These particles can influence the properties of the bubble and slug, such as shape, speed and wake. Thus, the effect of solid particles is first studied by observing the motion of bubbles and snails in any magnetic fluid. The patterns of bubble and slug movement are investigated to predict the effective conditions for power generation.
Introduction
Thus, the influence of the magnetic force on the current field was studied by various researchers. Thus, it is difficult to observe a clear effect of the magnetic force under normal gravitational conditions. However, under microgravity conditions, the effect of the magnetic force can be observed, and the magnetic force can drive the bubble.
Investigation of bubble movement
- Bubble dynamics
- Level-set method
- Conditions for simulation
- Validation of the solver
- Comparison with the bubble regime diagram
- Comparison with experimental data
- Results and discussion
- Effect of solid particle
- Effective bubble movement for energy generation
In other words, the properties such as bubble rise velocity and bubble shape can be predicted by the bubble regime diagram. In this study, the level set method is used to investigate the bubble motion numerically. In the equalization equation, the LHS gives the correct motion of the bubble surface, and the RHS is needed for numerical stability.
In figure 2.5 it is easily observed that the numerical results agree well with the bubble regime diagram. Thus, the solver used in this study is reliable to investigate the bubble motion. The effect of solid particles can therefore be observed by comparing the bubble motion in each magnetic fluid.
However, the shape of the bubble in each magnetic fluid is almost the same if the bubble diameter is the same. In the bubble regime diagram, however, both cases are located in the same region (sphere shape). Thus, the bubble shape is almost the same for each case, even though the dimensionless numbers are different.
However, the bubble shape can be changed if a much larger amount of solid particles are dispersed in the liquid. Thus, the bubble motion in EFH3 is more strongly disrupted than in the EFH1 case. As time passes, the velocity of the surrounding magnetic fluid is gradually increased due to the bubble motion.
Investigation of slug movement
Phase-field method
The effect of the magnetic force can also be investigated by adding the magnetic force to the RHS of the momentum equation. From this, as with the level setting method, the LHS gives the correct movement of the interface. In this case, the convective term (u ∙ ∇𝜙𝑝𝑓) of the phase field equation is in a non-conservative form.
It will be verified that this convective term can give good results for slug motion. On the RHS, 𝜖𝑝𝑓 is the controlling parameter related to the thickness of the interface, and 𝛾𝑝𝑓 is the mobility related to the time scale of the interface diffusion. It can therefore be expressed by the surface tension and interface thickness control parameter, as discussed above.
For the stability of the system, the RHS of the phase field equation aims to minimize the total free energy with a relaxation time controlled by the mobility. In COMSOL Multiphysics, the mobility is determined by a mobility spin parameter (𝜉) which is a function of the interfacial thickness, as discussed above. In this study, the default value of the mobility parameter (𝜉 = 1) is used to investigate the movement of the snail.
This value can give good results for most cases [24], and it will be validated in a later section.
Conditions for simulation
In Figure 3.1, the flow field is first filled with some fluid and the slug is placed in it. One of the side boundaries (walls) is treated as a no-slip boundary condition, and the other is an axisymmetric boundary condition. When the nozzle moves in stagnant fluid, the upper and lower boundaries are treated as a pressure outlet and no-slip wall, respectively.
The movement of the slug with liquid backflow is also investigated in this study, because it can occur in real situations. Thus, the upper limit is treated as a fluid velocity inlet and the lower is treated as a pressure outlet when the plug moves with fluid return. As in the bubble study, the steam is used as a slag and EFH1 and EFH3 are used as the surrounding liquid.
Furthermore, similar to the bubble simulation, the computational domain is constructed with fixed triangular meshes evenly distributed over the entire domain to investigate the snail's motion. Unlike bubble simulation, a small amount of mass loss can be generated in this case because the convective term is set as a non-conservative form for easy convergence of the calculation. Figure 3.2 shows that both parameters change as the number of elements increases.
Validation of the solver
- Comparison with previous research studies
- Comparison with experimental data
Like bubble dynamics, these dimensionless numbers are related to fluid properties (viscosity, density, and surface tension), the acceleration of gravity, and the rising velocity of the slug. In other words, the characteristics of the slug can be determined by these three-dimensional numbers. This means that fluid viscosity does not affect slug velocity for low viscosity fluids.
