- Email: [email protected]
A numerical study on condensation flow and heat transfer of refrigerant in minichannels of printed circuit heat exchanger
International Journal of Refrigeration 102 (2019) 96–111
Contents lists available at ScienceDirect
International Journal of Refrigeration journal homepage: www.elsevier.com/locate/ijrefrig
A numerical study on condensation flow and heat transfer of refrigerant in minichannels of printed circuit heat exchanger Zhongchao Zhao∗, Yanrui Zhang, Xudong Chen, Xiaolong Ma, Shan Yang, Shilin Li School of Energy and Power, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu, China
a r t i c l e
i n f o
Article history: Received 26 December 2018 Revised 5 March 2019 Accepted 15 March 2019 Available online 22 March 2019 Keywords: Printed circuit heat exchanger Minichannel Condensation flow Heat transfer Flow pattern
a b s t r a c t Printed circuit heat exchanger (PCHE), with the core comprising many mini/microchannels, have been extensively studied, but few works involved two-phase flow. A simplified channel model of PCHE hot side was herein established to numerically explore the heat transfer and condensation flow performance of R22 in minichannels under different conditions. The model was a semicircular minichannel with 0.91 mm hydraulic diameter and 50 mm full length. The heat flux was kept at −77,195 W m−2 , the inlet pressure was 0.63 MPa and the mass fluxes ranged from 58 to 93 kg m−2 s−1 . The condensation flow characteristics along the channel were analyzed. Four flow patterns, i.e., smooth-annular, wavy-annular, slug and bubbly, were noticed at different refrigerant mass fluxes and plotted as a flow pattern map. The effects of import vapor quality from 0.5 to 1 on pressure drop and heat transfer performance were evaluated. The heat transfer performance was optimal at the import vapor quality of 0.7. The impacts of refrigerant mass flux on pressure drop and local condensation heat transfer coefficient were assessed. Intermittent flow enhanced heat transfer. In addition, the correlations for local Nusselt number and Fanning friction factor were presented and compared with numerical data. © 2019 Elsevier Ltd and IIR. All rights reserved.
Étude numérique sur l’écoulement par condensation et le transfert de chaleur du frigorigène dans les mini-canaux d’un échangeur de chaleur à circuit imprimé Mots-clés: Échangeur de chaleur à circuit imprimé; Mini-canal; Écoulement par condensation; Transfert de chaleur; Configuration d’écoulement
1. Introduction Printed circuit heat exchanger (PCHE), a mini/microchannel heat exchanger, was devised in Australia in 1980 and developed by Heatric in England in the same year (Baek et al., 2012). PCHE is a compact and efficient heat exchanger in which flow paths are generated by photochemical etching on metal plates. Then the plates are tightly connected by diffusion bonding to form the heat exchanger core (Nikitin et al., 2006). Due to special processing technology, PCHE has been widely used in various fields with excellent properties, such as small hydraulic diameter, high heat exchange efficiency, temperature resistance and pressure resistance. Researchers have endeavored to study the
∗
Correspondence author. E-mail address: [email protected] (Z. Zhao).
https://doi.org/10.1016/j.ijrefrig.2019.03.016 0140-7007/© 2019 Elsevier Ltd and IIR. All rights reserved.
thermal-hydraulic performance of PCHE through experimental and numerical methods. Kim and No (2011) studied the thermalhydraulic characteristics for PCHE with horizontal and vertical layouts in helium-water conditions by experiments and CFD simulations. Shin and No (2017) experimentally studied the pressure drop and flow instability of water in a PCHE applied as a SMRs steam generator. Besides, Mylavarapu et al. (2014) also experimentally explored the thermal-hydraulic characteristics of two PCHEs at the HTHF, where the working fluid is helium. Wang et al. (2015) explored the heat transfer of supercritical water in a narrow annulus experimentally and numerically. Aneesh et al. (2016) assessed the effects of various working conditions and channel arrangements on the thermal-hydraulic characteristics of PCHE in helium-helium conditions by using the CFD model. Additionally, Yoon et al. (2014) derived correlations of Fanning factor and Nusselt number applied to airfoil fin PCHE by CFD, and evaluated the thermal–hydraulic performances of PCHEs for different channel
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Nomenclature P h G PCHE T
pressure (Pa) heat transfer coefficient (W m− 2 K−1 ) mass flux (kg m−2 s−1 ) printed circuit heat exchanger temperature (K)
F
surface tension source term (N m−3 s−1 )
u
velocity vector (m s−1 ) pressure drop (Pa) mass source term (kg m−3 s−1 ) energy source term (J m−3 s−1 ) thermal conductivity (W m−1 K−1 ) specific internal energy (J kg−1 ) constant volume specific heat (J kg−1 K−1 ) gravity acceleration (m s−2 ) latent heat for liquid-vapor phase change (J kg−1 ) heat flux (W m−2 ) vapor quality axial local (mm) Nusselt number Reynolds number Prandtl number Fanning friction factor hydraulic diameter
P S SE k E cv g hlv q x z Nu Re Pr f Dh Greeks
ρ α μ γ σ
density (kg m−3 ) volume fraction dynamic viscosity (kg m−1 s−1 ) kinematic viscosity (m2 s−1 ) surface tension (N m−1 )
Subscripts v vapor l liquid e effective s saturation b bulk in inlet out outlet ave average pred prediction c critical r reduced f frictional de deceleration types. Jeon et al., (2016) numerically investigated the thermal performance of a heterogeneous PCHE, using S-CO2 and LNG flue gas as cold fluid and hot fluid respectively. Kim and No (2013) experimentally and numerically analyzed a PCHE, using He–CO2 mixture and water as working fluids. Although PCHEs have been widely studied, PCHE single-phase working fluids were mostly used, without involving phase transition processes. The two-phase flow in mini/microchannels of PCHE has seldom been referred. The core of PCHE consists of many mini/microchannels. Compared to conventional channels, the flows in mini/microchannels are slightly different, which are more prone to factors such as surface tension, wall wettability and roughness, exhibiting different flow characteristics and transformation mechanisms (Shao et al., 2009). In addition, the two-phase flow characteristics and patterns can strongly affect heat transfer. Two-phase condensation flow in mini/microchannels has attracted extensive attention, laying a theoretical foundation for the development of heat transfer technolo-
97
gies and compact heat exchangers. Wang et al. (2017) experimentally studied condensation flow and pressure drop for R134a in microchannels, and observed four flow patterns. Liu et al. (2016) experimentally assessed the impacts of different operating parameters on the condensation heat transfer and pressure of working fluid in circular and square minichannels. Besides, Chen et al. (2014) researched the condensation flow of FC-72 in a rectangular microchannel (Dh =1 mm) using a two-phase volume of fluid (VOF) model. Kim et al. (2012) and Kim and Mudawar (2012) performed experiments to study the condensation and heat transfer characteristics of FC-72 inside parallel microchannels with L of 29.9 cm (Dh =1 mm). High-speed video and photography techniques have been used to observe the transformation of two-phase flow regimes. Vanderputten et al. (2017) developed a test bed to study the condensation flow for R-134a inside square microchannels and evaluated the predictability of various flow maps. Zhang et al. (2016) numerically researched the influences of aspect ratio, mass flux and vapor quality on the heat transfers and pressure differences of R410A and R134a through horizontal round and flattened minichannels. Additionally, Al-Zaidi et al. (2017) experimentally investigated the condensation flow regimes and heat transfer of HFE-7100 inside microchannels. Ramírez-Rivera et al. (2015) tested the two-phase pressure drops for R134a and R32 at minichannel tubes through condensation and boiling experiments. Moreover, Kim and Mudawar (2013)and Kim and Mudawar (2012) proposed a novel universal approach for forecasting the coefficient of heat transfer and frictional pressure gradient of condensation flow in mini/microchannel. Bohdal et al. (2011) experimentally researched the condensations for R134a and R404A refrigerants in minichannels of single pipe, and presented the empirical correlation of local heat transfer coefficient. We herein used a simplified channel model of PCHE hot side to investigate the condensation flow in minichannels. The model was verified through experimental data, and then utilized to study the condensation flow and heat transfer characteristics for R22 inside minichannels of PCHE at different inlet vapor qualities and mass fluxes. New local Nusselt number correlations were proposed for annular flow and transition from annular to slug and bubbly flow respectively. The Fanning friction factor correlation of two-phase condensation flow was also fitted by simulation data. Meanwhile, the accuracies of the proposed correlations were tested by comparison with numerical data.
