- Email: [email protected]
Effects of operational parameters on liquid nitrogen spray cooling
Accepted Manuscript Effects of operational parameters on liquid nitrogen spray cooling Yixiao Ruan, Yu Hou, Rong Xue, Gaoqiao Luo, Kuizhang Zhu, Xiufang Liu, Liang Chen PII: DOI: Reference:
S1359-4311(18)33253-8 https://doi.org/10.1016/j.applthermaleng.2018.09.098 ATE 12707
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
26 May 2018 29 August 2018 23 September 2018
Please cite this article as: Y. Ruan, Y. Hou, R. Xue, G. Luo, K. Zhu, X. Liu, L. Chen, Effects of operational parameters on liquid nitrogen spray cooling, Applied Thermal Engineering (2018), doi: https://doi.org/10.1016/ j.applthermaleng.2018.09.098
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effects of operational parameters on liquid nitrogen spray cooling Yixiao Ruan1, Yu Hou1, Rong Xue1, Gaoqiao Luo2, Kuizhang Zhu2, Xiufang Liu1, Liang Chen1,* 1
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
2
Anhui Province Key Laboratory of Cryogenic Technology, Hefei 230088, China *Corresponding author; E-mail: [email protected]
Abstract: To determine the influence of design parameters on droplet evaporation and distribution of liquid nitrogen (LN2) spray cooling, experimental and numerical studies are performed by varying the mass flow rate, flow velocity, droplet diameter, injection orientation, and droplet velocity. The results demonstrate that backward injection yields the highest droplet evaporation ratio, which is 40% and 10% higher than the evaporation ratios obtained through forward and transverse injections, respectively. Counter-rotating vortex pairs are observed in the transverse injection, which improves the temperature distribution via convective mixing. Reducing the droplet diameter provides a more effective means of enhancing the evaporation than increasing the droplet velocity, and a linear increase in the droplet evaporation is observed by reducing the droplet diameter from 0.6 to 0.2 mm. The results and findings provide guidelines for the design of LN2 spray cooling systems for cryogenic wind tunnels. Keywords: spray cooling; liquid nitrogen; wind tunnel; computational fluid dynamics
1. Introduction Wind tunnels are used for aerodynamic testing of proposed aircraft models. The most efficient means of achieving a high Reynolds number in these wind tunnels is by increasing the gas density through lowering the gas temperature [1]. The National Transonic Facility (NTF) and European Transonic Wind Tunnel (ETW) have adopted the method of spray cooling with liquid nitrogen (LN2) to reduce the gas temperature, thereby achieving a high Reynolds number [2, 3]. LN2 spray cooling plays an important role in the operation and
performance of cryogenic wind tunnels. Spray cooling has been used extensively in the thermal management of high-power electronic devices [4, 5]. Previous studies have focused on using water rather than LN2 in cooling tunnels and large spaces. Montazeri [6, 7] numerically studied the use of a water spray cooling system to comply with urban environmental regulations, and compared the predictions with experimental results [8]. The results demonstrated that a low moisture content, temperature, and droplet diameter generally improved the evaporative cooling of water. Wang [9] proposed a low-pressure spray cooling system for near-space flight thermal control, and experimentally studied the evaporative heat transfer of the water spray, focusing on the film flash boiling and sub-cooled spray phenomena. Yan [10] numerically investigated multi-nozzle spray cooling, indicating that the change in droplet size was not significant with an increase in the number of nozzles. Water spray cooling has also been studied for applications in cooling towers and room humidity control [11-13]. Several experimental studies on the LN2 spray have been reported, with a focus on film boiling and spray characteristics. Somasundaram [14] proposed an intermittent LN2 spray cooling method for the thermal management of high-power electronics, and achieved a critical heat flux of 70 W/cm2. Liu [15, 16] and Xue [17] performed experiments to determine the LN2 flow rate correlation, droplet distribution, and spray angles by means of solid-cone pressure swirl nozzles. However, no studies have been carried out yet on the use of LN2 sprays to cool gas flows in wind tunnels. In this study, experiments and computational fluid dynamics (CFD) simulations were performed to research the effect of LN2 spray cooling in wind tunnels. The cooling performance of a LN2 spray was investigated by varying operational parameters such as the spray direction, droplet diameter, and droplet velocity. The results of this study provide guidelines for the design of LN2 spray cooling systems in cryogenic wind tunnels.
