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Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes
Annals of Nuclear Energy xxx (xxxx) xxx
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Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes Han-zhong Tao a,⇑, Chuan-yang Xie a, Mi-mi Wang b a b
School of Energy Science and Engineering, Nanjing Tech University, Nanjing, Jiangsu, China Xuzhou Hong Kong and China Gas Company Limited, China
a r t i c l e
i n f o
Article history: Received 19 June 2019 Received in revised form 19 September 2019 Accepted 16 October 2019 Available online xxxx Keywords: Sub-cooled boiling Numerical simulation Heat transfer coefficient Average vapor volume fraction Pressure drop
a b s t r a c t Sub-cooled boiling is crucial in dominating the operation performance in several engineering processes. In spite of the experimental investigations conducted in the previous reports, the mechanism of how tube shape affects the heat transfer is still in vagueness. Here, a simulation study on the sub-cooled water flow boiling in tubes of various shapes is performed by adopting the RPI (Rensselaer Polytechnic Institute) model to elucidate the structural effect on the hydraulic and thermal performance, including the average vapor volume fraction and pressure drop. The results demonstrate that for tubes with aspect ratio (AR) ranging from 0 to 5 the heat transfer performance varies greatly, among which the testing tube with AR = 3 exhibits the supreme. The heat transfer coefficient and pressure drop show an around 20% and 7% enhancement, respectively, when the tube AR increases from 0 to 3. Our results show: for these geometric and physical models, when aspect ratio (AR = 0, 1, 3 and 5) of flattened tube is equal to 3 which has the best heat transfer performance and then tends to be stable. For other factors, the heat transfer coefficient enhances by increasing heat flux (395.8 kW/m2, 475 kW/m2 and 570.0 kW/m2), mass flux (900, 990 and 1080 kg/(m2s)). Heat transfer coefficient increases about 20%, pressure drop augments about 7% when the flattened tube’s AR increases from 0 to 3. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Flow boiling, with better heat transfer performance, was widely applied in industrial applications such as the boiler, power generation equipment, heat exchanger and so on, and has been intensively studied by means of experiments and developing empirical correlations to demonstrate its superiority in heat transfer. Pierre and Bankoff (1967) experimentally measured the void ratio on different sections of a vertical rectangular channel with sub-cooled boiling heat transfer. Bartolomej and Chanturiya (1967) experimentally investigated the wall superheat, bulk sub-cooling, and vapor volume fraction in vertical circular tubes. Yan et al. (2015), Hata and Masuzaki (2009, 2010) experimentally studied subcooled flow boiling under high heat flux and high mass flux (HHHM) in vertical tubes, and the corresponding correlations were proposed. However, experiments and empirical correlations are limited to specified and complicated conditions. Zhang et al. (2015a,b) analyzed the influence of different turbulence models on sub-cooled boiling in the vertical pipe with wall boiling model and two-phase model. And the k-e models were recommended for
⇑ Corresponding author. E-mail address: [email protected] (H.-z. Tao).
sub-cooled boiling. He also employed CHF (critical heat flux) model to investigate DNB (departed nucleate boiling regime) and critical heat flux. Nemitallah et al. (2015) used CFD with user-defined functions to analyze flow boiling characteristics in the highpressure system with non-uniform axial heating profiles. It indicated that non-uniform heating profiles improve the void fraction distribution and heat transfer coefficient. In the industrial field, there exist many applications of vertical tube flow heat transfer, such as boiler drum system et al. Flattened tubes, a passive technique, are used to improve heat transfer, especially in the heat exchanger. Kim et al. (2013), Nasr et al. (2010) experimentally studied pressure drop and heat transfer in flattened tubes. The results showed the pressure drop and the heat transfer coefficient have the positive correlation with the aspect ratio of tubes. These results are also suitable for the two-phase condensation (Wilson et al., 2003). The simulation analysis of flow heat transfer of nanofluids with laminar flow was conducted by Huminic and Huminic (2013). Thome and Hajal (2002) numerically analyzed the effects of different dimensions. The results pointed out that flow boiling heat transfer coefficients in horizontal flattened were 100– 150% higher than that in horizontal round tubes at the same mass velocity. Flattened tube, which has a smaller height than the circular tube, has a significant influence on boiling flow heat transfer characteristics (Cheng et al., 2007; Cheng and Mewes, 2006).
https://doi.org/10.1016/j.anucene.2019.107144 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
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Nomenclature Ab Aif CD Cl C p;l C p;v C wl d Dw f ! F !q F !lift;q F !wl F !v m;q F td g G Gk;m hC hf v hq hpq hsl H kl K pq , K qp l L lv _ m _E m
ll lt;m lm lq kl kq s Qq Qkm em
_ lt m
nucleating bubbles area, m2 Interfacial area, m2 the drag force coefficient lift force coefficient single phase specific heat, J=ðkg KÞ vapor phase specific heat, J=ðkg KÞ wall lubrication coefficient diameter of tube, mm default bubble departure diameter bubble departure frequency external body force, N lift force, N wall lubrication force, N virtual mass force, N turbulent dispersion force, N gravity mass flow rate, (kg/s) production of turbulence kinetic energy single phase heat transfer coefficient latent heat of evaporation, kJ/kg specific enthalpy of the qth phase, kJ/kg interphase enthalpy, kJ/kg the volumetric heat transfer coefficient, W=ðm2 KÞ enthalpy, J/kg single phase conductivity, W=ðm KÞ interaction momentum exchange coefficient liquid length of tube, mm Liquid-vapor interfacial mass transfer rate evaporation mass flux liquid viscosity of phase q, kg=ðm sÞ turbulent viscosity for the mixture, kg=ðm sÞ molecular viscosity of mixture phase, kg=ðm sÞ bulk viscosity of phase q, kg=ðm sÞ diffusivity shear of phase q stress tenser of phase p source terms, kg=ðm s3 Þ source terms, kg=ðm s4 Þ mass flux from the bubble to liquid
As can be noticed from the study in the literature, few simulation studies are conducted for sub-cooled boiling in vertical flattened tubes. In this paper, a numerical investigation on the flow and heat transfer characteristic for sub-cooled water boiling in the vertical round and flattened tubes are conducted. 2. Physical and mathematical models
_ pq m _ qp m _ vt m ! nw Nw p q qC qE q_ lt qQ q_ v t qW Q pq , Q qp ! ! R pq , R qp Sq t Tw Tl T inlet T sat rT sub Vd ! mm ! ! v pq , v qp ! vg ! vl ! vq !
