Experimental study of free-surface jet impingement heat transfer with molten salt

International Journal of Heat and Mass Transfer 149 (2020) 119160

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt

Experimental study of free-surface jet impingement heat transfer with molten salt Feng Gao, Yongchang Chen∗, Jianbo Cai, Chongfang Ma Key Laboratory of Enhanced Heat Transfer and Energy Conservation, Ministry of Education, and Key Laboratory of Heat Transfer and Energy Conversion, Beijing Education Commission, Beijing University of Technology, Beijing 100124, China

a r t i c l e

i n f o

Article history: Received 24 September 2019 Revised 27 November 2019 Accepted 2 December 2019

Keywords: Jet impingement Free-surface Molten salt Heat transfer

a b s t r a c t An experimental study of free-surface jet impingement was carried out with compound molten salt to understand its characteristics of heat transfer. Based on pre-experimental verification on the reliability of experimental method by water as working fluid, a compound molten salt was chosen as a new working fluid to conduct experiment of free-surface jet impingement. The heat transfer of molten salt at stagnation point was investigated in detail, and the Nusselt number of molten salt increased with increasing of the Reynolds number and the Prandtl number, and was nearly constant with increasing of nozzle-to-plate spacing at present ranges. The data was correlated by an empirical formula, which was compared with those classical correlations from references. Next, the variation of the Nusselt number of molten salt was also verified along heated surface. It was shown that the local Nusselt number decreased monotonously with increasing of lateral distances from stagnation point, and increased with increasing of the Reynolds number. The profiles of the Nusselt number were nearly unchanged for different nozzle-to-plate spacing, which can be well correlated by a normalized formula. This work focused on the heat transfer characteristics of the molten salt in free-surface jet impingement, which may be recognized as a reference for promoting the application of molten salt in heat transfer process, especially in high temperature situations. © 2019 Elsevier Ltd. All rights reserved.

1. Introduction As one of the most effective means of heat transfer enhancement, jet impingement has been widely used in industrial processes [1], such as thermal treatment of metal, turbine blade cooling and microelectronic chip cooling etc. A number of researches have been proposed in jet impingement heat transfer, especially in geometric parameters of nozzle, shape of target surface, types of jet and thermal properties of working fluids [2–5]. Webb and Ma [3] summarized literatures on heat transfer of liquid jet impingement and indicated the four regions of flow along heat transfer surface for free surface jet impingement, the transition from lamina to turbulence and the potential core of jet for submerged jet impingement. Zuckerman and Lior [4] concluded that the turbulence in free gas jet may have effects on the Nusselt number along heat transfer surface. For higher nozzle-to-plate spacing a maximum of Nusselt number will exist at stagnation point, whereas for small spacing the local maximum may displace downstream

∗

Corresponding author. E-mail address: [email protected] (Y. Chen).

https://doi.org/10.1016/j.ijheatmasstransfer.2019.119160 0017-9310/© 2019 Elsevier Ltd. All rights reserved.

around r/d = 0.4–0.6 from stagnation point. Jambunathan et al. [5] analyzed experimental data of circular air jet impingement from references, with Reynolds Number ranging of 50 0 0–124,0 0 0 and nozzle-to-plate spacing of 1.2–16. It was shown that the Nusselt number of jet impingement was proportional to Reynolds number with its exponent varied from 0.5 to 0.8. The jet velocity distribution at nozzle exit, the initial turbulence of jet and entrainment from ambient fluid will have impact on the axial flow in free jet, and subsequently on the heat transfer performance along the heated surface. Garimella and Nenaydykh [6] investigated the influence of length-diameter ratio on the heat transfer coefficient by confined submerged liquid jet impingement with FC-77. They found that the heat transfer coefficient is much higher when length-diameter ratio L/d is smaller than unity. The heat transfer coefficient decreased rapidly for 1
2

F. Gao, Y. Chen and J. Cai et al. / International Journal of Heat and Mass Transfer 149 (2020) 119160

Nomenclature A C d h I m n Nu Nu0 Pr q Qv Qvm Qvf r R Re tj tw u z

heat transfer area at test section, m2 coefficient of correlation inner diameter of nozzle m heat transfer coefficient, W/(m2 · K) electrical current, A exponent of Reynolds number exponent of Prandtl number local Nusselt number Nusselt number at stagnation point Prandtl number heat flux, W/m2 volume flow of fluid, mL/s volume flow of rotameter, mL/s volume flow of flow chamber, mL/s radial distance from stagnation point, m resistance of constantan foil,  Reynolds number jet temperature, ◦ C surface temperature of constantan foil, ◦ C jet velocity, m/s nozzle-to-plate spacing, m

