- Email: [email protected]
Flow characteristics of liquid nitrogen through solid-cone pressure swirl nozzles
Applied Thermal Engineering 110 (2017) 290–297
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Flow characteristics of liquid nitrogen through solid-cone pressure swirl nozzles Xiufang Liu, Rong Xue, Yixiao Ruan, Liang Chen, Xingqun Zhang, Yu Hou ⇑ State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China
h i g h l i g h t s Analyzed flow characteristics of liquid nitrogen through solid-cone nozzles. Discharge coefficient of liquid nitrogen increases with pressure difference. A discharge coefficient correlation of liquid nitrogen was developed.
a r t i c l e
i n f o
Article history: Received 20 June 2016 Revised 12 August 2016 Accepted 23 August 2016 Available online 24 August 2016 Keywords: Flow characteristics Liquid nitrogen Pressure swirl nozzle Discharge coefficient Gas-liquid phase change
a b s t r a c t Liquid nitrogen spray cooling is receiving increasing attention due to its promising potential in cryogenic cooling applications. In this study, an experimental apparatus of liquid nitrogen spray cooling system was built. The influence of injection pressure difference on the flow characteristics of liquid nitrogen through solid-cone pressure swirl nozzles was investigated and compared with that of water. It is found that the mass flow rate of water is much larger than that of liquid nitrogen in the whole range of injection pressure difference. The discharge coefficient of liquid nitrogen increases as the injection pressure difference increases. Contrarily, a slight decreasing trend in the discharge coefficient is observed for water. At low injection pressure differences, the orifice diameter presents a significant influence on the discharge coefficient. The nozzle with a larger orifice diameter exhibits a larger discharge coefficient. As the injection pressure difference increases, the influence of orifice diameter reduces. A discharge coefficient correlation for liquid nitrogen was developed based on the experimental data. In this correlation, the influence of gas-liquid phase change in the nozzle was taken into consideration. The results show that the proposed correlation exhibits a good agreement with the experimental data. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Liquid nitrogen spray cooling exhibits a great potential in cryogenic cooling applications, such as the gas cooling in cryogenic wind tunnels [1], thermal management of high-power electronic devices [2], cooling of super-conducting magnets with high temperatures [3], cryogenic food processing [4], cryogenic machining [5], and cryosurgery [6]. The atomizing nozzles break up liquid into numerous fine droplets in the spray cooling systems, which significantly influence the spray cooling effect [7–11]. Therefore, it is of crucial importance to study the flow characteristics of an atomizing nozzle so as to provide guidelines for the design and optimization of spray cooling systems.
⇑ Corresponding author. E-mail address: [email protected] (Y. Hou). http://dx.doi.org/10.1016/j.applthermaleng.2016.08.150 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.
Various spray nozzles have been developed and studied, among which the pressure swirl nozzle is the most commonly used type owning to its simple geometry and excellent atomizing performance [9,12,13]. Based on the spray pattern, the pressure swirl nozzle is categorized into two types: hollow-cone pressure swirl nozzle and solid-cone pressure swirl nozzle [8,10]. In a hollowcone pressure swirl nozzle, high-pressure liquid is supplied into a swirl chamber through tangential holes or slots, discharged from the nozzle exit orifice in the form of a thin conical sheet, and finally broken into ligaments and drops. Due to the tangential entry, a gas-cored vortex flow occurs in the swirl chamber and a central gas core forms at the nozzle exit orifice consequently. This gas core has a strong influence on the effective flow area as well as the flow characteristics of a hollow-cone pressure swirl nozzle [8,14,15]. For the solid-cone pressure swirl nozzle, there are two basic types based on the geometry. The first type uses a slotted swirl vane at the entrance of the swirl chamber to impose swirl and turbulence
291
X. Liu et al. / Applied Thermal Engineering 110 (2017) 290–297
Nomenclature Cd qm,th Ao DP ds Ls Pcr Ai DTsub qm,act
qm
discharge coefficient theoretical mass flow rate (kg s1) nozzle exit orifice area (mm2) injection pressure difference (Pa) swirl chamber diameter (mm) swirl chamber length (mm) critical pressure (Pa) nozzle inlet orifice area (mm2) subcooling degree (K) actual mass flow rate (kg s1)
q Ap do dp di Tcr
mass flow rate (kg s1) density (kg m3) total inlet slots area (mm2) nozzle exit orifice diameter (mm) inlet slot dimension (mm) nozzle inlet orifice diameter (mm) critical temperature (K)
on the liquid and obtain an even distribution of atomized droplets over the entire spray field. The second type is named as ‘‘jet-swirl nozzle”, in which high pressure liquid enters the swirl chamber partially through a central cylindrical port and partially through tangential ports to obtain a solid-cone spray field [10,16,17]. Fig. 1 shows the structural sketches of the above-mentioned three types of pressure swirl nozzles. The flow characteristic of an atomizing nozzle is mainly governed by nozzle geometries, liquid properties, operating conditions, etc. It is usually characterized by the discharge coefficient. The discharge coefficient is defined as the ratio of the actual and theoretical flow rates under an imposed injection pressure difference [19,20], as shown in Eq. (1).
nozzle and analyzed the influences of the Reynolds number, swirl number, flow ratio (the ratio of total flow rate to flow rate through central port), and diameter ratio (the ratio of swirl chamber diameter to central port diameter) on the discharge coefficient [20]. In addition, based on the theoretical analysis and experimental investigations, many empirical and semi-empirical correlations for the discharge coefficients of atomizing nozzles have been proposed with the aim of providing guidelines to spray system design. Four of the widely used correlations are as follows.
qm;act qm Cd ¼ ¼ qm;th Ao ð2qDPÞ0:5
C d ¼ 1:323 103
ð1Þ
Researchers have conducted numerous investigations on the flow characteristics of pressure swirl nozzle over the past decades. Lan et al. evaluated the effect of nozzle pressure drop on the flow characteristics of water through solid-cone pressure swirl nozzles and found that the discharge coefficient significantly decreases with the increasing nozzle pressure drop. They assumed that the discharge coefficient consists of two components, namely, a constant component (denoting the influence of nozzle geometry) and a variable component (denoting the influence of operating condition) [19]. Jain et al. studied the influences of the nozzle constant and the Reynolds number on the discharge coefficient of water with 12 different solid-cone pressure swirl nozzles, and concluded that the discharge coefficient is independent of the Reynolds number and is insensitive to the nozzle constant number [18]. Halder et al. performed numerical and experimental investigations on the flow characteristics of water through a jet-swirl
C d ¼ 0:35
Ap ds do
0:50 0:25 ds do
Ap ds do
C d ¼ 0:9ð0:676 24do Þ
0:29
ð2Þ
0:82
do
DP0:03
ð3Þ
0:13
ð4Þ
0:021 0:203 0:314 0:616 Ap ds Ls dp C d ¼ 1:03 ds do do do do
ð5Þ
Eq. (2) was proposed by Rizk and Lefebvre [6], and Eq. (3) was developed by Ballester and Dopazzo [21]. Both of the two correlations are based on the measurements of hollow-cone pressure swirl nozzles. Eq. (4) was proposed by Bayvel based on the theoretical analysis of a jet-swirl nozzle [10]. Eq. (5) was developed by Jain et al. based on the experimental results of a solid-cone pressure swirl nozzle with a slotted swirl vane [18]. Although extensive studies have been carried out on the flow characteristics of pressure swirl nozzles, most of them focused on the room-temperature working media (water). The conclusions obtained are not necessarily applicable to cryogenic fluids due to their significant differences in the normal boiling points (water: 373 K, liquid nitrogen: 78 K) and thermophysical properties. Table 1 shows the thermophysical parameters of liquid nitrogen (1 atm, 78 K) and water (1 atm, 298 K) [22]. Because of its low boiling point, the atomization process of liquid nitrogen is accompanied by significant gas-liquid phase change, which is much different from the single-phase atomization process of water. Therefore, this paper conducted a comprehensive study on the flow characteristics of liquid nitrogen through solid-cone pressure swirl nozzles so as to contribute to the understanding of the cryogenic spray cooling and further provide guidelines for the system development. An experimental apparatus was built up. Two
Table 1 Thermophysical parameters of liquid nitrogen and water. Working medium Fig. 1. Structural sketches of three types of pressure swirl nozzles: (a) hollow-cone pressure swirl nozzle [8], (b) solid-cone pressure swirl nozzle with slotted swirl vane [18] and (c) jet-swirl nozzle [10].