mp
x
mass transfer from the p to q phase mass transfer from q phase to p phase mass flux from the interface to vapor unit normal pointing away from the wall active nucleate site density, kg/m3 pressure, Pa heat flux, W/m2 convective heat flux, W/m2 evaporative heat flux, W/m2 heat transfer from the bubble to liquid, W/m2 quenching heat flux, W/m2 heat transfer from the interface to vapor, W/m2 wall heat flux, W/m2 heat exchange between phases, W interaction force between phases, N source term, W/m3 periodic time wall temperatures, K liquid temperatures, K inlet temperature, K saturation temperature, K subcooling, K volume of the bubble, m3 velocity of mixture phase m/s interphase velocity, m/s velocity of gas, m/s velocity of liquid, m/s velocity of phase q, m/s velocity of phase p, m/s vapor quality
Greek symbols ql single phase density, kg/m3 qm mixture density, kg/m3 qq primary phase density, kg/m3 qv vapor density, kg/m3 ap second phase volume fraction aq primary phase volume fraction av vapor phase volume fraction dt time scale
tubes. RPI wall boiling model is adopted. The conservation of mass, momentum and energy are solved with control-volume method. 2.2.1. Conservation equation Mass equation: @ @t
aq qq þ r aq qq ! mq ¼
2.2. Mathematical models In this paper, Eulerian multiphase model is employed to simulate the flow and heat transfer in vertical round and flattened
_ pq m _ qp þ Sq m
ð1Þ
p¼1
2.1. Physical models In the present work, upward sub-cooled water flow boiling in vertical round and flattened tubes with the total length of 2 m are adopted. The three-dimensional computational domain is presented in Fig. 1. Aspect ratios (AR = W/H): 1, 3, and 5 are investigated in this paper while the internal diameter of the round tube is 15.4 mm. Geometric dimensions of tubes are shown in Table 1.
n X
Momentum equation: The equation for conservation of momentum for the phase q yields: @ @t
aq qq ! m q þ r aq qq ! m q! m q ¼ aq rpþ r sq þ aq qq ! g þ
n ! P _ pq ! R pq þ m m pq m_ qp ! m qp
p¼1
! ! ! ! ! þ F q þ F lift;q þ F v m;q þ F td;q þ F wl;q ð2Þ q is the q phase stress-strain tensor and is expressed as: Here s
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
H.-z. Tao et al. / Annals of Nuclear Energy xxx (xxxx) xxx
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Fig. 1. Cross section and front view of computational geometry.
Table 1 Geometric dimensions. Tube
W (mm)
H (mm)
d (mm)
AR = 0 (Round tube) AR = 1 AR = 3 AR = 5
0.00 9.40 15.88 18.41
15.40 9.40 5.29 3.68
15.40 13.06 8.76 6.48
sq ¼ aq lq r! m q þ r! m q þ aq kq lq r ! m qI T
2 3
ð3Þ
Eq. (2) has to be closed with suitable expressions for the inter! phase force R pq , which is dependent on the pressure, cohesion, ! ! friction and other effects under the conditions that R pq ¼ R qp ! and R qq ¼ 0. n n X X ! ! ! R pq ¼ K pq m p m q p¼1
ð4Þ
p¼1
where K pq (=K qp ) is the interphase momentum exchange coefficient, ! m p and ! m q are the phase velocities. Energy equation: @ @t
@p ! q r! aq qq hq þ r aq qq ! u q hq ¼ aq @tq þ s u q r q q þ Sq
þ
Reynolds number model, the RNG theory provides an analyticallyderived differential formula for effective viscosity that accounts for low-Reynolds number flow. Therefore, the RNG k- e turbulence model is adopted due to its wide application range, economic operation cost and reasonable precision. 2.2.2. Wall boiling model Based on the RPI model (Kurul and Podowski, 1991), the total heat flux, which transfers heat from the wall to the liquid, is consists of three parts:
qW ¼ qC þ qQ þ qE
ð6Þ
The convective heat flux qC is expressed as:
qC ¼ hC ðT w T l Þð1 Ab Þ
ð7Þ
where hc Tw and Tl are the single-phase heat transfer coefficient, the wall and liquid temperatures, respectively. The proportion of heated wall surface is subdivided into area with nucleating bubbles Ab and area that is covered by the fluid (1-Ab). The quenching heat flux qQ is defined as:
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 kl ql C p;l f qQ ¼ pffiffiffiffiffiffiffiffiffi ðT w T l Þ pkl t
ð9Þ
where kl and t are the conductivity and the waiting time, kl ¼ kl =ql C pl is the diffusivity.
n ! P _ pq hpq m _ qp hqp Q pq þ m
p¼1
ð5Þ The heat exchange between phases must abide by the local balance conditions Q pq ¼ Q qp and Q qq ¼ 0. In the simulated conditions, not all of the flow states reach high Reynolds number. Even though the standard k- e model is a high-
Ab ¼ minð1; K
Nw pD2w Þ 4
ð8Þ
The empirical constant K is set based on Valle and Kenning (1985).
Ja sub K ¼ 4:8e 80
ð10Þ
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
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(a) Meshing graph with grid for differnent structures
Fig. 2. (a) Meshing graph with grid for differnent structures. (b) Grid independence test. (c) Experimented vs. simulated average vapor volume fraction. (d) Experimented vs. simulated bulk sub-cooling. (e) Experimented vs. simulated wall superheat.
DT w Dw ¼ min 0:0014; 0:0006e 45
The sub-cooled Jacob number Jasub is defined as:
Jasub ¼
ql C pl DT sub qv hf v
ð11Þ
where DT sub ¼ T sat T l The default bubble departure diameter, which is used in the RPI model, can be calculated by empirical correlations (Tolubinsky and Kostanchuk, 1970);
ð12Þ
The bubble departure frequency f is given by Robert (1960):
1 f ¼ ¼ T
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4gðql qg Þ 3dbw ql
ð13Þ
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
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Fig. 3. Effect of heat flux on heat transfer coefficient (G = 900 kg/(m2s)).
where H is the enthalpy of the bulk sub-cooling temperature, Hl denotes the enthalpy of saturation liquid, and Hlv is the latent heat.
