تجزیه و تحلیل عملکرد حرارتی هیدرولیک CFD بر اساس یک بخارکننده هوا خورشیدی مصنوعی زبر با داشتن مثلث متساوی الاضلاع ناهمواری دنده دار برش در صفحه جذب کننده

In this article, a numerical investigation is conducted to analyze the two-dimensional incompressible Navier–Stokes flows through the artificially roughened solar air heater for relevant Reynolds number ranges from 3800 to 18,000. Twelve different configurations of equilateral triangular sectioned rib (P/e = 7.14–35.71 and e/d = 0.021–0.042) have been used as roughness element. The governing equations are solved with a finite-volume-based numerical method. The commercial finite-volume based CFD code ANSYS FLUENT is used to simulate turbulent airflow through artificially roughened solar air heater. The RNG k–ε turbulence model is used to solve the transport equations for turbulent flow energy and dissipation rate. A total numbers of 432,187 quad grid intervals with a near wall elements spacing of y+ ≈ 2 are used. Detailed results about average heat transfer and fluid friction in an artificially roughened solar air heater are presented and discussed. The effects of grid distributions on the numerical predictions are also discussed. It has been observed that for a given constant value of heat flux (1000 W/m2), the performance of the artificially roughened solar air heater is strong function of the Reynolds number, relative roughness pitch and relative roughness height. Optimum configuration of the roughness element for artificially roughened solar air heater is evaluated.

Solar energy, radiant light and heat from the sun, has been harnessed by humans since ancient times using a range of ever-evolving technologies. Before 1970, some research and development was carried out in a few countries to exploit solar energy more efficiently, but most of this work remained mainly theoretical and academic. After the dramatic rise in oil prices in the 1970s, several countries began to formulate extensive research and development programs to exploit solar energy. Solar air heater is an effective device to harness solar energy and used for heating purposes i.e., drying of crops, seasoning of timber, space heating etc. A simple solar air heater consists of an absorber plate to capture solar radiation and transfers this solar (thermal) energy to air via conduction heat transfer. This heated air is then ducted to the building space or to the process area where the heated air is used for space heating or process heating needs [1]. Artificial roughness is a well-known method to increase the heat transfer from a surface to roughen the surface either randomly with a sand grain or by use of regular geometric roughness elements on the surface. However, the increase in heat transfer is accompanied by an increase in the resistance to fluid flow. Several investigators have attempted to design an artificially roughened rectangular duct which can enhance the heat transfer with minimum pumping losses. Many investigators have studied this problem in an attempt to develop accurate predictions of the behavior of a given roughness geometry and to define a geometry which gives the best transfer performance for a given flow friction. A lot of studies have been reported in the literature on artificially roughened surfaces for heat transfer enhancement but most of the studies were carried out with two opposite or all the four walls roughened. An early study of the effect of roughness on friction factor and velocity distribution was performed by Nikuradse [2], who conducted a series of experiments with pipes roughened by sand grains and since then many experimental investigations were carried out on the application of artificial roughness in the areas of gas turbine airfoil cooling system, gas cooled nuclear reactors, cooling of electronic equipment, shipping machineries, combustion chamber liners, missiles, re-entry vehicles, ship hulls and piping networks etc. In the case of solar air heater, roughness elements have to be considered only on one wall, which is the only heated wall comprising the absorber plate. These applications make the fluid flow and heat-transfer characteristics distinctly different from those found in case of two roughened walls and four heated wall duct. In the case of solar air heater, only one wall of the rectangular air passage is subjected to uniform heat flux while the remaining three walls are insulated. It is well known that the heat transfer coefficient between the absorber plate and air of solar air heater is generally poor and this result in lower efficiency. The effectiveness of solar air heater can be improved by using artificial roughness in the form of different types of repeated ribs on the absorber plate. It has been found that the artificial roughness applied to