Water Liquid nitrogen
Dynamic viscosity (Pas) 4
8.9 10 1.6 104
Density(kg m3) 998 808
292
X. Liu et al. / Applied Thermal Engineering 110 (2017) 290–297
solid-cone pressure swirl nozzles with different exit orifice diameters were used to study the effect of injection pressure difference on the flow characteristics of liquid nitrogen. The flow characteristics of liquid nitrogen and water were compared and discussed. Furthermore, a discharge coefficient correlation for liquid nitrogen was proposed according to the experimental results, which could provide guidelines for the design and optimization of cryogenic spray cooling systems. 2. Experiments 2.1. Experimental apparatus Figs. 2 and 3 show the schematic and photo of the experimental apparatus, respectively. It is composed of four main parts based on their functions: liquid nitrogen supply system, mass flow rate measuring system, subcooled system, and spraying system. A 175 L high-pressure liquid nitrogen dewar (Sichuan Air Separation Group) is used to store liquid nitrogen at 1.5 MPa. Pressurized gaseous nitrogen in nitrogen gas cylinders was used to fill the 500 L buffer tank, which was set to suppress the gas supply pressure fluctuation through its large volume, and also pressurize and drive liquid nitrogen out of the high-pressure dewar 1. The gas supply pressure can be precisely controlled at the required stable states by adjusting the pressure reducing valves and regulating valves connected to the nitrogen gas cylinders and electric proportional valve located between the buffer tank and the highpressure liquid nitrogen dewar 1 [2,3]. The mass flow rate measuring system comprises a custom-built cryostat, a cryogenic mass flow meter, and a gas-liquid separator. Expanded perlite with low thermal conductivity was filled in the cryostat to reduce the heat leak into the mass flow meter. The gas-liquid separator was used to ensure that the state of liquid nitrogen entering the mass flow meter was gas-free, thereby improving the accuracy and reliability of the measurement. Gas discharged from the gas-liquid separator was directly vented to the ambient atmosphere, and its flow rate was controlled by the regulating valve 4. Besides, a safety valve was fixed on the top of the gas-liquid separator to avoid the buildup of high pressure in it [2]. A subcooled system was used to control the temperature fluctuation of liquid nitrogen at the nozzle inlet within a narrow range. This system was composed of a shell-and-coil heat exchanger and a high-pressure liquid nitrogen dewar (dewar 2). Before enter-
ing the spray nozzle, the liquid nitrogen from the mass flow rate measuring system was cooled down first through the heat exchanger of the subcooled system. High-pressure liquid nitrogen from dewar 2 was used to supply gas-liquid nitrogen mixture to the subcooled heat exchanger. Because the shell side of the heat exchanger was connected to the atmospheric environment and the cooling coil was sufficiently long, the liquid nitrogen temperature at the nozzle inlet was maintained approximately at 78 K [2,3]. Two solid-cone pressure swirl nozzles from Spraying Systems Co., B1/8HH-SS3.5 (orifice diameter: 1.6 mm, designated as #1 nozzle) and B1/8HH-SS5 (orifice diameter: 2.0 mm, designated as #2 nozzle) were adopted in the spraying system, as shown in Fig. 4. Liquid nitrogen was first axially introduced into the nozzle and flowed through the inserted swirl vane and into the swirl chamber, finally discharged from the exit orifice at high speed and disintegrated into numerous droplets, which were evenly distributed over the entire spray field in the shape of a solid cone [16,18]. The detailed structure parameters of #2 nozzle, which is used for the fitting of the discharge coefficient correlations, are as follows. di: 6.39 mm, dp: 1.314 mm, ds: 5.9 mm, Ls: 5.2 mm, do: 2.0 mm. 2.2. Experimental instruments and uncertainty analysis The arrangement of main temperature and pressure measuringpoints in the experimental system are shown in Fig. 2. All the temperatures were measured by T-type thermocouples (Omega). A pressure transducer (PSE530-R06, SMC, measuring range: 0– 1 MPa) was used to measure the nozzle inlet pressure. Other pressure measuring-points were monitored by pressure gages (measuring range: 0–1 MPa. The liquid nitrogen mass flow rate was measured by a Coriolis mass flow meter (ROTAMASS RCCS34, YOKOGAWA, measuring range: 0–5000 kg h1) for cryogenic applications. All the readings of the thermocouples and pressure transducer were monitored and collected in real time by a data acquisition device (MV2000, YOKOGAWA). The obtained mass flow rates were transmitted to personal computers by using the corresponding software for further processing. According to the methodology detailed in Refs. [23,24], the uncertainty analysis was carried out for the directly measured variables (temperature, mass flow rate and pressure) and indirectly measured variable (discharge coefficient). For a directly measured variable, the overall uncertainty depends on the equipment’s uncertainty and the measuring uncertainty. In the present study,
Fig. 2. Schematic of the experimental apparatus.
X. Liu et al. / Applied Thermal Engineering 110 (2017) 290–297
293
Fig. 3. Photo of the experimental apparatus.
down the whole system. The precooling process was crucial for the cryogenic experiment and usually took a very long time until the liquid nitrogen was discharged from the vent of the gas-liquid separator and the nozzle exit orifice. At the end of precooling, set the nozzle inlet pressure at the desired value by venting or pressurizing the buffer tank, and then switch on the regulating valve 5 of the liquid nitrogen dewar 2 to supply liquid nitrogen to the subcooled heat exchanger. When the liquid nitrogen temperature at the nozzle inlet was stabilized to approximate 78 K, the test system and data acquisition system were initiated. Throughout the entire experiment, the openings of the regulating valves 4 and 5 should remain as small as possible while still to ensure the required gas-liquid separation and subcooled effect, respectively. A series of experiments corresponding to different injection pressure differences were conducted until the liquid nitrogen in dewar 1 had run out or the nozzle had to be replaced. Notably, sufficient precooling was indispensable after replacing the liquid dewar or the nozzle because the flow characteristics of liquid nitrogen were highly sensitive to the operating conditions [2,3].
Fig. 4. Structural sketch of the solid-cone pressure swirl nozzle.
the T-type thermocouple was pre-calibrated and has an accuracy of ±0.1 K. The mass flow meter was pre-calibrated by the manufacturer and has a full-scale accuracy of ±0.39%. The pressure transducer has a full-scale accuracy of ±0.25% (provide by the manufacturer). Taking measuring uncertainty into account, the overall uncertainties of temperature, mass flow rate and pressure were estimated to be ±0.2 K, ±0.42% and ±0.53%, respectively. For an indirectly measured variable, the uncertainty can be estimated by the error transfer function. In this study, the uncertainty of the discharge coefficient is a function of mass flow rate and pressure difference. According to the error transfer theory in Ref. [23], it can be calculated by Eq. (6).
dC d
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 @f @f ¼ d2qm þ d2DP @qm @ DP
3. Results and discussion 3.1. Flow characteristics of liquid nitrogen and water The influence of the injection pressure difference on the mass flow rate of liquid nitrogen through two solid-cone pressure swirl nozzles is shown in Fig. 5. Meanwhile, the corresponding mass flow rates of water are also presented in the same figure for comparison. One point to note is that the mass flow rates of water in Fig. 5 are tested by the nozzle manufacturer, as shown in the nozzle product catalog [15]. To verify the flow rate data of water spray
ð6Þ
where dCd , dqm and dDP refer to the uncertainties of the discharge coefficient, mass flow rate and pressure difference, respectively. The maximum uncertainty of the discharge coefficient was estimated to be 0.75%. 2.3. Experimental procedure In the experiments, liquid nitrogen was directly injected into the atmospheric environment, and the liquid nitrogen temperature at the nozzle inlet was maintained approximately at 78 K. Prior to each experiment, the entire system was cleaned with dry gas nitrogen to expel moisture so as to prevent possible plugging in the pipelines or the nozzle orifice. Then the regulating valve 3 of the high-pressure liquid nitrogen dewar 1 was partially opened to cool
Fig. 5. Mass flow rate versus injection pressure difference.
