A Study On The Turbulence Generation Mechanism Of Transitional Fountains In Linearly Stratified Fluid And Its Application

Fountains injected into stratified fluids are widely found in the nature and engineering settings.The transition to asymmetry and the asymmetric behavior of transitional fountains are the keys to shed light on the turbulence generation mechanism in fountains.The stratification of the ambient fluid further complicates the transition to asymmetry and the asymmetric behavior of transitional fountains.In this thesis,a series of three-dimensional direct numerical simulation(DNS)have been carried out for transitional round fountains in linearly-stratified fluids over the ranges of 100 ? Re ? 400,1 ? Fr ? 8 and 0.0 ? s ? 0.3,where Fr,Re and s are the Froude number,the Reynolds number and the dimensionless temperature stratification parameters,respectively,to examine qualitatively and quantitatively the effect of these parameters on the transition of axisymmetric fountains to be asymmetric,their asymmetric behavior,and their maximum penetration heights,etc.It is found that:(1)the transition to asymmetry and the asymmetric behavior of round fountains are well represented and quantified by tangent velocity;when a round fountain maintains its axisymmetric behavior,the tangent velocity should be zero everywhere in the flow field and any non-zero or non-negligibly small tangent velocity will indicate an asymmetric behavior.(2)When Fr or Re is small,a fountain usually keeps its axisymmetric behavior all the time;however,when Fr is increased or Re is large,the axisymmetric behavior will be present only at the early development stage and the fountain will become asymmetric after the time for transition to asymmetry is passed and the asymmetric behavior is at the quasi-steady state,with the maximum tangent velocity fluctuating around an essentially constant time-average value.(3)On the contrary,the stratification of the ambient fluid plays a positive role to stabilize the flow and to reduce or even to eliminate the asymmetric behavior.(4)The numerical results have also been used to develop a series of scaling relations,in conjunction with the scalings obtained with dimensional analysis,for the time for transition to asymmetry,the initial and time-averages fountain penetration heights,the time for the fountain to attain the initial penetration height,etc;it is found that in general these characteristic parameters are under significant influences of Fr and s,but the effect of Re is in general much weaker than those of Fr and s.In this thesis,the storage tank of a typical solar water heating system has been chosen to illustrare the application of fountains in linearly stratified fluid,through using numerical simulation to analyse the hot water removal behavior at the water discharge stage at three commonly used flowrates.It is found that:(1)the change of the local dimensionless thermocline within the temperature stratification does not follow the change of flowrate well,but the average dimensionless thermocline increases with the inlet flowrate of cold water;the average thickness of the dimensionless thermocline at the large flowrate is about twice of that at intermediate and small flowrates;at intermediate and small flowrates,although the thickness of the dimensionless thermocline increases with flowrate,the change is small;however,at the large flowrate,the dimensionless thermocline is very thick at the discharge stage,but then reduces very quickly,until at about the dimensioless time 0.4,which subsequently changes slowly.This is because at the early discharge stage,the mixing between the cold and hot water is strong when the flowrate is large;but with the increase of the cold water region,the influence of the larger momentum of the ejected cold water reduces gradually;with the increase of flowrate,the temperature in the cold water region becomes higher at the same location;at the flowrates of 2.5 L/min and 10 L/min,the temperature difference is about 14 K at the dimensionless tank height of 0.2,indicating that with the increase of flowrate,the mixing becomes stronger and the amount of hot water that can be removed is reduced.(2)the dimensionless exergy in the tank gradually decreases,with similar trends for different flowrates;at the same dimensionless time,the dimensionless exergy in the tank increases with flowrate,with the average dimensionless exergy of 0.578 at the flowrate of 10 L/min,which is 2.48 times of that at the flowrate of 2.5 L/min,indicating that the useful heat in the tank reduces gradually with the discharge time and the mixing in the tank is stronger when the flowrate increases,resulting in smaller amount of useful heat in the tank.After the analysis of the effect of the inlet cold water flowrate on the water discharge,this thesis has carried out numerical simulation to study the flow behavior at the temperate stratification gradients of 5 K/m,10 K/m and 20 K/m at the intermediate flowrate widely used in practical applications.The results show that: the thickness of the dimensionless thermocline reduces and then increases with time,but its average value does not vary noticeably at different temperate stratification gradients,with the the value of about 0.1,indicating that the change of the thinkness of the dimensionless thermocline does not represent the mixing of the cold and hot water in the tank.(2)The dimensionless exergy decreases gradually with time and the thinkness of the dimensionless thermocline,but the change trend at the temperate stratification gradient of 20 K/min is different from that at smaller temperate stratification gradients;the average dimensionless exergy is 0.3263 at the temperate stratification gradient of 5 K/min,compared to 0.2103 at 20 K/min,indicating that when the thinkness of the dimensionless thermocline is increased,the average dimensionless exergy reduces significantly so the useful heat in the tank becomes larger.Such results further confirm the main conclusions obtained previously from the analysis of the behavior of round transitional fountains in linearly stratified fluids,that is,the stratification reduces the mixing between cold and hot water,with the reduction increasing with the dimensionless temperate stratification gradient,thus the stratification of the ambient fluid plays a positive role to stabilize the flow and to reduce or even to eliminate the asymmetric behavior.(3)The average dimensionless exergy in the tank increases with the dimensionless temperate stratification gradient in a linear manner.