Budgets of turbulent kinetic energy, Reynolds stresses, and dissipation in a turbulent round jet discharged into a stagnant ambient

Abstract

This paper presents a set of stereoscopic particle image velocimetry (SPIV) measurements of a turbulent round water jet (jet exit Reynolds number $$Re = 2679$$ and turbulent Reynolds number $$Re_T = 113$$ ) discharged into an initially stationary ambient. The data were taken on the jet centerplane and at non-dimensional downstream distances $$x/D = 27{-}37$$ ( $$x =$$ axial coordinate and $$D =$$ orifice diameter), where the jet turbulence had evolved into a self-preserving state. Budgets of turbulent kinetic energy k and individual components of the Reynolds stress tensor $$R_{ij}$$ are extracted from the velocity measurements and compared to recent experimental data of an air jet ( $$x/D = 30, Re = 140{,}000$$ ) and direct numerical simulation data ( $$x/D = 15, Re = 2000$$ ). The comparison reveals that the datasets are consistent with each other but that the turbulent transport of energy $$\overline{u^2_i}$$ appears to differ between the present low-Re water jet and the high-Re air jet. Nonetheless, the non-dimensional profile of turbulent dissipation rate $${\overline{\epsilon }}$$ , obtained as the closing term (balance) of the k-budget, is very similar in all studies. The commonly used Lumley’s model for pressure–velocity correlation (pressure transport term in k-budget) is evaluated using the instantaneous pressure field computed from the time-resolved planar velocity data. We find that Lumley’s model is deficient in the jet core $$|r/b_g| < 0.3$$ ( $$r =$$ radial coordinate and $$b_g =$$ Guassian half-width), while performing adequately away from it. Finally, the present data are used to compute terms appearing in the exact transport equation of $${\overline{\epsilon }}$$ . Combining both the k and $${\overline{\epsilon }}$$ budgets, model coefficients in the commonly used two-equation $$k-{\overline{\epsilon }}$$ turbulence closure model are evaluated from the present data. If a fixed set of model coefficients is to be employed in a jet simulation, the following values of the model coefficients are recommended to optimize predictions for the mean flow field, for k, and for $${\overline{\epsilon }}$$ : $$C_{1\epsilon } = 1.2, C_{2\epsilon } = 1.6, C_{\mu } = 0.11, \sigma _k = 1.0$$ and $$\sigma _\epsilon = 1.3$$ .