294
X. Liu et al. / Applied Thermal Engineering 110 (2017) 290–297
from the product catalog, the mass flow rates of water at several operating conditions were measured with an experimental apparatus of water spray. By comparison, it is found that the measured data agree well with the data from the product catalog. Therefore, the mass flow rates of water from the product catalog are used in the present study in comparison with the flow rate measurements of liquid nitrogen spray. As shown in Fig. 5, the mass flow rates significantly increase with the increasing injection pressure difference for liquid nitrogen and water. At any given injection pressure difference, the mass flow rate of water is larger than that of liquid nitrogen. This difference can be partially attributed to their different densities, as shown in Table 1 [22]. However, the predominant reason could be the differences in the discharge coefficients between liquid nitrogen and water. The discharge coefficient of an atomizing nozzle depends not only on the frictional loss inside the nozzle passageway but also on the extent to which the sectional area of the nozzle discharge orifice is effectively utilized [8,25]. Based on the injection pressure differences and the corresponding mass flow rates, the discharge coefficients for liquid nitrogen and water are obtained (Fig. 6). As shown in Fig. 6, the discharge coefficient of liquid nitrogen is much smaller than that of water regardless of the given injection pressure difference. This trend is mainly attributed to significant differences in the thermophysical properties of these media. The normal boiling point of water is much higher than that of liquid nitrogen. However, the dynamic viscosity of liquid nitrogen is far lower than that of water as shown in Table 1. Therefore, it can be concluded that the discharge coefficient of liquid nitrogen is mainly determined by the effective flow area of the nozzle discharge orifice. Remarkable gas-liquid phase change can occur inside the nozzle due to the throttling effect and the possible heat leakage into the nozzle [3,26–28], which will result in significant reduction of mass flow rate during the spray process. However, the discharge coefficient of water mainly depends on frictional loss because of its relatively high viscosity. The influence of the gasliquid phase change is more prominent than that of frictional loss. From Fig. 6, it can also be found changes in the injection pressure difference exhibit varied effects on the discharge coefficients of liquid nitrogen and water. The discharge coefficient of liquid nitrogen increases as the injection pressure difference increases. Contrarily, a slight decreasing trend in the discharge coefficient can be observed for water. The dominant reason for the small discharge coefficients of water at high injection pressure differences is that frictional resistance increases as the injection pressure difference increases. However, the behavior of liquid nitrogen is mainly
Fig. 6. Discharge coefficient versus injection pressure difference for different working media.
Fig. 7. Discharge coefficient versus injection pressure difference for different nozzle orifice diameters.
ascribed to the effect of gas-liquid phase change inside the nozzle. In this study, the liquid nitrogen temperature at the nozzle inlet is maintained approximately at 78 K (78.77–80.13 K), but the nozzle inlet pressure varies from 0.20 MPa to 0.82 MPa. Therefore, the corresponding subcooling degree of liquid nitrogen at the nozzle inlet changes within a wide range (4.91–20.66 K). As the injection pressure difference increases, the subcooling degree of liquid nitrogen at the nozzle inlet increases and gas-liquid phase change inside the nozzle weakens correspondingly. This trend indicates that the discharge orifice area is utilized more effectively at higher nozzle inlet pressure, thereby increases the corresponding discharge coefficient. Fig. 7 shows the effect of the nozzle orifice diameter on the flow characteristics of liquid nitrogen. At low injection pressure differences, the discharge coefficient of #2 nozzle (orifice diameter: 2.0 mm) is larger than that of #1 nozzle (orifice diameter: 1.6 mm) and the gap between them gradually narrows with the increasing injection pressure difference. This decrease is attributed to the influence of the gas-liquid phase change on the discharge coefficient, which is more pronounced for the nozzle with a small orifice diameter than that with a large orifice diameter. At high injection pressure differences, gas-liquid phase change inside the nozzle weakens because of the high subcooling degree of liquid nitrogen at the nozzle inlet. Therefore, the difference between the discharge coefficients of #2 nozzle and #1 nozzle decreases. 3.2. Correlation for the discharge coefficient of water For the design of spray system, it is quite necessary to develop a correlation to predict the discharge coefficient accurately. As such, the experimental discharge coefficients of water were first compared with the corresponding predicted values by the aforementioned correlations (Eqs. (2)–(5)) to verify their applicability to the present study of water spray. Fig. 8 shows the changes in the discharge coefficient of water through #2 nozzle with the injection pressure difference. It is found that the discharge coefficients predicted by Eqs. (2) and (3) are significantly lower than the experimental data. This is because both of these correlations were developed for hollowcone pressure swirl nozzles, in which a gas core exists at the discharge orifice because of the strong swirling effect as mentioned earlier. The corresponding discharge coefficient is thus lower than that of solid-cone pressure swirl nozzles with the same geometric size. The predicted values of Eqs. (4) and (5) are in better agreement with the experimental data. Moreover, the experimental discharge coefficients at low injection pressure differences are in great agreement with the values predicted by Eq. (4). However,
X. Liu et al. / Applied Thermal Engineering 110 (2017) 290–297
295
Fig. 10. Comparison between the experimental discharge coefficients of liquid nitrogen and the predicted values by correlations developed for room-temperature working media.
Fig. 8. Discharge coefficient of water versus injection pressure difference.
Fig. 9. Comparison between the experimental discharge coefficients and the predicted values (water). Fig. 11. Discharge coefficient of liquid nitrogen versus injection pressure difference.
at high injection pressure differences, the experimental data are more consistent with those predicted by Eq. (5). As shown in Fig. 8, a disadvantage of Eqs. (4) and (5) for predicting the discharge coefficient of water is that they overlook the influences of the injection pressure difference. In the present study, the influences of the injection pressure difference on the discharge coefficient are evident, particularly for low injection pressure differences, and cannot be ignored. As such, a new discharge coefficient correlation is proposed as a function of the dimensionless nozzle orifice area and injection pressure difference, which is expressed as:
C d;
H2 O
0:035 0:191 DP Ao ¼ 0:445 Pcr Ai
ð7Þ
Eq. (7) is applicable to the nozzles with orifice diameter near 1.6–2.0 mm. The density of water involved in Eq. (7) is 998 kg m3, which is corresponding to the state point (1 atm, 298 K). For comparing, the discharge coefficients predicted by Eq. (7) are also shown in Fig. 8. It is observed that the predicted results show a good agreement with the experimental data. The fitting quality of Eq. (7) can be clearly seen in Fig. 9. The maximum relative deviation between the experimental discharge coefficients of water and the predicted values is 2.8%. The average deviation and the standard deviation are 0.01% and 1.29%, respectively. 3.3. Correlation for discharge coefficient of liquid nitrogen The discharge coefficients of water as predicted by Eqs. (4), (5) and (7) show better agreements with the corresponding
experimental data. However, whether these correlations are applicable to cryogenic fluids remains unclear. Thus, the three empirical correlations developed for room-temperature fluids are compared with the corresponding experimental data of liquid nitrogen (Fig. 10). It is found that all of the aforementioned correlations significantly overestimate the discharge coefficient of liquid nitrogen. This discrepancy occurs because liquid nitrogen spraying is a typical flashing atomization process associated with remarkable gasliquid phase change, which has a great influence on the effective flow area of the nozzle exit orifice and then the discharge coefficient. Nevertheless, the influence of phase change on the discharge coefficient is not considered in Eqs. (4), (5) and (7), which were developed for room-temperature working media. Hence, a discharge coefficient correlation based on the experimental results of liquid nitrogen is developed as expressed in Eq. (8), where the influence of gas-liquid phase change inside the nozzles is considered by introducing a dimensionless subcooling degree.
C d;
LN2
¼ 1:075
0:420 DP DT sub 0:807 Ao 0:186 Pcr T cr Ai
ð8Þ
The density of liquid nitrogen involved in Eq. (8) is 808 kg m3, which is corresponding to the state point (1 atm, 78 K). Comparisons between the predicted discharge coefficients of liquid nitrogen and the corresponding experimental data of #1 and #2 nozzles are shown in Fig. 11. The values predicted by Eq. (8) present a good agreement with the experimental data.