3. Results and discussions 3.1. Model validation
3.3. Heat transfer coefficient The discretization results of the calculation region and the wall temperature under different grid numbers are shown in the Fig. 2 (a) and (b). The grid number has little influence on the simulation results when the number is more than 882,000. The model validation is conducted by comparing with experimental data from Bartolomej and Chanturiya (1967), Bartolomej et al. (1982). The correlation coefficients are 0.885 and 0.895 which indicate that adopted model could have accurate prediction on real situation (as shown in Fig. 2(c)–(e)). 3.2. Parameter definition Heat transfer coefficient is defined as:
h¼
q T w;i T b
ð14Þ
Tb is bulk sub-cooling temperature, Tw,i is . . .. Vapor quality is expressed as:
x¼
H Hl H lv
ð15Þ
3.3.1. Heat flux It is shown that heat flux has a significant effect on heat transfer coefficient of sub-cooled flow boiling as presented in Fig. 3. The variation of heat transfer coefficient is positively correlated with the heat flux (395.8 kW/m2, 475.0 kW/m2 and 570.0 kW/m2). The average heat transfer coefficient for tubes (AR = 0, 1, 3 and 5) are 2.57 kW/(m2K), 9.00 kW/(m2K), 8.58 kW/(m2K), and 7.22 kW/ (m2K), respectively. In this process, nucleate boiling heat transfer mechanism is dominant, which leads to the improvement of heat transfer coefficient. With the same vapor quality, the difference of heat transfer coefficient between two heat fluxes increase with the augmentation in vapor quality. For fixed heat flux, increasing in vapor quality results in an exponential increment in heat transfer coefficient, as presented in Fig. 3. This tendency is similar to the experimental results in circular tube of Yan et al. (2015). 3.3.2. Mass flux For experiments with different mass flux, the heat transfer coefficient convergent finally with increasing vapor quality. The effect
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
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Fig. 4. Effect of mass flux on heat transfer coefficient (q = 395.7 kW/m2).
Fig. 5. Effect of aspect ratio on heat transfer coefficient (q = 395.8 kW/m2).
of mass flux on sub-cooled flow boiling heat transfer coefficient is shown in Fig. 4. When mass flux increases from 990 kg/(m2s) to 1080 kg/(m2s), the heat transfer coefficient for tubes (AR = 0, 1, 3 and 5) increases for 0.79%, 5.54%, 8.48% and 0.12%, respectively. It was also found that the effect of mass flow rate on the heat transfer is more prominent at relatively small vapor quality value.
3.3.3. Aspect ratio The specific structure of the tubes can improve significantly the heat transfer performance of sub-cooled boiling. Fig. 5 illustrates the influence of the aspect ratio on the heat transfer coefficient. When AR is selected as 1, 3 and 5, the average heat transfer coefficient at G = 900 kg/(m2s) increases 7.90%, 19.23% and
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
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Fig. 6. Axial average vapor volume fraction with different heat fluxes (G = 900 kg/(m2s)).
20.06% compared with the round tube, AR = 0, respectively. And the average heat transfer coefficient at G = 1080 kg/(m2s) augments 9.85%, 23.42% and 24.90% (compared with AR = 0), respectively. The decrease of hydraulic diameter caused by the increase of AR (showed in Table 1) is the reason for the enhanced forced convection heat transfer and nucleate boiling heat transfer in confined channel. It indicates that the smaller hydraulic diameter is conducive to heat transfer in this study range. This conclusion can be verified by Bonjour and Lallemand (1998, 1997). AR increases from 3 to 5, the average heat transfer coefficient at two different mass fluxes increases 0.83% and 1.48%, respectively. It indicates that increase of AR has little influence on enhancing heat transfer coefficient when AR is over 3. 3.3.4. Heat flux The influence of heat flux on average vapor volume fraction is presented in Fig. 6. With the increases of heat flux and average vapor volume fraction, and ONB will occur earlier. When heat flux increases from 395.8 kW/m2 to 570.0 kW/m2, the increased average vapor volume fraction for AR = 0, 1, 3 and 5 are 0.10, 0.15, 0.20 and 0.17, respectively. At the same time, fluid generated steam earlier and more frequently.
In the liquid flow region (before the ONB), vapor volume fraction keeps constantly zero. Then vapor accumulates gradually along the axial direction after ONB to the maximum at the exit. In the fluid flow direction, steam first generates rapidly, and then tends to be gentle. Vapor that adhered on the heated wall rapidly grow due to liquid evaporation. Vapor eventually departs from the wall and moves to the bulk fluid, and then vanishes in the sub-cooling fluid which results in slowly increase in the vapor. More vapor fraction generates at the top of the tubes with higher heat flux. The wall surface temperature with constant flux input is higher than the bulk, which is reason that the steam volume fraction of the wall is higher than that of the bulk. The distribution of (as shown in Fig. 7) steam volume friction shows a similar trend with the fluid flows from the bottom of the pipe. 3.3.5. Mass flux The influence of mass flux on average vapor volume fraction in vertical tubes is analyzed and displayed in Fig. 8. Typically, the increment in mass flux leads to the reduction in average vapor volume fraction. With mass fluxes increases from 900 kg/(m2s) to 1080 kg/(m2s), the decrease of vapor volume fraction in axial
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
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Fig. 7. The contour of vapor volume fraction distribution with different heat flux (G = 900(kg/(m2s))).
Fig. 8. Axial average vapor volume fraction under different mass fluxes (q = 395.8 kW/m2).
