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Research Papers: Fundamental Issues and Canonical Flows

Morphing Continuum Theory: Incorporating the Physics of Microstructures to Capture the Transition to Turbulence Within a Boundary Layer

[+] Author and Article Information
Louis B. Wonnell, James Chen

Department of Mechanical
and Nuclear Engineering,
Kansas State University,
Manhattan, KS 66506

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 15, 2016; final manuscript received July 11, 2016; published online October 18, 2016. Assoc. Editor: Praveen Ramaprabhu.

J. Fluids Eng 139(1), 011205 (Oct 18, 2016) (8 pages) Paper No: FE-16-1171; doi: 10.1115/1.4034354 History: Received March 15, 2016; Revised July 11, 2016

A boundary layer with Re = 106 is simulated numerically on a flat plate using morphing continuum theory. This theory introduces new terms related to microproperties of the fluid. These terms are added to a finite-volume fluid solver with appropriate boundary conditions. The success of capturing the initial disturbances leading to turbulence is shown to be a byproduct of the physical and mathematical rigor underlying the balance laws and constitutive relations introduced by morphing continuum theory (MCT). Dimensionless equations are introduced to produce the parameters driving the formation of disturbances leading to turbulence. Numerical results for the flat plate are compared with the experimental results determined by the European Research Community on Flow, Turbulence, and Combustion (ERCOFTAC) database. Experimental data show good agreement inside the boundary layer and in the bulk flow. Success in predicting conditions necessary for turbulent and transitional (T2) flows without ad hoc closure models demonstrates the theory's inherent advantage over traditional turbulence models.

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Figures

Grahic Jump Location
Fig. 1

Evolution of a microstructure with associated micromotion vector ξ and macromotion vector x [7]

Grahic Jump Location
Fig. 2

Uniform flow U=5 m/s over a 2 m flat plate, plots of y/δ versus u/U. Data obtained at (a) x = 0.5 for the transitional case and (b) x = 0.75 for turbulent case, boundary-layer thickness δ obtained from point where u = 0.99U. Numerical simulations show good agreement with the experimental data [26] for all cases.

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