Supercritical fluids have wide range of industrial applications owing to the substantial impact of their heat transfer characteristics [1 - 8]. Supercritical fluids, in comparison with conventional fluids, have attracted growing amount of attention because of relatively higher heat transfer rate and lower energy losses . The thermophysical properties of supercritical fluids considerably vary near the critical (Tc) or pseudo critical temperature (Tpc). The heat transfer coefficient, owing to dramatic variations near pseudo-critical point, depends upon pressure, tube diameter, flow direction, heat flux and type of working fluid . Therefore, this results in complex heat transfer characteristics which may account for heat transfer enhancement or deterioration .
Most of the experimental and numerical investigations have been conducted to explore supercritical water and carbon dioxide (sCO2) [12 - 18]. Dang and Hihara [19 , 20] investigated the effects of tube diameter on heat transfer coefficient of sCO2 under cooling conditions and proposed the modified Gnielinski equation. Zhang and Hu  measured the effects of buoyancy and tube diameter for sCO2. The influence of mass flux, pressure and tube diameter were plotted against heat transfer coefficient and pressure drop. Further to that, dimensionless diameter was incorporated in the development of correlation which can precisely estimate heat transfer in large-diameter tube. Wang and Guan  computationally investigated underlying mechanism of buoyancy effects for supercritical carbon dioxide flowing through large horizontal tube. At higher heat flux, the buoyancy is more pronounced and can cause considerable difference in the temperature at top and bottom walls. Zahlan and Groeneveld  performed extensive experimental tests for sCO2 under vertical conditions.
However, supercritical organic fluids have not been thoroughly investigated for in tube heat transfer. Zhao and Jiang  examined that fluid temperature, mass flux and pressure can considerably impact the in-tube cooling heat transfer and flow of supercritical fluid R134a. Experimental data predicated (using the least square curve-fitting method) a modified Gnielinski’s correlation which can give heat transfer coefficient within ±15% accuracy. Wang and Tian  conducted experimental investigations for supercritical fluid R134a flowing through micro-fin and smooth tube under horizontal position. These measurements under different mass fluxes, heat fluxes and pressures suggested that micro-fin tube resulted in higher heat
transfer coefficient than that of smooth tube. Herein, buoyancy criteria of was suggested to
accurately predict results. Further to that, micro-fin tube can significantly reduce the buoyancy effects. In more recent work, Wang and Tian  suggested that internally ribbed tube resulted in higher heat transfer coefficient than that of smooth tube under similar working conditions.
Kang and Chang  performed experiments for steady-state and transient-pressure in upward flow of supercritical fluid R134a. The study suggested that pressure transient rates have slight impact upon heat transfer rate. Cui and Wang  experimentally examined supercritical fluid R134a for different flow directions in a vertical tube. The data suggested good heat transfer in downward flow as compared to upward direction. He and Dang [28 , 29] experimentally investigated supercritical fluid R245fa in vertical tube under heating condition. The experimental results revealed 70% data can be calculated by Yamagata’s correlation within ±30% accuracy. The experimental data of supercritical fluid R1233zd (E) showed good agreement with Petukhov’s correlation. In comparison with supercritical fluid R245fa, supercritical fluid R1233zd(E) can bring higher heat transfer coefficient. Jiang et al.  compared supercritical fluid R-22 and ethanol using smaller tube (1.004 mm) under higher heat flux (110 - 1800 kW∙m−2). Ethanol was suggested for better flow and heat transfer performance; therefore, it’s reasonable for cooling applications in combustion chambers.
