Effective method for construction of low-dimensional models for heat transfer process

Blinov, D.G.; Prokopov, Viktor; Sherenkovskii, Yu.V.; Fialko, Nataliia; Yurchuk, V. M.

doi:10.1016/j.ijheatmasstransfer.2004.07.020

Cited by 12 publications

(5 citation statements)

References 13 publications

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“…The resolution of this problem by the classical global method [Eq. (5)] is made after spatial discretization in time via an implicit first-order Euler scheme with adaptive time step. The resulting linear system is solved by the preconditionned BICGSTAB algorithm designed for sparse matrices.…”

Section: Results With the Complete Modelmentioning

confidence: 99%

“…These dimensions can be compared with the dimension of the classical finite-element formulation, described by Eq. (5).…”

Section: Appendix: Discrete Formulationmentioning

confidence: 99%

“…Among the different techniques, such as the classical thermal modes computation [1,2], the modal identification Method (MIM) [3,4], and proper orthogonal decomposition (POD) [5,6], a recent one is the branch eigenmodes reduction method (BERM), which uses particular eigenmodes called branch modes [7][8][9]. The origin of the branch modes is that the branch eigenvalues problem uses an unusual boundary condition that depends on the eigenvalue, therefore the branch modes possess the distinctive feature of forming a basis for nonlinear thermal problems in the domain and on the boundary.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Modal Substructuring Method: An Efficient Technique for Large-Size Numerical Simulations

Laffay

Quemener

Neveu

et al. 2011

Numerical Heat Transfer, Part B: Fundamentals

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This article presents an extension of the branch Eigenmodes reduction method (BERM) to substructuring models. One of the method's interests lies in its capacity to build a reduced modal model for complex geometries which are characterized by very large matrix sizes. This article treats a 3-D nonlinear application. Such a substructuring reduced model permits us to obtain precise results over the whole domain, with an important gain of CPU time. In the case considered, a global reduced branch model can also be built. A comparison between the two reduced models shows the interest of the substructuring technique.

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Section: Results With the Complete Modelmentioning

confidence: 99%

“…These dimensions can be compared with the dimension of the classical finite-element formulation, described by Eq. (5).…”

Section: Appendix: Discrete Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Modal Substructuring Method: An Efficient Technique for Large-Size Numerical Simulations

Laffay

Quemener

Neveu

et al. 2011

Numerical Heat Transfer, Part B: Fundamentals

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show abstract

“…The most common is a Galerkin projection, but some authors explored alternatives like Method of Polyargumental Systems (MPS), Blinov et al (2004), Linear Stochastic Estimation (LSE), Bonnet et al (1994), Equation Free (EF) modeling, Sirisup et al (2005), and balanced truncation, Rowley (2005); Rowley and Marsden (2000).…”

Section: Galerkin Projectionmentioning

confidence: 99%

Analysis of Chaotic Natural Convection in a Tall Rectangular Cavity With Non-Isothermalwalls

Dillon¹,

Emery²,

Mescher³

2013

Frontiers in Heat and Mass Transfer

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A computational model is presented that extends prior work on unsteady natural convection in a tall rectangular cavity with aspect ratio 10 and applies Proper Orthogonal Decomposition to the results. The solution to the weakly compressible Navier-Stokes equation is computed for a range of Rayleigh numbers between 2 × 10 7 and 2.2 × 10 8 with Prandtl number 0.71. A detailed spectral analysis shows dynamic system behavior beyond the Hopf bifurcation that was not previously observed. The wider Rayleigh range reveals new dynamic system behavior for the rectangular geometry, specifically a return to a stable oscillatory behavior that was not predicted in prior work. Proper Orthogonal Decomposition (POD) has been used to analyze the computational results. Five eigenvalue modes were required to capture correctly the basic flow structure. The POD failed to capture subtle aspects of the flow structure at high Rayleigh numbers for the model, indicating that a POD and Galerkin projection for several Rayleigh numbers will be needed to reproduce the complex behavior of the system.

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“…Podvin and Quere (2001) POD Convection in a tall cavity. Sahan (2000) POD Galerkin Natural convection in a vertical channel Blinov et al (2004) POD MPS Conduction Tarman (2003) POD Galerkin Rayleigh-Benard Convection. Asokan and Zabaras (2005) POD Rayleigh-Benard Convection.…”

Section: Proper Orthogonal Decompositionmentioning

confidence: 99%

Chaotic Natural Convection in an Annular Cavity With Non-Isothermal Walls

Dillon¹,

Emery²,

Mescher³

et al. 2011

Frontiers in Heat and Mass Transfer

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The stability of free convection in an annulus is governed by the boundary conditions on the inner and outer walls of the annulus and the upper and lower boundaries. This paper explores the effect of free convection on the inner surface of the annulus, where the boundary conditions for the outer wall and the upper and lower boundaries are controlled. The temperature is measured in the center of the air cavity and just below the surface of the inner annular boundary. Experimental results are shown for a radius ratio of 0.40, aspect ratio of 20.7. These more recent experimental results are compared to prior work for a radius ratio of 0.60, aspect ratio of 31.0. The results indicate that as the Rayleigh number is increased, the flow experiences a transition from steady flow to a very regular oscillatory flow, and then a supercritical Hopf bifurcation as the flow finally transitions to chaotic behavior. Proper orthogonal decomposition analysis is presented as a method for quantifying the complex dynamic behavior of the system.

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Effective method for construction of low-dimensional models for heat transfer process

Cited by 12 publications

References 13 publications

The Modal Substructuring Method: An Efficient Technique for Large-Size Numerical Simulations

The Modal Substructuring Method: An Efficient Technique for Large-Size Numerical Simulations

Analysis of Chaotic Natural Convection in a Tall Rectangular Cavity With Non-Isothermalwalls

Chaotic Natural Convection in an Annular Cavity With Non-Isothermal Walls

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