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Experimental study of magnetic field effect on bubble lift-off diameter in sub-cooled flow boiling
Accepted Manuscript Experimental Study of Magnetic Field Effect on Bubble Lift-Off Diameter in Sub-Cooled Flow Boiling R. Amirzehni, H. Aminfar, M. Mohammadpourfard PII: DOI: Reference:
S0894-1777(17)30219-4 http://dx.doi.org/10.1016/j.expthermflusci.2017.07.022 ETF 9164
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
28 October 2016 10 July 2017 30 July 2017
Please cite this article as: R. Amirzehni, H. Aminfar, M. Mohammadpourfard, Experimental Study of Magnetic Field Effect on Bubble Lift-Off Diameter in Sub-Cooled Flow Boiling, Experimental Thermal and Fluid Science (2017), doi: http://dx.doi.org/10.1016/j.expthermflusci.2017.07.022
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Experimental Study of Magnetic Field Effect on Bubble Lift-Off Diameter in Sub-Cooled Flow Boiling
R. Amirzehni1, H. Aminfar1, and M. Mohammadpourfard2 1Faculty
of Mechanical Engineering, University of Tabriz, Tabriz, Iran.
Email addresses: [email protected] and [email protected] 2Faculty
of Chemical and Petroleum Engineering, University of Tabriz, Tabriz, Iran.
Email address: [email protected]
Abstract. Boiling heat transfer is a process that consist intensive liquid to vapor phase change. Higher heat transfer capacity and lower wall temperatures, which are essential for industrial cooling applications requiring high heat transfer capacities, are vital characteristics of the boiling heat transfer. In spite of tremendous efforts, bubble nucleation and lift-off phenomena in subcooled flow boiling still requires additional studies. Therefore, in this study, the effects of two important parameters including mass flux (85-125 Kg/m2.s) and heat flux (10-40 kW/m2) on the bubble lift-off diameter in the isolated bubble regime of subcooled flow boiling are studied in the absence and presence of magnetic field caused by quadrupole magnets. The obtained results indicate that by increase of the heat flux and decrease of the mass flux, the bubble lift-off diameter increases. Besides, in the presence of the magnetic field, changes in bubble liftoff diameter follow the same trend. However, it is evident that in the presence of the magnetic field, bubble lift-off diameter decreases 5-10 %. Keywords: Experimental study; Sub-cooled flow boiling; Non-uniform magnetic field; Bubble lift-off diameter; Bubble dynamics.
1
Nomenclature G
Mass flux
Bubble lift-off diameter
q’’
Heat flux
r*
Di
Outer diameter of the inner tube
L
Heated length
Nucleus critical radius Wall superheat
1. Introduction Boiling heat transfer is a change in phase from liquid to vapor. In cooling industry, specifically in microfluidic devices, boiling is the crucial key to remove high heat fluxes. Flow boiling has a higher heat transfer rate in comparison with pool boiling and other conventional approaches. Moreover, the subcooled flow boiling is also preferred to saturated flow boiling due to its higher heat transfer rate and lower wall temperature. It is worth noting that critical heat flux is a constraint to the boiling heat transfer accompanied by sharp reduction in local boiling heat transfer coefficient and abrupt increase in wall temperature [1]. Numerous methods have been examined so far to increase heat transfer rate and particularly the CHF in forced convection. Despite studies with basic fluids, there are two different approaches to increase heat transfer rate including active and passive approaches. As a passive method, nanoparticles are used for further increase of the heat transfer coefficient. Besides, applying external fields such as magnetic or electrical fields can enhance the heat transfer coefficient as well [2] [3] [4] [5]. Although experimental results and numerical simulations [6] [7] [8] complement each other, there still is a demand for experimental data and precise knowledge of bubble dynamics, in particular, bubble nucleation site density and bubble departure or lift-off diameter in order to comprehend the elaborate evolution of nucleate boiling. Therefore, a high-speed video camera is used to capture images of bubbles during their growth to reveal the complex phenomenon of nucleate boiling. Ultimately, due to the sophisticated processes of numerical modeling and stochastic nature of boiling [1], it is crucial to study the nucleate boiling and bubble dynamics experimentally.
2
More recently, mechanistic models have been developed to account for most of the phenomenon involved in nucleate boiling process. Klausner et al. [6] developed a mechanistic model based on the force balance acting on the bubbles during their growth. They could satisfactorily predict bubble departure diameter for saturated flow boiling of R113. Klausner’s model has been used as an original model to predict bubble departure or bubble lift-off diameter. Over the years, the aforementioned model has been modified slightly by other authors to predict their own experimental data. Zeng et al. [9] extended the original model to predict bubble lift-off diameter in pool and flow boiling of R113. Later on, Situ et al. [10] experimentally measured bubble lift-off diameter in sub-cooled flow boiling of water in a vertical channel and verified their data against the modified model. Mass flux range was 500-900 kg/m2. s, and relative error in predicting bubble lift-off diameter was ±35.2%. Subsequently, Wu et al. [11] conducted an experiment for horizontal flow boiling of refrigerant R134a. It should be noted that Klausner [6] used Mikic [12] model for bubble growth rate, whereas others employed that of Zuber’s [7]. Taking account of condensation on the bubble cap, Yun et al. [13] used a model for a non-uniform temperature field coupled with Ranz and Marshal correlation [14] stated by Zuber [7]. Mechanistic model is important for predicting a bubble lift off and experimental studies are crucial to have a deep insight to phenomena. An enormous amount of experimental data is available in literature regarding bubble departure and lift-off diameter. Unal et. al. [15] studied the subcooled boiling of water at high pressure in a steam generator pipe as well as bubble departure diameter. Bibeau et al. [16] investigated bubble growth, detachment diameter and condensation during subcooled boiling of water in a vertical annulus. Thorncraft et. al. [17] conducted an experiment in a vertical up-flow and down-flow boiling of refrigerant FC-87 to measure bubble departure and lift-off diameter. The ass flux range was 190-660 kg/m2.s and they concluded that heat transfer rate in up-flow boiling is much higher. Prodanovic [18] studied bubble behavior for sub-cooled boiling of water in a vertical annulus from inception to collapse. Chen [19] measured bubble departure diameter, active nucleation sites as well as bubble departure frequency for a sub-cooled horizontal flow boiling of refrigerant R-407C in an annular duct. Sugru [20] carried out a complete experiment to measure bubble departure diameter for different orientation angles of a square channel. 3
The range of mass flux used in their experiment was 250-400 kg/m2. s. They compared their experimental data with the predicted diameters from Klausner [6] and Yun [13] model and stated a relative error of 35.68% ± 24.23% and 16.64% ±11.66%, respectively. Moreover, as stated before, applying external electrical or magnetic field can be an alternative to increase heat transfer rate. Fujimura [21] studied surface tension of water-air interface in the presence of magnetic field. They detected an increase in surface tension in the presence of a 10T magnetic field. Stoian [22] investigated the effect of magnetic field at different orientations with respect to gravity on bubble departure diameter of a nano-fluid. They could reach the state that bubble diameters vary from -16% to +12% in departure by applying a magnetic field. According to the above information, most of the mechanistic models to predict bubble lift-off and departure diameters have relative error of almost 30-50%. This is due to lack of the terms that consider condensation of bubble while it is in contact with subcooled liquid. Furthermore, velocity profile and many other parameters need a more concise approach for better prediction ofbubble diameter. It should be noted that predicting bubble lift-off diameter is not the scope of current study. However, for the non-magnetic flow, a code using the forces acting on a single bubble is written to predict the forces during the bubble growth. A thorough literature review acknowledges that there is limited research on bubble lift-off diameter in convective boiling, which is more important than departure diameter to the interfacial area transport equation while modeling flow boiling. In addition, there is still little data and information regarding the bubble lift-off diameter in the presence of magnetic field in low mass fluxes for subcooled nucleate boiling. Therefore, the primary objective of this study is to investigate the effect of heat flux and low mass fluxes on the lift-off diameter of bubbles in the isolated bubble regime of subcooled flow boiling. Ultimately, the main novelty of this study is to find out the effects of a nonuniform magnetic field on the bubble lift-off diameter. A range of heat fluxes were chosen to ensure that the subcooled flow boiling occurs in a so called ‘isolated bubbles’ regime, where the interactions between bubbles at adjacent nucleation sites could be neglected. 4
2. Force balance on a single bubble at nucleation sites It is important to know the forces acting on a single bubble in order to determine the bubble lift-off and departure diameter. A bubble in an active nucleation site starts to grow. As soon as the buoyancy force is larger than the other forces in the direction parallel to the flow, the bubble departs from its site and starts to slide along the heated surface until the time that shear lift force exceeds other forces in the direction perpendicular to the flow. That is the point when lift-off takes place. To find out the diameter in which lift-off occurs, it is essential that the balance equations of the forces acting on a bubble to be solved. Fig 1 shows a schematic diagram of the forces acting on a single bubble in its nucleation site. The force balances in x-direction and y-direction are given by Klausner [6]: (1) (2)
In the above equations, ,
,
,
,
,
and
are respectively surface tension
force, quasi-steady drag force, shear lift force, unsteady drag force, buoyancy force, contact pressure force and hydrodynamic pressure force. Whilst a bubble is in equilibrium, the sum of the forces is zero in both directions. If the forces in the x direction overcome the forces in y direction, lift-off occurs.