Greek symbols ρ density, kg/m3 λ thermal conductivity, W/(m•K) ν kinetic viscosity, m2 /s and pressure may increase sharply when nozzle closed to surface, then keep nearly constant for 0.65. A second peak of the convection heat

transfer coefficient appeared at radial distance r/d ≈ 2 when z/d<5 with Reynolds number in the range of 850 0–23,0 0 0. Wang et al. [13] investigated experimentally both free-surface and submerged jet impingement heat transfer with R-113 as working fluid. They found that for submerged jet impingement at a radial distance r/d ≈ 1.5, a second peak of heat transfer coefficient existed obviously, which indicated a transition from laminar to turbulent flow, but disappeared when z/d>4 at relatively small Reynolds numbers. Qin et al. [14] examined the radial distribution of heat transfer coefficients with FC-72 for both circular free-surface and submerged jet impingement. It was found that the convective heat transfer coefficient of stagnation point increased significantly with increasing nozzle-to-plate spacing, which was relevant to entrainment of surrounding gas for free-surface jet impingement and to the average velocity and turbulence intensity of free jet for submerged jet impingement. Liu [15] carried out an experiment on heat transfer characteristics of transformer oil in both free-surface and submerged jet impingement. It was confirmed that the stagnation Nusselt number for submerged jet impingement was generally higher than that for free-surface jet impingement. A minimum of the Nusselt number at stagnation point and a second peak of the Nusselt number at radial distance r/d = 0.5 can be found for both small nozzle-to-plate spacing and nozzle diameter. With rapid development of nano-material technology recently, heat transfer characteristics of nanofluid in jet impingement have attracted many researchers [16]. It has been shown that volume fraction, type and size of nano-particles may have remarkable effect on thermal conductivity of the nano-fluids and so on the heat transfer characteristics of the fluid. With nano-particles added to water, the Nusselt number of nanofluid in jet impingement may increase significantly up to 110%. Lv et al. [17] provided experimental data of heat transfer in circular free-surface jet impingement by water-based SiO2 nanofluid. Their results showed that the convection heat transfer coefficient of the nanofluid may be significantly increased with increasing of volume fraction of nanoparticles SiO2 and Reynolds number. Nguyen et al. [18] conducted an experiment of heat transfer of confined submerged jet impingement using water-based Al2 O3 nanofluid as a working fluid. It was found that the convective heat transfer coefficient of the nanofluid may increase only in some range of volume fraction of nanoparticles. In recent years, molten salt has been recognized as a new type working fluid in heat transfer with advantages of high specific heat, small viscosity, low vaporization pressure, and more extensive range of temperature available [19], and has been used in solar thermal power generation system, molten salt reactor and so on [20]. Instead of normal medium such as water vapor and heatconducting oil etc., the molten salt can be used as a new working fluid, which may further improve heat transfer performance in solar thermal power generation system [21,22]. Some molten salts were also used as heat transfer medium, for example, fluoride molten salt may remarkably improve the heat transfer efficiency in molten salt reactors [23]. In view of good thermal properties of molten salt, many researchers have focused on the heat transfer characteristics of molten salt. Takahashi et al. [24–26] measured thermophysical properties including specific heat, thermal conductivity, viscosity etc. of molten nitrate. Yang et al. [27] used a ternary mixed nitrate as a working fluid to investigate heat transfer performance of a spirally corrugated tube. Under the same conditions, the average Nusselt number of the spirally corrugated tube was about 3 times that of the smooth tube. Shen et al. [28] conducted experimental research on enhanced heat transfer of ternary mixed nitrate molten salt in both spirally corrugated tube and transversely corrugated tubes. Their results showed that the Nusselt number of enhanced tubes was clearly higher than that of the smooth tube.

F. Gao, Y. Chen and J. Cai et al. / International Journal of Heat and Mass Transfer 149 (2020) 119160

Qian et al. [29] investigated heat transfer of liquid/gas heat exchanger with mixed nitrate molten salt as a hot fluid. The convective heat transfer of molten salt satisfied the Gnielinski’s relation with a maximum deviation of ±20% in the range of Reynolds number 30 0 0–12,0 0 0. Liu et al. [30] gave the empirical correlations of forced convective heat transfer with molten salt of lithium nitrate for both transitional flow and fully developed turbulent flow in tube. He et al. [31] carried out an experiment of heat transfer with molten salt flowing outside tube and proposed modified relations of heat transfer for both transitional and turbulent flow by correction of viscosity of the molten salt. Sun et al. [32] proposed a more accurate correlation of heat transfer for molten salt in laminar flow by modifying factor from the Sieder-Tate correlation. Chen et al. [33] experimentally investigated heat transfer performance of the HITEC molten salt in compound convection process. Their results showed that the Nusselt number of mixed convection heat transfer was increased up to 50% higher than that of sole forced convection heat transfer. Many researches have shown that molten salt can be used as a novel working fluid with good heat transfer characteristics in industrial application, especially in high temperature heat transfer process. The molten salt is generally similar with water in thermal properties and is of very good heat transfer and thermal storage performance, thus largely extending its scope in heat transfer application. The suitable temperature of molten salt can be extended up to 10 0 0◦ C, which makes up for the shortage of conventional fluid such as water and oil etc. However, up to now, the research on molten salts is still limited in convection heat transfer inside tube and is far from knowledge of the elemental heat transfer characteristics of them. To the best knowledge of present authors, as the most effective method, jet impingement of molten salt has not been studied and verified for heat transfer. Because of the complex influence of nozzle geometry, flow pattern and fluid properties, the results for conventional fluid such as water and air etc. could not be flush applied in jet impingement heat transfer for molten salt, which restrained the application of molten salt as heat transfer medium in industries. Thus, based on former study on submerged jet impingement [34], this work focused on the heat transfer of the molten salt in free-surface jet impingement and provided detailed information on heat transfer performance both for stagnation and radial distribution. Some empirical relations obtained in this study could be applied in new heat exchanger design with molten salt and the experimental results could be utilized to promote the heat transfer application of molten salt in actual process under high temperature and high heat flux. 2. Experimental apparatus and methods Fig. 1 shows the schematic diagram of experimental setup for jet impingement heat transfer, which consists of storage tank with electrical heater, gear pump, flow meter, test chamber and data acquisition system. The working fluid from a storage tank was driven by a gear pump, flowing through a filter and a flow meter to a buffer plenum and ejecting from a nozzle, and then impinged on a heated surface in jet chamber, and then flowed back to the storage tank after a flow-measuring chamber and a cooling fan. The working fluid used in experiment was preheated to a given temperature (less than 70 ◦ C for water and less than 150 ◦ C for molten salt) by an electric heater adjustable with a maximum power of 5 kW mounted inside the storage tank. The mass flux of the working fluid can be adjusted by the gear pump with range of 1.6–4.2 L/min and can be measure by the rotameter in a range of (0.016–0.16 m3 /h) for water. As the high temperature of molten salt the mass flux of it had to be measured by a specially produced flow chamber based on the volume-metage method for molten salt. The flow chamber

