INTRODUCTION
P ROBLEM STATEMENT
M ETHODOLOGY
An important work has been done to check the physical parameters of the experimental simulation. It is then chosen to model the turbulent dispersion and the freezing process of the particles in the wind tunnel using simple models.
O UTLINE OF THE T HESIS
Chapter five deals with the numerical modeling and the analysis of the growth obtained during the experimental campaign. Thus, the role of particle inertia and liquid water content on wet snow accumulations is quantified.
LITERATURE REVIEW ON WET SNOW ACCRETION PROCESS
O VERVIEW OF THE SNOW INTERACTION ON STRUCTURES
- Interactions with buildings
- Interactions with cables
- Interactions with terrestrial transports
- Interactions with wind turbines
- Overview conclusion
Terrestrial transport, which focuses on the train box, can also be affected by wet-snow accretion problems. The last branch that was examined for wet-snow accretion was the wind turbine case.
P HYSICAL CHARACTERIZATION OF SNOW PARTICLES RESPONSIBLE OF WET SNOW ACCRETIONS
- An approach to reproduce wet snow: artificial snow produced by a snow gun
- Snow particles characterization conclusion
Artificial snow consists of water droplets that freeze when injected into the ambient air. Moreover, due to the physical atomization process, the artificial snow particles are close to a spherical shape [27, 28].
E FFECTS OF LWC ON IN CLOUD ICING ACCRETIONS
One of the most relevant works on the variation effects on the resulting accretion was presented by Lozowski et al. The works of Lozowski also noted how the increase of the can affects the accretion form as also reported by Lynch et al.[29].
M ODELING WET SNOW ACCRETIONS : THE APPROACH CHOSEN
- Aerodynamic aspect of accretion process: collision efficiency
- Mechanical aspect of accretion process: sticking efficiency
- Thermal aspect of accretion process: accretion efficiency
- Accretion modeling conclusion and synthesis of the accretion steps
Considering the liquid part of the influent mass flow, the collection efficiency can be expressed as (4). Where ̇ represents the aggregate mass flux associated with the liquid and solid part of the particles.
T HEORETICAL APPROACH TO CONTROL PARTICLE : THE PARTICLE FREEZING THEORY
- Particle freezing theory conclusion
In this work, this equation will be solved by a time discretization as a function of the particle temperature 𝑇. In this phase of the freezing process, the particle temperature 𝑇 is assumed equal to the equilibrium freezing temperature: 𝑇.
T HEORETICAL APPROACH TO MODEL SNOW PARTICLES DYNAMIC IN THE AIR FLOW
- Forces acting on particles
- Stokes number definition
- Particle-flow interaction modeling
- Modeling of the turbulence fluctuation
- modeling conclusions
- Inertia effect and Crossing trajectories effect
The lift force is the force with which the fluid acts on the particle in the perpendicular direction of the particle movement. 𝑇 𝑇 [ ] (34) Where 𝑇 is the integral time scale of the fluid seen by the particles as a result of the inertial effect.
C ONCLUSION
Tropea, "Droplet-wall collisions: Experimental studies of the deformation and breakup process," International Journal of Multiphase Flow, vol. Graham, "On the inertia effect in eddy interaction models," International Journal of Multiphase Flow, vol.
EXPERIMENTAL APPROACH TO INVESTIGATE WET SNOW ACCRETIONS
C LIMATIC CONDITIONS REPRODUCTION : CLIMATIC WIND TUNNEL
This large temperature range allows the reproduction of several climatic conditions, including storms with wet snow. A set of rotating vanes is placed upstream of the flow inlet to ensure a level flow in the test chamber (Figure 34).
W ET SNOW PRODUCTION : SNOW GUN
The measurements were carried out as in Figure 36, with the snow cannon placed on one side of the wind tunnel. One is aware that the distribution of figure 35 does not exactly correspond to the distribution at the exit of the snow cannon. Since our studies focus on the mass of the accreted snow, the diameter is the most appropriate to deal with.
Thanks to the trap door, a good part of the mixture flowed away under the soil of the test section.
T EST CAMPAIGN DEVICES TO STUDY WET SNOW ACCRETIONS
- Investigation of the aerodynamic aspect: test structure
- Estimation of the incoming snow flow rate: snow collectors
- Temperature monitoring: thermocouples, flow visualization: GoPro camera
- Characterization of the incoming flow: ultrasonic anemometer
Where 〈 〉 is the average snow mass accumulated in the four snow collectors, the area of the snow collector and the duration of the test. The test is based on the estimation of the average snow flow between the four collectors: 〈 〉, defined in equation (38). In order to investigate this problem, a series of measurements of the snow flux distribution was carried out.