5
Figure 1: Schematic diagram of force balance on a single bubble
2.1.
Surface tension force
Equations for surface tension force in x and y directions are [10]: (3)
(4)
where
is bubble contact diameter on the heated wall,
advancing contact angle and
is surface tension,
receding contact angle. It is worth mentioning that the
images taken during current experiment indicate that the advancing and receding contact angles are 85o and 12o, respectively. 2.2.
Shear lift force
Shear lift force is given by many authors suitable for a viscos flow. The following correlation is given by Klausner [6]: (5)
where
is the velocity of bubble and
is as follows:
6
(6) (7)
The liquid velocity profile used here is the universal single-phase turbulent flow profile. It is defined as follows: (8)
(9)
(10)
(11)
2.3.
Growth force
Unsteady drag force or growth force is due to bubble growth. It is applied in the opposite direction of a bubble growth. (12)
where
is liquid density and
is bubble radius which is a function of the effective
Jacob number, Reynolds number, Prandtl number and growth time [10]. (13)
(14)
2.4.
Quasy-steady drag force
For considering the Quasy-steady drag force, the following formula by Klausner [6] is used: 7
(15)
(16)
where
2.5.
is the dynamic viscosity of the liquid and n is 0.65.
Buoyancy, hydrodynamic and contact pressure forces
The buoyancy, hydrodynamic and contact pressure forces are expressed as follows according to Klausner [6]: (17) (18) (19)
3. Experimental databases An experimental facility has been set up in order to investigate the bubble lift-off diameter in subcooled flow boiling [23]. The experiments are conducted using water under the conditions of low flow velocity at atmospheric pressure. Digital high-speed video camera is utilized in order to capture consecutive images of bubbles from inception of growth to the point that lift-off occurs. The main loop in this experiment consists a centrifugal pump with mass flux and head respectively ranging from 0.6-2.4 m3/hr and 9-32 water meters, a preheater including 16 heating elements, the test section, a condenser, a DC power supply and measuring instruments. The schematics of the main loop and the cooling loop is shown in Fig 2 and Fig 3. The test section is an annulus with outer transparent glass tube having inner diameter of 19mm and a heated inner steel tube with outer diameter of 12mm. The heated steel tube has an overall length of 750 mm. Copper rods with 12mm O.D. and 0.27m long are installed to both endpoints of the inner tube, copper electrodes are attached to these rods for connecting to a 24kW DC power supply (30V and 800A). The
8
applied heat flux is calculated by considering the electrical current and the electrical potential as follows: (20)
Where, V and I stand for potential difference between two electrodes and electric current, respectively.
, is the outer diameter and is the heated length of the inner
heated tube. Various measuring devices are used in order to control the temperature and pressure of the flow and determine the relevant parameters of the experiment. Fluid temperatures arerecorded with K-type thermocouples. The relevant devices have been checked in the calibration tests to determine the measurement accuracies. A high-speed video camera is used to measure the bubble lift-off diameter during the experimental runs. The camera is capable of capturing images at the rate of 1200 fps. However, since the flow rates are low in this study, the growth rate is slow enough to capture images at the rate of 480fps with the size of 224*160 pixels. Two LED lights are used as direct backlighting during the experiments. They provide sufficient light for the desired camera acquisition rate and avoid the flickering associated with AC, one of the typical problems associated with high-speed video for clear visualization. In addition, uncertainty of the size of a measured bubble is approximately equal to one pixel, which is nearly 0.0337 mm.
9
Figure 2: Schematic diagram of experimental loop
Figure 3: Schematic diagram of the cooling water loop
10
Figure 4: a) Cross sectional view of the test section and the direction of magnetic field forces in the presence of the quadrupole, b) Quadrupole magnetic field direction
4. Experimental Procedure To begin, the loop is filled with distilled water. Then, degassing takes place by boiling the water for half an hour, being careful of not reaching the critical heat flux. Afterwards, while preheater and heat exchanger are working simultaneously, water reaches to a desired inlet subcooling temperature of 80oC, which could be read from the K-Type thermocouple installed in the entrance of the test section. It is worth mentioning that making any change in flow conditions requires at least 45 minutes for the flow to reach steady-state condition. In order to initiate data acquisition, mass flux is fixed at a specific value, however, heat flux is varied. An electrical current with a related voltage is applied to the inner rod from two end points in order to heat the test section. Starting with lower power levels then raising it gradually and reaching a stable condition at each level, suitable experimental conditions are chosen in a way that a stable active nucleation site is observed and could be captured by the high speed video camera. Hot fluid coming out from the test section enters the heat exchanger and it is cooled and 11
finally returned to the main tank. Then, it is pumped to the cycle again, see Fig. 2. After imaging at different heat fluxes in a constant mass flux and inlet temperature, mass flux is changed and the same procedure is repeated. In all of the experiments, the inlet temperature is remained unchanged. To provide an external magnetic field inside the annulus, permanent magnets are used. Four magnets are placed two by two in front of each other in order to make a quadrupole magnetic field. Magnitude of the external magnetic field grows rapidly with radial distance from its longitudinal axis. It reaches to maximum adjacent of the magnets which is 200mT. The installation position of the magnets and magnetic force directions are shown in Fig 4. During the experiment, the first one third of the inlet was discarded due to the entrance effect. High speed video camera is adjusted to focus on the active nucleation sites, chosen approximately one third of the way up the entrance in order to skip the entrance effect. In each flow condition, bubbles are recorded from inception until lift-off. This procedure is repeated for 15 times in order to decrease the error in reporting thebubble lift-off diameter. After taking videos, each video is converted to images. In accordance to the frame rate of the camera in this study which is 480 fps, 28800 frames of image are extracted from each video. Next, they are probed thoroughly in order to find the moment in which lift-off occurs. Finally, for each experimental condition, there are 15 images of the moment in which a specific bubble lifts off. In each image, there exists a scale to measure the diameter accurately, see Fig 5,. In addition, bubbles are assumed to be fully spherical. At the end, bubble lift-off diameter in that experimental condition is stated as the average of those 15 data along with a standard deviation.
Fig 5: The scale used in the experiments for measuring the exact bubble lift-off diameter.
12
5. Results and discussion According to the literature review, it is clear that most of the studies are related to the effect of various parameters on bubble departure diameter in high mass fluxes and heat fluxes. However, in newly emerging industrial applications such as microfluidic devices, lower ranges of mass flux should be studied as well. Furthermore, there is lack of study aboutthe effects of magnetic field on the bubble lift-off diameter in low mass fluxes and heat fluxes. Therefore, the problem will be studied in low mass fluxes and low heat fluxes, The main parameters considered here include heat flux, mass flux and non-uniform magnetic field effects. Bubble diameters are measured for different combinations of aforementioned parameters and all experiments are run at atmospheric pressure. Heat flux and mass flux values along with other information are available in Table1 and Table2, in the absence and in the presence of the magnetic field, respectively.