3

Fig. 1. Experimental setup for jet impingement heat transfer.

was made of stainless steel with a range of 0.5–1.5 L. In order to prevent the molten salt from solidification when flowing inside the pipe, a heating cable was wrapped additionally on the pipeline for preheating, and the pipe was externally enwrapped with the aluminum silicate wool as a thermal insulation layer to reduce heat loss to environment. As shown in Fig. 2, during experimental process the working fluid was supplied from vertical delivery tube to the jet nozzle passing a plenum box of 27 cm3 . Both the delivery tube and jet tube were made of stainless steel and fixed with the plenum box. The nozzle-delivery tube assembly was fixed on a threedimensional coordinate rack and could be adjusted with respect to the test section with placements accomplished with ±0.01 mm. The buffer plenum was made of aluminum alloy with a type-T thermocouple up to 400 ◦ C placed near the inlet of nozzle to measure the temperature of the fluid jet. The jet nozzle was carefully produced with the inner diameter of 2 ± 0.02 mm. The lengthdiameter ratio of the nozzle was about 20 for the developed flow of working fluid obtained at exit of the nozzle. Fig. 3 shows the details of the test section assembly. The main part was a constant foil of 10-μm thick with heated section of 21 mm x 8 mm. The active section of the foil was used as an electrical heating element as well as a heat transfer surface exposed to the working fluid. The foil on either side of the active section was welded to copper bus blocks, which were in turn connected by electrical leads to a DC power supply of 30 A in maximum. The heated section of foil was cemented to a PTFE block inserted between copper blocks. The temperature of the inner surface of the heater was measured by a type-T thermocouple, which was adhered to the backside of constantan foil and was electrically insulated from the heater yet in close thermal contact. The test section was highly insulated in thermal design by aluminum silicate wool to minimize heat loss. Before experimental test the working fluid should be adjusted at given conditions in steady state, i.e. stable mass flux and temperature. Then the jet nozzle was moved transversely or vertically over the heated surface by adjusting the three-dimensional coordinate rack, and the wall temperature and jet temperature were recorded as local values by an Agilent 34,972 device for data acquisition. By recording the temperatures for various locations of the nozzle, the horizontal temperature distributions could be obtained for given jet conditions and surface heat flux. Thermophysical properties of working fluid were evaluated at film temperature by averaging the jet and wall temperatures. The area of the heated surface was carefully measured for each test section assembly with a microscope of 0.001 mm resolution.

4

F. Gao, Y. Chen and J. Cai et al. / International Journal of Heat and Mass Transfer 149 (2020) 119160

Fig. 2. Plenum box.

Fig. 3. Test section.

Heat flux was calculated from the electrical power supplied to the test section and the area of the heated surface. The heat flux was determined by the following formula:

q=

I2 R A

(1)

where the electrical current I through the foil was measured by an amperemeter with a grade-0.5 in range of 0–30 A, and the resistant R was accurately measured with direct current before experiments. It was verified in preliminary test that the variation of the resistance with temperature could be neglected (less than 0.5%), as the variation of resistivity with temperature is extremely small for constantan. The heat transfer coefficient h between working fluid and heat transfer surface was calculated by

h=

q

t

=

q tw − t j

(2)

where tw is the surface temperature of constantan foil and tj is the jet temperature. Consequently, the Reynolds number and the Nusselt number for working fluid can be determined, respectively, by

Re =

ud

ν

=

4Qv

π dν

Nu =

hd

λ

(4)

where the jet velocity u was measured by flowmeter calibrated before experiment, and the inner diameter of nozzle d was measured accurately by a standard vernier caliper (±0.02 mm) before experiment. The uncertainty of Nusselt number was influenced primarily by the determination of heat flux and wall temperature. It was shown from preliminary experiment for heat loss check that with jet impingement the maximum conduction loss to the back of the heater assembly was less than 0.8% of the power put into the heater. The conclusion was also supported by a conduction analysis for this study. So, no correction was included in this work for conduction loss. All the thermocouples were calibrated within an accuracy of ±0.05 ◦ C by a standard platinum resistance before experiment. The uncertainty of Reynolds number was affected by the measurement of flowrate and nozzle diameter. As the high temperature of molten salt, the flowrate of molten salt had to be measured by the flow chamber which was calibrated by the grade-0.5 flowmeter before experiment, and the calibration result was shown in Fig. 4. According to the linear superposition method [35], the deviation of function with some independent variables could be calculated as follows:

