Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-05-17T01:20:58.925Z Has data issue: false hasContentIssue false
  • English
  • Français

Investigation of species-mass diffusion in binary-species boundary layers at high pressure using direct numerical simulations

Published online by Cambridge University Press:  06 October 2021

Takahiko Toki Open the ORCID record for Takahiko Toki [Opens in a new window]  and
Josette Bellan Open the ORCID record for Josette Bellan [Opens in a new window]
Takahiko Toki
Affiliation:
California Institute of Technology, Pasadena, CA 91125, USA
Josette Bellan*
Affiliation:
California Institute of Technology, Pasadena, CA 91125, USA Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
*
†Email address for correspondence: josette.bellan@jpl.nasa.gov
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations of single-species and binary-species temporal boundary layers at high pressure are performed with special attention to species-mass diffusion. The working fluids are nitrogen or a mixture of nitrogen and methane. Mean profiles and turbulent fluctuations of mass fraction show that their qualitative characteristics are different from those of streamwise velocity and temperature, due to the different boundary conditions. In a wall-parallel plane near the wall, the streamwise velocity and temperature have streaky patterns and the fields are similar. However, the mass fraction field at the same location is different from the streamwise velocity and temperature fields indicating that species-mass diffusion is not similar to the momentum and thermal diffusion. In contrast, at the centre and near the edge of the boundary layer, the mass fraction and temperature fields have almost the same pattern, indicating that the similarity between thermal and species-mass diffusion holds away from the wall. The lack of similarity near the wall is traced to the Soret effect that induces a temperature-gradient-dependent species-mass flux. As a result, a new phenomenon has been identified for a non-isothermal binary-species system – uphill diffusion, which in its classical isothermal definition can only occur for three or more species. A quadrant analysis for the turbulent mass flux reveals that near the wall the Soret effect enhances the negative contributions of the quadrants. Due to the enhancement of the negative contributions, small species-concentration fluid tends to be trapped near the wall.