Table1: Parameters of the experiment in the absence of magnetic field
In the absence of the magnetic field parameters
Experiment range
Units
Annulus orientation
Vertical
-
Mass flux
88
kg/m2.s
sub cooling
20
℃
Heat flux
15-40
kW/m2
Table2: Parameters of the experiment in the presence of magnetic field
In the absence of the magnetic field parameters
Experiment range
Units
Annulus orientation
Vertical
-
Mass flux
65, 100, 125
kg/m2.s
sub cooling
20
℃
Heat flux
10-40
kW/m2
13
The average bubble lift-off diameter in the absence and presence of magnetic field are listed in Table 3 and Table 4, respectively. All values of diameters are reported along with their standard deviation from the spread of data around a mean diameter. The results for various conditions will be discussed in the following section. Table 3: Bubble lift-off diameter in the absence of magnetic field
No magnetic field G1=88 [kg/m2. s]
[kW/m2]
[mm]
15 22 23 27 28 29 34
2.19±0.07 2.2±0.05 2.23±0.09 2.29±0.07 2.36±0.08 2.36±0.07 2.69±0.09
Table 4: Bubble lift-off diameter in the presence of magnetic field
In the presence of magnetic field G1=65[kg/m2. s]
[kW/m2]
[mm]
12
2.71±0.16
15
G2 =100[kg/m2. s]
[kW/m2]
G3 =125[kg/m2. s]
[mm]
[kW/m2]
[mm]
23
1.96±0.1
35
1.91±0.07
2.93±0.24
27
2.11±0.1
41
2.02±0.06
17
3.01±0.1
31
2.16±0.1
30
3.42±0.1
39
2.32±0.1
41
2.38±0.1
14
It is worth mentioning that in all of the experimental studies, uncertainties and errors are inevitable. It is tried to reduce these errors to the possible minimum amount in order to avoid their interference with the result. Likewise, in this study, all approaches are considered to minimize the errors. However, some are demonstrated in the form of standard deviation. The standard deviation is calculated as follows. (21)
where
represents bubble lift-off diameter, M is the mean diameter, Σ is the
summation (or total), and N is the number of bubbles captured in one condition. In current study, in each condition, 15 bubble lift-off diameters are measured. Therefore, N is 15. Moreover, M indicates the average diameter of these 15 data. Nevertheless, there are undeniable uncertainties in measuring power, heat flux, flow rate, and temperature. The magnitude of each uncertainty is less than 4%, 4%, 2-3% and 5oC, respectively [23]. 4-1 Without Magnetic Field Since most of the experiments mentioned in the literature review have been done for the mass fluxes of 250 – 300 kg/m2.s, the first goal of the present study is to investigate the effects of several parameters on the bubble lift-off diameter in lower mass fluxes (50 – 150 kg/m2.s). In order to validate the first section of the experiment, which is to determine the effect of various parameters on bubble lift-off diameter in lower ranges of mass flux, the obtained data for nucleate subcooled boiling in the absence of the magnetic field is compared to that of the experiment done by Sugru [20]. The average bubble lift-off diameter in ongoing work is between 2.19 mm – 2.69 mm while this range in the study of Sugru [20] differs from 0.22 mm – 0.37 mm, despite the higher heat flux. It could be concluded that the higher the mass flux, the smaller the bubble lift-off diameter. This significant increase in the diameter in lower mass fluxes is due to the decrease of quasisteady drag force acting on the bubble while shear lift becomes significant to make a bubble lift off. 15
In order to analyze this outcome physically, the mechanistic model of Klausner [6] which was modified by Situ [10] is used. A single bubble in its nucleation site undergoes different forces which are mentioned in section 2. A MATLAB code was written for the conditions of current study using equation (1) and (2) which is the equilibrium condition for a bubble in the direction opposite to the flow. In order to validate this code, the forces calculated in Klausner’s [6] study is compared to the forces resulted from the same input in the MATLAB code of current study, seetable 5. Relative error of 20% is stated which is reasonable. Therefore, this code could be used to find out which forces have the most important role in bubble lift-off diameter. Thus, the sum of forces in x direction is assumed to be greater than zero and all the forces from the inception of nucleation until the bubble’s lift-off are plotted in Fig 6. Table 5: Comparison of the forces applied on a single bubble of refrigerant R113 derived from Klausner [6] study and current MATLAB code
Force
Klausner [6]
Current model
-9/9E-08
9/8E-08-
-2/5E-06
2/4E-06-
2/8E-07
2/5E-07
1/3E-06
0/8E-06
1/0E-07
1/3E-07
2/7E-07
2/4E-07
1/7E-07
2/6E-07
16
Forces in the direction of fluid flow [N]
1.50E-05 1.00E-05 F_cp
5.00E-06 0.00E+00 0.00E+00 -5.00E-06
F_sl
5.00E-04
1.00E-03
1.50E-03
F_dux F_sx
F_h
-1.00E-05
-1.50E-05
Bubble lift-off diameter [mm]
Fig 6: The evolution of various forces acting on a single bubble in the direction of flow from the inception of growth until lift-off
All the parameters used in this model have been summarized in table 6. Fig. 6 shows the evolution of various forces acting on a single bubble in the direction perpendicular to the flow. As it is evident, shear lift force and surface tension force are the most dominant ones that affect the bubble. Surface tension force tends to maintain the bubble in its nucleation site, however, shear lift force encourages the bubble in an active nucleation site to lift off. As soon as shear lift force grows larger than surface tension force, bubble lifts off. Table 6: Parameters used in the current MATLAB model
Parameters Sub cooling Mass flux Heat flux Hydraulic diameter Annulus length
Definition 10 - 20 50 - 150 10 0/017 76 4/203 968 0/3569 2296 0/3455E-6 0/675 0/05885
𝛔
17
Unit
Fig. 7 shows the bubble lift-off diameter versus heat flux for a mass flux of 88 kg/m 2. s. Evidently, bubble lift-off diameter increases with the increase of heat flux, since the increase in heat flux contributes to the increase of wall superheat. Consequently, bubbles grow more rapidly and lift-off takes place in larger bubble diameters. To be more specific, using experimental points in Fig. 7, there is 12.5% increase in bubble liftoff diameter for approximately 27% increase of heat flux.
Bubble lift-off diameter [mm]
2.6 2.4 2.2 2 1.8 1.6 In the absence of magnetic field, G=100 kg/m^2. s
1.4 1.2
10
15
20
25
30
35
40
Heat flux, q" [kW/m^2] Figure 7: Bubble lift-off diameter versus heat flux in the absence of magnetic field
4-2 With a Non-Uniform Magnetic Field Two-phase flow systems are well-known for their instability which is problematic in industrial applications. Therefore, it is essential that a better approach be devised to increase the stability of the flow. Applying an external magnetic field is one of the recommended solutions. In this study, a non-uniform magnetic field is applied to a vertical flow of water in an annulus. As it is shown in Fig 4, these four magnets exert a radial force on bubbles. External magnetic field could affect various important parameters like surface tension, contact angle and viscosity [23]. Mechanistic analysis of magnetic field effect on a single bubble is not the scope of current study. However, according to the literature review, it is concluded that surface tension increases due to magnetic field, which helps bubbles retain their spherical shape and flow becomes steadier. Fig 8, shows a single bubble about to lift-off in the presence and absence of 18
magnetic field. It is clear that a bubble in the presence of magnetic field is more of a spherical than the one in the absence of a magnetic field, according to the contact angle shown in the picture. During the experiments, it is observed that magnetic field has a significant influence on bubble lift-off diameter. As can be seen in Fig. 9, the effect of heat flux on bubble liftoff diameter in the presence of a constant magnetic field is studied for three different mass fluxes. Bubble lift-off diameter follows the same ascending trend with heat flux by the appliance of magnetic field. It is worth mentioning that bubbles grow more controlled in the presence of magnetic field. This outcome is the result of external magnetic forces applied on the bubbles which seem to increase surface tension force and retain the bubble in equlibrium. According to Fig 7 and Fig 9, for 22% increase of bubble lift-off diameter, 100% and 62% increase in heat flux is required in the presence and absence of magnetic field, respectively. Moreover, taking a close look at Fig 10, it could be seen that bubble lift-off diameter is inversly proportional to the mass flux.
Fig 8: Spotted magnetic field effect on retaining a bubble in a spherical shape
19
Bubble lift-off diameter [mm]
4 3.5 3 2.5 2 1.5 in the presence of magnetic field, G = 65 kg/m^2.s in the presence of magnetic field, G=100 kg/m^2.s in the presence of magnetic field, G=125 kg/m^2.s
1 0.5 0
10
20
30
40
50
60
Heat flux, q" [kW/m^2]
70
80
Figure 9: Bubble lift-off diameter versus heat flux in the presence of magnetic field
bubble lift-off diameter [mm]
2.9 2.8
in the presence of magnetic field, q"=35 kW/m^2
2.7
in the presence of magnetic field, q"=45 kW/m^2
2.6 2.5 2.4 i
2.3
g
2.2
u
2.1
r
2
e
1.9 90
100
110
120
130
140
150
Mass flux, G [kg/m^2.s]
1 0 :
Bubble lift-off diameter versus mass flux in the presence of magnetic field
4-3 Comparison of the Bubble Lift-Off Diameters in the Presence and Absence of Magnetic Field 20
All experiments are performed in fluid inlet temperature of 80oC. As can be seen in Fig. 11, bubble lift-off diameter is shown against heat flux in the presence and absence of the magnetic field. Obviously, applied magnetic field decreases the bubble lift-off diameter to a considerable degree and bubble’s growth is more controlled than the case without magnetic field. The main goal of these studies is to present a new approach to increasethe CHF in order to increase the efficiency of microfluidic devices in cooling industry. As bubbles are smaller, they do not occupy more places adjacent to the surface. As a result, there would not be a blanket of bubbles and according to the literature review, the frequency of lift-off will be increased, which is also observed in current experiments. Therefore, bubbles leave the surface more rapidly and sub-cooled fluid takes its place and removes the heat from the wall, which is so called quenching heat transfer. If bubble lift-off diameter is indicated against mass flux as in Fig 12, a decreasing trend of bubble lift-off diameter is detected, as the mass flux increases. In particular, the higher the mass flux, the smaller the bubble lift-off diameter. In another words, in higher mass fluxes the effect of the magnetic field on bubble lift-off diameter is stronger.
