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Ta Phuoc Loc
Two main purposes determine the trend of our works.
The first one interests the fundamental works on basic phenomena of real fluid dynamics. In particular, the separation phenomenon around a bluff body, an airfoil, a blade, the generation of the vorticity at the wall and their transport and effects in the wake, the transition phenomena (steady - unsteady , laminar - turbulent ) , are our principal preoccupations.
The second one is oriented to applied fluid mechanics engineering. Our experience and knowledge in computational fluid dynamics, are used to treat industrial problems.
To reach these goals , simultaneous research is made :
- on the amelioration of classic numerical methods and the creation of new methods suited to new generation of parallel computers
- on the validation of these numerical methods by comparison with experimental visualization and measurements particularly in the domain of unsteady flows
- and on the detailed analysis of complex fluid flow phenomena
Generally, research realized in this group are carried out in collaboration with academic laboratories as Laboratoire de Mécanique des Fluides de Poitiers, LIMHP de Villetaneuse, public research centers as ONERA, Bassin des Carènes de Paris , or industrial companies as SEP , SNECMA... and supported financially by public and industrial contracts
Our researches are regrouped actually in four themes.
TOPIC 1- NUMERICAL METHODS FOR COMPUTATIONAL FLUID MECHANICS( J.L. Guermond )
Are classified in this theme studies concerning the choice of the mathematical formulation and the improvements of numerical methods, for the resolution of unsteady Navier Stokes equations.
Numerical method studies developed in the group are presently focused on the time accuracy of the projection method, applied to the pressure-velocity formulation of Navier Stokes equations. The aim is to improve the accuracy of the time stepping scheme, which is needed for long time large eddy simulation. Some new techniques have been proposed and theoretical results obtained are confirmed by numerical experiments. The extension of these techniques to finite elements methods has been also achieved in collaboration with Professor L. Quartapelle . Some examples of numerical results are given in this report .
In parallel with studies dealing with pressure-velocity formulation, in connection with some difficulties met when external flows are to be studied , research on vorticity-velocity formulation of Navier Stokes equations has been investigated at LIMSI. Important progress have been obtained. Theoretical equivalence between pressure-velocity , vorticity-velocity formulations has been demonstrated. The number of equations to be solved has been reduced. New numerical schemes satisfying divergence free constraints of velocity and vorticity fields have been developed.
Flow around multi-bodies or interaction flow between several obstacles in relative movement are often met in realistic cases . A soft numerical method to solve any case is the domain decomposition method linking the advantages of the eulerian (FD or FE ) and lagrangian ( vortex particles ) techniques . In order to extend to 3D the domain decomposition methods mixing eulerian and lagrangian domains developed previously at LIMSI , the 2D classical stream function vorticity formulation used in eulerian domain is replaced by velocity pressure formulation or velocity vorticity formulation . Unsteady flows around a isolated 3D obstacles and unsteady interaction flows between a circular cylinder and a NACA0012 airfoil have been studied and satisfactory results are obtained .
TOPIC 2 - DIRECT NUMERICAL SIMULATION AND LARGE EDDY SIMULATION OF UNSTEADY SEPARATED EXTERNAL INCOMPRESSIBLE VISCOUS FLOWS ( Ta Phuoc Loc )
Works in theme 2 are oriented to direct numerical simulation and large eddy simulation of unsteady separated viscous flows .
First at all ,the 2D flow approximation has been considered . So , high Reynolds number ( > 5x104 ) direct numerical and large eddy simulations have been realized . The aim is to analyse the validity of classical turbulence subgrid models in separated flows. Unsteady flows around a NACA0012 airfoil have been considered. Numerical results of DNS and LES are compared with experimental visualization in order to classify these subgrid models : a "good" model is one which does not destruct the large structure of the flow. Interesting results have been obtained, showing a too large dissipation of some models ( Smagorinsky , Balwin Lomax ). New models have been proposed in collaboration with the Aerodynamic Department of ONERA , based on vorticity , turbulent kinetic energy. Eddy viscosity introduced by these subgrid scale models vanishs naturally at the solid wall and anywhere the flow is fully resolved . Results obtained concerning unsteady flow around the NACA0012 airfoil are in good agreement with experimental visualizations and measurements . The extension of the models to other geometric configurations has been also realized showing a good behaviour of the proposed models .
Unsteady 3D flow around an obstacle is improving thanks to the progress realized in the velocity vorticity formulation .
Direct numerical simulations can be used for instant only for low or moderate Reynolds numbers because the technological limitations of actual computers . It is a tool adapted to study fundamental phenomena appearing in the transition from steady to unsteady regime . So , starting regime and periodic regime flow around a finite plate , a cube , a sphere fixed or in rotation have been studied for Reynolds numbers up to 1000 . These studies are made in collaboration with ONERA and the Laboratoire de Mécanique des fluides de Poitiers . Satisfactory comparisons with experimental visualizations and others numerical methods are obtained . Some results are given in this report .
TOPIC 3 - NUMERICAL SIMULATION OF UNSTEADY COMPRESSIBLE VISCOUS FLOWS ( C. Tenaud )
Steady hypersonic and unsteady subsonic compressible viscous flows around an obstacle are the dominant trend of theme 3.
Numerical methods developed previously at CEAT de Poitiers for simulation of steady hypersonic flow around a bluff body are applied now to simulate the rapid expansion of supercritical fluid , in collaboration with LIMHP de Villetaneuse who is in charge of experimental studies. The results obtained are very encouraging from a qualitative point of view : results seem to be in agreement with experiment data. However, some checks on these numerical results must be undertaken from quantitative point of view.
Modifications are brought to previous numerical schemes transforming steady algorithm to unsteady algorithm. The validation of the unsteady numerical method has been made on the comparison between numerical and experimental data.
This method is applied to study the influence of compressibility effects in the vortex - airfoil interaction. The aim is to give new information necessary to the construction of simplified models for aeroacoustic analysis.
Large eddy simulation for unsteady separated compressible fluid flow is introduced recently in this topic . Following the same process appied in incompressible fluid flows , classical subgrid scale models have been analyzed , pointing out their advantages and disadvantages . Modifications will be brought to adapt these models and news models may be proposed . Results concerning flow around the NACA0012 with incidence of 20deg. are presented in this report , showing the influence of Leonard and cross terms which are probably not negligible .
TOPIC 4 - TURBOMACHINES AND MARINE PROPELLERS OPTIMISATION DESIGN ( T.S. Luu )
Internal flows in turbomachines is one major research direction developed in this theme.
Numerical codes based on the S1 - S2 approximation have been established and are now extensively used to optimize the design of turbomachine blades, in particular for the ARIANE 5 H2 turbopump. This research was supported by SEP.
Using same S1 - S2 theory and similar algorithms a new method for the optimum design of heavily loaded marine propellers has been developed. In comparison with classic inviscid fluid theory method, this new approach permits to take into account the upstream rotational flow and to refine the blade design of the propeller.This research was realized in collaboration with Les Bassins d'Essai des Carènes de Paris and supported by a DRET contract.
These methods are generally based on the assumption of inviscid fluid, which limits their scope of applicability to operating regimes close to nominal point. To increase their range of validity, it is necessary to take into account unsteady and viscous effects, which is the subject of current research.
Some examples of results are given in this report, illustrating the position of our research in different topics.