Skip to main content
SpringerLink
Log in

PIV mapping of pressure and velocity fields in the plane magnetohydrodynamic Couette flow

  • Research Article
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

We present the first simultaneous mapping of two-dimensional, time-dependent velocity and pressure fields in a plane Couette flow pervaded by a transverse magnetic field. While electromagnetic forces are strongest in fluids of high electric conductivity such as liquid metals, their opacity excludes optical measurement methods. We circumvent this difficulty using a transparent electrolyte (sulphuric acid), whose weaker conductivity is offset by higher magnetic fields. We describe an experimental rig based on this idea, where the Couette flow is entrained by a tape immersed in sulphuric acid and positioned flush onto the bore of large superconducting magnet, so that most of the flow is pervaded by a sufficiently homogeneous transverse magnetic field. Velocity and pressure fields are obtained by means of a bespoke PIV system, capable of recording the fluid’s acceleration as well as its velocity. Both fields are then fed into a finite difference solver that extracts the pressure field from the magnetohydrodynamic governing equations. This method constitutes the first implementation of the pressure PIV technique to an MHD flow. Thanks to it, we obtain the first experimental velocity and pressure profiles in an MHD Couette flows and show that the transitional regime between laminar and turbulent states is dominated by near-wall, isolated, anisotropic perturbations.

Graphic abstract

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

Similar content being viewed by others

References

  • Andreev A, Thess A and Haberstroh, Ch (2003) Visualization of magnetoconvection. Phys Fluids 15(12):3886

    Article  Google Scholar 

  • Andreev O, Kolesnikov Y, Thess A (2013) Visualization of the Ludford column. J Fluid Mech 721:438

    Article  MathSciNet  Google Scholar 

  • Aujogue K, Pothérat A, Debray F, Bates I, Sreenivasan B (2016) Little earth experiment: a device to model planetary cores. Rev Sci Instrum 87(8):084502

    Article  Google Scholar 

  • Baker N, Pothérat A, Davoust L, Debray F (2018) Inverse and direct energy cascades in three-dimensional magnetohydrodynamic turbulence at low magnetic Reynolds number. Phys Rev Lett 120:224502

    Article  Google Scholar 

  • Baker N, Pothérat A, Davoust L, Debray F, Klein R (2017) Controlling the dimensionality of MHD turbulence at low Rm experimentally. Exp Fluids 58(7):79

    Article  Google Scholar 

  • Balbus S, Hawley J (1998) Instability, turbulence, and enhanced transport in accretion disks. Rev Mod Phys 70(1):1

    Article  Google Scholar 

  • Barkley D, Tuckerman LS (2005) Computational study of turbulent laminar patterns in Couette flow. Phys Rev Lett 94:014502

    Article  Google Scholar 

  • Boniface P, Lebon L, Limat L, Receveur M (2017) Absolute stability of a Bénard–von Kármán vortex street in a confined geometry. EPL Europhys Lett 117(3):34001

    Article  Google Scholar 

  • Darling HE (1964) Conductivity of sulfuric acid solutions. J Chem Eng Data 9(3):421

    Article  Google Scholar 

  • Dauchot O, Daviaud F (1995) Finite amplitude perturbation and spots growth mechanism in plane Couette flow. Phys Fluids 7(2):335–343

    Article  Google Scholar 

  • Daviaud F, Hegseth J, Bergé P (1992) Subcritical transition to turbulence in plane Couette flow. Phys Rev Lett 69(17):2511–2514

    Article  Google Scholar 

  • Davidson PA (1997) Role of angular momentum in the magnetic damping of turbulence. J Fluid Mech 336:123

    Article  MathSciNet  Google Scholar 

  • Davidson PA (2001) An introduction to magnetohydrodynamics. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Drazin PG, Reid WH (1995) Hydrodynamic stability. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Duguet Y, Schlatter P, Henningson DS (2010) Formation of turbulent patterns near the onset of transition in plane Couette flow. J Fluid Mech 650:119–129

    Article  Google Scholar 

  • Eckert S, Gerbeth G, Witke W, Langenbrunner H (2001) MHD turbulence measurements in a sodium channel exposed to a transverse magnetic field. Int J Heat Fluid Flow pp 358–364

  • Grossmann S, Lohse D, Sun C (2016) High-Reynolds number Taylor–Couette turbulence. Annu Rev Fluid Mech 48(1):53

    Article  MathSciNet  Google Scholar 

  • Kakutani T (1964) The hydromagnetic stability of the modified plane Couette flow in the presence of a transverse magnetic field. J Phys Soc Jpn 19(6):1041–1057

    Article  Google Scholar 

  • de Kat R, van Oudheusden B (2012) Instantaneous planar pressure determination from PIV in turbulent flow. Exp Fluids 52:1089

    Article  Google Scholar 

  • Meiron D, Moore D, Pullin D (2000) On steady compressible flows with compact vorticity; the compressible Stuart vortex. J Fluid Mech 409:29

