Kazuyoshi Nishihara

Critical Reynolds Number in Constant-Acceleration Pipe Flow From an Initial Steady Laminar State

The transition to turbulence in a constant-acceleration pipe flow from an initial laminar state was investigated in a custom-made apparatus permitting visual access to the water flow in the pipe. The apparatus allowed both laser Doppler velocimetry measurements and flow visualization using a tracer. The experiment was carried out by accelerating the flow from a steady laminar state to a steady turbulent state. The relation between the critical Reynolds number for transition to turbulence and the acceleration was found to be similar to that in a constant-acceleration pipe flow started from rest. In addition, with increased acceleration, the turbulent transition was found to be delayed to higher Reynolds numbers using flow visualization with simultaneous laser Doppler velocimetry measurements.

Effect of Initial Constant Acceleration on the Transition to Turbulence in Transient Circular Pipe Flow

Experimental investigation is carried out on the transition to turbulence in a transient circular pipe flow. The flow is accelerated from rest at a constant acceleration until its cross-sectional mean velocity reaches a constant value. Accordingly, the history of the flow thus generated consists of the initial stage of constant acceleration and the following stage of constant cross-sectional mean velocity. The final Reynolds number based on the constant cross-sectional mean velocity and the pipe diameter is chosen to be much greater than the transition Reynolds number of a steady pipe flow of about 3000. The transition to turbulence is judged from the output signal of the axial velocity component and its root-mean-square value measured with a hot-wire anemometer. A turbulent slug appears after the cross-sectional mean velocity of the flow reaches the predetermined constant value under every experimental condition. Turbulence production therefore is suppressed, while the flow is accelerated. The time lag for the appearance of the turbulent slug after the cross-sectional mean velocity of the flow reaches the constant value decreases with an increase in the constant acceleration value. An empirical equation is proposed for estimating the time lag. The propagation velocity of the leading edge of the turbulent slug is independent of the constant acceleration value under the present experimental conditions.

Suppression of Transition to Turbulence at High Reynolds Numbers Due to Unsteadiness Imposition

Transition from laminar to turbulent flow has been a primary concern on the study of a pipe flow. This study provides the analytical solutions of the axisymmetric Navier-Stokes equations for an arbitrary-accelerating laminar flow with a given cross-sectional mean velocity in a circular pipe. The cross-sectional mean velocity is imposed as cubic polynomial with respect to time. The exact solutions obtained are thought to be useful to verify the accuracy of the corresponding experimental results for investigating the transition process to turbulence and, to control the cross-sectional mean velocity in the experiment. Unfortunately, the exact solutions involve the infinite series with respect to the time and the zeros of the second-order usual Bessel function of the first kind. To avoid a difficulty of computing the infinite series for a very small time, this study investigates the asymptotic behavior for the early stage of motion. In addition, a singular perturbation approach is presented in Appendix and th...