GPU Accelerated Sonochemistry and Bubble Dynamics

The chemical industry is one of the most energy-intensive branches of heavy industry. It was the largest energy consumer (19% of total) in the OECD industrial sector in 2012. Thus, the chemical industry plays a significant role in the economic development worldwide today and in the future as well. One possible candidate to achieve a breakthrough in the sector is the utilization of ultrasound on a liquid domain to increase the yield of various chemical reactions. This novel approach is known as sonochemistry. Its physical basis is a special kind of cavitation phenomenon called acoustic cavitation, during which bubble clusters are formed in the liquid domain. Their radial pulsation can be so rapid that thousands of degrees of K of the temperature is generated inside a bubble. This induces various chemical reactions exploited by many sonochemical applications. This project intends to solve the biggest problem sonochemistry has to face: scale up the production feasible for real industrial applications. The main tool is the high performance GPU programming.
Sonochemistry, bubble dynamics, GPU programming, multi-stability, non-linear dynamics

Collapse Strength

Investigation of the collapse strength of acoustically excited (with dual-frequency) bubbles via high-resolution, 5 dimensional parameter scan. The overall number of the parameter combinations is approximately 1 billion. The project is carried out within the framework of an international co-operation with the Drittes Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen (Prof. Dr. Werner Lauterborn and Dr. Robert Mettin); and with the Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany (Prof. Dr. Ulrich Parlitz).

Control of Multistability

Exploration of multistable solutions of acoustic cavitation bubbles with dual-frequency excitation. The overlapping domains with different colours means different kind of co-existing stable solutions. The high-resolution parameter scan allowed us to develop a novel non-feedback technique to control multistability in which direct attractor selection is possible. In cooperation with the Drittes Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen (Prof. Dr. Werner Lauterborn and Dr. Robert Mettin); and with the Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany (Prof. Dr. Ulrich Parlitz).

Resonances and Chaotic Oscillations

Harmonic and subharmonic resonance regions of a harmonically excited cavitation bubble together with the indication of chaotic (yellow regions) and regular periodic (greyscale area) oscillations. The identification of resonant solutions exhibiting high-amplitude radial pulsation with strong collapses is the keen interest of sonochemistry. Moreover, chaotic bubble behaviour can enhance the effect of micromixing further increase the chemical yield of the applications.

High-Speed Imaging of Bubble Clusters

Dual-frequency measurements carried out in the laboratory of the Drittes Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen (under the supervision of Dr. Robert Mettin). The main aim of the project is to validate the numerical simulations performed on single bubbles, and later on bubble clusters. Due to the high-dimensional parameter space, high performance computations are inevitable to propose optimised operation strategies; however, validation the numerical results with experiments is also an important ingredient of the project.

Investigation Techniques: High Performance Computing (HPC) using the Massively Parallel Architecture of GPUs

In order to highlight the complex physics inside a sonochemical reactor, consider that its size is of the order of decimetres while the size of the thousands of bubbles inside is of the order of micrometres. Moreover, in the time domain, the oscillation period of a single bubble is of the order of microseconds while the collapse phase with chemical reactions is of the order of nanoseconds. And there are many other physical factors having large spatial and/or temporal scale difference. In addition, the number of the involved parameters in a sonochemical process is quite high. Particularly, when using more than one driving frequency, meanwhile it is a common approach, the parameter space is at least composed by the amplitudes, the frequencies and the phase shifts between the harmonic components (e.g. 5D parameter space in dual-frequency case). Not to mention other significant factors, like the bubble size distribution, the ambient pressure and temperature, and the compositions of the liquid and the dissolved gas.

We believe that without a clear theoretical background of multi-frequency driven sonochemical reactor chambers, there is no hope to solve the biggest problem sonochemistry has to face: the scale up to magnitudes feasible for real industrial applications. Moreover, due to the complexity of the physics and the involved large parameter space, high-performance computation must play an important role in such a theoretical understanding. In this regard, our main aim is to take advantage of the high processing power of professional graphics cards (GPUs) due to their very favourable processing power/price ratio compared to CPU supercomputers and CPU clusters.

