A Residual Thermodynamic Analysis of Turbulence – Part 2: Pipe Flow Computations and Further Development of Theory

Abstract

Single-phase turbulent pipe flows are analysed utilizing a new theory presented in a parallel paper. Arguably this new theory implies improvements in matching modelling results with experimental observations: To illustrate, unique for these computations is that a 1st law balance agreement between simulations and corresponding experiments is achieved, while resolving the time-averaged fluid flow velocity (including the various inner turbulent zones) and accounting for the wall surface roughness. Testing this new approach, the computations of 20 cases of turbulent pipe flow arrives at a remarkably high amount of kinetic energy dissipation occurring at near-wall positions, where some 54-83% of the net kinetic energy dissipation occurs within the viscous sublayer-, and 17-39% within the buffer layer. Although turbulence incorporates time-varying phenomena, e.g. swirls, large eddies, and breakup of the latter, it is argued that simulating these would have practically no effect on the net kinetic energy dissipation – and the associated wall shear stress – for the present pipe flow cases. Another illustration of the improvements relate to transition computations: While a proposed nominal transition model arrives at fair values of transition Reynolds numbers, some improvements on this transition analysis can be made, e.g. allowing for the modelling of the turbulence onset/offset hysteresis behaviour. For scientists who wish to model time-varying phenomena, e.g. for the study of mixing, boundary layer thickness, or wall-pressure fluctuations, there should be possibilities to implement this new theory in computational flow solvers.

Keywords

• Kinetic energy dissipation
• onset and offset
• wall surface roughness
• defect web

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