This project aims at studying a particular sort of jet that is often encountered in internal aerodynamic: the jets in crossflow (see Figure -top). The originality of this project stems from the simultaneous and strongly coupled experimental and numerical studies of such jets.

From an experimental point of view, the test facility
Maveric

A close interaction during the course of the project between experiments and simulation will be established. From the simulation point of view, the aim is to be able to perform within two years a direct numerical simulation of an isothermal configuration of an inclined jet in crossflow in turbulence conditions, with a compressible solver that must be still accurate at low Mach number. Considering the challenge that such a task represents, a collaboration has been established with the Bacchus team in order to avoid too many useless redundancies. The Cagire team shares with Bacchus a common framework of development in which both common and team specific tools are being elaborated. From a numerical point of view, the challenge stems from the recourse to hybrid unstructured meshes, which is mandatory for our flow configuration, and implicit time integration, which is induced by the low Mach number of the flow. From the point of view of the interaction between experiments and CFD, the challenge will be mostly related to the capability of ensuring that the flow simulated and the flow experimentally investigated are as identical as possible.

A typical continuous solution of the Navier Stokes equations is governed
by a spectrum of time and space scales.
The broadness of that spectrum is directly controlled by the
Reynolds number defined as the ratio
between the inertial forces and the viscous forces. This number
is quite helpful to determine if the flow is turbulent or not.
In the former case, it indicates the range of scales of fluctuations
that are present in the flow under study. Typically, for instance for the
velocity field, the ratio between the largest scale
(the integral length scale) to the smallest one
(Kolmogorov scale) scales as **(i)** to improve our knowledge of turbulent
flows and **(ii)** to test (i.e. validate or invalidate)
and improve the numerous
modelling hypotheses inherently associated to the RANS and LES approaches.
From a numerical point of view, if the steady nature of the RANS equations
allows to perform iterative
convergence on finer and finer meshes, this is no longer possible for LES or
DNS which are time-dependent. It is therefore necessary to develop
high accuracy schemes in such frameworks. Considering that the Reynolds number
in an engine combustion chamber is significantly larger than 10000, a direct
numerical simulation of the whole flow domain is not conceivable on a routine
basis but the simulation of generic flows which feature some of the phenomena
present in a combustion chamber is accessible considering the recent
progresses in High Performance Computing (HPC).
Along these lines, our objective is to develop a DNS
tool to simulate a jet in crossflow configuration which is the generic flow
of an aeronautical combustion chamber as far as its effusion cooling is
concerned.

All the methods we describe are mesh-based methods: the computational
domain is divided into *cells*, that have an elementary shape:
triangle and
quadrangle in two dimensions, and tetrahedra, hexahedra, pyramids, and prism
in three dimensions. If the cells are
only regular hexahedra, the mesh is said to be *structured*.
Otherwise, it is said to be unstructured. If the mesh is composed of
more than one sort of elementary shape, the mesh is said to be
*hybrid*.

The basic numerical model for the computation of internal flows is based on the Navier-Stokes equations. For fifty years, many sorts of numerical approximation have been tried for this sort of system: finite differences, finite volumes, and finite elements.

The finite differences have met a great success for some equations, but for the approximation of fluid mechanics, they suffer from two drawbacks. First, structured meshes must be used. This drawback can be very limiting in the context of internal aerodynamics, in which the geometries can be very complex. The other problem is that finite difference schemes do not include any upwinding process, which is essential for convection dominated flows.

