Development of Accelerating Pipe Flow Starting From Rest

Abstract

A uniformly accelerated laminar flow in a pipe, initially at rest, is analyzed. One-dimensional unsteady flow equations for start-up flow were derived from the Navier–Stokes and continuity equations. The dynamical boundary layer in a pipe is described theoretically with the Laplace transformation method for small values of time. A mathematical model describing the development of the velocity profile for accelerating flow starting from rest up to the point of transition to turbulence is given. The theoretical results are compared with experimental findings gained in a large-scale pipeline. Particle image velocimetry (PIV) technique is used to deduce the development of accelerating pipe flow starting from rest. The measured values of the axial velocity component are found to be in a good agreement with the analytical values.

Development of radial velocity component in accelerating start-up pipe flow

“…The formation of wavy structures seems to be asymmetrical and off centre. Similar findings have been reported in accelerating flows (e.g., [17,23]), in fully developed laminar flows (e.g., [14]), and in transient flows (e.g., [24][25][26]). In addition, a criterion describing the dependence between the critical Reynolds number and the acceleration rate is discussed on the basis of all data available.…”

“…The abrupt transition from laminar to turbulent state has no immediate effects on the mean velocity (Fig. 2) or on the shape of the velocity profile [23]. At the beginning of the flow excursion there is a rapid increase in turbulent intensity in the near-wall region, but the bulk flow acceleration causes the velocity in the core to increase at a constant rate.…”

“…The transition process in accelerating pipe flow can be divided into three stages [30,29,23]. In the first stage the response of shear stress at the wall reflects the condition that turbulence over the pipe cross-section remains largely frozen (delay stage).…”

“…The test rig was gravity driven and acceleration was controlled by the downstream end valve. The test rig is described in detail in [27][28][29] and the PIV setup in [23].…”

“…For PIV measurements the camera was set to record at a frequency f s = 3000 Hz. The repeatability of measurements was good (the difference in hot-film reaction times to turbulence between single cases varied up to ±2%) [28,23].…”