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Effect of droplets on water vapor compression performance
Desalination 464 (2019) 33–47
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Effect of droplets on water vapor compression performance a
a
a,⁎
Hong Wu , Haoyu Yin , Yulong Li , Xianghua Xu
T
b
a National Key Laboratory of Science and Technology on Aero Engines Aero-thermodynamics & Collaborative Innovation Center for Advanced Aero-Engine, School of Energy and Power Engineering, Beihang University, Beijing 100191, PR China b School of Aerospace Engineering, Tsinghua University, Beijing 100084, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Mechanical vapor recompression Water vapor compression Heat transfer Mass transfer Two-phase flow
Mechanical vapor recompression (MVR) technology has broad prospects for application in saving energy. The compression in the MVR system often involves mixing vapor and liquid, and therefore, studies of the process can help establish a theoretical model to solve the problem of controlling compression temperature and improving the compression process's efficiency. However, the mixed phase-change in water vapor compression is complex and differs from that in air wet compression. In this paper, we studied droplets' effect on water vapor compression performance and the mechanism of heat and mass transfer during the process. A 2D single droplet evaporation model for water vapor compression was established and analyzed with Python, and a 3D numerical simulation was solved with CFD software to investigate the effect on water vapor compression of droplet diameter, ambient pressure and temperature, spray flow rate, and flow velocity. The results showed that the compressor's outlet temperature can be reduced by reducing the droplet diameter and increasing the spray flow rate, thus decreasing the work required for compression. The results also indicated that a high pressure ratio and superheat can enhance the cooling effect greatly.
1. Introduction Mechanical vapor recompression technology (MVR technology) has broad prospects for application and tremendous potential for development in saving energy [1] and reducing consumption in such fields as the chemical industry [2] and wastewater treatment [3]. The core equipment that determines the MVR system's efficiency and reliability is a water vapor compressor [4]. The steam compressor compresses low-temperature and -pressure water vapor to high-temperature and -pressure superheated steam so that the heat can be recycled. The water vapor compression process has a decisive effect on the compressor's efficiency and reliability. Ideally, MVR system compressors should draw in only water vapor. However, in the system's actual operation, the compressor absorbs liquid water along with the water vapor because of the high water level during evaporation, the feed liquid's excessive foaming, unstable operation of the vapor-liquid separator, and the need to reduce the compressed water vapor's superheat [5]. Therefore, MVR often is a vapor-liquid mixing compression process (Fig. 1). The water droplets in the compressed steam cause problems, such as erosion in blades and reducing surge margins [6]. However, from the theory of thermal compression, it is known that the droplets' evaporation absorbs heat and cools the water vapor, thus reducing the outlet steam temperature. In particular, the vapor compression process will be closer to a ⁎
saturation state, and the compression work is lower than that of adiabatic compression [7]. Therefore, the vapor-liquid mixing compression in MVR can reduce the compression work. However, the mechanism of heat and mass transfer during the two-phase compression process also is more complex than in one-phase compression. Therefore, it is necessary to study the mechanism of two-phase flow, heat and mass transfer, and phase change during vapor-liquid mixing compression. This air-based, gas-liquid compression process is referred to often as “wet compression” [8]. To establish the air-liquid compression model, many scholars have conducted systematic research and conducted detailed thermodynamic analysis of different theoretical models [9–15]. Albernaz et al. [9] used the Lattice Boltzmann (LBM) method to simulate suspended droplets' evaporation in the air, and found that when convection occurs in the gravitational field, the droplets and air's relative motion can enhance static droplets' heat transfer effect. Xie et al. [10] established a multiphase LBM model in which single droplets evaporated in air, and proposed the critical diameter to describe gravity's effect on droplet evaporation. Yang et al. [11] investigated wet compression's effects on a transonic compressor with CFD 3D numerical simulation, while Kim et al. [12] used approximate analytical solutions to simulate the wet compression process and studied the transient behaviors of important variables in wet compression, such as droplet diameter and mass, gas and droplet temperature, and evaporation rate,
Corresponding author. E-mail address: [email protected] (Y. Li).
https://doi.org/10.1016/j.desal.2019.04.011 Received 10 July 2018; Received in revised form 29 March 2019; Accepted 9 April 2019 Available online 24 April 2019 0011-9164/ © 2019 Elsevier B.V. All rights reserved.
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Fig. 3. Single droplet evaporation model.
and obtained results consistent with existing studies. It has been found that the droplet-wall interaction model is important for wet compression studies, and Sun et al. [7] used the spray theory to analyze the interaction and compared elastic and inelastic collision models' 3D flow simulation results. In addition, the actual operation of existing gas turbines has shown that wet compression technology can help increase the gas turbine's power by up to 14% [16], and reduce the compression power by up to 5% [17]. However, these models all focus on the wet air compression process in the field of gas turbines. They are all air-based and thus, lack systemic research on the water vapor environment. However, there are both similarities and significant differences in the vapor-liquid mixing compression and air wet compression processes. Vapor-liquid mixing compression is a heat transfer and phase change process of the same material. The pressure on the droplet during evaporation is no longer the partial pressure of water vapor in the air. Moreover, the droplets' vaporization leads to an increase in the mass of steam, which affects the heat and mass transfer process and causes changes in the compressor's performance characteristics and operating points. In addition, water vapor's physical properties are very different from those of air, and the state parameters of environmental water vapor are constantly changing in the process of droplet evaporation. Therefore, as vapor-liquid mixing compression's heat and mass transfer characteristics differ from those of wet compression in which air is the working fluid, it is necessary to study the mechanism of two-phase flow and heat and mass transfer during the process and analyze the droplets' effect on the water vapor compression performance. In this paper, a 2D heat and mass transfer model for vapor-liquid mixing compression was established and a single droplet's evaporation during the process was analyzed with Python language programming. Thereafter, a 3D numerical simulation was solved with CFD software to analyze the heat and mass transfer mechanism in the process. The factors that affect the droplet evaporation process were studied, and the droplets' effect on water vapor compression performance was analyzed to provide a theoretical model for studies of the flow, and heat and mass transfer mechanism in vapor-liquid mixing compression.
Fig. 1. Process of vapor-liquid mixing compression. Table 1 Rotor 37 design parameters. Number of blades
Rotational speed/(r·min−1)
Pressure ratio
Design flow rate/(ks·s−1)
Efficiency%
36
17,188
2.016
20.19
88.9
(a) rotor 37
2. Models and methods The goal of this study was to establish a mathematical single-droplet model, which is a necessary condition for the analysis of vapor-liquid mixing compression's heat and mass transfer mechanism. To validate the mathematical model, 3D numerical simulation also is needed. At the same time, the effect on compression of flow and other factors also can be simulated in the 3D models.
(b) Leading edge at the roof of the blade Fig. 2. Grid structure. Table 2 Grid independence verification. Number
Number of grid layers
1 2 3 4
73 57 73 57
Number of grids/million 1.009 0.906 0.685 0.353
Flow rate/(kg·s−1) 20.716 20.726 20.728 20.684
2.1. 2D model
Pressure ratio
The following 2D mathematical models were used to make assumptions about the droplets:
2.026 2.026 2.026 2.026
(1) the droplet is spherical; (2) there is no flow within the droplet; (3) the temperature distribution inside the droplet is a spherical symmetry distribution, and (4) physical property parameters are 34
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(b) The relation between the ratio of droplet diameter to initial diameter and time
(a) The relation between droplet temperature and diameter
Fig. 4. Droplet diameter's effect on evaporation.
differential (time format) is used for time. The N-layer uniform grid is divided along the radius, and the volume of each layer is given by:
constant. The droplet's interior was purely thermally conductive and the temperature control equation is:
Vi =
∂T 1 ∂ ∂T = α 2 ⎛r 2 ⎞ ∂t r ∂r ⎝ ∂r ⎠
in which Δr is the grid spacing and i is the grid number. The heat flux on the two adjacent layers is given by:
α=
(1)
k ρcp
4 π Δr 3 [(i + 1)3 − i3] 3
qi = k
(2)
Ti − Ti + 1 Δr
(7)
(8)
The evaporation rate determines the outermost layer's (outer droplet surface's) heat flux:
in which α is the droplet's thermal diffusivity; T is the temperature; r is the radial coordinate, and t is time. The boundary conditions are:
q0 = γm
∂T r = 0, =0 ∂r
(3)
The temperature rise (fall) of the i-layer during Δt is calculated by the heat flow input and the layer's heat capacity:
(4)
ΔTi =
r = R, −k =
• ∂T = γm ∂r
•
in which m is the evaporation rate (kg/s·m ); R is the droplet's radius; γ is the droplet's latent heat of vaporization, and k is its thermal conductivity. The evaporation rate at the droplet surface can be given by a kinetic model [18]:
(9)
4π [(i − 1)Δr ]2 qi − 1 − 4π (iΔr )2qi 4π 3
[(i + 1)3Δr 3 − (iΔr )3]
(10)
2
•
m=
1 ⎛ Pi − ⎜ 2πRg ⎝ Ti
Pv ⎞ ⎟ Tv ⎠
In addition, various physical parameters, such as the water vapor environment's thermal conductivity and diffusivity, specific heat, density, and saturation pressure during the simulation of droplet evaporation were defined in the program. 2.2. 3D numerical simulation
(5)
Flow's influence is not considered in the 2D model. Therefore, the flow and other factors were studied using 3D numerical simulation instead. In addition, the results of 3D numerical simulation were verified with the 2D calculation results.