the absorber plate of a solar air heater, penetrates the viscous sub-layer to promote turbulence that, in turn, increases the heat transfer from the surface as compared to smooth solar air heater. This increase in heat transfer is accompanied by a rise in frictional loss and hence greater pumping power requirements for air through the duct. In order to keep the friction losses at a low level, the turbulence must be created only in the region very close to the duct surface, i.e., in the laminar sub-layer. Artificially roughened solar air heater has been the topic of research for last thirty years. Several designs for artificially roughened solar air heaters have been proposed and discussed in the literature [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29] and [30]. Several investigators have attempted to optimize a roughness element, which can enhance convective heat transfer with minimum pumping power requirement by adopting experimental and numerical approaches. Most of the experiments are also conducted to specifically understand the influence of pitch-to-rib height ratio (P/e) and/or rib height-to-hydraulic diameter ratio (e/D) on average heat transfer and flow friction characteristics, and distributions of the mean velocities, pressure and turbulent statistics in the flows through the duct of an artificially roughened solar air heater. Literature search in this areas revealed that the heat transfer enhancement is strongly dependent on the relative roughness pitch (P/e) and relative roughness height (e/D) of roughness elements together with the flow Reynolds number (Re). There are lot of experiments have been done and so many experiments are going on right now to optimize roughness parameters for heat transfer enhancement in roughened duct of solar air heaters [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29] and [30]. Table 1 lists the major experimental works for different roughness geometries and configurations applied on the absorber plate of a solar air heater. Table 1. Summary of major experimental works on artificially roughened solar air heater having different roughness geometries applied on the absorber plate. S. No. Investigator/s Roughness geometry Range of parameters Principal findings 1. Prasad and Mullick [3] Transverse wire rib roughness e/D: 0.019 P/e: 12.7 Re: 10,000–40,000 14% improvement in thermal performance was reported at a Reynolds number of 40,000 over smooth duct. 2. Prasad and Saini [4] e/D: 0.02–0.033 P/e: 10–20 Re: 5000–50,000 2.38 and 4.25 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct. 3. Prasad [30] e/D: 0.0092–0.0279 e: 0.41–1.24 mm P/e: 10–40 P: 5–30.4 mm Re: 2959–12,631 1.786, 1.806 and 1.842 times enhancement in collector heat removal factor, collector efficiency factor and thermal efficiency respectively were reported over smooth duct. 4. Karwa et al. [8] Chamfered repeated rib-roughness e/D: 0.014–0.032 L/D: 32 & 66 P/e: 4.5–8.5 Φ: −15°–18° Re: 3000–20,000 W/H: 4.8–12 2 and 3 times enhancement in Stanton number and friction factor respectively were reported over smooth duct. 5. Karwa et al. [9] e/D: 0.0197–0.0441 P/e: 4.58 & 7.09 Φ: −15° Re: 3750–16,350 W/H: 6.88–9.38 50–120% and 80–290% enhancement in Nusselt number and friction factor respectively were reported over smooth duct. 6. Kumar et al. [27] Multi V-shaped rib roughness with gap e/D: 0.043 g/e: 0.5–1.5 Gd/Lv: 0.24–0.80 P/e: 10 Re: 2000–20,000 W/H: 12 W/w: 6 α: 60° 6.32 and 6.12 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct. 7. Kumar et al. [29] Re: 2000–20,000 e/D: 0.022–0.043 α: 30°–75° g/e: 0.5–1.5 Gd/Lv: 0.24–0.80 W/w: 1–10 P/e: 6–12 6.74 and 6.37 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct. 8. Singh et al. [24] Discrete V-down rib roughness d/w: 0.2–0.8 e/D: 0.015–0.0.043 g/e: 0.5–2.0 P/e: 4–12 Re: 3000–15,000 α: 30°–75° 3.04 and 3.11 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct. 9. Karwa and Chitoshiya [28] B/S: 6 e/D: 0.047 e: 3.2 mm P/e: 10.63 P: 34 mm Re: 2750–11,150 W/H: 7.8 W: 6.58 mm α: 60° 12.5–20% enhancement in the thermal efficiency was reported over smooth duct. 10.. Gupta [5] Inclined wire rib roughness e/D: 0.018–0.032 P/e: 10 Re: 5000–50,000 W/H: 6.8–11.5 α: 30°–90° 1.8 and 2.7 times enhancement in Nusselt number and friction factor respectively were reported over duct with transverse ribs. 11. Saini and Saini [6] Expanded metal mesh roughness e/D: 0.012–0.0390 L/e: 25–71.87 Re: 1900–13,000 S/e: 15.62–46.87 4 and 5 times enhancement in Nusselt number and friction factor respectively were reported over duct with transverse ribs. 12. Karwa [7] Transverse, inclined, V-up continuous, V-down continuous, V-up discrete and V-down discrete rib roughness B/S: 3.0 e/D: 0.0467–0.05 P/e: 10 Re: 2800–15,000 W/H: 7.19–7.75 α: 60°–90° 65–90%, 87–112%, 102–137%, 110–147%, 93–134%, 102–142% enhancement in Stanton number was reported over smooth duct for transverse, inclined, V-up continuous, V-down continuous, V-up discrete and V-down discrete rib arrangement respectively. 