The glass tube is placed at the outlet of the evaporator to observe the movement of the sludge. In this figure, it is observed that the surface of the sludge in HFE7300 is rough and that the small bubbles are. However, the surface of the varnish in DI water is relatively smooth and small bubbles are not observed in this case.
Thus, the surface of the felt can be stable and the small bubbles cannot be separated from the body of the slug in DI water. However, the slug in HFE7300 has relatively low interfacial strength due to low surface tension. Thus, the surface of the slug becomes unstable and small bubbles can separate from the body of the slug.
Thus, the solver used in this study can provide reliable results for the slug shape.
Results and discussion
- Effect of solid particle and slug length
- Effect of liquid backflow
- Effective slug movement for energy generation
In Figure 3.7, it is observed that the slug in EFH1 grows slightly faster than that in EHF3. Then, the velocity of the liquid film barely changes along the (fully developed) slug body. Because of this, the rising speed of the slug does not change if the slug is long enough.
In the streamline distribution, it is observed that the recirculation flow is generated at the back of the plug in each magnetic fluid. From this dimensionless number, they first identified the wake pattern on the back of the slug. This figure shows that the ascent speed of the slug decreases as the speed of the fluid flow increases.
In this figure, it is also observed that the rising velocity of the slug decreases when the velocity of the liquid backflow increases. This means that the upward movement of the slug is more important than the liquid flow for generating the recirculation flow. The upward motion of the slug is an important factor for the recirculation flow at the back of the slug.
As time passes, the speed of the magnetic fluid gradually increases due to the movement of the snail and the fluid flow.
Investigation of the magnetic force effect
Theory for investigation
From the above equation, the total magnetic force acting on a bubble or slug can be calculated to predict the direction of the magnetic force. In the above equation, 𝜒𝑔 and 𝜒𝑙 are the magnetic susceptibility of the gas and the surrounding liquid, respectively. In other words, if (𝜒𝑔− 𝜒𝑙) is a (+) value, the bubble and slug can be driven from a lower magnetic field to a higher location.
But if (𝜒𝑔− 𝜒𝑙) is a (-) value, the bubble and slug can go in opposite directions. Finally, the momentum equation must be reformulated to investigate the fluid phenomena with the magnetic force by adding the above equation (4-2) as an external force, as shown below. Finally, the motion of the bubble and slug with the magnetic force can be investigated by solving the above equation.
Conditions for simulation
Results and discussion
- Magnetic field distribution and direction of the magnetic force
- Motion of a single bubble driven only by the magnetic force
- Effect of the magnetic force for bubble and slug movement
It is thus confirmed that the magnetic force model is correctly applied in this simulation. In the previous section, it was confirmed that the magnetic force model is correctly applied in the present work. Thus, in this section, the magnetic force is applied in a real situation to investigate the effect of the magnetic force.
Thus, the vertical magnetic force can be ignored when gravity is applied to the system. This means that the magnetic force can affect the bubble movement in the horizontal direction, unlike the case in the vertical direction. Because of this, the magnetic force can affect the bubble movement in the horizontal direction, as in Figure 4.5.
Thus, we can also ignore the effect of the horizontal magnetic force when gravity acts on the system. From the above investigation, it is predicted that even the magnetic force cannot affect the movement of the snail. In this work, the influence of the magnetic force on the motion of bubbles and slugs is investigated.
The magnetic force does not affect the motion of the bubble and slug when gravity is applied to the system.
Conclusions
When the liquid flows downward, the slug's rising velocity and the size of the recirculation flow decrease according to the increase in the liquid velocity. Thus, the upward motion of the slug is more important than the fluid flow for generating the recirculation flow. Its direction is determined by the magnetic properties of each liquid and the magnetic field distribution.
When normal gravity is applied to the system, the magnetic force cannot affect the bubble and slug characteristics because the gravitational force is much greater than the magnetic force. For the generation of electrical energy, the important factor for magnetic fluid disturbance is not the magnetic force, but the hydrodynamic force. Poncsak, An experimental investigation of the motion of single bubbles under a slightly inclined surface, International Journal of Multiphase Flow pp.
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