δy =

    δ xi   ∂ xi 

n   ∂y i=1

(5)

F. Gao, Y. Chen and J. Cai et al. / International Journal of Heat and Mass Transfer 149 (2020) 119160

5

Table 1 Uncertainties of the parameters. Item

δ d /d

δ I /I

δ A /A

δ q /q

δ h /h

δ Qvf/Qvf

δ Re/Re

δ Nu/Nu

Uncertainty (%)

1.0

0.94

0.017

2.23

5.68

3.367

6.262

6.489

Fig. 4. Calibrated curve for flow chamber.

Fig. 5. Variation of stagnation Nusselt number with Reynolds numbers for water.

Thus, the uncertainties of heat flux, heat transfer coefficient, Reynolds number and Nusselt number could be determined based on basic parameters. And Reynolds number and Nusselt number were both less than 7% in the uncertainties. The detailed information for uncertainties of the parameters is shown in Table 1. In this work, a new quaternary molten salt (LiNO3 +NaNO3 +KNO3 +Ca(NO3 )2 ) [36] was chosen as a working fluid for study of jet impingement heat transfer because it has much lower melting point and better thermal properties suitable for the experiment. 3. Results and discussion Jet impingement has been widely used in heat transfer enhancement process, in which the water is generally recognized as a very good working fluid and has been studied detailedly in heat transfer characteristics. Therefore, before the experiment with the molten salt, the water was chosen as a working fluid for comparison and to verify reliability of the experimental setup. Fig. 5 gives variation of the Nusselt number at stagnation point with the Reynolds numbers, and the experimental results indicated the significant dependence of the Nusselt number on the Reynolds numbers. According to the basic theory of jet impingement heat transfer, the Nusselt number at stagnation point can be well correlated as a form of

Nu = CRem P r n

(6)

where the exponent n of the Prandtl number was generally taken as 1/3 for liquid and 0.4 for gas [10]. Base on the Eq. (6), the experimental data for water were correlated for the range of Re from 770 0 to 23,50 0 and Pr≈5.0 with z/d ≤ 7.0, and the correlation of stagnation heat transfer was obtained

N u0 =0.938Re

0.488

Pr

1/3

(7)

where the coefficient 0.938 and exponent 0.488 were determined from a least-squares regression of the data. The deviation for fitting equation was less than 1.95%. In addition, some classical em-

pirical correlations from literatures were also displayed in Fig. 5 for comparison. Liu et al. [37] analyzed stagnation heat transfer of water jet impingement according to the laminar flow theory and proposed a correlation as

N u0 =0.797Re0.5 P r 1/3

(8)

where Pr >3, 30 0 0≤ Re ≤34,0 0 0. Zhao and Ma [38] theoretically analyzed heat transfer of freesurface jet impingement under arbitrary heat flux by the integral method and obtained the formula of the stagnation Nusselt number as

N u0 =0.8598Re0.5 P r 1/3

(9)

Stevens and Webb [39] carried out an experiment of water freesurface jet impingement with nozzle diameter of 2.2–8.9 mm and nozzle-to-plate spacing z/d<35. They gave a comprehensive correlation of stagnation heat transfer as follows −0.11

N u0 =1.51 Re0.44 P r 0.4 (z/d )

(10)

Wang et al. [13] conducted experimental study of circular freesurface jet with R-113 and a nozzle diameter of 534 μm. They obtained a correlation of heat transfer at stagnation point for 490 0
N u0 = 1.344Re0.492 P r 1/3

(11)

Based on experimental results of circular free-surface jet impingement with FC-72 in a nozzle diameter of 987 μm, Qin et al. [14] proposed a correlation of stagnation heat transfer for 350 0
N u0 = 1.636Re0.465 P r 1/3

(12)

The above mentioned correlations (8–10) are also plotted in Fig. 5, in which the Nusselt number increased obviously with increase of the Reynolds number. A good agreement can be observed between present experimental data and correlations from literatures. The maximum deviation among them is no more than 1.31%. All the exponents of Reynolds numbers in correlations closed to

6

F. Gao, Y. Chen and J. Cai et al. / International Journal of Heat and Mass Transfer 149 (2020) 119160

Fig. 6. Variation of stagnation Nusselt number with Reynolds numbers for molten salt.