2.68–2.94, 3.02–3.42, 3.40–3.92, 3.32–3.65, 2.35–2.47 and 2.46–2.58 times 3 times enhancement in friction factor ratio was reported over smooth duct for transverse, inclined, V-up continuous, V-down continuous, V-up discrete and V-down discrete rib arrangement respectively. 13. Momin et al. [10] V-shaped rib roughness e/D: 0.02–0.034 P/e: 10 Re: 2500–18,000 W/H: 10.15 α: −30°–90° 2.30 and 2.83 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct. 14. Bhagoria et al. [11] Transverse wedge shaped rib roughness e/D: 0.015–0.033 P/e: 60.17x Φ: −8°–15° Φ−1.0264<p/e<12.12 Re: 3000–18,000 W/H: 5 2.4 and 5.3 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct. 15. Sahu and Bhagoria [12] 90° broken rib roughness e/D: 0.0338 e: 1.5 P: 10, 20, 30 Re: 3000–12,000 W/H: 8 1.25–1.4 times enhancement in heat transfer coefficient was reported over smooth duct. 16. Jaurker et al. [13] Rib-grooved roughness e/D: 0.0181–0.0363 g/P: 0.3–0.7 P/e: 4.5–10 Re: 3000–21,000 2.7 and 3.6 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct. 17. Layek et al. [14] Chamfered rib-grooved roughness e/D: 0.022–0.04 g/P: 0.3–0.6 P/e: 4.5–10 Φ: −5°–30° Re: 3000–21,000 3.24 and 3.78 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct. 18. Karmare and Tikekar [15] Metal grit rib roughness e/D: 0.035 to 0.044 Re: 4000–17,000 P/e: 12.5–36 l/s: 1.72–1 2 and 3 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct. 19. Saini and Saini [16] Arc shaped rib roughness e/d: 0.0213–0.0422 P/e: 10 Re: 2000–17,000 W/H: 12 α/90: 0.3333–0.6666 3.8 and 1.75 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct. 20. Aharwal et al. [17] Inclined continuous rib roughness with gap d/W: 0.167–0.5 e & b: 2 mm e/D: 0.0377 g/e: 0.5–2 P/e: 10 Re: 3000–18,000 W/H: 5.87 α: 60° 2.59 and 2.9 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct. 21. Saini and Verma [18] Dimple-shaped rib roughness e/D: 0.0189–0.038 P/e: 8–12 Re: 2000–12,000 The maximum value of Nusselt number was found corresponds to e/D = 0.0379 and P/e = 10. 22. Varun et al. [19] Combination of transverse and inclined rib roughness e/D: 0.030 e: 1.6 mm P/e: 3–8 P: 5–13 Re: 2000–14,000 W/H: 10 Best thermal performance was reported over smooth duct for P/e = 8. 23. Bopche and Tandale [20] Inverted U-shaped rib roughness e/D: 0.018–0.0396 e: 0.7–1.5 mm P/e: 6.669–57.14 P: 10–40 mm Re: 3800–18,000 W/H: 6 α: 90° 2.82 and 3.72 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct. 24. Kumar et al. [21] Discrete W-shaped rib roughness e/D: 0.0168–0.0338 e: 0.75–1.5 mm P/e: 10 Re: 3000–15,000 W/H: 8:1 α: 30–75° 2.16 and 2.75 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct. 25. Hans et al. [22] Multi V-shaped rib roughness e/D: 0.019–0.043 α: 30°–75° Re: 2000–20,000 W/w: 1–10 P/e: 6–12 6 and 5 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct. 26. Lanjewar et al. [23] W-shaped rib roughness e/D: 0.018–0.03375 e: 0.8–1.5 mm P/e: 10 Re: 2300–14,000 W/H: 8 α: 30°–75° 2.36 and 2.01 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct. 27. Tanda [25] Angled continuous rib, transverse continuous and broken rib, and discrete V-shaped rib roughness e/D: 0.09 e: 3 mm P/e: 6.66–20 Re: 5000–40,000 W/H: 5 α: 45° & 60° Roughening the heat transfer surface by transverse broken ribs was found to be the most promising enhancement technique of the investigated rib geometries. 28. Sethi et al. [26] Dimple shaped elements arranged in angular fashion e/D: 0.021–0.036 e/d: 0.5 P/e: 10–20 Re: 3600–18,000 W/H: 11 α: 45°–75° The maximum value of Nusselt number was reported over smooth duct for P/e = 10 and e/D = 0.036. Table options Conventional techniques used for the design and development of an artificially roughened solar air heater are mostly tedious, expensive and time consuming. CFD approach has emerged as a cost effective alternative and it provides speedy solution to design and optimization of an artificially roughened solar air heater. Computational fluid dynamics (CFD) is a design tool that has been developed over the past few decades and will be continually developed as the understanding of the physical and chemical phenomena underlying CFD theory improves. The goals of CFD are to be able to accurately predict fluid flow, heat transfer and chemical reactions in complex systems, which involve one or all of these phenomena. CFD uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. High speed computers are used to perform the calculations required to simulate the interaction of gases and liquids with surfaces defined by boundary conditions. With the development of numerical