Open Access

ARTICLE

The Importance of Adequate Turbulence Modeling in Fluid Flows

L.Q. Moreira¹, F.P. Mariano², A. Silveira-Neto¹

1 Universidade Federal de Uberlândia - UFU, Faculdade de Engenharia Mecânica - FEMEC, Av.:João Naves de Ávila, 2121, Campus Santa Mônica, Bl.:5P, CEP: 38400-902, Uberlândia, MG,Brasil, lqmoreira@mecanica.ufu.br; aristeus@mecanica.ufu.br
2 Escola de Engenharia Elétrica e Computação, Universidade Federal de Goiás, Av.: Universitária,1488, Qd.: 86, Bl.: A, Setor Leste Universitário, Goiânia, GO, Brasil

Computer Modeling in Engineering & Sciences 2011, 75(2), 113-140. https://doi.org/10.3970/cmes.2011.075.113

Abstract

Turbulence in fluid flow is one of the most challenging problems in classical physics. It is a very important research problem because of its numerous implications, such as industrial applications that involve processes using mixtures of components, heat transfer and lubrication and injection of fuel into the combustion chambers and propulsion systems of airplanes. Turbulence in flow presents characteristics that are fully nonlinear and that occur at high Reynolds numbers. Because of the nonlinear nature of turbulent flow, an increase in the Reynolds number implies an increase in the Kolmogorov wave numbers, and the flow spectrum becomes larger in both length and time scales. Because of the variety of frequencies and wave numbers involved in turbulent flows, the computational cost becomes prohibitive. An alternative is to solve part of the frequency spectrum; the other part must be modeled. In this context, the Navier-Stokes equations must be filtered, modeled and solved based on the large eddy simulation (LES) methodology. The part of the spectrum related to the higher frequencies or wave numbers that is not solved must be modeled. In the present work, the [Smagorinsky (1963)] model and the dynamic Smagorinsky model [Germano, Piomelli, and Moin (1991)] were used. The goal is to show the importance of turbulence modeling in the simulation of turbulent flows. The problem of homogeneous isotropic turbulence in a periodic box was chosen. There are several ways to model and simulate this flow, and in the present work, a body force was added to the Navier-Stokes equations in order to model the injection of energy at low wave numbers. Because of the energy cascade, the energy injected to the large structures is transferred to the small structures to achieve the Kolmogorov dissipative scales. When the energy spectrum reaches steady state, it is maintained at equilibrium. Many values were used for the Smagorinsky model constant (Cs), yielding an excessive energy transfer for Cs=0.30 and an insufficient energy transfer for Cs=0.10. Therefore, energy was accumulated at the higher wave number of the spectrum. The value Cs=0.18 was determined to be acceptable. This value is the same one that was determined analytically by [Lilly (1992)]. The mean value Cs=0.12 was determined using the dynamic Smagorinsky model simulation.

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