Experimental study of vertical jets in JONSWAP random waves

Abstract

The most common practice for wastewater disposal is to discharge the treated effluent into a large water body, such as oceans and streams. This is because the large volume of fluid provides a very good environment for dilution of the treated effluent. Consequently, an initial lower level of treatment scheme is sufficient before the discharge. Wastewater discharged into ambient fluid, thus, offers an economically attractive form of disposal. Waves appear in all open coastal areas around the world. Waves are usually generated by wind and distant swell and normally have various frequencies and are random. The effect of regular surface waves on jets has been studied before and the results show that the jet fluid mixing process will be enhanced. Similar effect is expected for jet discharge in natural random wave environments. The jet-wave interaction process has been investigated for many years with most studies focusing on the interaction between jet and regular waves. However, an investigation of the jet characteristics in the presence of random waves has received less attention. In an attempt to fill this knowledge gap and deepen the understanding of jet behaviour, an experimental study on a round jet in random surface waves is carried out in a laboratory wave flume. A submerged turbulent jet, fed from a constant head water tank, discharges vertically at the bottom of the flume in which random waves are generated by a DHI random-wave maker. An acoustic Doppler velocimeter (ADV) is employed to measure the jet velocity as well as the associated velocity fluctuation within the jet body for time-averaged analysis. Wave-induced characteristic velocities and wave-induced momentum characteristic lengths are developed based on the wave energy spectrum. Those developed scaled parameters are then used in the data analysis. The time-varying experimental data are collected. The jet characteristics such as the declining rate of jet centerline velocity, the jet spread rate, cross-sectional velocity profiles and the turbulence intensity are investigated. The results show that the jet centerline velocity in the random wave environment, in general, decays faster than that in the stagnant environment. With the use of dimensional analysis, the velocity variation is similar to that in the pure jet condition when the non-dimensional jet distance is short (i.e. z/lw<=0.1) while the degree of data scattering increases when z/lw > 0.1 . This result can be explained by the existence of transition region between the jet-momentum governed region and the wave momentum governed region. A non-linear jet half-width spread rate is also observed. This can be explained by that more ambient water is entrapped into the jet body due to the additional turbulent entrainment contributed by the wave-induced cross-current. Empirical formulas are proposed to predict the velocity decay rate and the jet width spread rate. The cross-sectional velocity profiles, in general, follow the normal distribution curves while multi-peak velocity profiles occasionally appear. The occurrence of multi-peak profiles in an Eulerian frame is possibly due to the periodic lateral movement of the jet trajectory arising from the wave motion. The experimental results show that waves cause a shift of the location of peak turbulence towards the jet outlet. The extent of shift in location depends on the wave properties, showing that the jet turbulence is generated by both the wave motion and jet motion. A Lagrangian integral model of jets in random waves has been proposed. With the use of appropriate entrainment coefficients, the results obtained from the integral model are in good agreement with the experimental results. Both the integral model and the empirical formulas are also extended to prototype situation. The results show that the jet centerline dilution can be increased by 25%.