Budgets of turbulent kinetic energy, Reynolds stresses, and dissipation in a turbulent round jet discharged into a stagnant ambient
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© 2018, Springer Nature B.V. 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 ReT= 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 Rij 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 ui2¯ 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 ϵ¯ , 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/ bg| < 0.3 (r= radial coordinate and bg= 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 ϵ¯. Combining both the k and ϵ¯ budgets, model coefficients in the commonly used two-equation k- ϵ¯ 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 ϵ¯ : C1ϵ= 1.2 , C2ϵ= 1.6 , Cμ= 0.11 , σk= 1.0 and σϵ= 1.3.
author list (cited authors)
Lai, C., & Socolofsky, S. A.