In this model, Pv is the gas phase pressure adjacent to the interface; Tv is the temperature; Pi refers to the liquid phase pressure at the interface (or the saturation pressure derived according to the temperature); Ti represents temperature; Rg is the gas constant, and σ is the coordination coefficient (0.03). As the droplets evaporate, their radius decreases. According to quality conservation, the following equation is derived: •
m=ρ
dR dt
2.2.1. Physical model NASA's rotor 37 is used as a physical model for numerical simulation. The model has a rotor that was designed by NASA in the 1970s [19,20], the specific parameters of which are shown in Table 1. There are detailed experimental data on this type of blade. After a large number of calculations and comparisons, the data calculated and the experimental data largely have been shown to be consistent. Therefore, it often is used as an example of the calculation of CFD. Although the working fluid in this paper was water vapor, this model still was adopted to improve the calculations' reliability. The grid was
(6)
in which ρ is the droplets' density. Because the mathematical model established is a 1D non-stationary problem, the space (r) and the time (t) need to be discretized. The center difference is used for spatial dispersion, and the forward 35
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(a) The relation between pressure and diameter in 10 μm
(b) The relation between pressure and diameter in 50 μm
(c) The relation between temperature and diameter in 10 μm
(d) The relation between temperature and diameter in 50 μm
Fig. 5. Ambient pressure and temperature's effects on droplet evaporation.
in water vapor compression process with droplets. The droplets evaporate into water vapor during the compression process, and latent heat of evaporation causes changes in the temperature of the mainstream. Therefore, the continuous phase's (gas phase's) control equation is no longer conserved and source terms need to be added. The source term M in the mass conservation equation represents the droplet's mass from the discrete phase (liquid phase) into the continuous phase (gas phase) attributable to evaporation. The evaporation model of this process requires the use of the Antoine equation [21] to determine the saturation pressure (Pa), and is given by:
generated using NUMECA/AutoGrid5. As can be seen in Fig. 2, a single runner was selected in the calculation domain, and the O4H grid was used. The total number of grid layers was 73, and the total number of grids was 685,000. The min skewness angle was 24.706, the max aspect ratio was 342.25, and the max expansion ratio was 2.9277. The flow field was calculated using commercial CFD software CFX for numerical simulation under no-slip, adiabatic boundary conditions. The inlet condition was set as the total temperature and pressure, and the outlet was set as the average static pressure. The rotating boundaries were specified by blades and hubs, and the stationary boundary was specified by shroud. Periodic boundary conditions exist on both sides of the channel. The turbulent discrete format adopts the first-order upwind style and the SST turbulence model was selected. Every residual converges to 10−5. The grid independence was verified first, and the working medium was air. The results are shown in Table 2. According to the table, the number of grids has little effect on the results calculated. Considering that the liquid phase requires an adequate number of grids, approximately 685,000 were chosen.
lg(10−5psat ) = A −
B T + C − 273.15
(11)
in which A is 5.11564, B is 1687.54 K, and C is 230.23 K. Water droplets' evaporation rate [22,23] is:
dmp dt
= πdp ρg Dg Sh
1 − fp ⎞ lg ⎜⎛ ⎟ M ⎝1−f ⎠
Mg
(12)
in which ρg is the vapor density; Dg is the vapor diffusion coefficient; Mg and M are the molar masses of water vapor and the main stream, respectively; fp is the molar fraction of liquid water and gaseous water,
2.2.2. Control equation The heat and mass transfer of the two phases need to be considered 36
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(a) The relation between the change in pressure and diameter
(b) The relation between constant pressure and diameter
Fig. 6. The pressure ratio's effect on droplet evaporation.
(a) The relation between flow rate and efficiency
(b) The relation between flow rate and pressure ratio
Fig. 7. Rotor 37 performance curves with water vapor.
The gas phase settings have been described previously, with the liquid phase set to Particle Transport Fluid, assuming that it is mixed well with the gas phase at the inlet, with boundary conditions that specify diameter, temperature, flow, and velocity. From the inlet, the droplets enter the flow path with the main stream. According to the method mentioned above, a 3D numerical simulation model of vaporliquid mixing compression was established by combining the basic equations of fluid mechanics.
respectively, and Sh is the Sherwood number. In summary, the mass conservation equation's source term is given by:
M=
dmp (13)
dt
The latent heat of droplet evaporation affects the temperature of the gas phase, so the continuous phase's energy equation is no longer conserved. The present source terms are the heat droplets absorb, and the droplet has the following transfer equation:
mp Cl
dTp dt
= πdp λNu (T − Tp) +
dmp dt
3. Results and analysis
hfg
(14)
In this paper, the 2D calculation results and 3D numerical simulation results were analyzed. The effect of the factors such as droplet diameter, pressure, temperature, droplet spray flow rate, and droplet spray velocity on compression performance was analyzed.
in which mp is the droplet's mass; Cl is its specific heat; λ is the thermal conductivity of the gas phase; hfg is the latent heat of vaporization; Tp is the droplet's temperature, and Nu is the Nusselt number. 37
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(a) The relation between total temperature and diameter
(b) The S1 surface’s relative Mach number distribution at 0.95 blade height in dry compression
(c) The S1 surface’s relative Mach number distribution at 0.95 blade height (1 μm diameter) in vapor-liquid mixing compression
(d) The S1 surface’s relative Mach number distribution at 0.95 blade height (20 μm diameter) in vapor-liquid mixing compression
Fig. 8. The droplet diameter's effect on compression.
analyzed based on the verification of mesh independence and step length independence. The droplet's initial temperature was 300 K, the ambient pressure was 0.4 MPa, the ambient temperature was 450 K, and the calculated operating condition was superheated steam. Under the pressure of 0.4 MPa, the saturated steam temperature was 416.79 K. Based on the existing air wet compression studies, the initial diameters of the droplets in the study were set as 10, 30, 50, 70, and 100 μm [24–26]. Fig. 4 shows the analysis of droplet diameter's effect on the evaporation process after calculation. Fig. 4(a) shows the change in the droplet's temperature over time corresponding to different initial droplet diameters. Fig. 4(b) shows the ratio of droplet diameter to initial diameter over time. It can be seen from the figures that the droplet's initial diameter affected the rate of temperature change strongly. In the range of 10–30 μm, the larger the droplet's initial diameter, the slower the evaporation. However, the speed overall still is relatively fast and evaporation is completed within 0.5 ms. As the initial diameter increases (from 50 μm to 100 μm), the evaporation rate drops
3.1. Analysis of 2D calculation results As shown in Fig. 3, in the droplet evaporation model, the unknowns are droplet initial diameter, and ambient pressure and temperature. The droplet diameter and environmental conditions in existing research also are factors that must be considered in the evaporation process [7,14]. Therefore, it is necessary to investigate these factors' effect on the droplet's evaporation in vapor-liquid mixing compression. Superheated steam at a pressure of 0.4 MPa was used in the study conditions. According to the droplet evaporation model established, the droplet's initial diameter, the ambient pressure and temperature, and the pressure ratio are the important factors that affect the liquid-vapor compression process. Thus, these factors' influence on the droplet evaporation process was analyzed. 3.1.1. Initial droplet diameter Droplet diameter's influence on the evaporation process was 38
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(b) Static pressure distribution at 0.5 blade height (from leading edge to trailing edge)
(a) Static pressure distribution at 0.1 blade height (from leading edge to trailing edge)
(c) Static pressure distribution at 0.9 blade height (from leading edge to trailing edge) Fig. 9. The relation between static pressure and diameter.
Therefore, choosing a reasonable range for the droplet diameter distribution is an important factor in accelerating the evaporation rate and improving the wet compression efficiency.
significantly and the evaporation time increases to nearly 2–4 times that of the droplets with a diameter of 10–30 μm Within 0.5 ms, the droplets' average temperature within the range of 10–30 μm initial diameter is 416 K, reaching the saturation temperature. However, droplets with a diameter of 50–100 μm do not evaporate fully, with the maximum temperature of 360 K and the minimum temperature of approximately 330 K. The difference in temperature between droplets with the two ranges of diameters is 56–86 K. Under the same conditions, the difference in individual droplets' heat absorption is 13–21%. As Fig. 4(b) shows, when the droplets with a diameter in the range of 10–30 μm evaporate completely, those in the range of 50–100 μm has a residual diameter 20–60% of their original diameter. More than half of the droplets do not evaporate. In summary, the droplet's initial diameter has a great influence on its rate of evaporation. The larger the droplet diameter, the larger the feature length and the Bi. This means that the internal thermal resistance becomes stronger, resulting in a lower evaporation rate.
