillo de programar con una formulación recursiva. Los resultados demuestran que su sencillez junto con sus altas capacidades de adaptación lo convierten en un método fácilmente extensible a órdenes altos, a la vez que reduce el coste comparado con otros métodos clásicos

Application and assessment of time-domain DGM for intake acoustics using 3D linearized Euler equations

Fan noise is one of the major sources of aircraft noise. This can be modelled by means of frequency and time domain CAA methods. Frequency domain methods based on the convected Helmholtz equation are widely used for noise propagation and radiation from turbofan intakes. However, these methods are unsuited to deal easily with turbofan exhaust noise and presently unable to solve large 3D (three-dimensional) problems at high frequencies. In this thesis the application of time-domain Discontinuous Galerkin Methods (DGM) for solving linearized Euler equations is investigated. The research is focused on large 3D problems with arbitrary mean flows. A commercially available DGM code, Actran DGM, is used.An automatic procedure has been developed to perform the DGM simulations for axisymmetric and 3D intake problems by providing simple control of all the parameters (flow, geometry, liners). Moreover, a new method for integrating source predictions obtained from CFD calculations for the fan stage of a turbofan engine with the DGM code to predict tonal noise radiation in the far field has been proposed, implemented and validated.The DGM is validated and benchmarked for intake and exhaust problems against analytical solutions and other numerical methods. The principal properties of the DGM are assessed, best practice is defined, and important issues which relate to the accuracy and stability of the liner model are identified. The accuracy and efficiency of the CFD/CAA coupling are investigated and results obtained are compared to rig test data.The influence of the 3D intake shapes and the mean flow distortion on the sound field is investigated for static rig and flight conditions by using the DGM approach. Moreover, it is shown that the mean flow distortion can have a significant effect on the sound attenuation by a liner

A coupled LES/high-order acoustic method for jet noise analysis

Aircraft noise is one of the main areas of active research for the aeronautical industry due to the increasingly stringent regulations on noise emission that aviation authorities are imposing. Among the different sources that contribute to the total emitted aircraft noise, jet noise is one of the most important during take-off. Furthermore, as the by-pass ratio of turbofan engines is increased, the interaction of the jet exhaust with the high-lift devices and the wing can potentially produce new mechanisms for noise generation. On the simulation front, the rapid increase of computing power over the last decades is enabling the use of high-fidelity simulations for the study of jet noise at both industrial and academic research levels. However, most of the numerical methods used by different research groups are either too dissipative for propagating the acoustic waves or are limited to the study of simple configurations. In many cases, surface integral methods have been the preferred choice with encouraging results for isolated jet configurations. Among these methods, the Ffowcs Williams-Hawkings (FWH) formulation has been commonly applied within research communities. However, applying them in complex configurations can be challenging, which may not provide sufficient information when it comes to studying noise generation mechanisms. The work reported in this thesis is devoted to the development of a coupling framework that is suitable for complex jet noise propagation cases. In this framework, the jet noise problem is divided into two different steps. First, the acoustic sources are computed using a robust compressible Large Eddy Simulation (LES) finite volume solver, which are then transferred to a spectral/hp high-order finite element Acoustic Perturbation Equations (APE) solver that propagates the sound waves to the far-field. Two different coupling strategies are investigated. Initially, a simple methodology based on the exchange of files between the solvers is implemented with only minor modifications made to the solvers’ source code. However, the poor efficiency of data transfer meant this method is applicable only to small problems. Thus, a more efficient parallel-interface coupling technique is developed to overcome this issue. With this technique all the required data is transferred via a parallel Message Passing Interface (MPI), avoiding the bottleneck of I/O and file systems. Both coupling techniques are validated with a 2-D cylinder case demonstrating the superiority of the parallel interface method. The parallel interface coupling framework is then tested on a low Reynolds number jet, being validated against experimental and numerical results in the literature, during which a well-established FWH method is used for references. More promising results are obtained using the LES/APE method than with the FWH method. The LES/APE method is then applied to the study of a more realistic isolated jet case and is compared to the experimental data obtained at NASA. A source analysis is further carried out, in this case, to reveal the distribution and convection of sources along the jet plume at different locations. The source distribution is in good agreement with the far-field noise results. Finally, the study of a jet-flat plate installed configuration is conducted. This simplified configuration is representative of a realistic installation scenario and is particularly useful to the understanding of the installation effects. The coupling framework captures these additional flow-acoustic effects demonstrating its potential to tackle complex configurations

