Abstract
The present study introduces third-order quasi-analytical solutions of a turbulence-modeling equation, where the standard [Formula: see text] model equation is used because this model is commonly and widely used in engineering applications. These quasi-analytical solutions describe the robustness of decaying homogeneous turbulence. In the present study, decaying homogeneous turbulence influenced by a weak fluid acceleration of mean flow, which is equivalent to the small strain of the mean flow, is considered. Here, the small strain of the mean flow only slightly affects the anisotropy of the decaying homogeneous turbulence, as shown in previous experiments. Simplified governing equations are derived from the governing equations of the turbulence modeling by introducing the conditions of the small strain. Here, two nondimensional functions are introduced in order to describe the influence on the turbulent kinetic energy and its dissipation using decay laws of the turbulent kinetic energy and its dissipation. Three constants included in the quasi-analytical solutions could be obtained using observable parameters.
Highlights
IntroductionHomogeneous turbulence, which is accompanied by the production of kinetic energy due to the mean shear, decays as time proceeds
Fluid flow in turbulence is widely found in fluidengineering applications
The present study considers the sensitivity of decaying homogeneous turbulence, especially turbulent kinetic energy in the turbulence, to small influences due to the mean flow based on several previous studies
Summary
Homogeneous turbulence, which is accompanied by the production of kinetic energy due to the mean shear, decays as time proceeds. Turbulent kinetic energy k in the decaying homogeneous turbulence has been extensively studied, both experimentally and theoretically. Grid-generated turbulence is equivalent to decaying homogeneous turbulence. The decay power law of turbulent kinetic energy[1] is used to derive the basis of turbulence models, such as the standard k À e model. Decay exponent n is included in the decay power law of turbulent kinetic energy. The value of the decay exponent n has been investigated in previous studies.[2] In high-Reynolds-number grid-generated turbulence, the value of the decay exponent may approach that of Saffman turbulence.[3] Direct numerical simulation (DNS) is used to study the gridgenerated turbulence.[4]
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