JFM classification

Boundary Layers: Boundary layer structure Mass Transport: Coupled diffusion and flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 928 , 10 December 2021 , A18
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bae, J.H., Yoo, J.Y. & Choi, H. 2005 Direct numerical simulation of turbulent supercritical flows with heat transfer. Phys. Fluids 17, 105104.CrossRefGoogle Scholar
Bae, J.H., Yoo, J.Y. & McEligot, D.M. 2008 Direct numerical simulation of heated $\mathrm {CO}_{2}$ flows at supercritical pressure in a vertical annulus at $Re=8900$. Phys. Fluids 20, 055108.CrossRefGoogle Scholar
Duan, L., Beekman, I. & Martín, M.P. 2010 Direct numerical simulation of hypersonic turbulent boundary layers. Part 2. Effect of wall temperature. J. Fluid Mech. 655, 419–445.CrossRefGoogle Scholar
Duan, L., Beekman, I. & Martín, M.P. 2011 Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number. J. Fluid Mech. 672, 245–267.CrossRefGoogle Scholar
Duncan, J.B. & Toor, H.L. 1962 An experimental study of three component gas diffusion. AIChE J. 8 (1), 38–41.CrossRefGoogle Scholar
Ern, A. & Giovangigli, V. 1998 Thermal diffusion effects in hydrogen–air and methane–air flames. Combust. Theor. Model. 2, 349–372.CrossRefGoogle Scholar
Foysi, H., Sarkar, S. & Friedrich, R. 2004 Compressibility effects and turbulence scalings in supersonic channel flow. J. Fluid Mech. 509, 207–216.CrossRefGoogle Scholar
Gaitonde, D.V. & Visbal, M.R. 1998 High-order schemes for Navier–Stokes equations: algorithm and implementation into FDL3DI. Air Force Research Lab Wright-Patterson AFB OH Air Vehicles Directorate AFRL-VA-WP-TR-1998-3060.CrossRefGoogle Scholar
Harstad, K., Miller, R.S. & Bellan, J. 1997 Efficient high-pressure state equations. AIChE J. 43, 1605–1610.CrossRefGoogle Scholar
Harstad, K. & Bellan, J. 2000 An all-pressure fluid drop model applied to a binary mixture: heptane in nitrogen. Intl J. Multiphase Flow 26, 1675–1706.CrossRefGoogle Scholar
Harstad, K. & Bellan, J. 2004 Mixing rules for multicomponent mixture mass diffusion coefficients and thermal diffusion factors. J. Chem. Phys. 120 (12), 5664–5673.CrossRefGoogle ScholarPubMed
Huang, P.G., Coleman, G.N. & Bradshaw, P. 1995 Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech. 305, 185–218.CrossRefGoogle Scholar
Kawai, S. 2019 Heated transcritical and unheated non-transcritical turbulent boundary layers at supercritical pressures. J. Fluid Mech. 865, 563–601.CrossRefGoogle Scholar
Kim, K., Hickey, J. & Scalo, C. 2019 Pseudophase change effects in turbulent channel flow under transcritical temperature conditions. J. Fluid Mech. 871, 52–91.CrossRefGoogle Scholar
Knapp, H., Döring, R., Oellrich, L., Plöcker, U. & Prausnitz, J.M. 1982 Vapor-Liquid Equilibria for Mixtures of Low Boiling Substances, vol. VI. Dechema.Google Scholar
Kozul, M., Chung, D. & Monty, J.P. 2016 Direct numerical simulation of the incompressible temporally developing turbulent boundary layer. J. Fluid Mech. 796, 437–472.CrossRefGoogle Scholar
Lee, J., Jung, S.Y., Sung, H.J. & Zaki, T.A. 2013 Effect of wall heating on turbulent boundary layers with temperature-dependent viscosity. J. Fluid Mech. 726, 196–225.CrossRefGoogle Scholar
Lele, S.K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1), 16–42.CrossRefGoogle Scholar
Ma, P.C., Yang, X.I.A. & Ihme, M. 2018 Structure of wall-bounded flows at transcritical conditions. Phys. Rev. Fluids 3, 034609.CrossRefGoogle Scholar
Martín, M.P. 2004 DNS of hypersonic turbulent boundary layers. AIAA 2004-2337.CrossRefGoogle Scholar
Masi, E., Bellan, J., Harstad, K.G. & Okong'o, N.A. 2013 Multi-species turbulent mixing under supercritical-pressure conditions: modelling, direct numerical simulation and analysis revealing species spinodal decomposition. J. Fluid Mech. 721, 578–626.CrossRefGoogle Scholar
Moin, P. & Mahesh, K. 1998 Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30, 539–578.CrossRefGoogle Scholar
Muller, S.M. & Scheerer, D. 1991 A method to parallelize tridiagonal solvers. Parallel Comput. 17, 181–188.CrossRefGoogle Scholar
Nemati, H., Patel, A., Boersma, B.J. & Pecnik, R. 2015 Mean statistics of a heated turbulent pipe flow at supercritical pressure. Intl J. Heat Mass Transfer 83, 741–752.CrossRefGoogle Scholar
Nemati, H., Patel, A., Boersma, B.J. & Pecnik, R. 2016 The effect of thermal boundary conditions on forced convection heat transfer to fluids at supercritical pressure. J. Fluid Mech. 800, 531–556.CrossRefGoogle Scholar
Okong'o, N. & Bellan, J. 2002 Consistent boundary conditions for multicomponent real gas mixtures based on characteristics wave. J. Comput. Phys. 176, 330–344.CrossRefGoogle Scholar
Okong'o, N., Harstad, K. & Bellan, J. 2002 Direct numerical simulation of $\mathrm {O}_2 /\mathrm {H}_{2}$ temporal mixing layers under supercritical conditions. AIAA J. 40 (5), 914–926.CrossRefGoogle Scholar
Okong'o, N. & Bellan, J. 2003 Real-gas effects on mean flow and temporal stability of binary-species mixing layers. AIAA J. 41 (12), 2429–2443.CrossRefGoogle Scholar
Patel, A., Boersma, B.J. & Pecnik, R. 2016 The influence of near-wall density and viscosity gradients on turbulence in channel flows. J. Fluid Mech. 809, 793–820.CrossRefGoogle Scholar
Peeters, J.W.R., Pecnik, R., Rohde, M., van der Hagen, T.H.J.J. & Boersma, B.J. 2016 Turbulence attenuation in simultaneously heated and cooled annular flows at supercritical pressure. J. Fluid Mech. 799, 505–540.CrossRefGoogle Scholar
Pirozzoli, S. & Bernardini, M. 2011 Turbulence in supersonic boundary layers at moderate Reynolds number. J. Fluid Mech. 688, 120–168.CrossRefGoogle Scholar
Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126.CrossRefGoogle Scholar
Sciacovelli, L. & Bellan, J. 2019 The influence of the chemical composition representation according to the number of species during mixing in high-pressure turbulent flows. J. Fluid Mech. 863, 293–340.CrossRefGoogle Scholar
Taylor, R. & Krishna, R. 1993 Multicomponent Mass Transfer. John Wiley & Sons.Google Scholar
Toki, T., Teramoto, S. & Okamoto, K. 2020 Velocity and temperature profiles in turbulent channel flow at supercritical pressure. J. Propul. Power 36, 3–13.CrossRefGoogle Scholar
Wallace, J.M. 2016 Quadrant analysis in turbulence research: history and evolution. Annu. Rev. Fluid Mech. 48, 131–158.CrossRefGoogle Scholar
Wallace, J.M., Eckelmann, H. & Brodkey, R.S. 1972 The wall region in turbulent shear flow. J. Fluid Mech. 54, 39–48.CrossRefGoogle Scholar
Zonta, F., Marchioli, C. & Soldati, A. 2012 Modulation of turbulence in forced convection by temperature-dependent viscosity. J. Fluid Mech. 697, 150–174.CrossRefGoogle Scholar