A spatially accelerating turbulent flow with longitudinally contracting walls

Abstract

This paper describes a study of spatially accelerating turbulent flow based on the direct numerical simulation of a flow with longitudinally accelerating moving walls to create a relative acceleration between the fluid and the wall without inducing streamline curvature. The results show a broad similarity to those of previous investigations of spatial acceleration, albeit with some differences. A new interpretation has been proposed considering this spatially accelerating flow to be characterised by the formation of a new boundary layer superimposed on the pre-existing turbulent flow. This is followed by the transition of the flow in response to the development of this new boundary layer. This can be seen as an extension of the transition theory for temporally accelerating turbulent flows (He & Seddighi, J. Fluid Mech., vol. 715, 2013, pp. 60–102). The existing turbulent structures act as disturbances for the new boundary layer similar to the role of free-stream turbulence in bypass transition. This boundary layer modulates the pre-existing near-wall structures, amplifying and elongating the streaks. Some streaks eventually become unstable in a sinuous mechanism reminiscent of streak breakdown in near-wall turbulence, resulting in the formation localised turbulent spots which spread until the entire wall is covered in new turbulence. This interpretation naturally splits the flow into a new boundary layer region and a core (or free-stream) flow with interactions between the two dominating a significant length of the flow development and potentially offers a new explanation for the slow evolution of the turbulent stresses observed previously.

Turbulent–turbulent transient concept in pulsating flows

“…The magnitude of indicates the strength of the streaks relative to the surrounding flow in the corresponding – plane (Mathur et al. 2018 b ; Falcone & He 2022), …”

“…The multistage process of the turbulent-turbulent transient concept has since been confirmed for temporally accelerating pipe flows (He, Seddighi & He 2016;Guerrero, Lambert & Chin 2021), ramp-up, spatially accelerating channel flows (Falcone & He 2022), and ramp-up, temporally accelerating channel flow (Seddighi et al 2014). The more gradual, ramp-up acceleration rates resulted in an increase in the time period of the pretransition stage, and a delay in the onset of transition.…”

“…The multistage process of the turbulent–turbulent transient concept has since been confirmed for temporally accelerating pipe flows (He, Seddighi & He 2016; Guerrero, Lambert & Chin 2021), ramp-up, spatially accelerating channel flows (Falcone & He 2022), and ramp-up, temporally accelerating channel flow (Seddighi et al. 2014).…”

“…The streamwise correlation R 11x quantifies the length of the streaks, whilst the spanwise correlation R 11z quantifies the spanwise spacing between the streaks, which is assumed to be equal to twice the spanwise distance at which R 11z reaches its minimum value, (R z11 ) min . The magnitude of (R z11 ) min indicates the strength of the streaks relative to the surrounding flow in the corresponding x-z plane (Mathur et al 2018b;Falcone & He 2022),…”