Pascal MENEGAZZI | Valeo - Academia.edu (original) (raw)

Papers by Pascal MENEGAZZI

Research paper thumbnail of A New Approach to the Modelling of Engine Cooling Systems

Oil & Gas Science and Technology-revue De L Institut Francais Du Petrole, Sep 1, 1997

L'optimisation des circuits de refroidissement internes est devenue une Žtape indispensable lors ... more L'optimisation des circuits de refroidissement internes est devenue une Žtape indispensable lors de la conception des moteurs actuels. Bien que la modŽlisation numŽrique tridimensionnelle des phŽnom•nes hydrodynamiques se soit rŽvŽlŽe un outil bien adaptŽ ce type d'application, elle implique la nŽcessitŽ de consacrer un temps tr•s long ˆ la phase prŽliminaire de gŽnŽration des maillages. Ceci reste certainement un obstacle majeur l 'intŽgration systŽmatique de ces mŽthodes dans les processus de dŽveloppement des moteurs. Cet article propose une approche originale du probl•me, permettant de gŽnŽrer des maillages 3D pour des circuits internes de formes complexes, dans des cas o• les mŽthodes traditionnelles de maillage s'av•rent inapplicables dans des temps raisonnables. Les maillages non structurŽs de tŽtra•dres obtenus de cette mani•re, sont directement utilisables pour des calculs d'hydrodynamique au moyen du code N3S, mettant en Ïuvre des mŽthodes numŽriques par ŽlŽments finis. Pour illustrer cette mŽthode, un exemple complet est prŽsentŽ, depuis l'Žtape de gŽnŽration des maillages jusqu'au calcul hydrodynamique. A NEW APPROACH TO THE MODELLING OF ENGINE COOLING SYSTEMS Optimizing the internal cooling circuits has become vital for the design of modern engines. Although three dimensional (3D) Computational Fluid Dynamics (CFD) proves to be a powerful tool, well suited to this kind of application, a very long time is still spent in the mesh generation step. This is certainly a major obstacle to its systematic use in the engine development process.

Research paper thumbnail of A Simulation Tool for Vehicle Emissions, Consumption and Performance Analysis - Applications to DPF Modeling and DID Turbocharged Engine Control Design

SAE Technical Paper Series, Sep 14, 2006

Research paper thumbnail of Development of a Coupling Approach between 0D D.I. Diesel Combustion and Pollutant Models: Application to a Transient Engine Evolution

Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles, Jul 1, 2008

-Modélisation 0D des émissions polluantes Diesel : développement et utilisation d'une méthodologi... more -Modélisation 0D des émissions polluantes Diesel : développement et utilisation d'une méthodologie de couplage entre un modèle de combustion Diesel 0D et un modèle de polluants-Afin de satisfaire les normes de pollution de plus en plus sévères, les constructeurs automobiles ont généralisé l'utilisation du contrôle électronique du moteur. Ce contrôle permet de s'assurer en permanence du fonctionnement optimum du moteur en adéquation avec la demande de couple du conducteur et le bon fonctionnement des organes de post-traitement. Le développement et la calibration des algorithmes de contrôle moteur ne peuvent se faire qu'avec une compréhension fine du comportement dynamique du groupe motopropulseur, couplé à sa ligne d'échappement. Jusqu'à présent, un grand nombre d'essais sur banc moteur et sur véhicule était nécessaire pour atteindre des niveaux de calibration suffisants pour le contrôleur. Afin de diminuer les coûts de production, il devient de plus en plus important de limiter ces essais expérimentaux en ayant recours à la simulation. Dans ce contexte, il est important de disposer de modèles de combustion et de polluants prédictifs, calibrés sur un nombre limité de points expérimentaux et utilisables sur une grande plage de points de fonctionnement moteur. Ce papier présente un modèle 0D de combustion Diesel, basé sur le modèle de Barba [Barba C. et al. (2000)-A Phenomenological Combustion Model for Heat Release Rate Prediction in High Speed DI Diesel Engines with Common Rail Injection, SAE Technical Paper 2000-01-2933], permettant en particulier de prendre en compte l'impact de la multi-injection sur le déroulement de la combustion. Le modèle répartit chaque injection en deux zones : une première pour la flamme de pré-mélange lors du début de la combustion et une autre pour la flamme de diffusion. Afin de simuler la production de polluants, un modèle de mélange indexé sur l'énergie cinétique turbulente générée par le spray a été introduit. Ce dernier modèle permet de créer une zone de gaz brûlés dans la chambre de combustion dans laquelle les émissions de CO, NO x et suies sont calculées. Les modèles de polluants sont d'abord validés en utilisant le logiciel CHEMKIN et des résultats de calculs 3D. Des résultats expérimentaux obtenus sur un moteur 4 cylindres Diesel à injection directe en fonctionnement stabilisé sont ensuite utilisés pour valider et calibrer le couplage entre le modèle de combustion et les modèles de polluants. Le simulateur ainsi calibré est enfin utilisé pour simuler un fonctionnement en transitoire de charge du moteur.

