CFD based performance analysis of a solar air heater duct provided with artificial roughness

Renewable Energy 34 (2009) 1285–1291

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CFD based performance analysis of a solar air heater duct provided with artificial roughness Sharad Kumar, R.P. Saini* Alternate Hydro Energy Centre, Indian Institute of Technology Roorkee, AHEC, Roorkee, Uttarakhand 247667, India

a r t i c l e i n f o

a b s t r a c t

Article history: Received 15 July 2008 Accepted 19 September 2008 Available online 20 November 2008

In the present work the performance of a solar air heater duct provided with artificial roughness in the form of thin circular wire in arc shaped geometry has been analysed using Computational Fluid Dynamics (CFD). The effect of arc shaped geometry on heat transfer coefficient, friction factor and performance enhancement was investigated covering the range of roughness parameter (relative roughness height (e/D) from 0.0299 to 0.0426 and relative roughness angle (a/90) from 0.333 to 0.666) and working parameter (Reynolds number, Re from 6000 to 18,000 and solar radiation of 1000 W/m2). Different turbulent models have been used for the analysis and their results are compared. Renormalization-group (RNG) k-3 model based results have been found in good agreement and accordingly this model is used to predict heat transfer and friction factor in the duct. The overall enhancement ratio has been calculated in order to discuss the overall effect of the roughness and working parameters. A maximum value of overall enhancement ratio has been found to be as 1.7 for the range of parameters investigated. Ó 2008 Elsevier Ltd. All rights reserved.

Keywords: Solar air heater Artificial roughness CFD Heat transfer Friction Turbulence

1. Introduction The thermal efficiency of solar air heaters has been found to be generally poor because of their inherently low heat transfer capability between the absorber plate and air flowing in the duct. In order to make the solar air heaters economically viable, their thermal efficiency needs to be improved by enhancing the heat transfer coefficient. In order to attain higher heat transfer coefficient, the laminar sub-layer formed in the vicinity of the absorber plate is broken and the flow at the heat-transferring surface is made turbulent by introducing artificial roughness on the surface. Various investigators have studied different types of roughness geometries and their arrangements. Kays [1] used thin wires having diameter of the order of thickness of laminar sub-layer in the transverse direction to the flow with relative pitch ranging from 10 to 20. Gupta and Garg [2] carried out an experimental investigation to study the performance characteristics of four solar air heaters; two of corrugated type and other two of mesh type. Prasad and Mullick [3] and Prasad and Saini [4] used thin wires in transverse direction to increase heat transfer coefficient and tried to optimize the roughness parameter of absorber surface for maximum heat transfer for a given flow direction. Chaudhury et al. [5] carried out analysis of one pass corrugated, bare plate solar air heater. An investigation of fully developed turbulent flow in a solar air heater * Corresponding author. Tel.:þ91 1332 285841; fax: þ91 1332 273517. E-mail address: [email protected] (R.P. Saini). 0960-1481/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2008.09.015

duct with small diameter protrusion wires on the absorber plate was carried out by Prasad and Saini [6]. Saini and Saini [7] carried out an experimental study of solar air heater with roughness provided in the form of expanded metal mesh. An experimental investigation was carried out for fully developed turbulent flow in a rectangular duct with large aspect ratio (11: 1) and having expanded metal mesh as artificial roughness. Gupta et al. [8] carried out an experimental investigation on solar air heater with angled ribs with circular cross-section. They have investigated the effect of relative roughness height (e/D), inclination of rib with respect to flow direction and Reynolds number on fluid flow characteristics in transitionally rough flow region and evaluated the thermohydraulic performance of solar air heaters. Karwa et al. [9] carried out an experimental investigation of heat transfer and friction for the flow of air in rectangular ducts with repeated chamfered rib roughness on one broad wall. Muluwork [10] carried out an experimental analysis of air heater with artificial roughness provided by V-shaped staggered discrete ribs and reported that maximum heat transfer enhancement occurred at an angle of attack of 60 . Verma and Prasad [11] determined the optimal thermohydraulic performance of artificially roughened solar air heaters which was roughened by circular cross-section wires, by considering the optimum value of roughness Reynolds number. Momin et al. [12] used V-shaped ribs to study the effect of geometry on heat transfer and fluid flow characteristics of rectangular duct of solar air heaters with absorber plate having V-shaped ribs on its underside.