Nomenclature u
fluid velocity
Ap
droplet surface area
up
droplet velocity
T∞
fluid temperature
g
gravity
Tp
droplet temperature
ρ
fluid density
h
convective heat transfer coefficient
ρp
droplet density
hfg
latent heat
μ
fluid dynamic viscosity
εp
particle emissivity
dp
droplet diameter
σ
Stefan-Boltzmann constant
CD
drag coefficient
θR
radiation temperature
Red
droplet Reynolds number
k∞
fluid thermal conductivity
mp
droplet mass
cp,∞
heat capacity of fluid
cp
droplet specific heat
2. Experimental study on LN2 spray cooling of airflow 2.1 Experimental apparatus The spray cooling system consists of three sections: the LN2 spray system, air duct, and measurement system, as illustrated in Fig. 1. The air duct consists of a rectangular duct and ventilator with a variable frequency motor, where the duct size is 300 × 300 × 1600 mm. The airflow velocity in the duct can be changed within the range of 1.34 to 6.7 m/s by controlling the power frequency. In order to maintain a uniform airflow velocity at the duct cross-section, a fan was installed at the duct outlet and the air was induced into the duct. The measurement system includes a hot-wire anemometer, T-type thermocouples, a pressure transducer, Pitot tubes, differential pressure meters, a data acquisition system, and an electro-pneumatic regulator. The T-type thermocouples are calibrated to an accuracy of ±0.1 K [18]. The thermal anemometer measures velocity to an accuracy of ± (0.1 m/s + 5% of measured velocity). The mass flow meter calibrated by the manufacturer has a full-scale accuracy of ±0.39%. In this study, the absolute error ranged from ±0.167 to ±0.535 m/s. The
temperature was measured at the duct inlet and outlet, and nine thermocouples were arranged in a grid at each cross-section. The electro-pneumatic regulator regulated the pressure of the high-pressure gas cylinder connected to LN2 dewar 1. In the experiment, the higher-pressure LN2 flowed through the helical tube, where it was sub-cooled by the LN2 at atmospheric pressure from dewar 2. The 10 m copper tube provided a large heat transfer area in order to maintain the temperature at approximately 78 K. The Malvern Spraytec was used to measure the droplet size and distribution through a laser diffraction approach.
Fig. 1. Photograph and schematic of experimental apparatus of LN2 spray cooling in air duct
2.2 Experimental results Figure 2a illustrates the varying drops in air temperature with the mass flow rate at a given airflow velocity. The drop in air temperature from the inlet to outlet increased when the LN2 flow rate was increased. The mean diameter D(3,2) is widely used to represent the scale
of the average particle size of the entire spray field, and is defined as the diameter of a droplet with a volume to surface area ratio that is equal to that of the complete spray sample. As indicated in Table 1, the D(3,2) values of 439 and 322 μm are the characteristic lengths of spray droplets under pressure differences of 0.1 and 0.6 MPa, respectively. The D(3,2) of the LN2 droplets decreases under a higher pressure difference. Smaller droplets have a high specific surface area per volume, which enhances droplet evaporation. At a highest LN2 flow rate of 0.0076 kg/s, the Weber number of a LN2 droplet is 41.3, while it is only 16.4 for droplets at the lowest LN2 flow rate of 0.005 kg/s. The Reynolds numbers are 137601 and 27520 at airflow velocities of 6.7 and 1.34 m/s, respectively. Intense turbulence at a high Reynolds number may enhance convective heat transfer as well as LN2 droplet evaporation, leading to more rapid decreases in air temperature at high airflow velocities (Fig. 2a). As illustrated in Fig. 2b, the drop in air temperature decreased with an increase in the airflow velocity at a given mass flow rate. At a mass flow rate of 0.0076 kg/s, the drop in temperature decreased from 14.4℃ to 5.5℃ as the airflow velocity increased from 1.34 to 6.7 m/s. When the airflow velocity was increased, the declining temperature-decrease trend was reduced. This was because the breakup probability of LN2 droplets increases and the LN2 droplet evaporation is enhanced under a high airflow velocity.
Fig. 2. (a) Variations in temperature drop as a function of LN2 mass flow rate under different airflow velocities; (b) variations in temperature drop as a function of airflow velocity under different LN2 mass flow rates
Table 1 displays the Rosin−Rammler (R-R) distributions of the droplets. In the experiments, the Malvern Spraytec laser was focused at a location 5 mm downstream from the nozzle outlet. The mean/maximum diameter of the R-R distribution and D(3,2) decreased with an increase in pressure difference, while the R-R minimum diameter exhibited no consistent dependence on the pressure difference. As a result, the predominant droplets in the LN2 spray were recommended to be of large diameters. The high Weber numbers of large droplets indicate significant breakup potential, so the R-R maximum diameter would decrease by more than 10% when the pressure difference increased from 0.1 to 0.6 MPa. Table 1 Variation of droplet diameters with pressure difference Pressure difference (MPa)
0.1
0.2
0.3
0.4
0.5
0.6
R-R max. diameter (μm)
757
753
738
713
698
680
R-R min. diameter (μm)
307
283
323
320
307
296
R-R mean diameter (μm)
629
616
636
620
603
585
D(3,2) (μm)
439
397
367
356
330
322
3. CFD simulations of LN2 spray cooling in cryogenic wind tunnel 3.1 Computational geometry and grid In this section, a CFD model of the LN2 spray cooling system is developed and validated, and the effects of the operating parameters on LN2 spray cooling in a cryogenic wind tunnel are investigated with a simplified model. The size of the cooling section in the NTF is Ф 16.8 ft × 48.6 ft [19], while 230 spray nozzles are used in the EWT to generate a uniform LN2 spray with a high flow rate. For this model, the spray cooling section of the wind tunnel was simplified to a domain with dimensions of 0.3 × 0.3 × 1.6 m, based on the periodic features of the nozzle array. The geometry and grid generation were implemented with the ICEM CFD 15.0 pre-processor, resulting in a grid with 144,000 hexahedral cells. The grid independence test demonstrated that the outlet temperature variation was only 0.015% compared to that of a 1.5 times finer grid. The distance from the wall to the cell adjacent to the wall was 1.8 mm, which yielded y+ values between 30 and 150 for all inlet air velocities.