The finite volumes methods have imposed themselves in the last thirty years in the context of aerodynamic. They intrinsically contain an upwinding mechanism, so that they are naturally stable for linear as much as for nonlinear convective flows. The extension to diffusive flows has been done in . Whereas the extension to second order with the MUSCL method is widely spread, the extension to higher order has always been a strong drawback of finite volumes methods. For such an extension, reconstruction methods have been developed (ENO, WENO). Nevertheless, these methods need to use a stencil that increases quickly with the order, which induces problems for the parallelisation and the efficiency of the implementation. Another natural extension of finite volume methods are the so-called discontinuous Galerkin methods. These methods are based on the Galerkin' idea of projecting the weak formulation of the equations on a finite dimensional space. But on the contrary to the conforming finite elements method, the approximation space is composed of functions that are continuous (typically: polynomials) inside each cell, but that are discontinuous on the sides. The discontinuous Galerkin methods are currently very popular, because they can be used with many sort of partial differential equations. Moreover, the fact that the approximation is discontinuous allows to use modern mesh adaptation (hanging nodes, which appear in non conforming mesh adaptation), and adaptive order, in which the high order is used only where the solution is smooth.

Discontinuous Galerkin
methods where introduced by Reed and Hill and first studied by
Lesaint and Raviart .
The extension to the Euler system with explicit time integration
was mainly led by Shu, Cockburn and their collaborators. The steps of
time integration and slope limiting were similar to high order ENO schemes,
whereas specific constraints given by the finite elements nature of
the scheme were progressively solved,
for scalar conservation laws , ,
one dimensional systems ,
multidimensional scalar conservation laws ,
and multidimensional systems . For the same system, we can
also cite the work of
, , which is slightly different: the stabilisation is
made by adding a nonlinear stabilisation term, and the time
integration is implicit.
Then, the extension to the
compressible Navier-Stokes system was made by Bassi and Rebay
, first by a mixed type finite element method,
and then simplified by means of lifting operators.
The extension to the

For concluding this section, there already exist numerical schemes based on the discontinuous Galerkin method which proved to be efficient for computing compressible viscous flows. Nevertheless, there remain things to be improved, which include for example: efficient shock capturing term methods for supersonic flows, high order discretization of curved boundaries, or low Mach behaviour of these schemes (this last point will be detailed in the next subsection). Another drawback of the discontinuous Galerkin methods is that they are very computationally costly, due to the accurate representation of the solution. A particular care must be taken on the implementation for being efficient.

A great deal of experiments has been devoted to the study of jet in
crossflow configurations. They essentially differ
one from each other by the hole shape (cylindrical or shaped), the hole
axis inclination, the way by which the hole is fed, the characteristics of
the crossflow and the jet (turbulent or not, isothermal or not), the number
of holes considered and last but not least the techniques used to investigate
the flow.
A good starting point to assess the diversity of the studies carried out is
given by . For inclined cylindrical holes, the experimental
database produced by Gustafsson
and Johansson

The industrial applications of our project is the cooling of the walls of the combustion chambers encountered in the helicopter engines, and more precisely, we wish to contribute to the improvement of effusion cooling.

Effusion cooling is nowadays very widespread, especially in the aeronautical context. It consists in piercing holes on the wall of the combustion chamber. These holes induce cold jets that enter inside the combustion chamber. The goal of this jet is to form a film of air that will cool the walls of the chamber, see Figure .

Effusion cooling in a combustion chamber takes at the wall where thousands of small holes allow cool air to enter inside the combustion chamber. This induces jets in crossflow in charge of cooling the walls, whatever the heat and the acoustic waves present inside the chamber. Nevertheless, this technique is not straightforward to put in practice: the size, design and position of the holes can have an important effect on the cooling efficiency. For a safe and efficient functioning of the combustion chamber, it is required that the cooling jets and the combustion effects be as much independent as possible. For example, this means that

The jets of cool air should not mix too much with the internal flow. Otherwise it will decrease the efficiency of the combustion.

The jets should be as much stable as possible when submitted to waves emitted in the combustion chamber, e.g. acoustic waves induced by combustion instabilities. Otherwise the jets may not cool enough the walls of the combustion chamber which can then undergoes severe damages.

The first point is what we aim at simulate in this project. As the model chosen is the fully compressible Navier Stokes system, there should not be any problem in the future for being able to simulate the effect of an acoustic forcing on the jet in crossflow.