Xiong and Gu  performed experiments and numerical simulations to evaluate the intermittent heating effects for supercritical fluid R134a. After analyzing experimental data and simulation models, SST k-ω model was suggested to accurately predict heat transfer enhancement as well as heat transfer deterioration. The decrease in velocity for near-wall region can cause heat transfer deterioration. Liu and Xu  compared nine turbulence models with experimental results of sCO2 passing through helical tube and suggested the Shear Stress Transport model for best prediction to heat transfer characteristics. The comparisons of various turbulent models were performed in previous research works for different supercritical fluids including sCO2 [32 - 36], supercritical water [37 - 42], supercritical methane , supercritical nitrogen , supercritical fluid R134a [31 , 45 , 46] and supercritical fluid R1234ze (E) . These findings suggested good agreement between simulations (performed by SST k-ω model) and experimental data. This model can provide most accurate prediction to heat transfer coefficient, wall and bulk temperatures ; therefore, the present simulations of supercritical fluid R515A were performed using SST k-ω model.
R515A is non-flammable and azeotrope replacement of R134a , and the mixture information is shown in Table 1. It has a lower global warming potential (GWP) of 403 than that of R134a (1300 GWP of R134a). R515A/R1234yf system was suggested to lower emissions and increase energy efficiency as compared to R744 system .
In the previous research , supercritical fluid R1234ze (E) was thoroughly investigated to describe the heat transfer characteristics near pseudo-critical point. The correlations were divided into two regions (above and below pseudo-critical point) which can increase prediction accuracy. This work is continued for supercritical fluid R515A and it is a step forward to study and explore the environment-friendly refrigerants. The simulations performed in this study can provide details about heat transfer of supercritical fluid R515A under different mass fluxes, pressures and tube diameters. The heat transfer correlations were also developed on the basis of simulation results.
2. NUMERICAL SIMULATIONS
2.1. Physical Model
Thermophysical properties of supercritical fluid R515A vary considerably near pseudo-critical point, as shown in Figure 1. Therefore, it is crucial to investigate the supercritical heat transfer in the vicinity of Tpc under different pressure rates. A 3D physical model is employed in the simulations to consider the effects of buoyancy for supercritical fluid R515A, as shown in Figure 2. Most of the commercial heat exchangers, which are employing organic Rankine cycle, are using horizontal flow direction rather than vertical [1 , 2 , 25]. Therefore, the present simulations adopted horizontal flow to explore the heat transfer. An adiabatic section (200 mm) is considered to eliminate the entrance effect, and constant heat flux boundary (q) is used for the wall (1000 mm) with different diameters.
2.2. Mathematical Model
The detailed mathematical model is described below .
The continuity equation is described as:
Figure 1. Supercritical fluid R515A at 3.8 MPa pressure showing variation in the values of density, specific heat, thermal conductivity and viscosity (REFPROP 9.1).
Figure 2. 3D physical model.
Table 1. Mixture information of R515A.
The momentum equation is described as:
The energy equation is described as:
where describes effective viscosity coefficient, and describes energy dissipation.
The turbulent kinetic energy equation is described as [1 , 35]:
The dissipation rate equation is described as:
where and denotes the generation of k and , and denotes the effective diffusivity of k and , respectively, and denotes the dissipation of k and due to turbulence, defines the cross-diffusion term, and are user-defined source terms.
2.3. Boundary Conditions
ANSYS FLUENT was employed for 3D simulation of turbulent flow. The thermophysical properties of supercritical fluid R515A at different temperatures were taken from REFPROP 9.1 and input by piecewise-linear function. SST model was adopted for present simulations owing to relatively accurate results for a range of supercritical fluids. This model has been widely used for predicting reliable results. The detailed working conditions are described in Table 2. The reference values including inlet velocity are computed from inlet for each case using ANSYS FLUENT. The following boundary conditions were adopted: mass flow inlet, outflow boundary, and constant wall heat flux. SIMPLE algorithm is used for pressure and velocity coupling.
The bulk temperature and heat transfer coefficient were calculated as follows:
where Tb is the bulk temperature, Tw is the wall temperature, u is the local velocity and A is the cross-sectional area of the tube.
2.4. Mesh Independence Verification and Model Validation
ANSYS ICEM is used to generate high-quality hexahedral mesh as shown in Figure 3. Keeping all the working conditions same, h is plotted for different mesh sizes as illustrated in Figure 4. The deviation in h values obtained from different mesh sizes is trivial and further details have been described in Table 3. A reasonable compromise is to use mesh 2 for further simulations which can bring satisfactory accuracy and calculation speed.
