## An Experimental Investigation of Velocity Distribution and Head Loss of Oscillatory Flow in a Rectangular Duct with Sand Roughness

##### Abstract

Frequency and amplitude dependency of velocity distribution and head loss of oscillatory flow in a rectangular duct have been studied experimentally with a model tunnel system.
Tests were carried out with the duct of both smooth and rough walls. The smooth wall was made of Plexiglas. Sand roughness was used for the rough wall. Velocity, pressure and differential pressure of stationary flow, pure oscillatory flow and combined oscillatory flow were measured. The combined oscillatory flow was classified as oscillation dominant flow, stationary dominant flow, and oscillation-and-stationary balanced flow. Various oscillating frequencies, amplitudes and steady flow percentages were tested for oscillatory flows. The oscillating frequencies tested were varied from 0.01 Hz to 1.00 Hz. Oscillatory amplitude and stationary part were varied from 10 to 100%. Velocity of the flow was measured with a 2D PIV (Particle Image Velocimetry) and a 2D LDV (Laser Doppler Velocimetry) respectively at different test stages. The maximum mainstream velocity was ranged from 0.05 m/s to 1.1 m/s. Data of pressure variations along the tunnel were collected with differential pressure sensors. Flow rate and instant wall pressures at multiple points along the test tunnel were measured simultaneously. The static pressure in the test tunnel was about 1.0 mWC. The differential pressure along the tunnel was less than 20 mmWC per meter.
Examples of velocity distribution in the test rig from LDV measurement are presented, for both stationary flow and oscillatory flow. The dimensionless velocity distributions of stationary flow are in good agreement with the universal velocity distribution law. Deviations are obvious between the velocity distributions of oscillatory flow and the universal velocity distribution law, when the measured velocity is scaled to dimensionless by friction velocity from Clauser chart. Examples of PIV velocities of different flow regimes are presented in the forms of velocity profile and velocity waveform. Generally, the velocity distributions are in good agreement with the results from LDV, in agreement with the normal turbulent velocity distribution in a duct, if the velocity magnitude is not too small. Dimensionless velocity profiles at various phase angles of the same oscillatory flow regime have quite consistent distribution. The annular effect is observed in some cases. Its occurrence depends on the complex actions of oscillating frequency, amplitude and stationary flow percentage. The velocity waveform confirms the characteristics of mass oscillation of the flow. No significant phase shift is displayed between the velocity waveform of the boundary and centreline in most cases tested. The vertical velocity, which is normal to the mainstream, is quite small and has similar features to the mainstream velocity.
The velocity profiles got from both LDV and PIV show that the flows in the test tunnel were typical turbulence, with typical velocity distribution of turbulence. No transition between laminar and turbulence is observed even at the turning point of oscillation.
Pressure variations measured along the tunnel of different flow regimes are presented. The accelerative heads of oscillatory flow are calculated. The friction head losses along the tunnel are evaluated. The dependencies of pressure variation and friction head loss on oscillatory frequency and amplitude are investigated for both pure oscillatory flow and combined oscillatory flow. It is proven that the friction head loss of oscillatory flow increases along with the increase of frequency if the mean flow rate is kept constant. The peak friction head loss increases along with the increase of oscillatory amplitude. Comparison of pressure variation and friction head loss between stationary flow and oscillatory flow shows that the friction head loss of unsteady flow is much bigger than that of steady flow. This is in good agreement with the expectancy based on the experimental results of laminar flow. The head loss of pure oscillatory flow was greater than that of the stationary flow for dozens or more times for various flow regimes running at equivalent flow rate. The ratio of head loss of combined oscillatory flow to stationary flow running at equivalent flow rate is smaller than that of pure oscillatory flow to stationary flow, several times to dozen times. In general, the frequency dependency of head loss on oscillatory frequency and amplitude is clear, though the measuring length is only 9 metres and the absolute magnitude of pressure variation is less than 0.20 mWC.