Having a database of Direct Numerical Simulations is also fundamental for testing closure laws that are used in turbulence models encountered in RANS and LES models. With such models, it is possible for example to perform optimisation.

A last aspect, that will not be dealt with in this project, but that could be dealt with in the future, is the interaction between the flow and the wall. The aim is to understand the effect of coupling between the heat propagation in the wall and the flow near the wall. A careful study of this interaction can allow to determine the exchange coefficients, and so the efficiency of the cooling by the jet. Such determination may particularly useful to develop one or multidimensional models of wall-fluid interaction .

From the application point of view,
compressibility effects must be taken into account since the Mach
number of the flow can reach values equal to

The software AeroSol is jointly developed in the team Bacchus and the team Cagire. It is a high order finite element library written in C++. The code design has been carried for being able to perform efficient computations, with continuous and discontinuous finite elements methods on hybrid and possibly curvilinear meshes. The distribution of the unknowns is made with the software PaMPA, developed within the team Bacchus and the team Pumas. This year, Dragan Amenga-Mbengoué was recruited on the ANR Realfluids, and François Rué (Service Experimentation et Développement) joined the team Bacchus for working on Aerosol.

At the end of 2011, Aerosol had the following features

**development environement** use of CMake for compilation,
CTest for automatic tests and memory checking,
lcov and gcov for code coverage reports.

**In/Out**
link with the XML library for handling with parameter files. Reader for
GMSH, and writer on the VTK-ASCII legacy format.

**Quadrature formula** up to 11th order
for Lines, Quadrangles, Hexaedra, Pyramids, Prisms,
up to 14th order for tetrahedron, up to 21st order for triangles.

**Finite elements** up to fourth degree for Lagrange finite elements
on lines, triangles and quadrangles.

**Geometry** elementary geometrical functions for first order
lines, triangles, quadrangles.

**Time iteration** explicit Runge-Kutta up to fourth order, explicit
Strong Stability Preserving schemes up to third order.

**Linear Solvers** link with the external linear solver UMFPack.

**Memory handling** discontinuous and continuous discretizations
based on PaMPA for triangular and quadrangular meshes.

**Numerical schemes** continuous Galerkin method for the Laplace
problem (up to fifth order) with non consistent time iteration or with direct
matrix inversion.
Scalar stabilized residual distribution schemes with explicit Euler time
iteration have been implemented for steady problems.

This year, the following features were added

**development environement** development of a CDash server for
collecting the unitary tests and memory checking. Beginning of the
development of an interface for functional tests.

**General structure** Parts of the code were abstracted in
order to allow for parallel development: Linear solvers (template type
abstraction for generic linear solver external library), Generic integrator
classes (integrating on elements, on faces with
handling neighbour elements, or for working on Lagrange points of a given
element), models (template abstraction for generic hyperbolic systems),
equations of state (template-based abstraction for a generic
equation of state).

**In/Out**
Parallel GMSH reader, cell and point centered visualization based
on VTK-legacy formats. XML paraview files on unstructured meshes (vtu), and
parallel XML based files (pvtu).

**Quadrature formula** Gauss-Lobatto type quadrature formula.

**Finite elements** Hierarchichal orthogonal finite element
basis on lines, triangles (with Dubiner transform).
Finite element basis that are interpolation basis on Gauss-Legendre points
for lines, quadrangles, and hexaedra. Lagrange, and
Hierarchical orthogonal finite elements basis for hexaedra, prisms and
tetrahedra.

**Geometry** elementary geometrical functions for first order
three dimensional shapes: hexaedra, prisms, and tetrahedra.