Bubble lift-off diameter [mm]
2.6 2.4 2.2 2 1.8
1.6 in the absence of magnetic field, G=100 kg/m^2.s
1.4
in the presence of magnetic field, G=100 kg/m^2.s
1.2 10
15
20
25
30
35
40
45
Heat flux, q" [kW/m^2] Figure 11: Comparison of bubble lift-off diameter in the presence and absence of magnetic field versus heat flux
21
Bubble lift-off diameter [mm]
2.9 in the absence of magnetic field, q''=35 kW/m^2 in the presence of magnetic field, q''=35 kW/m^2
2.7 2.5 2.3 2.1 1.9
1.7 70
80
90
100
110
120
130
Mass flux, G [kg/m^2.s]
Figure 12: Comparison of bubble lift-off diameter in the presence and absence of magnetic field versus mass flux
In Fig. 13, we can have a thorough outlook about the effect of mass flux and the strong effect of magnetic field. In each specific mass flux, percentage of the change in bubble lift-off diameter in presence and absence of magnetic field is calculated and plotted. It is evident that by increasing the mass flux, the percentage of change in bubble lift-off diameter is increased. Another point to be mentioned is in the mass flux ranging from 80-130 kg/m2. s, there is about 3.5-9.5% of decrease in bubble lift-off diameter which leads to lower CHF and better performance in cooling applications.
22
Bubble lift-off diameter decrease [%]
-3.0% -4.0% -5.0% -6.0% -7.0% -8.0% Prominent decrease of bubble lift-off diameter in larger mass fluxes in the presence of magnetic field
-9.0% -10.0% 70
80
90
100
110
120
130
Mass flux, G [kg/m^2.s] Figure 13: Prominent decrease of bubble lift-off diameter in larger mass fluxes in the presence of magnetic field
Fig. 14 shows typical consecutive images of bubble growth. Bubble starts to initiate when required wall superheat is reached. Then, bubbles gain heat from the wall and start to grow until they reach departure diameter, which is the time to depart from the nucleation site and slide along the heating surface with the flow. Gaining excessive heat from the wall, they grow further to reach lift-off diameter, which is the bubble diameter when it leaves the surface. On account of the fact that nucleation sites are dependent on the heat flux and wall superheat, in each experiment, the same nucleation site might not have been activated. This phenomenon is more probable to occur in higher heat fluxes. Therefore, to be precise, at each step, several nucleation sites are under inspection and the growth and lift-off diameter of more bubbles are recorded. Then, they are averaged and written along with an error of standard deviation.
23
Figure 14: Typical consecutive images of bubble from initial condition of growth to departure and lift-off
A visual insight into the effect of magnetic field on bubble dynamics is obtained by comparing different conditions in Fig. 15 and Fig. 16. The first one pinpoints a mass flux effect on nucleation site density in an approximately same heat flux. All images are captured in partial boiling regime so that heat is transferred via two approaches including nucleate boiling and forced convection. Evidently, by the increase of mass flux, nucleation site density tends to decrease. The reason is that, when mass flux increases, so does the convective heat transfer coefficient. Therefore, a major portion of heat is transferred and wall superheat decreases and consequently, less nucleation sites would remain active. To further discuss the reason, theoretical explanation is given below. Boiling models are classified by combining convective boiling and nucleate boiling coefficients to obtain two phase flow heat transfer coefficient. The general model which was given by Chen [24], is as follows: (22) This indicates that heat is removed not only by single phase convection, but also by nucleate boiling. If a great portion of heat is removed by convective heat transfer, nucleate boiling heat transfer, and, consequently, wall superheat will reduce. On the other hand, there are initial considerations relating to the formation of vapor from a specific thermodynamic state of liquid that denotes a condition in which a spherical vapor nucleus is in mechanical equilibrium [1]. (23)
24
Regarding the above equation, critical radius of vapor nucleus to be formed is inversely proportional to the wall superheat. It means that if wall superheat is lower, as discussed above, the required critical radius of vapor nucleus for starting nucleation is bigger. Therefore, in higher mass fluxes, bigger nucleation sites are active. Since the existence of larger nucleation sites are less probable, therefore, nucleation site density in higher mass fluxes will decrease. Furthermore, when the case of magnetic field is considered, reduction in nucleation site density due to magnetic force could not be overlooked.
Figure 15: Mass flux effect on bubble nucleation density
The result of studying the effect of heat flux is depicted in Fig 16-b. It is obvious that nucleation site density proliferates as heat flux goes up in a constant mass flux. This could be due to the increase of the wall superheat and the subsequent smaller critical
25
nucleus’ radius. The effect of magnetic field in lowering the number of nucleation sites is also evident. In order to visually comprehend the effect of applied magnetic field and heat flux on the bubble lift-off diameter, Fig. 16-a is given. Referring to Fig. 16-a, bubbles are smaller in the presence of magnetic field, unmindful of heat flux magnitude. An undeniable magnetic field effect as a vital mean to decrease bubble lift-off diameter could be a novel interpretation.
Figure 16: a) Heat flux effect on bubble lift-off diameter, b) Heat flux effect on nucleation site density
6. Conclusion Forced convective subcooled flow boiling experiments in the presence and absence of a non-uniform magnetic field were carried out in a vertical-upward annular channel by 26
using water as a testing fluid to realize the effect of magnetic field and other effective parameters on bubble lift-off diameter. The experiments were done in atmospheric pressure. The inlet water temperature was constant at 80oC; heat flux changed from 10 to 40kW/m2; the mass flux varied from 65 to 125 kg/m2. s. The magnetic field was made by four magnets, two by two situated in front of each other makes a non-uniform magnetic field with a maximum magnitude of 200mT. A high-speed digital video camera was utilized in order to capture bubble lift-off diameter during subcooled nucleate boiling. Bubble liftoff diameters were obtained from measuring so many bubbles as they tend to leave the surface. The results indicate that bubble lift-off diameter decreases by increasing mass flux and decreasing heat flux. Furthermore, applying a magnetic field brings about a more controlled bubble growth as well as lower bubble nucleation density and smaller bubbles at lift-off. All in all, it could be concluded that applying a magnetic field can decrease bubble lift-off diameter for 5-10% which leads to higher CHF. Reaching higher CHF is an admirable approach since this is an important parameter to be considered in cooling industries. Moreover, during these experiments, it is observed that the effect of magnetic field on bubble lift-off diameter is increased in higher mass fluxes. However, it requires more and thorough studies.
References [1]. Collier. Convective boiling and condensation handbook. [2]. Flow boiling critical heat flux for water in a vertical annulus at low pressure and velocities. J. Rogers, M. Salcudean, A. Tahir. 1982, Proceedings of the seventh International Heat Transfer Conferance, pp. 339-344. [3]. Experimental studies of critical heat flux for low flow of water in vertical annuli at near atmosphere pressure. M.S. El-Genk, S.J. Haynes, K. Sung-Ho. International Journal of Heat and Mass Transfer. [4]. Bubble dynamics and boiling heat transfer; a study in the absence and in the presence of electric field. Siedel, S. 2012.
27
[5]. Heat transfer enhancement by magnetic nanofluids- A review. I. Nkurikiyimfura, Y. Wang, Z. Pan. [6]. Vapor bubble departure in forced convection boiling. J. Klausner, R. Mei, D. Bernhard et al. 1993, International Journal of Heat and Mass Transfer, Vol. 36, pp. 651662. [7]. The dynamics of the vapor bubbles in nonuniform temperature fields. Zuber, N. 1961, International Journal of Heat and Mass Transfer, pp. 83-98. [8]. Prediction of bubble departure in forced convection boiling: A mechanistic model. M. Colombo, M. Fairweather. 2005, 2015, International Journal of Heat and Mass Transfer, pp. 1-13. [9]. A unified mmodel for the prediction of bubble detachment diameters in boiling systems- pool boiling. L. Zeng, J. Klausner, R. Mei. 1993, International Journal of Heat and Mass Transfer, Vol. 36, pp. 2261-2270. [10]. Bubble departure frequency in forced convective subcooled boiling flow. R. Situ, M. Ishii, T. Hibiki. 25-26, 2008, International Journal of Heat and Mass Transfer, Vol. 51, pp. 6268-6282. [11]. A study of bubble detachment and the impact of heated surface structure in subcooled nucleate boiling flow. W. Wu, P. Chen, B.G. Jones, T.A. Newell. 2008, Journal of Nuclear Engineering, pp. 2693-2698. [12]. On bubble growth rates. B.B. Mikic, W.M. Rohsenow, P. Griffith. 1970, International Journal of Heat and Mass Transfer, pp. 657-666. [13]. Prediction of a subcooled boiling flow with mechanistic wall boiling and bubble size model. B. Yun, A. Splawski, S. Lo. 2010, Vol. 12. [14]. Evaporation from drops. W.E. Ranz, W.R. Marshal. 1952, Chemical Engineering, pp. 141-146. [15]. Maximum bubble diameter, Maximum rate during the subcooled nucleate boiling. Unal. 1976, International Journal of Heat and Mass Transfer, Vol. 19, pp. 643-649.