Research paper thumbnail of Numerical Study on Knock for an SI Engine by Thermally Coupling Combustion Chamber and Cooling Circuit Simulations

SAE technical paper series, Mar 3, 2003

The present research focuses on the understanding and improved prediction of knock at full load i... more The present research focuses on the understanding and improved prediction of knock at full load in a four-cylinder passenger car spark-ignition (SI) engine using computational fluid dynamics (CFD) methodology. The emphasis is on the possibility of controlling the knock limit via optimised engine cooling mechanisms. To date, CFD simulations of the combustion chamber and cooling circuit are performed separately, while chamber wall temperatures are derived from either experiments or experience. This, however, entails the risk of employing inadequate boundary and hence in-cylinder conditions for a combustion and knock simulation. CFD simulations are performed for all four combustion chambers and metal components, including the cooling circuit. Both types of simulations are thermally coupled via the conditions on the chamber walls. Several engine cycles are simulated with the knock model switched off to converge in terms of wall temperatures and in-cylinder conditions, therefore allowing for more appropriate conditions in the combustion chambers. Thereafter one engine cycle is calculated including the knock model. A sensitivity study for wall temperatures on knock was performed. The CFD results were compared against local wall temperature measurements on the cylinder head and engine block. The predictions reveal a highly non-uniform temperature distribution on the chamber walls. It is also demonstrated that knock is influenced primarily by the wall temperatures via the resulting thermodynamic state of the in-cylinder mixture due to wall heat transfer rather than via local wall temperature effects.

Research paper thumbnail of Development and Application of a 0D D.I. Diesel combustion model for Emissions Prediction

SAE technical paper series, Jul 23, 2007

Research paper thumbnail of A New Tool for Advanced Vehicle Simulations

SAE technical paper series, Sep 11, 2005

To overcome future stringent regulations on pollutant emissions and to decrease CO emissions and ... more To overcome future stringent regulations on pollutant emissions and to decrease CO emissions and fuel consumption, hybrid vehicles seem to be one of the near future most promising technologies. This type of car uses complex energy management and control strategy. Simulation can be very useful for the development of such a control system. This paper highlights a new library developed under the AMESim software that enables the simulation of complex interactive systems in vehicles. In addition, the possibility to combine with other AMESim modules, allows the users to add more complexity to any of the sub-components of the vehicle. As an illustration of this new tool capability, we propose in this paper a simulation example of the Prius, the most known hybrid vehicle which was the first commercial vehicle in 1997 and selected as the 2004 Car of the Year in Europe. Comparisons between measurements and simulations of the response of different components are presented on different driving cycles.

Research paper thumbnail of Rapport final du projet VECSim. Rapport de synthèse

HAL (Le Centre pour la Communication Scientifique Directe), 2007

Research paper thumbnail of Application of a New 1D Combustion Model to Gasoline Transient Engine Operation

SAE Technical Paper Series, 2005

Research paper thumbnail of A New Coupling Approach Using a 1D System Simulation Software and a 3D Combustion Code Applied to Transient Engine Operation

SAE Technical Paper Series, Oct 25, 2004

Research paper thumbnail of Understanding and Improving Evaporative Engine Cooling at High Load, High Speed by Engine Tests and 3D Calculations

SAE Technical Paper Series, 1997

Research paper thumbnail of X-Ray CT-Scan Digitizing for the Inspection and Computational Analysis of Complex Engine Parts

SAE Technical Paper Series, 1998

Research paper thumbnail of NSDI-3: A Small Bore GDI Engine

SAE Technical Paper Series, 1999

Research paper thumbnail of MBSE Approach Adapted to Vehicle Energy Consumption Optimization