3.1.2. Environmental pressure and ambient temperature Fig. 5 shows the change in the ratio of droplet diameter to initial diameter over time for different ambient pressures (fixed values) and temperatures. The boundary conditions in Fig. 5(a) and (b) were: 10 μm and 50 μm for the droplet diameter, 300 K for the initial temperature, and 450 K for the ambient temperature. The ambient pressure was set to 0.15 MPa, 0.2 MPa, 0.25 MPa, 0.3 MPa, 0.35 MPa, and 0.4 MPa, respectively. Fig. 5(a) shows that as the ambient pressure increases from 0.15 MPa to 0.4 MPa, the droplet's evaporation time decreases from 0.3 ms to approximately 0.1 ms, and the speed increases nearly 3 times. As shown in Fig. 5(b), this effect is even more pronounced as the droplets diameter increases from 10 μm to 50 μm. When the droplet evaporation is completed at 0.4 MPa, the droplet evaporates only 60% at 39
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(a) Total temperature distribution at 0.1 blade height (from pressure surface to suction surface)
(b) Total temperature distribution at 0.5 blade height (from pressure surface to suction surface)
(c) Total temperature distribution at 0.9 blade height (from pressure surface to suction surface) Fig. 10. The relation between total temperature and diameter.
environmental pressure and ambient temperature demonstrated significant effects on the evaporation process, in that the higher the pressure, the faster the evaporation, and the higher the ambient temperature, the faster the evaporation.
0.15 MPa. Fig. 5(c) and (d) show how the droplets with diameters of 10 μm and 50 μm evaporate at under different conditions of ambient temperature. The boundary conditions were: initial temperature 300 K and ambient pressure 0.4 MPa. The ambient temperature was set to 420 K, 440 K, 460 K, and 480 K, respectively. The figures show that as the temperature increases, the droplets evaporation time decreases and the evaporation rate increases. Further, with the increase in diameter, this effect is more pronounced, and the ambient temperature increases from 420 K to 480 K and the speed nearly doubled. The change in the environmental pressure causes a pressure gap on the droplet's surface, which drives its evaporation. The greater the pressure gap, the greater the evaporation rate. As the ambient temperature increases, the temperature gap increases, and the droplet evaporation rate increases. The change in ambient temperature is the change in superheat. In summary, during the vapor-liquid compression process, the
3.1.3. Pressure ratio In the actual compression process, the environmental pressure is changing constantly, but the environmental pressure studied above was constant. Therefore, to study pressure's influence on the evaporation process, it is necessary to study the pressure ratio's effect on droplets' evaporation process when the ambient pressure changes over time. This study assumed that the pressure changes linearly during compression. The boundary conditions calculated were 10 μm for droplet diameter, 300 K for initial temperature, 450 K for ambient temperature, and 0.1 MPa for initial ambient pressure. Fig. 6 shows the pressure ratio's effect on droplets' evaporation. The k value in the figures represents the pressure ratio. Fig. 6(a) shows that, 40
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(a) The relation between total temperature and spray flow rate
(b) The S1 surface’s relative Mach number distribution at 0.95 blade height in dry compression
(c) The S1 surface’s relative Mach number distribution at 0.95 blade height (1% spray flow rate) in vapor-liquid mixing compression
(d) The S1 surface’s relative Mach number distribution at 0.95 blade height (5% spray flow rate) in vapor-liquid mixing compression
Fig. 11. Spray flow rate's effect on compression.
performance were investigated. The inlet boundary conditions for the 3D numerical simulation were 0.1 MPa for total pressure, and 373.15 K for total temperature. The performance curves based on the water vapor are shown in Fig. 7.
as the vapor pressure ratio increases from 1.5 to 4, the droplets' evaporation time decreases from 0.3 ms to approximately 0.1 ms, and the speed increases nearly 3 times. A comparison of Fig. 6(a) and (b) shows that when the pressure changes over time, the droplets' final evaporation time and pressure largely remains constant, but the instantaneous evaporation speed gradient changes with the linear function. This change is attributable to the fact that when the pressure changes over time, the initial stage pressure is less than the set value of the ambient pressure, and the study above shows that the greater the pressure, the faster the evaporation. In summary, during vapor-liquid mixing compression, as the pressure ratio increases, the evaporation velocity increases.
3.2.1. Droplet diameter The operating conditions above were selected as standard operating conditions. As the 2D calculation results show, the droplet diameter evaporation efficiency is improved when the droplet was 30 μm in diameter. Accordingly, in the process of the 3D simulation, the droplet diameter in the calculation conditions was specified as 1, 5, 10, 15, and 20 μm, respectively. The droplet temperature was set as 288.15 K, the spray flow rate was 1% of the total inlet flow, the spray velocity was 50 m/s [14], and the outlet static pressure was 94,000 Pa. The results calculated are shown in the figures: When the droplet diameter is 1 μm, the water vapor and the droplets are mixed and compressed, and the temperature at the compressor's outlet is significantly lower than the
3.2. Analysis of 3D calculation results In this section, the droplet diameter, spray flow rate, spray velocity, and the effect of different operating conditions on compression 41
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(a) Static pressure distribution at 0.1 blade height (from leading edge to trailing edge)
(b) Static pressure distribution at 0.5 blade height (from leading edge to trailing edge)
(c) Static pressure distribution at 0.9 blade height (from leading edge to trailing edge) Fig. 12. The relation between static pressure and spray flow rate.
Fig. 8(b), (c), and (d). However, as the diameter increases, the low velocity area at the trailing edge, and the trailing edge of the pressure surface becomes larger, after which the flow decreases. In addition, small diameter droplets have little effect on the static pressure distribution on the blade surface at the root of the blade, and the pressure distribution (within 0.2–0.4) at the tip and the middle of blade affected only a limited area. The static pressure decreases slightly (Fig. 9), which coincides with the increase in the relative Mach number mentioned above. Compared to the tip of the blade, the cooling effect of vapor-liquid mixing compression is more obvious at its root, as shown in Fig. 10(a), (b), and (c). However, the influences on the pressure and the suction surfaces largely are the same and there is no obvious change. In summary, the droplet diameter should not exceed 10 μm.
dry compression. Because of the water droplets' evaporation, the inlet air flow cools at the tip of the blades and the temperature drops. As the gas passes through the blade with the droplets, the gas's temperature rises. However, this process is still accompanied by evaporation. The total temperature of the outlet during the vapor-liquid mixing compression is 390 K, which is lower than the total temperature of the dry compressed outlet, 405 K. When the diameter increases to 5 μm, the total temperature is 398 K. When the diameter is 20 μm, the cooling amplitude is very small, approximately 1 K, as shown in Fig. 8(a). This is consistent with the 2D calculation results. A large droplet diameter increases the droplet's evaporation time. Therefore, the evaporation rate decreases before entering the blade, and this affects the droplets' heat absorption. Compared with dry compression, the vapor-liquid mixing compression increases the relative Mach number at the tip of the blade and causes a slight increase in fluid momentum near it. The low velocity area at the trailing edge of the pressure surface and the blade shrinks significantly, which reduces the loss in the flow, as can be seen in
3.2.2. Spray mass flow rate In this section, we selected the standard operating point and calculated the spray flow rate from 1%, 2%, 3%, 4%, and 5% of the inlet's 42
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(b) Total temperature distribution at 0.5 blade height (from pressure surface to suction surface)
(a) Total temperature distribution at 0.1 blade height (from pressure surface to suction surface)
(c) Total temperature distribution at 0.9 blade height (from pressure surface to suction surface) Fig. 13. The relation between total temperature and spray flow rate.
total flow. The droplet temperature was 288.15 K and the diameter was 5 μm, the spray velocity was 50 m/s, and the outlet static pressure was 94,000 Pa. The calculation results are shown below. When the spray mass flow rate was 1% of the inlet mass flow rate, the compressor outlet's total temperature is 398 K, which is significantly lower than the 405 K for the total temperature of dry compression. As the spray flow rate increases, the cooling rate also increases. When the diameter is 3%, the outlet's total temperature drops to 391 K. When the spray flow rate is 5%, the outlet's total temperature drops to 386 K, as shown in Fig. 11(a). The increase in flow rate allows more droplets to enter the flow channel to evaporate, thereby enhancing the cooling effect. Compared with dry compression, the increase in the spray flow rate reduces the relative Mach number at the tip of the blade. However, the low velocity area decreases significantly after the trailing edge of the blade, thereby improving the flow and reducing the flow loss, as can be seen in Fig. 11(b), (c), and (d). Increasing spray flow rate improves the
static pressure distribution on the suction surface of the blade, but has little effect on the pressure surface, as Fig. 12(a), (b), and (c) show. The degree of influence increases from the root to the tip of the blade. Compared to dry compression, the spray flow rate has a greater effect on the root and the tip of the blade's total temperature, but a smaller effect on the total temperature at the middle of the blade, as illustrated in Fig. 13(a), (b), and (c). The effect on the suction surface is greater than that on the pressure surface. We found a significant decrease in the root and tip temperatures on the suction side, which was attributable to droplets hitting the blade. In summary, when the droplet is in an ideally vaporized state, an increase in the droplet spray flow rate is beneficial to the vapor-liquid mixing compression.
