Experimental studies have been carried out to improve our understanding of the behaviour of turbulence under transient conditions by expanding the new perspective recently established numerically by He and Seddighi (J. Fluid Mech., 715: 60-102, 2013), Seddighi et al. (Flow Turbulence Combustion., 92: 473-502, 2014) and He and Seddighi (J. Fluid Mech., 764: 395-427, 2015). The present work significantly extends the flow conditions investigated in a previous study by Mathur et.al. (J. Fluid Mech., 835: 471-490, 2018) using the same experimental facility. Particle Image Velocimetry (PIV) has been used to measure instantaneous velocities during the transient conditions and Constant Temperature Anemometry (CTA) with hot-film sensors is used to measure the wall shear stress. The length, width, and height of the test rig measured 8000 mm, 350 mm and 50 mm, respectively, and water is used as the working fluid. Flow is accelerated from an initial statistically steady turbulent flow to final statistically steady turbulent flow. This is achieved using a pneumatic control valve. The ramp rate, start and end Reynolds numbers and the period of acceleration are varied to study their effects.
The response of all the accelerating flows investigated is shown to be characterised by laminar-turbulent transition, which follows a three-stage development that is similar to the three-stage response reported by He and Seddighi (J. Fluid Mech., 715: 60-102, 2013) resembling the three stages of boundary layer bypass transition induced by free-stream turbulence. These are buffeted laminar boundary layer, intermittent turbulence spot formation, and a fully developed turbulent boundary layer. The first stage consists of an enhancement and elongation of the pre-existing streaky structures in the flow. In the second stage, the secondary instabilities of the streaky structures increase, and the formation of isolated turbulence spots can be seen. The turbulence spots grow with time and merge with each other. These turbulence spots fill the entire wall-bounded surface when the flow has become fully developed turbulent flow in the third stage. In accordance with this three-stage response, the skin friction coefficient (C_f) increases sharply initially and reaches its maximum value due to the creation of a thin boundary layer near the wall that results in an increase of velocity gradient, strain rate and viscous force. As the boundary layer thickness increases by diffusion, the viscous force and skin friction coefficient decrease. The minimum point of the skin friction coefficient marks the beginning of transition. It increases again during the transitional period due to the generation of ‘‘new’’ turbulence near the wall. The first peak that the C_f attains after its recovery marks the completion of transition.
It has been shown that as the initial Reynolds number increases while the final Reynolds number remains fixed, the time of onset of transition reduces. The process of transition to turbulence becomes very subtle and the transition features are not clearly seen from the visualisation and C_f responses when the initial Reynolds number is high. The characteristic of transition is however unambiguously seen in the response of turbulence especially in the wall normal fluctuating velocity, which remains unchanged during the pre-transition period. On the other hand, the process of transition to turbulence is strong when the initial Reynolds number is small and the transition features are visible in the responses of C_f as well as turbulence. The effect of varying the acceleration period is investigated while the initial Reynolds number and final Reynolds numbers remain fixed. The time at which transition to turbulence occurs increases as the acceleration period increases and vice versa. The response of the wall shear stress follows rather closely the quasi-steady variations when the acceleration is very slow. However, again, the response of turbulence clearly demonstrates the distinct nature of transition even in such slow accelerations.
It has previously been shown that the time-developing boundary layer in a step increase of flow rate forms rapidly near the wall and grows into the flow. In the present study, it has been demonstrated that a temporally developing boundary layer is also resulted in the gradually accelerating flows which is formed as a result of a continuous change in velocity gradient near the wall and then expands into the flow. The pre-transitional stage of the temporally developing boundary layer of the present gradual acceleration coincides with the temporally developing boundary layer illustrated by an extended solution to Stokes’ first problem based on the integration of many small step increases in flow rate.
Modifications have been made to the equivalent Reynolds number (〖Re〗_t) and the initial turbulence intensity (〖Tu〗_0) proposed by He and Seddighi (J. Fluid Mech., 764: 395-427, 2015) in order to account for the slow accelerating flows and the continuous change of the bulk velocities of the cases investigated. It has been shown that the critical equivalent Reynolds number (〖Re〗_(t,cr)) based on these modifications and the initial turbulence intensity (〖Tu〗_0) are well correlated for all cases studied and a power-law relation is established.