0.5 indicate obviously the laminar flow at stagnation region on heat transfer surface. Due to different experimental conditions, the coefficients of correlations were slightly different because of the varied velocity profile and turbulence intensity in free jet of working fluid. Furthermore, the molten salt was used as a new working fluid for experimental study of free-surface jet impingement heat transfer. Usually the most important feature for jet impingement is the heat transfer characteristics at stagnation zone. Thus, the stagnation Nusselt number of the molten salt was first presented with the Reynolds number range Re=350 0–850 0 and nozzle-to-plate spacing z/d = 1–7. Fig. 6 displays the variation of the Nusselt number with the Reynolds number. It is clearly seen that at present range of Re, the dependence of the Nusselt number is significantly on the Reynolds numbers, and the stagnation Nusselt number becomes much higher when the Reynolds number is larger, which indicates that the stagnation heat transfer can be enhanced with the higher Reynolds number due to the higher velocity of jet. The experimental data of the molten salt for 350 0≤Re≤850 0 and z/d ≤ 7 with Pr≈16.0 were well correlated in the form of Eq. (6), and the stagnation Nusselt number for molten salt was obtained as

N u0 = 0.675Re0.492 P r 1/3

cal properties of the working fluids may have great influence on the characteristics of heat transfer in jet impingement. It is sure that the molten salt displays a good heat transfer performance at stagnation flow not less than the water, and a new correlation for the molten salts is proposed necessarily for real heat transfer application. This work with the molten salt focuses on the heat transfer of free-surface jet impingement, which is extremely different from that of the submerged jet impingement. As a coupled study of present work the heat transfer correlation for the submerged jet impingement [34] is also displayed for comparison in Fig. 6. It is seen that the Nusselt numbers at stagnation point for freesurface jet impingement is generally smaller than those for the submerged. Because of the different flows of jet for free-surface and submerged, e.g. the entrainments of gas for free-surface and of liquid for submerged, the impingement flow of the fluid at the stagnation zone present distinct features, thus resulting in variation of heat transfer characteristics of working fluid. The entrainment of liquid for the submerged jet may bring in much stronger turbulence and therefore the enhancement of heat transfer at stagnation zone [2,3], which may be confirmed by the exponent 0.522 of Reynolds number in the correlation for submerged jet impingement. Additionally, it is noted that the heat transfer data for molten salt displayed in Fig. 6 cover the nozzle-to-plate spacing in range of 1–7, in which the Nusselt numbers for stagnation zone show nearly irrelevant to the nozzle-to-plate spacing. The heat transfer data are replotted in Fig. 7 for clear display of the relationship between the stagnation Nusselt numbers and nozzle-to-plate spacing. Fig. 7 gives the variation of the stagnation Nusselt number of molten salt with nozzle-to-plate spacing at certain Reynolds numbers. It can be seen from the figure that the stagnation Nusselt number slightly varies with increase of nozzle-to-plate spacing at given Reynolds number, indicating that the heat transfer at stagnation zone is hardly affected by the nozzle-to-plate spacing. As the free-surface jet impingement with ambient gas entrained, the axial flow of the free jet will not be violently affected by the gas entrainment, thus resulting in the heat transfer at stagnation zone nearly constant. The phenomenon is consistent with the experimental results in reference [3] and provides also more choices in nozzle-to-plate spacing for the molten salt in free-surface jet impingement application.

(13)

where the exponent of the Pr was chosen as 1/3 based on the Eq. (6), and the coefficient 0.675 and exponent 0.492 were all determined from a least-squares regression of the experimental data. The deviation for the fitting equation was less than 3.93%. It is also noted from the Eq. (13) that the exponent of Reynolds number is very close to 0.5, indicating that the impingement flow of molten salt at stagnation region is laminar, which is consistent with the classical empirical relations for free-surface jet impingement. This phenomenon results from the high pressure gradient along the lateral direction at stagnation zone due to strong impingement of fluid on heat transfer surface. In addition, some heat transfer relations for free-surface jet impingement with different fluids including R-113 [13], FC-72 [14], and water [37,38] are also displayed in the figure for comparison. It can be seen from Fig. 6 that the stagnation Nusselt numbers for molten salt are a little higher than those of water under the same Reynolds numbers, but are obviously lower than those of the R-113 and the FC72. As the different Prandtl numbers among the several fluids, the stagnation Nusselt numbers present different values even at the same Reynolds numbers, which indicates that the thermophysi-

Fig. 7. Variation of stagnation Nusselt number for molten salt with nozzle-to-plate spacing.

F. Gao, Y. Chen and J. Cai et al. / International Journal of Heat and Mass Transfer 149 (2020) 119160

(a)

7

(b)

(c)

Fig. 8. (a) Radial distribution of Nu with molten salt at z/d = 1. (b) Radial distribution of Nu with molten salt at z/d = 4. (c) Radial distribution of Nu with molten salt at z/d = 7.

Subsequently, the heat transfer of free-surface jet impingement with the molten salt was verified along the heat transfer surface. Fig. 8 shows the radial distribution of local Nusselt number with molten salt under different Reynolds Number at z/d = 1, 4, 7, respectively. It is clearly seen that all the profiles of the local Nusselt numbers are symmetrically bell-shaped with a center at stagnation point. The maximum value of the local Nusselt numbers exists at stagnation point for a given Reynolds number, and it decreases gradually with radial distance far from the stagnation point, which results chiefly from the rapid decline of flow velocity of the molten salt with radial displacement. Besides, with increasing of Reynolds number, the profile of local Nusselt number gradually rises, which is consistent with the variation of Nu at stagnation point, and indicates the important effect of Reynolds number on the heat transfer coefficient. As the limited range of the Reynolds number in this work, the local heat transfer coefficient may not change remarkably with different Reynolds numbers. It is also noticed that there is no obvious local maximum of the Nusselt number (so called the second peak) appeared at r/d = 1–2 as previous work reported in literature [13,15]. This can be explained that, duo to relatively low Reynolds numbers in the test, the boundary layer at wall flow region may quickly become thicker with the decreasing of flow velocity when the molten salt flows far away from the stagnation point, thus resulting in indistinct flow transition and weakened heat transfer gradually along the heat transfer surface. From the Fig. 8, it is also seen that the nozzle-to-plate spacing does not so evidently affect the distribution of the local Nus-

Fig. 9. Radial distribution of Nu with molten salt under nozzle-to-plate spacing.

selt number, which is replotted in Fig. 9. It is noted that the radial distributions of Nusselt number with molten salt under different nozzle-to-plate spacing z/d = 1–7 are nearly the same at a given Reynolds number, which indicates important effect of Reynolds number on the heat transfer, and irrelevant of the nozzle-to-plate spacing to the local heat transfer.