2. Numerical methodology 2.1. Geometrical model and boundary conditions The internal core structure of the tested PCHE is schematized in Fig. 1. It is rather complicated to simulate the flow processes of the entire PCHE because of limited computing resource and time, so this paper concentrated on the condensation flow and heat transfer of R22 inside hot channels. The simplified model was a single straight channel on hot side of PCHE with the overall length of 50 mm (Fig. 2(a)). The channel cross-section was semicircular, with a 2 mm width and a 1.75 mm height (Fig. 2(b)). The following assumptions were made: (1) PCHE was operated in the steady state. (2) The R22 flow was distributed uniformly in each hot channel with identical temperature and mass flux profiles. (3) Pressure hardly affected the physical properties of R22, because pressure drop through the channel was negligible compared to the operating pressure. Three types of surfaces were set in the computational model, i.e. inlet, outlet and wall. The boundary conditions for the inlet and outlet were respectively set as mass flow inlet and outflow. There were two kinds of walls in the calculation model, where the
98
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Fig. 1. Schematic diagram of internal core structure of tested PCHE.
Fig. 2. Numerical model and boundary conditions.
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
99
surface between fluid area and solid area was a coupled wall. The boundary conditions for outer walls are displayed in Fig. 2(b). 2.2. Mathematical modeling The VOF model is a kind of surface tracking method under a fixed Euler mesh. The governing equations based on the VOF model are as follows: 1. Continuity equations
∇ · αv ρv uv = Sv
(1)
∇ · αl ρl ul = Sl
(2)
∂v + ∂l = 1
(3)
Eqs. (1) and (2) are the continuity equations of vapor phase and liquid phase respectively, where α v is the volume fraction of vapor phase, α l is that of liquid phase, Sv and Sl are the vapor
Fig. 3. Sectional view of channel mesh for PCHE model.
and liquid mass source terms respectively, and u is the velocity vector. 2. Momentum equation
T ∇ ρ uu = −∇ p + ∇ μ ∇ u + ∇ u + ρg + F
Vapor mass source term : Sv =
(4)
s) fe αl ρl (T −T , T > Ts Ts s) fc αv ρv (T −T , T < Ts Ts
) fe αl ρl (TsT−T , T > Ts s
(12)
Where ρ and μ are the density and viscosity of mixture given by:
Liquid mass source term : Sl =
ρ = αl ρl + αv ρv
(5)
where fe and fc are adjustable mass transfer factors for evaporation and condensation, respectively. SE in Eq. (8) is the energy source term determined as:
(6)
SE = hl v Sl
and
μ = αl μl + αv μv
) fc αv ρv (TsT−T , T < Ts s
The surface tension F between two contacting phases, which is calculated through the continuum surface force (CSF) model (Brackbill et al., 1992), is calculated by:
in which hlv is the latent heat of vaporization for refrigerant. The thermal conduction equation in solid region is:
where λ is the thermal conductivity of solid wall. The transport equations of the realizable κ -ε model are:
ρ ∇ · nˆ ∇ αl F =σ 1 ( ρl + ρv ) 2
(7)
in which σ is the surface tension coefficient and nˆ is the unit normal vector determined as nˆ = ∇ αl /|∇ αl |. 3. Energy equation
∇ · u ( ρ E + p ) = ∇ · ( ke ∇ T ) + SE
(8)
where SE is the energy source term and ke is the effective thermal conductivity for mixture calculated by:
ke = αv kv + αl kl
(9)
E is the specific internal energy calculated by:
E=
αv ρv Ev + αl ρl El αv ρv + αl ρl
(10)
∂ ∂ ρκ u j (ρκ ) + ∂t ∂xj
∂ μt ∂κ = + Gκ + Gb − ρε − YM + Sκ μ+ ∂xj σκ ∂ x j ∂ ∂ ρε μ j (ρε ) + ∂t ∂xj
∂ μ ∂ε ε2 = + ρC1 Sε − ρC2 μ+ t √ ∂xj σε ∂ x j κ + γε ε + C1ε C3ε Gb + Sε κ
(14)
(15)
(16)
(17)
Where the detailed parameters were recommended by the FLUENT help manual (FLUENT 6.3 User’s Guide 2006).
where Ev and El are determined as:
Ei = cv,i (T − Ts ), i = v or l
∇ (λ∇ T ) = 0
(13)
(11)
where cv is the constant-volume specific heat and Ts is the saturation temperature. For the source terms in the governing equations, different computational submodels are added to simulate the vapor-liquid phase changes at the interface. The mass source terms Sv and Sl in Eqs. (1) and (2) are defined as (Yang et al., 2008):
2.3. Grid and solution methodology The numerical model was meshed into hexahedral and wedge elements by Gambit (Fig. 3). Grid-independent verification was necessary to ensure the accuracy of extensive case research. We compared the simulation results of six sets of grid numbers under the condition that the R22 inlet pressure was 0.63 MPa and the inlet temperature was 287.6 K (Table 1). Ultimately, the grid of
100
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Table 1 Mesh independence study. Grid number
6.53 × 105
9.19 × 105
1.32 × 106
2.07 × 106
3.6 × 106
4.18 × 106
Real value
Outlet temperature (K)
267.12
265.5
262.43
261.8
261.5
261.32
260.78
Table 2 Thermo-physical properties of R22.
average temperature of fluid given by:
Parameter
Liquid phase
Vapor phase
ρ (kg m ) C p (kJ kg−1 K−1 ) μ (kg m−1 s−1 ) k (mW m−1 K−1 ) hl v (kJ kg−1 ) σ (mN m−1 )
1255.8 1.19 1.99 ×10−4 91.398 198.89 10.594
26.697 0.77 1.168 ×10−5 9.925 198.89 10.594
−3
2.07 × 106 was employed for the accuracy and efficiency of subsequent study. The simulation was performed by the FLUENT software. The source terms in governing equations were considered by loading user-defined functions. The realizable k-ε model was selected for flow turbulence according to a previous literature (Huang et al., 2011). The VOF model and CSF model were used as the twophase flow model and surface tension model respectively. Velocitypressure coupling was solved using the PISO solution algorithm. The body force weighted scheme was selected for pressure and the power law scheme was selected for momentum. The other items were discretized with the second order upwind scheme. Condensation heat transfer coefficient and pressure drop were used to analyze the condensation flow and heat transfer of R22 in PCHE minichannels. The pressure drop data was extracted directly from FLUENT software. The condensation heat transfer coefficient h was determined by:
h=
q Tb − Twall
(18)
in which q is the heat flux applied to wall, Twall is the areaweighted average temperature of wall and Tb is the mass-weighted
n Ti ρiVi Tb = i=1 n i=1 ρiVi
(19)
in which ρ i , Vi , Ti are the density, volume and temperature of the ith grid. The thermo-physical properties of R22 were obtained from REFPROP software. Table 2 lists the simulated thermo-physical properties of R22 at the saturation temperature of 280.59 and the pressure of 0.63 MPa. 3. Results and discussion 3.1. Model verification An experimental rig was designed to study the heat transfer performance for PCHE, using N2 and R22 as cold fluid and hot fluid respectively, which consisted of a N2 loop, a refrigerant R22 loop and a heating water loop (Fig. 4). Through selected laser sintering, a 3D printing technology, the tested crossflow PCHE was fabricated, with airfoil cold channel and straight hot channel (Fig. 5). During the experiment, some parameters such as temperature, pressure and mass flow rate of the inlet and outlet of R22 and liquid nitrogen were measured, which were used for thermal balance analysis, determination of heat flux in boundary conditions and verification of R22 condensation model for numerical study. Before numerical studies, the accuracy of this model was first verified through experimental data by the following equation:
CF D − Experiment
Error =
Expriment
× 100% .
(20)
We selected 25 sets of experimental conditions of R22 in hot side for simulation, and compared the numerical outlet
Fig. 4. Schematic diagram of test rig.
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
101
Fig. 5. Tested PCHE.
