Introduction
2
Introduction
Problem of transonic buffet and current approach
In industrial behaviour as in engineering applications there are many cases of turbulent fluxes accompanied by strong unsteady oscillations of involved parameters; clear examples are flutter and transonic buffeting of airplane wings or turbine blades. Unsteadiness can be caused by solid walls moving in the fluid or by boundary conditions changing in time, but can also be due to self-excited instability of the flux, i.e. without the need of an external forcing. Examples of this second type of instability are Von Karman’s wake, caused by flux separation from a bluff body with consequent alternating detachment of vortices, and transonic buffet.
These unsteady phenomena can be troublesome generating noise or be dangerous resulting in structure overloading; for example, a commercial aircraft, flying often during cruise phase at Mach numbers so high that flux can be considered in transonic regime, may be subjected to buffeting due to gusts or to manoeuvres causing wing overloading or fatigue troubles. Consequently, needs to limit flight envelope of such aircrafts to possibly avoid these unsteady phenomena thus limiting flight velocity with not negligible economic effects. Controlling transonic buffeting could have some advantages on aircraft performances, e.g. shortening flight time and enlarging its operating life. To achieve such results, it needs a deep comprehension of this physical phenomenon starting from its origin.
Despite it has been more than half a century from first studies on transonic buffet by many scientific teams, does not exist today a clear and definitive explanation of the reasons why this phenomenon starts and grows up.
Transonic buffeting is an aeroelastic coupling, i.e. a structural vibration, for example a wing responding to a forcing introduced by the surrounding fluid. Practically the most interesting aspect is to foresee structural behaviour, i.e. the dynamic response, of a body due to flux unsteadiness; from a theoretical point of view, the most important aspect to analyse is the forcing instead. A fluid surrounding a solid body, deformable in general, it’s disturbed by the last and react with its proper frequencies. Problem can not be uncoupled because flux, in a feedback way, responds to a disturbance caused by the solid body. To simplify the problem, it can be assumed having a rigid body; under this assumption fluid response first depends on the shape of the rigid body itself. Anyway, buffet it’s a complicate challenge because its existence is accompanied with transonic regime. In this condition indeed, some parts of the flux surrounding the body will be in subsonic regime, some other parts in supersonic one; these last are commonly named “supersonic bubbles”. Handling these mixed regimes of fluxes is a very complicate challenge because they cannot be treated as a single body because equations valid in subsonic region are not valid in supersonic ones. Furthermore, isentropic condition drops due to presence of shock waves.
Introduction
3
At present day transonic buffet, following literature, should be a complex phenomenon linked to boundary layer thickening and thinning, and the shifting shock wave interaction.
Assuming having a body, an airfoil for example, at fixed Mach number and in transonic regime, with growing incidence angle with respect to flux, can be observed that shock wave on the upper body surface moves to the trailing edge becoming stronger. Consequently, the positive pressure gradient grows up becoming increasingly unfavourable; this fact produces shear layer, although turbulent, separation and thickening. Thus, shock wave moves to the trailing edge becoming weaker. At a certain point shear layer will come back attached to body surface, shock wave comes back towards leading edge increasing its intensity and a new cycle will start. This process might produce the self-excitation move of shock wave. Separation downstream of the shock practically always exists, its influence becoming larger as this separated zone grows (when the separated zone becomes larger it deviates flux around the airfoil, practically simulating a thickening of the airfoil itself).
Three authors, Crouch, Garbaruk, Magidov and Strelets in three papers about transonic buffet, published in 2007,2009 and in June 2018 (Ref. [7]-[8]-[11]), wrote that between shear layer separation from an airfoil starts and, while growing, arrives to trailing edge there is a critical condition in which shock wave oscillation and thickening and thinning of the shear layer become synchronous; this fact, in their opinion, might be the cause of self-excited oscillation of shock wave and lead to a global instability of flow field. By virtue of this hypothesis they treated flow field with a global instability method justifying use of a ROM (reduced order model) and a smoothing of shock wave; their method can predict buffet onset in good accordance with experimental data, but only for flux condition quite far from Mach equal to 0.80 and above. Thus, this method has some gaps probably due to poor physical modelling of buffet phenomenon.
Another team, whose components are Ren, Zhao, Gao, Liu, Luo and Xiong, in a paper published in January 2013 (Ref. [12]), tried to study buffet onset experimentally on NACA 0012 airfoil and by use of CFD (computational fluid dynamics). They did not explain physical phenomena but proposed a predicting method of buffet onset based on root mean square of static pressure measured on airfoil surface; they identified unsteadiness born by plotting RMS values found with respect to incidence angle, noting a sudden increase in resulting curve. They obtained some good data, only quite far below Mach = 0.80. Same situation again of previous authors. Furthermore, they studied values of Mach quite higher than 0.80 finding critical values for buffet onset at zero incidence angles too large with respect to experimental data.
Tijdeman in 1977 (Ref. [13]) and Lee in 2001 (Ref. [14]), proposed different hypothesis on self-sustainment of shock oscillation on an airfoil surface based on pressure wave propagation (practically acoustic waves) through shear layer downstream of the shock travelling towards trailing edge and there causing disturbances. These disturbances would form new waves travelling outside shear layer towards shock wave. Tijdeman postulated born of that waves justifying their existence by satisfaction of Kutta condition at the trailing edge; thus, he named them “Kutta waves”.
Lee, however, demonstrated that there was too large difference between propagation time of a Kutta wave from trailing edge to shock wave and oscillation period of this last,
Introduction
4
thus, concluding that Tijdeman’s theory was incomplete and proposed an alternative model of a closed loop of self-exiting oscillation. At first shock oscillation, pressure waves would form at the foot of shock itself travelling through separated flux region and through the shear layer towards the trailing edge, where interacting with disturbances formed there due to Kutta condition satisfaction would cause born of waves travelling in opposite direction outside shear layer. These waves would go up the current up to shock wave and, being incapable of velocity higher than sound speed, their path would stop at the shock and interacting with the last they would give the necessary energy to sustain mechanism of self-exciting shock oscillation; thus, closing the loop.
Therefore, at present day exist many understandings of buffet phenomenon, whose physical models offer predictions on unsteadiness onsets no one capable of reply a whole curve of buffet onset in a Mach-incidence axes chart. In particular, interval about Mach = 0.80 and above appears to be the most troublesome. Consequently, for velocities of higher practical interest, does not exists a sufficiently accurate and reliable model to describe and predict this physical unsteady phenomenon, relegating its study to expensive and long-lasting test phases and CFD analyses.
Aim of thesis
The purpose of this thesis is to numerically approach transonic buffet problem simulating dynamic behaviour of flow in this condition after validated model and methods used to perform numerical analyses and try to clarify some aspects of an important manifestation of unsteadiness. Validation was a test to explore capabilities of commercial software ANSYS® Workbench and ‘realizable k-ε’ model to capture and to describe this unsteady phenomenon.
NACA 0012 airfoil was chosen as subject of analysis since is used to validate wind tunnels and was widely employed in previous studies on this theme; thus it promised enough experimental data for comparisons with simulation results making the lasts sufficiently reliable to propose speculations on this physical phenomenon.