Le Centre pour la Communication Scientifique Directe - HAL - Diderot, Jun 11, 2017

Research paper thumbnail of Convection naturelle dans les structures geologiques poreuses: etude numerique bidimensionnelle et stabilite des ecoulements

INIST T 70703 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc

Research paper thumbnail of MBSE Approach for Vehicle Powertrain System Design

Complex Systems Design & Management (CSD&M) conference, Dec 12, 2017

Research paper thumbnail of Modeling the oxidative regeneration process taking into account the effect of water vapor

Доклады Башкирского университета, 2020

dustrial process does not harm the ecology of the environment, therefore it is important to monit... more dustrial process does not harm the ecology of the environment, therefore it is important to monitor the gases emitted during the process. Analysis of the data shows that when water is added during regeneration, the rate of carbon combustion will be faster than when blowing with oxygen. The amount of carbon monoxide emitted when water is added is less.

Research paper thumbnail of Parallel industrial incompressible CFD calculations with HPCN3S

Lecture Notes in Computer Science, 1996

In this paper we give an overview of the parallelization of the 3-D CFD package N3S for complex i... more In this paper we give an overview of the parallelization of the 3-D CFD package N3S for complex industrial incompressible flow simulation on parallel distributed memory platforms using the message passing paradigm. Parallel performances on IBM SP2 are presented on some today's representative needs in industry such as flow simulation in a car engine cooling circuit (IFP) or natural convection in pressure suppression pool (CISE).

Research paper thumbnail of Improving overhead transmission line usage efficiency on a caribbean island power system

2014 IEEE PES T&D Conference and Exposition, 2014

Research paper thumbnail of Design of an electric supercharger for downsized engines

MTZ worldwide, 2013

For many applications, the electric supercharger is used as a secondary charging device in conjun... more For many applications, the electric supercharger is used as a secondary charging device in conjunction with a turbocharger. In such cases, the position of the electric supercharger in the engine air-path is an important factor influencing air-charging performance. Different configurations were quickly evaluated using system simulation, ❷. On the one hand, it was observed that an upstream configuration where the electric supercharger was installed at the turbocharger inlet has a lower air-charging performance because the electric supercharger compressed the air first. This means that the turbocharger works with a higher inlet pressure and higher temperature. This pushes the turbocharger’s operating point closer to the surge line with a lower isentropic efficiency. On the other hand, a downstream configuration where the electric supercharger is installed at the turbocharger outlet provides better system performance because it has less influence on the turbocharger. In this case, it also leads to poorer thermal conditions for the electric supercharger, which may even require an additional intercooler between the turbocharger and the electric supercharger. Finally, the choice between configurations is always a multi-criteria decision between thermal combustion tolerance for diesel or gasoline, performance/cost ratio, and other integration problems. Open image in new window ❶ Example of models with upstream and downstream configuration used for system analysis Since the objective was to provide high-level performance results, the engine was equipped with a larger turbocharger in combination with the new electric supercharger. The longer time-to-torque response inherent to the larger turbocharger is compensated by the electric supercharger’s operation. With this kind of configuration, the small 1.2-l PFI gasoline engine provides the driver with a very impressive torque characteristic, ❸. In practice, the larger turbocharger alone is able to match the target of above 2250 rpm, but the benefits of applying the electric supercharger set-up are clearly demonstrated in ➂. There is a tremendous torque increase at low rpm. In addition, the resulting engine still maintains very good torque performance: the time-to-torque is less than 1 s for all engine speeds and significantly better than the baseline engine below 2000 rpm. Open image in new window ❸ Steady-state and transient performance of the 1.2-l PFI engine with the electric supercharger

Research paper thumbnail of ST2D3D: A Finite-Element Program to Compute Stability Criteria for Natural Convection in Complex Porous Structures

Numerical Heat Transfer, Part B: Fundamentals, 1996

... Riahi's work [11]gives a good Received 7 November 1994; accepted 25 July 1995. Part of t... more ... Riahi's work [11]gives a good Received 7 November 1994; accepted 25 July 1995. Part of this work was funded by the research group TRABAS from the CNRS. The present address for P. Menegazzi is IFP, dept. ... (15a) (15b) (15c) 1 e =-g g 1 A=-A* Aref H h'=~11 Are! ...