Fig. 6. Outlet temperature on hot side of PCHE (CFD vs. experiment).
temperature and pressure drop with the experimental ones. The errors between the outlet temperatures of simulation and experiment are shown in Fig. 6. The maximum error was 2.5% and the minimum one was 0.3%, and the numerical outlet temperatures agreed well with the experimental ones, with a 1.35% average error. The error map for pressure drop is shown in Fig. 7, with a 5% minimum error and a 24% maximum error. All the numerical pressure drops were smaller than the experimental ones, because the numerical model is idealized with smooth inner wall of the channel. Besides, the inlet and outlet pressure drop contained in the
experimental pressure drop was not considered during simulation. Collectively, this model can be reliably applied to extensive numerical research. 3.2. Two-phase flow patterns The validated model was applied for simulating the R22 condensation flow patterns in PCHE minichannels. The heat flux was kept at −77,195 W m−2 and the mass fluxes ranged from 58 to 93 kg m−2 s−1 . The cross sections at various vapor qualities and
102
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Fig. 7. Pressure drop on hot side of PCHE (CFD vs. experiment).
the mass flux of 58 kg m−2 s−1 were obtained to observe the twophase distribution along the flow (Fig. 8). Liquid phase first appeared at the sharp corners where the upper and lower surfaces of channel met along the flow direction, and then extended toward the middle along the surface. Finally, the vapor phase at the channel center condensed into liquid phase, and the refrigerant became supercooled liquid at the outlet. Fig. 9 shows the velocity vector at x = 0.47. The flow velocity was low at the sharp corner, accompanied by vortex flow, so the fluid began to exchange heat more effectively. As a result, liquid phase first appeared at the sharp corners. Since heat flux was applied to the fluid from the upper and lower surfaces, the fluid near the surface liquefied earlier than that at the center did. The flow pattern analysis of simulation results revealed four different flow patterns at various locations and mass fluxes (Table 3). The annular flow existed at each mass flux and became dominant at high mass fluxes. The annular flow can be classified into smooth annular flow and wavy annular flow, with the former typified by a smooth and indistinguishable liquid film along the channel inner wall and the latter characterized by a thick and wavy liquid film. Other flow patterns, such as slug and bubbly ones, were also observed at low mass fluxes (G = 58, 64 and 69 kg m−2 s−1 ), whereas the bubbly pattern appeared only at the mass fluxes of 58 and 64 kg m−2 s−1 . The slug flow has characteristic long, isolated bubbles flowing in the liquid phase, while the bubbly flow features small bubbles. The above flow patterns at different mass fluxes were plotted as a flow pattern map (Fig. 10). The bubbly, the slug, wavy-annular and smooth-annular patterns appeared sequentially with increasing vapor quality. Along the flow direction, the flow pattern was
converted from annular to bubbly at low mass fluxes, and from smooth-annular to wavy-annular at high mass fluxes. 3.3. Impact of inlet vapor quality The effects of import vapor quality from 0.5 to 1 on heat transfer and pressure drop were explored at the mass flux of 58 kg m−2 s−1 . The inlet pressure was 0.63 MPa and the saturation temperature was 280.59 K. Fig. 11 shows the effects of import vapor quality on local condensation heat transfer coefficient. The coefficient increased first and then decreased along the channel at the same inlet quality. Given that the refrigerant condensed continuously to a completely liquid phase with the flow (Fig. 12), the phase-change heat transfer was stronger than the single-phase heat transfer due to latent heat. The position of complete liquefaction differed at various inlet vapor qualities. In addition, the local condensation heat transfer coefficient increased with reducing inlet vapor quality before complete liquefaction, and then dropped after complete liquefaction. The trend before complete liquefaction may be attributed to flow pattern conversion of the coefficient. After complete liquefaction, however, the condensation accelerated at a low inlet quality. At the same channel position, the fluid temperature and the temperature difference of wall surface reduced, thus decelerating heat exchange and decreasing the heat transfer coefficient. Fig. 13 displays the influences of inlet vapor quality on pressure. The fluid pressure drop in the channel varied irregularly along with the import vapor quality, reaching minimum and maximum at the import qualities of 0.7 and 1, respectively. As exhibited in Fig. 14, the average heat transfer coefficient comes up to maximum and
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
103
Fig. 8. Cross-sectional views of two-phase distribution at different vapor qualities.
minimum at the import qualities of 0.8 and 0.7 respectively. Moreover, the coefficient at 0.8 inlet quality was 6.5% higher than that at 0.7 inlet quality, and the pressure drop was 20% higher. Thus, the heat transfer performance was optimal at the import vapor quality of 0.7.
wavy-annular flow exceeded that of smooth-annular flow (Kim and Mudawar, 2012; Agarwal and Garimella, 2010). As demonstrated in Fig. 16, the total pressure drop rises with rising R22 mass flux, possibly because raising the vapor velocity increased the interfacial shear force between the formed liquid film and R22 vapor.
3.4. Impact of refrigerant mass flux The impact of R22 mass flux on pressure difference and local condensation heat transfer coefficient was tested through simulation at the mass fluxes of 58, 64, 69, 75, 81, 87 and 93 kg m−2 s−1 , the import vapor quality of 0.7 and the inlet pressure of 0.63 MPa. As displayed in Fig. 15, the local condensation heat transfer coefficient rises with rising R22 mass flux. At higher mass flux, the interfacial vapor shear stress was elevated, giving thinner liquid film and lower thermal resistance, being consistent with the results of Kim and Mudawar (2012), Al-Zaidi et al. (2017) and Al-Hajri et al. (2013). In addition, the local condensation heat transfer coefficient increased along the fluid flow direction when the mass flux is constant, probably because of flow pattern conversion of the coefficient. In contrast to the previous flow pattern map (Fig. 10), the flow pattern was converted from annular to intermittent along the flow direction. Accordingly, intermittent flow enhanced heat transfer by attenuating the liquid film, the heat transfer coefficient of
3.5. Proposal of Nusselt number and Fanning friction factor correlations According to the simulation data at various mass fluxes, a numerical correlation that described the local Nusselt number of R22 in PCHE minichannel was obtained by regression analysis, for annular flow:
Nu = 6.4048 × Re0.9357 × P r −8.0262 × Pr −0.1047 ×
x −0.5746 1−x (21)
for transition from annular to slug and bubbly flow:
Nu = 88.4387 × Re−0.2437 × P r −9.4989 × Pr −4.728 ×
x −0.0646 1−x (22)
104
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Fig. 9. Velocity vector at x = 0.475.
Table 3 Representative flow patterns with corresponding vapor quality at different mass fluxes.
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Fig. 10. Flow pattern map at seven mass fluxes from 58 to 93 kg m−2 s−1 .
Fig. 11. Impact of inlet vapor quality on local condensation heat transfer coefficient.
105
106
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Fig. 12. Flow patterns at different inlet vapor qualities.
Fig. 13. Effect of import vapor quality on pressure.
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Fig. 14. Average heat transfer coefficient and pressure drop at different import vapor qualities.
Fig. 15. Impact of refrigerant mass flux on local condensation heat transfer coefficient.
107
108
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Fig. 16. Impact of refrigerant mass flux on pressure.
Fig. 17. Contrast of predicted Nusselt number with simulation values for annular flow.
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Fig. 18. Contrast of predicted Nusselt number with simulation values for transition from annular to slug and bubbly flow.
Fig. 19. Contrast of predicted Fanning friction factor with simulation values.
109
110
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
where Re stands for Reynolds number and Pr stands for the reduced pressure given by:
u Dh
Re = Pr =
γ
P Pc
(23) (24)
where Dh represents the hydraulic diameter, γ represents the kinematic viscosity, and Pc represents the critical pressure. The Nusselt number Nu was calculated by the equation below:
Nu =
hDh . k
(25)
The Fanning friction factor correlation of two-phase condensation flow was also fitted by simulation data:
ft p = 0.04839 × Re−0.2986
minimum at the 0.7 inlet quality and maximum at the 1 inlet quality. The heat transfer performance was optimized at the import vapor quality of 0.7. (5) The local condensation heat transfer coefficient increased with rising R22 mass flux. Furthermore, the coefficient increased along the flow direction at the same mass flux, indicating that intermittent flow augmented heat transfer. As the refrigerant mass flux increased, the total pressure drop was elevated. (6) The local Nusselt number and Fanning friction factor correlations for R22 condensation flow and heat transfer in PCHE minichannel were in good agreement with the numerical data.
(26)
Conflict of interest None.
where ftp was calculated by:
ft p =
P f D h 2Lρb u2b
Acknowledgment
(27)
where L represents the channel length, ρ b and ub represent the bulk mean density and bulk mean velocity of R22, and Pf is the frictional pressure drop calculated by:
Pf = P + Pde = P + ρin u2in − ρout u2out
(28)
To evaluate the accuracy of the proposed correlations, the error was tested:
pred − CF D Error = × 100% . CF D
The authors gratefully acknowledge that this work was supported by Jiangsu Marine and Fishery Science and Technology Innovation and Extension Project (HY2017-8) and Zhenjiang Funds for the Key Research and Development Project (GY2016002-1).
