Two non-equilibrium flows, namely, a transient turbulent pipe flow following a sudden change of flow rate and a turbulent pipe flow subjected to a non-uniform body force are systematically studied using direct numerical simulation (DNS). It is revealed that the transient response of a turbulent pipe flow to a sudden increase of flow rate is a laminar-turbulent transition. The response of the flow is not a progressive evolution from the initial turbulence to a new one, but shows a three-stage development, i.e., a pre-transitional stage, a transitional stage and a fully developed stage. This is similar to a typical boundary layer bypass transition with three characteristical regions, i.e., pre-transitional region, transitional region and fully developed region. The results are carefully compared with those of a channel flow of He & Seddighi, J. Fluid Mech. (2013). The statistical and instantaneous behaviours of the two flows are similar in the near-wall region, but there are distinctive differences in the centre of the flow. The transitional critical Reynolds numbers for the transient pipe and channel flow are predicted with the same correlation. The possibility of predicting such transient flow using transitional turbulence modelling, such as γ-Reθ SST, is discussed. The effect of the rate of the change of the flow is also examined. In a fast ramp-up case, the flow is similar to that of a step-change flow, also showing a three-stage development. In a slow ramp-up case, the flow response is not as clear as that in a fast ramp-up case but the main features of the response are similar.
A series prescribed body forces are used to emulate flows, which contain features similar to those of real buoyancy-aiding flows. It has been shown that the body force with various amplitudes, coverages and distribution profiles can systematically influence the base flow. The body force influenced flows are classified into four groups, namely, partially laminarized flow, 'completely' laminarized flow, partially recovery flow and strongly recovery flow. A new perspective has been proposed for the partially laminarized flow and 'completely' laminarized flow. In contrast to the conventional view, which views the flow to be re-laminarized, the new theory proves that the turbulence of the flow remains largely unchanged following the imposition of the body force. The body force induces a perturbation flow, which lowers the pressure gradient required to maintain the same Reynolds number. This is the mechanism of turbulence relaminarization. The recovery flows show two-layer turbulence. The outer turbulence is generated by a shear layer in the core of the flow caused by the body force. The inner turbulence is generated in the wall layer, increasing with the outer turbulence. The two layers of turbulence increase hand in hand. The stronger the outer generation, the stronger the inner recovery is. The inner turbulence structure is very similar to an equilibrium turbulent flow. In the region very close to the wall (y+0 < 10), it shows similar budget patterns and flow structures (sweeps and ejections) to those of the base flow. In the region between y+0=10 and the new shear layer, the turbulence structure is complicated, where the turbulence is a mixture of the inner turbulence and the outer turbulence.
The transient response of the turbulence to the imposition of a non-uniform body force has been examined. The turbulence decay and recovery features of the flows with non-uniform body forces are studied in detail. It is found that the transient features are mainly determined by the total amplitude of the body force. The higher the amplitude, the stronger the turbulence decay is. In some flows, the near wall turbulence is recovered toward the later stage of the transient process. Under such condition, the inner self-sustaining regeneration interacts strongly with the turbulence from the outer shear layer.
