Boiling heat transfer is a mode using the phase change of working medium to strengthen the heat exchange due to its good heat exchange capability, and it is widely used in heat exchange engineering. Nanofluids have been used in the direction of enhanced heat transfer for their superior thermophysical property. The wetting, spreading and ripple phenomena of superhydrophobic surfaces widely exist in nature and daily life. It has great application value for engineering technology. In this article, the boiling heat exchange characteristics of nanofluids on superhydrophobic surface are numerically studied. It was found that with the increase of superheating degree, the steam volume ratio of unmodified heated surface increases to saturation, while the steam volume and evaporation ratio of modified superhydrophobic surface increase firstly and then decrease. At the same time, bubbles are generated and accumulated more fully on superhydrophobic surface. It was also found that nanofluids with low viscosity are more affected by superhydrophobic surface characteristics, and the increase is more significant with high superheating degree, and the superhydrophobic surface is beneficial to enhancing boiling heat exchange. Compared with the simulation results, it could be concluded that the boiling heat exchange performance of CuO-water nanofluids on the modified superhydrophobic surface is better than that of CuO-ethylene glycol nanofluids under high superheating degree.
With the vigorous progress of contemporary industry, the heat exchange process has penetrated into various fields; especially the electronic heat dissipation problem needs to be solved urgently to realize the efficient and stable operation of equipment. The traditional working media such as air and water commonly used in the heat dissipation process can no longer reach the work condition under overheating load, while nanofluids, as a new working medium, has superior and unique flow and heat exchange characteristics [
Until now, many researchers have done a lot of researches on boiling and phase change heat transfer [
As important performance parameters of nucleate boiling heat transfer, critical heating flux (CHF) and heat transfer coefficient (HTC) have a great relationship with microstructure and wettability of the boiling surface. As a new bionic surface, superhydrophobic surface is widely used in the field of heat transfer and flow enhancement due to its wettability and roughness [
As mentioned above, many different studies on boiling heat transfer performance of superhydrophobic surfaces have been introduced in the references. However, there are few studies on boiling heat transfer of nanofluids on superhydrophobic modified surfaces, which needs further study. In this paper, the difference between the boiling research of superhydrophobic modified surface and some scholars’ are shown in
Researchers | Influence factor | Contributions in this article |
---|---|---|
Li et al. [ |
Nanoparticle concentration | The concentration of nanoparticles affects boiling heat transfer |
Izadi et al. [ |
External magnetic field | External magnetic field enhances melting heat transfer |
Allred et al. [ |
Highly wet textured surface | The modified surface improves the heat transfer performance |
This article | Different base fluid and superhydrophobic surface | Low viscosity nanofluids and superhydrophobic surface enhance heat transfer |
The mixture model is selected in this paper to solve the equation of continuity, momentum equation, equation of energy, phase-to-phase slip velocity (relative velocity) equation and volume fraction formula of the second term. Because the mixture model is only aimed at a set of governing equations including energy and momentum, the mixture model belongs to the category of single-fluid model.
