Araştırma Makalesi
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Numerical solution and stability analysis of transient MHD duct flow

Yıl 2018, Cilt: 20 Sayı: 3, 53 - 61, 29.10.2018
https://doi.org/10.25092/baunfbed.476597

Öz

This paper simulates the 2D transient magnetohydrodynamic (MHD) flow in a rectangular duct in terms of the velocity of the fluid and the induced magnetic field by using the radial basis function (RBF) approximation.  The inhomogeneities in the Poisson’s type MHD equations are approximated using the polynomial functions (1+r) and the particular solution is found satisfying both the equations and the boundary conditions (no-slip and insulated walls).  The Euler scheme is used for advancing the solution to steady-state with a time increment and a relaxation parameter which are determined for achieving stable solution.  It is shown that, as Hartmann number increases, the fluid becomes stagnant at the center of the duct, the flow is flattened and boundary layers are developed on the Hartmann and side walls.  These are the well-known characteristics of the MHD duct flow.  The stability analysis is also carried in terms of the spectral radius of the coefficient matrix of the discretized coupled system.  Stable solutions are obtained with RBF by using quite large time increment and suitable relaxation parameters on the expense of explicit Euler time-integration scheme used.

Kaynakça

  • Tezer-Sezgin, M. and Dost, S., Boundary element method for MHD channel flow with arbitrary wall conductivity, Applied Mathematical Modelling, 18, 429-436, (1994).
  • Tezer-Sezgin, M. and Aydın Han, S., Dual reciprocity boundary element method for magnetohydrodynamic flow using radial basis functions, International Journal of Computational Fluid Dynamics, 16, 49-63, (2002).
  • Tezer-Sezgin, M., Solution of magnetohydrodynamic flow in a rectangular duct by differential quadrature method, Computers and Fluids, 33, 533-547, (2004).
  • Tezer-Sezgin, M. and Aydın Han, S., Solution of magnetohydrodynamic flow problems using the boundary element method, Engineering Analysis with Boundary Elements, 30, 411-418, (2006).
  • Bozkaya, C. and Tezer-Sezgin, M., Fundamental solution for coupled magnetohydrodynamic flow equations, Journal of Computational and Applied Mathematics, 203, 125-144, (2007).
  • Carabineanu, A. and Lungu, E., Pseudospectral method for MHD pipe flow, International Journal for Numerical Methods in Engineering, 68, 173-191, (2006).
  • Li, Y. and Tian, Z.F., An Exponential compact difference scheme for solving 2D steady magnetohydrodynamic (MHD) duct flow problems, Journal of Computational Physics, 231, 5443-5468, (2012).
  • Bozkaya, C. and Tezer-Sezgin, M., Boundary element solution of unsteady magnetohydrodynamic duct flow with differential quadrature time integration scheme, International Journal for Numerical Methods in Fluids, 51, 567-584, (2006).
  • Dehghan, M. and Mirzaei, D., Meshless Local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity, Applied Numerical Mathematics, 59, 1043-1058, (2009).
  • Dehghan, M. and Mohammadi, V., The method of variably scaled radial kernels for solving two-dimensional magnetohydrodynamic (mhd) equations using two discretizations: the Crank-Nicolson scheme and the method of lines, Computers and Mathematics with Applications, 70, 2292-2313, (2015).
  • Sharp, S., Stability analysis for boundary element methods for diffusion equation, Applied Mathematical Modelling, 10, 41-48, (1986).
  • Ramesh, P.S. and Lean, M.H., Stability of the multiple reciprocity method for transient heat conduction, Communication in Numerical Methods in Engineering, 9, 629-634, (1993).
  • Dragos, L., Magneto-fluid Dynamics. 2nd ed. Abacus Press, England, (1975).
  • Chen, C.S., Fan, C.M. and Wen, P.H., The method of approximate particular solutions for solving certain partial differential equations, Numerical Methods for Partial Differential Equations, 28, 506-522, (2012).
  • Buhmann M.D., Radial Basis Functions: Theory and Implementations. 1st ed. Cambridge University Press, UK, (2004).
  • Gürbüz, M., Radial basis function and dual reciprocity boundary element solutions of fluid dynamics problems, Doctoral Thesis, Middle East Technical University, Graduate School of Natural and Applied Sciences, Ankara, (2017).

Zamana bağımlı MHD kanal akışının nümerik çözümü ve kararlılık analizi

Yıl 2018, Cilt: 20 Sayı: 3, 53 - 61, 29.10.2018
https://doi.org/10.25092/baunfbed.476597

Öz

Bu çalışmada, dikdörtgen kesit içerisindeki iki boyutlu zamana bağlı olan MHD akışı, sıvının hızı ve indüklenen manyetik alan cinsinden radyal baz fonksiyon yaklaştırımı kullanılarak sunulmuştur.  Poisson tipinde olan MHD denklemlerindeki homojen olmayan kısımlar, polinom fonksiyonları (1+r) ile yaklaştırılmıştır ve hem denklemleri hem de kaymaz ve iletken olmayan sınır koşullarını sağlayan özel bir çözüm bulunmuştur.  Euler yöntemi, kararlı çözümü veren zaman aralığı ve yumuşama katsayıları ile kullanılmıştır. Hartmann sayısı artıkça sıvının kanal ortasında durgunlaştığı, akışın düzleştiği, Hartmann ve yan duvarlardaki sınır tabakalarının geliştiği gösterilmiştir.  Bunlar MHD kanal akışının en iyi bilinen özellikleridir.  Ayrıca, kararlılık analizi, ayrıklaştırılmış birbirine bağlı olan sistemdeki katsayı matrisinin spektral yarıçapı doğrultusunda yapılmıştır.  Açık Euler zaman integrasyonu yöntemi kullanılmasına rağmen RBF ile oldukça geniş zaman aralığı ve uygun yumuşama parametreleri kullanılarak kararlı çözümler elde edilmiştir.

