Exergetic efficiency prediction of roughened solar air heater
Journal of Thermal Engineering 2023, Vol. 9, Issue 3, pp. 718-732; doi.org/10.18186/thermal.1299177
Abstract
Keywords: Roughness; Exergetic Efficiency; Thermal Efficiency; Solar Air Heater; Nusselt Number
Introduction
The energy demand increasing day-by-day globally because of rapid growth in population and industrialization due to which world fossil fuel reserve depletes drastically. Also, power generation from fossil fuels causes environmental degradation. Hence there is a need to shift from convention fuels- towards the non-conventional energy resources. Among available renewable energy sources solar
energy is the freely available, easily accessible, cost effective, clean and inexhaustible source of energy. So, solar energy has great potential to strengthen industrialization and economic development. Solar energy will be the solution of future energy crises. The effective and adequate utilization of solar energy leads to amelioration in social, economic and environmental aspects of any nation. In the thermal route of solar energy application, the solar air heater
*Corresponding author. *E-mail address: naveen.gupta@gla.ac.in This paper was recommended for publication in revised form by Regional Editor Ahmet Selim Dalkılıç Published by Yıldız Technical University Press, İstanbul, Turkey Copyright 2021, Yıldız Technical University. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
(SAH) is used to convert solar energy into thermal energy. Generally, it is used for low grade thermal energy applications [1, 2]. The design of SAH is very simple, maintenance free and cheap. The efficiency of SAH is poor due to lesser value of convective coefficient in between absorber plate and flowing air. The heat transfer can be enhanced by using roughness in the SAH duct [3, 4]. The roughness may be of distinct shape and size [5-7]. Sahu and Prasad [8] studied performance of arc shape protrusions using exergetic efficiency. They suggest that at Re higher than 20000 the conventional smooth SAH is suitable because at higher Re exergy of thermal energy collected by SAH fall behind the value of exergy of required pumping power. Singh et al. [9] studied discrete-V-down rib roughened SAH using exergy analysis. The exergy analysis based on second law incorporates required pumping power and output energy. The highest amount of energy that can be obtained from a particular type of energy is called exergy [10, 11]. The analysis based on second law of efficiency of rib roughened SAH has been reported by Kumar et al. [12], Gupta and Kaushik [13–15] and Layek et al. [16]. Kumar et al. [12] studied performance of winglet type roughness roughened absorber surface of SAH by using exergy analysis. Kaushik and Gupta [13, 14] did thermo-hydraulic performance evaluation of SAH with the help of thermal, exergetic and effective efficiencies. They reported that for the optimum value of aspect ratio of collector and duct height there will be an optimal value of number of glass cover (M) for a particular application. For higher value of M low aspect ratio of collector and higher duct depth will give higher exergetic efficiency and in case of lower value of M high aspect ratio of collector and low duct height will give higher value of exergetic efficiency. They reported that circular and V-shaped rib shows appreciable value of exergy efficiency in the higher range of Re. Gupta and Kaushik [15] studied performance of expanded metal-mesh type of roughness. They carried out performance evaluation in terms of effective and exergy energy enhancement ratio at distinct value of Re. the enhancement ratios increase with the increase in I and duct depth. They reported that exergy enhancement ratio is a meaningful criterion for SAH performance evaluation. Layek et al. [16] studied numerically entropy generation in chamfered rib grove type of roughness in repeated manner. The set of parameter relative pitch ratio (p/e) = 6, relative grove position (g/p) = 0.4 and chamfer angle (φ) = 18° shows minimum rise in entropy generation. Momin et al. [17] experimentally studied performance of V-shape rib roughened SAH. The parameter relative rib height (e/Dh), angle of attack (α) and Reynolds number (Re) varies as 0.02-0.034, 30-90° and 2500-18000 respectively whereas p/e = 10. They reported that the Nu enhances by1.14 times more as comparison to inclined ribs at Re = 17034. The highest augmentation in Nu and f were 2.30 and
2.83. times at α = 60°. They also reported that the effect of
Re on Nu is much stronger as that of α. Istanto et al. [18] studied performance of continuous ribs of V-down shape