3.2.3. Pressure ratio and temperature The pressure ratio and temperature's effect on droplets' evaporation displayed in the 2D calculation can be verified further by the 3D 43
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(a) Different spray flow rate performance curves
(b) Different droplet diameters’ performance curves
Fig. 14. Pressure ratio's effect on compression.
and the results were highly consistent. Hishik's team [29] found that when the droplets' diameter was 10 μm, the discharge temperature decreased by approximately 22 °C at any pressure ratio, while the experimental spray mass flow rate was 2.3% of the outlet flow rate, and in our 3D simulation, the spray mass flow rate was 2% of the inlet and the diameter was 5 um, which is basically consistent with Hishik et al.'s experiment, in which the outlet temperature decreases by approximately 10 °C. According to Fig. 14(b), the high pressure ratio's enhancing effect on the performance of water vapor compression with droplets largely is the same as that of the low pressure ratio. This conclusion is consistent with Hishik et al.'s experiment results. However, they conducted a comparative experiment on the pressure-spray mass flow rate, but did not conduct experiments on droplet diameterspray mass flow rate. Halbe et al. [30] observed that the evaporation rate depended on the droplet size, and the pressure ratio decreased as the droplet size increased. With respect to the conclusion about the evaporation rate, our results are consistent with his, which shows that the droplet size affects the evaporation rate. However, he pointed out that the larger the droplet diameter, the faster the evaporation in the gas, because their diameters were larger than 100 um. With respect to break up, the size of the droplets the large droplets generated in this range was smaller than that of the small droplets, which is consistent with our conclusion. Essentially, the smaller the droplet size in the evaporation process, the faster the evaporation. The conclusion that the pressure ratio decreases as the droplet size increases is consistent with Fig. 14(a).
numerical simulation, and the results are shown in Fig. 14. With the increase of pressure ratio, droplet diameter and spray flow rate's effect on compressive performance is improved. The amplitude is large on the side with a high pressure ratio and small on the side with a low pressure ratio is small. The high pressure ratio indicates that the temperature in the compressor is high, so the droplets' effect on compression performance at a high pressure ratio and temperature is enhanced, which is consistent with the 2D calculation results. The droplets increase the pressure ratio and flow rate under the same working conditions compared with dry compression, as shown in Fig. 14. Therefore, the water vapor compression performance is improved. 3.2.4. Inlet spray velocity The standard operating point was selected. The inlet spray velocities were specified as 50 m/s, 60 m/s, 70 m/s, 80 m/s, and 90 m/s, respectively. The inlet boundary conditions were 0.1 MPa for total pressure and 373.15 K for total temperature. The droplet temperature was 288.15 K and the diameter was 5 μm. The spray speed was 1%, and the outlet static pressure was 94,000 Pa. The results calculated are shown in Fig. 15. The compressor outlet's total temperature is 398 K and the total dry compression temperature is 405 K. However, as the inlet spray velocity increases, the cooling rate remains largely unchanged, as shown in Fig. 15(a). The change in velocity essentially has no effect on the static pressure distribution on the surface of the blade, as Fig. 14(b), (c), and (d) show. The difference in inlet spray velocity has a greater influence on the root and tip suction surfaces' total temperature than that of the pressure surface. In the middle of the blade, this effect primarily is the same, as can been seen in Fig. 16(a), (b), and (c). In summary, the vapor-liquid mixing compression's spray velocity has no significant effect on the compression performance overall. In this paper, a 2D model, the object of which is a single droplet, is the mechanism used to study the factors affecting droplet evaporation in a simulated compressor environment. The influencing factors' range of working conditions was obtained. The 3D simulation, the object of which is the compression system, evaluates the flow field parameters' effects on the heat and mass transfer. In summary, the 3D simulation's conclusion is an extension of the 2D model's conclusion, not a comparison. However, we still chose some conclusions that can be compared, as shown in Table 3. We compared the conclusions with those of the two papers [29,30],
4. Conclusion In this paper, a 2D evaporation model for vapor-liquid mixing compression was established and a 3D numerical simulation was solved. The initial droplet diameter, pressure ratio, temperature, spray mass flow rate, and inlet spray velocity's effects on the vapor-liquid mixing compression were calculated and analyzed. After 2D calculation and 3D verification, we reached the following conclusions. 1) The initial droplet diameter and spray flow rate affect the droplet evaporation process significantly. Changes in these parameters affect the droplet evaporation mass and the amount of heat absorbed. Specifically, they can reduce the gas's temperature and the compression work and increase the pressure ratio, which makes the 44
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(a) The relation between total temperature and spray velocity
(b) Static pressure distribution at 0.1 blade height (from leading edge to trailing edge)
(c) Static pressure distribution at 0.5 blade height (from leading edge to trailing edge)
(d) Static pressure distribution at 0.9 blade height (from leading edge to trailing edge)
Fig. 15. Spray velocity's effect on compression.
The conclusions obtained in this paper provide a basic theory for vapor-liquid mixing compression and a reference range for the selection of spray droplet diameter, flow rate, and velocity in future experiments and engineering applications. In this paper, water vapor was considered the ideal gas in 3D numerical simulation. Some researchers have proven that this method provided similar results to a real gas model [27,28]. However, in future studies, it can be calculated as real gas and compared with experiments to obtain results more similar to the actual process.
process more similar to saturation compression and improves compression performance. 2) Based on the boundary conditions given in this paper and other research results [7,14], the droplet diameter should not exceed 10 μm. The larger the droplet's initial diameter, the greater the Bi number. A small diameter ensures good evaporation conditions for the droplets, which in turn reduces the flow loss after the trailing edge. Increasing the spray flow rate also can reduce the loss in the flow. 3) The higher the compressor pressure ratio, the higher the ambient pressure. Driven by the pressure differences, the droplet evaporation speed increases and the evaporation effect strengthens. Therefore, the vapor-liquid mixing compression is more effective under conditions of high pressure ratio and high superheat. 4) The inlet spray velocity has no obvious effect on the vapor-liquid mixing compression. Therefore, it is unnecessary to increase the inlet spray velocity.
Acknowledgement The authors acknowledge the financial support from the National Natural Science Foundation of China (grant no. 51706009).
45
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(a)Total temperature distribution at 0.1 blade height (from pressure surface to suction surface)
(b)Total temperature distribution at 0.5 blade height (from pressure surface to suction surface)
(c)Total temperature distribution at 0.9 blade height (from pressure surface to suction surface) Fig. 16. The relation between total temperature and spray velocity. Table 3 Conclusions comparison. Influencing factor
2D model
3D simulation
Droplet diameter
The smaller the initial diameter of the droplet, the faster the evaporation. Increasing the pressure ratio enhances the droplets' evaporation effect.
The smaller the initial diameter of the droplet, the more obvious the cooling effect.
Pressure ratio
Under the premise of increasing the spray mass flow rate, the high pressure ratio's effect in enhancing the performance of water vapor compression with droplets is stronger than that of the low pressure ratio. Under the premise of reducing the droplet diameter, the high pressure ratio's effect in enhancing the performance of water vapor compression with droplets largely is the same as that of the low pressure ratio.
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References
699–704. [16] M. Li, Q. Zheng, Wet compression system stability analysis: part I-wet compression Moore Greitzer transient model, ASME Turbo Expo 2004: Power for Land, Sea, and Air. Vienna, Austria, 2004 (Paper No. GT2004-54018). [17] A. Abdelwahab, An investigation of the use of wet compression in industrial centrifugal compressors, ASME Turbo Expo 2006: Power for Land, Sea, and Air. Barcelona, Spain, 2006 (Paper No. GT2006-90695). [18] J.R. Maa, Evaporation coefficient of liquids, Ind. Eng. Chem. Fundam. 6 (1967) 504–518. [19] L. Reid, R.D. Moore, Design and Overall Performance of Four Highly-loaded, Highspeed Inlet Stages for an Advanced, High-pressure-ratio Core Compressor, NASA TP-1337 (1978). [20] R.D. Moore, L. Reid, Performance of single-stage axial-flow transonic compressor with rotor and stator aspect ratios of 1.19 and 1.26 respectively, and with design pressure ratio of 2.05, NASA TP-1659, (1980). [21] B.E. Poling, J.M. Prausnitz, J.P. O'Connell, et al., The Properties of Gases and Liquids, McGraw-Hill, New York, 2001. [22] B. Abramzon, W.A. Sirignano, Droplet vaporization model for spray combustion calculations, Heat Mass Transf. 32 (1989) 1605–1618. [23] Sergei S. Sazhin, Advanced models of fuel droplet heating and evaporation, Prog. Energy Combust. Sci. 32 (2006) 162–214. [24] W.R. Sexton, M.R. Sexton, The effects of wet compression on gas turbine engine operating performance, ASME Paper No: GT2003-38045, 2003. [25] C. Hartel, P. Pfeiffer, Model analysis of high-fogging effects on the work of compression, ASME Paper No: GT2003-38117, 2003. [26] T. Wang, X. Li, V. Pinninti, Simulation of mist transport for gas turbine inlet air cooling, Numerical Heat Transfer 53 (Part A) (2008) 1013–1036P. [27] S. Aphornratana, Theoretical and Experimental Investigation of a Combine Ejectorabsorption Refrigerator, PhD thesis University of Sheffield, UK, 1994. [28] T. Sriveerakul, S. Aphornratana, K. Chunnanond, Performance prediction of steam ejector using computational fluid dynamics: part 1. Validation of the CFD results, Int. J. Therm. Sci. 46 (2007) 812–822. [29] Tsubasa Hishik, Shuhei Nakamura, et al. Experiment and Analysis of Two-phase Compression in a Rocking Type Steam Compressor. DOI:https://doi.org/10.1299/ kikaib.79.2826.2013-JBR-0650. [30] Chaitanya V. Halbe, Walter F. O'Brien, et al., A CFD analysis of the effects of twophase flow in a two-stage centrifugal compressor, ASME Paper No: GT2015-42534, 2015.
