A CFD based thermo-hydraulic performance analysis of an artificially roughened solar air heater having equilateral triangular sectioned rib roughness on the absorber plate

International Journal of Heat and Mass Transfer 70 (2014) 1016–1039

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A CFD based thermo-hydraulic performance analysis of an artificially roughened solar air heater having equilateral triangular sectioned rib roughness on the absorber plate Anil Singh Yadav a,b,⇑, J.L. Bhagoria b a b

Mechanical Engineering Department, Technocrats Institute of Technology – Excellence, Bhopal, MP 462021, India Mechanical Engineering Department, Maulana Azad National Institute of Technology, Bhopal, MP 462051, India

a r t i c l e

i n f o

Article history: Received 1 June 2013 Received in revised form 11 November 2013 Accepted 24 November 2013 Available online 25 December 2013 Keywords: Solar air heater Absorber plate Heat transfer Artificial roughness Thermo-hydraulic performance CFD

a b s t r a c t 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–e 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. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction 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].

⇑ Corresponding author at: Mechanical Engineering Department, Technocrats Institute of Technology – Excellence, Bhopal, MP 462021, India. Tel.: +91 9229220126. E-mail address: [email protected] (A.S. Yadav). 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.11.074

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.

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Nomenclature Cp D e H h I k L L1 L2 L3 m P q T T0 Tam Ti To Tpm Tw u U0 us v W DP

specific heat of air, J/kg k equivalent or hydraulic diameter of duct, mm rib height, mm depth of duct, mm heat transfer coefficient, W/m2k intensity of solar radiation, W/m2 thermal conductivity of air, W/m k length of duct, mm inlet length of duct, mm test length of duct, mm outlet length of duct, mm mass flow rate, kg/s pitch, mm heat flux, W/m2 air temperature, K ambient temperature, K mean air temperature, K air inlet temperature, K air outlet temperature, K mean plate temperature, K wall temperature, K air flow velocity in the x direction, m/s mean air flow velocity in the duct, m/s friction velocity, m/s air flow velocity in the y direction, m/s width of duct, mm pressure drop, Pa

Dimensionless parameters B/S relative roughness length d/w relative gap position e/D relative roughness height e/H rib to channel height ratio f friction factor fr friction factor for rough surface fs friction factor for smooth surface g/e relative gap width g/P relative groove position Gd/Lv relative gap distance L/D test length to hydraulic diameter ratio of duct

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

l/e l/s Nu Nur Nus P/e Pr Re S/e St W/H W/w y+

relative logway length of mesh relative length of grit Nusselt number Nusselt number for rough duct Nusselt number for smooth duct relative roughness pitch Prandtl number Reynolds number relative short way length of mesh Stanton number duct aspect ratio relative roughness width non dimensional wall coordinate

Greek symbols a angle of attack, degree C molecular thermal diffusivity, m2/s Ct turbulent thermal diffusivity, m2/s d transition sub-layer thickness, mm e dissipation rate, m2/s3 j turbulent kinetic energy, m2/s2 l dynamic viscosity, Ns/m2 lt turbulent viscosity, Ns/m2 q density of air, kg/m3 x specific dissipation rate, 1/sec Subscripts a ambient am air mean f fluid (air) i inlet m mean o outlet pm plate mean r roughened s smooth t turbulent w wall

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 [3–30]. 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 pitchto-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

1018

Table 1 Summary of major experimental works on artificially roughened solar air heater having different roughness geometries applied on the absorber plate. 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

2.

Prasad and Saini [4]

14% improvement in thermal performance was reported at a Reynolds number of 40,000 over smooth duct. 2.38 and 4.25 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct. 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. 2 and 3 times enhancement in Stanton number and friction factor respectively were reported over smooth duct.

Air

e

3.

Prasad [30]

4.

Karwa et al. [8]

Wires

P

Chamfered repeated rib-roughness

P e

Karwa et al. [9]

Air

6.

Kumar et al. [27]

7.

Kumar et al. [29]

8.

Singh et al. [24]

9.