Fig. 3. Computational domain and schematic of injection direction 3.2 Mathematical model In this study, the Lagrangian−Eulerian approach was employed. For continuous phase flows, the momentum equation is solved using the realizable k-ε turbulence model [20]. The SIMPLE algorithm is used for velocity-pressure coupling with second-order interpolations, while the discrete phase model is used to describe the droplet motions and heat transfer. The motion equation is governed by the droplet inertia and forces [21]. du p dt
FD u u p
g p
p
F
(1) ,
where the drag force on each droplet is determined by FD
18 CD Red p d p2 24
(2) .
The droplet energy equation incorporates the heat convection, radiation heat transfer, and latent heat of vaporization.
mp c p
dm p hAp T Tp h fg p Ap R4 TP4 dt dt
dTp
(3)
The boiling rate equation is applied when the droplet temperature reaches boiling point. The radiation heat transfer is neglected, as it is substantially smaller than the convective heat transfer.
d d p dt
c p , T Tp 4 k 1 0.23 Red ln 1+ p c p , d p h fg
(4)
The uniform velocity and temperature at the inlet were assumed, considering that an inlet buffer and a converging section are used to stabilize airflow. When the droplets are impinged on the surface, different phenomena may occur, such as reflection, trapping, and wall-film formation, depending on the droplet surface tension, density, viscosity, and temperature [22-26]. In this study, the wall-film condition was used to describe the LN2 film formation and evaporation on the duct wall. 3.3 Model validation The simulations were validated against the experimental values of total drop in air temperature from the inlet to the outlet of the tested wind tunnel. The results in Table 2 demonstrate that the simulation results deviated from the experimental results within a range of 20%. In the beginning of the experiment, the droplets evaporate immediately upon impingement on the wall, and thereafter a thin film is formed on the bottom wall. As a result, the cooling capacity is partly lost and the drop in airflow temperature in the experiment was slightly smaller than in the simulation results, as indicated in Table 2. The other reason is the moisture of air, while the heat to condense the water vapor in the air can be neglected compared to the large amount latent heat of LN2 evaporation.
Table 2 Comparison of model predictions with experimental results Flow Case
velocity (m/s)
Mass flow rate (kg/s)
Experimental
Predicted
temperature
temperature drop
drop (K)
(K)
Relative error
1
6.7
0.005
3.946
4.310
9.22%
2
5.36
0.005
4.206
4.587
9.07%
3
4.02
0.005
5.61
6.01
7.13%
4
2.68
0.005
10.35
11.17
7.92%
5
1.34
0.005
10.65
11.51
8.08%
6
1.34
0.00612
12.41
13.59
9.51%
7
1.34
0.00702
13.61
15.63
14.84%
8
1.34
0.00756
14.27
16.37
14.72%
3.4 Simulation results and discussion The cooling effect, LN2 evaporation ratio, and temperature distribution uniformity are important factors during the operation of actual wind tunnels. The evaporation ratio is defined as the ratio of the evaporated mass to the total LN2 mass flow rate. The initial droplet diameter and droplet velocity play important roles in the evaporation. The injection orientations not only affect the relative velocity between the droplets and flow, but also determine the temperature distribution uniformity. The periodic boundary condition was used to simulate the spray cooling of the nozzle array in large-diameter wind tunnels. 3.4.1 Impact of injection direction A schematic of the injection directions used is presented in Fig. 3. Figure 4 (a) illustrates the axial variations in average temperatures for a forward injection with a 4.02 m/s airflow. The inlet air temperature, LN2 mass flow rate, and injection velocity were 282.15 K, 0.005 kg/s, and 3.72 m/s, respectively. The average temperature was observed to decrease linearly downstream from the nozzle, and finally reach 278.3 K at the outlet. The nozzle was located 400 mm from the inlet and the lowest temperature occurred at a cross-section 520 mm from the inlet. A large number of LN2 droplets are generated at the nozzle outlet where the spray intensity is highest, and the evaporative cooling of the droplets results in the lowest value of minimum temperature. Thereafter, the minimum temperature increases owing to the airflow advection. The axial temperature distribution for transverse injection was similar to that for forward injection. The relative velocity between the LN2 droplets and airflow ranged from 10.12 to 15.76 m/s under the transverse injection condition, which was generally larger than that under the forward injection condition (8.44 to 10.08 m/s). The average air temperature at the outlet reached 277.3 K, which was lower than that reached during forward injection because a larger velocity difference enhances droplet evaporation. A backward injection further increased the velocity difference and enhanced droplet evaporation, and obtained the lowest value of air temperature at the outlet (Fig. 4 (c)). Previous studies [27-32] demonstrated that a large-scale counter-rotating vortex pair
(CVP) could be formed when a spray is injected transversely into a cross-flow. Figure 5 illustrates the cross-section velocity vector and temperature distributions at different downstream positions for transverse injection. The CVP structure occurred near the spray nozzle at the beginning, and grew as the distance increased. The temperature contours indicated that the CVP formation improved the cross-sectional temperature uniformity. At a later stage, the CVP structure gradually disappeared with the airflow energy dissipation, and the temperature distribution became uniform. Because the CVP promotes droplet and air mixing, the temperature difference in the outlet cross-section under transverse injection was lower than in the other two cases. For forward and backward injections, two symmetric vortexes were identified along the central line. However, these two vortexes are formed owing to natural convection, which differs from the CVP in the transverse injection case. These vortexes have little effect on the temperature distribution, as the magnitude of velocity is too small.