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Nomenclature H W D p e e/D

a

Height of the solar air heater duct, mm Width of the solar air heater duct, mm Hydraulic diameter of duct, m Pitch, mm Roughness height, mm Relative roughness ratio Wire arc angle, degree

Bhagoria et al. [13] used wedge shaped ribs to study enhancement of heat transfer coefficient and they have shown experimentally that a maximum enhancement of heat transfer occurs at a wedge angle of about 10 while on either side of this wedge angle, Nusselt number decreases. The friction factor increases as the wedge angle increases. Karwa [14] investigated the effect of repeated rectangular cross-section ribs on heat transfer and friction factor. Tanda [15] carried out an experimental study in a rectangular channel with transverse and V-shaped broken ribs. Jaurker et al. [16] made an experimental investigation on heat transfer and frictional characteristics rib-grooved artificial roughness. The presence of rib-grooved artificial roughness yields Nusselt number up to 2.7 times while the friction factor rises up to 3.6 times. Layek et al. [17] carried out an experimental investigation to study the heat transfer and friction for repeated transverse compound ribgroove arrangement on absorber of solar air heater. In all the cases it has been observed that efficiency of roughened solar heater higher than that of smooth air heater [18]. Use of artificial roughness to increase heat transfer coefficient has been studied using CFD by various investigators [19–26]. Turbulent flow and heat transfer in rotating ribbed ducts of different aspect ratios were studied numerically using Reynolds averaged Navier-Stokes procedure by Saha and Acharya [20]. Ozceyhan et al. [21] conducted numerical investigation on heat transfer enhancement in tube with the circular cross-sectional rings. Iaccarino et al. [24] studied effect of thermal boundary conditions in numerical heat transfer predictions in rib-roughened passages. A study of effect of artificial roughness in solar air heater using CFD was carried out by Chaube et al. [26]. CFD analysis of heat transfer and flow analysis due to roughness in the form of ribs was carried out by these investigators using 2-D models only. In the present work, roughness element in the form of arc shaped geometry has been used. The heat transfer and flow analysis of the chosen roughness element has been carried out using 3-D models. The ribs are provided on the absorber plate whereas other sides of the duct are kept smooth. 2. Details of the solar air heater duct considered As per the ASHARE 93-77 [27] recommendations, the system and operating parameters have been considered for the present investigation. The most important part of the system considered was the duct. The duct considered was having inner cross-sectional dimensions of 300 mm  25 mm as shown in Fig. 1. The aspect ratio has been kept 12 in this study, as many investigators have established this aspect ratio for such studies. The flow system consists of 900 mm long entry section, 1000 mm long test section and 500 mm long exit section. The entry and exit length of the flow have been kept to reduce the end effects on the test section considering the recommendation provided in ASHRAE Standard 93-77 [27]. A constant heat flux of 1000 W/m2 was considered to be supplied by having a heater plate placed over the absorber plate as shown in Fig. 2.

a/90 p/e Nur Nus fr fs Pr Re

Relative arc angle Relative roughness pitch Nusselt number for roughened duct Nusselt number for smooth duct Friction factor for roughened duct Friction factor for smooth duct Prandtl number Reynolds number