8

F. Gao, Y. Chen and J. Cai et al. / International Journal of Heat and Mass Transfer 149 (2020) 119160

(a)

(b)

Fig. 10. (a) Normalized distribution of Nu with molten salt at z/d = 1. (b) Normalized distribution of Nu with molten salt at z/d = 4.

In order to understand the characteristics of jet impingement heat transfer with molten salt, the local Nusselt number along the radial distance was normalized by the stagnation Nusselt number as Nu/Nu0 . The radial distributions of Nu/Nu0 are shown in Fig. 10 for nozzle-to-plate spacing z/d = 1 and 4, respectively. It is seen that at the same z/d for different Reynolds numbers, the local normalized Nusselt numbers may collapse to a single band, which clearly expresses independent of the Reynolds number. Just at r/d = 2, the local Nusselt number decrease rapidly to about 55% of its maximum value at stagnation point for different Reynolds numbers. According to distribution of normalized local Nusselt numbers the experimental data could be correlated as a function of r/d. Thus a general correlation of Nu/Nu0 was proposed for 350 0≤Re≤850 0 and z/d ≤ 7 as Eq. (14), in which the Nu/Nu0 varies only with the radial distance from stagnation point, other than the Reynolds number and nozzle-to-plate spacing. The coefficients 0.5 and 1.48 were determined from the fitting of a selfdefined non-linear function by least-square regression method. The correlation may be presented for all the data and the maximum deviation of the fitting curve from experimental data was less than 7.51% for range r/d<2.5.



Nu 1 = 0.5 1+ 2 N u0 1+1.48(r/d )



(14)

Usually, the water can be used as a good working fluid for heat transfer, but for higher temperature situations, the molten salt may be better as a new fluid instead of water in heat transfer because of its similar thermal properties to water. Therefore, a comparison of the stagnation heat transfer for molten salt and water is provided and shown in Fig. 11. It is clearly seen that the Nusselt number of molten salt is generally higher than that of water at the same Reynolds number, which indicates the better heat transfer characteristics of the molten salt. With the previous study [36], the molten salt has nearly the same heat conductivity as water, and a little higher viscidity than water, thus preserving good heat transfer characteristics similar to water even in high temperature application. Further, the radial distribution of Nusselt number for molten salt and water is proposed and shown in Fig. 12. The Nusselt numbers for both molten salt and water all decrease with increasing radial distance and increase with increasing Reynolds number. However, the Nusselt number of molten salt is a little higher than that of water at stagnation region under nearly the same Reynolds number, but it decreases more rapidly and becomes lower than that of water at wall jet region. According to the ther-

Fig. 11. Comparison of Nu at stagnation point between molten salt and water.

mophysical properties of molten salt [36] and water, the viscosity of molten salt is slightly higher than that of water, which may provide a relatively higher velocity of jet at the same Reynolds number, thus resulting in much violent impingement of free-surface jet on the heat transfer surface at stagnation zone. But for wall jet zone the flow boundary layer of molten salt may increase more rapidly than that of water because of its higher viscosity. Therefore, the profiles of local heat transfer coefficient along the target surface display very distinct distributions for the water and the molten salt, respectively. Many researches on jet impingement proposed the empirical correlations for stagnation heat transfer, but in which the effect of Prandtl number on heat transfer was usually displayed in different powers. Therefore, in this work the influence of thermophysical properties of working fluid on heat transfer was further verified. Fig. 13 gives the stagnation Nu0 /Re0.5 with different working fluids, displaying as a function of Prandtl number. Based on the experimental data from references [13,14,40], the working fluids including water, R-113, FC-72, transformer oil and molten salt were all correlated to verify the influence of Prandtl number on heat transfer. A correlation by a least-square method for different fluid was provided and shown in the figure. It is clearly seen that stagnation Nusselt number of working fluid shows significant dependence on the Prandtl number with exponent of 0.364, which is

F. Gao, Y. Chen and J. Cai et al. / International Journal of Heat and Mass Transfer 149 (2020) 119160

Fig. 12. Radial distribution of Nu between molten salt and water at z/d = 4.

