Analytical Solutions for the Modeled k Equation

Abstract

The semitheoretical function of Nezu and Nakagawa (1993, Turbulence in Open-Channel Flows, A. A. Balkema, ed., Rotterdam, The Netherlands) for the turbulent kinetic energy k is valid only where local equilibrium is a good approximation. From an estimation of the difference between the energy production and its dissipation G−ϵ, we present in this study an analytical solution for the modeled k equation. Comparisons with direct numerical simulation data of turbulent channel flows show good agreement. A universal function for k+ is deducted for y+<20.

Influence of gas inlet angle on the mixing process in a Venturi mixer

“…As it was mentioned before, in the numerical calculations the turbulence model k-was applied. Turbulence kinetic energy (TKE) can be generated by fluid shear, friction or buoyancy, or through an external force at low-frequency eddy scales [1]. Analysing in Figure 8 the distributions of Turbulent Kinetic Energy (TKE) through the Venturi mixer for different gas inlet angles it could be seen how the TKE is growing up through the Venturi throat.…”

A simple eddy viscosity formulation for turbulent boundary layers near smooth walls

“…On the other hand, from the modeled k-equation, we developed a function for k + for y + < 20 [4]. For steady channel flows, we write the k-equation as ∂ y (ν t ∂ y k) = − (G + ∂ y (ν ∂ y k) − ), where G and are respectively the energy production and dissipation.…”

“…For steady channel flows, we write the k-equation as ∂ y (ν t ∂ y k) = − (G + ∂ y (ν ∂ y k) − ), where G and are respectively the energy production and dissipation. With an approximation for the right-hand side as (G + d y (ν d y k) − ) ≈ 1/y 2 and by integrating, we obtained [4] k + = B y +2C e (−y + /A + k ) [4]. We write therefore k + for y + ≤ 20 as…”

Comments on “turbulent velocity profile in fully-developed open channel flows”

“…This parabolic profile was not proposed by Yang et al [2] as indicated by the authors, but was proposed some decades ago (see Yalin [3, p. 202], and Nezu and Nakagawa [4, p. 66], as indicated by Yang et al [2]). The discusser indicates that it is possible to write a more accurate eddy viscosity based on an analytical solution for the turbulent kinetic energy [5] with a suitable mixing length equation.…”