3. Analysis 3.1. Solution domain The arrangement of roughness elements in the form of arc shaped ribs fixed on the inner side of the absorber plate has been considered. The solution domain used for CFD analysis has been generated as shown in Fig. 3. The duct used for CFD analysis having the height (H) of 25 mm and width (W) of 300 mm. Thickness of the absorber plate has been considered as 0.5 mm. A 28 mm thick wooden plank was considered for the sides of the duct and 40 mm thick wooden plank as bottom of the duct. A uniform heat flux of 1000 W/m2 was considered for analysis. Roughness was considered at the underside of the top of the duct to have roughened surface while other three sides were considered as smooth surfaces. 3.2. Grid The chosen geometry is such that secondary flows are bound to occur, thus possibility of using 2-D solution domain and gird is ruled out. Thus 3-D solution domain and grid were selected. In order to examine the flow and heat transfer critically in the interrib regions, finer meshing at these locations has been done. In other regions coarser mesh has been used. For the present work, meshing has been done using commercially available software GAMBIT 2.3.16. Number of cells in each set of geometries varies from 1 to 1.7 millions depending on roughness height and arc angle. To ensure that all results reported here are grid independent and well resolved, all simulations were repeated with twice the number of grid points in each spatial direction. No noticeable differences in the solutions were observed. 3.3. CFD analysis Under the present study, commercial code FLUENT Version 6.3.26 was used. As the secondary flow takes place with the selected geometry, 3-D model has been setup instead of 2-D model to simulate flow and heat transfer. The assumptions were made in the mathematical model: i. The flow is study, fully developed, turbulent and three dimensional. ii. The thermal conductivity of the duct wall and roughness material does not change with temperature. iii. The duct wall and roughness material is homogeneous and isotropic. The working fluid, air is assumed to be incompressible for the operating range of solar air heaters since variation in density is very less. This reference was made with respect to experimental study of solar air heaters by other investigators. The mean inlet velocity of the flow was calculated using Reynolds number. Velocity boundary condition has been considered as

S. Kumar, R.P. Saini / Renewable Energy 34 (2009) 1285–1291

1287

390 Wooden Ply

12

12

20

76

12

Insulation (Glass Wool)

40 25

25 150

Absorber Plate Heater Plate

12

25

25

25 40

Wooden Plank

35

350

40

430 Length of Duct - 2400 mm Fig. 1. Sectional view of solar air heater duct.

inlet boundary condition and outflow as outlet boundary condition. Second order upwind numerical scheme and SIMPLE algorithm were used to discretize the governing equations. 3.4. Roughness geometry and range of parameters Galvanized Iron (G.I) wires in the shape of arc having diameters 1.4 and 2.0 mm were considered to form an artificial roughness element on the underside of the absorber plate. Two values of arc angle (a) namely 30 and 60 were used for each set of wire diameters. Relative pitch (p/e) value was kept as 10 as this value has been optimized by most of the investigators. The range of Reynolds number was considered from 6000 to 18,000 in which solar air heaters normally operate. Other roughness parameters used for the present study are as given in Table 1.

Fig. 4 shows the variation of Nusselt number with Reynolds number for different models and the results are compared with results computed from Dittus–Boelter empirical relationship for a smooth duct. It has been observed that the results obtained by Renormalization-group (RNG) k-3 model are in good agreement with Dittus– Boelter empirical results. Numerical model results obtained by SST ku have more deviation with empirical correlation results, whereas results obtained by other models namely Realizable k3 and Standard k3 have less deviation. Furthermore for low Reynolds number flows, both in Dittus–Boelter empirical and Renormalization-group (RNG) k-3 model indicates almost same results, whereas for higher Reynolds number flows some deviation has been observed in the values. It is therefore, for the present numerical study Renormalization-group (RNG) k-3 model has been employed to simulate the flow and heat transfer.

4. Results and discussions 4.2. Heat transfer in roughened duct 4.1. Selection and validation of the model Different models namely Standard k3 model, Renormalizationgroup (RNG) k-3 model, Realizable k3 model and Shear Stress Transport (SST) ku have been tested for smooth duct having same cross-section of roughened duct in order to find out the validity of the models. The results obtained by different models have been compared with Dittus–Boelter empirical correlation for Nusselt number given below for smooth duct [28].