9

the Reynolds number, but kept nearly unchanged for different nozzle-to-plate spacing at present conditions. 3 The molten salt displays good characteristics of heat transfer, which is closed to that of the water. Under the same Reynolds numbers, the Nusselt number of molten salt was higher than that of water at stagnation area and decreased far more rapidly than water at radial flow, which results from the variation of thermal properties of different working fluids. 4 With good properties of molten salt in heat transfer, presently, it has been recognized as a good working fluid in heat transfer, which has been widely used in nuclear reaction power, solar thermal power generation and other chemical processes. With jet impingement tech the molten salt could be well applied in many heat transfer process, especially with high temperature and high heat flux. For example, the heat exchanger used in solar energy collector could be designed in jet impingement with molten salt, which may remarkably improve the heat transfer performance by increasing the uniformity of temperature distribution on heat transfer surface under high heat flux of solar energy. Based on the better performance of jet impingement with molten salt, the results from this work will be expected to promote the application of molten salt in industries under extreme conditions. Declaration of Competing Interest The authors declared that they have no conflicts of interest to this work. CRediT authorship contribution statement Feng Gao: Data curation, Investigation, Validation, Writing original draft. Yongchang Chen: Conceptualization, Methodology, Formal analysis, Writing - review & editing. Jianbo Cai: Data curation, Investigation, Software. Chongfang Ma: Conceptualization, Supervision, Funding acquisition.

Fig. 13. Dependence of Nu0 /Re0.5 at stagnation point on Pr number.

considerably consistent with the recommended value of 1/3 from Ref. [10]. The relation of Nusselt number with Reynolds number and Prandtl number for jet impingement heat transfer may be remarkably confirmed by the present experimental results, the heat transfer of molten salt can also be determined according to the classical formula (6) in spite of slightly different coefficient for different working fluids. 4. Conclusions In this paper, a new compound molten salt was used as a working fluid for heat transfer research. An experiment of free-surface jet impingement with the molten salt was conducted in detail. And the heat transfer characteristics of the molten salt were obtained thoroughly for jet impingement including stagnation and wall jet zone. 1 The heat transfer characteristics of free-surface jet impingement of molten salt are investigated for stagnation flow. The experimental results can be well correlated and compared with classical formula from literatures, and a good agreement in Nu~Re0.5 Pr1/3 was observed among them. 2 Lateral heat transfer characteristics were verified under different Reynolds number and nozzle-to-plate spacing along heat transfer surface. The effect of Re on local heat transfer was confirmed. The local Nusselt number increased with increasing of

Acknowledgement This research was financially supported by National Natural Science Foundation of China (Grant No. 51276004). Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.ijheatmasstransfer. 2019.119160. References [1] N.G. Patil, T.K. Hotta, A review on cooling of discrete heated modules using liquid jet impingement, Front. Heat Mass Transf. (FHMT) 11 (16) (2018) 1–13. [2] M. Molana, S. Banooni, Investigation of heat transfer processes involved liquid impingement jets: a review, Brazil. J. Chem. Eng. 30 (03) (2013) 413–435. [3] B.W. Webb, C.F. Ma, Single-phase liquid jet impingement heat transfer, Adv. Heat Transf. 26 (8) (1995) 105–217. [4] N. Zuckerman, N. Lior, Jet impingement heat transfer: physics, correlations, and numerical modeling, Adv. Heat Transf. 39 (06) (2006) 565–631. [5] K. Jambunathan, E. Lai, M.A. Moss, et al., A review of heat transfer data for single circular jet impingement, Int. J. Heat Fluid Flow 13 (2) (1992) 106–115. [6] S.V. Garimella, B. Nenaydykh, Nozzle-geometry effects in liquid jet impingement heat transfer, Int. J. Heat Mass Transf. 39 (14) (1996) 2915–2923. [7] K. Choo, B.K. Friedrich, A.W. Glaspell, et al., The influence of nozzle-to-plate spacing on heat transfer and fluid flow of submerged jet impingement, Int J Heat Mass Transf 97 (2016) 66–69. [8] A.M. Kuraan, S.I. Moldovan, K. Choo, Heat transfer and hydrodynamics of free water jet impingement at low nozzle-to-plate spacings, Int. J. Heat Mass Transf. 108 (2017) 2211–2216. [9] J.B. Baonga, H. Louahlia-Gualous, M. Imbert, Experimental study of the hydrodynamic and heat transfer of free liquid jet impinging a flat circular heated disk, Appl. Therm. Eng. 26 (11–12) (2006) 1125–1138.