The continuity equation is as follows:
In
Meanwhile,
The momentum equation of the mixed phase can be solved firstly for each single phase, and then the items are summed up, which is specifically expressed as
In
In
For the phase of compressible,
The relative speed (
The relationship between drift velocity and relative velocity is described by
The volume fraction equation of the second phase can be described by the the second phase’s equation of continuity, which is expressed as
Traditional nanofluids are multiphase, and nanoparticles may deposit on the flowing surface. Because the simulation is a boiling model, nanofluids are constantly disturbed by bubbles, and the deposition of nanoparticles is not obvious. Therefore, nanofluids can be regarded as a single-phase fluid, and the physical parameter equations of nanofluids can be summarized as follows. The thermal conductivity of nanofluids is as
Dynamic viscosity is shown in the following
The specific heat capacity is shown in
The density of nanofluids is shown in
In the boiling process, the phase change process of heat and mass exchange occurs between liquid and gas, and the liquid phase is gasified to produce gas phase, and the gas phase condenses into liquid phase, which can be expressed by vapor phase transport equation (
In the equation,
As an unsteady flow, turbulence is complex and irregular. At present, in the numerical method of heat exchange, the
According to Navier-Stokes equation, the
In the above equations,
Wettability is an important property of solid surface and a common interface phenomenon in nature and daily life. Due to the great roughness and low surface energy of the surface, there are many small bubbles in the microstructure, which makes an air cushion layer between the fluid and the interface, and it makes the solid surface superhydrophobic. At the same time, superhydrophobic surfaces are widely used in engineering fields such as surface drag reduction and pipeline transportation. The surface wettability will be affected when the roughness and free energy of surface on solid surface change. Generally, when the contact between solid, liquid and gas is stable, the angle between solid and gas is called contact angle, which is usually expressed as
According to Young’s equation, the solid surface can be called hydrophobic surface when
In this work, a single-fluid model is adopted to simulate the boiling heat exchange of nanofluids. Firstly, the geometric dimensions are determined, the whole model is described in
There is a 1 mm heating wall in the middle of the container bottom, a pressure outlet at the top, and both sides of the container are set as walls. Boundary conditions of the simulation are set according to
Boundary areas | Boundary names | Boundary styles | Numerical value |
---|---|---|---|
Bottom middle heating | Heating | Non-slip wall boundary | According to the working conditions |
Top | Outlet | Pressure boundary | Atmospheric pressure |
Two side walls | Wall_1, Wall_2 | Non-slip adiabatic wall | 0 |
As boiling is a typical unstable transient process, physical quantities such as velocity, temperature and pressure will change with time, so the initial conditions must be given in transient conditions. At the beginning of calculation, the temperature of the fluid working medium in the container is set close to its boiling point, and it is assumed that only static liquid is contained in the calculation area, and the gas phase volume fraction is zero at the initial time. After comprehensive consideration, the time step finally selected in this paper is 0.001 s, and each time step is iterated 30 times to ensure convergence.
Because the simulation results will be affected by the number of grids in numerical simulation, for the purpose of ensuring the rationality of the calculation results and the irrelevance between the number of grids and the calculation results, grid independence validation is carried out. By setting different spacing sizes and node numbers, different numbers of grids are generated for irrelevant verification as
Grid | Grid number | Heating flux (W/m^{2}) | Relative deviation from grid 3 |
---|---|---|---|
1 | 4000 | 90344.1117 | 0.318 |
2 | 16000 | 118150.3088 | 0.109 |
3 | 25000 | 132604.8039 | 0 |
4 | 40000 | 134761.1402 | 0.016 |
It can be seen that the error between the second grid and the third grid is about 10%. Under the condition of ensuring accuracy, considering the calculation time and speed, the third grid is finally selected.
Due to the heat exchange of nanofluids boiling is complex. The following assumptions are made in this simulation: (1) Nanoparticles are uniformly dispersed in the base fluid, due to the fluid properties of nanoscale particles, therefore the nanofluids can be regarded as a single-phase fluid with the same properties. (2) The component concentration of nanofluids studied in this work is relatively low, so it is assumed that the component concentration of nanofluids will not change during boiling heat transfer. (3) Due to the limitation of high-precision correlation, this paper does not consider the effect of temperature on the physical properties of substrate fluid and nanofluids in the simulation process. (4) The influence of the fluid height in the container on the heat exchange influence is not considered, and the container is full of fluid. (5) The heating contact surface is an ideal superhydrophobic surface.