The model verification is performed against experimental data presented by Dang and Hihara  and Jiang and Hu . The present simulations resulted in a reliable heat transfer performance and better consistency with the experimental results (Figure 5) and can be employed for supercritical fluid R515A.
Figure 3. Details of mesh.
Figure 4. Mesh independence for different cell numbers.
Figure 5. Model validation by comparing previous experimental data (a) Dang and Hihara  and (b) Jiang and Hu .
Table 2. Working conditions considered for CFD simulations.
Table 3. Mesh independence for different cell numbers.
3.1. Effect of Mass Flux
Herein, the effects of mass flux on h were considered by keeping other conditions the same. The increase in mass flux corresponded to an increase in Re value (Figure 9) which resulted in a higher h value (Figure 6) and this behavior is in agreement with Gnielinski equation. At Tb = 385.8 K, slightly higher than Tpc, the heat transfer coefficient increased from 3242.4 W/(m2∙K) to 5139.9 W/(m2∙K) by increasing mass flux from 240 kg/(m2∙s) to 400 kg/(m2∙s), respectively. The peak values of h occur near Tpc = 384.7 K for all the three cases with different mass fluxes. The influence of G is considerably prominent around Tpc, specifically when the Tb is slightly higher than Tpc. Higher values of G resulted in increased Re with thin boundary layer, consequently, increase in heat transfer and higher h values as demonstrated in Figure 6.
The considered range of heat flux in the present simulations showed slight impact upon h (Figure 7). When , heat transfer coefficient changes slightly with heat flux, however, when , the h values remained almost unchanged with different q values. The rest of the simulations were performed under heat flux of 10 kW/m2. The turbulent kinetic energy distribution was demonstrated in Figure 8 at bulk temperature of 390 K. Meanwhile, the bulk mean Reynolds numbers are plotted in Figure 9. The higher value of mass flux can considerably increase both the k and Re which correspond to the enhancement of heat transfer and higher h values.
3.2. Effect of Pressure
Higher pressure may bring a decrement in heat transfer coefficient, meanwhile, the peak values move towards right, as demonstrated in Figure 10. There is considerable change in thermo-physical properties, specifically the sudden change in cp when pressure is in the vicinity of Tpc as illustrated in Figure 1. Herein, specific heat plays crucial role in the heat transfer of supercritical fluid R515A cooled in horizontal tubes. For different pressure values at , h values are decreasing with increasing pressure. However, totally opposite trend was noticeable at because of existing differences in thermo-physical properties and Tpc for various pressure values. At lower temperature ( ), there is a trivial change in the values of h at different pressures; however, the higher temperature ( ) may result in a noticeable change in h. Further increasing the temperature can result in a little effect of Tb on h values.
3.3. Effect of Tube Diameter and Gravity
Tube geometry, concerning different diameter, was considered for further simulations. The heat transfer coefficient may slightly lower with relatively large dimeter tube as demonstrated in Figure 11. The temperature contours at different tube diameters are shown in Table 4. The non-uniformity of temperature distributions was higher at large diameter tube, and the working fluid is inclined at upper regions owing to buoyancy effects.
The gravitational buoyancy showed trivial impact on heat transfer for the considered tube diameter (4.12 - 9.44 mm), as manifested in Figure 12. The influence of buoyancy is related to Richardson number:
Figure 6. Effect of different mass fluxes on h values.
Figure 7. Effect of different heat flux on h values.
Figure 8. Radial (a) velocity and (b) turbulent kinetic energy distributions for the crosssection with the bulk temperature of 390 K under different mass fluxes.
Figure 9. Reynolds numbers under different mass fluxes.
Figure 10. Effect of different pressures on h.
Figure 11. Influence of tube diameter on h.
Table 4. Temperature contours.
