Skip to main content
SpringerLink
Log in

Development of an Ideal Magnetohydrodynamics Flowsolver for High Speed Flow Control

  • Original Contribution
  • Published:
Journal of The Institution of Engineers (India): Series C Aims and scope Submit manuscript

Abstract

This paper presents the baseline development of an ideal magnetohydrodynamics (MHD) solver towards enhancing the knowledge base on the numerical and flow physics complexities associated with MHD flows. The ideal MHD governing equations consisting of the coupled fluid flow equations and the Maxwell’s equations of electrodynamics are implemented in the three dimensional finite volume flowsolver, CERANS. Upwind flux functions such as AUSM-PW+, KFVS and the local Lax-Friedrichs schemes were used for solving the discretized form of governing equations. The solenoidal constraint which requires that the magnetic field to be divergence free all through the flow field evolution is ensured using the artificial compressibility analogy method or the Powell’s source term method. The code had been validated for standard MHD test cases involving complex flowfields such as the MHD shock tube, blast, vortex, cloud-shock interaction and cylinder shock interaction problems. The flow control effect of MHD interaction had been demonstrated for supersonic flow past a wedge and the results are compared with analytical results obtained by solving the MHD Rankine Hugoniot relations. Further, MHD flow control for high speed flows had been demonstrated for the hypersonic blunt body problem. Through rigorous testing and validation, it is observed that the CERANS-MHD code is able to mimic the complex flows due to MHD interactions and the comparison of results are found to be in good agreement with similar literature.

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
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29

Similar content being viewed by others

Abbreviations

A:

Area of surface

Bj :

jth component of magnetic field intensity

C:

Characteristic speed

e:

Specific energy

Fj :

jth component of flux vector

M:

Mach number

\({\hat{\text{n}}}_{\text{j}}\) :

jth component of surface outward normal

p, \({\text{p}}_{\text{t}}\) :

Static and total pressure

t:

Time in seconds

\({\text{S}}\) :

Source term vector

T:

Fluid temperature

\({\text{U}}\) :

Conserved variable vector

Un :

Contra-variant velocity

u:

Velocity vector

V:

Volume of cell element

Vref :

Reference velocity for ACA method

u, v, w:

Velocity components along x, y, z directions

x, y, z:

Cartesian coordinate directions

L, R:

Left, right states

γ:

Ratio of specific heats

ϕ:

Divergence free variable for ACA method

ρ:

Density of fluid

λ:

Eigenvalue

μo :

Magnetic permeability of free space (4π × 10−7 N/A2)

References

  1. K. Dolag, F. Stasyszyn, An MHD GADGET for cosmological simulations. Mon. Not. R. Astron. Soc. (MNRAS) 398, 1678–1697 (2009)

    Article  Google Scholar 

  2. V. Kopchenov, A. Vatazhin, O. Gouskov, Estimation of possibility of use of MHD control in Scaramjet. AIAA Paper 99–4971 (1999)

  3. Y-M. Lee, P.A. Czysz, D. Petley, Magnetohydrodynamic energy bypass applications for single stage-to-orbit vehicles. AIAA Paper No. AIAA 2001-1901, AIAA/NAL-ISAS, 10th International Space Planes and Hypersonic Systems and Technologies Conference, Kyoto, Japan (2001)

  4. K.G. Powell, An approximate Riemann solver for magnetohydrodynamics (that works in more than one dimension). Technical Report 94-24, ICASE, Langley, VA (1994)

  5. A. Dedner, F. Kemm, D. Kröner, C.-D. Munz, T. Schnitzer, M. Wesenberg, Hyperbolic divergence cleaning for the MHD equations. J. Comput. Phys. 175(2), 645–673 (2002)

    Article  MathSciNet  Google Scholar 

  6. M.S. Yalim, D.V. Abeele, A. Lani, T. Quintino, H. Deconinck, A finite volume implicit time integration method for solving the equations of ideal magnetohydrodynamics for the hyperbolic divergence cleaning approach. J. Comput. Phys. 230(15), 6136–6154 (2011)

    Article  MathSciNet  Google Scholar 

  7. K.H. Kim, C. Kim, O.H. Rho, Methods for accurate computations of hypersonic flows. I. AUSMPW+ scheme. J. Comput. Phys. 174, 38–80 (2001)

    Article  MathSciNet  Google Scholar 

  8. S.H. Han, J.I. Lee, K.H. Kim, Accurate and robust pressure weight advection upstream splitting method for magnetohydrodynamics equations. AIAA J. 47, 970–981 (2009)