    Article  MathSciNet  Google Scholar 

  • Moffatt HK (1967) On the suppression of turbulence by a uniform magnetic field. J Fluid Mech 28(3):571

    Article  Google Scholar 

  • Moreau R (1990) Magnetohydrodynamics. Kluwer Academic Publisher, New York

    Book  Google Scholar 

  • Moudjed B (2013) Caractérisation expérimentale et théorique des écoulements entrainés par ultrasons. Perspectives d'utilisation dans les procédés de solidification du silicium photovoltaïque. Ph.D. thesis, INSA, Lyon

  • Nagata M (1996) Nonlinear solution the plane Couette flow modified by the presence of a tranverse magnetic field. J Fluid Mech 307:231

    Article  MathSciNet  Google Scholar 

  • van Oudheusden BW (2013) PIV-based pressure measurement. Meas Sci Technol 24:032001

    Article  Google Scholar 

  • O’Reilly G, Pullin D (2003) Structure and stability of the compressible Stuart vortex. J Fluid Mech 493:231–254

    Article  MathSciNet  Google Scholar 

  • Patouillet K, Davoust L, Doche O, Ebrahimian V (2018) Relevance of low-Rm MHD for surface viscosimetry of liquid metals. IOP Conf Ser Mater Sci Eng 424:012043

    Article  Google Scholar 

  • Poelma C, Westerweel J, Ooms G (2006) Turbulence statistics from optical whole-field measurements in particle-laden turbulence. Exp Fluids 40(3):347

    Article  Google Scholar 

  • Pothérat A, Klein R (2014) Why, how and when MHD turbulence at low Rm becomes three-dimensional. J Fluid Mech 761:168

    Article  MathSciNet  Google Scholar 

  • Pothérat A, Kornet K (2015) The decay of wall-bounded MHD turbulence at low \(Rm\). J Fluid Mech 783:605.

    Article  MATH  Google Scholar 

  • Pothérat A, Klein R (2017) Do static magnetic fields enhance turbulence at low magnetic Reynolds number ? Phys Rev Fluids 2(6):063702

  • Raffel M, Willert C, Scarano F, Kähler C, Wereley S, Kompenhans J (2018) Particle image velocimetry: a practical guide. Springer, New York

    Book  Google Scholar 

  • Roberts PH (1967) Introduction to magnetohydrodynamics. Longmans, Harlow

    Google Scholar 

  • Rüdiger G, Gellert M, Schutz M, Stefani F (2018) Stability and instability of hydromagnetic Taylor–Couette flows. Phys Rep 741:1

    Article  MathSciNet  Google Scholar 

  • Schumann U (1976) Numerical simulation of the transition from three- to two-dimensional turbulence under a uniform magnetic field. J Fluid Mech 74(1):31

    Article  Google Scholar 

  • Seilmayer M, Stefani F, Gundrum T, Weier T, Gerbeth G, Gellert M, Rüdiger G (2012) Experimental evidence for a transient Tayler instability in a cylindrical liquid-metal column. Phys Rev Lett 108:244501

    Article  Google Scholar 

  • Shercliff JA (1965) A simple demonstration of the Hartmann layer. J Fluid Mech 22(4):701

    Article  Google Scholar 

  • Sommeria J, Moreau R (1982) Why, How and When MHD turbulence becomes two-dimensional. J Fluid Mech 118:507

    Article  Google Scholar 

  • Stefani F, Gundrum T, Gerbeth G, Rüdiger G, Schultz M, Szklarski J, Hollerbach R (2006) Experimental evidence for magnetorotational instability in a Taylor–Couette flow under the influence of a helical magnetic field. Phys Rev Lett 97:184502

    Article  Google Scholar 

  • Tillmark N, Alfredsson PH (1992) Experiments on transition in plane Couette flow. J Fluid Mech 235:89–102

    Article  Google Scholar 

  • Zikanov O, Krasnov D, Boeck T, Thess A, Rossi M (2014) Laminar-turbulent transition in magnetohydrodynamic duct, pipe, and channel flows. ASME Appl Mech Rev 66(3):030802

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fluid and Complex Systems Research Centre, Coventry University, Priory Street, Coventry, CV1 5FB, UK

    B. Moudjed, A. Pothérat & M. Holdsworth

  2. Laboratoire National des Champs Magnétiques Intenses, CNRS/UGA-UPS-INSA, Grenoble, France

    B. Moudjed

Authors
  1. B. Moudjed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Pothérat
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Holdsworth
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Pothérat.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Moudjed, B., Pothérat, A. & Holdsworth, M. PIV mapping of pressure and velocity fields in the plane magnetohydrodynamic Couette flow. Exp Fluids 61, 255 (2020). https://doi.org/10.1007/s00348-020-03090-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00348-020-03090-7

Search

Navigation