Space probes, rockets and satellites are equipped with small thrusters providing the necessary propulsion for attitude control, re-boost or re-entrance to the atmosphere. Gaseous methane and liquid oxygen (LOX) is one promising combination of fuel and oxidiser in state-of-the-art thrusters. Given the near-vacuum conditions of the outer space the pressure in the combustion chamber will be below the saturation pressure of the injected LOX. Small vapour bubbles will rapidly nucleate and grow, resulting in an explosive expansion of the liquid jet. This process is called flash boiling, which will determine the spray formation and eventually improve the efficiency of the combustion process.
Most of the current simulations of flash boiling use an additional transport equation for the volume (or mass) fraction of one phase along with the homogeneous relaxation model to include phase transition from the liquid to the vapour. This strategy has two major constraints: Firstly, the characteristic properties of the unresolved bubbles or droplets cannot be derived from the volume fraction and secondly, the closure terms in the homogeneous relaxation model account for the relaxation of the superheated liquid towards a global equilibrium rather than for the nucleation and interaction of the vapour bubbles at a sub-grid scale.
It is hypothesised that these small-scale bubble interactions affect bubble growth and spray break-up. Therefore, direct numerical simulations (DNS) of small sections of the liquid jet are conducted such that individual bubbles are fully resolved on the computational mesh. The setup involves multiple bubbles, their growth and interactions. The early growth of the vapour bubbles is strongly affected by inertia and pressure forces. These aspects are investigated using a fully compressible DNS code. Results suggest that the pressure in the liquid will locally increase and bubble expansion is slowed down. Later stages of bubble growth up to jet break-up are controlled by inertia and can be modelled by an incompressible approach that allows for larger length and time scales to be computed. The ultimate goal is the development of more accurate models for bubble growth that can be implemented in large-eddy simulations as sub-grid scale models and lead to an improved prediction of the entire process of LOX injection, liquid spray break-up and mixing.
This project is part of the SFB/TRR 75 Droplet Dynamics Under Extreme Ambient Conditions and of the HAoS-ITN project that has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 675676.
Movie 1: Direct numerical simulation of multiple bubble growth in a superheated jet. Isosurfaces (white and transparent light blue) indicate the surface of the bubbles and of the liquid jet. The bottom right plot shows the density field. The top and middle plots show the instantaneous (labelled "Momentandruck") and the time-averaged pressure field (labelled "Gemittelter Druck"), respectively.
Movie 2: Direct numerical simulations of water jet atomization at standard conditions and flash boiling in cryogenic liquids. More details on the simulations are given in the movie.
- D. D. Loureiro, A. Kronenburg, J. Reutzsch, B. Weigand, and K. Vogiatzaki, “Droplet size distributions in cryogenic flash atomization,” International Journal of Multiphase Flow, vol. 142, p. 103705, (2021).
- A. Rees, M. Oschwald, J. W. Gärtner, and A. Kronenburg, “Difficulties in Defining the Degree of Superheat in Flash Boiling Liquid Nitrogen Sprays,” in ICLASS Edinburgh 2021, Edinburgh, (2021).
- J. W. Gärtner, Y. Feng, A. Kronenburg, and O. T. Stein, “Numerical Investigation of Spray Collapse in GDI with OpenFOAM,” Fluids, vol. 6, no. 3, (2021).
- D. D. Loureiro, J. Reutzsch, A. Kronenburg, B. Weigand, and K. Vogiatzaki, “Towards full resolution of spray break-up in flash atomization conditions using DNS,” in High Performance Computing in Science and Engineering ’19, (2020), pp. 209–224.
- J. W. Gärtner, A. Kronenburg, and T. Martin, “Efficient WENO library for OpenFOAM,” SoftwareX, vol. 12, p. 100611, (2020).
- J. W. Gärtner, A. Kronenburg, A. Rees, J. Sender, M. Oschwald, and G. Lamanna, “Numerical and experimental analysis of flashing cryogenic nitrogen,” International Journal of Multiphase Flow, vol. 130, p. 103360, (2020).
- D. D. Loureiro, J. Reutzsch, A. Kronenburg, B. Weigand, and K. Vogiatzaki, “Primary breakup regimes for cryogenic flash atomization,” International Journal of Multiphase Flow, vol. 132, p. 103405, (2020).
- D. Dietzel, T. Hitz, C.-D. Munz, and A. Kronenburg, “Numerical simulation of the growth and interaction of vapour bubbles in superheated liquid jets,” International Journal of Multiphase Flow, vol. 121, p. 103112, (2019).
- D. Loureiro, J. Reutzsch, A. Kronenburg, B. Weigand, and K. Vogiatzaki, “Resolving breakup in flash atomization conditions using DNS,” in 10th Int’l Conf. Multiphase Flow 2019, 19-24 May 2019, Rio de Janeiro, Brazil, (2019).
- D. Dietzel, T. Hitz, C.-D. Munz, and A. Kronenburg, “Single vapour bubble growth under flash boiling conditions using a modified HLLC Riemann solver,” International Journal of Multiphase Flow, vol. 116, pp. 250–269, (2019).
- J. W. Gärtner, A. Rees, A. Kronenburg, J. Sender, M. Oschwald, and D. D. Loureiro, “Large Eddy Simulation of Flashing Cryogenic Liquid with a Compressible Volume of Fluid Solver,” in ILASS, 2019, 2-4 Sept., Paris, France, (2019).
- D. Loureiro, J. Reutzsch, D. Dietzel, A. Kronenburg, B. Weigand, and K. Vogiatzaki, “DNS of multiple bubble growth and droplet formation in superheated liquids,” in 14th Triennial Int’l Conf. Liquid Atomization Spray Systems (ICLASS), Chicago, USA, (2018).
- B. Wang, A. Kronenburg, D. Dietzel, and O. T. Stein, “Assessment of scaling laws for mixing fields in inter-droplet space,” Proc. Combust. Inst., vol. 36, pp. 2451–2458, (2017).
- D. Dietzel, T. Hitz, C.-D. Munz, and A. Kronenburg, “Expansion rates of bubble clusters in superheated liquids,” in ILASS – Europe 2017, 28th Conf. Liquid Atomization Spray Systems, Sep. 6-8. 2017, Valencia, Spain, (2017).
- D. Dietzel, S. Fechter, C.-D. Munz, and A. Kronenburg, “Vapor bubble growth in superheated liquids,” in ICLASS 2015, 13th Triennial Conf Liquid Atomization Spray Systems, Aug. 23-27. 2015, Tainan, Taiwan, (2015).
- D. Dietzel, S. Fechter, C.-D. Munz, and A. Kronenburg, “Investigation of vapor bubble growth under flash boiling conditions,” in 26th Ann. Conf. Liquid Atomization Spray Systems (ILASS Europe), Bremen, Germany, (2014).
Andreas KronenburgUniv.-Prof. Dr.
Director of the Institute