Karwa and Chitoshiya [28]

e/D: 0.02–0.033 P/e: 10–20 Re: 5000–50,000 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

w

5.

Absorber plate

Rib

Multi V-shaped rib roughness with gap

Discrete V-down rib roughness

φ

e/D: 0.014–0.032 L/D: 32 & 66 P/e: 4.5–8.5 U: 15°–18° Re: 3000–20,000 W/H: 4.8–12 e/D: 0.0197–0.0441 P/e: 4.58 & 7.09 U: 15° Re: 3750–16,350 W/H: 6.88–9.38 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 a: 60° Re: 2000–20,000 e/D: 0.022–0.043 a: 30°–75° g/e: 0.5–1.5 Gd/Lv: 0.24–0.80 W/w: 1–10 P/e: 6–12 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 a: 30°–75° 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 a: 60°

50–120% and 80–290% enhancement in Nusselt number and friction factor respectively were reported over smooth duct.

6.32 and 6.12 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct.

6.74 and 6.37 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct.

3.04 and 3.11 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct.

12.5–20% enhancement in the thermal efficiency was reported over smooth duct.

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10.

Gupta [5]

Inclined wire rib roughness α

Flow

e/D: 0.018–0.032 P/e: 10 Re: 5000–50,000 W/H: 6.8–11.5 a: 30°–90°

1.8 and 2.7 times enhancement in Nusselt number and friction factor respectively were reported over duct with transverse ribs.

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.

B/S: 3.0 e/D: 0.0467–0.05 P/e: 10 Re: 2800–15,000 W/H: 7.19–7.75 a: 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.

p

11.

Saini and Saini [6]

Expanded metal mesh roughness Expanded Metal Mesh

L

Air S

12.

Karwa [7]

Wire pieces

P

Transverse

V-up discrete Air

Inclined

V- down continuous

V- down discrete

V-up continuous

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 a: 30°–90°

p

Flow

14.

Bhagoria et al. [11]

α

Transverse wedge shaped rib roughness P

φ

e P

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. 2.30 and 2.83 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct.

e/D: 0.015–0.033 P/e: 60.17x U: 8°–15° U1.0264

2.4 and 5.3 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct.

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.

P

15.

Sahu and Bhagoria [12]

90° broken rib roughness

P

Wires

Absorber Plate

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Transverse, inclined, V-up continuous, V-down continuous, V-up discrete and V-down discrete rib roughness

Air

1019

(continued on next page)

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Table 1 (continued) Investigator/s

Roughness geometry

Range of parameters

Principal findings

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 U: 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.

e/d: 0.0213–0.0422 P/e: 10 Re: 2000–17,000 W/H: 12 a/90: 0.3333–0.6666

3.8 and 1.75 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct.

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 a: 60°

2.59 and 2.9 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct.

1500 mm

l p

19.

Saini and Saini [16]

S

e = 2 mm

θ =600

Arc shaped rib roughness

P Air

W L

20.

Aharwal et al. [17]

Inclined continuous rib roughness with gap

P

W

600

d

d Continuous rib

d

d

d d/W = 0.33

d/W = 0.25

d/W = 0.16

d/W = 0.5

d/W = 0.67

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21.

Saini and Verma [18]

Dimple-shaped rib roughness

P

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.

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.

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 a: 90°

2.82 and 3.72 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct.

e/D: 0.0168–0.0338 e: 0.75–1.5 mm P/e: 10 Re: 3000–15,000 W/H: 8:1 a: 30–75°

2.16 and 2.75 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct.

d Air

22.

Varun et al. [19]

Combination of transverse and inclined rib roughness

P

W 60

0

L 23.

Bopche and Tandale [20]

Inverted U-shaped rib roughness Pitch, p

Direction of air flow (upstream)

e

50 mm

12 mm

2. 5 mm

24.

Kumar et al. [21]

Discrete W-shaped rib roughness

1021

(continued on next page)

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e

1022

Table 1 (continued) Investigator/s

Roughness geometry

Range of parameters

Principal findings

25.