(29)
Fig. 17 compares 104 numerical annular flow data with correlated Nusselt number, showing a 26% maximum error. Additionally, Fig. 18 compares 78 numerical values of transition from annular to slug and bubbly flow with correlated Nusselt number, exhibiting a 25% maximum error. Hence, the heat transfer characteristics for R22 in PCHE minichannel can be well predicted by the proposed correlations. Furthermore, Fig. 19 compares the Fanning friction factor calculated by correlation with numerical values, suggesting a satisfactory predictability with a 5% maximum error. 4. Conclusions The condensation flow of R22 in minichannels of PCHE hot side (Dh = 0.91 mm) was studied. A simplified channel model was established to numerically investigate the condensation flow and heat transfer characteristics in minichannels under various working conditions. The main findings are as follows: (1) The error between outlet temperatures of simulation and experiment was ≤2.5% and that of pressure drop was ≤25%, proving that the numerical model and methods were reliable. (2) During condensation, liquid phase first appeared at the sharp corners where the top and bottom surfaces of the channel met along the flow direction, and then extended toward the middle along the surface. (3) Smooth-annular, wavy-annular, slug and bubbly flow patterns were discovered at different refrigerant mass fluxes and plotted as a flow pattern map. Increasing the mass flux of R22 extended the annular region downstream with reducing vapor quality. (4) The local condensation heat transfer coefficient rose first and then decreased along the channel at the same inlet quality. The coefficient rose with decreasing inlet vapor quality before complete liquefaction. The fluid pressure drop in the channel changed irregularly along with the inlet vapor quality, reaching
References Agarwal, A., Garimella, S., 2010. Representative results for condensation measurements at hydraulic diameters ∼100 Microns. J. Heat Transf. 132, 1667–1681. doi:10.1115/IMECE2007-43749. Al-Hajri, E., Shooshtari, A.H., Dessiatoun, S., Ohadi, M.M., 2013. Performance characterization of R134a and R245fa in a high aspect ratio microchannel condenser. Int. J. Refrig. 36, 588–600. doi:10.1016/j.ijrefrig.2012.10.007. Al-Zaidi, A.H., Mahmoud, M.M., Karayiannis, T.G., 2017. Condensation flow patterns and heat transfer in horizontal microchannels. Exp. Therm. Fluid Sci. 90, 153– 173. doi:10.1016/j.expthermflusci.2017.09.009. Aneesh, A.M., Sharma, A., Srivastava, A., Vyas, K.N., Chaudhuri, P., 2016. Thermalhydraulic characteristics and performance of 3D straight channel based printed circuit heat exchanger. Appl. Therm. Eng. 98, 474–482. doi:10.1016/j. applthermaleng.2015.12.046. Baek, S., Kim, J.H., Jeong, S., Jung, S., 2012. Development of highly effective cryogenic printed circuit heat exchanger (PCHE) with low axial conduction. Cryogenics 52, 366–374. doi:10.1016/j.cryogenics.2012.03.001. Bohdal, T., Charun, H., Sikora, M., 2011. Comparative investigations of the condensation of R134a and R404A refrigerants in pipe minichannels. Int. J. Heat Mass Transf. 54, 1963–1974. doi:10.1016/j.ijheatmasstransfer.2011.01.005. Brackbill, J.U., Kothe, D.B., Zemach, C., 1992. A continuum method for modeling surface tension, J. Comput. Phys. 100, 335–354. doi:10.1016/0021- 9991(92)90240- Y. Chen, S., Yang, Z., Duan, Y.Y., Chen, Y., Wu, D., 2014. Simulation of condensation flow in a rectangular microchannel. Chem. Eng. Process. Process. Intensif. 76, 60–69. doi:10.1016/j.cep.2013.12.004. FLUENT 6.3 User’s Guide. Fluent, Inc. Lebanon, NH, 2006 September. Huang, M., Yang, Z., Duan, Y.Y., Lee, D.J., 2011. Bubble growth for boiling bubbly flow for R141b in a serpentine tube. J. Taiwan Inst. Chem. Eng. 42, 727–734. doi:10.1016/j.jtice.2011.02.007. Jeon, S., Baik, Y.J., Byon, C., Kim, W., 2016. Thermal performance of heterogeneous PCHE for supercritical CO2 energy cycle. Int. J. Heat Mass Transf. 102, 867–876. doi:10.1016/j.ijheatmasstransfer.2016.06.091. Kim, I.H., No, H.C., 2011. Thermal hydraulic performance analysis of a printed circuit heat exchanger using a helium–water test loop and numerical simulations. Appl. Therm. Eng. 31, 4064–4073. doi:10.1016/j.applthermaleng.2011.08.012. Kim, I.H., No, H.C., 2013. Thermal-hydraulic physical models for a printed circuit heat exchanger covering He, He–CO2 mixture, and water fluids using experimental data and CFD. Exp. Therm. Fluid Sci. 48, 213–221. doi:10.1016/j. expthermflusci.2013.03.003. Kim, S.M., Kim, J., Mudawar, I., 2012. Flow condensation in parallel micro-channels – part 1: experimental results and assessment of pressure drop correlations. Int. J. Heat Mass Transf. 55, 971–983. doi:10.1016/j.ijheatmasstransfer.2011.10.013. Kim, S.M., Mudawar, I., 2012. Flow condensation in parallel micro-channels – part 2: heat transfer results and correlation technique. Int. J. Heat Mass Transf. 55, 984–994. doi:10.1016/j.ijheatmasstransfer.2011.10.012. Kim, S.M., Mudawar, I., 2012. Universal approach to predicting two-phase frictional pressure drop for adiabatic and condensing mini/micro-channel flows. Int. J. Heat Mass Transf. 55, 3246–3261. doi:10.1016/j.ijheatmasstransfer.2012.02.047. Kim, S.M., Mudawar, I., 2013. Universal approach to predicting heat transfer coefficient for condensing mini/micro-channel flow. Int. J. Heat Mass Transf. 56, 238– 250. doi:10.1016/j.ijheatmasstransfer.2012.09.032.
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111 Liu, N., Xiao, H., Li, J., 2016. Experimental investigation of condensation heat transfer and pressure drop of propane, R1234ze(E) and R22 in minichannels. Appl. Therm. Eng. 102, 63–72. doi:10.1016/j.applthermaleng.2016.03.073. Mylavarapu, S.K., Sun, X., Glosup, R.E., Christensen, R.N., Patterson, M.W., 2014. Thermal hydraulic performance testing of printed circuit heat exchangers in a hightemperature helium test facility. Appl. Therm. Eng. 65, 605–614. doi:10.1016/j. applthermaleng.2014.01.025. Nikitin, K., Kato, Y., Ngo, L., 2006. Printed circuit heat exchanger thermal–hydraulic performance in supercritical CO2 experimental loop. Int. J. Refrig. 29, 807–814. doi:10.1016/j.ijrefrig.20 05.11.0 05. Ramírez-Rivera, F., López-Belchí, A., Vera-García, F., García-Cascales, J.R., IllánGómez, F., 2015. Two phase flow pressure drop in multiport mini-channel tubes using R134a and R32 as working fluids. Int. J. Therm. Sci. 92, 17–33. doi:10.1016/j.ijthermalsci.2015.01.014. Shao, N., Gavriilidis, A., Angeli, P., 2009. Flow regimes for adiabatic gas–liquid flow in microchannels. Chem. Eng. Sci. 64, 2749–2761. doi:10.1016/j.ces.2009.01.067. Shin, C.W., No, H.C., 2017. Experimental study for pressure drop and flow instability of two-phase flow in the PCHE-type steam generator for SMRs. Nucl. Eng. Des. 318, 109–118. doi:10.1016/j.nucengdes.2017.04.004.
111
Vanderputten, M.A., Jacob, T.A., Sattar, M., Ali, N., Fronk, B.M., 2017. Two-phase flow regimes of condensing R-134a at low mass flux in rectangular microchannels. Int. J. Refrig. 84, 92–103. doi:10.1016/j.ijrefrig.2017.08.021. Wang, H., Bi, Q., Yang, Z.D., Wang, L.C., 2015. Experimental and numerical investigation of heat transfer from a narrow annulus to supercritical pressure water. Ann. Nucl. Energy 80, 416–428. doi:10.1016/j.anucene.2015.02.029. Wang, J., Wang, J., Li, J.M., 2017. R134a condensation flow regime and pressure drop in horizontal microchannals cooled symmetrically and asymmetrically. Int. J. Heat Mass Transf. 115, 1091–1102. doi:10.1016/j.ijheatmasstransfer.2017.08.003. Yang, Z., Peng, X.F., Ye, P., 2008. Numerical and experimental investigation of two phase flow during boiling in a coiled tube. Int. J. Heat Mass Transf. 51, 1003– 1016. doi:10.1016/j.ijheatmasstransfer.2007.05.025. Yoon, S.H., No, H.C., Kang, G.B., 2014. Assessment of straight, zigzag, S-shape, and airfoil PCHEs for intermedia heat exchangers of HTGRs and SFRs. Nucl. Eng. Des. 270, 334–343. doi:10.1016/j.nucengdes.2014.01.006. Zhang, J., Li, W., Sherif, S.A., 2016. A numerical study of condensation heat transfer and pressure drop in horizontal round and flattened minichannels. Int. J. Therm. Sci. 106, 80–93. doi:10.1016/j.ijthermalsci.2016.02.019.