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
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Fig. 9. Axial average vapor volume fraction under different aspect ratios (q = 395.8 kW/m2).
direction for AR = 0, 1, 3 and 5 are 0.0068, 0.0223, 0.0882 and 0.0937, respectively. 3.3.6. Aspect ratio The effect of aspect ratio on average vapor volume fraction in tubes is exhibited in Fig. 9. As aspect ratio increases, average vapor volume fraction augments and ONB occurs earlier for all tubes. AR increases from 0 to 1, 3 and 5, the increased average vapor volume at G = 900 kg/(m2s) is 0.01915%, 0.1671%, and 0.3137%, respectively, and for G = 1080 kg/(m2s) is 0.0192%, 0.1480%, and 0.1466%, respectively. As AR increases, hydraulic diameter decreases, heat gain per mass liquid increases, steam generates earlier and more steam accumulates at the outlet. 3.4. Pressure drop 3.4.1. Aspect ratio The irregularity of tube will increase the pressure drop of fluid flow. The pressure drop with different ARs of tubes is investigated (showed in Fig. 10). AR increases from 0 to 3, pressure drop at G = 900 kg/(m2s) and 1080 kg/(m2s) rises by average of 5.55% and 7.90% respectively. The pressure drop increases exponentially as the aspect ratio increases uniformly (Table 1). The relationship between pressure drop and aspect ratio at flow rate under 1080 kg/(m2s) and other specific conditions is obtained by nonlinear formula fitting:
y ¼ 16:7 þ 0:176ex=1:61
ð16Þ
In practice, pressure drop is related to other factors, and it requires a lot of experimental summary to get the mathematical expression of all factors. It can be concluded that the smaller hydraulic diameter with smaller tube height leads to larger pressure drop, as described by Quibén et al. Flattened tubes AR from 3 to 5, pressure drop increases sharply 15.60% and 17.33% at two different mass fluxes. It indicated that AR has obviously impact on pressure drop when AR is over 3 in this study without significant effect on heat transfer. 4. Conclusions Based on finite volume method, the present work focuses on the influences of heat flux, mass flux, and aspect ratio of tubes on the flow and heat transfer characteristics in vertical round and flattened tubes with sub-cooled flow boiling heat transfer. The
Fig. 10. Effect of aspect ratio on pressure drop under different cross sections (q = 395.8 kW/m2).
simulation results show a good agreement with the experiments data, which indicates that the adopted mathematics model can estimate the sub-cooling boiling heat transfer in the round and flattened tubes. Based on the simulation results, the following conclusions could be achieved: 1. Flattened tube could improve heat transfer performance at the cost of increased pressure drop. It is of engineering significance to study special-shaped tubes. Based on this geometry model, when AR increases from 0 to 3, heat transfer coefficient improves about 20%, and pressure drop increases about 7%. When AR increases from 3 to 5, heat transfer coefficient slightly enhances about 1%, and pressure drop sharply augments about 16%. Flattened tube AR = 3 is proposed for engineering applications in this study range after the comprehensive consideration. 2. Heat transfer coefficient is improved by increasing heat flux, mass flux and aspect ratio. As AR increase, heat transfer coefficient is enhanced, and the maximum increase in flattened tube heat transfer coefficient reaches 24.90%. 3. As a key parameter that reflect the fluid flow, the pressure drop is governed by fluid viscosity, steam velocity, liquid–vapor friction and heat flux changes. Increasing mass flux and AR both
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
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lead to the increase in pressure drop. However, the effect of AR on pressure drop is more obvious. In detail, pressure drop for flattened tube is higher than round tube, and the largest increased pressure drop reaches 22% when the flattened tube is used in this simulation research. 4. Augmenting heat flux, aspect ratio, and decreasing mass flux could promote the steam generation.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The computational resources generously provided by the HighPerformance Computing Center of Nanjing Tech University are greatly appreciated. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.anucene.2019.107144. References Bartolomej, G.G., Chanturiya, V.M., 1967. Experimental study of true void fraction when boiling subcooled water in vertical tubes. Therm. Eng. 14, 123–128. Bartolomej, G.G., Brantov, V.G., Molochnikov, Y.S., Kharitonov, Y.V., Solodkii, V.A., Batashova, G.N., Mikhailov, V.N., 1982. An experimental investigation of the true volumetric vapour content with subcooled boiling tubes. Thermal Eng. 29, 132–135. Bonjour, J., Lallemand, M., 1997. Effects of confinement and pressure on critical heat flux during natural convective boiling in vertical channels. Int. Commun. Heat Mass Trans. 24 (24), 191–200. Bonjour, J., Lallemand, M., 1998. Flow patterns during boiling in a narrow space between two vertical surfaces. Int. J. Multiphase Flow 24 (6), 947–960.
Cheng, L., Mewes, D., 2006. Review of two-phase flow and flow boiling of mixtures in small and mini channels. Int. J. Multiphase Flow 32 (2), 183–207. Cheng, L., Mewes, D., Luke, A., 2007. Boiling phenomena with surfactants and polymeric additives: a state-of-the-art review. Int. J. Heat Mass Transf. 50 (13– 14), 2744–2771. Hata, K., Masuzaki, S., 2009. Subcooled boiling heat transfer in a short vertical SUS304-tube at liquid Reynolds number range 5.19 10 4 to 7.43 10 5. Nucl. Eng. Des. 239 (12), 2885–2907. Hata, K., Masuzaki, S., 2010. Subcooled boiling heat transfer for turbulent flow of water in a short vertical tube. Proc. Natl. Heat Trans. Symp., 201–213 Huminic, G., Huminic, A., 2013. Numerical analysis of laminar flow heat transfer of nanofluids in a flattened tube. Int. Commun. Heat Mass Trans. 44 (5), 52–57. Kim, N.H., Lee, E.J., Byun, H.W., 2013. Evaporation heat transfer and pressure drop of R-410A in flattened smooth tubes having different aspect ratios. Int. J. Refrig. 36 (2), 363–374. Kurul, N., Podowski, M., On the modeling of multidimensional effects in boiling channels. In ANS Proc. 27th National Heat Transfer Conference 1991, pp. 28–31. Nasr, M., Akhavan-Behabadi, M.A., Marashi, S.E., 2010. Performance evaluation of flattened tube in boiling heat transfer enhancement and its effect on pressure drop q. Int. Commun. Heat Mass Trans. 37 (4), 430–436. Nemitallah, M.A., Habib, M.A., Mansour, R.B., Nakla, M.E., 2015. Numerical predictions of flow boiling characteristics: current status, model setup and CFD modeling for different non-uniform heatingprofiles. Appl. Therm. Eng. 75 (28), 451–460. Pierre, C.C.S., Bankoff, S.G., 1967. Vapor volume profiles in developing two-phase flow. Int. J. Heat Mass Transf. 10 (2), 237–249. Robert, C., 1960. A photographic study of pool boiling in the region of the critical heat flux. AICHE J. 6 (4), 533–538. Thome, J.R., Hajal, J.E., 2002. Simulation of flow patterns and evaporation in horizontal flattened tubes. Ashrae Trans. 108. Tolubinsky, V.I., Kostanchuk, D.M., Vapor bubbles growth rate and heat transfer intensity at subcooled water boiling. In 4th International Heat Transfer Conference 1970. Valle, V.H.D., Kenning, D.B.R., 1985. Subcooled flow boiling at high heat flux. Int. J. Heat Mass Transf. 28 (10), 1907–1920. Wilson, M.J., Newell, T.A., Chato, J.C., Ferreira, C.A.I., 2003. Refrigerant charge, pressure drop, and condensation heat transfer in flattened tubes. Int. J. Refrig. 26 (4), 442–451. Yan, J., Bi, Q., Liu, Z., Zhu, G., Cai, L., 2015. Subcooled flow boiling heat transfer of water in a circular tube under high heat fluxes and high mass fluxes. Fusion Eng. Des. 100, 406–418. Zhang, R., Cong, T., Tian, W., Qiu, S., Su, G., 2015b. Prediction of CHF in vertical heated tubes based on CFD methodology. Prog. Nucl. Energy 78, 196–200. Zhang, R., Cong, T., Tian, W., Qiu, S., Su, G., 2015a. Effects of turbulence models on forced convection subcooled boiling in vertical pipe. Ann. Nucl. Energy 80, 293– 302.