Nu ¼ 0:024Re0:8 Pr0:4

(1)

G.I. Sheet, 22 Gauge thick

The flow and heat transfer characteristics get affected in the flow direction due to rib provided in the form of artificial roughness. Fig. 5 shows the variation in the values of Nusselt number between adjacent ribs. In the vicinity of the rib the values of Nusselt number has been found to be low. The reason may be that heat transfer takes place around the rib due to conduction only. The values of Nusselt number have been observed to attain very high value upstream and downstream of the rib. Nusselt number starts decreasing as the flow approaches the rib and near rib region it drops down to lower value. However, as the flow past the rib in the downstream, the Nusselt number increases. The increase in Nusselt

Arc Shaped Wires

325

500

1500

400

2400 Fig. 2. Arrangement of roughness elements in the form of arc shaped ribs on the inner side of the absorber plate.

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60 Dittus-Boelter Empirical Relationship Standard kε

55

Renormalization group kε Realizable kε

is attributed to the variation in flow parameters downstream of the rib. The presence of rib along the flow direction creates vortices just downstream of the rib and the fluid also separates from the wall. Separation of flow decreases heat transfer whereas vortices makes fluid to mix thus increasing heat transfer. Downstream of the rib in its vicinity, vortices effect will be predominant than flow separation effect, thus values of Nusselt number increases in this region. Further downstream of the rib, where flow is in separated condition and vortices effect is negligible, both of these effects minimize the value of Nusselt number. Still further downstream of the rib, flow reattachment takes place increasing the value of Nusselt number sharply. As Reynolds number increases, Nusselt number also increases in inter-rib regions. On the either sides of the rib, the values of Nusselt number are same for both low and high values of Reynolds number flows, whereas in the downstream of the rib Nusselt number is higher for higher Reynolds number flow as compared to low Reynolds number flows. Fig. 6 shows pathlines for flow past the rib along the mid plane for a given value of Reynolds number of 14,000. Vortices, separation of flow and reattachment have been predicted by CFD model. For a fixed value of relative arc angle (a/90) and relative roughness height (e/D), number of vortices, intensity and reattachment point varies with respect to the Reynolds number. As depicted in Fig. 7, the velocity vectors for Reynolds number of 14,000 shows stronger vortices because of the presence of roughness element which results in more heat transfer rate. CFD results have critically analysed the flow separation and reattachment to explain other related phenomenon such as increase in Nusselt number for different roughness parameters. 4.2.1. Effect of relative roughness height on Nusselt number Fig. 8 shows variation of Nusselt number for different values of relative roughness height (e/D) for a particular value of relative roughness angle (a/90) of 0.333. Nusselt number increases with increase in Reynolds number. Nusselt number has been found to be increased with increase in relative roughness height (e/D). The increase in Nusselt number is attributed to increase in heat transfer rate. Nusselt number increases with increase in relative roughness height (e/D) for all values of Reynolds number. Nusselt number increases as relative roughness height (e/D) increases from 0.0299 to 0.0426. Table 1 Range of parameters.

SST kε

45

40

35

30

25

20 4000

6000

8000

10000 12000 14000 16000 18000 20000

Reynolds number Fig. 4. Comparison between Nusselt number predictions of different CFD models with Dittus–Boelter empirical relationship for smooth duct.

4.2.2. Effect of relative arc angle on Nusselt number Fig. 9 shows variation of Nusselt number for different values of relative arc angle (a/90) for a given value of relative roughness height (e/D) of 0.0299. The CFD model predicts increase in Nusselt number as Reynolds number increase for a particular value of relative arc angle (a/90). When relative arc angle (a/90) increases from 0.333 to 0.666, the Nusselt decreases. Thus a geometry having relative arc angle (a/90) of 0.33, has higher Nusselt number as compared to geometry with relative arc angle (a/90) of 0.66 for the same values of Reynolds number and relative roughness height (e/D). Nusselt number decreases as relative arc angle (a/90) increases from 0.333 to 0.666. Decrease in Nusselt number with increase in relative arc angle (a/90) for a fixed relative roughness

140 For e/D=0.0299 α/90=0.333 RE=14000

120

RE=10000

Nusselt number (Nu)

Fig. 3. Solution domain for CFD analysis.