[1] Liang Lin, Han Dong, Ran Ma, Tao Peng, Treatment of high-concentration wastewater using double-effect mechanical vapor recompression, Desalination 314 (2) (2013) 139–146. April. [2] Viviani C. Onishi, Alba Carrero-Parreño, et al., Shale gas flowback water desalination: single vs multiple-effect evaporation with vapor recompression cycle and thermal integration, Desalination 404 (17) (2017) 230–248 February. [3] Chen Yue, Bin Wang, Banshou Zhu, Thermal analysis for the evaporation concentrating process with high boiling point elevation based exhaust waste heat recovery, Desalination 436 (15) (2018) 39–47 June. [4] H. Wu, Y. Li, J. Chen, Analysis of an evaporator-condenser-separated mechanical vapor compression system, J. Therm. Sci. 22 (2) (2013) 152–158. [5] K. Alexander, B. Donohue, T. Feese, et al., Failure analysis of an MVR (mechanical vapor recompressor) impeller, Eng. Fail. Anal. 17 (6) (2010) 1345–1358. [6] Shao-Lee Soo, Wet-compression in an axial-flow compressor, Transactions of the ASME, 1952. [7] Sun. Lanxin, Qun Zheng, et al., On the behavior of water droplets when moving onto blade surface in a wet compression transonic compressor, J. Eng. Gas Turbines Power 133 (8) (Apr 07, 2011) 082001 (10 pages). [8] R. Kleinschmidt, Value of wet compression in gas turbine cycles, Mech. Eng. 69 (2) (1947) 115–116. [9] D.L. Albernaz, M. Do-Quang, G. Amberg, Lattice Boltzmann method for the evaporation of a suspended droplet, Interfacial Phenomena and Heat Transfer 1 (3) (2013). [10] C. Xie, J. Zhang, V. Bertola, M. Wang, Droplet evaporation on a horizontal substrate under gravity field by mesoscopic modeling, J. Colloid Interface Sci. 463 (2016) 317–323. [11] Yang. Huaifeng, Qun Zheng, et al., Wet compression performance of a transonic compressor rotor at its near stall point, J. Mar. Sci. Appl. 10 (2011) 49–62. [12] Kyoung Hoon Kim, Hyung-Jong Ko, et al., Analytical modeling of wet compression of gas turbine systems, Appl. Therm. Eng. 31 (2011) 834e840. [13] K. Kim, H. Ko, H. Perez-Blanco, Analytical modeling of wet compression of gas turbine systems, Appl. Therm. Eng. 31 (5) (2011) 834–840. [14] K. Kim, K. Kim, Analytical modeling and assessment of overspray fogging process in gas turbine systems, J. Eng. Thermophys. 24 (3) (2015) 270–282. [15] S. Bracco, A. Pierfederici, A. Trucco, The wet compression technology for gas turbine power plants: thermodynamic model, Appl. Therm. Eng. 27 (4) (2007)
47
Contents lists available at ScienceDirect
Desalination journal homepage: www.elsevier.com/locate/desal
Effect of droplets on water vapor compression performance a
a
a,⁎
Hong Wu , Haoyu Yin , Yulong Li , Xianghua Xu
T
b
a National Key Laboratory of Science and Technology on Aero Engines Aero-thermodynamics & Collaborative Innovation Center for Advanced Aero-Engine, School of Energy and Power Engineering, Beihang University, Beijing 100191, PR China b School of Aerospace Engineering, Tsinghua University, Beijing 100084, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Mechanical vapor recompression Water vapor compression Heat transfer Mass transfer Two-phase flow
Mechanical vapor recompression (MVR) technology has broad prospects for application in saving energy. The compression in the MVR system often involves mixing vapor and liquid, and therefore, studies of the process can help establish a theoretical model to solve the problem of controlling compression temperature and improving the compression process's efficiency. However, the mixed phase-change in water vapor compression is complex and differs from that in air wet compression. In this paper, we studied droplets' effect on water vapor compression performance and the mechanism of heat and mass transfer during the process. A 2D single droplet evaporation model for water vapor compression was established and analyzed with Python, and a 3D numerical simulation was solved with CFD software to investigate the effect on water vapor compression of droplet diameter, ambient pressure and temperature, spray flow rate, and flow velocity. The results showed that the compressor's outlet temperature can be reduced by reducing the droplet diameter and increasing the spray flow rate, thus decreasing the work required for compression. The results also indicated that a high pressure ratio and superheat can enhance the cooling effect greatly.
1. Introduction Mechanical vapor recompression technology (MVR technology) has broad prospects for application and tremendous potential for development in saving energy [1] and reducing consumption in such fields as the chemical industry [2] and wastewater treatment [3]. The core equipment that determines the MVR system's efficiency and reliability is a water vapor compressor [4]. The steam compressor compresses low-temperature and -pressure water vapor to high-temperature and -pressure superheated steam so that the heat can be recycled. The water vapor compression process has a decisive effect on the compressor's efficiency and reliability. Ideally, MVR system compressors should draw in only water vapor. However, in the system's actual operation, the compressor absorbs liquid water along with the water vapor because of the high water level during evaporation, the feed liquid's excessive foaming, unstable operation of the vapor-liquid separator, and the need to reduce the compressed water vapor's superheat [5]. Therefore, MVR often is a vapor-liquid mixing compression process (Fig. 1). The water droplets in the compressed steam cause problems, such as erosion in blades and reducing surge margins [6]. However, from the theory of thermal compression, it is known that the droplets' evaporation absorbs heat and cools the water vapor, thus reducing the outlet steam temperature. In particular, the vapor compression process will be closer to a ⁎
saturation state, and the compression work is lower than that of adiabatic compression [7]. Therefore, the vapor-liquid mixing compression in MVR can reduce the compression work. However, the mechanism of heat and mass transfer during the two-phase compression process also is more complex than in one-phase compression. Therefore, it is necessary to study the mechanism of two-phase flow, heat and mass transfer, and phase change during vapor-liquid mixing compression. This air-based, gas-liquid compression process is referred to often as “wet compression” [8]. To establish the air-liquid compression model, many scholars have conducted systematic research and conducted detailed thermodynamic analysis of different theoretical models [9–15]. Albernaz et al. [9] used the Lattice Boltzmann (LBM) method to simulate suspended droplets' evaporation in the air, and found that when convection occurs in the gravitational field, the droplets and air's relative motion can enhance static droplets' heat transfer effect. Xie et al. [10] established a multiphase LBM model in which single droplets evaporated in air, and proposed the critical diameter to describe gravity's effect on droplet evaporation. Yang et al. [11] investigated wet compression's effects on a transonic compressor with CFD 3D numerical simulation, while Kim et al. [12] used approximate analytical solutions to simulate the wet compression process and studied the transient behaviors of important variables in wet compression, such as droplet diameter and mass, gas and droplet temperature, and evaporation rate,
Corresponding author. E-mail address: [email protected] (Y. Li).
https://doi.org/10.1016/j.desal.2019.04.011 Received 10 July 2018; Received in revised form 29 March 2019; Accepted 9 April 2019 Available online 24 April 2019 0011-9164/ © 2019 Elsevier B.V. All rights reserved.
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Fig. 3. Single droplet evaporation model.
and obtained results consistent with existing studies. It has been found that the droplet-wall interaction model is important for wet compression studies, and Sun et al. [7] used the spray theory to analyze the interaction and compared elastic and inelastic collision models' 3D flow simulation results. In addition, the actual operation of existing gas turbines has shown that wet compression technology can help increase the gas turbine's power by up to 14% [16], and reduce the compression power by up to 5% [17]. However, these models all focus on the wet air compression process in the field of gas turbines. They are all air-based and thus, lack systemic research on the water vapor environment. However, there are both similarities and significant differences in the vapor-liquid mixing compression and air wet compression processes. Vapor-liquid mixing compression is a heat transfer and phase change process of the same material. The pressure on the droplet during evaporation is no longer the partial pressure of water vapor in the air. Moreover, the droplets' vaporization leads to an increase in the mass of steam, which affects the heat and mass transfer process and causes changes in the compressor's performance characteristics and operating points. In addition, water vapor's physical properties are very different from those of air, and the state parameters of environmental water vapor are constantly changing in the process of droplet evaporation. Therefore, as vapor-liquid mixing compression's heat and mass transfer characteristics differ from those of wet compression in which air is the working fluid, it is necessary to study the mechanism of two-phase flow and heat and mass transfer during the process and analyze the droplets' effect on the water vapor compression performance. In this paper, a 2D heat and mass transfer model for vapor-liquid mixing compression was established and a single droplet's evaporation during the process was analyzed with Python language programming. Thereafter, a 3D numerical simulation was solved with CFD software to analyze the heat and mass transfer mechanism in the process. The factors that affect the droplet evaporation process were studied, and the droplets' effect on water vapor compression performance was analyzed to provide a theoretical model for studies of the flow, and heat and mass transfer mechanism in vapor-liquid mixing compression.
Fig. 1. Process of vapor-liquid mixing compression. Table 1 Rotor 37 design parameters. Number of blades
Rotational speed/(r·min−1)
Pressure ratio
Design flow rate/(ks·s−1)
Efficiency%
36
17,188
2.016
20.19
88.9
(a) rotor 37
2. Models and methods The goal of this study was to establish a mathematical single-droplet model, which is a necessary condition for the analysis of vapor-liquid mixing compression's heat and mass transfer mechanism. To validate the mathematical model, 3D numerical simulation also is needed. At the same time, the effect on compression of flow and other factors also can be simulated in the 3D models.