For the purpose of comparing the influences of components and superheating on the boiling exchange transfer of nanofluids, it is necessary to design multiple sets of operating conditions for parameter comparison. In this paper, a coupled solver based on pressure is used for unsteady calculation, considering the influence of gravity, and the value of gravity is –9.81 m/s^{2}. Because there are positive and negative directions in the numerical simulation model, and there are direction requirements in gravity setting, it is necessary to add a negative sign before the value of 9.81 m/s^{2}. Discrete governing equations are solved by the semi-implicit method (SIMPLE algorithm), and the SIMPLE algorithm’s core is the process of guessing and correcting. For gradient interpolation of diffusion term, it is set based on Green-Gaussian element. Momentum equation, turbulence kinetic energy equation, turbulent dissipation rate equation and energy equation are all solved by the QUICK scheme, which has higher accuracy in solving structured grids. VOF is a module in FLUENT software, which is a gas-liquid two-phase mixing module. In the simulation process, simulation calculation is carried out by setting the gas phase and liquid phase regions. For the relaxation factor, set the pressure to 0.5, and leave the rest settings at the default values. And the physical parameters of nanofluids used in this simulation are shown in
Parameters | ||||
---|---|---|---|---|
Water | 997.1 | 4179 | 0.001004 | 0.613 |
CuO | 6500 | 540 | / | 18 |
Nanofluids (5%) | 1272.245 | 3249.403106 | 0.001141365 | 0.700092941 |
Parameters | ||||
---|---|---|---|---|
Ethylene glycol | 1114.4 | 2415 | 0.0157 | 0.252 |
CuO | 6500 | 540 | / | 18 |
Nanofluids (5%) | 1383.68 | 2321.25 | 0.017848044 | 0.290081945 |
According to the simulation conditions described above, the working parameters of the fluid are set.
It is exhibited in
As
It can be observed from
It can be indicated that only the middle of the bottom is the heating area in the simulation, and the vapor is concentrated in the middle due to the high viscosity of ethylene glycol. At the same time, the proportion of gas increases with the ascending trend of mass fraction, which indicates that the thermal conductivity caused by the larger mass fraction increases the degree of phase change heat transfer, thus more liquid is converted into gas.
At the same time, by observing the change of gas volume in the simulation model, as shown in
The velocity vector indicates that the velocity has a direction. The vector diagram of velocity can be obtained by Tecplot software. It can be seen from the overall diagram of
Comparing the nanofluids of the two base fluids, it can be found that different viscosities of the base fluids will lead to different situations when bubbles leave the heating surface. When the viscosity of liquid is higher, bubbles are more difficult to get off the bottom surface, but when the viscosity is lower, bubbles are easier to get off the substrate and float upwards. The reason is that the bottom of the bubble is mainly affected by the adhesive force, which forms an obvious speed difference with other parts, providing a larger separation speed, and intensifying the fracture and rise of the bubble here. At the same time, under the action of gravity, the water-based nanofluids with lower density can be quickly replenished to the position before the bubble leaves the heating surface and rises with the gas phase, so the whole container is disturbed more violently. During the boiling process of water-based nanofluids, bubbles move more violently, and the degree of bubble rupture is greater. During the whole process, the energy of bubble movement is converted into kinetic energy, potential energy and surface energy, and its dynamic behavior is accompanied by greater energy dissipation, while the energy dissipation of bubbles is relatively small during the boiling process of glycol-based nanofluids. In the energy conversion process of bubble movement, the heat energy possessed by bubbles is gradually converted into potential energy with the increase of rising distance, while the energy required in the movement process is the consumed kinetic energy. At the same time, bubbles expand, and small bubbles gather into large bubbles to change the surface tension. However, with the increase in the number of small bubbles, the surface energy increases and the bubble energy is consumed. These energy transformations form a dynamic balance.