Hans et al. [22]

Multi V-shaped rib roughness

e/D: 0.019–0.043 a: 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 a: 30°–75°

2.36 and 2.01 times enhancement in Nusselt number and friction factor respectively were reported over smooth duct.

p

Air

60o

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 a: 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 a: 45°–75°

The maximum value of Nusselt number was reported over smooth duct for P/e = 10 and e/D = 0.036.

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(a)

(b) Fig. 1. Computational domain for (a) smooth solar air heater (b) equilateral triangular sectioned rib roughened solar air heater.

transfer enhancement in roughened duct of solar air heaters [3–30]. Table 1 lists the major experimental works for different roughness geometries and configurations applied on the absorber plate of a solar air heater. 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

Fig. 2. Schematic representation of a roughened absorber plate.

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– x 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–e 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

1024

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Table 2 Twelve different configurations of equilateral triangular sectioned ribs on the absorber plate. Roughness configurations

Hydraulic diameter of duct, D(mm)

Rib height, e (mm)

Rib pitch, P (mm)

Relative roughness pitch, P/ e

Relative roughness height, e/ D

Type-1 Type-2 Type-3 Type-4

33.33

0.7

10 15 20 25

14.29 21.43 28.57 35.71

0.021

Type-5 Type-6 Type-7 Type-8

33.33

1

10 15 20 25

10 15 20 25

0.03

Type-9 Type-10 Type-11 Type-12

33.33

1.4

10 15 20 25

7.14 10.71 14.29 17.86

0.042

Fig. 3. Different configurations of equilateral triangular sectioned rib roughness.

Table 3 Geometric parameters of the solar air heater roughened with equilateral triangular sectioned transverse ribs. L1(mm)

L2(mm)

L3(mm)

W(mm)

H(mm)

D(mm)

e(mm)

P(mm)

245

280

115

100

20

33.33

0.7, 1, 1.4

10, 15, 20, 25

metal grit ribs as roughness elements on the absorber plate. Commercial CFD code FLUENT 6.2.16 and Standard k–e turbulence were employed in the simulation. Authors reported the absorber plate of square cross-section rib with 58° angle of attack was thermohydraulically 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–e turbulence model. Maxi-

mum 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–e 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

A.S. Yadav, J.L. Bhagoria / International Journal of Heat and Mass Transfer 70 (2014) 1016–1039 Table 4 Range of operating parameters for CFD analysis. Operating parameters

Range

Uniform heat flux, ‘q’ Reynolds number, ‘Re’ Prandtl number, ‘Pr’ Relative roughness pitch, ‘P/e’ Relative roughness height, ‘e/D’ Duct aspect ratio, ‘W/H’

1000 W/m2 3800–18,000 (6 values) 0.71 7.14–35.71(12 values) 0.021–0.042 (3 values) 5

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 Table 5 Thermo-physical properties of air and absorber plate for CFD analysis. Properties

Air

Absorber plate (aluminum)

Density, ‘q’ (kgm3) Specific heat, ‘Cp’ (Jkg1K1) Viscosity, ‘l’ (Nsm2) Thermal conductivity, ‘k’(Wm1K1)

1.117 1007 1.857e05 0.0262

2719 871 – 202.4

1025

turbulent flows through a solar air heater roughened with square sectioned transverse rib roughness. Three different values of ribpitch (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 thermohydraulic performance parameter were strongly dependent on the relative roughness height. A maximum value of thermohydraulic 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–e 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–e 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

Fig. 4. Schematic of grid systems.

A.S. Yadav, J.L. Bhagoria / International Journal of Heat and Mass Transfer 70 (2014) 1016–1039

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.