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[16]. A study of bubble ebullition in forced convective subcooled nucleate boiling at low pressure. E.L. Bibeau, M. Salcudean. 1994, International Journal of Heat and Mass Transfer, pp. 2245-2259. [17]. an experimental investigation of bubble growth and detachment in vertical upflow and downflow boiling. G.E. Thorncraft, J.F. Klausner, R. Mei. 1998, International Journal of heat and Mass Transfer, pp. 3857-3871. [18]. Bubble behaviour in subcooled flow boiling of water at low pressure and low flow rates. V. Prodanovic, D. Frase, M. Salcudean. 2002, International Journal of Multiphase Flow, pp. 1-19. [19]. Subcooled flow boiling heat trasnfer of R-407C and associate bubble characteristics in a narrow annular duct. C.A. chen, W.R. Chang, K.W. Li, Y.M. Lie, T.F. Lin. 2009, International Journal of Heat and Mass Transfer, pp. 3147-3158. [20]. The effects of orientation angle, subcooling, heat flux, mass flux, and pressure on bubble growth and detachment in subcooled flow boiling. Sugru, R.M. 2012, Master thesis in nuclear science and engineering, MIT. [21]. Y. Fujimura, M. Iino. Magnetic field increases the surface tension of water. 2009. [22]. Bubbles generation mechanism in magnetic fluid and its control by an applied magnetic field. F.D. Stoian, S. Holotescu, L. Vekas. 2010, Physics Procedia. [23]. Experimental study on the effect of magnetic field on critical Heat flux of ferrofluid flow boiling in a vertical annulus. H. Aminfar, M. Mohammadpourfard, R. Maroofiazar. 2014, Experimental Thermal and Fluid Science. [24]. Correlation for boiling heat transfer to saturated fluids in convective flow. Chen, J.C. 1966, Ind. Eng. Chem. Res. [25]. A. Bejan, A.D. Kraus. Heat transfer hand book. s.l.: Wiley-interscience, 2003. [26]. Numerical investigation of subcooled boiling characteristics of magnetic nanofluid under the effect of quadrupole magnetic field, M. Mohammadpour Fard, H. Aminfar, M. Karimi. Journal of engineering thermophysiscs, 2017.
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S0894-1777(17)30219-4 http://dx.doi.org/10.1016/j.expthermflusci.2017.07.022 ETF 9164
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
28 October 2016 10 July 2017 30 July 2017
Please cite this article as: R. Amirzehni, H. Aminfar, M. Mohammadpourfard, Experimental Study of Magnetic Field Effect on Bubble Lift-Off Diameter in Sub-Cooled Flow Boiling, Experimental Thermal and Fluid Science (2017), doi: http://dx.doi.org/10.1016/j.expthermflusci.2017.07.022
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Experimental Study of Magnetic Field Effect on Bubble Lift-Off Diameter in Sub-Cooled Flow Boiling
R. Amirzehni1, H. Aminfar1, and M. Mohammadpourfard2 1Faculty
of Mechanical Engineering, University of Tabriz, Tabriz, Iran.
Email addresses: [email protected] and [email protected] 2Faculty
of Chemical and Petroleum Engineering, University of Tabriz, Tabriz, Iran.
Email address: [email protected]
Abstract. Boiling heat transfer is a process that consist intensive liquid to vapor phase change. Higher heat transfer capacity and lower wall temperatures, which are essential for industrial cooling applications requiring high heat transfer capacities, are vital characteristics of the boiling heat transfer. In spite of tremendous efforts, bubble nucleation and lift-off phenomena in subcooled flow boiling still requires additional studies. Therefore, in this study, the effects of two important parameters including mass flux (85-125 Kg/m2.s) and heat flux (10-40 kW/m2) on the bubble lift-off diameter in the isolated bubble regime of subcooled flow boiling are studied in the absence and presence of magnetic field caused by quadrupole magnets. The obtained results indicate that by increase of the heat flux and decrease of the mass flux, the bubble lift-off diameter increases. Besides, in the presence of the magnetic field, changes in bubble liftoff diameter follow the same trend. However, it is evident that in the presence of the magnetic field, bubble lift-off diameter decreases 5-10 %. Keywords: Experimental study; Sub-cooled flow boiling; Non-uniform magnetic field; Bubble lift-off diameter; Bubble dynamics.
1
Nomenclature G
Mass flux
Bubble lift-off diameter
q’’
Heat flux
r*
Di
Outer diameter of the inner tube
L
Heated length
Nucleus critical radius Wall superheat
1. Introduction Boiling heat transfer is a change in phase from liquid to vapor. In cooling industry, specifically in microfluidic devices, boiling is the crucial key to remove high heat fluxes. Flow boiling has a higher heat transfer rate in comparison with pool boiling and other conventional approaches. Moreover, the subcooled flow boiling is also preferred to saturated flow boiling due to its higher heat transfer rate and lower wall temperature. It is worth noting that critical heat flux is a constraint to the boiling heat transfer accompanied by sharp reduction in local boiling heat transfer coefficient and abrupt increase in wall temperature [1]. Numerous methods have been examined so far to increase heat transfer rate and particularly the CHF in forced convection. Despite studies with basic fluids, there are two different approaches to increase heat transfer rate including active and passive approaches. As a passive method, nanoparticles are used for further increase of the heat transfer coefficient. Besides, applying external fields such as magnetic or electrical fields can enhance the heat transfer coefficient as well [2] [3] [4] [5]. Although experimental results and numerical simulations [6] [7] [8] complement each other, there still is a demand for experimental data and precise knowledge of bubble dynamics, in particular, bubble nucleation site density and bubble departure or lift-off diameter in order to comprehend the elaborate evolution of nucleate boiling. Therefore, a high-speed video camera is used to capture images of bubbles during their growth to reveal the complex phenomenon of nucleate boiling. Ultimately, due to the sophisticated processes of numerical modeling and stochastic nature of boiling [1], it is crucial to study the nucleate boiling and bubble dynamics experimentally.