    Article  Google Scholar 

  9. J.C. Mandal, S.M. Deshpande, Kinetic flux vector splitting for Euler equations. Comput. Fluids 23, 447 (1994)

    Article  MathSciNet  Google Scholar 

  10. K. Xu, Gas-kinetic theory based flux splitting method for ideal magnetohydrodynamics. J. Comput. Phys. 153, 334–352 (1999)

    Article  MathSciNet  Google Scholar 

  11. R. Balasubramanian, K. Anandhanarayanan, Viscous computations for complex flight vehicles using CERANS with wall function. CFD J. 16(4), 386–390 (2008)

    Google Scholar 

  12. M. Brio, C.C. Wu, An upwind differencing scheme for the equations of ideal magnetohydrodynamics. J. Comput. Phys. 75(2), 400–422 (1988)

    Article  MathSciNet  Google Scholar 

  13. S. Serna, A characteristic-based non-convex entropy-fix upwind scheme for the ideal magnetohydrodynamic equations. J. Comput. Phys. 250, 141–164 (2013)

    Article  MathSciNet  Google Scholar 

  14. A. Susanto, L. Ivan, H.C.P.T. De Sterck, H.C.P.T. Groth, High-order central ENO finite-volume scheme for ideal MHD. J. Comput. Phys. 228, 4232–4247 (2009)

    Article  MathSciNet  Google Scholar 

  15. T. Miyoshi, K. Kusano, A multi-state HLL approximate riemann solver for ideal magnetohydrodynamics. J. Comput. Phys. 208, 315–344 (2005)

    Article  MathSciNet  Google Scholar 

  16. C.M. Xisto, J.C. Pascoa, P.J. Oliveira, A pressure-based method with AUSM-type fluxes for MHD flows at arbitrary Mach numbers. Int. J. Numer. Methods Fluids 72, 1165–1182 (2013)

    Article  MathSciNet  Google Scholar 

  17. G. Toth, The \({ \nabla}{{\vec{\rm B}} = 0}\) constraint in shock-capturing magnetohydrodynamics codes. J. Comput. Phys. 161, 605–652 (2000)

    Article  MathSciNet  Google Scholar 

  18. H.D. Sterck, B.C. Low, S. Poedts, Complex magnetohydrodynamic bow shock topology in field-aligned low-beta flow around a perfectly conducting cylinder. Phys. Plasmas 5(11), 4015–4027 (1998)

    Article  Google Scholar 

  19. A.P. Singh, Magnetically dominated flow around a circular cylinder. M.Tech. Thesis, Department of Aerospace Engineering, Indian Institute of Technology, Bombay, Mumbai, India, July 2013

  20. V. Wheatley, D.I. Pullin, P. Samtaney, Regular shock refraction at an oblique planar density interface in magnetohydrodynamics. J. Fluid Mech. 522, 1790–2140 (2005)

    Article  MathSciNet  Google Scholar 

  21. H. Sitaraman, L.L. Raja, A matrix free implicit scheme for solution of resistive magneto-hydrodynamics equations on unstructured grids. J. Comput. Phys. 251, 364–382 (2013)

    Article  MathSciNet  Google Scholar 

  22. J.S. Shang, P.W. Canupp, D.V. Gaitonde, Computational magneto-aerodynamic hypersonics. AIAA 99-4903, 9th International Space Planes and Hypersonic Systems and Technologies Conference and 3rd Weakly Ionized Gases Workshop, Norfork, VA, Nov 1999

  23. P.W. Canupp, Resolution of magnetogasdynamic phenomena using a flux-vector splitting method. AIAA 2000-2477, Fluids 2000, Denver, CO, USA, June 2000

Download references

Author information

Authors and Affiliations

  1. Computational Fluid Dynamics Division, Directorate of Computational Dynamics, Defence Research and Development Laboratory, Kanchanbagh, Hyderabad, 500058, India

    Ramakrishnan Balasubramanian & Karupannasamy Anandhanarayanan

Authors
  1. Ramakrishnan Balasubramanian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karupannasamy Anandhanarayanan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ramakrishnan Balasubramanian.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Balasubramanian, R., Anandhanarayanan, K. Development of an Ideal Magnetohydrodynamics Flowsolver for High Speed Flow Control. J. Inst. Eng. India Ser. C 99, 489–502 (2018). https://doi.org/10.1007/s40032-017-0393-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40032-017-0393-7

Keywords

Search

Navigation