Numerical Investigation of Semi-Turbulent Pipe Flow

Surface deformations of a jet ejected from a straight-pipe atomizer may be due to the turbulent fluctuations in the interior of the pipe. At relatively low Reynolds number (Re) near the transition from laminar to turbulent pipe flow (e.g. Re = 3000 based on the mean velocity and the pipe diameter), an unsteady semi-turbulent state exists which differs from the better known fully developed flow at higher Re. In the present work low- and high-Re jets are investigated experimentally by the DLR group. To identify the influence of the inner injector flow condition to the jet surface phenomena a special injector set-up has been designed. With this setup it was possible to eliminate relative velocity effects between jet and ambient fluid. Using shadowgraphy and a novel image processing approach, wavelengths, amplitudes and undisturbed jet length could be determined. The corresponding pipe flow is simulated numerically using Direct Numerical Simulation (DNS) by the University group. A new second order finite difference scheme in space and time for the incompressible Navier-Stokes equations in cylindrical coordinates is applied. The slope of the axial mean velocity profile near the wall is smaller than that for higher Reynolds number. The turbulent intensities are smaller than those at higher Re. The observed jet surface waves agree well with the computed lengths scales of the turbulent structures within the injector. Varicose instability is observed. Atomization is affected when Re is reduced to the semi-turbulent state(Re=3000), due to the thicker laminar envelope.