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes Han-zhong Tao a,⇑, Chuan-yang Xie a, Mi-mi Wang b a b
School of Energy Science and Engineering, Nanjing Tech University, Nanjing, Jiangsu, China Xuzhou Hong Kong and China Gas Company Limited, China
a r t i c l e
i n f o
Article history: Received 19 June 2019 Received in revised form 19 September 2019 Accepted 16 October 2019 Available online xxxx Keywords: Sub-cooled boiling Numerical simulation Heat transfer coefficient Average vapor volume fraction Pressure drop
a b s t r a c t Sub-cooled boiling is crucial in dominating the operation performance in several engineering processes. In spite of the experimental investigations conducted in the previous reports, the mechanism of how tube shape affects the heat transfer is still in vagueness. Here, a simulation study on the sub-cooled water flow boiling in tubes of various shapes is performed by adopting the RPI (Rensselaer Polytechnic Institute) model to elucidate the structural effect on the hydraulic and thermal performance, including the average vapor volume fraction and pressure drop. The results demonstrate that for tubes with aspect ratio (AR) ranging from 0 to 5 the heat transfer performance varies greatly, among which the testing tube with AR = 3 exhibits the supreme. The heat transfer coefficient and pressure drop show an around 20% and 7% enhancement, respectively, when the tube AR increases from 0 to 3. Our results show: for these geometric and physical models, when aspect ratio (AR = 0, 1, 3 and 5) of flattened tube is equal to 3 which has the best heat transfer performance and then tends to be stable. For other factors, the heat transfer coefficient enhances by increasing heat flux (395.8 kW/m2, 475 kW/m2 and 570.0 kW/m2), mass flux (900, 990 and 1080 kg/(m2s)). Heat transfer coefficient increases about 20%, pressure drop augments about 7% when the flattened tube’s AR increases from 0 to 3. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Flow boiling, with better heat transfer performance, was widely applied in industrial applications such as the boiler, power generation equipment, heat exchanger and so on, and has been intensively studied by means of experiments and developing empirical correlations to demonstrate its superiority in heat transfer. Pierre and Bankoff (1967) experimentally measured the void ratio on different sections of a vertical rectangular channel with sub-cooled boiling heat transfer. Bartolomej and Chanturiya (1967) experimentally investigated the wall superheat, bulk sub-cooling, and vapor volume fraction in vertical circular tubes. Yan et al. (2015), Hata and Masuzaki (2009, 2010) experimentally studied subcooled flow boiling under high heat flux and high mass flux (HHHM) in vertical tubes, and the corresponding correlations were proposed. However, experiments and empirical correlations are limited to specified and complicated conditions. Zhang et al. (2015a,b) analyzed the influence of different turbulence models on sub-cooled boiling in the vertical pipe with wall boiling model and two-phase model. And the k-e models were recommended for
⇑ Corresponding author. E-mail address: [email protected] (H.-z. Tao).
sub-cooled boiling. He also employed CHF (critical heat flux) model to investigate DNB (departed nucleate boiling regime) and critical heat flux. Nemitallah et al. (2015) used CFD with user-defined functions to analyze flow boiling characteristics in the highpressure system with non-uniform axial heating profiles. It indicated that non-uniform heating profiles improve the void fraction distribution and heat transfer coefficient. In the industrial field, there exist many applications of vertical tube flow heat transfer, such as boiler drum system et al. Flattened tubes, a passive technique, are used to improve heat transfer, especially in the heat exchanger. Kim et al. (2013), Nasr et al. (2010) experimentally studied pressure drop and heat transfer in flattened tubes. The results showed the pressure drop and the heat transfer coefficient have the positive correlation with the aspect ratio of tubes. These results are also suitable for the two-phase condensation (Wilson et al., 2003). The simulation analysis of flow heat transfer of nanofluids with laminar flow was conducted by Huminic and Huminic (2013). Thome and Hajal (2002) numerically analyzed the effects of different dimensions. The results pointed out that flow boiling heat transfer coefficients in horizontal flattened were 100– 150% higher than that in horizontal round tubes at the same mass velocity. Flattened tube, which has a smaller height than the circular tube, has a significant influence on boiling flow heat transfer characteristics (Cheng et al., 2007; Cheng and Mewes, 2006).