At lower diameter the dimensionless buoyancy (Richardson number) is much lower than unity (Figure 13) which results in trivial impact of buoyancy in the flow. Meanwhile, for 9.44 mm diameter tube at a lower temperature, the value of Richardson number is greater than 0.1. Herein, the influence of buoyancy increases the heat transfer coefficient (Figure 12). However, the increase in temperature may results in lowering the buoyancy influence (Figure 13(a)). At higher temperature, heat transfer is more influenced by which causes an increase in h values with increase in tube diameter.
Figure 12. Influence of gravitational buoyancy on h.
Figure 13. Comparison of the dimensionless numbers at different diameters.
4. CORRELATION DEVELOPMENT
Newly developed correlations applicable to present working conditions for supercritical fluid R515A were introduced, which can accurately predict heat transfer. Meanwhile, a reasonable approach is to divide the temperature range into two regions ( and ) [1 , 2], which can increase prediction accuracy. The newly developed simulated correlations have prediction accuracy of 10% (Figure 14). The suggested correlation for the whole region is as follows:
A better prediction is as follows:
The average absolute deviation and root mean square deviation of the prediction are 3.98% and 6.02%, respectively. This means that the new correlation performs very well in the heat transfer prediction of the cooling heat transfer characteristics of supercritical fluid R515A in tubes. Its application range is , , and for horizontal tubes of d = 4.12 - 9.44 mm.
Figure 14. Simulated and calculated Nusselt numbers by dividing into two regions ( and ).
The present simulations attempted to investigate supercritical fluid R515A under cooling conditions flowing through horizontal tube. Herein, investigated the influence of different pressures, heat fluxes, mass fluxes and tube diameters on the heat transfer coefficient as follows:
• The increase in mass flux from 240 kg/(m2∙s) to 400 kg/(m2∙s) can enhance the heat transfer owing to increase in Reynolds number. However, the increase in pressure from 3.8 MPa to 4.8 MPa can possibly decrease the h values and can shift the peak value of heat transfer coefficient in the right region. This is possibly due to variations in thermo-physical properties, specifically the sudden change in specific heat, when the pressure is in the vicinity of pseudo critical point.
• The 9.44 mm diameter tube showed slightly lowered heat transfer coefficient than that of 4.12 mm. There is a slight influence of gravitational buoyancy on heat transfer for a relatively large diameter tube (9.44 mm) under considered operating conditions.
• For the considered range of heat flux (−5 to −15 kW/m2), heat transfer coefficient remained almost unchanged for lower temperature ( ). However, h values changed slightly at higher temperature ( ).
• Moreover, heat transfer correlations were suggested to accurately predict Nusselt number within 10%. The average absolute deviation and root mean square deviation of the prediction are 3.98% and 6.02%, respectively. The experimental investigations would be crucial that can further validate and improve the accuracy of prediction for heat transfer coefficient.
Owing to environmental issues, the present simulations suggest that R515A is a considerable replacement of R134a. Further investigations are required to thoroughly explore the heat transfer characteristics of potential alternatives in cooling and heating conditions.
This work is supported by the National Natural Science Foundation of China (Grant No. 51576187).
A cross-sectional area (mm2)
specific heat [J/(kg∙K)]
average specific heat [J/(kg∙K)]
d diameter (mm)
G mass flux [kg/(m2∙s)]
Gr Grashof number
h heat transfer coefficient [W/(m2∙K)]
i enthalpy (J/kg)
k turbulent kinetic energy (m2/s2)
mass flow rate (kg/s)
Nu Nusselt number
P pressure (MPa)
Pr Prandtl number
q heat flux (kW/m2)
Q heat exchange amount (kW)
r radial coordinate (mm)
R tube radius (mm)
Re Reynolds number
Ri Richardson number
T temperature (K)
u fluid velocity (m/s)
v velocity (m/s)
Thermal conductivity [W/(m∙K)]
GWP Global Warming Potential
ODP Ozone Depletion Potential
SST Shear Stress Transport
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