Aerofoil broadband and tonal noise modelling using Fast-Random-Particle-Mesh method and Large Eddy Simulation

PhD thesisThe aim of this work is to critically examine state-of-the art numerical methods used in computational aero-acoustics with the goal to further develop methods of choice that satisfy the industry requirements for aero-acoustic design, that is being fast, physical and potentially applicable to a variety of airframe noise problems. At the core of this thesis, two different modelling techniques are applied to benchmark aerofoil noise problems. One is based on a modern Fast Random Particle Mesh (FRPM) method with the mean flow and turbulence statistics supplied from the Reynolds-Averaged Navier-Stokes (RANS) simulation. The second technique is a Large Eddy Simulation (LES) method utilising the new in-house fast-turn-around GPU CABARET code. The novelty of the work presented herein consists in the development of new modifications to the stochastic FRPM method featuring both tonal and broadband noise sources. The technique relies on the combination of incorporated vortex-shedding resolved flow available from Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulation with the fine-scale turbulence FRPM solution generated via stochastic velocity fluctuations in the context of vortex sound theory. In contrast to the existing literature, proposed methodology encompasses a unified treatment for broadband and tonal acoustic noise sources at the source level, thus, accounting for linear source interference as well as possible non-linear source interaction effects. Results of the method’s application for two aerofoil benchmark cases, with sharp and blunt trailing edges are presented. In each case, the importance of individual linear and non-linear noise sources was investigated. Several new key features related to the unsteady implementation of the method were tested and brought into the equation. The source terms responsible for noise generation in accordance with the vortex sound theory are computed to assess the validity range of a digital filter calibration parameter used in the FRPM method for synthetic turbulence generation as compared to the same source reconstructed from the first principle LES solution. Such comparison at the source level has been achieved for the first time in the modelling literature, which allows for the physical interpretation of results obtained by the FRPM method. Finally, solutions of the FRPM method with the calibration parameter tailored in accordance with the LES are used for far-field noise predictions which are compared with experimental measurementsBAE Systems Ltd.Engineering and Physical Sciences Research Council (EPSRC)

Development of predictive methods for tiltrotor flows

This thesis presents evidence on the ability of grid-based, Computational Fluid Dynamics methods based on the Unsteady Reynolds Averaged Navier-Stokes equations to accurately predict axial flight performance of rotors with modest computer resources. Three well-studied blades, the B0-105, S-76, and PSP main rotor blades, are used and results are compared with experimental data. Likewise, performance analyses of the JORP propeller and XV-15 tiltrotor blades are carried out, respectively, aiming to validate the employed CFD method for such relevant flows. Validation of the HMB3 CFD solver for complete tiltrotors is also presented. The aim is to assess the capability of the present CFD method in predicting tiltrotor airloads at different flight configurations. In this regard, three representative cases of the ERICA tiltrotor were selected, corresponding to aeroplane, transition corridor, and helicopter modes, covering most modes of tiltrotor flight. Aerodynamic optimisation of tiltrotor blades with high-fidelity computational fluid dynamics coupled with a discrete adjoint method is also carried out. This work shows how the main blade shape parameters influence the optimal performance of the tiltrotor in helicopter and aeroplane modes, and how a compromise blade shape can increase the overall tiltrotor performance. Finally, the implementation and validation of an efficient, high-order, finite-volume scheme (up to 4th-order of spatial accuracy) in the HMB3 CFD solver is presented. The scheme shows a higher level of accuracy if compared with the standard-MUSCL, and 4th-order accuracy was achieved on Cartesian grids. Furthermore, a significantly high spectral resolution (dispersion and dissipation) of the new scheme is observed. Two-and three-dimensional test cases were considered to demonstrate the new formulation. Results of the steady flow around the 7AD, S-76, JORP propeller, and XV-15 blades showed a better preservation of the vorticity and higher resolution of the vortical structures compared with the standard MUSCL solution. The method was also demonstrated for three-dimensional unsteady flows using overset and moving grid computations for the UH-60A rotor in forward flight and the ERICA tiltrotor in aeroplane mode. For medium grids, the new high-order scheme adds CPU and memory overheads of 22% and 23%, respectively. The parallel performance of the scheme is fair but can be further improved