Simplified Transition and Turbulence Modeling for Oscillatory Pipe Flows

Alexander Shapiro,David Greenblatt,Gershon Grossman

doi:10.3390/en14051410

Alexander Shapiro, David Greenblatt + Show 1 more

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https://doi.org/10.3390/en14051410

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Journal: Energies	Publication Date: Mar 4, 2021
Citations: 2	License type: CC BY 4.0

Affiliation: Technion – Israel Institute of Technology

Abstract

One-dimensional unsteady Reynolds-averaged Navier–Stokes computations were performed for oscillatory transitional and turbulent pipe flows and the results were validated against existing experimental data for a wide variety of oscillatory Reynolds and Womersley numbers. An unsteady version of the Johnson–King model was implemented with optional near-wall modification to account for temporal pressure gradient variations, and the predictions were compared with those of the Spalart–Allmaras and k–ε turbulence models. Transition and relaminarization were based on empirical Womersley number correlations and assumed to occur instantaneously: in the former case, this assumption was valid, but in the latter case, deviations between data and predictions were observed. In flows where the oscillatory Reynolds numbers are substantially higher than the commonly accepted steady critical value (~2000), fully or continuously turbulent models produced the best correspondence with experimental data. Critically and conditionally turbulent models produced slightly inferior correspondence, and no significant benefit was observed when near-wall pressure gradient effects were implemented or when common one- and two-equation turbulence models were employed. The turbulent velocity profiles were mainly unaffected by the oscillations and this was explained by noting that the turbulent viscosity is significantly higher than its laminar counterpart. Thus, a turbulent Womersley number was proposed for the analysis and categorization of oscillatory pipe flows.

Highlights

Oscillating pipe flows with zero net flowrates are common in engineering systems and in Stirling-based engines and heat pumps, e.g., pulse-tube cryogenic coolers [1,2,3]
With increasing Reynolds number and critically turbulent computations, the velocity profile amplitude tends toward a conventional turbulent profile
Oscillatory pipe flows are challenging to model because their flow state depends on both the Reynolds number and the dimensionless frequency or Womersley number

Summary

Introduction

Oscillating pipe flows with zero net flowrates are common in engineering systems and in Stirling-based engines and heat pumps, e.g., pulse-tube cryogenic coolers [1,2,3]. Oscillatory Reynolds numbers (Reos ≡ Uos2a/ν) can be on the order of hundreds or thousands [1,3] in small devices and well over 106 for large-scale devices (e.g., Wollan et al [4]). A central challenge in modeling these systems is that the Reynolds number varies greatly within the cycle, often crossing from laminar to turbulent flow regimes [5]. When Reynolds numbers are super-critical, the flow can undergo both laminar–turbulent and turbulent–laminar transitions; the latter is sometimes referred to as relaminarization (Narasimha and Sreenivasan [6]). Contrary to a steady flow in which the transition between the laminar and the turbulent regimes is determined only by the Reynolds number, for oscillating flow, the transition is determined empirically by a combination of the peak oscillatory Reyn√olds number Reos and a dimensionless frequency. A compendium of results from different investigations is presented in the detailed and extensive review by Çarpınlıoglu and Özahi [7]

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