120

100

60

20

(a) 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Re 140 120

Nu r

100

Smooth duct P/e=10 P/e=15 P/e=20 P/e=25

e/D=0.03

80 60 40

2.1. Computational domain and grid generation

20

(b)

0

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Re 160 140 120

Smooth duct P/e=7.14 P/e=10.71 P/e=14.29 P/e=17.86

e/D=0.042

100

Nu r

In the present numerical study, two-dimensional turbulent flow through the artificially roughened solar air heater having equilateral triangular sectioned transverse rib roughness on the underside of the absorber plate is simulated. Two-dimensional numerical simulation model of artificially roughened solar air heater having square sectioned transverse rib roughness on the underside of the absorber plate has previously been successfully simulated and validated against available experimental results in Yadav and Bhagoria [36]. Hence, in the present analysis, a 2-dimensional computational domain of artificially roughened solar air heater has been adopted which is similar to the computational domain of Yadav and Bhagoria [36]. The computational domain is simply the physical region over which the simulation has been performed. The computational domain is a simple rectangle of length 640 mm and height 20 mm and consisted of three sections, namely, entrance section (L1 = 245 mm), test section (L2 = 280 mm) and exit section (L3 = 115 mm) (Fig. 1). In the present numerical work, 2-dimensional equilateral triangular sectioned transverse ribs have been considered as roughness element. The equilateral triangular sectioned transverse ribs are considered on the underside of the top absorber plate while other sides are considered as smooth surfaces. The absorber plate is 6 mm thick aluminum plate and the lower surface of the plate provided with artificial roughness in the form of equilateral triangular sectioned transverse ribs. A typical absorber plate with equilateral triangular sectioned transverse ribs is shown in Fig. 2. The maximum and minimum height of equilateral triangular sectioned rib has been selected to 1.4 and 0.7 mm respectively, so that the fin/flow passage blockage effects may be negligible and laminar sub-layer would be of the same order as of roughness height, as reported by Verma and Prasad [41]. In the Present CFD analysis, twelve different configurations of equilateral triangular sectioned transverse rib roughness on the absorber plate have been simulated. Each of the combinations has been performed on six different values of Reynolds number. Thus, a total of seventy-two sets of CFD simulations having different combinations of Reynolds number (Re), relative roughness

e/D=0.021

40

2. CFD investigation In the present article a numerical investigation is conducted to analyze the two-dimensional incompressible Navier–Stokes flows through the artificially roughened solar air heater with equilateral triangular sectioned transverse ribs on the absorber plate. The commercial finite-volume based CFD code ANSYS FLUENT 12.1, has been used to simulate fluid dynamics and heat transfer. Computational domain, grid generation, governing equations, boundary conditions, selection/validation of appropriate turbulence model and solution procedure is presented in detail in the following sub-sections.

Smooth duct P/e=14.29 P/e=21.43 P/e=28.57 P/e=35.71

80

Nu r

1026

80 60 40 20

(c)

0

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Re Fig. 5. Effect of relative roughness pitch on average Nusselt number for different values of Reynolds number and for fixed value of relative roughness height.

pitch (P/e) and relative roughness height (e/D) have been investigated. Each of the combinations has been carefully simulated to predict the heat transfer and flow friction behavior. The simulations are conducted over the relevant range of Reynolds number, 3800 6 Re 6 18,000 as reported by Gupta et al. [42]. Table 2 shows twelve different configurations of equilateral triangular sectioned ribs on the absorber plate. Similar twelve different configurations of equilateral triangular sectioned rib roughness on the absorber plate have been displayed in Fig. 3. A constant heat flux value (1000 W/m2) is set at the top of the computational domain. The

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120

e/D=0.021

140

100

P/e=14.29

120

Re=3800

80

Smooth duct e/D=0.021 e/D=0.03 e/D=0.042

Re=5000

Nu r

Re=8000 Re=12000

100

Re=15000

60

Re=18000

Nu r

40 20

80

60

(a) 0 10

15

20

25

30

35

40

40

P/e 140

20

e/D=0.03

120 0

Re=3800

2000

Re=5000

100

4000

6000

8000 10000 12000 14000 16000 18000 20000

Re=8000

Re

Nu r

Re=12000

80

Re=15000 Re=18000

60 40 20

(b)

0 8

10

12

14

16

18

20

22

24

26

P/e 180

e/D=0.042

Nu r

160 140

Re=3800

120

Re=8000

100

Re=15000

Re=5000 Re=12000 Re=18000

80 60 40 20

Fig. 7. Effect of relative roughness height on average Nusselt number for different values of Reynolds number and for fixed value of relative roughness pitch.