Fig. 4. Temperature variations along flow direction for (a) forward injection; (b) transverse injection; and (c) backward injection
Fig. 5. Temperature contours and velocity vector fields for different cross-sections during transverse injection with airflow velocity = 4.02 m/s (vector length = 6 cm/magnitude)
3.4.2 Impact of initial droplet diameter As illustrated in Fig. 6, the evaporation ratio decreased with an increase in the initial mean diameter of the droplets, and less nitrogen vaporization led to an increase in the average temperature at the outlet. In the LN2 spray, droplets with an initial mean diameter of 0.2 mm can evaporate completely. When the initial mean diameter increases to 0.6 mm, the evaporation ratio is below 50%. Droplets with a smaller diameter have a high specific surface area, which increases the convective heat transfer and droplet evaporation, and this result consistent with Montazeri’s [6]conclusion.
Fig. 6. Average temperature at outlet and evaporation ratio as a function of initial mean diameter of droplets Although the evaporation ratio may be increased by reducing the droplet diameter, the temperature distribution of droplets with a 0.6 mm diameter was more uniform than that of droplets with a 0.2 mm diameter, as illustrated in Fig. 7. When the droplet diameter increases, the droplet deceleration decreases with a constant initial velocity. A low deceleration indicates that the reduction in velocity is slower and the droplet flight distance is longer. Therefore, droplets with large diameters can spread more widely, leading to a more uniform spray and temperature distribution.
Fig. 7. Temperature and droplet distribution for forward injection with initial diameters of 0.6 mm (upper graph) and 0.2 mm (lower graph)
3.4.3 Impact of initial droplet velocity As the length of the wind tunnel test section is fixed, the droplet residence time in the wind tunnel will decrease with an increase in the droplet injection velocity. The residence time of forward injection was the longest at the smallest injection velocity of 4 m/s; therefore, the highest evaporation ratio was achieved, as indicated in Table 3. Meanwhile, the velocity difference between the droplets and airflow increases as the injection velocity increases, which also enhances droplet evaporation. Owing to the combined effects of the residence time and velocity difference, the LN2 evaporation ratio decreased to a constant value of 32% for an injection velocity above 8 m/s. Therefore, for the design of spray cooling in an area with space constraints, an appropriate injection velocity may be selected in order to maintain the necessary residence time for optimal cooling performance.
Table 3 Evaporation ratios and outlet temperatures in forward injection with different droplet velocities Droplet
Outlet Mass flow
Evaporation
Evaporation
rate (kg·s-1)
rate (kg·s-1)
ratio (%)
velocity
temperature
(m·s-1)
(K)
4
0.01
0.0045
44
279.0
5
0.01
0.0038
38
279.5
8
0.01
0.0032
32
279.8
10
0.01
0.0032
32
279.8
4. Conclusions In this study, experiments and numerical simulations on LN2 spray cooling were carried out to investigate the influence of operational parameters on the airflow cooling of wind tunnels. The results demonstrate that backward injection can achieve the highest evaporation, while transverse injection improves the temperature distribution owing to the occurrence of the CVP. Reducing the droplet diameter from 600 to 200 μm can increase the evaporation ratio by more than 110%, but this deteriorates the temperature uniformity. A lower initial droplet velocity can increase the evaporation time and result in a higher evaporation ratio in tunnels with a fixed length. In order to enhance LN2 evaporation in spray cooling, the study recommends using transverse or backward injection with a small droplet diameter.
Acknowledgements This project was supported by the National Natural Science Foundation of China (51706169 and 51406160), the National Key Basic Research Program (613322), and the Fundamental Research Funds for the Central Universities of China.
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The impact of spray and flow parameters on liquid nitrogen spray cooling of air flow Yixiao Ruan1, Yu Hou1, Rong Xue1, Gaoqiao Luo2, Kuizhang Zhu2, Xiufang Liu1, Liang Chen1,* 1
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
2
Anhui Province Key Laboratory of Cryogenic Technology, Hefei 230088, China *Corresponding author, Email: [email protected]
Research Highlights 1. LN2 spray cooling is studied for cryogenic wind tunnel applications. 2. Backward and transverse injections yield higher evaporation of LN2. 3. Counter-rotating vortex pairs in transverse injection improve temperature distribution.
