An Algebraic Non-Equilibrium Turbulence Model of the High Reynolds Number Transition Region

Abstract

We present a mixing length-based algebraic turbulence model calibrated to pipe flow; the main purpose of the model is to capture the increasing turbulence production-to-dissipation ratio observed in connection with the high Reynolds number transition region. The model includes the mixing length description by Gersten and Herwig, which takes the observed variation of the von Kármán number with Reynolds number into account. Pipe wall roughness effects are included in the model. Results are presented for area-averaged (integral) quantities, which can be used both as a self-contained model and as initial inlet boundary conditions for computational fluid dynamics simulations.

The Chimera Revisited: Wall- and Magnetically-Bounded Turbulent Flows

“…The model is calibrated against measurements and the position of the interface is fitted to a Gaussian distribution that is independent of Re τ . The resulting velocity jumps and deviations of the fit from the log law are also independent of Re τ , except for pipe flow below Re τ = 3400, which is interesting and may be related to the high Re transition region for pipe flow [25].…”

“…The loss of this IIL/ITB leads to higher levels of core turbulence since the quiescent core is reduced or disappears and is replaced with structures from the log law region. This is also reflected in an increasing turbulent length scale at the transition [25]. The proposed mechanism implies that turbulence in pipe flow ends up similar to open channel flow for sufficiently high Re [56].…”

“…It has been speculated that a similar phenomenon occurs during the high Re transition in pipe flow [25]. Here, increased core turbulence was observed with increasing Re τ , leading to the question: does low (high) Re τ for pipe flow correspond to good (bad) confinement in PP?…”

“…see [25] and the associated Supplementary Information for more details. The Kolmogorov scale is the smallest scale and L is the largest scale.…”

“…Increasing core fluctuations for pipe flow high Reynolds number (Re) transitions (we use Re without subscript as a general term; later in the review, two specific definitions, the bulk and friction Reynolds number, are defined using subscripts) [25] is similar to controlled confinement transitions in fusion plasmas [26,27] • Travelling wave solutions in pipe flow [28] are reminiscent of the magnetic field structure (islands) in fusion plasmas…”