roughened SAH duct. The Re varies from 3500 to 10000. Highest value of thermal performance has been achieved at α = 60°. Singh et al. [19, 20] studied performance of V-shape down discrete rib roughness. The parameter α, relative gap width (g/e), relative gap position (d/w), Re, e/ Dh and p/e varies as 30°-75°, 0.5-2.0, 0.20-0.80, 3000-15000, 0.015-0.043 and 4-12 respectively. Deo et al. [21] studied performance of V-down shape rib combine with staggered rib with multi gap roughened SAH duct. The experimental parameters e/Dh, α, Re and p/e ranges as 0.026 - 0.057, 40° 80°, 4000 - 12000 and 4 – 14 respectively. The value of fixed parameter staggered rib length to rib height ratio (w/e), g/e and relative staggered rib pitch (P/p) 4.5, 1 and 0.65 respectively. Hans et al. [22] studied performance of multi-Vshaped rib roughness. The experimental parameter Re, e/ Dh, W/w, α and p/e varies as 2000-20000, 0.019-0.043, 1- 10, 30° - 75°, and 6 -12 respectively. They maximum augmentation in Nu and f occurs at p/e = 8. Singh et al. [23] studied multi V-shaped ribs with uniform gap roughened SAH duct. The f and Nu were increased by 5.67 and 6.46 at W/ w=6. Kumar et al. [24, 25] studied V-shape rib roughness with parameters W/e, e/Dh, g/e, W/w, p/e, and d/x equals to 12, 0.0433, 1.0, 6, 10 and 0.69 respectively. The value of α varies from 30-75°. They Nu has highest value at α = 60°. Yadav et al. [26] studied performance of circular-protrusion type of roughness. The study parameter arc angle (α’) and Re varies as 45°- 75° and 3600 – 18100 respectively. The maximum increment Nu is 2.89 times at α’ equals to 60°. Hans et al. [27] studied performance of broken arc rib type of roughness. The broken arc contains uniform gaps. The experimental parameter g/e, d/w, p/e, α’, e/Dh and Re varies as 0.5 -2.5, 0.5 - 0.8, 4 - 12, 15-75°, 0.0220.043 and 2000 to16000 respectively. They reported that the Nu enhanced by 2.63 times at e/Dh = 0.043. Gill et al. [28] studied performance of hybrid-rib roughness. The study parameter e/Dh, α’, and Re varies as 0.022-0.043, 15-75°, and 2000-16000 respectively. The Nu was enhanced by 3.16 times at e/Dh equals to 0.043. Lanjewar et al. [29] studied W-shape rib roughness both in W-down and W-up pattern type of roughness. The parameter e/Dh = 0.03375 and Re equal to 2300 -14000. The W-down pattern has better performance as that of W-up pattern. The highest value of thermohydraulic ratio for W-up and W-down patterns is
1.73. and 1.95 respectively. Kumar et al. [30] studied effect
of discrete-W-shape rib roughness. The value of parameter p/e = 10 and α = 30° to 75°, e/Dh varies from 0.0168 to 0.0338. Nu enhances with the increase in the value of Re. Gawande et al. [31] studied performance of reverse L-shape repeated roughness. The experimental parameter p/e and Re varies as 7.14 - 17.86 and 3800-18000 respectively. The THPP was found in the range of 1.92 to 1.90. Kumar and Layek [32, 33] studied performance of winglet types of turbulators with small hole at tip. The experimental parameter varies as α = 30° - 75, W/w = 3 – 7 and Re = 3000 – 22000. Patel et al. [34] studied performance of reverse-NACA 0040 profile rib roughness. The parameter
p/e and e/Dh equal to 8 and 0.065 respectively. Kumar and Layek [35] also have done exergetic performance evaluation for the above roughness. Promvonge et al. [36] experimentally studied performance of V-shape ribs and delta-groove roughness. The parameter Re = 7000 -30000. Hans et al. [37] studied performance of broken arc ribs. The experimental parameter p/e, g/e, e/Dh and α varies as 4-12, 0.5-2.5, 0.2-0.8, and 15°-75° respectively. Al-Dulaimi et al. [38] studied performance of rectangular turbulators in a square duct. The thermal performance augmented remarkably. Afsharpanah et al. [39] studied performance of multitwisted tape insert type of roughness. Sachdeva et al. [40] studied performance of U-shape fin by placing longitudinally in the duct. The air outlet temperature decreased by 25°C as flowing rate of air increased from 40 kg/hr to 180 kg/hr. The detailed review of different artificial roughness of distinct shape and size used in SAH have been presented in the past [41, 42]. The literature shows that various rib configuration has been investigated experimentally. The results have been presented in term of Nu, f and thermal performance and theses parameters have been compared individually. Also, it has been found that those ribs configuration which have high Nusselt number, also have high friction factor (higher air Pm). So, it is become necessary to mutual consideration of Nusselt number and friction factor to assess the most advantageous configuration. Therefore, exergetic efficiency of various rib configuration have been evaluated considering Nu and f. Also, exergetic efficiency of various ribs configurations have been compared with smooth duct. In view of above, the present study is carried out to meet out the following objective: to study the exergetic efficiency characteristics distribution for various ribs configuration and compared with exergetic efficiency with conventional smooth absorber in SAH. Also, best ribs configuration have been identify which provide maximum exergetic efficiency.