2
More recently, mechanistic models have been developed to account for most of the phenomenon involved in nucleate boiling process. Klausner et al. [6] developed a mechanistic model based on the force balance acting on the bubbles during their growth. They could satisfactorily predict bubble departure diameter for saturated flow boiling of R113. Klausner’s model has been used as an original model to predict bubble departure or bubble lift-off diameter. Over the years, the aforementioned model has been modified slightly by other authors to predict their own experimental data. Zeng et al. [9] extended the original model to predict bubble lift-off diameter in pool and flow boiling of R113. Later on, Situ et al. [10] experimentally measured bubble lift-off diameter in sub-cooled flow boiling of water in a vertical channel and verified their data against the modified model. Mass flux range was 500-900 kg/m2. s, and relative error in predicting bubble lift-off diameter was ±35.2%. Subsequently, Wu et al. [11] conducted an experiment for horizontal flow boiling of refrigerant R134a. It should be noted that Klausner [6] used Mikic [12] model for bubble growth rate, whereas others employed that of Zuber’s [7]. Taking account of condensation on the bubble cap, Yun et al. [13] used a model for a non-uniform temperature field coupled with Ranz and Marshal correlation [14] stated by Zuber [7]. Mechanistic model is important for predicting a bubble lift off and experimental studies are crucial to have a deep insight to phenomena. An enormous amount of experimental data is available in literature regarding bubble departure and lift-off diameter. Unal et. al. [15] studied the subcooled boiling of water at high pressure in a steam generator pipe as well as bubble departure diameter. Bibeau et al. [16] investigated bubble growth, detachment diameter and condensation during subcooled boiling of water in a vertical annulus. Thorncraft et. al. [17] conducted an experiment in a vertical up-flow and down-flow boiling of refrigerant FC-87 to measure bubble departure and lift-off diameter. The ass flux range was 190-660 kg/m2.s and they concluded that heat transfer rate in up-flow boiling is much higher. Prodanovic [18] studied bubble behavior for sub-cooled boiling of water in a vertical annulus from inception to collapse. Chen [19] measured bubble departure diameter, active nucleation sites as well as bubble departure frequency for a sub-cooled horizontal flow boiling of refrigerant R-407C in an annular duct. Sugru [20] carried out a complete experiment to measure bubble departure diameter for different orientation angles of a square channel. 3
The range of mass flux used in their experiment was 250-400 kg/m2. s. They compared their experimental data with the predicted diameters from Klausner [6] and Yun [13] model and stated a relative error of 35.68% ± 24.23% and 16.64% ±11.66%, respectively. Moreover, as stated before, applying external electrical or magnetic field can be an alternative to increase heat transfer rate. Fujimura [21] studied surface tension of water-air interface in the presence of magnetic field. They detected an increase in surface tension in the presence of a 10T magnetic field. Stoian [22] investigated the effect of magnetic field at different orientations with respect to gravity on bubble departure diameter of a nano-fluid. They could reach the state that bubble diameters vary from -16% to +12% in departure by applying a magnetic field. According to the above information, most of the mechanistic models to predict bubble lift-off and departure diameters have relative error of almost 30-50%. This is due to lack of the terms that consider condensation of bubble while it is in contact with subcooled liquid. Furthermore, velocity profile and many other parameters need a more concise approach for better prediction ofbubble diameter. It should be noted that predicting bubble lift-off diameter is not the scope of current study. However, for the non-magnetic flow, a code using the forces acting on a single bubble is written to predict the forces during the bubble growth. A thorough literature review acknowledges that there is limited research on bubble lift-off diameter in convective boiling, which is more important than departure diameter to the interfacial area transport equation while modeling flow boiling. In addition, there is still little data and information regarding the bubble lift-off diameter in the presence of magnetic field in low mass fluxes for subcooled nucleate boiling. Therefore, the primary objective of this study is to investigate the effect of heat flux and low mass fluxes on the lift-off diameter of bubbles in the isolated bubble regime of subcooled flow boiling. Ultimately, the main novelty of this study is to find out the effects of a nonuniform magnetic field on the bubble lift-off diameter. A range of heat fluxes were chosen to ensure that the subcooled flow boiling occurs in a so called ‘isolated bubbles’ regime, where the interactions between bubbles at adjacent nucleation sites could be neglected. 4
2. Force balance on a single bubble at nucleation sites It is important to know the forces acting on a single bubble in order to determine the bubble lift-off and departure diameter. A bubble in an active nucleation site starts to grow. As soon as the buoyancy force is larger than the other forces in the direction parallel to the flow, the bubble departs from its site and starts to slide along the heated surface until the time that shear lift force exceeds other forces in the direction perpendicular to the flow. That is the point when lift-off takes place. To find out the diameter in which lift-off occurs, it is essential that the balance equations of the forces acting on a bubble to be solved. Fig 1 shows a schematic diagram of the forces acting on a single bubble in its nucleation site. The force balances in x-direction and y-direction are given by Klausner [6]: (1) (2)
In the above equations, ,
,
,
,
,
and
are respectively surface tension
force, quasi-steady drag force, shear lift force, unsteady drag force, buoyancy force, contact pressure force and hydrodynamic pressure force. Whilst a bubble is in equilibrium, the sum of the forces is zero in both directions. If the forces in the x direction overcome the forces in y direction, lift-off occurs.
5
Figure 1: Schematic diagram of force balance on a single bubble
2.1.
Surface tension force
Equations for surface tension force in x and y directions are [10]: (3)
(4)
where
is bubble contact diameter on the heated wall,
advancing contact angle and
is surface tension,
receding contact angle. It is worth mentioning that the
images taken during current experiment indicate that the advancing and receding contact angles are 85o and 12o, respectively. 2.2.
Shear lift force
Shear lift force is given by many authors suitable for a viscos flow. The following correlation is given by Klausner [6]: (5)
where
is the velocity of bubble and
is as follows:
6
(6) (7)
The liquid velocity profile used here is the universal single-phase turbulent flow profile. It is defined as follows: (8)
(9)
(10)
(11)
2.3.
Growth force
Unsteady drag force or growth force is due to bubble growth. It is applied in the opposite direction of a bubble growth. (12)
where
is liquid density and
is bubble radius which is a function of the effective
Jacob number, Reynolds number, Prandtl number and growth time [10]. (13)
(14)
2.4.
Quasy-steady drag force
For considering the Quasy-steady drag force, the following formula by Klausner [6] is used: 7
(15)
(16)
where
2.5.
is the dynamic viscosity of the liquid and n is 0.65.
Buoyancy, hydrodynamic and contact pressure forces
The buoyancy, hydrodynamic and contact pressure forces are expressed as follows according to Klausner [6]: (17) (18) (19)
3. Experimental databases An experimental facility has been set up in order to investigate the bubble lift-off diameter in subcooled flow boiling [23]. The experiments are conducted using water under the conditions of low flow velocity at atmospheric pressure. Digital high-speed video camera is utilized in order to capture consecutive images of bubbles from inception of growth to the point that lift-off occurs. The main loop in this experiment consists a centrifugal pump with mass flux and head respectively ranging from 0.6-2.4 m3/hr and 9-32 water meters, a preheater including 16 heating elements, the test section, a condenser, a DC power supply and measuring instruments. The schematics of the main loop and the cooling loop is shown in Fig 2 and Fig 3. The test section is an annulus with outer transparent glass tube having inner diameter of 19mm and a heated inner steel tube with outer diameter of 12mm. The heated steel tube has an overall length of 750 mm. Copper rods with 12mm O.D. and 0.27m long are installed to both endpoints of the inner tube, copper electrodes are attached to these rods for connecting to a 24kW DC power supply (30V and 800A). The
8
applied heat flux is calculated by considering the electrical current and the electrical potential as follows: (20)
Where, V and I stand for potential difference between two electrodes and electric current, respectively.
, is the outer diameter and is the heated length of the inner
heated tube. Various measuring devices are used in order to control the temperature and pressure of the flow and determine the relevant parameters of the experiment. Fluid temperatures arerecorded with K-type thermocouples. The relevant devices have been checked in the calibration tests to determine the measurement accuracies. A high-speed video camera is used to measure the bubble lift-off diameter during the experimental runs. The camera is capable of capturing images at the rate of 1200 fps. However, since the flow rates are low in this study, the growth rate is slow enough to capture images at the rate of 480fps with the size of 224*160 pixels. Two LED lights are used as direct backlighting during the experiments. They provide sufficient light for the desired camera acquisition rate and avoid the flickering associated with AC, one of the typical problems associated with high-speed video for clear visualization. In addition, uncertainty of the size of a measured bubble is approximately equal to one pixel, which is nearly 0.0337 mm.
9
Figure 2: Schematic diagram of experimental loop
Figure 3: Schematic diagram of the cooling water loop
10
Figure 4: a) Cross sectional view of the test section and the direction of magnetic field forces in the presence of the quadrupole, b) Quadrupole magnetic field direction
4. Experimental Procedure To begin, the loop is filled with distilled water. Then, degassing takes place by boiling the water for half an hour, being careful of not reaching the critical heat flux. Afterwards, while preheater and heat exchanger are working simultaneously, water reaches to a desired inlet subcooling temperature of 80oC, which could be read from the K-Type thermocouple installed in the entrance of the test section. It is worth mentioning that making any change in flow conditions requires at least 45 minutes for the flow to reach steady-state condition. In order to initiate data acquisition, mass flux is fixed at a specific value, however, heat flux is varied. An electrical current with a related voltage is applied to the inner rod from two end points in order to heat the test section. Starting with lower power levels then raising it gradually and reaching a stable condition at each level, suitable experimental conditions are chosen in a way that a stable active nucleation site is observed and could be captured by the high speed video camera. Hot fluid coming out from the test section enters the heat exchanger and it is cooled and 11
finally returned to the main tank. Then, it is pumped to the cycle again, see Fig. 2. After imaging at different heat fluxes in a constant mass flux and inlet temperature, mass flux is changed and the same procedure is repeated. In all of the experiments, the inlet temperature is remained unchanged. To provide an external magnetic field inside the annulus, permanent magnets are used. Four magnets are placed two by two in front of each other in order to make a quadrupole magnetic field. Magnitude of the external magnetic field grows rapidly with radial distance from its longitudinal axis. It reaches to maximum adjacent of the magnets which is 200mT. The installation position of the magnets and magnetic force directions are shown in Fig 4. During the experiment, the first one third of the inlet was discarded due to the entrance effect. High speed video camera is adjusted to focus on the active nucleation sites, chosen approximately one third of the way up the entrance in order to skip the entrance effect. In each flow condition, bubbles are recorded from inception until lift-off. This procedure is repeated for 15 times in order to decrease the error in reporting thebubble lift-off diameter. After taking videos, each video is converted to images. In accordance to the frame rate of the camera in this study which is 480 fps, 28800 frames of image are extracted from each video. Next, they are probed thoroughly in order to find the moment in which lift-off occurs. Finally, for each experimental condition, there are 15 images of the moment in which a specific bubble lifts off. In each image, there exists a scale to measure the diameter accurately, see Fig 5,. In addition, bubbles are assumed to be fully spherical. At the end, bubble lift-off diameter in that experimental condition is stated as the average of those 15 data along with a standard deviation.