S1359-4311(18)33253-8 https://doi.org/10.1016/j.applthermaleng.2018.09.098 ATE 12707
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
26 May 2018 29 August 2018 23 September 2018
Please cite this article as: Y. Ruan, Y. Hou, R. Xue, G. Luo, K. Zhu, X. Liu, L. Chen, Effects of operational parameters on liquid nitrogen spray cooling, Applied Thermal Engineering (2018), doi: https://doi.org/10.1016/ j.applthermaleng.2018.09.098
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effects of operational parameters on liquid nitrogen spray cooling Yixiao Ruan1, Yu Hou1, Rong Xue1, Gaoqiao Luo2, Kuizhang Zhu2, Xiufang Liu1, Liang Chen1,* 1
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
2
Anhui Province Key Laboratory of Cryogenic Technology, Hefei 230088, China *Corresponding author; E-mail: [email protected]
Abstract: To determine the influence of design parameters on droplet evaporation and distribution of liquid nitrogen (LN2) spray cooling, experimental and numerical studies are performed by varying the mass flow rate, flow velocity, droplet diameter, injection orientation, and droplet velocity. The results demonstrate that backward injection yields the highest droplet evaporation ratio, which is 40% and 10% higher than the evaporation ratios obtained through forward and transverse injections, respectively. Counter-rotating vortex pairs are observed in the transverse injection, which improves the temperature distribution via convective mixing. Reducing the droplet diameter provides a more effective means of enhancing the evaporation than increasing the droplet velocity, and a linear increase in the droplet evaporation is observed by reducing the droplet diameter from 0.6 to 0.2 mm. The results and findings provide guidelines for the design of LN2 spray cooling systems for cryogenic wind tunnels. Keywords: spray cooling; liquid nitrogen; wind tunnel; computational fluid dynamics
1. Introduction Wind tunnels are used for aerodynamic testing of proposed aircraft models. The most efficient means of achieving a high Reynolds number in these wind tunnels is by increasing the gas density through lowering the gas temperature [1]. The National Transonic Facility (NTF) and European Transonic Wind Tunnel (ETW) have adopted the method of spray cooling with liquid nitrogen (LN2) to reduce the gas temperature, thereby achieving a high Reynolds number [2, 3]. LN2 spray cooling plays an important role in the operation and
performance of cryogenic wind tunnels. Spray cooling has been used extensively in the thermal management of high-power electronic devices [4, 5]. Previous studies have focused on using water rather than LN2 in cooling tunnels and large spaces. Montazeri [6, 7] numerically studied the use of a water spray cooling system to comply with urban environmental regulations, and compared the predictions with experimental results [8]. The results demonstrated that a low moisture content, temperature, and droplet diameter generally improved the evaporative cooling of water. Wang [9] proposed a low-pressure spray cooling system for near-space flight thermal control, and experimentally studied the evaporative heat transfer of the water spray, focusing on the film flash boiling and sub-cooled spray phenomena. Yan [10] numerically investigated multi-nozzle spray cooling, indicating that the change in droplet size was not significant with an increase in the number of nozzles. Water spray cooling has also been studied for applications in cooling towers and room humidity control [11-13]. Several experimental studies on the LN2 spray have been reported, with a focus on film boiling and spray characteristics. Somasundaram [14] proposed an intermittent LN2 spray cooling method for the thermal management of high-power electronics, and achieved a critical heat flux of 70 W/cm2. Liu [15, 16] and Xue [17] performed experiments to determine the LN2 flow rate correlation, droplet distribution, and spray angles by means of solid-cone pressure swirl nozzles. However, no studies have been carried out yet on the use of LN2 sprays to cool gas flows in wind tunnels. In this study, experiments and computational fluid dynamics (CFD) simulations were performed to research the effect of LN2 spray cooling in wind tunnels. The cooling performance of a LN2 spray was investigated by varying operational parameters such as the spray direction, droplet diameter, and droplet velocity. The results of this study provide guidelines for the design of LN2 spray cooling systems in cryogenic wind tunnels.