Nusselt number (Nu)

50

100

80

60

40

S.no.

Parameters

Range

1. 2. 3. 4. 5. 6. 7. 6. 7.

Reynolds number (Re) Hydraulic diameter of duct, D (mm) Duct aspect ratio (W/H) Roughness height (mm) Relative roughness ratio, (e/D) Wire arc angle, a(degree) Relative arc angle, (a/90) Relative roughness pitch, p/e Heat flux or insolation(W/m2)

6000–18,000 46.86 12 1.4 and 2.0 0.0299 and 0.0426 30 and 60 0.333 and 0.666 10 1000

20

0 0.075

0.080

0.085

0.090

0.095

0.100

0.105

0.110

0.115

Length (m) Fig. 5. Variation of Nusselt number in inter-rib region along the length of duct.

S. Kumar, R.P. Saini / Renewable Energy 34 (2009) 1285–1291

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Fig. 6. Pathlines for relative arc angle (a/90) ¼ 0.333 and relative roughness height (e/D) ¼ 0.0299 at Reynolds number of 14,000.

height (e/D) is observed for all set of Reynolds numbers. However, this is observed to be more in case of lower Reynolds number flows as compared to higher Reynolds number flows. Thus decrease in Nusselt number is observed to be more in case of Reynolds number of 6000 whereas, for Reynolds number of 18,000, it almost remains the same. 4.3. Friction factor in roughened duct In order to analyse the effect of fluid flow characteristics, the values of friction factor are plotted against Reynolds number. It has been found that the friction factor decreases with increase in Reynolds number. 4.3.1. Effect of relative roughness height on friction factor Fig. 10 shows variation of friction factor with Reynolds number for different values of relative roughness height (e/D) at a particular value of relative roughness angle (a/90) of 0.333 and for a smooth

duct. Friction factor decreases with increase in Reynolds number. It has been found that friction factor increases as relative roughness height (e/D) increases from 0.0299 to 0.0426 for a given value of relative arc angle (a/90) and flow conditions. 4.3.2. Effect of relative arc angle on friction factor Fig. 11 shows variation of friction factor for different values of relative arc angle (a/90) at a particular value of relative roughness height (e/D) of 0.0426. The results show that there is an increase in friction factor with increase in relative arc angle for given values of roughness and flow parameters. The results discussed above have been on similar lines that of results reported in the past experimental studies conducted by various investigators. 4.4. Thermohydraulic performance of roughened duct CFD results predict increase in Nusselt number with increase in relative roughness height (e/D), however friction factor also

Fig. 7. Velocity vectors for relative arc angle (a/90) ¼ 0.333 and relative roughness height (e/D) ¼ 0.0299 at Reynolds number of 14,000.

1290

S. Kumar, R.P. Saini / Renewable Energy 34 (2009) 1285–1291

120

0.120

110

0.110

For α/90 = 0.333 e/D=0.0426

100 0.100

e/D=0.0299 Smooth

0.090 80

Friction factor,f

70 60 50 40 For

30

e/D=0.0426 e/D=0.0299

10

Smooth

0.070 0.060 0.050

α/90=0.333

20

0.080

0.040 0.030

0 00

0 00

20

0 00

18

0 00

Reynolds number (Re)

Reynolds number (Re) Fig. 8. Variation of Nusselt number with Reynolds number for different values of relative roughness height (e/D).

increases. Thus performance of collector efficiency is dependent on these two parameters. The enhancement in the collector performance due to artificial roughness is generally evaluated on the basis of thermohydraulic performance parameter which incorporates both the thermal as well as hydraulic considerations. Thermohydraulic performance parameter is defined as overall enhancement ratio and represented by the following expression [28]. Nur Nu

s Overall enhancement ratio ¼  1=3

(2)

fr fs

Fig. 10. Variation of friction factor with Reynolds number for different values of relative roughness height (e/D).

