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ABSTRACT
Distinct thermophysical properties encountered in supercritical fluids operating near the critical point have made them strong candidates for working fluids in various engineering applications. Particularly due to the existence of heat capacity maxima near the critical point, heat transfer involving supercritical fluids and their employment in power generation systems have received special attention. In this paper, the existence of optimal operating pressures that maximize the global conductance of supercritical heat exchangers is demonstrated. Analysis of the behavior of the isobaric specific heat along the heat transfer process shows that optimal performance is achieved when the average isobaric specific heat is maximized. Consequently, optimal pressure maps can be created to assist heat exchanger design for various combinations of inlet temperatures and heat transfer rates. Furthermore, it is demonstrated that simple dimensionless groups can correlate—with a mean absolute error (MAE) of 0.0332—the optimal operating pressures of up to 122 different fluids. In addition, it is shown that the correlation is even stronger closer to the critical point and for separate classes of fluids, where MAE can be as low as 0.0103 for triatomic substances.
Nomenclature
| c | = | specific heat [J/(kg · K)] |
| h | = | enthalpy (J/kg) |
| k | = | thermal conductivity [W/(m · K)] |
| u | = | velocity (m/s) |
| x | = | spatial coordinate (m) |
| A | = | area (m2) |
| L | = | duct length (m) |
| P | = | pressure (Pa) |
| R | = | gas constant [J/(kg · K)] |
| T | = | temperature (K) |
| U | = | global heat transfer coefficient [W/(m2 · K)] |
| Greek symbols | = | |
| ρ | = | density (kg/m3) |
| Δ | = | variation |
| φ | = | heat transfer group (–) |
| Other symbols | = | |
| l | = | cross-sectional perimeter (m) |
| = | mass flow rate (kg/s) | |
| = | heat flow rate (W) | |
| q″ | = | heat flux (W/m2) |
| Subscript | = | |
| c | = | critical |
| in | = | inlet |
| lm | = | logarithm mean |
| opt | = | optimal |
| out | = | outlet |
| p | = | at constant pressure |
| r | = | reduced |
| Superscript | = | |
| ∼ | = | dimensionless |
Nomenclature
| c | = | specific heat [J/(kg · K)] |
| h | = | enthalpy (J/kg) |
| k | = | thermal conductivity [W/(m · K)] |
| u | = | velocity (m/s) |
| x | = | spatial coordinate (m) |
| A | = | area (m2) |
| L | = | duct length (m) |
| P | = | pressure (Pa) |
| R | = | gas constant [J/(kg · K)] |
| T | = | temperature (K) |
| U | = | global heat transfer coefficient [W/(m2 · K)] |
| Greek symbols | = | |
| ρ | = | density (kg/m3) |
| Δ | = | variation |
| φ | = | heat transfer group (–) |
| Other symbols | = | |
| l | = | cross-sectional perimeter (m) |
| = | mass flow rate (kg/s) | |
| = | heat flow rate (W) | |
| q″ | = | heat flux (W/m2) |
| Subscript | = | |
| c | = | critical |
| in | = | inlet |
| lm | = | logarithm mean |
| opt | = | optimal |
| out | = | outlet |
| p | = | at constant pressure |
| r | = | reduced |
| Superscript | = | |
| ∼ | = | dimensionless |
Acknowledgments
Gustavo M. Hobold and Alexandre K. da Silva would like to thank the financial support received from ANEEL/PETROBRAS and CNPq.
Notes
1The pure and pseudo-pure substances available in CoolProp 6.0—and hence used in this paper—are, in alphabetical order: acetone, air, ammonia, argon, benzene, carbon dioxide, carbon monoxide, carbonyl sulfide, cyclohexane, cyclopropane, cyclopentane, D4, D5, D6, deuterium, dichloroethane, diethyl ether, ethane, ethanol, ethylbenzene, ethylene, ethylene oxide, fluorine, HFE143m, heavy water, helium, hydrogen, hydrogen chloride, hydrogen sulfide, iso-butane, iso-butene, iso-hexane, iso-pentane, krypton, MD2M, MD3M, MD4M, MDM, MM, methane, methanol, methyl linoleate, methyl linolenate, methyl oleate, methyl palmitate, methyl stearate, neon, neopentane, nitrogen, nitrous oxide, Novec 649, ortho-deuterium, ortho-hydrogen, oxygen, para-deuterium, para-hydrogen, propylene, propyne, R11, R113, R115, R115, R116, R12, R123, R1233zd(E), R1234yf, R1234ze(E), R1234ze(Z), R124, R125, R13, R134a, R13I1, R14, R141b, R142b, R143a, R152a, R161, R21, R218, R22, R227EA, R23, R236EA, R236FA, R245ca, R245fa, R32, R365MFC, R40, R404A, R407C, R41, R410A, R507A, RC318, SES36, sulfur dioxide, sulfur hexafluoride, toluene, water, xenon, cis-2-butene, m-xylene, n-butane, n-decane, n-dodecane, n-heptane, n-hexane, n-nonane, n-octane, n-pentane, n-propane, n-undecane, o-xylene, p-xylene, and trans-2-butene.