296
X. Liu et al. / Applied Thermal Engineering 110 (2017) 290–297
(3) At low injection pressure differences, the discharge coefficient of the nozzle with a large orifice diameter is higher than that of the nozzle with a small orifice diameter. The gap between these values gradually narrows with the increasing injection pressure difference. (4) A new correlation for the discharge coefficients of water is proposed. It is related to the dimensionless nozzle orifice area and injection pressure difference. For liquid nitrogen, the discharge coefficient correlation is governed not only by the dimensionless nozzle orifice area and injection pressure difference, but also by the dimensionless subcooling degree. The results indicate that the discharge coefficients of liquid nitrogen and water predicted by the developed empirical correlations show good agreements with the experimental data. Fig. 12. Comparison between the experimental discharge coefficients and the predicted values (LN2).
Acknowledgements The fitting quality of the proposed discharge coefficient correlation for liquid nitrogen is shown in Fig. 12. The maximum relative deviation between the predicted and experimental data is 8%. The average deviation and the standard deviation are 0.03% and 2.5% respectively. Thus, the proposed correlation presents a good agreement with the experimental data. 3.4. Discussion The flow characteristics of liquid nitrogen through solid-cone pressure swirl nozzles play an important role in cryogenic cooling applications. Due to the complexity of cryogenic measurement, there is no related research work in the published literature to the best of our knowledge. In the present study, preliminary research has been carried out on this topic. The findings could benefit the optimal design of cryogenic spray cooling systems. However, there are still some aspects to be improved. Liquid nitrogen spraying is a typical flashing atomization process associated with remarkable gas-liquid phase change inside the nozzle due to the throttling effect and the possible heat leakage [3,26–28]. In the present study, only qualitative analysis was presented on this point. In order to gain a better understanding and obtain a quantitative description of the spray process, numerical simulation of the internal flow of atomized nozzle should be carried out. The discharge coefficient correlation developed in this study is only valid for the solid-cone pressure swirl nozzles with slotted swirl vane within a relative small range of nozzle size (orifice diameter: near 1.6–2.0 mm). Further research should be performed using nozzles with wider range of dimensions/types so as to obtain more universal discharge coefficient correlations. 4. Conclusions A spray cooling experimental apparatus was built up to investigate the influence of the injection pressure difference on the flow characteristics of liquid nitrogen with two solid-cone pressure swirl nozzles. Through the systematic study, we obtained the following conclusions: (1) The mass flow rate of water is much larger than that of liquid nitrogen at any given injection pressure difference. (2) Changes in injection pressure difference exhibit contrary effects on the discharge coefficients for liquid nitrogen and water.
This project was supported by the National Nature Science Foundation of China (51406160), Postdoctoral Science Foundation of China (2014M560773), and partially supported by the Fundamental Research Funds for the Central Universities. References [1] C. Willert, G. Stockhausen, M. Beversdorff, J. Klinner, C. Lempereur, P. Barricau, J. Quest, U. Jansen, Application of Doppler global velocimetry in cryogenic wind tunnels, Exp. Fluids 39 (2005) 420–430. [2] S. Somasundaram, A.A.O. Tay, A study of intermittent liquid nitrogen sprays, Appl. Therm. Eng. 69 (2014) 199–207. [3] T.C. Lin, Y.J. Shen, M.R. Wang, Effects of superheat on characteristics of flashing spray and snow particles produced by expanding liquid carbon dioxide, J. Aerosol Sci. 61 (2013) 27–35. [4] S.O. Awonorin, An appraisal of the freezing capabilities of tunnel and spiral belt freezers using liquid nitrogen sprays, J. Food Eng. 34 (1997) 179–192. [5] B.D. Jerold, M.P. Kumar, Experimental comparison of carbon-dioxide and liquid nitrogen cryogenic coolants in turning of AISI 1045 steel, Cryogenics 52 (2012) 569–574. [6] N. Rizk, A.H. Lefebvre, Internal flow characteristics of simplex swirl atomizers, J. Propul. Power 1 (1985) 193–199. [7] A.C. Kheirabadi, D. Groulx, Cooling of server electronics: a design review of existing technology, Appl. Therm. Eng. 105 (2016) 622–638. [8] A. Lefebvre, Atomization and Sprays, CRC Press, Boca Raton, 1988. [9] N. Ashgriz, Handbook of Atomization and Sprays: Theory and Applications, Springer Science & Business Media, New York, 2011. [10] L. Bayvel, Liquid Atomization, CRC Press, London, 1993. [11] H. Montazeri, B. Blocken, J.L. Hensen, CFD analysis of the impact of physical parameters on evaporative cooling by a mist spray system, Appl. Therm. Eng. 75 (2015) 608–622. [12] Y. Tan, J. Xie, F. Duan, T. Wong, K. Toh, K. Choo, P. Chan, Y. Chua, Multi-nozzle spray cooling for high heat flux applications in a closed loop system, Appl. Therm. Eng. 54 (2013) 372–379. [13] Z. Zhang, J. Li, P.-X. Jiang, Experimental investigation of spray cooling on flat and enhanced surfaces, Appl. Therm. Eng. 51 (2013) 102–111. [14] M.S.F.M. Rashid, A.H.A. Hamid, O.C. Sheng, Z.A. Ghaffar, Effect of inlet slot number on the spray cone angle and discharge coefficient of swirl atomizer, Proc. Eng. 41 (2012) 1781–1786. [15] Industrial Spray Products Catalog, Spraying Systems Co. [16] A. Yule, R. Sharief, J. Jeong, G. Nasr, D. James, The performance characteristics of solid-cone-spray pressure-swirl atomizers, Atom. Sprays 10 (2000) 627–646. [17] G.G. Nasr, A.J. Yule, L. Bendig, Industrial Sprays and Atomization: Design, Analysis and Applications, Springer Science & Business Media, New York, 2013. [18] M. Jain, B. John, K.N. Iyer, S.V. Prabhu, Characterization of the full cone pressure swirl spray nozzles for the nuclear reactor containment spray system, Nucl. Eng. Des. 273 (2014) 131–142. [19] Z. Lan, D. Zhu, W. Tian, G. Su, S. Qiu, Experimental study on spray characteristics of pressure-swirl nozzles in pressurizer, Ann. Nucl. Energy 63 (2014) 215–227. [20] M.R. Halder, S.K. Dash, S.K. Som, A numerical and experimental investigation on the coefficients of discharge and the spray cone angle of a solid cone swirl nozzle, Exp. Therm. Fluid Sci. 28 (2004) 297–305. [21] J. Ballester, C. Dopazo, Discharge coefficient and spray angle measurements for small pressure-swirl nozzles, Atomization Sprays 4 (1994). [22] X.B. Zhang, L. Yao, J.Y. Chen, W. Zhang, W. Xiong, X.J. Zhang, L.M. Qiu, Prediction of the onset of flooding in an inclined tube at cryogenic temperatures, Cryogenics 61 (2014) 98–106.
X. Liu et al. / Applied Thermal Engineering 110 (2017) 290–297 [23] R.J. Moffat, Describing the uncertainties in experimental results, Exp. Therm. Fluid Sci. 1 (1988) 3–17. [24] M. Halder, S. Dash, S. Som, A numerical and experimental investigation on the coefficients of discharge and the spray cone angle of a solid cone swirl nozzle, Exp. Therm. Fluid Sci. 28 (2004) 297–305. [25] C. Hespel, J.-B. Blaisot, X. Margot, S. Patouna, A. Cessou, B. Lecordier, Influence of nozzle geometry on spray shape, particle size, spray velocity and air entrainment of high pressure diesel spray, in: THIESEL 2010-Conference on Thermo-and Fluid Dynamic Processes in Diesel Engines, 2010, pp. 383–394.