Contents lists available at ScienceDirect
International Journal of Refrigeration journal homepage: www.elsevier.com/locate/ijrefrig
A numerical study on condensation flow and heat transfer of refrigerant in minichannels of printed circuit heat exchanger Zhongchao Zhao∗, Yanrui Zhang, Xudong Chen, Xiaolong Ma, Shan Yang, Shilin Li School of Energy and Power, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu, China
a r t i c l e
i n f o
Article history: Received 26 December 2018 Revised 5 March 2019 Accepted 15 March 2019 Available online 22 March 2019 Keywords: Printed circuit heat exchanger Minichannel Condensation flow Heat transfer Flow pattern
a b s t r a c t Printed circuit heat exchanger (PCHE), with the core comprising many mini/microchannels, have been extensively studied, but few works involved two-phase flow. A simplified channel model of PCHE hot side was herein established to numerically explore the heat transfer and condensation flow performance of R22 in minichannels under different conditions. The model was a semicircular minichannel with 0.91 mm hydraulic diameter and 50 mm full length. The heat flux was kept at −77,195 W m−2 , the inlet pressure was 0.63 MPa and the mass fluxes ranged from 58 to 93 kg m−2 s−1 . The condensation flow characteristics along the channel were analyzed. Four flow patterns, i.e., smooth-annular, wavy-annular, slug and bubbly, were noticed at different refrigerant mass fluxes and plotted as a flow pattern map. The effects of import vapor quality from 0.5 to 1 on pressure drop and heat transfer performance were evaluated. The heat transfer performance was optimal at the import vapor quality of 0.7. The impacts of refrigerant mass flux on pressure drop and local condensation heat transfer coefficient were assessed. Intermittent flow enhanced heat transfer. In addition, the correlations for local Nusselt number and Fanning friction factor were presented and compared with numerical data. © 2019 Elsevier Ltd and IIR. All rights reserved.
Étude numérique sur l’écoulement par condensation et le transfert de chaleur du frigorigène dans les mini-canaux d’un échangeur de chaleur à circuit imprimé Mots-clés: Échangeur de chaleur à circuit imprimé; Mini-canal; Écoulement par condensation; Transfert de chaleur; Configuration d’écoulement
1. Introduction Printed circuit heat exchanger (PCHE), a mini/microchannel heat exchanger, was devised in Australia in 1980 and developed by Heatric in England in the same year (Baek et al., 2012). PCHE is a compact and efficient heat exchanger in which flow paths are generated by photochemical etching on metal plates. Then the plates are tightly connected by diffusion bonding to form the heat exchanger core (Nikitin et al., 2006). Due to special processing technology, PCHE has been widely used in various fields with excellent properties, such as small hydraulic diameter, high heat exchange efficiency, temperature resistance and pressure resistance. Researchers have endeavored to study the
∗
Correspondence author. E-mail address: [email protected] (Z. Zhao).
https://doi.org/10.1016/j.ijrefrig.2019.03.016 0140-7007/© 2019 Elsevier Ltd and IIR. All rights reserved.
thermal-hydraulic performance of PCHE through experimental and numerical methods. Kim and No (2011) studied the thermalhydraulic characteristics for PCHE with horizontal and vertical layouts in helium-water conditions by experiments and CFD simulations. Shin and No (2017) experimentally studied the pressure drop and flow instability of water in a PCHE applied as a SMRs steam generator. Besides, Mylavarapu et al. (2014) also experimentally explored the thermal-hydraulic characteristics of two PCHEs at the HTHF, where the working fluid is helium. Wang et al. (2015) explored the heat transfer of supercritical water in a narrow annulus experimentally and numerically. Aneesh et al. (2016) assessed the effects of various working conditions and channel arrangements on the thermal-hydraulic characteristics of PCHE in helium-helium conditions by using the CFD model. Additionally, Yoon et al. (2014) derived correlations of Fanning factor and Nusselt number applied to airfoil fin PCHE by CFD, and evaluated the thermal–hydraulic performances of PCHEs for different channel
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Nomenclature P h G PCHE T
pressure (Pa) heat transfer coefficient (W m− 2 K−1 ) mass flux (kg m−2 s−1 ) printed circuit heat exchanger temperature (K)
F
surface tension source term (N m−3 s−1 )
u
velocity vector (m s−1 ) pressure drop (Pa) mass source term (kg m−3 s−1 ) energy source term (J m−3 s−1 ) thermal conductivity (W m−1 K−1 ) specific internal energy (J kg−1 ) constant volume specific heat (J kg−1 K−1 ) gravity acceleration (m s−2 ) latent heat for liquid-vapor phase change (J kg−1 ) heat flux (W m−2 ) vapor quality axial local (mm) Nusselt number Reynolds number Prandtl number Fanning friction factor hydraulic diameter
P S SE k E cv g hlv q x z Nu Re Pr f Dh Greeks
ρ α μ γ σ
density (kg m−3 ) volume fraction dynamic viscosity (kg m−1 s−1 ) kinematic viscosity (m2 s−1 ) surface tension (N m−1 )
Subscripts v vapor l liquid e effective s saturation b bulk in inlet out outlet ave average pred prediction c critical r reduced f frictional de deceleration types. Jeon et al., (2016) numerically investigated the thermal performance of a heterogeneous PCHE, using S-CO2 and LNG flue gas as cold fluid and hot fluid respectively. Kim and No (2013) experimentally and numerically analyzed a PCHE, using He–CO2 mixture and water as working fluids. Although PCHEs have been widely studied, PCHE single-phase working fluids were mostly used, without involving phase transition processes. The two-phase flow in mini/microchannels of PCHE has seldom been referred. The core of PCHE consists of many mini/microchannels. Compared to conventional channels, the flows in mini/microchannels are slightly different, which are more prone to factors such as surface tension, wall wettability and roughness, exhibiting different flow characteristics and transformation mechanisms (Shao et al., 2009). In addition, the two-phase flow characteristics and patterns can strongly affect heat transfer. Two-phase condensation flow in mini/microchannels has attracted extensive attention, laying a theoretical foundation for the development of heat transfer technolo-
97
gies and compact heat exchangers. Wang et al. (2017) experimentally studied condensation flow and pressure drop for R134a in microchannels, and observed four flow patterns. Liu et al. (2016) experimentally assessed the impacts of different operating parameters on the condensation heat transfer and pressure of working fluid in circular and square minichannels. Besides, Chen et al. (2014) researched the condensation flow of FC-72 in a rectangular microchannel (Dh =1 mm) using a two-phase volume of fluid (VOF) model. Kim et al. (2012) and Kim and Mudawar (2012) performed experiments to study the condensation and heat transfer characteristics of FC-72 inside parallel microchannels with L of 29.9 cm (Dh =1 mm). High-speed video and photography techniques have been used to observe the transformation of two-phase flow regimes. Vanderputten et al. (2017) developed a test bed to study the condensation flow for R-134a inside square microchannels and evaluated the predictability of various flow maps. Zhang et al. (2016) numerically researched the influences of aspect ratio, mass flux and vapor quality on the heat transfers and pressure differences of R410A and R134a through horizontal round and flattened minichannels. Additionally, Al-Zaidi et al. (2017) experimentally investigated the condensation flow regimes and heat transfer of HFE-7100 inside microchannels. Ramírez-Rivera et al. (2015) tested the two-phase pressure drops for R134a and R32 at minichannel tubes through condensation and boiling experiments. Moreover, Kim and Mudawar (2013)and Kim and Mudawar (2012) proposed a novel universal approach for forecasting the coefficient of heat transfer and frictional pressure gradient of condensation flow in mini/microchannel. Bohdal et al. (2011) experimentally researched the condensations for R134a and R404A refrigerants in minichannels of single pipe, and presented the empirical correlation of local heat transfer coefficient. We herein used a simplified channel model of PCHE hot side to investigate the condensation flow in minichannels. The model was verified through experimental data, and then utilized to study the condensation flow and heat transfer characteristics for R22 inside minichannels of PCHE at different inlet vapor qualities and mass fluxes. New local Nusselt number correlations were proposed for annular flow and transition from annular to slug and bubbly flow respectively. The Fanning friction factor correlation of two-phase condensation flow was also fitted by simulation data. Meanwhile, the accuracies of the proposed correlations were tested by comparison with numerical data.
