Insights into laminarisation and turbulence dynamics in spatially accelerating flows

Spatially accelerating turbulent flows occur in many applications and contain intriguing flow phenomena, most notably laminarisation, which causes rapid changes in flow characteristics in strong accelerations. This study uses numerical simulations to provide new insights into the turbulence dynamics that lead to the emergence of laminarisation in these flows. This study has used the open-source solvers CHAPSim and Incompact3D, implementing and validating a method for simulating spatially accelerating turbulent boundary layers (TBLs). It is shown that the turbulence response in spatially accelerating flows is dominated by a three-stage transition-like process in the near-wall region similar to that which occurs in a temporally accelerating flow (He & Seddighi, J. Fluid Mech. 715:60-102, 2013), noting that spatially accelerating flows are more complex due to influence of flow contraction and spatial development.\par

The study comprises three investigations. First, a direct numerical simulation (DNS) of an idealised spatial acceleration is examined, where longitudinally accelerating moving walls are used to create a relative spatial acceleration, removing the influence of flow contraction. This flow has been found to be described by a three-stage process akin to the bypass transition of a laminar boundary layer. During pre-transition, a new boundary layer forms due to the viscous resistance to the acceleration provided by the wall. This thin layer of enhanced mean shear amplifies the near-wall streaks through the lift-up effect without significantly affecting the transverse motions. At the onset of the transition stage, these streaks break down, forming turbulent spots which grow in the spanwise direction until the wall is covered in newly generated turbulence. Finally, this turbulence spreads into the core in the fully turbulent stage. This flow exhibits many similarities with more typical spatial accelerating flows, such as the amplification of the streaks and the changes in their spanwise scale.

In the second investigation, spatially accelerating TBLs are studied, which incorporates the effect of the flow contraction. Four simulations were conducted over a range of acceleration rates, including laminarising accelerations and weaker cases that did not show signs of laminarisation. All cases are characterised by a transition process that resulted from the development of a new boundary layer similar to the moving wall acceleration. However, flow contraction also results in a flattening of the mean velocity profile away from the wall. Differences emerged between the stronger and weaker accelerations during the pre-transition stage, with the laminarising cases exhibiting an absolute attenuation of the transverse stresses in the inner layer, whereas in the weaker accelerations, the transverse stresses remain largely unchanged close to the wall. The differences between the weak and strong acceleration can be traced to distinct behaviours in the intercomponent energy transfer close to the wall, particularly for the wall-normal component.

Finally, spatially accelerating TBLs are compared with a carefully established equivalent temporally accelerating channel flow to improve the understanding of the similarities and differences between these two types of acceleration. Previous studies have often highlighted the apparent similarities between the accelerations, but no direct comparison has been done previously. To facilitate the comparison, the acceleration parameter and freestream/centreline velocities were matched throughout the accelerations. The mean flow parameters exhibit generally similar variations in both accelerations, but the excursions in the skin friction coefficient and shape factor are significantly greater in the spatial acceleration cases, primarily due to the influence of flow contraction. During the pre-transition region, the turbulence response shared some similarities, with the near-wall peak of the streamwise Reynolds stress nearly collapsing between the spatial and temporal accelerations. However, the strong reductions in streamwise turbulence away from the wall and the transverse components everywhere are observed in strong spatial accelerations but not in temporal cases.