Skip to main content
SpringerLink
Log in

Simulation of liquid micro-jet in free expanding high-speed co-flowing gas streams

  • Research Paper
  • Published:
Microfluidics and Nanofluidics Aims and scope Submit manuscript

Abstract

We present the development of an experimentally validated computational fluid dynamics model for liquid micro jets. Such jets are produced by focusing hydrodynamic momentum from a co-flowing sheath of gas on a liquid stream in a nozzle. The numerical model based on laminar two-phase, Newtonian, compressible Navier–Stokes equations is solved with finite volume method, where the phase interface is treated by the volume of fluid approach. A mixture model of the two-phase system is solved in axisymmetry using ~ 300,000 finite volumes, while ensuring mesh independence with the finite volumes of the size 0.25 µm in the vicinity of the jet and drops. The numerical model is evaluated by comparing jet diameters and jet lengths obtained experimentally and from scaling analysis. They are not affected by the strong temperature and viscosity changes in the focusing gas while expanding at nozzle outlet. A range of gas and liquid-operating parameters is investigated numerically to understand their influence on the jet performance. The study is performed for gas and liquid Reynolds numbers in the range 17–1222 and 110–215, and Weber numbers in the range 3–320, respectively. A reasonably good agreement between experimental and scaling results is found for the range of operating parameters never tackled before. This study provides a basis for further computational designs as well as adjustments of the operating conditions for specific liquids and gases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

Download references

Acknowledgements

The authors would like to thank Henry Chapman (CFEL-DESY, Univ. of Hamburg, Center for Ultrafast Imaging) and Kenneth Beyerlein (CFEL-DESY) for fruitful discussions, Fabian Wilde and Jörg U. Hammel (Helmholtz-Zentrum Geesthacht, Germany) for X-ray projection image and Luigi Adriano (DESY) for technical support.

Funding

Funding for this research is provided by Centre of Free Electron Laser (CFEL) under project: Innovative methods for imaging with the use of X-ray free electron laser (XFEL) and synchrotron sources: simulation of gas-focused microjets, by the Helmholtz Association through program-oriented funds, and Slovenian Grant Agency (ARRS) within Program Group P2-0162 and Project J2-7384. The computations were performed on resources at DESY, Hamburg, Faculty of Mechanical Engineering, University of Ljubljana, and Institute of Metals and Technology, Ljubljana.

Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva 6, 1000, Ljubljana, Slovenia

    Rizwan Zahoor & Božidar Šarler

  2. Laboratory for Simulation of Materials and Processes, Institute of Metals and Technology, Lepi pot 11, 1000, Ljubljana, Slovenia

    Grega Belšak & Božidar Šarler

  3. Photon Science, Deutsches Elektronen-Synchrotron DESY, Notkestraβe 85, 22607, Hamburg, Germany

    Saša Bajt

Authors
  1. Rizwan Zahoor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Grega Belšak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Saša Bajt
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Božidar Šarler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Božidar Šarler.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

The Mach number Ma2 at axial position \({z_4}\) along the nozzle axis is calculated from

$$\frac{{{\text{M}}{{\text{a}}_1}}}{{{\text{M}}{{\text{a}}_2}}}{\left( {\frac{{1+\frac{{\gamma - 1}}{2}{\text{Ma}}_{2}^{2}}}{{1+\frac{{\gamma - 1}}{2}{\text{Ma}}_{1}^{2}}}} \right)^{\frac{{\gamma +1}}{{2\left( {\gamma - 1} \right)}}}}=\frac{{{A_{g2}}}}{{{A_{g1}}}}$$
(28)

where \({A_{{\text{g1}}}}\) and \({A_{{\text{g}}2}}\) represent the cross-sectional area at the gas inlet axial position \({z_1}\) and at axial position \({z_4}\) along the nozzle axis. \(\gamma ={{{c_{\text{p}}}} \mathord{\left/ {\vphantom {{{c_{\text{p}}}} {{c_{\text{v}}}}}} \right. \kern-0pt} {{c_{\text{v}}}}}\) is the ratio of specific heats at constant pressure and constant volume. The pressure at any location \({p_{2,{\text{g}}}}\) can be calculated, with given inlet gas pressure \({p_{{\text{inlet}},{\text{g}}}}\) as

$$\frac{{{p_{{\text{inlet}},{\text{g}}}}}}{{{p_{2,{\text{g}}}}}}={\left( {\frac{{1+\frac{{\gamma - 1}}{2}{\text{Ma}}_{2}^{2}}}{{1+\frac{{\gamma - 1}}{2}{\text{Ma}}_{1}^{2}}}} \right)^{\frac{\gamma }{{\gamma - 1}}}}.$$
(29)

As from experimental data the pressure is known at a distance 1.5 m upstream, \({p_{{\text{inlet}},{\text{g}}}}\) is estimated by performing single-phase compressible simulations in such a way that pressure is adjusted at inlet until an experimentally reported gas flow rate is measured at the nozzle’s gas inlet.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zahoor, R., Belšak, G., Bajt, S. et al. Simulation of liquid micro-jet in free expanding high-speed co-flowing gas streams. Microfluid Nanofluid 22, 87 (2018). https://doi.org/10.1007/s10404-018-2110-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10404-018-2110-0

Keywords

Search

Navigation