Research paper thumbnail of A New Approach to the Modelling of Engine Cooling Systems

Oil & Gas Science and Technology-revue De L Institut Francais Du Petrole, Sep 1, 1997

L'optimisation des circuits de refroidissement internes est devenue une Žtape indispensable lors ... more L'optimisation des circuits de refroidissement internes est devenue une Žtape indispensable lors de la conception des moteurs actuels. Bien que la modŽlisation numŽrique tridimensionnelle des phŽnom•nes hydrodynamiques se soit rŽvŽlŽe un outil bien adaptŽ ce type d'application, elle implique la nŽcessitŽ de consacrer un temps tr•s long ˆ la phase prŽliminaire de gŽnŽration des maillages. Ceci reste certainement un obstacle majeur l 'intŽgration systŽmatique de ces mŽthodes dans les processus de dŽveloppement des moteurs. Cet article propose une approche originale du probl•me, permettant de gŽnŽrer des maillages 3D pour des circuits internes de formes complexes, dans des cas o• les mŽthodes traditionnelles de maillage s'av•rent inapplicables dans des temps raisonnables. Les maillages non structurŽs de tŽtra•dres obtenus de cette mani•re, sont directement utilisables pour des calculs d'hydrodynamique au moyen du code N3S, mettant en Ïuvre des mŽthodes numŽriques par ŽlŽments finis. Pour illustrer cette mŽthode, un exemple complet est prŽsentŽ, depuis l'Žtape de gŽnŽration des maillages jusqu'au calcul hydrodynamique. A NEW APPROACH TO THE MODELLING OF ENGINE COOLING SYSTEMS Optimizing the internal cooling circuits has become vital for the design of modern engines. Although three dimensional (3D) Computational Fluid Dynamics (CFD) proves to be a powerful tool, well suited to this kind of application, a very long time is still spent in the mesh generation step. This is certainly a major obstacle to its systematic use in the engine development process.

Research paper thumbnail of A Simulation Tool for Vehicle Emissions, Consumption and Performance Analysis - Applications to DPF Modeling and DID Turbocharged Engine Control Design

SAE Technical Paper Series, Sep 14, 2006

Research paper thumbnail of Development of a Coupling Approach between 0D D.I. Diesel Combustion and Pollutant Models: Application to a Transient Engine Evolution

Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles, Jul 1, 2008

-Modélisation 0D des émissions polluantes Diesel : développement et utilisation d'une méthodologi... more -Modélisation 0D des émissions polluantes Diesel : développement et utilisation d'une méthodologie de couplage entre un modèle de combustion Diesel 0D et un modèle de polluants-Afin de satisfaire les normes de pollution de plus en plus sévères, les constructeurs automobiles ont généralisé l'utilisation du contrôle électronique du moteur. Ce contrôle permet de s'assurer en permanence du fonctionnement optimum du moteur en adéquation avec la demande de couple du conducteur et le bon fonctionnement des organes de post-traitement. Le développement et la calibration des algorithmes de contrôle moteur ne peuvent se faire qu'avec une compréhension fine du comportement dynamique du groupe motopropulseur, couplé à sa ligne d'échappement. Jusqu'à présent, un grand nombre d'essais sur banc moteur et sur véhicule était nécessaire pour atteindre des niveaux de calibration suffisants pour le contrôleur. Afin de diminuer les coûts de production, il devient de plus en plus important de limiter ces essais expérimentaux en ayant recours à la simulation. Dans ce contexte, il est important de disposer de modèles de combustion et de polluants prédictifs, calibrés sur un nombre limité de points expérimentaux et utilisables sur une grande plage de points de fonctionnement moteur. Ce papier présente un modèle 0D de combustion Diesel, basé sur le modèle de Barba [Barba C. et al. (2000)-A Phenomenological Combustion Model for Heat Release Rate Prediction in High Speed DI Diesel Engines with Common Rail Injection, SAE Technical Paper 2000-01-2933], permettant en particulier de prendre en compte l'impact de la multi-injection sur le déroulement de la combustion. Le modèle répartit chaque injection en deux zones : une première pour la flamme de pré-mélange lors du début de la combustion et une autre pour la flamme de diffusion. Afin de simuler la production de polluants, un modèle de mélange indexé sur l'énergie cinétique turbulente générée par le spray a été introduit. Ce dernier modèle permet de créer une zone de gaz brûlés dans la chambre de combustion dans laquelle les émissions de CO, NO x et suies sont calculées. Les modèles de polluants sont d'abord validés en utilisant le logiciel CHEMKIN et des résultats de calculs 3D. Des résultats expérimentaux obtenus sur un moteur 4 cylindres Diesel à injection directe en fonctionnement stabilisé sont ensuite utilisés pour valider et calibrer le couplage entre le modèle de combustion et les modèles de polluants. Le simulateur ainsi calibré est enfin utilisé pour simuler un fonctionnement en transitoire de charge du moteur.