**Time iteration** CFL time stepping, optimized CFL time
schemes: SSP(2,3) and SSP (3,4)

**Linear Solvers** Internal solver for diagonal matrices.
Link with the external solvers PETSc and MUMPS.

**Memory handling** parallel degrees of freedom handling
for continuous and discontinuous approximations

**Numerical schemes** Discontinuous Galerkin methods for
hyperbolic systems. SUPG and Residual Distribution schemes.

**Models** Perfect gas Euler system, real gas Euler system, scalar
advection, Waves equation in first order formulation, generic interface
for defining space-time models from space models.

**Numerical fluxes** centered fluxes, exact Godunov' flux for
linear hyperbolic systems, and Lax-Friedrich flux.

**Parallel computing** Mesh redistribution, computation of Overlap
with PaMPA. collective asynchronous communications
(PaMPA based). Tests on the cluster Avakas from MCIA, and on Mésocentre de Marseille, and PlaFRIM.

**C++/Fortran interface** Tests for binding fortran with C++.

The time-step dependency and the scaling of the pressure-velocity coupling suitable for unsteady calculations of low Mach number flows including acoustic features has been identified in the Momentum Interpolation approach. It has been shown that the proper form of the inertia term in the transporting velocity definition is related to the time-step independency of the steady state. The suitable scaling of the pressure gradient dissipation has been used to suggest a modification of AUSM+-up that allows acoustic simulations of low Mach number flows. The accuracy improvement when the solution is compared to the one of the original AUSM+-up scheme indicates that the scaling identified in the Momentum Interpolation approach can be applied with advantage to Godunov-type schemes .

The MAVERIC test facility has been significantly upgraded with the acquisition of a complete GPU-based system (hardware+software) that speeds up by a factor of 10 the processing of the PIV data. The strong sensitivity of the flow topology to the presence of an acoustic standing wave in the cross-flow has been clearly evidenced. The presently available measurements give already the possibility of extracting numerous velocity profiles for a future fruitful LES assessment. The dedicated 1-jet experiment for DNS assessment will start at the beginning of 2013 .

Although DNS is mostly used in simplified geometries, issues remain for properly imposing boundary conditions. Indeed, considering for example an inflow boundary condition (BC), a number of variables depending on the subsonic or supersonic nature of the flow must be suitably imposed. As far as the velocity is concerned, it is highly desirable to prescribe boundary conditions with statistics which will match as much as possible those encountered in practice while controlling the reflective nature of the boundary. This can be highly beneficial to drastically reduce the computational domain, thus reducing the computational time. It has to be checked though that the best identified methodology suitable for the continuous problem is still compatible with the methods of resolution adopted to solve the related discrete problem.The long-term objective is to develop, implement and test an efficient method to prescribe boundary conditions for the DNS simulation of a jet in cross-flow. The focus here will be made on the constraints brought about by the compressible and low Mach nature of the flow. Accordingly, the successful low Mach number compressible laminar flow simulation will be considered as the criterion of success of the post-doc. Project: The activity will begin by properly identifying the different sets of physical inlet/outlet physical boundary conditions that are relevant for the low Mach compressible nature of the flow to be simulated; In that framework, a specific analysis of the popular Navier-Stokes characteristic boundary condition (NSCBC) will be carried out in the context of a low Mach number viscous flow. Second, the compatibility of these NSCBC’s with the finite element DG formulation retained in the Aerosol library will be investigated in depth in order to identify any potential incompatibility and the way to overcome it, if necessary. Then, the methodology for combining these BC’s with the various flux schemes and methods of solution of Aerosol will be developed. The programming of the proposed methodology in Aerosol will be carried out in a parallel environment. Then, a set of unitary tests will be defined and progressively addressed. Last, the simulation of a laminar low-Mach jet in cross-flow configuration will be carried out.Yann Moguen has been recruited on November 2012 to take up that post-doct position. The Conseil régional d'Aquitaine 6-month funding is supplemented by funding from the European programme IMPACT-AE so that the total duration of the post-doct will be 12 months.