(b) Leading edge at the roof of the blade Fig. 2. Grid structure. Table 2 Grid independence verification. Number
Number of grid layers
1 2 3 4
73 57 73 57
Number of grids/million 1.009 0.906 0.685 0.353
Flow rate/(kg·s−1) 20.716 20.726 20.728 20.684
2.1. 2D model
Pressure ratio
The following 2D mathematical models were used to make assumptions about the droplets:
2.026 2.026 2.026 2.026
(1) the droplet is spherical; (2) there is no flow within the droplet; (3) the temperature distribution inside the droplet is a spherical symmetry distribution, and (4) physical property parameters are 34
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(b) The relation between the ratio of droplet diameter to initial diameter and time
(a) The relation between droplet temperature and diameter
Fig. 4. Droplet diameter's effect on evaporation.
differential (time format) is used for time. The N-layer uniform grid is divided along the radius, and the volume of each layer is given by:
constant. The droplet's interior was purely thermally conductive and the temperature control equation is:
Vi =
∂T 1 ∂ ∂T = α 2 ⎛r 2 ⎞ ∂t r ∂r ⎝ ∂r ⎠
in which Δr is the grid spacing and i is the grid number. The heat flux on the two adjacent layers is given by:
α=
(1)
k ρcp
4 π Δr 3 [(i + 1)3 − i3] 3
qi = k
(2)
Ti − Ti + 1 Δr
(7)
(8)
The evaporation rate determines the outermost layer's (outer droplet surface's) heat flux:
in which α is the droplet's thermal diffusivity; T is the temperature; r is the radial coordinate, and t is time. The boundary conditions are:
q0 = γm
∂T r = 0, =0 ∂r
(3)
The temperature rise (fall) of the i-layer during Δt is calculated by the heat flow input and the layer's heat capacity:
(4)
ΔTi =
r = R, −k =
• ∂T = γm ∂r
•
in which m is the evaporation rate (kg/s·m ); R is the droplet's radius; γ is the droplet's latent heat of vaporization, and k is its thermal conductivity. The evaporation rate at the droplet surface can be given by a kinetic model [18]:
(9)
4π [(i − 1)Δr ]2 qi − 1 − 4π (iΔr )2qi 4π 3
[(i + 1)3Δr 3 − (iΔr )3]
(10)
2
•
m=
1 ⎛ Pi − ⎜ 2πRg ⎝ Ti
Pv ⎞ ⎟ Tv ⎠
In addition, various physical parameters, such as the water vapor environment's thermal conductivity and diffusivity, specific heat, density, and saturation pressure during the simulation of droplet evaporation were defined in the program. 2.2. 3D numerical simulation
(5)
Flow's influence is not considered in the 2D model. Therefore, the flow and other factors were studied using 3D numerical simulation instead. In addition, the results of 3D numerical simulation were verified with the 2D calculation results.
In this model, Pv is the gas phase pressure adjacent to the interface; Tv is the temperature; Pi refers to the liquid phase pressure at the interface (or the saturation pressure derived according to the temperature); Ti represents temperature; Rg is the gas constant, and σ is the coordination coefficient (0.03). As the droplets evaporate, their radius decreases. According to quality conservation, the following equation is derived: •
m=ρ
dR dt
2.2.1. Physical model NASA's rotor 37 is used as a physical model for numerical simulation. The model has a rotor that was designed by NASA in the 1970s [19,20], the specific parameters of which are shown in Table 1. There are detailed experimental data on this type of blade. After a large number of calculations and comparisons, the data calculated and the experimental data largely have been shown to be consistent. Therefore, it often is used as an example of the calculation of CFD. Although the working fluid in this paper was water vapor, this model still was adopted to improve the calculations' reliability. The grid was
(6)
in which ρ is the droplets' density. Because the mathematical model established is a 1D non-stationary problem, the space (r) and the time (t) need to be discretized. The center difference is used for spatial dispersion, and the forward 35
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(a) The relation between pressure and diameter in 10 μm
(b) The relation between pressure and diameter in 50 μm
(c) The relation between temperature and diameter in 10 μm
(d) The relation between temperature and diameter in 50 μm
Fig. 5. Ambient pressure and temperature's effects on droplet evaporation.
in water vapor compression process with droplets. The droplets evaporate into water vapor during the compression process, and latent heat of evaporation causes changes in the temperature of the mainstream. Therefore, the continuous phase's (gas phase's) control equation is no longer conserved and source terms need to be added. The source term M in the mass conservation equation represents the droplet's mass from the discrete phase (liquid phase) into the continuous phase (gas phase) attributable to evaporation. The evaporation model of this process requires the use of the Antoine equation [21] to determine the saturation pressure (Pa), and is given by:
generated using NUMECA/AutoGrid5. As can be seen in Fig. 2, a single runner was selected in the calculation domain, and the O4H grid was used. The total number of grid layers was 73, and the total number of grids was 685,000. The min skewness angle was 24.706, the max aspect ratio was 342.25, and the max expansion ratio was 2.9277. The flow field was calculated using commercial CFD software CFX for numerical simulation under no-slip, adiabatic boundary conditions. The inlet condition was set as the total temperature and pressure, and the outlet was set as the average static pressure. The rotating boundaries were specified by blades and hubs, and the stationary boundary was specified by shroud. Periodic boundary conditions exist on both sides of the channel. The turbulent discrete format adopts the first-order upwind style and the SST turbulence model was selected. Every residual converges to 10−5. The grid independence was verified first, and the working medium was air. The results are shown in Table 2. According to the table, the number of grids has little effect on the results calculated. Considering that the liquid phase requires an adequate number of grids, approximately 685,000 were chosen.
lg(10−5psat ) = A −
B T + C − 273.15
(11)
in which A is 5.11564, B is 1687.54 K, and C is 230.23 K. Water droplets' evaporation rate [22,23] is:
dmp dt
= πdp ρg Dg Sh
1 − fp ⎞ lg ⎜⎛ ⎟ M ⎝1−f ⎠
Mg
(12)
in which ρg is the vapor density; Dg is the vapor diffusion coefficient; Mg and M are the molar masses of water vapor and the main stream, respectively; fp is the molar fraction of liquid water and gaseous water,
2.2.2. Control equation The heat and mass transfer of the two phases need to be considered 36
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(a) The relation between the change in pressure and diameter
(b) The relation between constant pressure and diameter
Fig. 6. The pressure ratio's effect on droplet evaporation.
(a) The relation between flow rate and efficiency
(b) The relation between flow rate and pressure ratio
Fig. 7. Rotor 37 performance curves with water vapor.
The gas phase settings have been described previously, with the liquid phase set to Particle Transport Fluid, assuming that it is mixed well with the gas phase at the inlet, with boundary conditions that specify diameter, temperature, flow, and velocity. From the inlet, the droplets enter the flow path with the main stream. According to the method mentioned above, a 3D numerical simulation model of vaporliquid mixing compression was established by combining the basic equations of fluid mechanics.
respectively, and Sh is the Sherwood number. In summary, the mass conservation equation's source term is given by:
M=
dmp (13)
dt
The latent heat of droplet evaporation affects the temperature of the gas phase, so the continuous phase's energy equation is no longer conserved. The present source terms are the heat droplets absorb, and the droplet has the following transfer equation:
mp Cl
dTp dt
= πdp λNu (T − Tp) +
dmp dt
3. Results and analysis
hfg
(14)
In this paper, the 2D calculation results and 3D numerical simulation results were analyzed. The effect of the factors such as droplet diameter, pressure, temperature, droplet spray flow rate, and droplet spray velocity on compression performance was analyzed.
in which mp is the droplet's mass; Cl is its specific heat; λ is the thermal conductivity of the gas phase; hfg is the latent heat of vaporization; Tp is the droplet's temperature, and Nu is the Nusselt number. 37
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(a) The relation between total temperature and diameter
(b) The S1 surface’s relative Mach number distribution at 0.95 blade height in dry compression
(c) The S1 surface’s relative Mach number distribution at 0.95 blade height (1 μm diameter) in vapor-liquid mixing compression
(d) The S1 surface’s relative Mach number distribution at 0.95 blade height (20 μm diameter) in vapor-liquid mixing compression
Fig. 8. The droplet diameter's effect on compression.
analyzed based on the verification of mesh independence and step length independence. The droplet's initial temperature was 300 K, the ambient pressure was 0.4 MPa, the ambient temperature was 450 K, and the calculated operating condition was superheated steam. Under the pressure of 0.4 MPa, the saturated steam temperature was 416.79 K. Based on the existing air wet compression studies, the initial diameters of the droplets in the study were set as 10, 30, 50, 70, and 100 μm [24–26]. Fig. 4 shows the analysis of droplet diameter's effect on the evaporation process after calculation. Fig. 4(a) shows the change in the droplet's temperature over time corresponding to different initial droplet diameters. Fig. 4(b) shows the ratio of droplet diameter to initial diameter over time. It can be seen from the figures that the droplet's initial diameter affected the rate of temperature change strongly. In the range of 10–30 μm, the larger the droplet's initial diameter, the slower the evaporation. However, the speed overall still is relatively fast and evaporation is completed within 0.5 ms. As the initial diameter increases (from 50 μm to 100 μm), the evaporation rate drops
3.1. Analysis of 2D calculation results As shown in Fig. 3, in the droplet evaporation model, the unknowns are droplet initial diameter, and ambient pressure and temperature. The droplet diameter and environmental conditions in existing research also are factors that must be considered in the evaporation process [7,14]. Therefore, it is necessary to investigate these factors' effect on the droplet's evaporation in vapor-liquid mixing compression. Superheated steam at a pressure of 0.4 MPa was used in the study conditions. According to the droplet evaporation model established, the droplet's initial diameter, the ambient pressure and temperature, and the pressure ratio are the important factors that affect the liquid-vapor compression process. Thus, these factors' influence on the droplet evaporation process was analyzed. 3.1.1. Initial droplet diameter Droplet diameter's influence on the evaporation process was 38
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(b) Static pressure distribution at 0.5 blade height (from leading edge to trailing edge)
(a) Static pressure distribution at 0.1 blade height (from leading edge to trailing edge)
(c) Static pressure distribution at 0.9 blade height (from leading edge to trailing edge) Fig. 9. The relation between static pressure and diameter.
