Effet de la turbulence et de stratification atmosphérique sur la dynamique des tourbillons marginaux

Effect of turbulence and atmospheric stratification on the dynamics of trailing vortices

• Auteur / Autrice : Maël Benlarbi
• Direction : Jean-Philippe Laval, Vincent Brion
• Type : Projet de thèse
• Discipline(s) : Mécanique des milieux fluides
• Date : Inscription en doctorat le 01/10/2022
• Etablissement(s) : Université de Lille (2022-....)
• Ecole(s) doctorale(s) : ENGSYS Sciences de l'ingénierie et des systèmes
• Partenaire(s) de recherche : Laboratoire : LMFL Laboratoire de Mécanique des Fluides de Lille

Mots clés

Mots clés libres

Dynamique tourbillonaire

Turbulence de grille

Stratification atmosphér

Vélocimétrie par image de particules

Vortex dynamics

Grid generated turbulence

Atmospheric stratification

Particle image velocimetry

Résumé

Dans un environnement non stratifié, un avion génère un dipôle de tourbillons contrarotatifs. Au fur et à mesure que l'avion s'éloigne, cette paire de tourbillons descend et développe possiblement (cela dépend du taux de turbulence ambiant, essentiellement) deux types d'instabilités (tridimensionnelles), une à grande longueur d'onde [1] et une à faible longueur d'onde [2]. La connaissance du taux de décroissance de ces tourbillons en incluant les effets des conditions atmosphériques telles que la stratification de la densité est essentielle pour correctement caractériser le sillage d'un avion [3]. La stratification atmosphérique est connue pour modifier le profil de descente et changer les seuils d'apparition et la longueur d'onde des instabilités communes du cas non stratifié [4,5], à savoir les instabilités courte et le grande longueur d'onde, aussi appelée Widnall et Crow [1,6]. Des travaux théoriques récents [7] confirment qu'une stratification plus forte favorise la déstabilisation des longueurs d'onde plus courtes du sillage tourbillonnaire. Des résultats numériques suggèrent également que la stratification réduit la descente des tourbillons [8] mais très peu d'expériences existent [5] valider ces résultats. Bien qu'il existe différentes études sur l'effet de la stratification sur les tourbillons de bout d'aile, plusieurs questions importantes persistent. La première est celle de l'importance de la stratification en champ proche du sillage généré par l'objet portant. La plupart des études négligent ce problème et émettent l'hypothèse d'une configuration de sillage qui néglige la stratification au début du sillage. Le seuil où cette hypothèse est réalisée doit néanmoins être déterminé avec précision, car il pourrait éventuellement affecter l'état du sillage et sa dynamique.La seconde question est celle de la confirmation que le résultat théorique obtenu par Ortiz et al.[7], concernant les propriétés de stabilité du sillage en présence de stratification, sont bien observées dans les écoulements à plus grand nombre de Reynolds. Le travail expérimental de Delisi [5] suggère que c'est le cas, mais il ne fournit aucune indication de la structure de l'écoulement qui se cache derrière la dynamique de longueur d'onde plus courte. En particulier, le rôle du sillage secondaire formé par le couple barocline au-dessus des tourbillons dans une stratification légère à forte mérite une étude plus poussée pour comprendre sa formation et son interaction avec les tourbillons primaires. Références : [1] Crow, S. C. “Stability theory for a pair of trailing vortices” AIAA Vournal, 1970, vol. 8, no 12 [2] Roy, C., Leweke, T., Thompson, M. C., and Hourigan, K. (2011) “Experiments on the elliptic instability in vortex pairs with axial core flow” Journal of Fluid Mechanics, vol. 677 [3] Holzäpfel, F. (2014). “Effects of environmental and aircraft parameters on wake vortex behavior”. Journal of Aircraft, 51(5), [4] D. Lewellen & W. Lewellen (2001) “The effects of aircraft wake dynamics on contrail development,”Journal of the atmospheric sciences, vol. 58, no. 4 [5] Delisi D.P., Robins R.E. (2000) “Short-Scale Instabilities in Trailing Wake Vortices in a Stratified Fluid”, AIAA Journal, vol. 38 [6] Spalart, P. R. (1998) “Airplane trailing vortices” Annual Review of Fluid Mechanics, vol. 30, no 1 [7] Ortiz, S., Donnadieu, C., & Chomaz, J. M. (2015). ”Three-dimensional instabilities and optimal perturbations of a counter-rotating vortex pair in stratified flows”. Physics of Fluids vol. 27(10) [8] Nomura, K. K., Tsutsui, H., Mahoney, D., & Rottman, J. W. (2006) “Short-wavelength instability and decay of a vortex pair in a stratified fluid”. Journal of Fluid Mechanics, Vol. 553

