Modified transport equation for the turbulent kinetic energy dissipation of the grid turbulence in the transition period of decay

Abstract

This paper describes the modified transport equation of grid turbulence at low to moderate Reynolds number ($R_{\lambda} =\frac{u^{\prime } \lambda }{\nu }$, where $\lambda$ is the Taylor micro-scale and $u^{\prime }$ is the rms of the turbulent fluctuation) varies from $R_{\lambda} =0$ to $R_{\lambda} =100$ at $10 \le U_ot/M \le 530$ in the transition period of decay. Three different perforated passive grids have been used. It is well established that power law decay is described as $q^2 \propto x^{-n}$. However, this power law can also be described as $q^2 \propto x^{-(n+m(x))}$ (here, n is the decay exponent and m is a nonzero integer) in the transition region. Therefore, main aim is to establish a new transport equation in the grid turbulence within the transition region at low $R_{\lambda}$. To achieve results, hot-wire experiments were conducted in the fluid mechanics laboratory at the University of Newcastle, Australia. Higher-order curve fitting is used for obtaining the destruction coefficient (G) from the one-dimensional energy spectrum and curve fitting has helped us to optimize the noise of $K^4$ weighted energy spectrum. A modified equation of the destruction coefficient (G) is also shown, and the present results are well agreed with the modified equation of G as well as previous literature’s. The results of the Skewness (S) are observed as a function of $R_{\lambda}$ in the transition region, and it is found that behaviour of S is paradoxical. Relationship of skewness (S), destruction coefficient (G) with $R_{\lambda}$ has been discussed, and it is noticed that $(S+2G/ R_{\lambda} ) \propto R_{\lambda} ^{-1}$. Obtained results also confirm that local isotropy is satisfied at low $R_{\lambda}$.