This coefficient is taken equal to the average difference between the snow mass collected in the middle and on one side of the flow.
E XPERIMENTAL PROCEDURE TO REPRODUCE WET SNOW ACCRETIONS
- Wind tunnel setup
- Experimental principle to reproduce wet snow accretions
- Procedure undertaken during the experimental campaign
- Preliminary wind tunnel settings up: analysis of snow flow homogeneity and test
The influence of the particle state on the measurement is not well documented in the literature. For the setup of the test campaign, this particle has a flight time of (the purple line in Figure 53). The aerodynamic aspect is investigated by changing the diameter of the cylinder placed on the test structure.
The first was characterized by two snow cannons placed on both sides of the climate chamber (Figure 56).
T HE EXPERIMENTAL RESULTS
- Snow flow characterization through the ultrasonic anemometer
- Heat exchange blockage: estimation of the real flow speed
- Wet snow accretions quantification: coefficient β
- Experimental analysis of the thermal aspect of wet snow accretions
- Experimental analysis of the aerodynamic aspect of wet snow accretions: cylinders role
In the case of snow flow, the evaluation of the integral length scale leads to approximate values. Figure 71 shows the coefficient as a function of ambient temperature for a cylinder with a diameter of 50 mm. In this case, the effect of temperature on accretion is clearly visible from the images.
To study the aerodynamic aspect of the accretion, three cylinders with different diameters are used.
P HYSICAL MEASUREMENTS APPROACHED
As a conclusion of the analysis, the smaller the cylinder, the more favorable the accretion due to the more inertial behavior of the particles in front of the cylinder. The aerodynamic aspect with the assessment will be deeply investigated in the fifth chapter thanks to the numerical simulations of particle scattering near the cylinders. Due to the difficulty in obtaining the particle distribution through physical measurements, a stochastic particle model was established to estimate this distribution.
Seeing the difficulties encountered in estimating the particle through physical measurements, a numerical model has been created to overcome this issue.
C ONCLUSIONS
Gubler, “FlowCapt: a new acoustic sensor to measure snow drift and wind velocity for avalanche forecasting,” Cold Regions Science and Technology , vol. Zimmerli, “Snow Drift: Acoustic Sensors for Avalanche Warning and Research,” Natural Hazards and Earth System Sciences, vol.
PHYSICAL MODELS FOR THE DETERMINATION OF THE BOUNDARY CONDITIONS
M ODEL IMPLEMENTATION : ESTIMATION OF PARTICLE AT THE INSTANT OF IMPACT COUPLED WITH FLOW -
- Equations implementation in the coupled model: thermal and dynamic equations
- Hypothesis introduced to represent the experimental conditions
- Implementation in the model of the experimental conditions: thermal and flow
- Resolution procedure of the coupled model
- Model implementation conclusions
By taking a particle of, the particle freezing model presented in this chapter quantifies an average heat transfer coefficient. As a result, the particle distribution is assumed to be uniform along the central part of the cylinder. The temperature profile of the first stage is solved as (77) until the particle temperature reaches 𝑇.
Therefore, the time step of the coupled model will be based on the particle scattering aspect as (86).
M ODELS RESULTS DISCUSSION
- Boundary condition estimation: particle distribution “on” the cylinders
- Particle size distribution on the cylinder
- The role of the gravity on particle distribution
- Particles “on” the cylinder surface as a function of the ambient temperature
- Physical parameters which can drive the particle
- Boundary condition estimation: of the whole snow particle flow
Additionally the distribution will not be weighted with the snow gun particle distribution. Therefore, it can be considered that a slight change in the ambient temperature during the experimental campaign leads to a significant change in the liquid water content. Thanks to the coupled model, we analyze the effect of physical parameters on the particle.
This makes it possible to associate a unique value of liquid water content with the particle flow as a function of the ambient temperature.
C ONCLUSION
It can be observed that the consideration of a volume average diameter does not correspond to the global liquid water content. In addition, we have shown that the liquid water content is very sensitive to temperature changes: 𝑇. Bédécarrats, “Experimental study and modeling of water droplet crystallization,” International Journal of Refrigeration , vol.
Chen, “Experimental and numerical analysis of the temperature transition of a floating icy water droplet,” International Journal of Heat and Mass Transfer, vol.