Kaynakça

  • Tezer-Sezgin, M. and Dost, S., Boundary element method for MHD channel flow with arbitrary wall conductivity, Applied Mathematical Modelling, 18, 429-436, (1994).
  • Tezer-Sezgin, M. and Aydın Han, S., Dual reciprocity boundary element method for magnetohydrodynamic flow using radial basis functions, International Journal of Computational Fluid Dynamics, 16, 49-63, (2002).
  • Tezer-Sezgin, M., Solution of magnetohydrodynamic flow in a rectangular duct by differential quadrature method, Computers and Fluids, 33, 533-547, (2004).
  • Tezer-Sezgin, M. and Aydın Han, S., Solution of magnetohydrodynamic flow problems using the boundary element method, Engineering Analysis with Boundary Elements, 30, 411-418, (2006).
  • Bozkaya, C. and Tezer-Sezgin, M., Fundamental solution for coupled magnetohydrodynamic flow equations, Journal of Computational and Applied Mathematics, 203, 125-144, (2007).
  • Carabineanu, A. and Lungu, E., Pseudospectral method for MHD pipe flow, International Journal for Numerical Methods in Engineering, 68, 173-191, (2006).
  • Li, Y. and Tian, Z.F., An Exponential compact difference scheme for solving 2D steady magnetohydrodynamic (MHD) duct flow problems, Journal of Computational Physics, 231, 5443-5468, (2012).
  • Bozkaya, C. and Tezer-Sezgin, M., Boundary element solution of unsteady magnetohydrodynamic duct flow with differential quadrature time integration scheme, International Journal for Numerical Methods in Fluids, 51, 567-584, (2006).
  • Dehghan, M. and Mirzaei, D., Meshless Local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity, Applied Numerical Mathematics, 59, 1043-1058, (2009).
  • Dehghan, M. and Mohammadi, V., The method of variably scaled radial kernels for solving two-dimensional magnetohydrodynamic (mhd) equations using two discretizations: the Crank-Nicolson scheme and the method of lines, Computers and Mathematics with Applications, 70, 2292-2313, (2015).
  • Sharp, S., Stability analysis for boundary element methods for diffusion equation, Applied Mathematical Modelling, 10, 41-48, (1986).
  • Ramesh, P.S. and Lean, M.H., Stability of the multiple reciprocity method for transient heat conduction, Communication in Numerical Methods in Engineering, 9, 629-634, (1993).
  • Dragos, L., Magneto-fluid Dynamics. 2nd ed. Abacus Press, England, (1975).
  • Chen, C.S., Fan, C.M. and Wen, P.H., The method of approximate particular solutions for solving certain partial differential equations, Numerical Methods for Partial Differential Equations, 28, 506-522, (2012).
  • Buhmann M.D., Radial Basis Functions: Theory and Implementations. 1st ed. Cambridge University Press, UK, (2004).
  • Gürbüz, M., Radial basis function and dual reciprocity boundary element solutions of fluid dynamics problems, Doctoral Thesis, Middle East Technical University, Graduate School of Natural and Applied Sciences, Ankara, (2017).
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Münevver Tezer-sezgin Bu kişi benim 0000-0001-5439-3477

Merve Gürbüz 0000-0002-7746-9005

Yayımlanma Tarihi 29 Ekim 2018
Gönderilme Tarihi 2 Ağustos 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 20 Sayı: 3

Kaynak Göster

APA Tezer-sezgin, M., & Gürbüz, M. (2018). Numerical solution and stability analysis of transient MHD duct flow. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 20(3), 53-61. https://doi.org/10.25092/baunfbed.476597
AMA Tezer-sezgin M, Gürbüz M. Numerical solution and stability analysis of transient MHD duct flow. BAUN Fen. Bil. Enst. Dergisi. Ekim 2018;20(3):53-61. doi:10.25092/baunfbed.476597
Chicago Tezer-sezgin, Münevver, ve Merve Gürbüz. “Numerical Solution and Stability Analysis of Transient MHD Duct Flow”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20, sy. 3 (Ekim 2018): 53-61. https://doi.org/10.25092/baunfbed.476597.
EndNote Tezer-sezgin M, Gürbüz M (01 Ekim 2018) Numerical solution and stability analysis of transient MHD duct flow. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20 3 53–61.
IEEE M. Tezer-sezgin ve M. Gürbüz, “Numerical solution and stability analysis of transient MHD duct flow”, BAUN Fen. Bil. Enst. Dergisi, c. 20, sy. 3, ss. 53–61, 2018, doi: 10.25092/baunfbed.476597.
ISNAD Tezer-sezgin, Münevver - Gürbüz, Merve. “Numerical Solution and Stability Analysis of Transient MHD Duct Flow”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20/3 (Ekim 2018), 53-61. https://doi.org/10.25092/baunfbed.476597.
JAMA Tezer-sezgin M, Gürbüz M. Numerical solution and stability analysis of transient MHD duct flow. BAUN Fen. Bil. Enst. Dergisi. 2018;20:53–61.
MLA Tezer-sezgin, Münevver ve Merve Gürbüz. “Numerical Solution and Stability Analysis of Transient MHD Duct Flow”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 20, sy. 3, 2018, ss. 53-61, doi:10.25092/baunfbed.476597.
Vancouver Tezer-sezgin M, Gürbüz M. Numerical solution and stability analysis of transient MHD duct flow. BAUN Fen. Bil. Enst. Dergisi. 2018;20(3):53-61.