10

F. Gao, Y. Chen and J. Cai et al. / International Journal of Heat and Mass Transfer 149 (2020) 119160

[10] H. Sun, C.F. Ma, Y.Q. Tian, Local convective heat transfer from small heaters to impinging submerged axisymmetric jets of seven coolants with Prandtl number ranging from 0.7 to 348, J. Therm. Sci. 6 (4) (1997) 286–297. [11] D.W. Zhou, C.F. Ma, Radial heat transfer behavior of impinging submerged circular jets, Int. J. Heat Mass Transf. 49 (9) (2006) 1719–1722. [12] S.V. Garimella, R.A. Rice, Confined and submerged liquid jet impingement heat transfer, J. Heat Transf. 117 (4) (1995) 871–877. [13] L. Wang, Z.X. Yuan, C.F. Ma, et al., Experimental study on the heat transfer from simulated chips to impinging R-113 jets, Chin. J. Eng. Thermophys. 20 (4) (1999) 487–490. [14] M. Qin, Q. Zheng, C.F. Ma, et al., Experimental studies of local characteristics of heat transfer from a simulated microelectronic chip to an impinging circular dielectric liquid (FC-72) jet, Chin. J. Eng. Thermophys. 17 (1) (1996) 69–74. [15] X.H. Liu, Experimental Study On Heat Transfer of Single-Phase Liquid Jet Impingement, Xi’an Jiaotong University, 2003. [16] A.M. Darwish, A.M.R. Elkersh, M.N. Elsheikh, et al., A review on nanofluid impingement jet heat transfer, Int. J. Nanotechnol. Allied Sci 1 (1) (2017) 1– 15. [17] J. Lv, C. Hu, M. Bai, et al., Experimental investigation of free single jet impingement using SiO2 -water nanofluid, Exper. Therm. Fluid Sci. 84 (2017) 39–46. [18] C.T. Nguyen, N. Galanis, G. Polidori, et al., An experimental study of a confined and submerged impinging jet heat transfer using Al2 O3-water nanofluid, Int. J. Therm. Sci. 48 (2) (2009) 401–411. [19] Y.T. Wu, S.W. Liu, Y.X. Xiong, et al., Experimental study on the heat transfer characteristics of a low melting point salt in a parabolic trough solar collector system, Appl. Therm. Eng. 89 (2015) 748–754. [20] T.X. Zheng, J.L. Liang, H. Li, et al., Application status of molten salt technology in new energy, Inorgan. Chem. Ind. 50 (3) (2018) 12–15. [21] S.W. Liu, Experimental Study on Heat Transfer with Molten Salt in Trough Solar Collector System (2013). [22] H. Price, E. Lupfert, D. Kearney, et al., Advances in parabolic trough solar power technology, J. Sol. Energy Eng. 124 (2002) 109–125. [23] Q. Wang, H.X. Yu, H.F. Zhang, Study on molten salt circulation system in the reactor of nuclear power generation, Chem. Equip. Technol. 36 (4) (2015) 6– 33. [24] Y. Takahashi, R. Sakamoto, M. Kamimoto, Heat capacities and latent heats of LiNO3 , NaNO3 , and KNO3 , Int. J. Thermophys. 9 (6) (1988) 1081–1090. [25] R. Tufeu, J.P. Petitet, L. Denielou, et al., Experimental determination of the thermal conductivity of molten pure salts and salt mixtures, Int. J. Thermophys. 6 (4) (1985) 315–330.

[26] R. Ferri, A. Cammi, D. Mazzei, Molten salt mixture properties in RELAP5 code for thermodynamic applications, Int. J. Therm. Sci. 47 (12) (2008) 1676–1687. [27] M.L. Yang, X.X. Yang, X.P. Yang, et al., Heat transfer enhancement and performance of the molten salt receiver of a solar power tower, Appl. Energy 87 (9) (2010) 2808–2811. [28] X.Y. Shen, J.F. Lu, J. Ding, et al., Heat transfer enhancement of molten salt in spirally corrugated tube and transversely corrugated tube, Chin. J. Eng. Thermophys. 34 (6) (2013) 1149–1152. [29] J. Qian, Q.L. Kong, H.W. Zhang, et al., Experimental investigation for heat performance of molten salt-gas heat exchanger, Acta Enerciae Solaris Sinica 38 (11) (2017) 3012–3017. [30] B. Liu, Y.T. Wu, C.F. Ma, et al., Experimental study for forced convective heat transfer with molten salts in a circular tube, Chin. J. Eng. Thermophys. 31 (10) (2010) 1739–1742. [31] S.Q. He, J. Ding, J.F. Lu, et al., Convective heat transfer characteristics of high temperature molten salt outside tube, Chin. J. Eng. Thermophys. 34 (1) (2013) 103–105. [32] B. Sun, J.H. Zhou, C.F. She, Heat transfer characteristics of high-temperature, Nucl. Techniq. 38 (3) (2015) 70–74. [33] X. Chen, C. Wang, Y.T. Wu, et al., Characteristics of the mixed convection heat transfer of molten salts in horizontal square tubes, Solar Energy 147 (2017) 248–256. [34] B.T. Wang, Y.C. Chen, J.B. Cai, et al., Experimental investigation of circular submerged jet impingement heat transfer with mixed molten salt, Exper. Therm. Fluid Sci. 98 (2018) 30–37. [35] Z.L. Ding, Error Theory and Data Processing-2nd Edition [M], Harbin Institute of Technology Press, 2002. [36] N. Ren, Preparation and Experimental Study of Thermal Properties of Mixed Carbonates and Molten Salts with Low Melting Point, Beijing University of Technology, 2011. [37] X. Liu, J.H. Lienhard, J.S. Lombara, Convective heat transfer by impingement of circular liquid jets, J. Heat Transf. 113 (3) (1991) 571–582. [38] Y.H. Zhao, C.F. Ma, Analytical study of heat transfer with single circular free jets under arbitrary-heat-flux conditions, J. Beijing Polytech. Univ. 15 (3) (1989) 7–13. [39] J. Stevens, B.W. Webb, Local heat transfer coefficients under an axisymmetric, single-phase liquid jet, J. Heat Transf. 113 (1991) 71–78. [40] C.F. Ma, Q. Zheng, S.Y. Ko, Local heat transfer and recovery factor with impinging free surface circular jets of transformer oil, Int. J. Heat Mass Transf. 40 (18) (1997) 4295–4308.