https://doi.org/10.1016/j.anucene.2019.107144 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
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Nomenclature Ab Aif CD Cl C p;l C p;v C wl d Dw f ! F !q F !lift;q F !wl F !v m;q F td g G Gk;m hC hf v hq hpq hsl H kl K pq , K qp l L lv _ m _E m
ll lt;m lm lq kl kq s Qq Qkm em
_ lt m
nucleating bubbles area, m2 Interfacial area, m2 the drag force coefficient lift force coefficient single phase specific heat, J=ðkg KÞ vapor phase specific heat, J=ðkg KÞ wall lubrication coefficient diameter of tube, mm default bubble departure diameter bubble departure frequency external body force, N lift force, N wall lubrication force, N virtual mass force, N turbulent dispersion force, N gravity mass flow rate, (kg/s) production of turbulence kinetic energy single phase heat transfer coefficient latent heat of evaporation, kJ/kg specific enthalpy of the qth phase, kJ/kg interphase enthalpy, kJ/kg the volumetric heat transfer coefficient, W=ðm2 KÞ enthalpy, J/kg single phase conductivity, W=ðm KÞ interaction momentum exchange coefficient liquid length of tube, mm Liquid-vapor interfacial mass transfer rate evaporation mass flux liquid viscosity of phase q, kg=ðm sÞ turbulent viscosity for the mixture, kg=ðm sÞ molecular viscosity of mixture phase, kg=ðm sÞ bulk viscosity of phase q, kg=ðm sÞ diffusivity shear of phase q stress tenser of phase p source terms, kg=ðm s3 Þ source terms, kg=ðm s4 Þ mass flux from the bubble to liquid
As can be noticed from the study in the literature, few simulation studies are conducted for sub-cooled boiling in vertical flattened tubes. In this paper, a numerical investigation on the flow and heat transfer characteristic for sub-cooled water boiling in the vertical round and flattened tubes are conducted. 2. Physical and mathematical models
_ pq m _ qp m _ vt m ! nw Nw p q qC qE q_ lt qQ q_ v t qW Q pq , Q qp ! ! R pq , R qp Sq t Tw Tl T inlet T sat rT sub Vd ! mm ! ! v pq , v qp ! vg ! vl ! vq !
mp
x
mass transfer from the p to q phase mass transfer from q phase to p phase mass flux from the interface to vapor unit normal pointing away from the wall active nucleate site density, kg/m3 pressure, Pa heat flux, W/m2 convective heat flux, W/m2 evaporative heat flux, W/m2 heat transfer from the bubble to liquid, W/m2 quenching heat flux, W/m2 heat transfer from the interface to vapor, W/m2 wall heat flux, W/m2 heat exchange between phases, W interaction force between phases, N source term, W/m3 periodic time wall temperatures, K liquid temperatures, K inlet temperature, K saturation temperature, K subcooling, K volume of the bubble, m3 velocity of mixture phase m/s interphase velocity, m/s velocity of gas, m/s velocity of liquid, m/s velocity of phase q, m/s velocity of phase p, m/s vapor quality
Greek symbols ql single phase density, kg/m3 qm mixture density, kg/m3 qq primary phase density, kg/m3 qv vapor density, kg/m3 ap second phase volume fraction aq primary phase volume fraction av vapor phase volume fraction dt time scale
tubes. RPI wall boiling model is adopted. The conservation of mass, momentum and energy are solved with control-volume method. 2.2.1. Conservation equation Mass equation: @ @t
aq qq þ r aq qq ! mq ¼
2.2. Mathematical models In this paper, Eulerian multiphase model is employed to simulate the flow and heat transfer in vertical round and flattened
_ pq m _ qp þ Sq m
ð1Þ
p¼1
2.1. Physical models In the present work, upward sub-cooled water flow boiling in vertical round and flattened tubes with the total length of 2 m are adopted. The three-dimensional computational domain is presented in Fig. 1. Aspect ratios (AR = W/H): 1, 3, and 5 are investigated in this paper while the internal diameter of the round tube is 15.4 mm. Geometric dimensions of tubes are shown in Table 1.
n X
Momentum equation: The equation for conservation of momentum for the phase q yields: @ @t
aq qq ! m q þ r aq qq ! m q! m q ¼ aq rpþ r sq þ aq qq ! g þ
n ! P _ pq ! R pq þ m m pq m_ qp ! m qp
p¼1
! ! ! ! ! þ F q þ F lift;q þ F v m;q þ F td;q þ F wl;q ð2Þ q is the q phase stress-strain tensor and is expressed as: Here s
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
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Fig. 1. Cross section and front view of computational geometry.
Table 1 Geometric dimensions. Tube
W (mm)
H (mm)
d (mm)
AR = 0 (Round tube) AR = 1 AR = 3 AR = 5
0.00 9.40 15.88 18.41
15.40 9.40 5.29 3.68
15.40 13.06 8.76 6.48
sq ¼ aq lq r! m q þ r! m q þ aq kq lq r ! m qI T
2 3
ð3Þ
Eq. (2) has to be closed with suitable expressions for the inter! phase force R pq , which is dependent on the pressure, cohesion, ! ! friction and other effects under the conditions that R pq ¼ R qp ! and R qq ¼ 0. n n X X ! ! ! R pq ¼ K pq m p m q p¼1
ð4Þ
p¼1
where K pq (=K qp ) is the interphase momentum exchange coefficient, ! m p and ! m q are the phase velocities. Energy equation: @ @t
@p ! q r! aq qq hq þ r aq qq ! u q hq ¼ aq @tq þ s u q r q q þ Sq
þ
Reynolds number model, the RNG theory provides an analyticallyderived differential formula for effective viscosity that accounts for low-Reynolds number flow. Therefore, the RNG k- e turbulence model is adopted due to its wide application range, economic operation cost and reasonable precision. 2.2.2. Wall boiling model Based on the RPI model (Kurul and Podowski, 1991), the total heat flux, which transfers heat from the wall to the liquid, is consists of three parts:
qW ¼ qC þ qQ þ qE
ð6Þ
The convective heat flux qC is expressed as:
qC ¼ hC ðT w T l Þð1 Ab Þ
ð7Þ
where hc Tw and Tl are the single-phase heat transfer coefficient, the wall and liquid temperatures, respectively. The proportion of heated wall surface is subdivided into area with nucleating bubbles Ab and area that is covered by the fluid (1-Ab). The quenching heat flux qQ is defined as:
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 kl ql C p;l f qQ ¼ pffiffiffiffiffiffiffiffiffi ðT w T l Þ pkl t
ð9Þ
where kl and t are the conductivity and the waiting time, kl ¼ kl =ql C pl is the diffusivity.
n ! P _ pq hpq m _ qp hqp Q pq þ m
p¼1
ð5Þ The heat exchange between phases must abide by the local balance conditions Q pq ¼ Q qp and Q qq ¼ 0. In the simulated conditions, not all of the flow states reach high Reynolds number. Even though the standard k- e model is a high-
Ab ¼ minð1; K
Nw pD2w Þ 4
ð8Þ
The empirical constant K is set based on Valle and Kenning (1985).