2. Numerical methodology 2.1. Geometrical model and boundary conditions The internal core structure of the tested PCHE is schematized in Fig. 1. It is rather complicated to simulate the flow processes of the entire PCHE because of limited computing resource and time, so this paper concentrated on the condensation flow and heat transfer of R22 inside hot channels. The simplified model was a single straight channel on hot side of PCHE with the overall length of 50 mm (Fig. 2(a)). The channel cross-section was semicircular, with a 2 mm width and a 1.75 mm height (Fig. 2(b)). The following assumptions were made: (1) PCHE was operated in the steady state. (2) The R22 flow was distributed uniformly in each hot channel with identical temperature and mass flux profiles. (3) Pressure hardly affected the physical properties of R22, because pressure drop through the channel was negligible compared to the operating pressure. Three types of surfaces were set in the computational model, i.e. inlet, outlet and wall. The boundary conditions for the inlet and outlet were respectively set as mass flow inlet and outflow. There were two kinds of walls in the calculation model, where the
98
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Fig. 1. Schematic diagram of internal core structure of tested PCHE.
Fig. 2. Numerical model and boundary conditions.
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
99
surface between fluid area and solid area was a coupled wall. The boundary conditions for outer walls are displayed in Fig. 2(b). 2.2. Mathematical modeling The VOF model is a kind of surface tracking method under a fixed Euler mesh. The governing equations based on the VOF model are as follows: 1. Continuity equations
∇ · αv ρv uv = Sv
(1)
∇ · αl ρl ul = Sl
(2)
∂v + ∂l = 1
(3)
Eqs. (1) and (2) are the continuity equations of vapor phase and liquid phase respectively, where α v is the volume fraction of vapor phase, α l is that of liquid phase, Sv and Sl are the vapor
Fig. 3. Sectional view of channel mesh for PCHE model.
and liquid mass source terms respectively, and u is the velocity vector. 2. Momentum equation
T ∇ ρ uu = −∇ p + ∇ μ ∇ u + ∇ u + ρg + F
Vapor mass source term : Sv =
(4)
s) fe αl ρl (T −T , T > Ts Ts s) fc αv ρv (T −T , T < Ts Ts
) fe αl ρl (TsT−T , T > Ts s
(12)
Where ρ and μ are the density and viscosity of mixture given by:
Liquid mass source term : Sl =
ρ = αl ρl + αv ρv
(5)
where fe and fc are adjustable mass transfer factors for evaporation and condensation, respectively. SE in Eq. (8) is the energy source term determined as:
(6)
SE = hl v Sl
and
μ = αl μl + αv μv
) fc αv ρv (TsT−T , T < Ts s
The surface tension F between two contacting phases, which is calculated through the continuum surface force (CSF) model (Brackbill et al., 1992), is calculated by:
in which hlv is the latent heat of vaporization for refrigerant. The thermal conduction equation in solid region is:
where λ is the thermal conductivity of solid wall. The transport equations of the realizable κ -ε model are:
ρ ∇ · nˆ ∇ αl F =σ 1 ( ρl + ρv ) 2
(7)
in which σ is the surface tension coefficient and nˆ is the unit normal vector determined as nˆ = ∇ αl /|∇ αl |. 3. Energy equation
∇ · u ( ρ E + p ) = ∇ · ( ke ∇ T ) + SE
(8)
where SE is the energy source term and ke is the effective thermal conductivity for mixture calculated by:
ke = αv kv + αl kl
(9)
E is the specific internal energy calculated by:
E=
αv ρv Ev + αl ρl El αv ρv + αl ρl
(10)
∂ ∂ ρκ u j (ρκ ) + ∂t ∂xj
∂ μt ∂κ = + Gκ + Gb − ρε − YM + Sκ μ+ ∂xj σκ ∂ x j ∂ ∂ ρε μ j (ρε ) + ∂t ∂xj
∂ μ ∂ε ε2 = + ρC1 Sε − ρC2 μ+ t √ ∂xj σε ∂ x j κ + γε ε + C1ε C3ε Gb + Sε κ
(14)
(15)
(16)
(17)
Where the detailed parameters were recommended by the FLUENT help manual (FLUENT 6.3 User’s Guide 2006).
where Ev and El are determined as:
Ei = cv,i (T − Ts ), i = v or l
∇ (λ∇ T ) = 0
(13)
(11)
where cv is the constant-volume specific heat and Ts is the saturation temperature. For the source terms in the governing equations, different computational submodels are added to simulate the vapor-liquid phase changes at the interface. The mass source terms Sv and Sl in Eqs. (1) and (2) are defined as (Yang et al., 2008):
2.3. Grid and solution methodology The numerical model was meshed into hexahedral and wedge elements by Gambit (Fig. 3). Grid-independent verification was necessary to ensure the accuracy of extensive case research. We compared the simulation results of six sets of grid numbers under the condition that the R22 inlet pressure was 0.63 MPa and the inlet temperature was 287.6 K (Table 1). Ultimately, the grid of
100
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Table 1 Mesh independence study. Grid number
6.53 × 105
9.19 × 105
1.32 × 106
2.07 × 106
3.6 × 106
4.18 × 106
Real value
Outlet temperature (K)
267.12
265.5
262.43
261.8
261.5
261.32
260.78
Table 2 Thermo-physical properties of R22.
average temperature of fluid given by:
Parameter
Liquid phase
Vapor phase
ρ (kg m ) C p (kJ kg−1 K−1 ) μ (kg m−1 s−1 ) k (mW m−1 K−1 ) hl v (kJ kg−1 ) σ (mN m−1 )
1255.8 1.19 1.99 ×10−4 91.398 198.89 10.594
26.697 0.77 1.168 ×10−5 9.925 198.89 10.594
−3
2.07 × 106 was employed for the accuracy and efficiency of subsequent study. The simulation was performed by the FLUENT software. The source terms in governing equations were considered by loading user-defined functions. The realizable k-ε model was selected for flow turbulence according to a previous literature (Huang et al., 2011). The VOF model and CSF model were used as the twophase flow model and surface tension model respectively. Velocitypressure coupling was solved using the PISO solution algorithm. The body force weighted scheme was selected for pressure and the power law scheme was selected for momentum. The other items were discretized with the second order upwind scheme. Condensation heat transfer coefficient and pressure drop were used to analyze the condensation flow and heat transfer of R22 in PCHE minichannels. The pressure drop data was extracted directly from FLUENT software. The condensation heat transfer coefficient h was determined by:
h=
q Tb − Twall
(18)
in which q is the heat flux applied to wall, Twall is the areaweighted average temperature of wall and Tb is the mass-weighted
n Ti ρiVi Tb = i=1 n i=1 ρiVi
(19)
in which ρ i , Vi , Ti are the density, volume and temperature of the ith grid. The thermo-physical properties of R22 were obtained from REFPROP software. Table 2 lists the simulated thermo-physical properties of R22 at the saturation temperature of 280.59 and the pressure of 0.63 MPa. 3. Results and discussion 3.1. Model verification An experimental rig was designed to study the heat transfer performance for PCHE, using N2 and R22 as cold fluid and hot fluid respectively, which consisted of a N2 loop, a refrigerant R22 loop and a heating water loop (Fig. 4). Through selected laser sintering, a 3D printing technology, the tested crossflow PCHE was fabricated, with airfoil cold channel and straight hot channel (Fig. 5). During the experiment, some parameters such as temperature, pressure and mass flow rate of the inlet and outlet of R22 and liquid nitrogen were measured, which were used for thermal balance analysis, determination of heat flux in boundary conditions and verification of R22 condensation model for numerical study. Before numerical studies, the accuracy of this model was first verified through experimental data by the following equation:
CF D − Experiment
Error =
Expriment
× 100% .
(20)
We selected 25 sets of experimental conditions of R22 in hot side for simulation, and compared the numerical outlet
Fig. 4. Schematic diagram of test rig.
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
101
Fig. 5. Tested PCHE.
