A coupling approach to modeling heat transfer during a full transient flight cycle

Errera, Marc-Paul; Lazareff, Marc; Garaud, Jean-Didier; Soubrié, Tristan; Douta, C.; Federici, T.

doi:10.1016/j.ijheatmasstransfer.2017.03.048

Cited by 16 publications

(14 citation statements)

References 33 publications

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“…Finally, let us recall that it was shown recently [19] that for stability reasons, the following condition in the fluid domain, must be verified to avoid a "spatial" exponential growth of f κ in Eq. (2):…”

Section: Biot Number and Numerical Biot Numbermentioning

confidence: 99%

“…This study is based on the formulation of the optimal coefficient highlighted for the first time in [17]. This concept has proved to be relevant and effective in academic test cases [18] [19] as well as in complex industrial applications [20]. This concept, based on a prototyping study, has provided a foundation for efficient methods of resolving high interaction thermal coupled problems, as discussed below.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A single stable scheme for steady conjugate heat transfer problems

Errera

Moretti

Salem

et al. 2019

Journal of Computational Physics

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A B S T R A C TThe goal of this paper is to propose a single interface treatment, based on the Dirichlet-Robin interface condition to deal with all steady CHT scenarios. These scenarios depend on the so-called numerical Biot number that controls the stability process and the optimal coefficient that ensures, in theory, unconditional stability. It is shown that this coefficient is closely related to fundamental thermal quantities. For very large thermal fluid-solid interactions, the Dirichlet-Robin condition may result in profound stability issues. A thorough examination of the stability behavior has highlighted a narrow and slow-varying stable zone located around the optimal coefficient. This allows us to determine coupling coefficients valid in any case and the reasonable value of these coefficients avoids significantly impairing the accuracy of CHT solutions. A flat plate, partially protected by a thermal barrier coating, is presented as a test case. Stability analysisThe Godunov-Ryabenkii (G-R) stability analysis [27] is very similar to the standard Fourier stability method, although unlike the Fourier method, the G-R method takes into account the boundary conditions. A normal mode solution is thus applied to the case defined by the discrete model problem [17][18], and after elementary transformations, we obtain the following temporal amplification factor

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Section: Biot Number and Numerical Biot Numbermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A single stable scheme for steady conjugate heat transfer problems

Errera

Moretti

Salem

et al. 2019

Journal of Computational Physics

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show abstract

“…Finally, it is worth noting that these conclusions are valid for a steady CHT procedure in which a transient (or steady-like) fluid solution is used. For other coupled aero-thermal problems, stability considerations must be considered specifically [33].…”

Section: • 1 > Bimentioning

confidence: 99%

“…A systematic comparison of various coefficients was undertaken and it was shown that the optimal coefficient outperformed the previous results in the literature [32]. In transient CHT problems, optimal coefficients can also be applied to analyze heat transfer during a full transient flight cycle as shown in [33] where specific numerical characteristics at the interface were provided.…”

Section: Introductionmentioning

confidence: 96%

Stability, convergence and optimization of interface treatments in weak and strong thermal fluid-structure interaction

Moretti

Errera

Couaillier

et al. 2018

International Journal of Thermal Sciences

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This paper presents the stability, convergence and optimization characteristics of interface treatments for steady conjugate heat transfer problems. The Dirichlet-Robin and Neumann-Robin procedures are presented in detail and compared on the basis of the Godunov-Ryabenkii normal mode analysis theory applied to a canonical aero-thermal coupling prototype. Two fundamental parameters are introduced, a "numerical" Biot number that controls the stability process and an optimal coupling coefficient that ensures unconditional stability. This coefficient is derived from a transition of the amplification factor. A comparative study of these two treatments is made in order to implement numerical schemes based on adaptive and local coupling coefficients, with no arbitrary relaxation parameters, and with no assumptions on the temporal advancement of the fluid domain. The coupled numerical test case illustrates that the optimal Dirichlet-Robin interface conditions provide effective and oscillation-free solutions for low and moderate fluidstructure interactions. Moreover, the computation time is slightly shorter than the time required for a CFD computation only. However, for higher fluid-structure interactions, a Neumann interface condition on the fluid side presents good numerical properties so that no relaxation coefficients are required.

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“…Solving for this interaction is not inherently stable [1] : the correct Dirichlet-Robin or Neumann-Robin boundary condition with the associated optimal parameter for the current Biot number [2] has to be used. See reference [3] for more details.…”

Section: Optimal Stability Schemementioning

confidence: 99%

Optimal Stability Schemes in Transient Conjugate Heat Transfer Coupling

Lazareff¹,

Errera²

2018

Proceedings of the 3rd World Congress on Momentum, Heat and Mass Transfer

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Transient flight cycles need accurate and stable solutions to the fluid flow/heat transfer problem. This is classically solved by coupling solvers for the fluid and thermal sub-problems, but this coupling is a new problem for which stable solutions are not easy to obtain in all cases. Here we show how Dirichlet-Robin and Neumann-Robin boundary conditions, with computed optimal parameter, have been successfully used for coupling fluid and thermal systems. These systems were respectively solved by the Fluent (ANSYS) and Z-set [4] (Onera/Northwest Numerics/Centre des Matériaux) codes.

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A coupling approach to modeling heat transfer during a full transient flight cycle

Cited by 16 publications

References 33 publications

A single stable scheme for steady conjugate heat transfer problems

A single stable scheme for steady conjugate heat transfer problems

Stability, convergence and optimization of interface treatments in weak and strong thermal fluid-structure interaction

Optimal Stability Schemes in Transient Conjugate Heat Transfer Coupling

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