Nomenclature u
fluid velocity
Ap
droplet surface area
up
droplet velocity
T∞
fluid temperature
g
gravity
Tp
droplet temperature
ρ
fluid density
h
convective heat transfer coefficient
ρp
droplet density
hfg
latent heat
μ
fluid dynamic viscosity
εp
particle emissivity
dp
droplet diameter
σ
Stefan-Boltzmann constant
CD
drag coefficient
θR
radiation temperature
Red
droplet Reynolds number
k∞
fluid thermal conductivity
mp
droplet mass
cp,∞
heat capacity of fluid
cp
droplet specific heat
2. Experimental study on LN2 spray cooling of airflow 2.1 Experimental apparatus The spray cooling system consists of three sections: the LN2 spray system, air duct, and measurement system, as illustrated in Fig. 1. The air duct consists of a rectangular duct and ventilator with a variable frequency motor, where the duct size is 300 × 300 × 1600 mm. The airflow velocity in the duct can be changed within the range of 1.34 to 6.7 m/s by controlling the power frequency. In order to maintain a uniform airflow velocity at the duct cross-section, a fan was installed at the duct outlet and the air was induced into the duct. The measurement system includes a hot-wire anemometer, T-type thermocouples, a pressure transducer, Pitot tubes, differential pressure meters, a data acquisition system, and an electro-pneumatic regulator. The T-type thermocouples are calibrated to an accuracy of ±0.1 K [18]. The thermal anemometer measures velocity to an accuracy of ± (0.1 m/s + 5% of measured velocity). The mass flow meter calibrated by the manufacturer has a full-scale accuracy of ±0.39%. In this study, the absolute error ranged from ±0.167 to ±0.535 m/s. The
temperature was measured at the duct inlet and outlet, and nine thermocouples were arranged in a grid at each cross-section. The electro-pneumatic regulator regulated the pressure of the high-pressure gas cylinder connected to LN2 dewar 1. In the experiment, the higher-pressure LN2 flowed through the helical tube, where it was sub-cooled by the LN2 at atmospheric pressure from dewar 2. The 10 m copper tube provided a large heat transfer area in order to maintain the temperature at approximately 78 K. The Malvern Spraytec was used to measure the droplet size and distribution through a laser diffraction approach.
Fig. 1. Photograph and schematic of experimental apparatus of LN2 spray cooling in air duct
2.2 Experimental results Figure 2a illustrates the varying drops in air temperature with the mass flow rate at a given airflow velocity. The drop in air temperature from the inlet to outlet increased when the LN2 flow rate was increased. The mean diameter D(3,2) is widely used to represent the scale
of the average particle size of the entire spray field, and is defined as the diameter of a droplet with a volume to surface area ratio that is equal to that of the complete spray sample. As indicated in Table 1, the D(3,2) values of 439 and 322 μm are the characteristic lengths of spray droplets under pressure differences of 0.1 and 0.6 MPa, respectively. The D(3,2) of the LN2 droplets decreases under a higher pressure difference. Smaller droplets have a high specific surface area per volume, which enhances droplet evaporation. At a highest LN2 flow rate of 0.0076 kg/s, the Weber number of a LN2 droplet is 41.3, while it is only 16.4 for droplets at the lowest LN2 flow rate of 0.005 kg/s. The Reynolds numbers are 137601 and 27520 at airflow velocities of 6.7 and 1.34 m/s, respectively. Intense turbulence at a high Reynolds number may enhance convective heat transfer as well as LN2 droplet evaporation, leading to more rapid decreases in air temperature at high airflow velocities (Fig. 2a). As illustrated in Fig. 2b, the drop in air temperature decreased with an increase in the airflow velocity at a given mass flow rate. At a mass flow rate of 0.0076 kg/s, the drop in temperature decreased from 14.4℃ to 5.5℃ as the airflow velocity increased from 1.34 to 6.7 m/s. When the airflow velocity was increased, the declining temperature-decrease trend was reduced. This was because the breakup probability of LN2 droplets increases and the LN2 droplet evaporation is enhanced under a high airflow velocity.
Fig. 2. (a) Variations in temperature drop as a function of LN2 mass flow rate under different airflow velocities; (b) variations in temperature drop as a function of airflow velocity under different LN2 mass flow rates
Table 1 displays the Rosin−Rammler (R-R) distributions of the droplets. In the experiments, the Malvern Spraytec laser was focused at a location 5 mm downstream from the nozzle outlet. The mean/maximum diameter of the R-R distribution and D(3,2) decreased with an increase in pressure difference, while the R-R minimum diameter exhibited no consistent dependence on the pressure difference. As a result, the predominant droplets in the LN2 spray were recommended to be of large diameters. The high Weber numbers of large droplets indicate significant breakup potential, so the R-R maximum diameter would decrease by more than 10% when the pressure difference increased from 0.1 to 0.6 MPa. Table 1 Variation of droplet diameters with pressure difference Pressure difference (MPa)
0.1
0.2
0.3
0.4
0.5
0.6
R-R max. diameter (μm)
757
753
738
713
698
680
R-R min. diameter (μm)
307
283
323
320
307
296
R-R mean diameter (μm)
629
616
636
620
603
585
D(3,2) (μm)
439
397
367
356
330
322
3. CFD simulations of LN2 spray cooling in cryogenic wind tunnel 3.1 Computational geometry and grid In this section, a CFD model of the LN2 spray cooling system is developed and validated, and the effects of the operating parameters on LN2 spray cooling in a cryogenic wind tunnel are investigated with a simplified model. The size of the cooling section in the NTF is Ф 16.8 ft × 48.6 ft [19], while 230 spray nozzles are used in the EWT to generate a uniform LN2 spray with a high flow rate. For this model, the spray cooling section of the wind tunnel was simplified to a domain with dimensions of 0.3 × 0.3 × 1.6 m, based on the periodic features of the nozzle array. The geometry and grid generation were implemented with the ICEM CFD 15.0 pre-processor, resulting in a grid with 144,000 hexahedral cells. The grid independence test demonstrated that the outlet temperature variation was only 0.015% compared to that of a 1.5 times finer grid. The distance from the wall to the cell adjacent to the wall was 1.8 mm, which yielded y+ values between 30 and 150 for all inlet air velocities.
