Our research group deals with the instability of shear flows. There are several flow phenomena, where with the increase of a parameter (e. g. flow velocity or a geometrical measure) the flow loses its stability and starts to swing. One of the most well-known such flow is the flow behind a cylinder where a Kármán vortex street may form. If the shedding frequency of the vortex street is equal to the eigenfrequency of the cylinder, severe problems may arise. These oscillations may cause problems in other flows either; their consequence may be fatigue crack or unwanted noise. Out of these flows our research group deals with the edge tone, the cavity tone and the stability of boundary layers. Our goal is to understand the mechanism of the oscillations by means of new theoretical models and to reduce or end their negative effects.
Keywords: Stability of shear flows, edge tone, cavity tone, noise reduction of vehicles, organ pipes, aeroacoustics, drag reduction.

Edge tone

If a plane jet impinges on a wedge, it starts to swing with a well-defined frequency and it may also emit sound. This configuration is called edge tone, and it occurs among others in wind instruments (organ pipe, recorder) but it can also be used to homogenise heterogeneous mixtures. In other cases the goal is to extinguish the oscillations since they may be harmful for example at the tongue of centrifugal pumps or in Y-branches. The plane jet is in itself unstable, the amplitude of small disturbances increases exponentially streamwise from the jet exit. This means that an arbitrarily small disturbance that is always present in practice will be significantly amplified and will be detectable. If we place a wedge in the jet, then this disturbance may be fed back to the initial part of the jet, close to the jet exit, leading to an oscillation of a well-defined frequency. The exact mechanism of the feedback is not yet known. Our research group could model the oscillations of the jet using the stability analysis methods of fluid mechanics. We verified the increased sensitivity of the jet close to the exit and we discovered a new oscillation mode near the exit. The figure shows the oscillation of the jet calculated by the Orr-Sommerfeld equation. Furthermore, we worked out methods to model the acoustic and the vortex excitement which may play a role in the feedback. They have been compared with experiments.

Cavity tone

The cavity tone is, similarly to the edge tone, a basic aeroacoustic configuration, where a flow instability and a feedback loop plays a role. Here, contrary to the edge tone, it is not a jet but a shear layer, passing over a cavity is unstable. The feedback is caused by the downstream edge of the cavity, rather than a wedge. There are long notches at the joints of cars and aeroplanes, or the current collectors of trains, which can emit a significant noise if not properly designed. Our research group works on the better understanding of the feedback loop of the cavity tone. We worked out a novel vortex detection scheme and performed aeroacoustic simulations. The figure shows the result of an aeroacoustic simulation, where the sound pressure is depicted at a certain instant. Note the order of magnitude difference between the wavelength and the size of the cavity. The cavity is on the bottem of the figure in the middle.

Stabilisation of the Blasius boundary layer

The boundary layer is a fluid layer in the vicinity of a body moving in a fluid, where the velocity changes rapidly from zero to the ambient velocity perpendicular to the wall. Above a certain Reynolds number, the boundary layer becomes unstable, that is, instability waves appear in it. After their discoverers they are called Tollmien-Schlichting waves. These waves are continuously amplified in the streamwise direction, leading eventually to the formation of turbulence. This is a problem because a turbulent boundary layer results in a much larger drag than a laminar one. Delaying the transition can significantly reduce losses in the case of streamlined bodies such as ships or airplanes. In the first figure we can see the stability map of a wall boundary layer, equipped by an active controller. The colours mean the growth (red) or the decay (blue) of the disturbance waves as a function of the disturbance frequency and the Reynolds number of the boundary layer. The flow can be stabilised even at large Reynolds number by increasing the control parameter cp, thus the losses can be reduced. The active control can be replaced by passive elements (mass-spring-damping) as well, which seems to be a promising direction for the reduction of losses. Currently we are working on the development of manufacturable geometries and their investigation.

List of Major Publications

  • Papers in high impact journals

    • P. T. Nagy and G. Paál: Modelling the perturbation growth in an acoustically excited plane jet, Physics of Fluids 29:11 p. 114102. (2017) Link

    • P. T. Nagy and G. Paál: On the sensitivity of planar jets, International Journal of Heat and Fluid Flow 62: pp. 114-123. (2016) Link

    • B. Farkas, G. Paál, K. G. Szabó: Descriptive analysis of a mode transition of the flow over an open cavity, Physics of Fluids 24:2 p. 027102. (2012) Link


The residence of the research lab:

    Budapest University of Technology and Economics, Faculty of Mechanical Engineering, Department of Hydrodynamic Systems

The members of the research lab:

    György Paál, DSc
    Péter Nagy, PhD
    András Szabó, MSc