methodology and high speed computers, better solutions of fluid flow problems can be achieved. Ongoing research yields software that improves the speed and accuracy of complex simulation scenarios such as turbulent flows, transonic flows etc. Literature search in the area of artificially roughened solar air heater revealed that very few CFD investigation of artificially roughened solar air heater has been done to evaluate the optimum rib shape and configuration, which can enhance convective heat transfer with minimum pumping power requirement. Chaube et al. [31] conducted two dimensional CFD based analysis of an artificially roughened solar air heater having ten different ribs shapes viz. rectangular, square, chamfered, triangular, etc., provided on the absorber plate. CFD code, FLUENT 6.1 and SST k–ω turbulence model were used to simulate turbulent airflow. The best performance was found with rectangular rib of size 3 × 5 mm and CFD simulation results were found to be in good agreement with existing experimental results. Kumar and Saini [32] performed three dimensional CFD based analysis of an artificially roughened solar air heater having arc shaped artificial roughness on the absorber plate. FLUENT 6.3.26 commercial CFD code and Renormalization group (RNG) k–ε turbulence model were employed to simulate the fluid flow and heat transfer. Overall enhancement ratio with a maximum value of 1.7 was obtained and results of the simulation were successfully validated with experimental results. Karmare and Tikekar [33] carried out CFD investigation of an artificially roughened solar air heater having metal grit ribs as roughness elements on the absorber plate. Commercial CFD code FLUENT 6.2.16 and Standard k–ε turbulence were employed in the simulation. Authors reported the absorber plate of square cross-section rib with 58° angle of attack was thermo-hydraulically more efficient. Yadav and Bhagoria [34] carried out CFD investigation of an artificially roughened solar air heater having circular transverse wire rib roughness on the absorber plate. A two-dimensional CFD simulation was performed using ANSYS FLUENT 12.1 code as a solver with RNG k–ε turbulence model. Maximum value of thermal enhancement factor was reported to be 1.65 for the range of parameters investigated. A CFD based study of conventional solar air heater was performed by Yadav and Bhagoria [35]. ANSYS FLUENT and RNG k–ε turbulence model were used to analyze the nature of the flow. Results predicted by CFD were found to be in good agreement with existing empirical correlation results. Yadav and Bhagoria [36] conducted a numerical analysis of the heat transfer and flow friction characteristics in an artificially roughened solar air heater having square sectioned transverse ribs roughness considered at underside of the top heated wall. The thermo-hydraulic performance parameter under the same pumping power constraint was calculated in order to examine the overall effect of the relative roughness pitch. The maximum value of thermo-hydraulic performance parameter was found to be 1.82 corresponding to relative roughness pitch of 10.71. Yadav and Bhagoria [37] carried out a numerical investigation of turbulent flows through a solar air heater roughened with semicircular sectioned transverse rib roughness o the absorber plate. The physical problem was represented mathematically by a set of governing equations, and the transport equations were solved using the finite element method. The numerical results showed that the flow-field, average Nusselt number, and average friction factor are strongly dependent on the relative roughness height. The thermo-hydraulic performance parameter was found to be the maximum for the relative roughness height of 0.042. Yadav and Bhagoria [38] performed a CFD based investigation of turbulent flows through a solar air heater roughened with square sectioned transverse rib roughness. Three different values of rib-pitch (P) and rib-height (e) were taken such that the relative roughness pitch (P/e = 14.29) remains constant. The relative roughness height, e/D, varies from 0.021 to 0.06 and Reynolds number, Re, varies from 3800 to 18,000. The results predicted by CFD showed that the average heat transfer, average flow friction and thermo-hydraulic performance parameter were strongly dependent on the relative roughness height. A maximum value of thermo-hydraulic performance parameter was found to be 1.8 for the range of parameters investigated. Yadav and Bhagoria [39] employed circular sectioned rib roughness on the absorber plate to predict heat transfer and fluid friction behavior of an artificially roughened solar air heater by adopting CFD approach. ANSYS FLUENT 12.1 and RNG k–ε turbulence model were employed in their simulation. The