The boiling gas phase contour of water-based nanofluids and glycol-based nanofluids on the superhydrophobic surface can be seen from
Secondly, by observing the gas phase changes in the boiling process of glycol-based nanofluids (as shown in
By observing
The boiling heat transfer characteristics of nanofluids with the two base fluids are obviously different, and the dispersion and agglomeration of nanoparticles in water and ethanol are also quite distinct. Because the density and viscosity of the two base fluids are different, the heat transfer characteristics of nanofluids are obviously affected, especially the critical heating flux (CHF) and heat transfer coefficient (HTC) of nanofluids. By observing the curves of bottom surface critical heating flux (CHF) with time in simulation of the two kinds of base liquid nanofluids in
It is shown in
The boiling heat exchange performance of two kinds of base fluid nanofluids on the superhydrophobic surface has changed somewhat. By observing
As shown in
By observing
As indicated in the article, the flow and heat exchange characteristics of nanofluids with different base fluids on superhydrophobic surface are simulated in boiling state, and the effects of superhydrophobic surface, base fluids and superheating on boiling heat exchange performance under different working conditions are studied. Some conclusions can be summarized below:
The fluidity of water-based nanofluids is better than that of glycol-based nanofluids. In the process of heating and boiling, the flow of water-based nanofluids is more disordered, producing more bubbles with larger volume and consuming more energy, the maximum bubble volume produced by glycol-based nanofluids on unmodified surface is 50.36% of that of water-based nanofluids. However, the glycol-based nanofluids with higher viscosity have less energy dissipation and slower bubble generation during boiling.
The large contact angle of superhydrophobic surface makes it difficult for solid surface to wet, and it is easier for solid-liquid interface to form and separate bubbles, while rough surface is easier to form vaporization core, which makes a large number of bubbles generated in boiling process disturb the flow and enhance heat exchange.
Compared with glycol-based nanofluids, water-based nanofluids have smaller viscosity and density and are more affected by superhydrophobic surface characteristics. Therefore, the formation, bubble aggregation and evaporation of glycol-based nanofluids are about 0.3 s behind those of water-based nanofluids.
Superhydrophobic surface is beneficial to enhancing boiling heat exchange. By comparing various working conditions, it is found that water-based nanofluids with a superheating degree of 30 K on superhydrophobic surface has the best heat exchange performance, and its average Nusselt number is 5354.519, it is about 15 times higher than the average Nusselt number of glycol-based nanofluids with the unmodified surface at 10 K superheat degree.
specific heat of nanofluids, J·kg^{1}·K^{–1}
specific heat of base fluid, J·kg^{–1}·K^{–1}
specific heat of particles, J·kg^{–1}·K^{–1}
relaxation factors, the reciprocal of relaxation time
relaxation factors
empirical coefficients
energy of the k phase
volume force
turbulence kinetic energy increment
gravity force
heat transfer coefficient, W·m^{–2}·K^{–1}
apparent enthalpy of the k phase
thermal conductivity, W·m^{–1}·K^{–1}
thermal conductivity of base fluid, W·m^{–1}·K^{–1}
thermal conductivity of nanofluids, W·m^{–1}·K^{–1}
thermal conductivity of nanoparticle, W·m^{–1}·K^{–1}
mass transfer of air pockets or user-defined mass sources
mass source terms of liquid phase
mass source terms of gas phase
Nusselt number
pressure drop of nanofluids, Pa
heating flux, W·m^{–2}
all volume heat sources
heating time, s
temperature of liquid, K
temperature of gas, K
temperatures of saturation, K
volume of vapor bubbles, m^{3}
drift velocity of the second phase
average velocity of phase
average velocity of phase
average velocity of phase
mass average velocity, m/s
gas phase velocity, m/s
length of heating surface, m
contact angle, °
volume fraction of the phase
volume fraction of the liquid phase
volume fraction of the gas phase
density of the phase
density of liquid phase, kg·m^{–3}
mixing density, kg·m^{–3}
density of nanofluids, kg·m^{–3}
density of base fluid, kg·m^{–3}
density of nanoparticle, kg·m^{–3}
density of gas phase, kg·m^{–3}
dispersed phase component of nanoparticles
dynamic viscosity of fluid, Pa·s
dynamic viscosity of phase
mixing dynamic viscosity, Pa·s
dynamic viscosity of nanofluids, Pa·s
dynamic viscosity of base fluid, Pa·s
turbulent viscosity coefficient, Pa·s
turbulent prandtl number related to turbulence kinetic energy
turbulent prandtl number related to turbulent dissipation
evaporation ratio, %
phase of
base fluid
phase of
liquid
gas
mass
nanofluids
nanoparticle