Research paper thumbnail of Numerical Study on Knock for an SI Engine by Thermally Coupling Combustion Chamber and Cooling Circuit Simulations

SAE technical paper series, Mar 3, 2003

The present research focuses on the understanding and improved prediction of knock at full load i... more The present research focuses on the understanding and improved prediction of knock at full load in a four-cylinder passenger car spark-ignition (SI) engine using computational fluid dynamics (CFD) methodology. The emphasis is on the possibility of controlling the knock limit via optimised engine cooling mechanisms. To date, CFD simulations of the combustion chamber and cooling circuit are performed separately, while chamber wall temperatures are derived from either experiments or experience. This, however, entails the risk of employing inadequate boundary and hence in-cylinder conditions for a combustion and knock simulation. CFD simulations are performed for all four combustion chambers and metal components, including the cooling circuit. Both types of simulations are thermally coupled via the conditions on the chamber walls. Several engine cycles are simulated with the knock model switched off to converge in terms of wall temperatures and in-cylinder conditions, therefore allowing for more appropriate conditions in the combustion chambers. Thereafter one engine cycle is calculated including the knock model. A sensitivity study for wall temperatures on knock was performed. The CFD results were compared against local wall temperature measurements on the cylinder head and engine block. The predictions reveal a highly non-uniform temperature distribution on the chamber walls. It is also demonstrated that knock is influenced primarily by the wall temperatures via the resulting thermodynamic state of the in-cylinder mixture due to wall heat transfer rather than via local wall temperature effects.

Research paper thumbnail of Development and Application of a 0D D.I. Diesel combustion model for Emissions Prediction

SAE technical paper series, Jul 23, 2007

Research paper thumbnail of A New Tool for Advanced Vehicle Simulations

SAE technical paper series, Sep 11, 2005

To overcome future stringent regulations on pollutant emissions and to decrease CO emissions and ... more To overcome future stringent regulations on pollutant emissions and to decrease CO emissions and fuel consumption, hybrid vehicles seem to be one of the near future most promising technologies. This type of car uses complex energy management and control strategy. Simulation can be very useful for the development of such a control system. This paper highlights a new library developed under the AMESim software that enables the simulation of complex interactive systems in vehicles. In addition, the possibility to combine with other AMESim modules, allows the users to add more complexity to any of the sub-components of the vehicle. As an illustration of this new tool capability, we propose in this paper a simulation example of the Prius, the most known hybrid vehicle which was the first commercial vehicle in 1997 and selected as the 2004 Car of the Year in Europe. Comparisons between measurements and simulations of the response of different components are presented on different driving cycles.

Research paper thumbnail of Rapport final du projet VECSim. Rapport de synthèse

HAL (Le Centre pour la Communication Scientifique Directe), 2007

Research paper thumbnail of Application of a New 1D Combustion Model to Gasoline Transient Engine Operation

SAE Technical Paper Series, 2005

Research paper thumbnail of A New Coupling Approach Using a 1D System Simulation Software and a 3D Combustion Code Applied to Transient Engine Operation

SAE Technical Paper Series, Oct 25, 2004

Research paper thumbnail of Understanding and Improving Evaporative Engine Cooling at High Load, High Speed by Engine Tests and 3D Calculations

SAE Technical Paper Series, 1997

Research paper thumbnail of X-Ray CT-Scan Digitizing for the Inspection and Computational Analysis of Complex Engine Parts

SAE Technical Paper Series, 1998

Research paper thumbnail of NSDI-3: A Small Bore GDI Engine

SAE Technical Paper Series, 1999

Research paper thumbnail of MBSE Approach Adapted to Vehicle Energy Consumption Optimization

