Entrainment in Pulsing plumes

Abstract

The main contribution of this work is to investigate the entrainment in plumes with constant and time-varying source conditions experimentally. The study aims to build up an experiment rig to conduct the bulk entrainment measurement in plumes. Secondly, the study aims to examine the influences the forcing frequency and amplitude have on entrainment in pulsing plumes, where the flow rate, momentum and buoyancy are sinusoidal functions of time. Finally, the study aims to investigate the validity of the integral model for pure plumes with constant source conditions established by Morton et al. (Proc R Soc Lond A 234(1196):1–23, 1956) in pulsing plumes, as well as the virtual origin correction method for lazy plumes proposed by Hunt and Kaye (J Fluid Mech 435:377–396, 2001) in both constant source plumes and pulsing plumes. Experiments were conducted to verify the pulses in pulsing plumes. Plumes are formed by issuing saline fluid downwards into a less dense uniform environment from a round pipe. The pulsing flow is generated by a programmable ISMATEC gear pump. The evolution of the pulses in pulsing plumes is revealed by applying the light-attenuation method with high frequency imaging. Pulsing is shown to affect the development of the flow, as the forcing frequency at the source dominates the frequency of the flow downstream. To study the bulk entrainment in pulsing plumes, turbulent axisymmetric lazy plumes with constant source conditions were examined initially. The bulk dilution and entrainment measurements were achieved by using the experimental approach of Hunt and Kaye (J Fluid Mech 435:377–396, 2001). The integral relationship for the local flow rate Q(z) and local momentum M(z) from the model established by Morton et al. (Proc R Soc Lond A 234(1196):1–23, 1956) for constant source plumes was used to determine the average local entrainment. Experiments with pulsing plumes were carried out with a flow rate amplitude ranged from 33% to 80% and the non-dimensional frequency - Strouhal number 〖St=fD/U〗_0 ranged from 0.012 to 1.2, where the maximum frequency f of this pulsing plume is in the order of the eddy turnover time scale at the source, D is the source diameter and U_0 is the average velocity at the source. The entrainment coefficient was determined in pulsing plumes and was found within the range of the entrainment values in plumes with constant source conditions. The influence of the forcing frequency and amplitude is examined, and found to be very small over the entire range of source conditions considered. The virtual origin correction method of Hunt and Kaye (J Fluid Mech 435:377–396, 2001) is found to give a reasonably good estimation in predicting the virtual origin in pulsing plumes. The results suggest that the local entrainment velocity is proportional to the time-average local plume velocity even in pulsing plumes where the local velocity is varying with time. This supports the application of the integral model of Morton et al. (Proc R Soc Lond A 234(1196):1–23, 1956) to building ventilation problems and environmental flows where these conditions exist.