297
[26] H. Vu, G. Aguilar, High-speed internal nozzle flow visualization of flashing jets, in: 11th Triennial International Annual Conference on Liquid Atomization and Spray Systems, Vail, Colorado, USA, 2009. [27] C.W. Roh, M.S. Kim, Macroscopic spray behavior and atomization characteristics of refrigerant R22 injection under increased ambient pressure, Int. J. Heat Mass Transf. 55 (2012) 3307–3315. [28] D.M. Althausen, E.L. Golliher, Testing of an R134a spray evaporative heat sink, SAE Technical Paper, 2008.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Flow characteristics of liquid nitrogen through solid-cone pressure swirl nozzles Xiufang Liu, Rong Xue, Yixiao Ruan, Liang Chen, Xingqun Zhang, Yu Hou ⇑ State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China
h i g h l i g h t s Analyzed flow characteristics of liquid nitrogen through solid-cone nozzles. Discharge coefficient of liquid nitrogen increases with pressure difference. A discharge coefficient correlation of liquid nitrogen was developed.
a r t i c l e
i n f o
Article history: Received 20 June 2016 Revised 12 August 2016 Accepted 23 August 2016 Available online 24 August 2016 Keywords: Flow characteristics Liquid nitrogen Pressure swirl nozzle Discharge coefficient Gas-liquid phase change
a b s t r a c t Liquid nitrogen spray cooling is receiving increasing attention due to its promising potential in cryogenic cooling applications. In this study, an experimental apparatus of liquid nitrogen spray cooling system was built. The influence of injection pressure difference on the flow characteristics of liquid nitrogen through solid-cone pressure swirl nozzles was investigated and compared with that of water. It is found that the mass flow rate of water is much larger than that of liquid nitrogen in the whole range of injection pressure difference. The discharge coefficient of liquid nitrogen increases as the injection pressure difference increases. Contrarily, a slight decreasing trend in the discharge coefficient is observed for water. At low injection pressure differences, the orifice diameter presents a significant influence on the discharge coefficient. The nozzle with a larger orifice diameter exhibits a larger discharge coefficient. As the injection pressure difference increases, the influence of orifice diameter reduces. A discharge coefficient correlation for liquid nitrogen was developed based on the experimental data. In this correlation, the influence of gas-liquid phase change in the nozzle was taken into consideration. The results show that the proposed correlation exhibits a good agreement with the experimental data. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Liquid nitrogen spray cooling exhibits a great potential in cryogenic cooling applications, such as the gas cooling in cryogenic wind tunnels [1], thermal management of high-power electronic devices [2], cooling of super-conducting magnets with high temperatures [3], cryogenic food processing [4], cryogenic machining [5], and cryosurgery [6]. The atomizing nozzles break up liquid into numerous fine droplets in the spray cooling systems, which significantly influence the spray cooling effect [7–11]. Therefore, it is of crucial importance to study the flow characteristics of an atomizing nozzle so as to provide guidelines for the design and optimization of spray cooling systems.
⇑ Corresponding author. E-mail address: [email protected] (Y. Hou). http://dx.doi.org/10.1016/j.applthermaleng.2016.08.150 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.
Various spray nozzles have been developed and studied, among which the pressure swirl nozzle is the most commonly used type owning to its simple geometry and excellent atomizing performance [9,12,13]. Based on the spray pattern, the pressure swirl nozzle is categorized into two types: hollow-cone pressure swirl nozzle and solid-cone pressure swirl nozzle [8,10]. In a hollowcone pressure swirl nozzle, high-pressure liquid is supplied into a swirl chamber through tangential holes or slots, discharged from the nozzle exit orifice in the form of a thin conical sheet, and finally broken into ligaments and drops. Due to the tangential entry, a gas-cored vortex flow occurs in the swirl chamber and a central gas core forms at the nozzle exit orifice consequently. This gas core has a strong influence on the effective flow area as well as the flow characteristics of a hollow-cone pressure swirl nozzle [8,14,15]. For the solid-cone pressure swirl nozzle, there are two basic types based on the geometry. The first type uses a slotted swirl vane at the entrance of the swirl chamber to impose swirl and turbulence
291
X. Liu et al. / Applied Thermal Engineering 110 (2017) 290–297
Nomenclature Cd qm,th Ao DP ds Ls Pcr Ai DTsub qm,act
qm
discharge coefficient theoretical mass flow rate (kg s1) nozzle exit orifice area (mm2) injection pressure difference (Pa) swirl chamber diameter (mm) swirl chamber length (mm) critical pressure (Pa) nozzle inlet orifice area (mm2) subcooling degree (K) actual mass flow rate (kg s1)
q Ap do dp di Tcr
mass flow rate (kg s1) density (kg m3) total inlet slots area (mm2) nozzle exit orifice diameter (mm) inlet slot dimension (mm) nozzle inlet orifice diameter (mm) critical temperature (K)
on the liquid and obtain an even distribution of atomized droplets over the entire spray field. The second type is named as ‘‘jet-swirl nozzle”, in which high pressure liquid enters the swirl chamber partially through a central cylindrical port and partially through tangential ports to obtain a solid-cone spray field [10,16,17]. Fig. 1 shows the structural sketches of the above-mentioned three types of pressure swirl nozzles. The flow characteristic of an atomizing nozzle is mainly governed by nozzle geometries, liquid properties, operating conditions, etc. It is usually characterized by the discharge coefficient. The discharge coefficient is defined as the ratio of the actual and theoretical flow rates under an imposed injection pressure difference [19,20], as shown in Eq. (1).
nozzle and analyzed the influences of the Reynolds number, swirl number, flow ratio (the ratio of total flow rate to flow rate through central port), and diameter ratio (the ratio of swirl chamber diameter to central port diameter) on the discharge coefficient [20]. In addition, based on the theoretical analysis and experimental investigations, many empirical and semi-empirical correlations for the discharge coefficients of atomizing nozzles have been proposed with the aim of providing guidelines to spray system design. Four of the widely used correlations are as follows.
qm;act qm Cd ¼ ¼ qm;th Ao ð2qDPÞ0:5
C d ¼ 1:323 103
ð1Þ
Researchers have conducted numerous investigations on the flow characteristics of pressure swirl nozzle over the past decades. Lan et al. evaluated the effect of nozzle pressure drop on the flow characteristics of water through solid-cone pressure swirl nozzles and found that the discharge coefficient significantly decreases with the increasing nozzle pressure drop. They assumed that the discharge coefficient consists of two components, namely, a constant component (denoting the influence of nozzle geometry) and a variable component (denoting the influence of operating condition) [19]. Jain et al. studied the influences of the nozzle constant and the Reynolds number on the discharge coefficient of water with 12 different solid-cone pressure swirl nozzles, and concluded that the discharge coefficient is independent of the Reynolds number and is insensitive to the nozzle constant number [18]. Halder et al. performed numerical and experimental investigations on the flow characteristics of water through a jet-swirl
C d ¼ 0:35
Ap ds do
0:50 0:25 ds do
Ap ds do
C d ¼ 0:9ð0:676 24do Þ
0:29
ð2Þ
0:82
do
DP0:03
ð3Þ
0:13
ð4Þ
0:021 0:203 0:314 0:616 Ap ds Ls dp C d ¼ 1:03 ds do do do do
ð5Þ
Eq. (2) was proposed by Rizk and Lefebvre [6], and Eq. (3) was developed by Ballester and Dopazzo [21]. Both of the two correlations are based on the measurements of hollow-cone pressure swirl nozzles. Eq. (4) was proposed by Bayvel based on the theoretical analysis of a jet-swirl nozzle [10]. Eq. (5) was developed by Jain et al. based on the experimental results of a solid-cone pressure swirl nozzle with a slotted swirl vane [18]. Although extensive studies have been carried out on the flow characteristics of pressure swirl nozzles, most of them focused on the room-temperature working media (water). The conclusions obtained are not necessarily applicable to cryogenic fluids due to their significant differences in the normal boiling points (water: 373 K, liquid nitrogen: 78 K) and thermophysical properties. Table 1 shows the thermophysical parameters of liquid nitrogen (1 atm, 78 K) and water (1 atm, 298 K) [22]. Because of its low boiling point, the atomization process of liquid nitrogen is accompanied by significant gas-liquid phase change, which is much different from the single-phase atomization process of water. Therefore, this paper conducted a comprehensive study on the flow characteristics of liquid nitrogen through solid-cone pressure swirl nozzles so as to contribute to the understanding of the cryogenic spray cooling and further provide guidelines for the system development. An experimental apparatus was built up. Two
Table 1 Thermophysical parameters of liquid nitrogen and water. Working medium Fig. 1. Structural sketches of three types of pressure swirl nozzles: (a) hollow-cone pressure swirl nozzle [8], (b) solid-cone pressure swirl nozzle with slotted swirl vane [18] and (c) jet-swirl nozzle [10].
