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ABSTRACT
Realizing the importance of the natural circulation loop (NCL), which is a passive heat transport device, an analytical study is undertaken to demonstrate the functioning of an NCL-based parabolic trough collector (PTC). Multiple validated analytical models were incorporated to evaluate the system performance. The parametric study involved variations in loop height, loop length, and solar radiation. The loop flow rate enhances by increasing its height or the receiver length. At maximum radiation, 1.3 kg/s flow rate was observed for loop geometry of 5 m height and 7.8 m length against 0.79 kg/s for 1 m height. The flow rate predicted for a 10 m length and 1 m height loop was 0.87 kg/s. Since instability rises with height and heat loss and receiver temperature increase with receiver length, a trade-off between the two is necessary to function NCL-based PTC properly. Otherside, though the higher heat output with an increase in the receiver length is evident, a noticeable drop in thermal efficiency (≈7%) during the peak hours of solar radiation is a matter of concern. Further, the outlet temperature was not affected by the loop height for the defined flow condition of the process fluid. Like in conventional PTC systems, the process fluid’s exit temperature or flow rate can also be maintained constant during a day operation by varying the flow condition. The proposed model can deliver ≈ 1500 liters of hot water in six hours with an average 68% thermal efficiency without external power, in contrast to the necessity of notable pumping power and associated overhead charges in conventional PTC. Further, the system’s stability was predicted using linear stability analysis, and stability maps were generated for different loop heights and found that as the loop height decreases, the unstable zone diminishes. Though the steady-state data points are in the unstable flow region, stable operation is expected by incorporating pertinent instability restraining technique, that is, loop tilt.
Highlights
Efficacy of NCL-based PTC is demonstrated.
Effect of geometrical and operational conditions of NCL on PTC performance is analyzed.
Stability analysis of NCL and instability restraining method is suggested.
NCL-based PTC model is proposed.
Nomenclature
| A | = | Area (m2) |
| Ar | = | Aspect ratio (Height/Width) |
| Cp | = | Specific heat (J/kgK) |
| D | = | Diameter (m) |
| f | = | Friction factor (-) |
| FR | = | Collector heat removal factor (-) |
| F’ | = | Collector efficiency factor (-) |
| g | = | Acceleration due to gravity (m/s2) |
| Grm | = | Modified Grashoff number |
| H | = | Loop height (m) |
| h | = | Heat transfer coefficient (W/m2K) |
| Ib | = | Beam radiation (W/m2) |
| k | = | Thermal conductivity (W/mK) |
| K | = | Flow losses (-) |
| L | = | Length (m) |
| m | = | Mass flow rate (kg/s) |
| Num | = | Modified Nusselt number = |
| Pr | = | Prandlt number (-) |
| Q | = | Heat input (W) |
| r | = | Radius (m) |
| Re | = | Reynolds number (Dm/Aμ) |
| s | = | Coordinate around the loop (m) |
| Stm | = | Modified Stanton number = |
| T | = | Temperature (K) |
| U | = | Overall heat transfer coefficient (W/m2K) |
| Greek symbols | = | |
| β | = | Thermal expansion coefficient (K−1)/(orifice diameter/loop diameter) |
| ρ | = | Density (kg/m3)/reflectivity |
| µ | = | Absolute viscosity (kg/m.s) |
| = | Dimensionless mass flow rate (m/mss) | |
| η | = | Efficiency |
| α | = | Absorptivity |
| γ | = | Intercept factor |
| τ | = | Transmissivity |
| = | Dimensionless temperature | |
| Subscripts | = | |
| a | = | Aperture/ambient |
| c | = | Cooler/cover |
| cl | = | Cold leg |
| e | = | Elbow |
| eff | = | Effective |
| g | = | Glass |
| h | = | Heater |
| hl | = | Hot leg |
| i | = | Inner |
| L | = | Loss |
| o | = | Outer/optical |
| r | = | Receiver/Radius |
| ss | = | Steady state |
| t | = | Total/thermal |
| u | = | Useful |
| Acronyms | = | |
| CFD | = | Computational fluid dynamics |
| DNI | = | Direct normal irradiance |
| HHHC | = | Horizontal heater horizontal cooler |
| HTF | = | Heat transfer fluid |
| NCL | = | Natural circulation loop |
| NCS | = | Natural circulation system |
| NREL | = | National renewable energy laboratory |
| PTC | = | Parabolic trough collector |
| SPNCL | = | Single phase natural circulation loop |
| VHVC | = | Vertical heater vertical cooler |
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Notes on contributors
Nakul S.
Nakul S. is Assistant professor in the Department of Mechanical and Industrial engineering, Manipal Accademy of higher education, Manipal India. His research interesrts include natural circulation flows, heat transfer, computational fluid dynamics and thermal mangement.
Arunachala U. C.
Arunachala U. C. is a Professor in the Department of Mechanical and Industrial Engineering at Manipal Institute of Technology, Manipal, India. He has more than 25 years of research and teaching experience. His research interests include analysis of solar thermal systems, thermal management of photovoltaic modules, stability analysis of natural circulation loops, thermosyphon heat transport systems, heat transfer augmentation of thermal systems and heat exchanger analysis.