Therefore, choosing a reasonable range for the droplet diameter distribution is an important factor in accelerating the evaporation rate and improving the wet compression efficiency.
significantly and the evaporation time increases to nearly 2–4 times that of the droplets with a diameter of 10–30 μm Within 0.5 ms, the droplets' average temperature within the range of 10–30 μm initial diameter is 416 K, reaching the saturation temperature. However, droplets with a diameter of 50–100 μm do not evaporate fully, with the maximum temperature of 360 K and the minimum temperature of approximately 330 K. The difference in temperature between droplets with the two ranges of diameters is 56–86 K. Under the same conditions, the difference in individual droplets' heat absorption is 13–21%. As Fig. 4(b) shows, when the droplets with a diameter in the range of 10–30 μm evaporate completely, those in the range of 50–100 μm has a residual diameter 20–60% of their original diameter. More than half of the droplets do not evaporate. In summary, the droplet's initial diameter has a great influence on its rate of evaporation. The larger the droplet diameter, the larger the feature length and the Bi. This means that the internal thermal resistance becomes stronger, resulting in a lower evaporation rate.
3.1.2. Environmental pressure and ambient temperature Fig. 5 shows the change in the ratio of droplet diameter to initial diameter over time for different ambient pressures (fixed values) and temperatures. The boundary conditions in Fig. 5(a) and (b) were: 10 μm and 50 μm for the droplet diameter, 300 K for the initial temperature, and 450 K for the ambient temperature. The ambient pressure was set to 0.15 MPa, 0.2 MPa, 0.25 MPa, 0.3 MPa, 0.35 MPa, and 0.4 MPa, respectively. Fig. 5(a) shows that as the ambient pressure increases from 0.15 MPa to 0.4 MPa, the droplet's evaporation time decreases from 0.3 ms to approximately 0.1 ms, and the speed increases nearly 3 times. As shown in Fig. 5(b), this effect is even more pronounced as the droplets diameter increases from 10 μm to 50 μm. When the droplet evaporation is completed at 0.4 MPa, the droplet evaporates only 60% at 39
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(a) Total temperature distribution at 0.1 blade height (from pressure surface to suction surface)
(b) Total temperature distribution at 0.5 blade height (from pressure surface to suction surface)
(c) Total temperature distribution at 0.9 blade height (from pressure surface to suction surface) Fig. 10. The relation between total temperature and diameter.
environmental pressure and ambient temperature demonstrated significant effects on the evaporation process, in that the higher the pressure, the faster the evaporation, and the higher the ambient temperature, the faster the evaporation.
0.15 MPa. Fig. 5(c) and (d) show how the droplets with diameters of 10 μm and 50 μm evaporate at under different conditions of ambient temperature. The boundary conditions were: initial temperature 300 K and ambient pressure 0.4 MPa. The ambient temperature was set to 420 K, 440 K, 460 K, and 480 K, respectively. The figures show that as the temperature increases, the droplets evaporation time decreases and the evaporation rate increases. Further, with the increase in diameter, this effect is more pronounced, and the ambient temperature increases from 420 K to 480 K and the speed nearly doubled. The change in the environmental pressure causes a pressure gap on the droplet's surface, which drives its evaporation. The greater the pressure gap, the greater the evaporation rate. As the ambient temperature increases, the temperature gap increases, and the droplet evaporation rate increases. The change in ambient temperature is the change in superheat. In summary, during the vapor-liquid compression process, the
3.1.3. Pressure ratio In the actual compression process, the environmental pressure is changing constantly, but the environmental pressure studied above was constant. Therefore, to study pressure's influence on the evaporation process, it is necessary to study the pressure ratio's effect on droplets' evaporation process when the ambient pressure changes over time. This study assumed that the pressure changes linearly during compression. The boundary conditions calculated were 10 μm for droplet diameter, 300 K for initial temperature, 450 K for ambient temperature, and 0.1 MPa for initial ambient pressure. Fig. 6 shows the pressure ratio's effect on droplets' evaporation. The k value in the figures represents the pressure ratio. Fig. 6(a) shows that, 40
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(a) The relation between total temperature and spray flow rate
(b) The S1 surface’s relative Mach number distribution at 0.95 blade height in dry compression
(c) The S1 surface’s relative Mach number distribution at 0.95 blade height (1% spray flow rate) in vapor-liquid mixing compression
(d) The S1 surface’s relative Mach number distribution at 0.95 blade height (5% spray flow rate) in vapor-liquid mixing compression
Fig. 11. Spray flow rate's effect on compression.
performance were investigated. The inlet boundary conditions for the 3D numerical simulation were 0.1 MPa for total pressure, and 373.15 K for total temperature. The performance curves based on the water vapor are shown in Fig. 7.
as the vapor pressure ratio increases from 1.5 to 4, the droplets' evaporation time decreases from 0.3 ms to approximately 0.1 ms, and the speed increases nearly 3 times. A comparison of Fig. 6(a) and (b) shows that when the pressure changes over time, the droplets' final evaporation time and pressure largely remains constant, but the instantaneous evaporation speed gradient changes with the linear function. This change is attributable to the fact that when the pressure changes over time, the initial stage pressure is less than the set value of the ambient pressure, and the study above shows that the greater the pressure, the faster the evaporation. In summary, during vapor-liquid mixing compression, as the pressure ratio increases, the evaporation velocity increases.
3.2.1. Droplet diameter The operating conditions above were selected as standard operating conditions. As the 2D calculation results show, the droplet diameter evaporation efficiency is improved when the droplet was 30 μm in diameter. Accordingly, in the process of the 3D simulation, the droplet diameter in the calculation conditions was specified as 1, 5, 10, 15, and 20 μm, respectively. The droplet temperature was set as 288.15 K, the spray flow rate was 1% of the total inlet flow, the spray velocity was 50 m/s [14], and the outlet static pressure was 94,000 Pa. The results calculated are shown in the figures: When the droplet diameter is 1 μm, the water vapor and the droplets are mixed and compressed, and the temperature at the compressor's outlet is significantly lower than the
3.2. Analysis of 3D calculation results In this section, the droplet diameter, spray flow rate, spray velocity, and the effect of different operating conditions on compression 41
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(a) Static pressure distribution at 0.1 blade height (from leading edge to trailing edge)
(b) Static pressure distribution at 0.5 blade height (from leading edge to trailing edge)
(c) Static pressure distribution at 0.9 blade height (from leading edge to trailing edge) Fig. 12. The relation between static pressure and spray flow rate.
Fig. 8(b), (c), and (d). However, as the diameter increases, the low velocity area at the trailing edge, and the trailing edge of the pressure surface becomes larger, after which the flow decreases. In addition, small diameter droplets have little effect on the static pressure distribution on the blade surface at the root of the blade, and the pressure distribution (within 0.2–0.4) at the tip and the middle of blade affected only a limited area. The static pressure decreases slightly (Fig. 9), which coincides with the increase in the relative Mach number mentioned above. Compared to the tip of the blade, the cooling effect of vapor-liquid mixing compression is more obvious at its root, as shown in Fig. 10(a), (b), and (c). However, the influences on the pressure and the suction surfaces largely are the same and there is no obvious change. In summary, the droplet diameter should not exceed 10 μm.
dry compression. Because of the water droplets' evaporation, the inlet air flow cools at the tip of the blades and the temperature drops. As the gas passes through the blade with the droplets, the gas's temperature rises. However, this process is still accompanied by evaporation. The total temperature of the outlet during the vapor-liquid mixing compression is 390 K, which is lower than the total temperature of the dry compressed outlet, 405 K. When the diameter increases to 5 μm, the total temperature is 398 K. When the diameter is 20 μm, the cooling amplitude is very small, approximately 1 K, as shown in Fig. 8(a). This is consistent with the 2D calculation results. A large droplet diameter increases the droplet's evaporation time. Therefore, the evaporation rate decreases before entering the blade, and this affects the droplets' heat absorption. Compared with dry compression, the vapor-liquid mixing compression increases the relative Mach number at the tip of the blade and causes a slight increase in fluid momentum near it. The low velocity area at the trailing edge of the pressure surface and the blade shrinks significantly, which reduces the loss in the flow, as can be seen in
3.2.2. Spray mass flow rate In this section, we selected the standard operating point and calculated the spray flow rate from 1%, 2%, 3%, 4%, and 5% of the inlet's 42
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(b) Total temperature distribution at 0.5 blade height (from pressure surface to suction surface)
(a) Total temperature distribution at 0.1 blade height (from pressure surface to suction surface)
(c) Total temperature distribution at 0.9 blade height (from pressure surface to suction surface) Fig. 13. The relation between total temperature and spray flow rate.