The main difficulty with GPUs is that a confident knowledge of their hardware architecture is necessary in order to fully utilize them. Nevertheless, our research group have made a significant step forward and developed a general purpose and modular program package capable to solve large number of independent ODE system using the massively parallel environment of GPUs. The code is written in C++ and CUDA C, and it is free to use under an MIT license. The package is called Massively Parallel GPU-ODE Solver (MPGOS) and can be downloaded from the website linked below. The package has a detailed manual with several tutorial examples.

List of Major Publications

  • Papers in high impact journals

    • Klapcsik, K., Hegedűs, F. (2019): Study of non-spherical bubble oscillations under acoustic irradiation in viscous liquid. Ultrason. Sonochem., (In Press)

    • Klapcsik, K., Varga, R., Hegedűs, F. (2018): Bi-parametric topology of subharmonics of an asymmetric bubble oscillator at high dissipation rate. Nonlinear Dyn., 94(4), pp. 2373-2389.

    • Hegedűs, F., Lauterborn, W., Parlitz, U., Mettin, R. (2018): Non-feedback technique to directly control multistability in nonlinear oscillators by dual-frequency driving. Nonlinear Dyn., 94(1), pp. 273-293.

    • Hegedűs, F., Kalmár, Cs. (2018): Dynamic stabilization of an asymmetric nonlinear bubble oscillator. Nonlinear Dyn., 94(1), pp. 307-324.

    • Klapcsik, K., Hegedűs, F. (2017): The effect of high viscosity on the evolution of the bifurcation set of a periodically excited gas bubble. Chaos Solitons Fract., 104, pp. 198-208.

    • Varga, R., Hegedűs, F. (2016): Classification of the bifurcation structure of a periodically driven gas bubble. Nonlinear Dyn., 86(2), pp. 1239-1248.

    • Garen, W., Hegedűs, F., Kai, Y., Koch, S., Meyerer, B., Neu, W., Teubner, U. (2016): Shock wave emission during the collapse of cavitation bubbles. Shock Waves, 26(4), pp. 385-394.

    • Hegedűs, F. (2016): Topological analysis of the periodic structures in a harmonically driven bubble oscillator near Blake's critical threshold: Infinite sequence of two-sided Farey ordering trees. Phys. Lett. A, 380(9-10), pp. 1012-1022.

    • Hegedűs, F., Klapcsik, K. (2015): The effect of high viscosity on the collapse-like oscillation of a harmonically excited gas bubble. Ultrason. Sonochem., 27, pp. 153-164.

    • Hegedűs, F. (2014): Stable bubble oscillations beyond Blake’s critical threshold. Ultrasonics, 54(4), pp. 1113-1121.

    • Hegedűs, F., Koch, S., Garen, W., Pandula, Z., Paál, G., Kullmann, L., Teubner, U. (2013): The effect of high viscosity on compressible and incompressible Rayleigh—Plesset bubble models. Int. J. Heat Fluid Flow, 42, pp. 200-208.

    • Hegedűs, F., Hős, C., Kullmann, L. (2013): Stable period 1,2 and 3 structures of the harmonically excited Rayleigh—Plesset equation applying low ambient pressure. IMA J. Appl. Math., 78(6), pp. 1179-1195.

    • Koch, S., Garen, W., Hegedűs, F., Neu, W., Reuter, R., Teubner, U. (2012): Time-resolved measurements of shock-induced cavitation bubbles in liquids. Appl. Phys. B-Lasers O., 108(2), pp. 345-351.

    • Hegedűs, F., Hős, C., Kullmann, L. (2010): Influence of heat transfer on the dynamic response of a spherical gas/vapour bubble. Int. J. Heat Fluid Flow, 31(6), pp. 1040-1049.


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:

    Ferenc Hegedűs, PhD (leader of the group)
    Kálmán Klapcsik, MSc (PhD candidate)
    Roxána Varga, MSc (PhD candidate)
    Csanád Kalmár, MSc (PhD student)