Fig. 3. Computational domain and schematic of injection direction 3.2 Mathematical model In this study, the Lagrangian−Eulerian approach was employed. For continuous phase flows, the momentum equation is solved using the realizable k-ε turbulence model [20]. The SIMPLE algorithm is used for velocity-pressure coupling with second-order interpolations, while the discrete phase model is used to describe the droplet motions and heat transfer. The motion equation is governed by the droplet inertia and forces [21]. du p dt
FD u u p
g p
p
F
(1) ,
where the drag force on each droplet is determined by FD
18 CD Red p d p2 24
(2) .
The droplet energy equation incorporates the heat convection, radiation heat transfer, and latent heat of vaporization.
mp c p
dm p hAp T Tp h fg p Ap R4 TP4 dt dt
dTp
(3)
The boiling rate equation is applied when the droplet temperature reaches boiling point. The radiation heat transfer is neglected, as it is substantially smaller than the convective heat transfer.
d d p dt
c p , T Tp 4 k 1 0.23 Red ln 1+ p c p , d p h fg
(4)
The uniform velocity and temperature at the inlet were assumed, considering that an inlet buffer and a converging section are used to stabilize airflow. When the droplets are impinged on the surface, different phenomena may occur, such as reflection, trapping, and wall-film formation, depending on the droplet surface tension, density, viscosity, and temperature [22-26]. In this study, the wall-film condition was used to describe the LN2 film formation and evaporation on the duct wall. 3.3 Model validation The simulations were validated against the experimental values of total drop in air temperature from the inlet to the outlet of the tested wind tunnel. The results in Table 2 demonstrate that the simulation results deviated from the experimental results within a range of 20%. In the beginning of the experiment, the droplets evaporate immediately upon impingement on the wall, and thereafter a thin film is formed on the bottom wall. As a result, the cooling capacity is partly lost and the drop in airflow temperature in the experiment was slightly smaller than in the simulation results, as indicated in Table 2. The other reason is the moisture of air, while the heat to condense the water vapor in the air can be neglected compared to the large amount latent heat of LN2 evaporation.
Table 2 Comparison of model predictions with experimental results Flow Case
velocity (m/s)
Mass flow rate (kg/s)
Experimental
Predicted
temperature
temperature drop
drop (K)
(K)
Relative error
1
6.7
0.005
3.946
4.310
9.22%
2
5.36
0.005
4.206
4.587
9.07%
3
4.02
0.005
5.61
6.01
7.13%
4
2.68
0.005
10.35
11.17
7.92%
5
1.34
0.005
10.65
11.51
8.08%
6
1.34
0.00612
12.41
13.59
9.51%
7
1.34
0.00702
13.61
15.63
14.84%
8
1.34
0.00756
14.27
16.37
14.72%
3.4 Simulation results and discussion The cooling effect, LN2 evaporation ratio, and temperature distribution uniformity are important factors during the operation of actual wind tunnels. The evaporation ratio is defined as the ratio of the evaporated mass to the total LN2 mass flow rate. The initial droplet diameter and droplet velocity play important roles in the evaporation. The injection orientations not only affect the relative velocity between the droplets and flow, but also determine the temperature distribution uniformity. The periodic boundary condition was used to simulate the spray cooling of the nozzle array in large-diameter wind tunnels. 3.4.1 Impact of injection direction A schematic of the injection directions used is presented in Fig. 3. Figure 4 (a) illustrates the axial variations in average temperatures for a forward injection with a 4.02 m/s airflow. The inlet air temperature, LN2 mass flow rate, and injection velocity were 282.15 K, 0.005 kg/s, and 3.72 m/s, respectively. The average temperature was observed to decrease linearly downstream from the nozzle, and finally reach 278.3 K at the outlet. The nozzle was located 400 mm from the inlet and the lowest temperature occurred at a cross-section 520 mm from the inlet. A large number of LN2 droplets are generated at the nozzle outlet where the spray intensity is highest, and the evaporative cooling of the droplets results in the lowest value of minimum temperature. Thereafter, the minimum temperature increases owing to the airflow advection. The axial temperature distribution for transverse injection was similar to that for forward injection. The relative velocity between the LN2 droplets and airflow ranged from 10.12 to 15.76 m/s under the transverse injection condition, which was generally larger than that under the forward injection condition (8.44 to 10.08 m/s). The average air temperature at the outlet reached 277.3 K, which was lower than that reached during forward injection because a larger velocity difference enhances droplet evaporation. A backward injection further increased the velocity difference and enhanced droplet evaporation, and obtained the lowest value of air temperature at the outlet (Fig. 4 (c)). Previous studies [27-32] demonstrated that a large-scale counter-rotating vortex pair
(CVP) could be formed when a spray is injected transversely into a cross-flow. Figure 5 illustrates the cross-section velocity vector and temperature distributions at different downstream positions for transverse injection. The CVP structure occurred near the spray nozzle at the beginning, and grew as the distance increased. The temperature contours indicated that the CVP formation improved the cross-sectional temperature uniformity. At a later stage, the CVP structure gradually disappeared with the airflow energy dissipation, and the temperature distribution became uniform. Because the CVP promotes droplet and air mixing, the temperature difference in the outlet cross-section under transverse injection was lower than in the other two cases. For forward and backward injections, two symmetric vortexes were identified along the central line. However, these two vortexes are formed owing to natural convection, which differs from the CVP in the transverse injection case. These vortexes have little effect on the temperature distribution, as the magnitude of velocity is too small.