total flow. The droplet temperature was 288.15 K and the diameter was 5 μm, the spray velocity was 50 m/s, and the outlet static pressure was 94,000 Pa. The calculation results are shown below. When the spray mass flow rate was 1% of the inlet mass flow rate, the compressor outlet's total temperature is 398 K, which is significantly lower than the 405 K for the total temperature of dry compression. As the spray flow rate increases, the cooling rate also increases. When the diameter is 3%, the outlet's total temperature drops to 391 K. When the spray flow rate is 5%, the outlet's total temperature drops to 386 K, as shown in Fig. 11(a). The increase in flow rate allows more droplets to enter the flow channel to evaporate, thereby enhancing the cooling effect. Compared with dry compression, the increase in the spray flow rate reduces the relative Mach number at the tip of the blade. However, the low velocity area decreases significantly after the trailing edge of the blade, thereby improving the flow and reducing the flow loss, as can be seen in Fig. 11(b), (c), and (d). Increasing spray flow rate improves the
static pressure distribution on the suction surface of the blade, but has little effect on the pressure surface, as Fig. 12(a), (b), and (c) show. The degree of influence increases from the root to the tip of the blade. Compared to dry compression, the spray flow rate has a greater effect on the root and the tip of the blade's total temperature, but a smaller effect on the total temperature at the middle of the blade, as illustrated in Fig. 13(a), (b), and (c). The effect on the suction surface is greater than that on the pressure surface. We found a significant decrease in the root and tip temperatures on the suction side, which was attributable to droplets hitting the blade. In summary, when the droplet is in an ideally vaporized state, an increase in the droplet spray flow rate is beneficial to the vapor-liquid mixing compression.
3.2.3. Pressure ratio and temperature The pressure ratio and temperature's effect on droplets' evaporation displayed in the 2D calculation can be verified further by the 3D 43
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(a) Different spray flow rate performance curves
(b) Different droplet diameters’ performance curves
Fig. 14. Pressure ratio's effect on compression.
and the results were highly consistent. Hishik's team [29] found that when the droplets' diameter was 10 μm, the discharge temperature decreased by approximately 22 °C at any pressure ratio, while the experimental spray mass flow rate was 2.3% of the outlet flow rate, and in our 3D simulation, the spray mass flow rate was 2% of the inlet and the diameter was 5 um, which is basically consistent with Hishik et al.'s experiment, in which the outlet temperature decreases by approximately 10 °C. According to Fig. 14(b), the high pressure ratio's enhancing effect on the performance of water vapor compression with droplets largely is the same as that of the low pressure ratio. This conclusion is consistent with Hishik et al.'s experiment results. However, they conducted a comparative experiment on the pressure-spray mass flow rate, but did not conduct experiments on droplet diameterspray mass flow rate. Halbe et al. [30] observed that the evaporation rate depended on the droplet size, and the pressure ratio decreased as the droplet size increased. With respect to the conclusion about the evaporation rate, our results are consistent with his, which shows that the droplet size affects the evaporation rate. However, he pointed out that the larger the droplet diameter, the faster the evaporation in the gas, because their diameters were larger than 100 um. With respect to break up, the size of the droplets the large droplets generated in this range was smaller than that of the small droplets, which is consistent with our conclusion. Essentially, the smaller the droplet size in the evaporation process, the faster the evaporation. The conclusion that the pressure ratio decreases as the droplet size increases is consistent with Fig. 14(a).
numerical simulation, and the results are shown in Fig. 14. With the increase of pressure ratio, droplet diameter and spray flow rate's effect on compressive performance is improved. The amplitude is large on the side with a high pressure ratio and small on the side with a low pressure ratio is small. The high pressure ratio indicates that the temperature in the compressor is high, so the droplets' effect on compression performance at a high pressure ratio and temperature is enhanced, which is consistent with the 2D calculation results. The droplets increase the pressure ratio and flow rate under the same working conditions compared with dry compression, as shown in Fig. 14. Therefore, the water vapor compression performance is improved. 3.2.4. Inlet spray velocity The standard operating point was selected. The inlet spray velocities were specified as 50 m/s, 60 m/s, 70 m/s, 80 m/s, and 90 m/s, respectively. The inlet boundary conditions were 0.1 MPa for total pressure and 373.15 K for total temperature. The droplet temperature was 288.15 K and the diameter was 5 μm. The spray speed was 1%, and the outlet static pressure was 94,000 Pa. The results calculated are shown in Fig. 15. The compressor outlet's total temperature is 398 K and the total dry compression temperature is 405 K. However, as the inlet spray velocity increases, the cooling rate remains largely unchanged, as shown in Fig. 15(a). The change in velocity essentially has no effect on the static pressure distribution on the surface of the blade, as Fig. 14(b), (c), and (d) show. The difference in inlet spray velocity has a greater influence on the root and tip suction surfaces' total temperature than that of the pressure surface. In the middle of the blade, this effect primarily is the same, as can been seen in Fig. 16(a), (b), and (c). In summary, the vapor-liquid mixing compression's spray velocity has no significant effect on the compression performance overall. In this paper, a 2D model, the object of which is a single droplet, is the mechanism used to study the factors affecting droplet evaporation in a simulated compressor environment. The influencing factors' range of working conditions was obtained. The 3D simulation, the object of which is the compression system, evaluates the flow field parameters' effects on the heat and mass transfer. In summary, the 3D simulation's conclusion is an extension of the 2D model's conclusion, not a comparison. However, we still chose some conclusions that can be compared, as shown in Table 3. We compared the conclusions with those of the two papers [29,30],
4. Conclusion In this paper, a 2D evaporation model for vapor-liquid mixing compression was established and a 3D numerical simulation was solved. The initial droplet diameter, pressure ratio, temperature, spray mass flow rate, and inlet spray velocity's effects on the vapor-liquid mixing compression were calculated and analyzed. After 2D calculation and 3D verification, we reached the following conclusions. 1) The initial droplet diameter and spray flow rate affect the droplet evaporation process significantly. Changes in these parameters affect the droplet evaporation mass and the amount of heat absorbed. Specifically, they can reduce the gas's temperature and the compression work and increase the pressure ratio, which makes the 44
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(a) The relation between total temperature and spray velocity
(b) Static pressure distribution at 0.1 blade height (from leading edge to trailing edge)
(c) Static pressure distribution at 0.5 blade height (from leading edge to trailing edge)
(d) Static pressure distribution at 0.9 blade height (from leading edge to trailing edge)
Fig. 15. Spray velocity's effect on compression.
The conclusions obtained in this paper provide a basic theory for vapor-liquid mixing compression and a reference range for the selection of spray droplet diameter, flow rate, and velocity in future experiments and engineering applications. In this paper, water vapor was considered the ideal gas in 3D numerical simulation. Some researchers have proven that this method provided similar results to a real gas model [27,28]. However, in future studies, it can be calculated as real gas and compared with experiments to obtain results more similar to the actual process.
process more similar to saturation compression and improves compression performance. 2) Based on the boundary conditions given in this paper and other research results [7,14], the droplet diameter should not exceed 10 μm. The larger the droplet's initial diameter, the greater the Bi number. A small diameter ensures good evaporation conditions for the droplets, which in turn reduces the flow loss after the trailing edge. Increasing the spray flow rate also can reduce the loss in the flow. 3) The higher the compressor pressure ratio, the higher the ambient pressure. Driven by the pressure differences, the droplet evaporation speed increases and the evaporation effect strengthens. Therefore, the vapor-liquid mixing compression is more effective under conditions of high pressure ratio and high superheat. 4) The inlet spray velocity has no obvious effect on the vapor-liquid mixing compression. Therefore, it is unnecessary to increase the inlet spray velocity.
Acknowledgement The authors acknowledge the financial support from the National Natural Science Foundation of China (grant no. 51706009).
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(a)Total temperature distribution at 0.1 blade height (from pressure surface to suction surface)
(b)Total temperature distribution at 0.5 blade height (from pressure surface to suction surface)
(c)Total temperature distribution at 0.9 blade height (from pressure surface to suction surface) Fig. 16. The relation between total temperature and spray velocity. Table 3 Conclusions comparison. Influencing factor
2D model
3D simulation
Droplet diameter
The smaller the initial diameter of the droplet, the faster the evaporation. Increasing the pressure ratio enhances the droplets' evaporation effect.
The smaller the initial diameter of the droplet, the more obvious the cooling effect.
Pressure ratio
Under the premise of increasing the spray mass flow rate, the high pressure ratio's effect in enhancing the performance of water vapor compression with droplets is stronger than that of the low pressure ratio. Under the premise of reducing the droplet diameter, the high pressure ratio's effect in enhancing the performance of water vapor compression with droplets largely is the same as that of the low pressure ratio.
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