Skip to main content
SpringerLink
Log in

Turbulent diffusion of a buoyant layer at a wall

  • Published:
Applied Scientific Research, Section A Aims and scope Submit manuscript

Summary

When a light fluid is injected at a steady rate at the roof of a tunnel in which there is a turbulent main flow of a heavier fluid, the turbulent diffusion of the light layer may be considerably reduced due to buoyancy. For large Richardson numbers turbulent mixing ceases altogether.

The equations of motion and diffusion were solved by introducing an eddy diffusivity which is dependant on the Richardson number. Experiments were made on brine (floor) layers in a water flow, and on methane (roof) layers in an air flow. Results were essentially in agreement with theory.

The motion and mixing of the layers depend mainly on the inclination of the tunnel and on a dimensionless combination of main-flow velocity, gravity, relative density difference, volume input rate of layer fluid, and tunnel width. Values of the dimensionless parameter are suggested to overcome the effects of buoyancy on mixing, and to prevent layers from moving up a slope against the main flow.

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

Similar content being viewed by others

References

  1. Bakke, P. and S. J. Leach, Leach, Methane roof layers, Safety in Mines Research Establishment Research Report No. 195 November, 1960.

  2. Bakke, P., J. Fluid Mech. 2 (1957) 467.

    Google Scholar 

  3. Coward, H. F., Trans. Inst. Mining Engineers 94 (1937–1938) 446.

    Google Scholar 

  4. Ellison, T. H., J. Fluid Mech. 2 (1957) 456.

    Google Scholar 

  5. Ellison, T. H. and J. S. Turner, J. Fluid Mech. 6 (1959) 423.

    Google Scholar 

  6. Ellison, T. H. and J. S. Turner, J. Fluid Mech. 8 (1960) 514.

    Google Scholar 

  7. Georgeson, E. H. M., Proc. Roy. Soc. A 180 (1942) 484.

    Google Scholar 

  8. Glauert, M. B., J. Fluid Mech. 1 (1956) 625.

    Google Scholar 

  9. Leach, S. J. and L. P. Barbero, Experiments on methane roof layers: single sources in rough and smooth tunnels with uphill and downhill ventilation, with an appendix on experimental techniques, Safety in Mines Research Establishment Research Report (to be published), 1964.

  10. Morton, B. R., G. I. Taylor and J. S. Turner, Proc. Roy. Soc. A 234 (1956) 1.

    Google Scholar 

  11. Pasquill, F., Proc. Roy. Soc. A 198 (1949) 116.

    Google Scholar 

  12. Richardson, L. F., Proc. Roy. Soc. A 97 (1920) 354.

    Google Scholar 

  13. Richardson, L. F., Phil. Mag. 49 (289) (1925) 81.

    Google Scholar 

  14. Schlichting, H., ZAMM 15 (1935) 313, also Proc. Fourth Int. Congr. Appl. Mech. Cambridge 245 1935.

  15. Taylor, G. I., Proc. Roy. Soc. A 132 (1931) 499.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Safety in Mines Research Establishment, Sheffield, England

    P. Bakke & S. J. Leach

Authors
  1. P. Bakke
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. J. Leach
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bakke, P., Leach, S.J. Turbulent diffusion of a buoyant layer at a wall. Appl. sci. Res. 15, 97–136 (1966). https://doi.org/10.1007/BF00411550

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00411550

Keywords

Search

Navigation