Ja sub K ¼ 4:8e 80
ð10Þ
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
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(a) Meshing graph with grid for differnent structures
Fig. 2. (a) Meshing graph with grid for differnent structures. (b) Grid independence test. (c) Experimented vs. simulated average vapor volume fraction. (d) Experimented vs. simulated bulk sub-cooling. (e) Experimented vs. simulated wall superheat.
DT w Dw ¼ min 0:0014; 0:0006e 45
The sub-cooled Jacob number Jasub is defined as:
Jasub ¼
ql C pl DT sub qv hf v
ð11Þ
where DT sub ¼ T sat T l The default bubble departure diameter, which is used in the RPI model, can be calculated by empirical correlations (Tolubinsky and Kostanchuk, 1970);
ð12Þ
The bubble departure frequency f is given by Robert (1960):
1 f ¼ ¼ T
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4gðql qg Þ 3dbw ql
ð13Þ
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
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Fig. 3. Effect of heat flux on heat transfer coefficient (G = 900 kg/(m2s)).
where H is the enthalpy of the bulk sub-cooling temperature, Hl denotes the enthalpy of saturation liquid, and Hlv is the latent heat.
3. Results and discussions 3.1. Model validation
3.3. Heat transfer coefficient The discretization results of the calculation region and the wall temperature under different grid numbers are shown in the Fig. 2 (a) and (b). The grid number has little influence on the simulation results when the number is more than 882,000. The model validation is conducted by comparing with experimental data from Bartolomej and Chanturiya (1967), Bartolomej et al. (1982). The correlation coefficients are 0.885 and 0.895 which indicate that adopted model could have accurate prediction on real situation (as shown in Fig. 2(c)–(e)). 3.2. Parameter definition Heat transfer coefficient is defined as:
h¼
q T w;i T b
ð14Þ
Tb is bulk sub-cooling temperature, Tw,i is . . .. Vapor quality is expressed as:
x¼
H Hl H lv
ð15Þ
3.3.1. Heat flux It is shown that heat flux has a significant effect on heat transfer coefficient of sub-cooled flow boiling as presented in Fig. 3. The variation of heat transfer coefficient is positively correlated with the heat flux (395.8 kW/m2, 475.0 kW/m2 and 570.0 kW/m2). The average heat transfer coefficient for tubes (AR = 0, 1, 3 and 5) are 2.57 kW/(m2K), 9.00 kW/(m2K), 8.58 kW/(m2K), and 7.22 kW/ (m2K), respectively. In this process, nucleate boiling heat transfer mechanism is dominant, which leads to the improvement of heat transfer coefficient. With the same vapor quality, the difference of heat transfer coefficient between two heat fluxes increase with the augmentation in vapor quality. For fixed heat flux, increasing in vapor quality results in an exponential increment in heat transfer coefficient, as presented in Fig. 3. This tendency is similar to the experimental results in circular tube of Yan et al. (2015). 3.3.2. Mass flux For experiments with different mass flux, the heat transfer coefficient convergent finally with increasing vapor quality. The effect
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
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Fig. 4. Effect of mass flux on heat transfer coefficient (q = 395.7 kW/m2).
Fig. 5. Effect of aspect ratio on heat transfer coefficient (q = 395.8 kW/m2).
of mass flux on sub-cooled flow boiling heat transfer coefficient is shown in Fig. 4. When mass flux increases from 990 kg/(m2s) to 1080 kg/(m2s), the heat transfer coefficient for tubes (AR = 0, 1, 3 and 5) increases for 0.79%, 5.54%, 8.48% and 0.12%, respectively. It was also found that the effect of mass flow rate on the heat transfer is more prominent at relatively small vapor quality value.
3.3.3. Aspect ratio The specific structure of the tubes can improve significantly the heat transfer performance of sub-cooled boiling. Fig. 5 illustrates the influence of the aspect ratio on the heat transfer coefficient. When AR is selected as 1, 3 and 5, the average heat transfer coefficient at G = 900 kg/(m2s) increases 7.90%, 19.23% and
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
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Fig. 6. Axial average vapor volume fraction with different heat fluxes (G = 900 kg/(m2s)).
20.06% compared with the round tube, AR = 0, respectively. And the average heat transfer coefficient at G = 1080 kg/(m2s) augments 9.85%, 23.42% and 24.90% (compared with AR = 0), respectively. The decrease of hydraulic diameter caused by the increase of AR (showed in Table 1) is the reason for the enhanced forced convection heat transfer and nucleate boiling heat transfer in confined channel. It indicates that the smaller hydraulic diameter is conducive to heat transfer in this study range. This conclusion can be verified by Bonjour and Lallemand (1998, 1997). AR increases from 3 to 5, the average heat transfer coefficient at two different mass fluxes increases 0.83% and 1.48%, respectively. It indicates that increase of AR has little influence on enhancing heat transfer coefficient when AR is over 3. 3.3.4. Heat flux The influence of heat flux on average vapor volume fraction is presented in Fig. 6. With the increases of heat flux and average vapor volume fraction, and ONB will occur earlier. When heat flux increases from 395.8 kW/m2 to 570.0 kW/m2, the increased average vapor volume fraction for AR = 0, 1, 3 and 5 are 0.10, 0.15, 0.20 and 0.17, respectively. At the same time, fluid generated steam earlier and more frequently.