In the litterature, the targeted direct numerical simulation (DNS) of a jet in a subsonic crossflow at low Mach number has been carried out by solving the zero Mach number Navier Stokes equations i.e. without acoustics. The reader is referred to the work by Muppidi and Mahesh (2007) or by Bagheri et al. (2009). Such an approach is acceptable since in a real combustion chamber, the Mach number is rarely above 0.3 and as long as thermo-acoustic instabilities are not to be dealt with. However, in the present project, it has been decided to adopt a compressible framework in order to be able to study in the future the interaction of a jet with a crossflow where a standing acoustic wave is present which corresponds to the configuration presently studied in the framework of the EU funded KIAI programme Workpackage 3.1). To the best of our knowledge, no DNS of an inclined turbulent JICF with a DG based compressible flow solver has been carried out so far. So a thesis work breakdown on that topic has been established as follows:

Year 1: Understanding the industrial and contractual context. Asymptotic analysis for small Mach numbers of the continuous problem. Study of the various alternatives for discretization schemes at low Mach number. Establishing the link with schemes adapted for zero Mach number flows. Writing of the corresponding thesis chapter; Writing a communication for an international symposium. Participating in a summer school on numerical simulation.

Year 2: Implementation of the schemes which exhibit a satisfactory asymptotic behavior at low mach number. Carrying out a DNS of an isothermal single jet in cross flow configuration with and without yaw angle in the framework of the IMPACT-AE programme. Analysis of the results, comparison with existing experimental data available in the team. Writing of the corresponding thesis chapter. Writing and submission of a journal paper.

Year 3: Improvement of the schemes if necessary. Carrying out the DNS of a cold jet in a hot crossflow configuration with and without yaw angle in the framework of the IMPACT-AE programme. Analysis of the results. Writing of the corresponding thesis chapter. Thesis defense.

Thus a thesis proposal has been established and submitted to the Conseil Général des Pyrénées Atlantiques who agreed to fund 18 months of this thesis. The remaining 18 months will be funded through the European programme IMPACT-AE. The recruitment procedure was launched in June 2012 for a provisional starting date in January 2013.

We are presently participating in the CNRS GIS (Groupement d'Intérêt Scientifique) which is provisionally called "Super-calcul en Combustion et en Mécanique des Fluides dans les Géométries Complexes" and is led by CORIA. A license agreement has been signed with CORIA to permit the installation of the code Yales 2. This installation has been completed on the LMA cluster by the end of december 2012 and the first test will begin in january 2013 in the framework of our benchmarking activity.

Jointly with the team Bacchus and with ONERA, we participated to the
project *Colargol*, which aimed at comparing implementations and
performances of high order finite elements methods implemented in our library
Aerosol, and in the high order discontinuous Galerkin library
Aghora developed at ONERA. For making fair comparisons
with this library, we had to extend our library to three dimensions, and to
finish the first parallel version of the code. Our first conclusions is the
necessity of stocking all geometrical terms of the finite elements
methods (Jacobian, Jacobian matrices, etc...) for having good
performances. We are still running the comparison tests on the Mésocentre
de Calcul Intensif Aquitain.

Program: Propulsion

Project acronym: IMPACT-AE

Project title: Intelligent Design Methodologies for Low Pollutant Combustors for Aero-Engines

Duration: 01/11/2011 - 31/10/2015

Coordinator: Roll Royce Deutschland

Other partners:

France: Insa of Rouen, ONERA, Snecma, Turbomeca.

Germany: Rolls-Royce Deutschland, MTU Aeo Engine Gmbh, DLR, Technology Institute of Karlsruhe, University of Bundeswehr (Munich)

Italy: AVIOPROP SRL, AVIO S.P.A., University of Florence

United Kingdom: Rolls Royce PLC, Cambridge University, Imperial College od Science, Technology and Medecine, Loughborough University.

