Multi‐scale time integration for transient conjugate heat transfer

He, L.; Fadl, Mohamed

doi:10.1002/fld.4295

Cited by 34 publications

(21 citation statements)

References 25 publications

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“…Various multiscale methods and techniques have been developed and applied for problems of distinctive scale disparities spatially for various flow regimes (eg, previous studies) or temporally for fluid‐solid transient thermal coupling (eg, previous studies). More specifically, a block spectral modeling technique has been recently developed to address the 2 conflicting requirements in the problems with 2 distinctive spatial length scales: ( a ) high resolution to capture relevant small‐scale flow features and ( b ) avoidance of having to have very fine resolution globally for a large domain.…”

Section: Introductionmentioning

confidence: 99%

Multiscale block spectral solution for unsteady flows

2017

Numerical Methods in Fluids

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Summary Many problems of interest are characterized by 2 distinctive and disparate scales and a huge multiplicity of similar small‐scale elements. The corresponding scale‐dependent solvability manifests itself in the high gradient flow around each element needing a fine mesh locally and the similar flow patterns among all elements globally. In a block spectral approach making use of the scale‐dependent solvability, the global domain is decomposed into a large number of similar small blocks. The mesh‐pointwise block spectra will establish the block‐block variation, for which only a small set of blocks need to be solved with a fine mesh resolution. The solution can then be very efficiently obtained by coupling the local fine mesh solution and the global coarse mesh solution through a block spectral mapping. Previously, the block spectral method has only been developed for steady flows. The present work extends the methodology to unsteady flows of short temporal and spatial scales (eg, those due to self‐excited unsteady vortices and turbulence disturbances). A source term–based approach is adopted to facilitate a two‐way coupling in terms of time‐averaged flow solutions. The global coarse base mesh solution provides an appropriate environment and boundary condition to the local fine mesh blocks, while the local fine mesh solution provides the source terms (propagated through the block spectral mapping) to the global coarse mesh domain. The computational method will be presented with several numerical examples and sensitivity studies. The results consistently demonstrate the validity and potential of the proposed approach.

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Section: Introductionmentioning

confidence: 99%

Multiscale block spectral solution for unsteady flows

2017

Numerical Methods in Fluids

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“…2 h K f > (14) This stability condition indicates that the fluid conductance in the near-wall region (diffusion) must be higher than half of the convective heat transfer coefficient. Clearly, this condition holds in the vast majority of situations in the fluid.…”

Section: Biot Number and Numerical Biot Numbermentioning

confidence: 98%

“…However, other methods exist to account for the thermal fluid-solid coupling, such as the energy method [8], a matrix analysis [9], a steady-state approach [10], or a frequency-domain method [11]. Currently, the computational cost of a CHT model can be prohibitive if a dynamic coupling process is considered, such as in the context of LES-CHT problems, and different solutions were suggested to accelerate CHT computations [12][13] [14] [15]. In the current paper, only steady solutions are sought and thus the CHT strategy adopted is such that time consistence is not of concern.…”

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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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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“…This relies on the fact that the nature of instabilities obtained thanks to a mathematical model can give insight into the potential instabilities in realistic coupled computations. Note that other approaches exist such as the energy method [13], the multi-scale time in-tegration for high fidelity computations [14] or a frequency-domain method for periodic unsteady flows [15]. Verstaete [16] proposed a stability criterion based on the Biot number for steady CHT.…”

Section: Introductionmentioning

confidence: 99%

Adaptive diffusive time-step in conjugate heat transfer interface conditions for thermal-barrier-coated applications

Salem¹,

Errera²,

Marty³

2019

International Journal of Thermal Sciences

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High pressure turbines are subjected to high temperature flow exiting the combustion chamber. This paper presents a reliable method for a conjugate heat transfer (CHT) procedure using different interface treatments. Indeed, a coupled approach is used to properly capture the transient heat load variations at the interface and have a better estimation of the conduction within the solid. The numerical methods developed in this paper are derived from a 1D CHT model problem in which the thermal properties of each domain drive the numerical stability. Thus, from this model, two fundamental parameters are introduced : a "numerical" Biot number, Bi ν , and an optimal coefficient. Even if the optimal coefficient is theoretically unconditionally stable, the stability zone is drastically reduced when the Biot number increases. In this paper, a unified approach applicable to a wide range of Biot numbers is proposed for the case of multiple materials involved in a coupling process. In order to properly estimate the transient variation, an adaptive diffusive time-step has been developed based on physical thermal properties. This time-step is able to capture the transient effects inside the thermal boundary layer. Coupled results demonstrate a fast and steady converging behavior. Special attention is given to properly define the variable relaxation parameter used in this algorithm. The gain in using an adaptive optimal coefficient is discussed.

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Multi‐scale time integration for transient conjugate heat transfer

Cited by 34 publications

References 25 publications

Multiscale block spectral solution for unsteady flows

Multiscale block spectral solution for unsteady flows

A single stable scheme for steady conjugate heat transfer problems

Adaptive diffusive time-step in conjugate heat transfer interface conditions for thermal-barrier-coated applications

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