In the liquid flow region (before the ONB), vapor volume fraction keeps constantly zero. Then vapor accumulates gradually along the axial direction after ONB to the maximum at the exit. In the fluid flow direction, steam first generates rapidly, and then tends to be gentle. Vapor that adhered on the heated wall rapidly grow due to liquid evaporation. Vapor eventually departs from the wall and moves to the bulk fluid, and then vanishes in the sub-cooling fluid which results in slowly increase in the vapor. More vapor fraction generates at the top of the tubes with higher heat flux. The wall surface temperature with constant flux input is higher than the bulk, which is reason that the steam volume fraction of the wall is higher than that of the bulk. The distribution of (as shown in Fig. 7) steam volume friction shows a similar trend with the fluid flows from the bottom of the pipe. 3.3.5. Mass flux The influence of mass flux on average vapor volume fraction in vertical tubes is analyzed and displayed in Fig. 8. Typically, the increment in mass flux leads to the reduction in average vapor volume fraction. With mass fluxes increases from 900 kg/(m2s) to 1080 kg/(m2s), the decrease of vapor volume fraction in axial
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
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Fig. 7. The contour of vapor volume fraction distribution with different heat flux (G = 900(kg/(m2s))).
Fig. 8. Axial average vapor volume fraction under different mass fluxes (q = 395.8 kW/m2).
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
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Fig. 9. Axial average vapor volume fraction under different aspect ratios (q = 395.8 kW/m2).
direction for AR = 0, 1, 3 and 5 are 0.0068, 0.0223, 0.0882 and 0.0937, respectively. 3.3.6. Aspect ratio The effect of aspect ratio on average vapor volume fraction in tubes is exhibited in Fig. 9. As aspect ratio increases, average vapor volume fraction augments and ONB occurs earlier for all tubes. AR increases from 0 to 1, 3 and 5, the increased average vapor volume at G = 900 kg/(m2s) is 0.01915%, 0.1671%, and 0.3137%, respectively, and for G = 1080 kg/(m2s) is 0.0192%, 0.1480%, and 0.1466%, respectively. As AR increases, hydraulic diameter decreases, heat gain per mass liquid increases, steam generates earlier and more steam accumulates at the outlet. 3.4. Pressure drop 3.4.1. Aspect ratio The irregularity of tube will increase the pressure drop of fluid flow. The pressure drop with different ARs of tubes is investigated (showed in Fig. 10). AR increases from 0 to 3, pressure drop at G = 900 kg/(m2s) and 1080 kg/(m2s) rises by average of 5.55% and 7.90% respectively. The pressure drop increases exponentially as the aspect ratio increases uniformly (Table 1). The relationship between pressure drop and aspect ratio at flow rate under 1080 kg/(m2s) and other specific conditions is obtained by nonlinear formula fitting:
y ¼ 16:7 þ 0:176ex=1:61
ð16Þ
In practice, pressure drop is related to other factors, and it requires a lot of experimental summary to get the mathematical expression of all factors. It can be concluded that the smaller hydraulic diameter with smaller tube height leads to larger pressure drop, as described by Quibén et al. Flattened tubes AR from 3 to 5, pressure drop increases sharply 15.60% and 17.33% at two different mass fluxes. It indicated that AR has obviously impact on pressure drop when AR is over 3 in this study without significant effect on heat transfer. 4. Conclusions Based on finite volume method, the present work focuses on the influences of heat flux, mass flux, and aspect ratio of tubes on the flow and heat transfer characteristics in vertical round and flattened tubes with sub-cooled flow boiling heat transfer. The
Fig. 10. Effect of aspect ratio on pressure drop under different cross sections (q = 395.8 kW/m2).
simulation results show a good agreement with the experiments data, which indicates that the adopted mathematics model can estimate the sub-cooling boiling heat transfer in the round and flattened tubes. Based on the simulation results, the following conclusions could be achieved: 1. Flattened tube could improve heat transfer performance at the cost of increased pressure drop. It is of engineering significance to study special-shaped tubes. Based on this geometry model, when AR increases from 0 to 3, heat transfer coefficient improves about 20%, and pressure drop increases about 7%. When AR increases from 3 to 5, heat transfer coefficient slightly enhances about 1%, and pressure drop sharply augments about 16%. Flattened tube AR = 3 is proposed for engineering applications in this study range after the comprehensive consideration. 2. Heat transfer coefficient is improved by increasing heat flux, mass flux and aspect ratio. As AR increase, heat transfer coefficient is enhanced, and the maximum increase in flattened tube heat transfer coefficient reaches 24.90%. 3. As a key parameter that reflect the fluid flow, the pressure drop is governed by fluid viscosity, steam velocity, liquid–vapor friction and heat flux changes. Increasing mass flux and AR both
Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144
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lead to the increase in pressure drop. However, the effect of AR on pressure drop is more obvious. In detail, pressure drop for flattened tube is higher than round tube, and the largest increased pressure drop reaches 22% when the flattened tube is used in this simulation research. 4. Augmenting heat flux, aspect ratio, and decreasing mass flux could promote the steam generation.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The computational resources generously provided by the HighPerformance Computing Center of Nanjing Tech University are greatly appreciated. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.anucene.2019.107144. References Bartolomej, G.G., Chanturiya, V.M., 1967. Experimental study of true void fraction when boiling subcooled water in vertical tubes. Therm. Eng. 14, 123–128. Bartolomej, G.G., Brantov, V.G., Molochnikov, Y.S., Kharitonov, Y.V., Solodkii, V.A., Batashova, G.N., Mikhailov, V.N., 1982. An experimental investigation of the true volumetric vapour content with subcooled boiling tubes. Thermal Eng. 29, 132–135. Bonjour, J., Lallemand, M., 1997. Effects of confinement and pressure on critical heat flux during natural convective boiling in vertical channels. Int. Commun. Heat Mass Trans. 24 (24), 191–200. Bonjour, J., Lallemand, M., 1998. Flow patterns during boiling in a narrow space between two vertical surfaces. Int. J. Multiphase Flow 24 (6), 947–960.
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Please cite this article as: H.-z. Tao, C. y. Xie and M. m. Wang, Numerical simulation study on the flow and heat transfer characteristics of sub-cooled boiling in vertical round and flattened tubes, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107144