Assessment Approach Of Roughened SAH
The useful heat gain (Qu) can be evaluated as [43], (1) where, (τα)avg– product of transmittance and absorbance Uo– overall heat loss coefficient, Tpm – absorbing plate mean temperature Ta – ambient temperature Ap – Absorber plate area. The overall heat loss coefficient [43],
Heat transfer due to convection between absorber plate and glass cover, (5) Heat transfer due to radiation between sky and glass cover, (6) The resistance to ambient,
The top loss coefficient from glass cover to the surrounding is,
The thermal efficiency is, (14) (11) The net effective efficiency is expressed as [44], (15) (12)
where, C (=0.18) is a conversion factor used for to convert Pm in to thermal energy. Pm is the required mechanical power by blower for propelling air. The Pm can be expressed as[45],
Where, ΔPd is the pressure drop. The ΔPd can be expressed as [34],
The exergetic efficiency can be defined as the ratio of net exergy flow rate to the air (En) and exergy related with solar irradiation (Es). Altified et al. [54] suggested following exergy loss componentsa) Exergy losses by friction. b) Exergy losses due to optical losses. c) Exergy losses due to absorption of irradiation. d) Exergy losses due to transferring of heat to the flowing air. e) Exergy losses from absorber surface to the environment.
Mathematical Model For Exergetic Performance Evaluation Of SAH
The calculation of thermal and exergetic efficiency of SAH proceeds by using value of parameters. The range of system parameter based on various experimental studies and operating parameters decided on the basis of application. The optimum thermal and exergetic efficiency has been calculated by using solar insolations (I) and ΔT/I. The distinct properties of air i.e. dynamic viscosity (μ), density (ρ) thermal conductivity (k) and specific heat (Cp) were calculated with the help of relations given by Bhushan and Singh [46] and Hans [47] and as,
Operating parameters Fixed Ambient temperature (Ta), K Wind velocity (Vw), m/s
The procedure adopted for calculation of thermal and effective efficiency is same as it was given by Alam et al.[44] and a Matlab code has been generated for the same. The calculation procedure of thermal and exergetic efficiency as suggested by Singh et al. [5], Yadav and Kaushal [48], Alam et al. [49], Sahu and Prasad [50], Chamoli and Thakur [51], and Karmveer [52, 53] is as follows:Step 1: Firstly, Initialize values of fixed system and operating parameter from Table1. Step 2: The outlet temperature (To) of the air is calculated as,
The inlet temperature of air is considered to be same as sourrounding temperature.
Step 5: The thermo physical properties of air are calculated with the help of correlation 14, 15, 16 and 17 given by Step 9: The Reynolds number is calculated as,
Bhushan and Singh [46] and Hans [47]. Step 6: The overall heat loss coefficient (Uo) is calculated as given in equation 2.
Step 10: The Nusselt number of different roughness surfaces have been estimated with help of their developed correlations. Then convection coefficient of heat transfer has been estimated as,
The Nu for smooth surface has been estimated with the help of Dittus-Boelter correlation as, (26)
Step 12: Then, Qu1 and Qu2 are compared if, these values are not matched with each other, the new value of Tpm is determined by using the value of heat gain, Qu2, from the eq. 23. Iteration continues until the values of Qu1 and Qu2, comes close enough
It can be maximized and minimized by increasing and decreasing the value of En and Es. where, En - Net exergy flow rate to the air Es – Exergy related with solar irradiation En can be expressed as;
where, I- Intensity of global radiation P- Pumping power ηc- Carnot efficiency (1- Ta/Tfm) Es can be expressed as [54];
(28) Step 11: Again, heat gain by the flowing air is evaluated as follows [43]; Step 13: The friction factor of different roughness surfaces has been estimated with help of their developed correlations. The friction factor of smooth surface has been estimated with the help of Blasius correlation as [13], (29) Step 14: The Pm is calculated with help of equation 13a. Step 15: The ΔPd has been calculated with the help of equation 13b. Step 16: The exergy efficiency is calculated as, (30)
Where, Ts is the surface temperature of the sun, its value considered as 5762 K. Step 17: Finally, thermal efficiency, effective efficiency and exergetic efficiency of different roughness has been estimated. The flow chart of the mathematical model is shown in Figure 1.
