A time-adaptive fluid-structure interaction method for thermal coupling

The thermal coupling of a fluid and a structure is of great significance for many industrial processes. As a model for cooling processes in heat treatment of steel we consider the surface coupling of the compressible Navier-Stokes equations bordering at one part of the surface with the heat equation in a solid region. The semi-discrete coupled system is solved using stiffly stable SDIRK methods of higher order, where on each stage a fluid-structure-coupling problem is solved. For the resulting method it is shown by numerical experiments that a second order convergence rate is obtained. This property is further used to implement a simple time-step control, which saves considerable computational time and, at the same time, guarantees a specified maximum error of time integration.

[1]  Noam Lior,et al.  The cooling process in gas quenching , 2004 .

[2]  Oddvar Bendiksen,et al.  A new approach to computational aeroelasticity , 1991 .

[3]  Udo Fritsching,et al.  Controlling of Distortion by means of Quenching in adapted Jet Fields , 2006 .

[4]  Charbel Farhat,et al.  On the significance of the geometric conservation law for flow computations on moving meshes , 2000 .

[5]  Hermann G. Matthies,et al.  Algorithms for strong coupling procedures , 2006 .

[6]  Udo Fritsching,et al.  Fluid flow and heat transfer in gas jet quenching of a cylinder , 2001 .

[7]  Barry Smith,et al.  Domain Decomposition Methods for Partial Differential Equations , 1997 .

[8]  H. Bijl,et al.  Implicit and explicit higher order time integration schemes for structural dynamics and fluid-structure interaction computations , 2005 .

[9]  Hester Bijl,et al.  Higher-order time integration through smooth mesh deformation for 3D fluid-structure interaction simulations , 2007, J. Comput. Phys..

[10]  Philipp Birken,et al.  On Coupling Schemes for Heat Transfer in FSI Applications , 2009 .

[11]  Meng-Sing Liou,et al.  A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities(Proceedings of the 12th NAL Symposium on Aircraft Computational Aerodynamics) , 1994 .

[12]  P. Hartman.  Ordinary Differential Equations , 1965 .

[13]  Paul Stratton,et al.  Gas Quenching with Helium , 2006 .

[14]  Rolf Radespiel,et al.  Investigation of Hypersonic Gap Flow of a Reentry Nosecap with Consideration of Fluid Structure Interaction , 2006 .

[15]  Charbel Farhat,et al.  CFD‐Based Nonlinear Computational Aeroelasticity , 2004 .

[16]  T. Gerhold,et al.  Calculation of Complex Three-Dimensional Configurations Employing the DLR-tau-Code , 1997 .

[17]  Andrew L. Banka.  PRACTICAL APPLICATIONS OF CFD IN HEAT PROCESSING Three case histories show , 2005 .

[18]  E. Hairer,et al.  Solving Ordinary Differential Equations I , 1987 .

[19]  Stefan Hartmann,et al.  A remark on the application of the Newton-Raphson method in non-linear finite element analysis , 2005 .

[20]  Ralf Massjung,et al.  Discrete conservation and coupling strategies in nonlinear aeroelasticity , 2006 .

[21]  Michael B. Giles,et al.  Stability analysis of numerical interface conditions in fluid-structure thermal analysis , 1997 .

[22]  Hester Bijl,et al.  Implicit Time Integration Schemes for the Unsteady Compressible Navier–Stokes Equations: Laminar Flow , 2002 .

[23]  Uday S. Dixit,et al.  Finite Element Methods For Engineers , 2009 .

[24]  Van Driest,et al.  Investigation of Laminar Boundary Layer in Compressible Fluids Using the Crocco Method , 1952 .

[25]  Oddvar O. Bendiksen,et al.  Transonic panel flutter , 1993 .

[26]  Phillip W. Yarrington,et al.  Finite element analysis of low-speed compressible flows within convectively cooled structures , 1994 .

[27]  Stefan Hartmann,et al.  Remarks on the interpretation of current non‐linear finite element analyses as differential–algebraic equations , 2001, International Journal for Numerical Methods in Engineering.

[28]  Vikram Sarabhai.  Numerical Computation of Heat Transfer on Reentry Capsules at Mach 5 , 2005 .

[29]  F. Krogh,et al.  Solving Ordinary Differential Equations , 2019, Programming for Computations - Python.

[30]  E. Hairer,et al.  Solving Ordinary Differential Equations II , 2010 .

[31]  J.-M. Buchlin.  CONVECTIVE HEAT TRANSFER AND INFRARED THERMOGRAPHY (IRTH) , 2010 .