Comparison of K-E Turbulence Model Wall Functions Applied on a T-Junction Channel Flow
Abstract
The flow acting in a T-junction channel is present in several industrial applications, such as air conditioning systems, water cooling circuits, gas exhaust systems and others. In order to numerically simulate this case, the Average Reynolds Navier-Stokes (RANS) equation is used for a two-dimensional stationary flow using the k-ε model together with wall functions such as standard wall function, Enhanced and Menter-Lechner wall treatments. The moment ratio used is 𝑀𝑅= 2 and the Reynolds number at the inlet of the flow parallel to the channel is Re = 15,000. The results were compared with the literature data using Large Scale Simulation (LES). The results obtained for k-ε model Enhanced and MenterLechner wall treatment were satisfactory and close to that found by the LES simulation, however, results obtained from k-ε model standard wall function presented large deviation to literature, mainly in the boundary layer and K production profiles. In general, the results presented small distortions for the profiles of turbulent kinetic energy production near walls, however, they illustrate in an analogous manner to the literature the production of turbulent kinetic energy K concentrated in the shear layers between flows. The main results analyzed in this paper are the length of the recirculation bubble, boundary layer profile, mean velocity magnitude and kinetic energy production k.
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Introduction
The main objective of the present work is the computational analysis of the geometry of a rectangular T-junction channel. In this situation, a flow parallel to the channel, called "parallel flow", enters the main channel and another flow transversal to the channel, called “jet flow”, enters the jet flow inlet. As the parallel flow approaches the inlet region of the jet stream, it bypasses the jet flow due to the high jet flow momentum. Since the parallel flow cannot penetrate the jet flow, it contours the jet flow as an obstacle. In addition, the jet flow cannot penetrate the parallel flow, curving until it becomes parallel to the parallel flow and the channel. Such changes of direction generate recirculation bubbles close to the inlet of the jet stream to the channel. This phenomenon, as illustrated in Fig. 1, has been extensively studied in the field of fluid dynamics and can be easily found in air conditioning, water cooling circuit in nuclear power plants, exhaust gas recirculation in internal combustion engines among other systems [1].
Conclusion
In the present work, the turbulence model based on the Average Reynolds Equations (RANS) was used: k-ε model with different wall treatments such as standard wall function, Enhanced Wall Treatment and Menter-Lechner Wall Treatment to analyse the turbulent flow in a T-junction channel having two flows, a flow parallel to the channel and another jet flow, perpendicular to the channel. The results were compared with the studies realised by [1], using the Large Scale Simulation (LES) model. The present work found two recirculation bubbles, one primary bubble downstream of the inlet of the jet stream and another smaller secondary bubble upstream of the jet stream. The same results were found by [1].
The results from all turbulence models are mostly in agreement with the data found by [1], however the k-ε model standard wall functions presented larger deviations for the K production, 𝑢 +. The production of turbulent kinetic energy in the wall region was higher in comparison to the result found in the LES simulation for all models. Additionally, the production of turbulent negative kinetic energy was not perceptible, as found by [1]. The k-ε model Enhanced Wall Treatment presented the best results, in accordance with the literature. All models presented smaller length of the recirculation bubble in comparison with literature.
The results presented from the models here analysed indicate that the turbulence model of two k-ε differential equations with standard wall function does not show good performance in cases with adverse pressure gradient and flow separation, especially in those regions near the wall are regions of great interest. Additionally, better results near the wall region were found by the use of k-ε model Enhanced Wall Treatment and Menter-Lechner Wall Treatment.