Discussion
The numerical analysis with different type of roughness geometry, shape and arrangements is carried out with the help exergetic evaluation of roughened duct of SAH. The system and operating parameter with various type of roughenss geometry and their arrangements are considered for evaluating exergetic performance of SAH. The parameters of exergetic evaluation are tabulated in Table 1. The investigated distinct roughness geometries against the smooth duct shown in Table 2.
Table 2: Investigated roughness geometries against the smooth SAH. Investigators
Table 3. Exergetic efficiency data at distinct value of ΔT/I
The thermohydraulic performance of SAH does not take into account the various energy losses in propelling the air through duct of SAH. The exergetic evaluation based on IInd law of efficiency is most suitable for design of artificially roughened SAH. In this paper an attempt has been made for exergetic evaluation of distinct type of roughness’s used by various researchers. The exergetic efficiency of distinct type of roughness’s evaluated numerically by using correlations
30 Smooth V-shaped rib [17] V-down continuous ribs [18] Discrete V-down ribs[19] Multigap V-down ribs [21] Multiple v-ribs [22] Multiple V-ribs with symmetric gaps [23] Multiple V-ribs with Gap [24] Circular protrusions [26] Broken arc with staggered rib [28] W-shaped rib [29] Discrete W-shaped ribs [30] L-shaped ribs [31] Winglet type [33] Broken arc ribs [37]
of Nu and f developed by respective researchers and results of these roughness’s compared with smooth SAH duct. The exergy efficiency is evaluated by using the methodology discussed above for distinct operating parameters of roughened SAH. It is found that the roughened surface of absorber plate remarkably augments the efficiencies as that of smooth surface. The staggered broken-arc hybrid rib shows consistently higher value of ηthermal over the other roughness’s. The pumping power required due to various ribs including conventional smooth absorber has been plotted as a function of temperature rise parameters as shown in Figure 2. It can be seen that pumping power due to all ribs configurations decrease at very fast rate at lower temperature rise parameter value, thereafter, pumping power requirement become stagnant at higher temperature rise parameters. Also, pumping power requirement for broken arc with staggered ribs [28] is found to be higher in comparison to other ribs configurations, however, this difference is not significant at higher temperature rise parameter. Similarly, heat gain due to various ribs configuration have been plotted as a function of temperature rise parameter as shown in Figure
3. The useful heat gain of all rib’s configuration decrease
with increase in temperature rise parameters. The maximum heat gain is found in case of broken arc with staggered ribs [28] which decrease 240 to 210 watts when temperature rise parameter vary from 0.002 to 0.03 K.m2/W. However, lowest heat gain is found in case of W-shaped rib configuration [29] which decrease 231 to 103 watts in same rage of
Smooth V-shaped rib [17] V-down continuous ribs [18] Discrete V-down ribs[19] Multigap V-down ribs [21] Multiple v-ribs [22] Multiple V-ribs with symmetric gaps [23] Multiple V-ribs with Gap [24] Circular protrusions [26] Broken arc with staggered rib [28] W-shaped rib [29] Discrete W-shaped ribs [30] L-shaped ribs [31] Winglet type [33] Broken arc ribs [37]
0.7 Smooth V-shaped rib [17] V-down continuous ribs [18] Discrete V-down ribs[19] Multigap V-down ribs [21] Multiple v-ribs [22] Multiple V-ribs with symmetric gaps [23] Multiple V-ribs with Gap [24] Circular protrusions [26] Broken arc with staggered rib [28] W-shaped rib [29] Discrete W-shaped ribs [30] L-shaped ribs [31] Winglet type [33] Broken arc ribs [37]
ΔT/I Figure 4. ηthermal of roughened duct with respect to ΔT/I.
