Research Papers: Fundamental Issues and Canonical Flows

Reduced Order Model for a Power-Law Fluid

[+] Author and Article Information
M. Ocana, D. Alonso

Aerospace Propulsion
and Fluid Mechanics Department,
School of Aeronautics,
Universidad Politecnica de Madrid,
Plaza del Cardenal Cisneros 3,
Madrid 28040, Spain

A. Velazquez

Aerospace Propulsion
and Fluid Mechanics Department,
School of Aeronautics,
Universidad Politecnica de Madrid,
Plaza del Cardenal Cisneros 3,
Madrid 28040, Spain
e-mail: angel.velazquez@upm.es

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 19, 2013; final manuscript received February 3, 2014; published online May 6, 2014. Assoc. Editor: D. Keith Walters.

J. Fluids Eng 136(7), 071205 (May 06, 2014) (9 pages) Paper No: FE-13-1382; doi: 10.1115/1.4026666 History: Received June 19, 2013; Revised February 03, 2014

This article describes the development of a reduced order model (ROM) based on residual minimization for a generic power-law fluid. The objective of the work is to generate a methodology that allows for the fast and accurate computation of polymeric flow fields in a multiparameter space. It is shown that the ROM allows for the computation of the flow field in a few seconds, as compared with the use of computational fluid dynamics (CFD) methods in which the central processing unit (CPU) time is on the order of hours. The model fluid used in the study is a polymeric fluid characterized by both its power-law consistency index m and its power-law index n. Regarding the ROM development, the main difference between this case and the case of a Newtonian fluid is the order of the nonlinear terms in the viscous stress tensor: In the case of the polymeric fluid these terms are highly nonlinear while they are linear when a Newtonian fluid is considered. After the method is validated and its robustness studied with regard to several parameters, an application case is presented that could be representative of some industrial situations.

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Fig. 1

(a) Sketch of the flow domain. (b) Illustration of the typical flow topology in the central cavity characterized by two recirculation regions. Lengths are dimensionless.

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Fig. 2

Dimensionless u velocity profiles at stations x = 3 and x = 4, for cases: (Re,n) = (20,0.5), (20,1.5), (120,0.5), and (120,1.5)

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Fig. 3

Selected snapshots. Set S1 depicted with shaded black squares. Set S2 depicted with transparent circles. The six test points TP1 to TP6 are plotted with crosses.

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Fig. 4

Visual impression of the areas where sets g_1 to g_6 are located inside the cavity

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Fig. 5

Results of cases (S1,g_3), top, and (S2,g_4), for TP5. Front: streamlines comparison between CFD (solid lines) and ROM (dashed lines). Back: map of pressure differences |Pcfd-Prom|/ΔP.

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Fig. 6

Visual impression of the first three POD modes and the cascade of eigenvalues in logarithmic scale




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