It is evident that a surface roughness that yields the value of this parameter greater than unity is only useful. Higher the value of this parameter better is the performance of the solar air heater. Fig. 12 shows overall enhancement ratio for the solar air heater having different rib configurations for Reynolds number range from 6000 to 18,000. It has been found that overall enhancement ratio is greater than unity for all set of roughness combinations and it is maximum around Reynolds number of 6000. Beyond Reynolds number 10,000 overall enhancement ratio decreases sharply and around 18,000 of its value becomes nearly 1. For the range of 0.110

α/90=0.333

e/D=0.0666

Reynolds number (Re) Fig. 9. Variation of Nusselt number with Reynolds number for different values of relative arc angle (a/90).

0

0

00 0

00 0

14

12

10

0

0

0

20 00

18 00

0 16 00

0 14 00

12 00

10 00

80 0

60 0

40 0

20 0

0

0.030 0

40 0

0.040

0

50

0

0.050

0

60

00 0

0.060

80 00

70

0.070

60 00

80

0.080

40 00

Frinction factor,f

90

0

Smooth

0.090

Smooth

20 00

100

20 00

e/D=0.0333

00 0

110

For e/D=0.0299 α/90=0.666

0.100

18 00

α/90=0.299

For

16

120

Nusselt number (Nu)

16

0 00

14

0 00

12

10

00 80

00 60

20

40

0

00

0

0

0

00

20

18

00

0 00 14

16

0 00

0

12

10

00

00

00

80

00

60

00

40

20

0

00

0.020

0

00

Nusselt number (Nu)

90

Reynolds number (Re) Fig. 11. Variation of friction with Reynolds number for different values of relative arc angle (a/90).

S. Kumar, R.P. Saini / Renewable Energy 34 (2009) 1285–1291

1291

arc angle (a/90) of 0.333 and relative roughness height (e/D) of 0.0426 for the range of parameters considered.

1.80

Overall enhancement ratio

1.70

References

1.60

1.50

1.40

1.30

1.20

1.10

α/90=0.333

e/D=0.0299

α/90=0.333

e/D=0.0426

α/90=0.666

e/D=0.0299

α/90=0.666

e/D=0.0426

0

0

00 20

0

00 18

0

00 16

0

00 14

0

00

00

00

12

10

80

00 60

00 40

00 20

0

1.00

Reynolds number (Re) Fig. 12. Overall enhancement ratio of various roughness geometries.

parameters considered the suitable operating range has been found between Reynolds number 6000 and 10,000. Further overall enhancement ratio has been found to be maximum for roughness geometry corresponding to relative arc angle (a/90) of 0.333 and relative roughness height (e/D) of 0.0426. The reason may be explained on the basis of Nusselt number and friction factor discussed earlier for the combination of geometry. Nusselt number increases with the increase in relative roughness height (e/D) and it decreases with increase in relative arc angle (a/ 90). Whereas friction factor increases with increase in both relative roughness height (e/D) and relative arc angle (a/90). It is therefore the value of overall enhancement ratio depends on net effect of these parameters. Fig. 12 shows that roughness geometry corresponding to relative arc angle (a/90) of 0.333 and relative roughness height (e/D) of 0.0426 has found to be most efficient geometry with maximum overall enhancement ratio of 1.7 under the range of parameters investigated. 5. Conclusions An attempt has been made to carry out CFD based analysis to fluid flow and heat transfer characteristics of a solar air heaters having roughened duct provided with artificial roughness in arc shaped geometry. Combined effect of swirling motion, detachment and reattachment of fluid which was considered to be responsible in the increase of heat transfer rate has been observed during CFD analysis. Nusselt number has been found to increase with increase in Reynolds number where friction factor decreases with increase in Reynolds number for all combinations of relative roughness height (e/D) and relative arc angle (a/90). CFD results have also been validated for smooth duct and different CFD model results were compared with Dittus–Boelter empirical relationship for smooth duct. Among all the models used, Renormalization-group (RNG) k-3 model results have been found to have good agreement. Overall enhancement ratio with a maximum value of 1.7 has been found for the roughness geometry corresponding to relative

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