Wing-tip vortices are of particular interest in aeronautical applications due to their significant contribution to the overall drag of an aircraft [1] and to their persistence in flight corridors and runways which poses a potential hazard and a flight safety concern. The wake vortices are also suspected to play a crucial role in the dilution and transport of contrails released by aircrafts. As these contrails form by condensation of jet exhausts [2] they undergo wrapping, shearing and instabilities by the couple of trailing vortices [3] which leads to increased diffusion and differential distribution and position of the ice panache in the atmosphere. Of interest here is the role that atmospheric stratification plays in the dynamics of these trailing vortices. Density stratification induces gravity effects in the course of the wake descent throughout the atmosphere that is known to alter the descent profile and change the thresholds and wavelength of the common instabilities of the unstratified case [3,8], namely the short and long, otherwise known as Widnall and Crow, instabilities [1,5]. Recent theoretical work [11] confirms that stronger stratification favor shorter wavelengths destabilization of the vortex wake. The problem at stake is that of longitudinal vortices in a vertically stratified fluid. Such a problem is determined by the Froude number which scales as the vortex circulation divided by the vortex separation and Brunt-Vaisala frequency (BVF), the stratification parameter. Infinite Froude number indicate an homogeneous situation while low Froude numbers correspond to strong gravity effects on the vortex dynamics. Realistic case of stratification encountered by aircrafts can lead to medium to strong stratification effects. Literature shows various investigations of this stratification effect, yet several important questions persist. The first one is that of the importance of the stratification in the near field of the wake generated by the lifting body. Most studies overlook this problem and hypothesize a wake configuration that neglects stratification in the early stage of the wake. In fact the threshold must be precisely determined as it could possibility affect the state of the wake and its dynamical properties. The second question is that of the confirmation that the theoretical result obtained by Ortiz et al. [11], concerning the stability properties of the wake in presence of stratification, are well observed in higher Reynolds number flows. The experimental work of Delisi [8] suggests that it is the case but it provides no indication of the flow structure that stands behind the shorter wavelength dynamics. In particular the role of the secondary wake formed by baroclinic torque above the vortices in mild to strong stratification deserves fundamental interest to understand its formation and interaction with the primary vortices. To answer these questions, we propose to run an experimental analysis of the dynamics of wake vortices in a towing tank experiment. Such an experiment allows investigating the wake from its formation down to large distances, therefore it is highly suited to investigate : - The importance of stratification in the formation of the vortex wake - The threshold and leading wavelengths of the vortex instabilities upon stratification effects - The nature of the secondary wake that forms above the main vortices and its role in the destabilization processes. References: [1] Spalart, P. R. (1998) “Airplane trailing vortices” Annual Review of Fluid Mechanics, ,vol. 30, no 1 [2] Paoli, R. & Shariff, K. (2016). “Contrail modeling and simulation” Annual Review of Fluid Mechanics, vol. 48 [3] D. Lewellen & W. Lewellen (2001) “The effects of aircraft wake dynamics on contrail development,” Journal of the atmospheric sciences, vol. 58, no. 4 [4] Crow, S. C. “Stability theory for a pair of trailing vortices” AIAA Vournal, 1970, vol. 8, no 12 [5] Roy, C., Leweke, T., Thompson, M. C., and Hourigan, K. (2011) “Experiments on the elliptic instability in vortex pairs with axial core flow” Journal of Fluid Mechanics, vol. 677 [6] Holzäpfel, F. (2014). “Effects of environmental and aircraft parameters on wake vortex behavior”. Journal of Aircraft, 51(5), [7] Nomura, K. K., Tsutsui, H., Mahoney, D., & Rottman, J. W. (2006) “Short-wavelength instability and decay of a vortex pair in a stratified fluid”. Journal of Fluid Mechanics, Vol. 553 [8] Delisi D.P., Robins R.E. (2000) “Short-Scale Instabilities in Trailing Wake Vortices in a Stratified Fluid”, AIAA Journal, vol. 38 [9] Cruz Marquez, R., Monnier, J. C., Tanguy, G., Couliou, M., Brion, V., Cattafesta, L., & Dupont, P. (2021). ”An experimental study of a trailing vortex alleviation using an undulated trailing edge”.. AIAA AVIATION 2021 FORUM [10] Leweke, T. & Williamson, C. H. (2011). “Experiments on long-wavelength instability and reconnection of a vortex pair”. Physics of Fluids, 23(2) [11] Ortiz, S., Donnadieu, C., & Chomaz, J. M. (2015). ”Three-dimensional instabilities and optimal perturbations of a counter-rotating vortex pair in stratified flows”. Physics of Fluids vol. 27(10)