Department MultiPhysics for Energetics

Spectral Difference (SD) method was first developed by Liu et al. [4] for conservative laws on unstructured grids and then extended to Euler equations by Wang et al. [8]. Lastly, this method has been applied to a broad of different applications such as aero-acoustic [2, 7] and aero-elasticity . This method is very similar to the Discontinuous Galerkin (DG) and Spectral Volume (SV) methods in the sense that they share the same solution space, i.e., the space of piece-wise discontinuous polynomials, and some Riemann solvers are used at the element interfaces to provide solution coupling between the discontinuous elements and appropriate numerical dissipation necessary to achieve stability. In addition, all of them are conservative at the element level, making them suitable for problems with discontinuities. They do differ on how solution unknowns or Degrees of Freedom (DoFs) are chosen, and how the DoFs are updated. In a DG method, the DoFs are either the expansion coefficients for a given set of polynomial basis functions or solutions at selected locations within the element. In a SV method, the DoFs are sub-cell averaged solutions, while in the SD method, the DoFs are the solutions at (usually) the quadrature points. The difference between the DG, SV, and SD methods is similar to the difference between the Galerkin Finite Element (FE), Finite Volume (FV), and Finite Difference (FD) methods. The SD method were devised in order to diminish the number of operations per DoF and to use an easier mathematical formalism than DG. Finally, the advantage of the SD method compare to the SV is that there is no dependence to a subdivision of the elements.

We enabled hybrid OpenMP/MPI computations for a new generation of CFD code based on a new high-order method (Spectral Difference method) dedicated to Large Eddy Simulation (LES). The code is written in Fortran 90 with MPI library and OpenMP directives for the parallelization. This white-paper is focused on achieving good performances with the OpenMP shared memory model on standard environment (bi-socket nodes and multi-core x86 processors). The goal was to reduce the number of MPI communications by considering MPI communications between nodes and OpenMP approach for all cores on any node. Three different approaches are compared: full MPI versus full OpenMP computations, full MPI versus hybrid OpenMP/MPI computations, etc. We observed that hybrid and full MPI computations took nearly the same time for a small number of cores.

In this article, we wish to investigate the behavior of a two-layer k − ε turbulence model from the mathematical point of view, as this model is useful for the near-wall treatment in numerical simulations. First, we explain the difficulties inherent in the model. Then, we present a new variable θ that enables the mathematical study. Due to a problem of definition of the turbulent viscosity on the wall boundary, we consider an alternative version of the original equation. We show that some physical aspects of the model are preserved by the new formulation, and in particular, we show how the physicists can help us to prove the existence of a solution of our problem. Finally, we are interested in the Navier-Stokes equations coupled with the modified turbulence model and we show that the alternative model may be preferred to the original one, because of its good properties (existence of a solution of the coupled problems).

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights • Uncertainty Quantification has been applied to RANS simulations of a high-speed jet. • Generalised Polynomial Chaos and Kriging surrogates have been used and compared. • Results using the Spalart-Allmaras turbulence model are compared with other data. • The investigation outlines details of the spatial distribution of uncertainty. • A global Sensitivity Analysis is carried out to show the contribution to uncertainty.

We enabled hybrid OpenMP/MPI computations for a new generation of CFD code based on a new high-order method (Spectral Difference method) dedicated to Large Eddy Simulation (LES). The code is written in Fortran 90 with MPI library and OpenMP directives for the parallelization. This white-paper is focused on achieving good performances with the OpenMP shared memory model on standard environment (bi-socket nodes and multi-core x86 processors). The goal was to reduce the number of MPI communications by considering MPI communications between nodes and OpenMP approach for all cores on any node. Three different approaches are compared: full MPI versus full OpenMP computations, full MPI versus hybrid OpenMP/MPI computations, etc. We observed that hybrid and full MPI computations took nearly the same time for a small number of cores.

This paper addresses how two time integration schemes, the Heun's scheme for explicit time integration and the second-order Crank-Nicolson scheme for implicit time integration, can be coupled spatially. This coupling is the prerequisite to perform a coupled Large Eddy Simulation / Reynolds Averaged Navier-Stokes computation in an industrial context, using the implicit time procedure for the boundary layer (RANS) and the explicit time integration procedure in the LES region. The coupling procedure is designed in order to switch from explicit to implicit time integrations as fast as possible, while maintaining stability. After introducing the different schemes, the paper presents the initial coupling procedure adapted from a published reference and shows that it can amplify some numerical waves. An alternative procedure, studied in a coupled time/space framework, is shown to be stable and with spectral properties in agreement with the requirements of industrial applications. The coupling technique is validated with standard test cases, ranging from one-dimensional to three-dimensional flows.

Some possible future High Fidelity CFD codes for LES simulation of turbomachinery are compared on several test cases increasing in complexity, starting from a very simple inviscid Vortex Convection to a multistage axial experimental compressor. Simulations were performed between 2013 and 2016 by major Safran partners (Cenaero, Cerfacs, CORIA and Onera) and various numerical methods compared: Finite Volume, Discontinuous Galerkin, Spectral Differences. Comparison to analytical results, to experimental data or to RANS simulations are performed to check and measure accuracy. CPU efficiency versus accuracy are also presented. It clearly appears that the level of maturity could be different between codes and numerical approaches. In the end, advantages and disadvantages of every codes obtained during this project are presented.

