Modified algebraic model of laminar-turbulent transition for internal flows

Abstract

Purpose For internal flows with small values of the Reynolds number, there is often at a considerable distance from the pipe inlet cross-section a change of the flow form from laminar to turbulent. To describe this phenomenon of laminar-turbulent transition in the pipe, also parallel-plate channel flow, a modified algebraic intermittency model was used. The original model for bypass transition developed by S. Kubacki and E. Dick was designed for simulating bypass transition in turbomachinery. Design/methodology/approach A modification of mentioned model was proposed. Modified model is suitable for simulating internal flows in pipes and parallel-plate channels. Implementation of the modified model was made using the OpenFOAM framework. Values of several constants of the original model were modified. Findings For selected Reynolds numbers and turbulence intensities (Tu), localization of laminar breakdown and fully turbulent flow was presented. Results obtained in this work were compared with corresponding experimental results available in the literature. It is particularly worth noting that asymptotic values of wall shear stress in flow channels and asymptotic values of axis velocity obtained during simulations are similar to related experimental and theoretical results. Originality/value The modified model allows precision numerical simulation in the area of transitional flow between laminar, intermittent and turbulent flows in pipes and parallel-plate channels. Proposed modified algebraic intermittency model presented in this work is described by a set of two additional partial differential equations corresponding with k-omega turbulence model presented by Wilcox (Wilcox, 2006).

Validation of Modified Algebraic Model during Transitional Flow in HVAC Duct

“…Extreme values of shear stress between the two models are different but the localisation of breakdown coincide. Shape of wall shear stress results from the modified k − ω model are sharpener due to the fact of the model formulation-it was also described in [20,26]. For k − omegaSST shape of wall shear stress is compatible with [29].…”

“…This model introduce factor γ which is a multiplier of the production term in the k-equation. As shown in [15,16,20,26] it enables more accurate description of the flow in the laminar, transitional, and turbulent range. The k and ω equations are defined:…”

“…To perform model validation, a measurement using 2-dimensional PTV method was made. Authors decided to measure the velocity profile in one section (x = 32D) of the pipe with different Reynolds numbers, because in this section can be observed the greatest change in velocity profile in pipe as pointed in [20,29]. Moreover in this section for Reynolds number Re = 630, the velocity profile was close to parabolic due to laminar flow.…”

“…Increase in frame exposure, thus a decrease in frame rate to 25 frames per second gives sufficient quantity in laser pulses-and distinct particle locations. Duration of image acquisition stems from the preliminary analysis of the convergence of coefficients A, B, C for the fitting curve given in Formula (20). The analysis of convergence of A, B, C consisted of 10 measurements of PTV for Re = 3108 for each given duration (5 s, 10 s, 15 s, .…”

“…Algebraic model was originally developed in [15]. Because this algebraic model was developed for high Reynolds number flow, a modification proposed in [20] was applied.…”