Fig. 4. Temperature variations along flow direction for (a) forward injection; (b) transverse injection; and (c) backward injection
Fig. 5. Temperature contours and velocity vector fields for different cross-sections during transverse injection with airflow velocity = 4.02 m/s (vector length = 6 cm/magnitude)
3.4.2 Impact of initial droplet diameter As illustrated in Fig. 6, the evaporation ratio decreased with an increase in the initial mean diameter of the droplets, and less nitrogen vaporization led to an increase in the average temperature at the outlet. In the LN2 spray, droplets with an initial mean diameter of 0.2 mm can evaporate completely. When the initial mean diameter increases to 0.6 mm, the evaporation ratio is below 50%. Droplets with a smaller diameter have a high specific surface area, which increases the convective heat transfer and droplet evaporation, and this result consistent with Montazeri’s [6]conclusion.
Fig. 6. Average temperature at outlet and evaporation ratio as a function of initial mean diameter of droplets Although the evaporation ratio may be increased by reducing the droplet diameter, the temperature distribution of droplets with a 0.6 mm diameter was more uniform than that of droplets with a 0.2 mm diameter, as illustrated in Fig. 7. When the droplet diameter increases, the droplet deceleration decreases with a constant initial velocity. A low deceleration indicates that the reduction in velocity is slower and the droplet flight distance is longer. Therefore, droplets with large diameters can spread more widely, leading to a more uniform spray and temperature distribution.
Fig. 7. Temperature and droplet distribution for forward injection with initial diameters of 0.6 mm (upper graph) and 0.2 mm (lower graph)
3.4.3 Impact of initial droplet velocity As the length of the wind tunnel test section is fixed, the droplet residence time in the wind tunnel will decrease with an increase in the droplet injection velocity. The residence time of forward injection was the longest at the smallest injection velocity of 4 m/s; therefore, the highest evaporation ratio was achieved, as indicated in Table 3. Meanwhile, the velocity difference between the droplets and airflow increases as the injection velocity increases, which also enhances droplet evaporation. Owing to the combined effects of the residence time and velocity difference, the LN2 evaporation ratio decreased to a constant value of 32% for an injection velocity above 8 m/s. Therefore, for the design of spray cooling in an area with space constraints, an appropriate injection velocity may be selected in order to maintain the necessary residence time for optimal cooling performance.
Table 3 Evaporation ratios and outlet temperatures in forward injection with different droplet velocities Droplet
Outlet Mass flow
Evaporation
Evaporation
rate (kg·s-1)
rate (kg·s-1)
ratio (%)
velocity
temperature
(m·s-1)
(K)
4
0.01
0.0045
44
279.0
5
0.01
0.0038
38
279.5
8
0.01
0.0032
32
279.8
10
0.01
0.0032
32
279.8
4. Conclusions In this study, experiments and numerical simulations on LN2 spray cooling were carried out to investigate the influence of operational parameters on the airflow cooling of wind tunnels. The results demonstrate that backward injection can achieve the highest evaporation, while transverse injection improves the temperature distribution owing to the occurrence of the CVP. Reducing the droplet diameter from 600 to 200 μm can increase the evaporation ratio by more than 110%, but this deteriorates the temperature uniformity. A lower initial droplet velocity can increase the evaporation time and result in a higher evaporation ratio in tunnels with a fixed length. In order to enhance LN2 evaporation in spray cooling, the study recommends using transverse or backward injection with a small droplet diameter.
Acknowledgements This project was supported by the National Natural Science Foundation of China (51706169 and 51406160), the National Key Basic Research Program (613322), and the Fundamental Research Funds for the Central Universities of China.
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The impact of spray and flow parameters on liquid nitrogen spray cooling of air flow Yixiao Ruan1, Yu Hou1, Rong Xue1, Gaoqiao Luo2, Kuizhang Zhu2, Xiufang Liu1, Liang Chen1,* 1
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
2
Anhui Province Key Laboratory of Cryogenic Technology, Hefei 230088, China *Corresponding author, Email: [email protected]
Research Highlights 1. LN2 spray cooling is studied for cryogenic wind tunnel applications. 2. Backward and transverse injections yield higher evaporation of LN2. 3. Counter-rotating vortex pairs in transverse injection improve temperature distribution.