Water Liquid nitrogen
Dynamic viscosity (Pas) 4
8.9 10 1.6 104
Density(kg m3) 998 808
292
X. Liu et al. / Applied Thermal Engineering 110 (2017) 290–297
solid-cone pressure swirl nozzles with different exit orifice diameters were used to study the effect of injection pressure difference on the flow characteristics of liquid nitrogen. The flow characteristics of liquid nitrogen and water were compared and discussed. Furthermore, a discharge coefficient correlation for liquid nitrogen was proposed according to the experimental results, which could provide guidelines for the design and optimization of cryogenic spray cooling systems. 2. Experiments 2.1. Experimental apparatus Figs. 2 and 3 show the schematic and photo of the experimental apparatus, respectively. It is composed of four main parts based on their functions: liquid nitrogen supply system, mass flow rate measuring system, subcooled system, and spraying system. A 175 L high-pressure liquid nitrogen dewar (Sichuan Air Separation Group) is used to store liquid nitrogen at 1.5 MPa. Pressurized gaseous nitrogen in nitrogen gas cylinders was used to fill the 500 L buffer tank, which was set to suppress the gas supply pressure fluctuation through its large volume, and also pressurize and drive liquid nitrogen out of the high-pressure dewar 1. The gas supply pressure can be precisely controlled at the required stable states by adjusting the pressure reducing valves and regulating valves connected to the nitrogen gas cylinders and electric proportional valve located between the buffer tank and the highpressure liquid nitrogen dewar 1 [2,3]. The mass flow rate measuring system comprises a custom-built cryostat, a cryogenic mass flow meter, and a gas-liquid separator. Expanded perlite with low thermal conductivity was filled in the cryostat to reduce the heat leak into the mass flow meter. The gas-liquid separator was used to ensure that the state of liquid nitrogen entering the mass flow meter was gas-free, thereby improving the accuracy and reliability of the measurement. Gas discharged from the gas-liquid separator was directly vented to the ambient atmosphere, and its flow rate was controlled by the regulating valve 4. Besides, a safety valve was fixed on the top of the gas-liquid separator to avoid the buildup of high pressure in it [2]. A subcooled system was used to control the temperature fluctuation of liquid nitrogen at the nozzle inlet within a narrow range. This system was composed of a shell-and-coil heat exchanger and a high-pressure liquid nitrogen dewar (dewar 2). Before enter-
ing the spray nozzle, the liquid nitrogen from the mass flow rate measuring system was cooled down first through the heat exchanger of the subcooled system. High-pressure liquid nitrogen from dewar 2 was used to supply gas-liquid nitrogen mixture to the subcooled heat exchanger. Because the shell side of the heat exchanger was connected to the atmospheric environment and the cooling coil was sufficiently long, the liquid nitrogen temperature at the nozzle inlet was maintained approximately at 78 K [2,3]. Two solid-cone pressure swirl nozzles from Spraying Systems Co., B1/8HH-SS3.5 (orifice diameter: 1.6 mm, designated as #1 nozzle) and B1/8HH-SS5 (orifice diameter: 2.0 mm, designated as #2 nozzle) were adopted in the spraying system, as shown in Fig. 4. Liquid nitrogen was first axially introduced into the nozzle and flowed through the inserted swirl vane and into the swirl chamber, finally discharged from the exit orifice at high speed and disintegrated into numerous droplets, which were evenly distributed over the entire spray field in the shape of a solid cone [16,18]. The detailed structure parameters of #2 nozzle, which is used for the fitting of the discharge coefficient correlations, are as follows. di: 6.39 mm, dp: 1.314 mm, ds: 5.9 mm, Ls: 5.2 mm, do: 2.0 mm. 2.2. Experimental instruments and uncertainty analysis The arrangement of main temperature and pressure measuringpoints in the experimental system are shown in Fig. 2. All the temperatures were measured by T-type thermocouples (Omega). A pressure transducer (PSE530-R06, SMC, measuring range: 0– 1 MPa) was used to measure the nozzle inlet pressure. Other pressure measuring-points were monitored by pressure gages (measuring range: 0–1 MPa. The liquid nitrogen mass flow rate was measured by a Coriolis mass flow meter (ROTAMASS RCCS34, YOKOGAWA, measuring range: 0–5000 kg h1) for cryogenic applications. All the readings of the thermocouples and pressure transducer were monitored and collected in real time by a data acquisition device (MV2000, YOKOGAWA). The obtained mass flow rates were transmitted to personal computers by using the corresponding software for further processing. According to the methodology detailed in Refs. [23,24], the uncertainty analysis was carried out for the directly measured variables (temperature, mass flow rate and pressure) and indirectly measured variable (discharge coefficient). For a directly measured variable, the overall uncertainty depends on the equipment’s uncertainty and the measuring uncertainty. In the present study,
Fig. 2. Schematic of the experimental apparatus.
X. Liu et al. / Applied Thermal Engineering 110 (2017) 290–297
293
Fig. 3. Photo of the experimental apparatus.
down the whole system. The precooling process was crucial for the cryogenic experiment and usually took a very long time until the liquid nitrogen was discharged from the vent of the gas-liquid separator and the nozzle exit orifice. At the end of precooling, set the nozzle inlet pressure at the desired value by venting or pressurizing the buffer tank, and then switch on the regulating valve 5 of the liquid nitrogen dewar 2 to supply liquid nitrogen to the subcooled heat exchanger. When the liquid nitrogen temperature at the nozzle inlet was stabilized to approximate 78 K, the test system and data acquisition system were initiated. Throughout the entire experiment, the openings of the regulating valves 4 and 5 should remain as small as possible while still to ensure the required gas-liquid separation and subcooled effect, respectively. A series of experiments corresponding to different injection pressure differences were conducted until the liquid nitrogen in dewar 1 had run out or the nozzle had to be replaced. Notably, sufficient precooling was indispensable after replacing the liquid dewar or the nozzle because the flow characteristics of liquid nitrogen were highly sensitive to the operating conditions [2,3].
Fig. 4. Structural sketch of the solid-cone pressure swirl nozzle.
the T-type thermocouple was pre-calibrated and has an accuracy of ±0.1 K. The mass flow meter was pre-calibrated by the manufacturer and has a full-scale accuracy of ±0.39%. The pressure transducer has a full-scale accuracy of ±0.25% (provide by the manufacturer). Taking measuring uncertainty into account, the overall uncertainties of temperature, mass flow rate and pressure were estimated to be ±0.2 K, ±0.42% and ±0.53%, respectively. For an indirectly measured variable, the uncertainty can be estimated by the error transfer function. In this study, the uncertainty of the discharge coefficient is a function of mass flow rate and pressure difference. According to the error transfer theory in Ref. [23], it can be calculated by Eq. (6).
dC d
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 @f @f ¼ d2qm þ d2DP @qm @ DP
3. Results and discussion 3.1. Flow characteristics of liquid nitrogen and water The influence of the injection pressure difference on the mass flow rate of liquid nitrogen through two solid-cone pressure swirl nozzles is shown in Fig. 5. Meanwhile, the corresponding mass flow rates of water are also presented in the same figure for comparison. One point to note is that the mass flow rates of water in Fig. 5 are tested by the nozzle manufacturer, as shown in the nozzle product catalog [15]. To verify the flow rate data of water spray
ð6Þ
where dCd , dqm and dDP refer to the uncertainties of the discharge coefficient, mass flow rate and pressure difference, respectively. The maximum uncertainty of the discharge coefficient was estimated to be 0.75%. 2.3. Experimental procedure In the experiments, liquid nitrogen was directly injected into the atmospheric environment, and the liquid nitrogen temperature at the nozzle inlet was maintained approximately at 78 K. Prior to each experiment, the entire system was cleaned with dry gas nitrogen to expel moisture so as to prevent possible plugging in the pipelines or the nozzle orifice. Then the regulating valve 3 of the high-pressure liquid nitrogen dewar 1 was partially opened to cool
Fig. 5. Mass flow rate versus injection pressure difference.