Le Centre pour la Communication Scientifique Directe - HAL - Diderot, Jun 11, 2017

Research paper thumbnail of Convection naturelle dans les structures geologiques poreuses: etude numerique bidimensionnelle et stabilite des ecoulements

INIST T 70703 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc

Research paper thumbnail of MBSE Approach for Vehicle Powertrain System Design

Complex Systems Design & Management (CSD&M) conference, Dec 12, 2017

Research paper thumbnail of Modeling the oxidative regeneration process taking into account the effect of water vapor

Доклады Башкирского университета, 2020

dustrial process does not harm the ecology of the environment, therefore it is important to monit... more dustrial process does not harm the ecology of the environment, therefore it is important to monitor the gases emitted during the process. Analysis of the data shows that when water is added during regeneration, the rate of carbon combustion will be faster than when blowing with oxygen. The amount of carbon monoxide emitted when water is added is less.

Research paper thumbnail of Parallel industrial incompressible CFD calculations with HPCN3S

Lecture Notes in Computer Science, 1996

In this paper we give an overview of the parallelization of the 3-D CFD package N3S for complex i... more In this paper we give an overview of the parallelization of the 3-D CFD package N3S for complex industrial incompressible flow simulation on parallel distributed memory platforms using the message passing paradigm. Parallel performances on IBM SP2 are presented on some today's representative needs in industry such as flow simulation in a car engine cooling circuit (IFP) or natural convection in pressure suppression pool (CISE).

Research paper thumbnail of Improving overhead transmission line usage efficiency on a caribbean island power system

2014 IEEE PES T&D Conference and Exposition, 2014

Research paper thumbnail of Design of an electric supercharger for downsized engines

MTZ worldwide, 2013

For many applications, the electric supercharger is used as a secondary charging device in conjun... more For many applications, the electric supercharger is used as a secondary charging device in conjunction with a turbocharger. In such cases, the position of the electric supercharger in the engine air-path is an important factor influencing air-charging performance. Different configurations were quickly evaluated using system simulation, ❷. On the one hand, it was observed that an upstream configuration where the electric supercharger was installed at the turbocharger inlet has a lower air-charging performance because the electric supercharger compressed the air first. This means that the turbocharger works with a higher inlet pressure and higher temperature. This pushes the turbocharger’s operating point closer to the surge line with a lower isentropic efficiency. On the other hand, a downstream configuration where the electric supercharger is installed at the turbocharger outlet provides better system performance because it has less influence on the turbocharger. In this case, it also leads to poorer thermal conditions for the electric supercharger, which may even require an additional intercooler between the turbocharger and the electric supercharger. Finally, the choice between configurations is always a multi-criteria decision between thermal combustion tolerance for diesel or gasoline, performance/cost ratio, and other integration problems. Open image in new window ❶ Example of models with upstream and downstream configuration used for system analysis Since the objective was to provide high-level performance results, the engine was equipped with a larger turbocharger in combination with the new electric supercharger. The longer time-to-torque response inherent to the larger turbocharger is compensated by the electric supercharger’s operation. With this kind of configuration, the small 1.2-l PFI gasoline engine provides the driver with a very impressive torque characteristic, ❸. In practice, the larger turbocharger alone is able to match the target of above 2250 rpm, but the benefits of applying the electric supercharger set-up are clearly demonstrated in ➂. There is a tremendous torque increase at low rpm. In addition, the resulting engine still maintains very good torque performance: the time-to-torque is less than 1 s for all engine speeds and significantly better than the baseline engine below 2000 rpm. Open image in new window ❸ Steady-state and transient performance of the 1.2-l PFI engine with the electric supercharger

Research paper thumbnail of ST2D3D: A Finite-Element Program to Compute Stability Criteria for Natural Convection in Complex Porous Structures

Numerical Heat Transfer, Part B: Fundamentals, 1996

... Riahi's work [11]gives a good Received 7 November 1994; accepted 25 July 1995. Part of t... more ... Riahi's work [11]gives a good Received 7 November 1994; accepted 25 July 1995. Part of this work was funded by the research group TRABAS from the CNRS. The present address for P. Menegazzi is IFP, dept. ... (15a) (15b) (15c) 1 e =-g g 1 A=-A* Aref H h'=~11 Are! ...