ESTIMATION OF THE PARAMETERS TO MODEL WET SNOW ACCRETIONS
D ETERMINATION OF THE AERODYNAMIC CONTRIBUTION TO WET SNOW ACCRETIONS : COLLISION EFFICIENCY
- Numerical modeling of the flowstream around the cylinders: setup
- Numerical modeling of the flowstream around the cylinders: results
- Lagrangian simulations of particle dispersion around the cylinders: setup
- Flowstream and lagrangian modeling setting up conclusions
Therefore, the first step of the analysis is to set up a numerical model to study the particle behavior close to the cylinders. Where is the integral length scale of the snow flow equal to as seen in the experimental section. The average wall distance of the first grid (96) for the three cylinders is close.
Particles are assumed to reach the cylinder at the same velocity of the flow.
C OLLISION EFFICIENCY EVALUATION OF THE EXPERIMENTAL CYLINDERS
- Relation between Stokes number and collision efficiency
- Particle size distribution on the cylinders and the resulting liquid water content
- Collision efficiency evaluation: conclusions
This part of the chapter presented the method to evaluate the crash efficiency for the three cylinders tested in the experimental campaign. To study the relationship between and collision efficiency, the Stokes number for each diameter class of the injected particle size distribution was evaluated. It is possible to estimate the collision efficiency of the cylinder starting from this curve.
This part of the chapter concerns the evaluation of the impact efficiency and the global liquid water content of the mass impacting the cylinders.
Q UANTIFICATION OF THE COLLISION EFFICIENCY IMPACT ON THE EXPERIMENTAL COEFFICIENT
When the accretion efficiency is lower than one, some of the particles that stick to the cylinder do not contribute to the accretion. According to previous accretion models (Messinger [4], Guffond [5], Makkonen [6] or the ISO 12494 standard [3]), the liquid part of the particles stuck on the cylinder does not completely freeze. As reported in Figure 134, the sticking coefficient increases with the increase in liquid water content of particles reaching the cylinders.
On the other hand, if one can assume that the differences are related to experimental errors that influence, one can assume that the adhesive efficiency is not just a function of global liquid water content.
Q UANTIFICATION OF MODELED ACCRETION SHAPES
An example of the approach undertaken to evaluate the accretion form is reported in Figure 136. With the accretion form obtained, a new numerical calculation of the flow around each cylinder was performed. As one can see from Figure 138, the calculation procedure associates the aerodynamic evaluation of the flow around the cylinder and the Lagrangian particle distribution model.
The result of the aerodynamic calculation affects the result of the particle distribution which determines the shape of the collection.
S TICKING EFFICIENCY AS A FUNCTION OF THE PARTICLE - SURFACE ANGLE OF IMPACT
- Theoretical implementation of the angle criterion and application to the experimental
- Accretion shape obtained with a threshold angle
- Accretion shape influence on the global collision efficiency
- Sticking efficiency evaluation for the experimental cases
As a consequence, models based only on the angle criterion may not be sufficient to reproduce the shape of the cluster. For step 24, only one particle is added to the stack according to the angle criterion (Figure 149 square 4). This explains how the mass adhering to the surface decreases with increasing aggregation.
Therefore, for the simulation cases presented, the adhesion efficiency affects the growth progress more than the collision efficiency.
A NALYSIS OF THE STICKING COEFFICIENT ( ) ON THE EXPERIMENTAL CASES
- Sticking efficiency analysis: conclusions
In any case, the growth on the upper and lower parts of the cylinders is not well predicted. Either way, it suggests that the adhesive efficiency is related to the velocity of the particles. It can be assumed that this "excessive fouling" is related to the decline of the liquid part of the fouling.
Moreover, the numerical results showed that ( ) fails in predicting the accretion on the upper and lower part of the cylinder.
C ONCLUSION
The second part of the chapter is focused on the modeling of the retention coefficient. In this part, the adhesion efficiency was investigated as a function of the global liquid water content. One can assume that the liquid part of the snow particles acts as a "glue".
However, it fails to predict accretion on the upper and lower part of the cylinder.
CONCLUSION
La modélisation soutient l'approche expérimentale consistant à ajuster le TEL des particules en fonction de la température ambiante. Le premier aspect a été analysé en modifiant le TEL des particules en ajustant la température ambiante. La première partie du chapitre présente l'analyse de la tendance des particules à entrer en collision dans le cylindre.
La deuxième partie du chapitre est consacrée à l'analyse de la tendance des particules à rester « collées » à la surface et à la modélisation de formes expérimentales.