294
X. Liu et al. / Applied Thermal Engineering 110 (2017) 290–297
from the product catalog, the mass flow rates of water at several operating conditions were measured with an experimental apparatus of water spray. By comparison, it is found that the measured data agree well with the data from the product catalog. Therefore, the mass flow rates of water from the product catalog are used in the present study in comparison with the flow rate measurements of liquid nitrogen spray. As shown in Fig. 5, the mass flow rates significantly increase with the increasing injection pressure difference for liquid nitrogen and water. At any given injection pressure difference, the mass flow rate of water is larger than that of liquid nitrogen. This difference can be partially attributed to their different densities, as shown in Table 1 [22]. However, the predominant reason could be the differences in the discharge coefficients between liquid nitrogen and water. The discharge coefficient of an atomizing nozzle depends not only on the frictional loss inside the nozzle passageway but also on the extent to which the sectional area of the nozzle discharge orifice is effectively utilized [8,25]. Based on the injection pressure differences and the corresponding mass flow rates, the discharge coefficients for liquid nitrogen and water are obtained (Fig. 6). As shown in Fig. 6, the discharge coefficient of liquid nitrogen is much smaller than that of water regardless of the given injection pressure difference. This trend is mainly attributed to significant differences in the thermophysical properties of these media. The normal boiling point of water is much higher than that of liquid nitrogen. However, the dynamic viscosity of liquid nitrogen is far lower than that of water as shown in Table 1. Therefore, it can be concluded that the discharge coefficient of liquid nitrogen is mainly determined by the effective flow area of the nozzle discharge orifice. Remarkable gas-liquid phase change can occur inside the nozzle due to the throttling effect and the possible heat leakage into the nozzle [3,26–28], which will result in significant reduction of mass flow rate during the spray process. However, the discharge coefficient of water mainly depends on frictional loss because of its relatively high viscosity. The influence of the gasliquid phase change is more prominent than that of frictional loss. From Fig. 6, it can also be found changes in the injection pressure difference exhibit varied effects on the discharge coefficients of liquid nitrogen and water. The discharge coefficient of liquid nitrogen increases as the injection pressure difference increases. Contrarily, a slight decreasing trend in the discharge coefficient can be observed for water. The dominant reason for the small discharge coefficients of water at high injection pressure differences is that frictional resistance increases as the injection pressure difference increases. However, the behavior of liquid nitrogen is mainly
Fig. 6. Discharge coefficient versus injection pressure difference for different working media.
Fig. 7. Discharge coefficient versus injection pressure difference for different nozzle orifice diameters.
ascribed to the effect of gas-liquid phase change inside the nozzle. In this study, the liquid nitrogen temperature at the nozzle inlet is maintained approximately at 78 K (78.77–80.13 K), but the nozzle inlet pressure varies from 0.20 MPa to 0.82 MPa. Therefore, the corresponding subcooling degree of liquid nitrogen at the nozzle inlet changes within a wide range (4.91–20.66 K). As the injection pressure difference increases, the subcooling degree of liquid nitrogen at the nozzle inlet increases and gas-liquid phase change inside the nozzle weakens correspondingly. This trend indicates that the discharge orifice area is utilized more effectively at higher nozzle inlet pressure, thereby increases the corresponding discharge coefficient. Fig. 7 shows the effect of the nozzle orifice diameter on the flow characteristics of liquid nitrogen. At low injection pressure differences, the discharge coefficient of #2 nozzle (orifice diameter: 2.0 mm) is larger than that of #1 nozzle (orifice diameter: 1.6 mm) and the gap between them gradually narrows with the increasing injection pressure difference. This decrease is attributed to the influence of the gas-liquid phase change on the discharge coefficient, which is more pronounced for the nozzle with a small orifice diameter than that with a large orifice diameter. At high injection pressure differences, gas-liquid phase change inside the nozzle weakens because of the high subcooling degree of liquid nitrogen at the nozzle inlet. Therefore, the difference between the discharge coefficients of #2 nozzle and #1 nozzle decreases. 3.2. Correlation for the discharge coefficient of water For the design of spray system, it is quite necessary to develop a correlation to predict the discharge coefficient accurately. As such, the experimental discharge coefficients of water were first compared with the corresponding predicted values by the aforementioned correlations (Eqs. (2)–(5)) to verify their applicability to the present study of water spray. Fig. 8 shows the changes in the discharge coefficient of water through #2 nozzle with the injection pressure difference. It is found that the discharge coefficients predicted by Eqs. (2) and (3) are significantly lower than the experimental data. This is because both of these correlations were developed for hollowcone pressure swirl nozzles, in which a gas core exists at the discharge orifice because of the strong swirling effect as mentioned earlier. The corresponding discharge coefficient is thus lower than that of solid-cone pressure swirl nozzles with the same geometric size. The predicted values of Eqs. (4) and (5) are in better agreement with the experimental data. Moreover, the experimental discharge coefficients at low injection pressure differences are in great agreement with the values predicted by Eq. (4). However,
X. Liu et al. / Applied Thermal Engineering 110 (2017) 290–297
295
Fig. 10. Comparison between the experimental discharge coefficients of liquid nitrogen and the predicted values by correlations developed for room-temperature working media.
Fig. 8. Discharge coefficient of water versus injection pressure difference.
Fig. 9. Comparison between the experimental discharge coefficients and the predicted values (water). Fig. 11. Discharge coefficient of liquid nitrogen versus injection pressure difference.
at high injection pressure differences, the experimental data are more consistent with those predicted by Eq. (5). As shown in Fig. 8, a disadvantage of Eqs. (4) and (5) for predicting the discharge coefficient of water is that they overlook the influences of the injection pressure difference. In the present study, the influences of the injection pressure difference on the discharge coefficient are evident, particularly for low injection pressure differences, and cannot be ignored. As such, a new discharge coefficient correlation is proposed as a function of the dimensionless nozzle orifice area and injection pressure difference, which is expressed as:
C d;
H2 O
0:035 0:191 DP Ao ¼ 0:445 Pcr Ai
ð7Þ
Eq. (7) is applicable to the nozzles with orifice diameter near 1.6–2.0 mm. The density of water involved in Eq. (7) is 998 kg m3, which is corresponding to the state point (1 atm, 298 K). For comparing, the discharge coefficients predicted by Eq. (7) are also shown in Fig. 8. It is observed that the predicted results show a good agreement with the experimental data. The fitting quality of Eq. (7) can be clearly seen in Fig. 9. The maximum relative deviation between the experimental discharge coefficients of water and the predicted values is 2.8%. The average deviation and the standard deviation are 0.01% and 1.29%, respectively. 3.3. Correlation for discharge coefficient of liquid nitrogen The discharge coefficients of water as predicted by Eqs. (4), (5) and (7) show better agreements with the corresponding
experimental data. However, whether these correlations are applicable to cryogenic fluids remains unclear. Thus, the three empirical correlations developed for room-temperature fluids are compared with the corresponding experimental data of liquid nitrogen (Fig. 10). It is found that all of the aforementioned correlations significantly overestimate the discharge coefficient of liquid nitrogen. This discrepancy occurs because liquid nitrogen spraying is a typical flashing atomization process associated with remarkable gasliquid phase change, which has a great influence on the effective flow area of the nozzle exit orifice and then the discharge coefficient. Nevertheless, the influence of phase change on the discharge coefficient is not considered in Eqs. (4), (5) and (7), which were developed for room-temperature working media. Hence, a discharge coefficient correlation based on the experimental results of liquid nitrogen is developed as expressed in Eq. (8), where the influence of gas-liquid phase change inside the nozzles is considered by introducing a dimensionless subcooling degree.
C d;
LN2
¼ 1:075
0:420 DP DT sub 0:807 Ao 0:186 Pcr T cr Ai
ð8Þ
The density of liquid nitrogen involved in Eq. (8) is 808 kg m3, which is corresponding to the state point (1 atm, 78 K). Comparisons between the predicted discharge coefficients of liquid nitrogen and the corresponding experimental data of #1 and #2 nozzles are shown in Fig. 11. The values predicted by Eq. (8) present a good agreement with the experimental data.