Fig 5: The scale used in the experiments for measuring the exact bubble lift-off diameter.
12
5. Results and discussion According to the literature review, it is clear that most of the studies are related to the effect of various parameters on bubble departure diameter in high mass fluxes and heat fluxes. However, in newly emerging industrial applications such as microfluidic devices, lower ranges of mass flux should be studied as well. Furthermore, there is lack of study aboutthe effects of magnetic field on the bubble lift-off diameter in low mass fluxes and heat fluxes. Therefore, the problem will be studied in low mass fluxes and low heat fluxes, The main parameters considered here include heat flux, mass flux and non-uniform magnetic field effects. Bubble diameters are measured for different combinations of aforementioned parameters and all experiments are run at atmospheric pressure. Heat flux and mass flux values along with other information are available in Table1 and Table2, in the absence and in the presence of the magnetic field, respectively.
Table1: Parameters of the experiment in the absence of magnetic field
In the absence of the magnetic field parameters
Experiment range
Units
Annulus orientation
Vertical
-
Mass flux
88
kg/m2.s
sub cooling
20
℃
Heat flux
15-40
kW/m2
Table2: Parameters of the experiment in the presence of magnetic field
In the absence of the magnetic field parameters
Experiment range
Units
Annulus orientation
Vertical
-
Mass flux
65, 100, 125
kg/m2.s
sub cooling
20
℃
Heat flux
10-40
kW/m2
13
The average bubble lift-off diameter in the absence and presence of magnetic field are listed in Table 3 and Table 4, respectively. All values of diameters are reported along with their standard deviation from the spread of data around a mean diameter. The results for various conditions will be discussed in the following section. Table 3: Bubble lift-off diameter in the absence of magnetic field
No magnetic field G1=88 [kg/m2. s]
[kW/m2]
[mm]
15 22 23 27 28 29 34
2.19±0.07 2.2±0.05 2.23±0.09 2.29±0.07 2.36±0.08 2.36±0.07 2.69±0.09
Table 4: Bubble lift-off diameter in the presence of magnetic field
In the presence of magnetic field G1=65[kg/m2. s]
[kW/m2]
[mm]
12
2.71±0.16
15
G2 =100[kg/m2. s]
[kW/m2]
G3 =125[kg/m2. s]
[mm]
[kW/m2]
[mm]
23
1.96±0.1
35
1.91±0.07
2.93±0.24
27
2.11±0.1
41
2.02±0.06
17
3.01±0.1
31
2.16±0.1
30
3.42±0.1
39
2.32±0.1
41
2.38±0.1
14
It is worth mentioning that in all of the experimental studies, uncertainties and errors are inevitable. It is tried to reduce these errors to the possible minimum amount in order to avoid their interference with the result. Likewise, in this study, all approaches are considered to minimize the errors. However, some are demonstrated in the form of standard deviation. The standard deviation is calculated as follows. (21)
where
represents bubble lift-off diameter, M is the mean diameter, Σ is the
summation (or total), and N is the number of bubbles captured in one condition. In current study, in each condition, 15 bubble lift-off diameters are measured. Therefore, N is 15. Moreover, M indicates the average diameter of these 15 data. Nevertheless, there are undeniable uncertainties in measuring power, heat flux, flow rate, and temperature. The magnitude of each uncertainty is less than 4%, 4%, 2-3% and 5oC, respectively [23]. 4-1 Without Magnetic Field Since most of the experiments mentioned in the literature review have been done for the mass fluxes of 250 – 300 kg/m2.s, the first goal of the present study is to investigate the effects of several parameters on the bubble lift-off diameter in lower mass fluxes (50 – 150 kg/m2.s). In order to validate the first section of the experiment, which is to determine the effect of various parameters on bubble lift-off diameter in lower ranges of mass flux, the obtained data for nucleate subcooled boiling in the absence of the magnetic field is compared to that of the experiment done by Sugru [20]. The average bubble lift-off diameter in ongoing work is between 2.19 mm – 2.69 mm while this range in the study of Sugru [20] differs from 0.22 mm – 0.37 mm, despite the higher heat flux. It could be concluded that the higher the mass flux, the smaller the bubble lift-off diameter. This significant increase in the diameter in lower mass fluxes is due to the decrease of quasisteady drag force acting on the bubble while shear lift becomes significant to make a bubble lift off. 15
In order to analyze this outcome physically, the mechanistic model of Klausner [6] which was modified by Situ [10] is used. A single bubble in its nucleation site undergoes different forces which are mentioned in section 2. A MATLAB code was written for the conditions of current study using equation (1) and (2) which is the equilibrium condition for a bubble in the direction opposite to the flow. In order to validate this code, the forces calculated in Klausner’s [6] study is compared to the forces resulted from the same input in the MATLAB code of current study, seetable 5. Relative error of 20% is stated which is reasonable. Therefore, this code could be used to find out which forces have the most important role in bubble lift-off diameter. Thus, the sum of forces in x direction is assumed to be greater than zero and all the forces from the inception of nucleation until the bubble’s lift-off are plotted in Fig 6. Table 5: Comparison of the forces applied on a single bubble of refrigerant R113 derived from Klausner [6] study and current MATLAB code
Force
Klausner [6]
Current model
-9/9E-08
9/8E-08-
-2/5E-06
2/4E-06-
2/8E-07
2/5E-07
1/3E-06
0/8E-06
1/0E-07
1/3E-07
2/7E-07
2/4E-07
1/7E-07
2/6E-07
16
Forces in the direction of fluid flow [N]
1.50E-05 1.00E-05 F_cp
5.00E-06 0.00E+00 0.00E+00 -5.00E-06
F_sl
5.00E-04
1.00E-03
1.50E-03
F_dux F_sx
F_h
-1.00E-05
-1.50E-05
Bubble lift-off diameter [mm]
Fig 6: The evolution of various forces acting on a single bubble in the direction of flow from the inception of growth until lift-off
All the parameters used in this model have been summarized in table 6. Fig. 6 shows the evolution of various forces acting on a single bubble in the direction perpendicular to the flow. As it is evident, shear lift force and surface tension force are the most dominant ones that affect the bubble. Surface tension force tends to maintain the bubble in its nucleation site, however, shear lift force encourages the bubble in an active nucleation site to lift off. As soon as shear lift force grows larger than surface tension force, bubble lifts off. Table 6: Parameters used in the current MATLAB model
Parameters Sub cooling Mass flux Heat flux Hydraulic diameter Annulus length
Definition 10 - 20 50 - 150 10 0/017 76 4/203 968 0/3569 2296 0/3455E-6 0/675 0/05885
𝛔
17
Unit
Fig. 7 shows the bubble lift-off diameter versus heat flux for a mass flux of 88 kg/m 2. s. Evidently, bubble lift-off diameter increases with the increase of heat flux, since the increase in heat flux contributes to the increase of wall superheat. Consequently, bubbles grow more rapidly and lift-off takes place in larger bubble diameters. To be more specific, using experimental points in Fig. 7, there is 12.5% increase in bubble liftoff diameter for approximately 27% increase of heat flux.
Bubble lift-off diameter [mm]
2.6 2.4 2.2 2 1.8 1.6 In the absence of magnetic field, G=100 kg/m^2. s
1.4 1.2
10
15
20
25
30
35
40
Heat flux, q" [kW/m^2] Figure 7: Bubble lift-off diameter versus heat flux in the absence of magnetic field
4-2 With a Non-Uniform Magnetic Field Two-phase flow systems are well-known for their instability which is problematic in industrial applications. Therefore, it is essential that a better approach be devised to increase the stability of the flow. Applying an external magnetic field is one of the recommended solutions. In this study, a non-uniform magnetic field is applied to a vertical flow of water in an annulus. As it is shown in Fig 4, these four magnets exert a radial force on bubbles. External magnetic field could affect various important parameters like surface tension, contact angle and viscosity [23]. Mechanistic analysis of magnetic field effect on a single bubble is not the scope of current study. However, according to the literature review, it is concluded that surface tension increases due to magnetic field, which helps bubbles retain their spherical shape and flow becomes steadier. Fig 8, shows a single bubble about to lift-off in the presence and absence of 18
magnetic field. It is clear that a bubble in the presence of magnetic field is more of a spherical than the one in the absence of a magnetic field, according to the contact angle shown in the picture. During the experiments, it is observed that magnetic field has a significant influence on bubble lift-off diameter. As can be seen in Fig. 9, the effect of heat flux on bubble liftoff diameter in the presence of a constant magnetic field is studied for three different mass fluxes. Bubble lift-off diameter follows the same ascending trend with heat flux by the appliance of magnetic field. It is worth mentioning that bubbles grow more controlled in the presence of magnetic field. This outcome is the result of external magnetic forces applied on the bubbles which seem to increase surface tension force and retain the bubble in equlibrium. According to Fig 7 and Fig 9, for 22% increase of bubble lift-off diameter, 100% and 62% increase in heat flux is required in the presence and absence of magnetic field, respectively. Moreover, taking a close look at Fig 10, it could be seen that bubble lift-off diameter is inversly proportional to the mass flux.