of operating parameters employed in this computational investigation are summarized in Table 4. The air is used as working fluid in all cases. The values of the thermo-physical properties of air have been assumed to remain constant and evaluated at temperature of 300 K. The bulk mean air temperature is considered as constant when considering the fact that air temperature rise from entrance to exit is less than 3 °C. Therefore the variation in properties of air is very small and negligible within the range of pressure and temperature involved. Experimental work of Wang and Sunden [43] also supports this assumption. The thermo-physical properties of working fluid and absorber plate are summarized in Table 5. One of the most important tasks in developing the 2D CFD simulation is to generate adequate fine grid to ensure accurate flow computations. A non-uniform quad grid has been used for the discretization of the computational domain. Combinations of uniform and non-uniform grid arrangements are generated in ANSYS ICEM CFD V12.1 software (Fig. 4). The entire computational domain has

(c)

0 6

8

10

12

14

16

18

160

20 140

P/e Fig. 6. Effect of Reynolds number on average Nusselt number for different values of relative roughness pitch and for fixed value of relative roughness height.

100 Nu r

flow of air is assumed to be turbulent two-dimensional, incompressible and steady. The thermal conductivity of air, absorber plate, duct wall, and roughness material are independent of temperature. The absorber plate, duct wall, and roughness material are homogeneous and isotropic. No-slip boundary conditions are applied on the duct walls for all cases as suggested by Chaube et al. [31]. No-slip condition is used almost universally in modeling of viscous flows. In fluid dynamics, the no-slip condition for viscous fluids states that at a solid boundary, the fluid will have zero velocity relative to the boundary. The fluid velocity at all fluid–solid boundaries is equal to that of the solid boundary. Theoretically, one can think of the outermost molecules of fluid as stuck to the surfaces past which it flows. Physical justification shows that particles close to a surface move along with a flow when adhesion is stronger than cohesion. The geometrical parameters for artificially roughened solar air heater are summarized in Table 3. The ranges

120

P/e=14.29

Re=3800 Re=5000 Re=8000 Re=12000 Re=15000 Re=18000

80

60

40

20

0.015

0.020

0.025

0.030

0.035

0.040

0.045

e/D

Fig. 8. Effect of Reynolds number on average Nusselt number for different values of relative roughness height and for fixed value of relative roughness pitch.

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Fig. 9. The contour plot of turbulent kinetic energy for e/D = 0.042 and P/e = 7.14 at a Reynolds number of (a) 3800, (b) 5000, (c) 8000, (d) 12,000, (e) 15,000 and (f) 18,000.

been meshed with quadrilateral elements with non-uniform quad grid having near wall elements spacing of y+  2 for all configurations of artificially roughened solar air heater. This size is suitable to penetrate the viscous sub-layer. After a careful check of the grid dependency, a total numbers of 432,187 cells have been used for all cases considered in the present CFD simulation. 2.2. Governing equation

and energy. With assumptions of 2-dimensional steady state, forced turbulent flow, incompressible fluid, and no radiation heat transfer, the governing equations in the rectangular Cartesian coordinate system are as follows: Continuity equation:

@u @ v þ ¼0 @x @y

ð1Þ

Momentum equation: The forced turbulent fluid flow and heat transfer in the artificially roughened solar air heater are described by the governing equations of flow continuity, and conservation of momentum

u

! @u @u 1 @p @2u @2u þv ¼ þ# þ @x @y @x2 @y2 q @x

ð2Þ

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Fig. 10. The contour plot of turbulent intensity for e/D = 0.042 and P/e = 7.14 at a Reynolds number of (a) Re = 3800, (b) Re = 5000, (c) Re = 8000, (d) Re = 12,000, (e) Re = 15,000 and (f) Re = 18,000.

@v @v 1 @p @2v @2v u þv ¼ þ# þ @x @y q @y @x2 @y2

! ð3Þ

Re ¼ quD=l

Energy equation:

u

@T @T @2T @2T þv ¼a þ @x @y @x2 @y2

number, friction factor and thermo-hydraulic performance parameter.Reynolds number is defined as

!