296
X. Liu et al. / Applied Thermal Engineering 110 (2017) 290–297
(3) At low injection pressure differences, the discharge coefficient of the nozzle with a large orifice diameter is higher than that of the nozzle with a small orifice diameter. The gap between these values gradually narrows with the increasing injection pressure difference. (4) A new correlation for the discharge coefficients of water is proposed. It is related to the dimensionless nozzle orifice area and injection pressure difference. For liquid nitrogen, the discharge coefficient correlation is governed not only by the dimensionless nozzle orifice area and injection pressure difference, but also by the dimensionless subcooling degree. The results indicate that the discharge coefficients of liquid nitrogen and water predicted by the developed empirical correlations show good agreements with the experimental data. Fig. 12. Comparison between the experimental discharge coefficients and the predicted values (LN2).
Acknowledgements The fitting quality of the proposed discharge coefficient correlation for liquid nitrogen is shown in Fig. 12. The maximum relative deviation between the predicted and experimental data is 8%. The average deviation and the standard deviation are 0.03% and 2.5% respectively. Thus, the proposed correlation presents a good agreement with the experimental data. 3.4. Discussion The flow characteristics of liquid nitrogen through solid-cone pressure swirl nozzles play an important role in cryogenic cooling applications. Due to the complexity of cryogenic measurement, there is no related research work in the published literature to the best of our knowledge. In the present study, preliminary research has been carried out on this topic. The findings could benefit the optimal design of cryogenic spray cooling systems. However, there are still some aspects to be improved. Liquid nitrogen spraying is a typical flashing atomization process associated with remarkable gas-liquid phase change inside the nozzle due to the throttling effect and the possible heat leakage [3,26–28]. In the present study, only qualitative analysis was presented on this point. In order to gain a better understanding and obtain a quantitative description of the spray process, numerical simulation of the internal flow of atomized nozzle should be carried out. The discharge coefficient correlation developed in this study is only valid for the solid-cone pressure swirl nozzles with slotted swirl vane within a relative small range of nozzle size (orifice diameter: near 1.6–2.0 mm). Further research should be performed using nozzles with wider range of dimensions/types so as to obtain more universal discharge coefficient correlations. 4. Conclusions A spray cooling experimental apparatus was built up to investigate the influence of the injection pressure difference on the flow characteristics of liquid nitrogen with two solid-cone pressure swirl nozzles. Through the systematic study, we obtained the following conclusions: (1) The mass flow rate of water is much larger than that of liquid nitrogen at any given injection pressure difference. (2) Changes in injection pressure difference exhibit contrary effects on the discharge coefficients for liquid nitrogen and water.
This project was supported by the National Nature Science Foundation of China (51406160), Postdoctoral Science Foundation of China (2014M560773), and partially supported by the Fundamental Research Funds for the Central Universities. References [1] C. Willert, G. Stockhausen, M. Beversdorff, J. Klinner, C. Lempereur, P. Barricau, J. Quest, U. Jansen, Application of Doppler global velocimetry in cryogenic wind tunnels, Exp. Fluids 39 (2005) 420–430. [2] S. Somasundaram, A.A.O. Tay, A study of intermittent liquid nitrogen sprays, Appl. Therm. Eng. 69 (2014) 199–207. [3] T.C. Lin, Y.J. Shen, M.R. Wang, Effects of superheat on characteristics of flashing spray and snow particles produced by expanding liquid carbon dioxide, J. Aerosol Sci. 61 (2013) 27–35. [4] S.O. Awonorin, An appraisal of the freezing capabilities of tunnel and spiral belt freezers using liquid nitrogen sprays, J. Food Eng. 34 (1997) 179–192. [5] B.D. Jerold, M.P. Kumar, Experimental comparison of carbon-dioxide and liquid nitrogen cryogenic coolants in turning of AISI 1045 steel, Cryogenics 52 (2012) 569–574. [6] N. Rizk, A.H. Lefebvre, Internal flow characteristics of simplex swirl atomizers, J. Propul. Power 1 (1985) 193–199. [7] A.C. Kheirabadi, D. Groulx, Cooling of server electronics: a design review of existing technology, Appl. Therm. Eng. 105 (2016) 622–638. [8] A. Lefebvre, Atomization and Sprays, CRC Press, Boca Raton, 1988. [9] N. Ashgriz, Handbook of Atomization and Sprays: Theory and Applications, Springer Science & Business Media, New York, 2011. [10] L. Bayvel, Liquid Atomization, CRC Press, London, 1993. [11] H. Montazeri, B. Blocken, J.L. Hensen, CFD analysis of the impact of physical parameters on evaporative cooling by a mist spray system, Appl. Therm. Eng. 75 (2015) 608–622. [12] Y. Tan, J. Xie, F. Duan, T. Wong, K. Toh, K. Choo, P. Chan, Y. Chua, Multi-nozzle spray cooling for high heat flux applications in a closed loop system, Appl. Therm. Eng. 54 (2013) 372–379. [13] Z. Zhang, J. Li, P.-X. Jiang, Experimental investigation of spray cooling on flat and enhanced surfaces, Appl. Therm. Eng. 51 (2013) 102–111. [14] M.S.F.M. Rashid, A.H.A. Hamid, O.C. Sheng, Z.A. Ghaffar, Effect of inlet slot number on the spray cone angle and discharge coefficient of swirl atomizer, Proc. Eng. 41 (2012) 1781–1786. [15] Industrial Spray Products Catalog, Spraying Systems Co. [16] A. Yule, R. Sharief, J. Jeong, G. Nasr, D. James, The performance characteristics of solid-cone-spray pressure-swirl atomizers, Atom. Sprays 10 (2000) 627–646. [17] G.G. Nasr, A.J. Yule, L. Bendig, Industrial Sprays and Atomization: Design, Analysis and Applications, Springer Science & Business Media, New York, 2013. [18] M. Jain, B. John, K.N. Iyer, S.V. Prabhu, Characterization of the full cone pressure swirl spray nozzles for the nuclear reactor containment spray system, Nucl. Eng. Des. 273 (2014) 131–142. [19] Z. Lan, D. Zhu, W. Tian, G. Su, S. Qiu, Experimental study on spray characteristics of pressure-swirl nozzles in pressurizer, Ann. Nucl. Energy 63 (2014) 215–227. [20] M.R. Halder, S.K. Dash, S.K. Som, A numerical and experimental investigation on the coefficients of discharge and the spray cone angle of a solid cone swirl nozzle, Exp. Therm. Fluid Sci. 28 (2004) 297–305. [21] J. Ballester, C. Dopazo, Discharge coefficient and spray angle measurements for small pressure-swirl nozzles, Atomization Sprays 4 (1994). [22] X.B. Zhang, L. Yao, J.Y. Chen, W. Zhang, W. Xiong, X.J. Zhang, L.M. Qiu, Prediction of the onset of flooding in an inclined tube at cryogenic temperatures, Cryogenics 61 (2014) 98–106.
X. Liu et al. / Applied Thermal Engineering 110 (2017) 290–297 [23] R.J. Moffat, Describing the uncertainties in experimental results, Exp. Therm. Fluid Sci. 1 (1988) 3–17. [24] M. Halder, S. Dash, S. Som, A numerical and experimental investigation on the coefficients of discharge and the spray cone angle of a solid cone swirl nozzle, Exp. Therm. Fluid Sci. 28 (2004) 297–305. [25] C. Hespel, J.-B. Blaisot, X. Margot, S. Patouna, A. Cessou, B. Lecordier, Influence of nozzle geometry on spray shape, particle size, spray velocity and air entrainment of high pressure diesel spray, in: THIESEL 2010-Conference on Thermo-and Fluid Dynamic Processes in Diesel Engines, 2010, pp. 383–394.
297
[26] H. Vu, G. Aguilar, High-speed internal nozzle flow visualization of flashing jets, in: 11th Triennial International Annual Conference on Liquid Atomization and Spray Systems, Vail, Colorado, USA, 2009. [27] C.W. Roh, M.S. Kim, Macroscopic spray behavior and atomization characteristics of refrigerant R22 injection under increased ambient pressure, Int. J. Heat Mass Transf. 55 (2012) 3307–3315. [28] D.M. Althausen, E.L. Golliher, Testing of an R134a spray evaporative heat sink, SAE Technical Paper, 2008.