Training the next generation of aeroacoustic researchers is vital for addressing some difficult yet very important societal challenges, such as the provision of environmentally sustainable air transport operations, both for what concerns airport noise pollution and cabin noise. Sustained demand for more fuel efficient, environmentally friendly, and quieter aircraft power plants is promoting the development of ultra-high bypass engines for large transport aircraft. These turbofan engines require trained aero-acousticians and improved industrial design tools, to tackle some of the difficult design challenges posed by the larger diameter and by the larger fraction of the thrust delivered through the secondary (annular) nozzle. Whilst aeroacoustics is a well-established discipline in its own right, it tends not to be offered as an undergraduate course. This creates a recruitment challenge in doctoral training, with new post-graduate students being recruited across a range of qualificati...

LES of industrial flows is associated with geometrical complexity and requires high order schemes to minimize dissipation and dispersion. To tackle these two issues it is necessary to use unstructured grids and High Performance Computing algorithms. In this context, CERFACS initiated two years ago the development of a new CFD code called JAGUAR based on a mathematical framework leading to high-level capability for LES. In this paper, many topics for HPC are introduced and solved in order to obtain the best code performance.

Shock-cell noise is a particular noise that appears in imperfectly expanded jets. Under these expansion conditions a series of expansions and compressions appear following a shock-cell type structure. The interaction between the vortices developed at the lip of the nozzle and the shock-cells generates what is known as shock-cell noise. This noise has the particularity to be propagated upstream with a higher intensity. This publication will focus on the shock-cell noise generated by an axisymmetric under-expanded 10 to the power of 6 Reynolds single jet. The LES computations are carried out using the elsA code developed by ONERA and extended by CERFACS with high-order compact schemes. They are validated against experimental results. The LES simulation is initialized with a RANS solution where the nozzle exit conditions are imposed. Even though no inflow forcing is applied, good agreement is obtained in terms of flow structures and broadband shock-cell noise that is propagated to the ...

We enabled hybrid OpenMP/MPI computations for a new generation of CFD code based on a new high-order method (Spectral Difference method) dedicated to Large Eddy Simulation (LES). The code is written in Fortran 90 with MPI library and OpenMP directives for the parallelization. This white-paper is focused on achieving good performances with the OpenMP shared memory model on standard environment (bi-socket nodes and multi-core x86 processors). The goal was to reduce the number of MPI communications by considering MPI communications between nodes and OpenMP approach for all cores on any node. Three different approaches are compared: full MPI, full OpenMP and hybrid OpenMP/MPI. We observed that hybrid and full MPI computations took nearly the same time for a small number of cores.

Shock-cell noise is a particular noise that appears in imperfectly expanded jets. Under these expansion conditions a serie of expansions and compressions appears following a shock-cell type structure. The interaction between the vortices developed at the lip of the nozzle and the shock-cells generates what is known as shock-cell noise. This noise has the particularity to be propagated upstream with a higher intensity. This paper will focus on the azimuthal modal analysis of the jet and the near-field of a nonscreeching supersonic axisymmetrical under-expanded jet at Reynolds Re = UjDj=vj = 106. Large eddy simulations (LES) are carried out using the elsA code developed by ONERA and extended byCERFACS with high-order compact schemes.

Abstract. In this article, we wish to investigate the behavior of a two-layer k − " turbulence model from the mathematical point of view, as this model is useful for the near-wall treatment in numerical simulations. First, we explain the diculties inherent in the model. Then, we present a new variable that enables the mathematical study. Due to a problem of denition of the turbulent viscosity on the wall boundary, we consider an alternative version of the original equation. We show that some physical aspects of the model are preserved by the new formulation, and in particular, we show how the physicists can help us to prove the existence of a solution of our problem. Finally, we are interested in the Navier-Stokes equations coupled with the modied turbulence model and we show that the alternative model may be preferred to the original one, because of its good properties (existence of a solution of the coupled problems). Resume. L’objectif de cet article est l’etude du modele de...

A time-domain harmonic balance method for the analysis of almost-periodic flows is presented. This kind of method uses the Fourier analysis to derive a more efficient time marching scheme than classical ones, on such flows. It has recently gain important interest, especially in the turbomachinery field where the flow spectrum is essentially a combination of the blade passing frequencies. Traditionally, researchers have used a uniform sampling but in the case of several frequencies non necessarily multiple of each other, harmonic balance methods can face stability issues due to a bad condition number of the Fourier operator. Two algorithms are derived to find a non uniform time sampling in order to minimize this condition number. Their behavior are studied on a wide range of frequencies and a model problem of a 1D flow with pulsating pressure enables to prove their efficiency. Finally, a turbomachinery flow is analyzed with different frequency sets. It demonstrates the stability and robustness of the present non-uniform Harmonic Balance method regardless of the frequency set.