maximum average Nusselt number ratio and friction factor ratio are found to be 2.31 and 3.14, respectively for the investigated range of parameters. Yadav and Bhagoria [40] presented a detailed literature survey about different CFD investigations on artificially roughened solar air heater. In order to find out the best turbulence model for the analysis of a solar air heater, a 2-dimensional CFD simulation was performed by authors. Authors also reported that the results obtained by Renormalization-group (RNG) k–ε model were in good agreement with the available experimental results. After conducting a comprehensive literature review, it has been observed that very few studies on CFD investigation of artificially roughened solar air heater have been done to evaluate the optimum rib shape and configuration, which can enhance convective heat transfer with minimum pumping power. An extensive literature search also indicates that there are very limited data available for predicting heat transfer and flow friction characteristics of solar air heaters roughened with equilateral triangular sectioned rib roughness. This paper is an attempt to bridge this gap by presenting a detailed CFD investigation of artificially roughened solar air heater having equilateral triangular sectioned rib roughness on the absorber plate. The present study is novel in a sense that no such type of study has previously been conducted on solar air heater having equilateral triangular sectioned rib roughness on the absorber plate. The main advantage of CFD simulation is that any complex geometry and any range of flow/roughness parameters can be implemented to predict the performance of an artificially roughened solar air heater, which cannot be done through experimental investigations. The main objectives of the present CFD analysis are: 1. To investigate the effect of flow and roughness parameters on average heat transfer and flow friction characteristics of an artificially roughened solar air heater having equilateral triangular sectioned transverse ribs on the absorber plate. 2. To find out optimal configuration of equilateral triangular sectioned transverse rib for heat transfer enhancement.

In this article a two-dimensional CFD model of an artificially roughened solar air heater having equilateral triangular sectioned rib roughness on the absorber plate has been proposed and used to predict the heat transfer and flow friction characteristics. Using this approach a detailed study is performed to analyze the impact of three parameters on the thermal and hydraulic performance of an artificially roughened solar air heater: relative roughness pitch (P/e), relative roughness height (e/D) and Reynolds number (Re). The major conclusions of this article are as follows: 1. The average Nusselt number tends to increase as the Reynolds number increases in all cases. The average Nusselt number tends to decrease as the relative roughness pitch increases for a fixed value of relative roughness height and it also tends to increase as the relative roughness height increases for a fixed value of relative roughness pitch. 2. The maximum enhancement in the Nusselt number has been found to be 3.073 times over the smooth duct corresponds to relative roughness height (e/D) of 0.042 and relative roughness pitch (P/e) of 7.14 at Reynolds number (Re) of 15,000 in the range of parameters investigated. 3. The average friction factor tends to decrease as the Reynolds number increases in all cases. The average friction factor tends to decrease as the relative roughness pitch increases for a fixed value of relative roughness height and it tends to increase as relative roughness height increases for a given value of relative roughness pitch. 4. The maximum enhancement in the friction factor has been found to be 3.356 times over the smooth duct corresponds to relative roughness height (e/D) of 0.042 and relative roughness pitch (P/e) of 7.14 at Reynolds number (Re) of 3800 in the range of parameters investigated. 5. A significant enhancement in the value of the thermo-hydraulic performance parameter has been found. The value of the thermo-hydraulic performance parameter varies between 1.36 and 2.11 for the range of parameters investigated. 6. The optimum value of thermo-hydraulic performance parameter has been found corresponds to relative roughness height (e/D) of 0.042 and relative roughness pitch (P/e) of 7.14. The optimum value of thermo-hydraulic performance parameter has been found to be 2.11 for Reynolds number (Re) of 15,000 within the range of the parameters investigated. Hence artificially roughened solar air heater with equilateral triangular sectioned rib roughness on the absorber plate having P/e = 7.14 and e/D = 0.042 can be employed for heat transfer augmentation.