Fig. 6. Outlet temperature on hot side of PCHE (CFD vs. experiment).
temperature and pressure drop with the experimental ones. The errors between the outlet temperatures of simulation and experiment are shown in Fig. 6. The maximum error was 2.5% and the minimum one was 0.3%, and the numerical outlet temperatures agreed well with the experimental ones, with a 1.35% average error. The error map for pressure drop is shown in Fig. 7, with a 5% minimum error and a 24% maximum error. All the numerical pressure drops were smaller than the experimental ones, because the numerical model is idealized with smooth inner wall of the channel. Besides, the inlet and outlet pressure drop contained in the
experimental pressure drop was not considered during simulation. Collectively, this model can be reliably applied to extensive numerical research. 3.2. Two-phase flow patterns The validated model was applied for simulating the R22 condensation flow patterns in PCHE minichannels. The heat flux was kept at −77,195 W m−2 and the mass fluxes ranged from 58 to 93 kg m−2 s−1 . The cross sections at various vapor qualities and
102
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Fig. 7. Pressure drop on hot side of PCHE (CFD vs. experiment).
the mass flux of 58 kg m−2 s−1 were obtained to observe the twophase distribution along the flow (Fig. 8). Liquid phase first appeared at the sharp corners where the upper and lower surfaces of channel met along the flow direction, and then extended toward the middle along the surface. Finally, the vapor phase at the channel center condensed into liquid phase, and the refrigerant became supercooled liquid at the outlet. Fig. 9 shows the velocity vector at x = 0.47. The flow velocity was low at the sharp corner, accompanied by vortex flow, so the fluid began to exchange heat more effectively. As a result, liquid phase first appeared at the sharp corners. Since heat flux was applied to the fluid from the upper and lower surfaces, the fluid near the surface liquefied earlier than that at the center did. The flow pattern analysis of simulation results revealed four different flow patterns at various locations and mass fluxes (Table 3). The annular flow existed at each mass flux and became dominant at high mass fluxes. The annular flow can be classified into smooth annular flow and wavy annular flow, with the former typified by a smooth and indistinguishable liquid film along the channel inner wall and the latter characterized by a thick and wavy liquid film. Other flow patterns, such as slug and bubbly ones, were also observed at low mass fluxes (G = 58, 64 and 69 kg m−2 s−1 ), whereas the bubbly pattern appeared only at the mass fluxes of 58 and 64 kg m−2 s−1 . The slug flow has characteristic long, isolated bubbles flowing in the liquid phase, while the bubbly flow features small bubbles. The above flow patterns at different mass fluxes were plotted as a flow pattern map (Fig. 10). The bubbly, the slug, wavy-annular and smooth-annular patterns appeared sequentially with increasing vapor quality. Along the flow direction, the flow pattern was
converted from annular to bubbly at low mass fluxes, and from smooth-annular to wavy-annular at high mass fluxes. 3.3. Impact of inlet vapor quality The effects of import vapor quality from 0.5 to 1 on heat transfer and pressure drop were explored at the mass flux of 58 kg m−2 s−1 . The inlet pressure was 0.63 MPa and the saturation temperature was 280.59 K. Fig. 11 shows the effects of import vapor quality on local condensation heat transfer coefficient. The coefficient increased first and then decreased along the channel at the same inlet quality. Given that the refrigerant condensed continuously to a completely liquid phase with the flow (Fig. 12), the phase-change heat transfer was stronger than the single-phase heat transfer due to latent heat. The position of complete liquefaction differed at various inlet vapor qualities. In addition, the local condensation heat transfer coefficient increased with reducing inlet vapor quality before complete liquefaction, and then dropped after complete liquefaction. The trend before complete liquefaction may be attributed to flow pattern conversion of the coefficient. After complete liquefaction, however, the condensation accelerated at a low inlet quality. At the same channel position, the fluid temperature and the temperature difference of wall surface reduced, thus decelerating heat exchange and decreasing the heat transfer coefficient. Fig. 13 displays the influences of inlet vapor quality on pressure. The fluid pressure drop in the channel varied irregularly along with the import vapor quality, reaching minimum and maximum at the import qualities of 0.7 and 1, respectively. As exhibited in Fig. 14, the average heat transfer coefficient comes up to maximum and
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
103
Fig. 8. Cross-sectional views of two-phase distribution at different vapor qualities.
minimum at the import qualities of 0.8 and 0.7 respectively. Moreover, the coefficient at 0.8 inlet quality was 6.5% higher than that at 0.7 inlet quality, and the pressure drop was 20% higher. Thus, the heat transfer performance was optimal at the import vapor quality of 0.7.
wavy-annular flow exceeded that of smooth-annular flow (Kim and Mudawar, 2012; Agarwal and Garimella, 2010). As demonstrated in Fig. 16, the total pressure drop rises with rising R22 mass flux, possibly because raising the vapor velocity increased the interfacial shear force between the formed liquid film and R22 vapor.
3.4. Impact of refrigerant mass flux The impact of R22 mass flux on pressure difference and local condensation heat transfer coefficient was tested through simulation at the mass fluxes of 58, 64, 69, 75, 81, 87 and 93 kg m−2 s−1 , the import vapor quality of 0.7 and the inlet pressure of 0.63 MPa. As displayed in Fig. 15, the local condensation heat transfer coefficient rises with rising R22 mass flux. At higher mass flux, the interfacial vapor shear stress was elevated, giving thinner liquid film and lower thermal resistance, being consistent with the results of Kim and Mudawar (2012), Al-Zaidi et al. (2017) and Al-Hajri et al. (2013). In addition, the local condensation heat transfer coefficient increased along the fluid flow direction when the mass flux is constant, probably because of flow pattern conversion of the coefficient. In contrast to the previous flow pattern map (Fig. 10), the flow pattern was converted from annular to intermittent along the flow direction. Accordingly, intermittent flow enhanced heat transfer by attenuating the liquid film, the heat transfer coefficient of
3.5. Proposal of Nusselt number and Fanning friction factor correlations According to the simulation data at various mass fluxes, a numerical correlation that described the local Nusselt number of R22 in PCHE minichannel was obtained by regression analysis, for annular flow:
Nu = 6.4048 × Re0.9357 × P r −8.0262 × Pr −0.1047 ×
x −0.5746 1−x (21)
for transition from annular to slug and bubbly flow:
Nu = 88.4387 × Re−0.2437 × P r −9.4989 × Pr −4.728 ×
x −0.0646 1−x (22)
104
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Fig. 9. Velocity vector at x = 0.475.
Table 3 Representative flow patterns with corresponding vapor quality at different mass fluxes.
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Fig. 10. Flow pattern map at seven mass fluxes from 58 to 93 kg m−2 s−1 .
Fig. 11. Impact of inlet vapor quality on local condensation heat transfer coefficient.
105
106
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Fig. 12. Flow patterns at different inlet vapor qualities.
Fig. 13. Effect of import vapor quality on pressure.
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Fig. 14. Average heat transfer coefficient and pressure drop at different import vapor qualities.
Fig. 15. Impact of refrigerant mass flux on local condensation heat transfer coefficient.
107
108
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Fig. 16. Impact of refrigerant mass flux on pressure.
Fig. 17. Contrast of predicted Nusselt number with simulation values for annular flow.
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
Fig. 18. Contrast of predicted Nusselt number with simulation values for transition from annular to slug and bubbly flow.
Fig. 19. Contrast of predicted Fanning friction factor with simulation values.
109
110
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111
where Re stands for Reynolds number and Pr stands for the reduced pressure given by:
u Dh
Re = Pr =
γ
P Pc
(23) (24)
where Dh represents the hydraulic diameter, γ represents the kinematic viscosity, and Pc represents the critical pressure. The Nusselt number Nu was calculated by the equation below:
Nu =
hDh . k
(25)
The Fanning friction factor correlation of two-phase condensation flow was also fitted by simulation data:
ft p = 0.04839 × Re−0.2986
minimum at the 0.7 inlet quality and maximum at the 1 inlet quality. The heat transfer performance was optimized at the import vapor quality of 0.7. (5) The local condensation heat transfer coefficient increased with rising R22 mass flux. Furthermore, the coefficient increased along the flow direction at the same mass flux, indicating that intermittent flow augmented heat transfer. As the refrigerant mass flux increased, the total pressure drop was elevated. (6) The local Nusselt number and Fanning friction factor correlations for R22 condensation flow and heat transfer in PCHE minichannel were in good agreement with the numerical data.
(26)
Conflict of interest None.
where ftp was calculated by:
ft p =
P f D h 2Lρb u2b
Acknowledgment
(27)
where L represents the channel length, ρ b and ub represent the bulk mean density and bulk mean velocity of R22, and Pf is the frictional pressure drop calculated by:
Pf = P + Pde = P + ρin u2in − ρout u2out
(28)
To evaluate the accuracy of the proposed correlations, the error was tested:
pred − CF D Error = × 100% . CF D
The authors gratefully acknowledge that this work was supported by Jiangsu Marine and Fishery Science and Technology Innovation and Extension Project (HY2017-8) and Zhenjiang Funds for the Key Research and Development Project (GY2016002-1).
