1 Quantités moyennées à partir des données expérimentales. . . xiv 2 Partition de la population de gouttes par classe de diamètre. . . xiv 1.1 Physical properties of a phase-incompressible two-phase flow in SI-Units. . . . 7 1.2 Operating conditions of a phase-incompressible two-phase flow. . . 7 1.3 Summary of the criteria for the cylindrical liquid jet fragmentation regimes. . . 8 1.4 Experimental conditions used in the study performed by Stevenin [57]. . . 9 1.5 Physical properties of the study-case in SI-units at normal conditions. . . 10 1.6 Dimensionless numbers for the study-case conditions. . . 10 2.1 Integration and interpolation methods used in the OpenFOAM solver. . . . 33 2.2 Spatial discretization methods used in the OpenFOAM solver. . . . 34 2.3 Boundary conditions expressed in OpenFOAM solver. . . . 35 2.4 Number of decomposed regions in the scalability test. . . 40 2.5 Mesh configurations for the mesh solution convergence test. . . 41 3.1 LDV BSA set-up for liquid and gas phases analysis. . . 51 3.2 Convergence criteria for the LDV liquid points. . . 53 3.3 Convergence criteria for the LDV gas points. . . 54 3.4 Partition of droplets population by class of diameter. . . 63
Nomenclature
Greek alphabet
Σ Mean liquid/gas interface surface per unit volume [m2
· m−3] ˜
Ω Mean liquid/gas interface surface per unit mass [m2
· kg]
τi j Viscous constraint tensor [kg · m−1· s−2]
ϵ Turbulent kinetic energy dissipation rate [m2
· s−3]
ρ Density [kg · m−3]
ν Kinematic viscosity [m2
· s−1]
µ Dynamic viscosity [kg · m−1· s−1]
σL−G Liquid-gas surface tension [N · m−1]
δi j Kronecker tensor [−]
Latin alphabet
x, y, z Cartesian axial distance [m]
ui Velocity vector [m · s−1]
Ri j Reynolds stresses tensor [m2· s−2]
Fi Turbulent mass flux vector [m · s−1]
k Turbulent kinetic energy [m2· s−2]
g Gravity acceleration [m · s−2]
p Pressure [P a]
˜
Y Liquid mass fraction [−]
Y Liquid volume fraction [−]
Nomenclature
Ln Nozzle length [m]
Lc Liquid column breakup length [m]
S Spreading rate [−]
A Axial centerline velocity decay rate [−]
y0.5u Axial velocity half-width [m]
d[30] Volume equivalent sphere diameter [m]
d[32] Sauter mean diameter or SMD [m]
Re Reynolds number [−]
W e Weber number [−]
Oh Ohnesorge number [−]
St Stokes number [−]
C Contrast ratio [−]
l Relative grey intensity level [−]
w Contour curve
Subscripts and superscripts
i Cartesian vector component, i = {1, 2, 3} or i = {x, y, z}
i j Cartesian tensor component, i , j = {1, 2, 3}
L Refers to the liquid phase
G Refers to the gas phase
S Refers to the liquid-gas slip
J Refers to the nozzle injection point
0 Refers to the jet’s centerline
t Turbulent quantity
(k) Refers to the droplet class k Symbols and operators
Reynolds average
Nomenclature ′
Reynolds turbulent fluctuation ′′
Favre turbulent fluctuation 〈 〉 Generic ensemble average
Abbreviations
R AN S Reynolds Averaged Navier-Stokes Equations
RSM Reynolds Stress Model
LDV Laser Doppler Velocimetry
DT V Droplet Tracking Velocimetry
OP Optical Probe
SN R Signal-to-Noise Ratio
B P Band-Pass Filter
Introduction
This doctoral thesis is a product of the joint collaboration between the Institut de Recherche
sur les Phénomènes Hors Equilibre (IRPHE) and the Institut National de Recherche en Sciences et Technologies pour l’Environnement et l’Agriculture (IRSTEA). All activities are carried out at
IRSTEA Montpellier Centre, under the particular research topics at the UMR ITAP (Unité Mixte de Recherche Information – Technologies – Analyse environnementale – Procédés agricoles) and UMR G-Eau (Unité Mixte de Recherche Gestion de l’Eau, Acteurs, Usages). This doctoral thesis is partially financed by a fellowship from the Chilean government CONICYT Becas Chile. The study subject of this thesis is the atomization of liquids in agricultural applications. Al-though this is not explicitly treated in this work, there are two main research topics accounted. From one side, on the use of pesticides sprayers for crop protection: to minimise problems due to the transport of polluting agents from the treated crops to air, water and ground. And in another side, on the optimisation of water usage for irrigation: to improve the efficiency of sprinklers that simulate the natural irrigation made by rain, limiting loses and heterogeneity. Both study subjects are not treated from any specific application point-of-view. Instead, a generic case is created to investigate the atomization and dispersion of a liquid jet, which may share some elements with the original subjects, like the type of fluid and operating regimes (geometry, flow-rate and pressure). These similarities and the justification for the construction of this study case are presented in Chapter 1, where a simplified water round nozzle is conceived. In particular, the importance of conducting experimental and numerical approaches at the same time.
A choice is made on the type of flow modelling and numerical simulations. This is addressed in Chapter 2, where the specific approach of a mixture RANS turbulence modelling is used. The numerical method to solve the flow equations is also detailed, where a custom solver is built using the OpenFOAM CFD code. Although the experimental observations are introduced later, the construction of the numerical simulation cases is made in accordance with the experimental results.
The experimental campaign is presented in Chapter 3. Two main optical non-intrusive techniques are used to measure in both liquid and gas phases. The objective is to estimate the velocity field and droplet’s sizes. LDV measurements are carried out first, where the main
Introduction
challenge is to capture separately the liquid from the gas acquisitions. To measure the droplet sizes and velocities, a custom DTV algorithm is constructed and applied to shadow images of droplets in the dispersed region of the jet. Using the data from the two experimental measurement techniques, the mean and fluctuating velocity fields are estimated, along with the droplet’s sizes distribution.
The comparison between the results from the experimental and numerical approaches is presented in Chapter 4. Several parameters like the axial velocity decay-rate and the spreading rate of the jet are compared with numerical model cases. A focus is made on the reconstruction of the Reynolds stresses by class of droplet sizes and role of the mean liquid-gas slip-velocity as a source of anisotropy seen by the particular turbulence modelling.
A final set of conclusions are given in Chapter 4.2.4, along with some perspectives on some specific subjects that are not treated in this work, and that may be useful to improve the analysis for such atomization study.