Fig 8: Spotted magnetic field effect on retaining a bubble in a spherical shape
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Bubble lift-off diameter [mm]
4 3.5 3 2.5 2 1.5 in the presence of magnetic field, G = 65 kg/m^2.s in the presence of magnetic field, G=100 kg/m^2.s in the presence of magnetic field, G=125 kg/m^2.s
1 0.5 0
10
20
30
40
50
60
Heat flux, q" [kW/m^2]
70
80
Figure 9: Bubble lift-off diameter versus heat flux in the presence of magnetic field
bubble lift-off diameter [mm]
2.9 2.8
in the presence of magnetic field, q"=35 kW/m^2
2.7
in the presence of magnetic field, q"=45 kW/m^2
2.6 2.5 2.4 i
2.3
g
2.2
u
2.1
r
2
e
1.9 90
100
110
120
130
140
150
Mass flux, G [kg/m^2.s]
1 0 :
Bubble lift-off diameter versus mass flux in the presence of magnetic field
4-3 Comparison of the Bubble Lift-Off Diameters in the Presence and Absence of Magnetic Field 20
All experiments are performed in fluid inlet temperature of 80oC. As can be seen in Fig. 11, bubble lift-off diameter is shown against heat flux in the presence and absence of the magnetic field. Obviously, applied magnetic field decreases the bubble lift-off diameter to a considerable degree and bubble’s growth is more controlled than the case without magnetic field. The main goal of these studies is to present a new approach to increasethe CHF in order to increase the efficiency of microfluidic devices in cooling industry. As bubbles are smaller, they do not occupy more places adjacent to the surface. As a result, there would not be a blanket of bubbles and according to the literature review, the frequency of lift-off will be increased, which is also observed in current experiments. Therefore, bubbles leave the surface more rapidly and sub-cooled fluid takes its place and removes the heat from the wall, which is so called quenching heat transfer. If bubble lift-off diameter is indicated against mass flux as in Fig 12, a decreasing trend of bubble lift-off diameter is detected, as the mass flux increases. In particular, the higher the mass flux, the smaller the bubble lift-off diameter. In another words, in higher mass fluxes the effect of the magnetic field on bubble lift-off diameter is stronger.
Bubble lift-off diameter [mm]
2.6 2.4 2.2 2 1.8
1.6 in the absence of magnetic field, G=100 kg/m^2.s
1.4
in the presence of magnetic field, G=100 kg/m^2.s
1.2 10
15
20
25
30
35
40
45
Heat flux, q" [kW/m^2] Figure 11: Comparison of bubble lift-off diameter in the presence and absence of magnetic field versus heat flux
21
Bubble lift-off diameter [mm]
2.9 in the absence of magnetic field, q''=35 kW/m^2 in the presence of magnetic field, q''=35 kW/m^2
2.7 2.5 2.3 2.1 1.9
1.7 70
80
90
100
110
120
130
Mass flux, G [kg/m^2.s]
Figure 12: Comparison of bubble lift-off diameter in the presence and absence of magnetic field versus mass flux
In Fig. 13, we can have a thorough outlook about the effect of mass flux and the strong effect of magnetic field. In each specific mass flux, percentage of the change in bubble lift-off diameter in presence and absence of magnetic field is calculated and plotted. It is evident that by increasing the mass flux, the percentage of change in bubble lift-off diameter is increased. Another point to be mentioned is in the mass flux ranging from 80-130 kg/m2. s, there is about 3.5-9.5% of decrease in bubble lift-off diameter which leads to lower CHF and better performance in cooling applications.
22
Bubble lift-off diameter decrease [%]
-3.0% -4.0% -5.0% -6.0% -7.0% -8.0% Prominent decrease of bubble lift-off diameter in larger mass fluxes in the presence of magnetic field
-9.0% -10.0% 70
80
90
100
110
120
130
Mass flux, G [kg/m^2.s] Figure 13: Prominent decrease of bubble lift-off diameter in larger mass fluxes in the presence of magnetic field
Fig. 14 shows typical consecutive images of bubble growth. Bubble starts to initiate when required wall superheat is reached. Then, bubbles gain heat from the wall and start to grow until they reach departure diameter, which is the time to depart from the nucleation site and slide along the heating surface with the flow. Gaining excessive heat from the wall, they grow further to reach lift-off diameter, which is the bubble diameter when it leaves the surface. On account of the fact that nucleation sites are dependent on the heat flux and wall superheat, in each experiment, the same nucleation site might not have been activated. This phenomenon is more probable to occur in higher heat fluxes. Therefore, to be precise, at each step, several nucleation sites are under inspection and the growth and lift-off diameter of more bubbles are recorded. Then, they are averaged and written along with an error of standard deviation.
23
Figure 14: Typical consecutive images of bubble from initial condition of growth to departure and lift-off
A visual insight into the effect of magnetic field on bubble dynamics is obtained by comparing different conditions in Fig. 15 and Fig. 16. The first one pinpoints a mass flux effect on nucleation site density in an approximately same heat flux. All images are captured in partial boiling regime so that heat is transferred via two approaches including nucleate boiling and forced convection. Evidently, by the increase of mass flux, nucleation site density tends to decrease. The reason is that, when mass flux increases, so does the convective heat transfer coefficient. Therefore, a major portion of heat is transferred and wall superheat decreases and consequently, less nucleation sites would remain active. To further discuss the reason, theoretical explanation is given below. Boiling models are classified by combining convective boiling and nucleate boiling coefficients to obtain two phase flow heat transfer coefficient. The general model which was given by Chen [24], is as follows: (22) This indicates that heat is removed not only by single phase convection, but also by nucleate boiling. If a great portion of heat is removed by convective heat transfer, nucleate boiling heat transfer, and, consequently, wall superheat will reduce. On the other hand, there are initial considerations relating to the formation of vapor from a specific thermodynamic state of liquid that denotes a condition in which a spherical vapor nucleus is in mechanical equilibrium [1]. (23)
24
Regarding the above equation, critical radius of vapor nucleus to be formed is inversely proportional to the wall superheat. It means that if wall superheat is lower, as discussed above, the required critical radius of vapor nucleus for starting nucleation is bigger. Therefore, in higher mass fluxes, bigger nucleation sites are active. Since the existence of larger nucleation sites are less probable, therefore, nucleation site density in higher mass fluxes will decrease. Furthermore, when the case of magnetic field is considered, reduction in nucleation site density due to magnetic force could not be overlooked.
Figure 15: Mass flux effect on bubble nucleation density
The result of studying the effect of heat flux is depicted in Fig 16-b. It is obvious that nucleation site density proliferates as heat flux goes up in a constant mass flux. This could be due to the increase of the wall superheat and the subsequent smaller critical
25
nucleus’ radius. The effect of magnetic field in lowering the number of nucleation sites is also evident. In order to visually comprehend the effect of applied magnetic field and heat flux on the bubble lift-off diameter, Fig. 16-a is given. Referring to Fig. 16-a, bubbles are smaller in the presence of magnetic field, unmindful of heat flux magnitude. An undeniable magnetic field effect as a vital mean to decrease bubble lift-off diameter could be a novel interpretation.
Figure 16: a) Heat flux effect on bubble lift-off diameter, b) Heat flux effect on nucleation site density
6. Conclusion Forced convective subcooled flow boiling experiments in the presence and absence of a non-uniform magnetic field were carried out in a vertical-upward annular channel by 26
using water as a testing fluid to realize the effect of magnetic field and other effective parameters on bubble lift-off diameter. The experiments were done in atmospheric pressure. The inlet water temperature was constant at 80oC; heat flux changed from 10 to 40kW/m2; the mass flux varied from 65 to 125 kg/m2. s. The magnetic field was made by four magnets, two by two situated in front of each other makes a non-uniform magnetic field with a maximum magnitude of 200mT. A high-speed digital video camera was utilized in order to capture bubble lift-off diameter during subcooled nucleate boiling. Bubble liftoff diameters were obtained from measuring so many bubbles as they tend to leave the surface. The results indicate that bubble lift-off diameter decreases by increasing mass flux and decreasing heat flux. Furthermore, applying a magnetic field brings about a more controlled bubble growth as well as lower bubble nucleation density and smaller bubbles at lift-off. All in all, it could be concluded that applying a magnetic field can decrease bubble lift-off diameter for 5-10% which leads to higher CHF. Reaching higher CHF is an admirable approach since this is an important parameter to be considered in cooling industries. Moreover, during these experiments, it is observed that the effect of magnetic field on bubble lift-off diameter is increased in higher mass fluxes. However, it requires more and thorough studies.
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