(29)
Fig. 17 compares 104 numerical annular flow data with correlated Nusselt number, showing a 26% maximum error. Additionally, Fig. 18 compares 78 numerical values of transition from annular to slug and bubbly flow with correlated Nusselt number, exhibiting a 25% maximum error. Hence, the heat transfer characteristics for R22 in PCHE minichannel can be well predicted by the proposed correlations. Furthermore, Fig. 19 compares the Fanning friction factor calculated by correlation with numerical values, suggesting a satisfactory predictability with a 5% maximum error. 4. Conclusions The condensation flow of R22 in minichannels of PCHE hot side (Dh = 0.91 mm) was studied. A simplified channel model was established to numerically investigate the condensation flow and heat transfer characteristics in minichannels under various working conditions. The main findings are as follows: (1) The error between outlet temperatures of simulation and experiment was ≤2.5% and that of pressure drop was ≤25%, proving that the numerical model and methods were reliable. (2) During condensation, liquid phase first appeared at the sharp corners where the top and bottom surfaces of the channel met along the flow direction, and then extended toward the middle along the surface. (3) Smooth-annular, wavy-annular, slug and bubbly flow patterns were discovered at different refrigerant mass fluxes and plotted as a flow pattern map. Increasing the mass flux of R22 extended the annular region downstream with reducing vapor quality. (4) The local condensation heat transfer coefficient rose first and then decreased along the channel at the same inlet quality. The coefficient rose with decreasing inlet vapor quality before complete liquefaction. The fluid pressure drop in the channel changed irregularly along with the inlet vapor quality, reaching
References Agarwal, A., Garimella, S., 2010. Representative results for condensation measurements at hydraulic diameters ∼100 Microns. J. Heat Transf. 132, 1667–1681. doi:10.1115/IMECE2007-43749. Al-Hajri, E., Shooshtari, A.H., Dessiatoun, S., Ohadi, M.M., 2013. Performance characterization of R134a and R245fa in a high aspect ratio microchannel condenser. Int. J. Refrig. 36, 588–600. doi:10.1016/j.ijrefrig.2012.10.007. Al-Zaidi, A.H., Mahmoud, M.M., Karayiannis, T.G., 2017. Condensation flow patterns and heat transfer in horizontal microchannels. Exp. Therm. Fluid Sci. 90, 153– 173. doi:10.1016/j.expthermflusci.2017.09.009. Aneesh, A.M., Sharma, A., Srivastava, A., Vyas, K.N., Chaudhuri, P., 2016. Thermalhydraulic characteristics and performance of 3D straight channel based printed circuit heat exchanger. Appl. Therm. Eng. 98, 474–482. doi:10.1016/j. applthermaleng.2015.12.046. Baek, S., Kim, J.H., Jeong, S., Jung, S., 2012. Development of highly effective cryogenic printed circuit heat exchanger (PCHE) with low axial conduction. Cryogenics 52, 366–374. doi:10.1016/j.cryogenics.2012.03.001. Bohdal, T., Charun, H., Sikora, M., 2011. Comparative investigations of the condensation of R134a and R404A refrigerants in pipe minichannels. Int. J. Heat Mass Transf. 54, 1963–1974. doi:10.1016/j.ijheatmasstransfer.2011.01.005. Brackbill, J.U., Kothe, D.B., Zemach, C., 1992. A continuum method for modeling surface tension, J. Comput. Phys. 100, 335–354. doi:10.1016/0021- 9991(92)90240- Y. Chen, S., Yang, Z., Duan, Y.Y., Chen, Y., Wu, D., 2014. Simulation of condensation flow in a rectangular microchannel. Chem. Eng. Process. Process. Intensif. 76, 60–69. doi:10.1016/j.cep.2013.12.004. FLUENT 6.3 User’s Guide. Fluent, Inc. Lebanon, NH, 2006 September. Huang, M., Yang, Z., Duan, Y.Y., Lee, D.J., 2011. Bubble growth for boiling bubbly flow for R141b in a serpentine tube. J. Taiwan Inst. Chem. Eng. 42, 727–734. doi:10.1016/j.jtice.2011.02.007. Jeon, S., Baik, Y.J., Byon, C., Kim, W., 2016. Thermal performance of heterogeneous PCHE for supercritical CO2 energy cycle. Int. J. Heat Mass Transf. 102, 867–876. doi:10.1016/j.ijheatmasstransfer.2016.06.091. Kim, I.H., No, H.C., 2011. Thermal hydraulic performance analysis of a printed circuit heat exchanger using a helium–water test loop and numerical simulations. Appl. Therm. Eng. 31, 4064–4073. doi:10.1016/j.applthermaleng.2011.08.012. Kim, I.H., No, H.C., 2013. Thermal-hydraulic physical models for a printed circuit heat exchanger covering He, He–CO2 mixture, and water fluids using experimental data and CFD. Exp. Therm. Fluid Sci. 48, 213–221. doi:10.1016/j. expthermflusci.2013.03.003. Kim, S.M., Kim, J., Mudawar, I., 2012. Flow condensation in parallel micro-channels – part 1: experimental results and assessment of pressure drop correlations. Int. J. Heat Mass Transf. 55, 971–983. doi:10.1016/j.ijheatmasstransfer.2011.10.013. Kim, S.M., Mudawar, I., 2012. Flow condensation in parallel micro-channels – part 2: heat transfer results and correlation technique. Int. J. Heat Mass Transf. 55, 984–994. doi:10.1016/j.ijheatmasstransfer.2011.10.012. Kim, S.M., Mudawar, I., 2012. Universal approach to predicting two-phase frictional pressure drop for adiabatic and condensing mini/micro-channel flows. Int. J. Heat Mass Transf. 55, 3246–3261. doi:10.1016/j.ijheatmasstransfer.2012.02.047. Kim, S.M., Mudawar, I., 2013. Universal approach to predicting heat transfer coefficient for condensing mini/micro-channel flow. Int. J. Heat Mass Transf. 56, 238– 250. doi:10.1016/j.ijheatmasstransfer.2012.09.032.
Z. Zhao, Y. Zhang and X. Chen et al. / International Journal of Refrigeration 102 (2019) 96–111 Liu, N., Xiao, H., Li, J., 2016. Experimental investigation of condensation heat transfer and pressure drop of propane, R1234ze(E) and R22 in minichannels. Appl. Therm. Eng. 102, 63–72. doi:10.1016/j.applthermaleng.2016.03.073. Mylavarapu, S.K., Sun, X., Glosup, R.E., Christensen, R.N., Patterson, M.W., 2014. Thermal hydraulic performance testing of printed circuit heat exchangers in a hightemperature helium test facility. Appl. Therm. Eng. 65, 605–614. doi:10.1016/j. applthermaleng.2014.01.025. Nikitin, K., Kato, Y., Ngo, L., 2006. Printed circuit heat exchanger thermal–hydraulic performance in supercritical CO2 experimental loop. Int. J. Refrig. 29, 807–814. doi:10.1016/j.ijrefrig.20 05.11.0 05. Ramírez-Rivera, F., López-Belchí, A., Vera-García, F., García-Cascales, J.R., IllánGómez, F., 2015. Two phase flow pressure drop in multiport mini-channel tubes using R134a and R32 as working fluids. Int. J. Therm. Sci. 92, 17–33. doi:10.1016/j.ijthermalsci.2015.01.014. Shao, N., Gavriilidis, A., Angeli, P., 2009. Flow regimes for adiabatic gas–liquid flow in microchannels. Chem. Eng. Sci. 64, 2749–2761. doi:10.1016/j.ces.2009.01.067. Shin, C.W., No, H.C., 2017. Experimental study for pressure drop and flow instability of two-phase flow in the PCHE-type steam generator for SMRs. Nucl. Eng. Des. 318, 109–118. doi:10.1016/j.nucengdes.2017.04.004.
111
Vanderputten, M.A., Jacob, T.A., Sattar, M., Ali, N., Fronk, B.M., 2017. Two-phase flow regimes of condensing R-134a at low mass flux in rectangular microchannels. Int. J. Refrig. 84, 92–103. doi:10.1016/j.ijrefrig.2017.08.021. Wang, H., Bi, Q., Yang, Z.D., Wang, L.C., 2015. Experimental and numerical investigation of heat transfer from a narrow annulus to supercritical pressure water. Ann. Nucl. Energy 80, 416–428. doi:10.1016/j.anucene.2015.02.029. Wang, J., Wang, J., Li, J.M., 2017. R134a condensation flow regime and pressure drop in horizontal microchannals cooled symmetrically and asymmetrically. Int. J. Heat Mass Transf. 115, 1091–1102. doi:10.1016/j.ijheatmasstransfer.2017.08.003. Yang, Z., Peng, X.F., Ye, P., 2008. Numerical and experimental investigation of two phase flow during boiling in a coiled tube. Int. J. Heat Mass Transf. 51, 1003– 1016. doi:10.1016/j.ijheatmasstransfer.2007.05.025. Yoon, S.H., No, H.C., Kang, G.B., 2014. Assessment of straight, zigzag, S-shape, and airfoil PCHEs for intermedia heat exchangers of HTGRs and SFRs. Nucl. Eng. Des. 270, 334–343. doi:10.1016/j.nucengdes.2014.01.006. Zhang, J., Li, W., Sherif, S.A., 2016. A numerical study of condensation heat transfer and pressure drop in horizontal round and flattened minichannels. Int. J. Therm. Sci. 106, 80–93. doi:10.1016/j.ijthermalsci.2016.02.019.