Abstract: The environmental benefits of low emissions lean burn technology in reducing NOx emissions up to 80only be effective when these are deployed to a large range of new aero-engine applications. While integrating methodologies for advanced engine architectures and thermodynamic cycles. It will support European engine manufacturers to pick up and keep pace with the US competitors, being already able to exploit their new low emission combustion technology to various engine applications with short turn-around times. Key element of the project will be the development and validation of design methods for low emissions combustors to reduce NOx and CO emissions by an optimization of the combustor aero-design process. Preliminary combustor design tools will be coupled with advanced parametrisation and automation tools. Improved heat transfer and NOx models will increase the accuracy of the numerical prediction. The advanced representation of low emission combustors and the capability to investigate combustor scaling effects allow an efficient optimisation of future combustors targeting a cut of combustor development time by 50work packages: WP1‘Development of smart design methodologies for clean combustion’ as central WP to deliver the new methodology for combustor design, WP2’Modelling and design of advanced combustor wall cooling concepts’ for combustor liner design definition as key technology area, WP3’Technology validation by detailed flame diagnostics’ to substantiate fuel injector design rules implemented into the design methodology and WP4’Methodology demonstration for efficient low NOx combustors’ will validate the combustor design. The consortium consists of all major aero-engine manufactures in Europe, 7 universities and 3 research establishments with recognised experience in low emission combustion research and 10 SMEs. The contribution of our team is to create a direct numerical simulations (DNS) database relevant to the configuration of film cooling for subsequent improvement of RANS based simulations of isothermal and non isothermal wall flows with discrete mass transfer.

Dr. A. Naïmanova, Institute of Mathematics, Almaty, Kazakhstan came for a one-month stay in September 2012.

The team members have been invited to review for the following journals:

Journal of Computational Physics [VP]

International Journal for Numerical Methods in Fluids [PB, VP]

Computers and FLuids [VP]

SIAM Journal on Applied Mathematics [VP]

Shock Waves [VP]

ESAIM: Mathematical Modelling and Numerical Analysis [VP]

Mathematics and Computers in Simulation [VP]

Review for the Engineering Computations [VP]

Combustion and Flame [PB]

Journal of Aerospace Engineering [PB]

Computational Thermal Science [PB]

Licence :

TP Transferts thermiques, 8h, L1, IUT-GTE-UPPA, Pau, France. [PB]

Programmation, 50h, L3, ENSGTI-UPPA, France [EF]

TP Composants, 40h, L3, ENSGTI-UPPA, France [EF]

Master :

An introduction to the numerical simulation of reacting flows, 15h, M2, ISAE-SupAéro, Toulouse, France. [PB]

Machines hydrauliques, 30h, M1, ENSGTI-UPPA, France [TK]

Machines aérauliques, 30h, M1, ENSGTI-UPPA, France [TK]

Thermo-économie, 30h M2, ENSGTI-UPPA, France [TK]

Modélisation des écoulements diphasiques, 30h, M1, ENSGTI-UPPA, France [TK]

TP systèmes, 50h, M1, ENSGTI-UPPA, France [TK]

Simulation industrielle, 40h, M1, ENSGTI-UPPA, France [EF]

Fluides compressibles, 20h, M1, ENSGTI-UPPA, France [EF]

Combustion industrielle, 30h, M1, ENSGTI-UPPA, France [EF]

Réseaux de chaleur, 4h, M2, ENSGTI-UPPA, France [EF]

Géothermie, 4h, M2, ENSGTI-UPPA, France [EF]

Biomasse, 4h, M2, ENSGTI-UPPA, France [EF]

PhD (PB, Referee) :J. Primus, Détermination de l’impédance acoustique de matériaux absorbants en écoulement par méthode inverse et mesures LDV, Université de Toulouse, 6 December 2012. Thesis advisors : F. Simon and E. Piot.

PhD (PB, external examiner) :L. Cheng, Combined PIV/PLIF measurements in a high swirl-fuel injector flowfield, Loughborough University, 19 december 2012. Thesis advisor: A. Spencer.