ð5Þ

Average Nusselt number for roughened solar air heater is defined as

ð4Þ

where t is the kinematic viscosity and a is the thermal diffusivity. The other relevant non-dimensional parameters of interest in the present CFD investigation are the Reynolds number, Nusselt

Nur ¼ hD=k

ð6Þ

where h is average convective heat transfer co-efficient. The friction factor is calculated by pressure drop, DP across the length of test section, and can be obtained by

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Table 6 Nusselt number enhancement ratio predicted by CFD analysis for different values of P/e and e/D. D = 33.33 mm

Nusselt number enhancement ratio

e (mm)

e/D

P (mm)

P/e

Re = 3800

Re = 5000

Re = 8000

Re = 12,000

Re = 15,000

Re = 18,000

0.7

0.021

10 15 20 25

14.29 21.43 28.57 35.71

1.943 1.844 1.773 1.691

1.971 1.871 1.798 1.715

2.017 1.915 1.841 1.755

2.050 1.954 1.879 1.791

2.057 1.957 1.900 1.821

2.038 1.942 1.890 1.800

1

0.03

10 15 20 25

10 15 20 25

2.372 2.251 2.164 2.064

2.405 2.283 2.195 2.093

2.463 2.338 2.247 2.143

2.513 2.385 2.293 2.187

2.543 2.412 2.319 2.211

2.520 2.390 2.302 2.199

1.4

0.042

10 15 20 25

7.14 10.71 14.29 17.86

2.929 2.867 2.715 2.548

3.017 2.876 2.754 2.579

3.025 2.905 2.772 2.620

3.030 2.918 2.788 2.644

3.073 2.931 2.801 2.655

3.025 2.896 2.767 2.615

Bold characters indicate maximum values.

fr ¼

ðDP=lÞD 2qu2

ð7Þ

It has been found that the artificial roughness in the form of equilateral triangular sectioned rib on the absorber plate results in substantial enhancement of heat transfer. This enhancement is, however, accompanied by a considerable increase in the friction factor. It is, therefore, desirable to choose the roughness geometry such that the heat transfer is maximized while keeping the pumping losses at the least possible value. In order to analyze overall performance of a solar air heater, thermo-hydraulic performance should be evaluated by simultaneously consideration of thermal as well as hydraulic performance. Thermal performance of a solar air heater concerns with the heat transfer process within the collector while hydraulic performance concerns with pressure drop in the duct. Webb and Eckert [44] suggested a thermo-hydraulic performance parameter, which evaluates the enhancement in heat transfer of a roughened duct compared to that of the smooth duct for the same pumping power requirement and is defined as

Thermo  hydraulic performance ¼

ðNur =Nus Þ 1 3

ð8Þ

ðfr =fs Þ

ð9Þ

Blasius equation [48]:

fs ¼ 0:0791Re

0:25

1. Along the bottom wall of the duct (0 6 x 6 L, y = H),

u ¼ 0;

This parameter has also been known as thermal enhancement factor as reported by Promvonge and Thianpong [45] and Eiamsa-ard and Promvonge [46]. The thermo-hydraulic performance parameter is used to estimate how effectively an artificially roughened surface enhances the heat transfer under constant pumping power constraints. A value of thermo-hydraulic performance parameter greater than one ensures the effectiveness of using an enhancement device and can be used to compare the performance of number of arrangements to decide the best among these. Nus represents Nusselt number for smooth duct of a solar air heater and can be obtained by Dittus–Boelter equation and fs represents friction factor for smooth duct of a solar air heater and can be obtained by Blasius equation.Dittus–Boelter equation [47]:

Nus ¼ 0:023Re0:8 Pr 0:4

cases. The tangential component of fluid velocity equals that of the solid at the interface represents no-slip boundary condition. The bottom surface is adiabatic, and a constant heat flux (1000 W/m2) is introduced on the top surface of the solar air heater. The temperature of air inside the duct is also taken as 300 K at the beginning. At the inlet of the computational domain, the velocity inlet boundary condition is specified. Velocity inlet boundary conditions are commonly used to define the flow velocity, along with all relevant scalar properties of the flow, at flow inlets. A uniform air velocity is introduced at the inlet. In this simulation, six uniform velocities and a fixed air temperature of 300 K are appointed at the domain inlet. The mean inlet velocity of the flow is calculated using Reynolds number. The range of inlet velocity of the air lies between 1.67–7.9 m/s. The outflow boundary condition is appointed at the exit of the computational domain. A pressure outlet boundary condition is applied with a fixed pressure of 1.013  105 Pa at the exit. The boundary conditions are expressed as follows:

ð10Þ

2.3. Boundary conditions The solution domain is a rectangle on the x–y plane, enclosed by the inlet, outlet and wall boundaries (Fig. 1(b)). Since the Navier– Stokes equations are solved inside the computational domain, no-slip boundary conditions are applied on the duct walls for all

v ¼ 0;

@T=@y ¼ 0:

2. Along the upper L2 + L1 6 x 6 L:

u ¼ 0;

v ¼ 0;

wall

of

ð11Þ the

duct

@T=@y ¼ 0:

(y = 0),0 6 x 6 L1,

ð12Þ

L1 6 x 6 LL3 (heated section):

u ¼ 0;

v ¼ 0;

q ¼ 1000W=m2 :

ð13Þ

3. At the duct inlet (x = 0, 0 6 y 6 H),

u ¼ U0

v ¼ 0;

T ¼ T0:

ð14Þ

4. At the duct exit (x = L, 0 6 y 6 H),

@u=@x ¼ 0;

@ v =@x ¼ 0;

@T=@x ¼ 0:

ð15Þ

2.4. Turbulence modeling As we know that the turbulent flows are significantly affected by the presence of walls. Close to the wall, the flow is influenced by viscous effects. The mean velocity field is affected through the no-slip condition that has to be satisfied at the wall. Toward the outer part of the near-wall region, however, the turbulence is rapidly augmented by the production of turbulent kinetic energy due to the large gradients in mean velocity. Therefore, accurate representation of the flow in the near-wall region determines successful predictions of wall-bounded turbulent flows. It is an unfortunate fact that no single turbulence model is universally accepted as

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0.030

e/D=0.021

0.030

Smooth duct P/e=14.29 P/e=21.43 P/e=28.57 P/e=35.71

(a)

0.025

e/D=0.021

Re=3800

(a)

Re=5000 Re=8000 Re=12000 Re=15000

0.025

Re=18000

fr

fr

0.020

0.020

0.015

0.015

0.010

0.005 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

0.010 10

15

20

25

e/D=0.03

0.035

Smooth duct P/e=10 P/e=15 P/e=20 P/e=25

(b)

0.030

0.025

35

40

P/e

Re 0.035

30

e/D=0.03

Re=3800

(b)

Re=5000 Re=8000 Re=12000

0.030

Re=15000 Re=18000

fr

fr

0.025 0.020

0.020 0.015

0.015

0.010

0.010

0.005

8

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

10

12

14

16

Re 0.040 0.035

18

20

22

0.040 e/D=0.042

e/D=0.042

Smooth duct P/e=7.14 P/e=10.71 P/e=14.29 P/e=17.86

(c)

0.030

24

26

P/e Re=3800

(c)

Re=5000 Re=8000 Re=12000

0.035

Re=15000 Re=18000

0.030 fr

fr

0.025

0.025

0.020 0.015

0.020 0.010

0.015

0.005 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Re Fig. 11. Effect of relative roughness pitch on average friction factor for different values of Reynolds number and for fixed value of relative roughness height.

being superior for all classes of problems. The choice of turbulence model will depend on considerations such as the physics encompassed in the flow, the established practice for a specific class of problem, the level of accuracy required, the available computational resources, and the amount of time available for the simulation. Main approach to turbulence modeling looks solely at the solutions generated using a given turbulence model and compares the solutions to those generated by others and to experimental data. According to this line of reasoning, the best turbulence model is simply the one that best matches the experimental data, no matter what its origin [49].