0.02 Smooth V-shaped rib [17] V-down continuous ribs [18] Discrete V-down ribs[19] Multigap V-down ribs [21] Multiple v-ribs [22] Multiple V-ribs with symmetric gaps [23] Multiple V-ribs with Gap [24] Circular protrusions [26] Broken arc with staggered rib [28] W-shaped rib [29] Discrete W-shaped ribs [30] L-shaped ribs [31] Winglet type [33] Broken arc ribs [37]
ΔT/I Figure 5. ηexergetic of roughened duct with respect to ΔT/I.
temperature rise parameters. Similarly, heat gain in smooth convention absorber have also been plotted for comparison purposes which have lowest heat gain. The thermal efficiency curves with respect to ΔT/I and Re have been plotted for distinct type of roughness’s in Figure 4. The staggered broken-arc hybrid rib shows consistently higher values of ηthermal over the other roughness’s and W-shaped ribs shows lower values of ηthermal over the other surface. The exergy efficiency curves with respect to ΔT/I and Re have been plotted for distinct type of roughness’s as shown in Figure 5. the value of exergetic efficiency at distinct value of ΔT/I for different roughness’s is shown in table 3. The staggered broken-arc hybrid rib shows consistently higher values of ηexergetic over the other roughness’s and W-shaped ribs shows lower values of ηexergetic over the other surface. The highest value of exergetic efficiency is achived by all distinct roughnesses at ΔT/I more than 0.012. The thermal and exergetic efficiency of the rough surfaces have been compared with the thermal and exergetic efficiency of the smooth surface in the same experimental conditions. It has been found that the optimum performance achieved at e/Dh = 0.043, p/e = 10, α = 60° and W/w = 6. Also, the unique combination of parameters e/Dh = 0.043, p/e = 10 and α = 60° are observed for best performance.
Conclusion
This paper persents a numerical study for predicting the exergy efficiency of SAH having roughened absorber surface. The effects of ΔT/I on the exergy efficiency were determined. The exergy efficiency of roughened SAH was calculated numerically with the help of developed correlations and the results also compared with conventional SAH under same operating parameters. The conclusions of the study are as follows1. The exergetic evaluation of roughened SAH suggest that use of staggered broken-arc shape roughened SAH for Re less than 20,000 and for more than 20,000 conventional smooth plat SAH is suitable.
4. A set of unique combination of parameters p/e = 10, e/
Dh = 0.043 and α = 60° have been observed for best exergetic performance. It is same for all insolation values.
6. The analysis persent in this paper facilitates the
researchers to design the absober plate of SAH by using concept of exergetic efficiency. 7. Hybrid ribs configuration exhibited the highest exergetic efficiencies when temperature rise parameters greater than 0.01 K.m/W, however, smooth duct also showed a significant exergetic efficiency when temperature rise parameters had low values.
Nomenclature
Symbol Title D Pipe inside diameter (to base of ribs) Hydraulic diameter of duct Dh e Roughness height Roughness Reynolds number e+ Relative roughness height e/Dh f Friction factor of roughened surface Heat removal factor FR g Heat transfer roughness function hr Radiative heat transfer coeff. hc Convective heat transfer coeff. hw Wind convective heat transfer coeff. I Insolation M Mass flow rate per unit collector area Nu Nusselt number Heat gain Qu Heat transfer function Qe+ R Momentum transfer roughness function Ra Rayleigh number Re Reynolds number St Stanton number Ambient temperature Ta Mean air temperature Tf Air inlet temperature Ti Plate temperature Tp Wall temperature Tw ΔP Pressure drops UO Overall heat loss coefficient V Velocity of air in SAH duct Thickness of insulation ti Thickness of glass cover tg Height of collector edge tg Back heat loss coefficient Ub Edge heat loss coefficient Ue Top heat loss coefficient Ut V Air velocity Wind Speed Vw α Angle of attack α’ Arc angle β’ Thermal expansion coefficient of air Glass cover emissivity εg Absorber plate emissivity εp υ Kinematic viscosity, τ Transmissivity σ Steafan-Boltzmann constant, η Thermal efficiency
Unit m m m W/m2.K W/m2.K W/m2.K W/m2 Kg/s m2 W K K K K K N/m2 W/m2.K m/s mm mm mm W/m2.K W/m2.K W/m2.K m/s m/s degree degree 1/K m2/s W/m2.K4 -
Data Availability Statement
The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.
Conflict Of Interest
The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Ethics
There are no ethical issues with the publication of this manuscript.
Share and Cite
KARMVEER, K.; GUPTA, N.K.; ALAM, T.; SINGH, H. Exergetic efficiency prediction of roughened solar air heater. Journal of Thermal Engineering 2023, Vol. 9, pp. 718-732. https://doi.org/10.18186/thermal.1299177