6

8

10

12

14

16

18

20

P/e Fig. 12. Effect of Reynolds number on average friction factor number for different values of relative roughness pitch and for fixed value of relative roughness height.

Fluent 12.1 [49] offers two approaches based on the classical theory describing the flow near-walls in turbulent flows: 1. The first one is a semi-empirical approach, and uses the so called ‘wall function’ to bridge the viscosity affected region between the wall and the fully turbulent region. The viscous sub-layer and buffer layer region are not resolved. Therefore, the near-wall mesh may be relatively coarse, the first grid point off the wall must be positioned in the log law region at y+ > 30

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0.035

P/e=14.29

Smooth duct e/D=0.021 e/D=0.03 e/D=0.042

0.030

Yadav and Bhagoria [34,40] presented a comparison between five different turbulence models, namely Standard k–e model, Renormalization-group k–e model, Realizable k–e model, Standard k– x and Shear stress transport k–x model, to simulate the flow through the solar air heater. The predictions were compared with available experimental data and the Renormalization-group k–e model was found to be the best one. Therefore, Renormalizationgroup (RNG) k–e turbulence model with ‘enhanced wall treatment’ has been selected for present study to predict the flow and forcedconvection characteristics of a fully developed turbulent flow through artificially roughened solar air heater. Transport equations and other details of each turbulence model can be found in Ref. [49,50].

fr

0.025

0.020

0.015

0.010

0.005 2000

4000

6000

8000 10000 12000 14000 16000 18000 20000

Re

2.5. Solution method

Fig. 13. Effect of relative roughness height on average friction factor number for different values of Reynolds number and for fixed value of relative roughness pitch.

0.030

P/e=14.29

Re=3800 Re=5000

0.028

Re=8000 Re=12000 Re=15000

0.026

Re=18000

fr

0.024

0.022

0.020

0.018

0.016

0.014 0.015

functions. Generally, it requires a very fine near-wall mesh. The first grid point off the wall must be from y+  1. This approach is more suited for low-Reynolds number flows with complex near-wall phenomena. Although it obviously requires a greater amount of computational resources.

0.020

0.025

0.030

0.035

0.040

0.045

e/D Fig. 14. Effect of Reynolds number on average friction factor for different values of relative roughness height and for fixed value of relative roughness pitch.

(the distance being measured in wall units y+ = yus/t, where us is the friction velocity). This approach is justified for industrial flows with high Reynolds numbers, because it saves computational time and it is sufficiently precise. There are two options for semi-empirical approach use in Fluent code. The first ‘Standard Wall Function’ is presented as default in Fluent 12.1. It assumes equilibrium between the production and dissipation of turbulent kinetic energy. The second ‘Non-Equilibrium Wall Function’ may be selected by the user. It does not assume this equilibrium, but allows to differ production and dissipation, as may be the case for flows where there is separation and reattachment or severe pressure gradients. 2. The second approach combines a two layer model (where the viscosity affected near-wall region is completely resolved, along the way to the viscous sub-layer), together with enhanced wall

Two dimensional model of the flow domain used for numerical analysis is built using ANSYS DESIGN MODELER v12.1. Grid is generated in ANSYS ICEM CFD v12.1. Meshed model is then exported to ANSYS FLUENT v12.1 for analysis. The continuity equation, energy equation and the Navier–Stokes equations in their steady, incompressible form, along with the associated boundary conditions are solved using the multipurpose finite volume based CFD software package, ANSYS FLUENT v12.10. In the present numerical study RNG k–e turbulence model with ‘enhanced wall treatment’ is used. In the discretization of governing equations, SIMPLE (semiimplicit method for pressure linked equations) algorithm is used in pressure–velocity coupling as suggested by Kumar and Saini [32]. This algorithm was developed by Patankar [51] and is based on a predictor–corrector approach. Double precision pressure based solver is selected in order to solve the set of equations used. Second order upwind discretization scheme is selected for all the transport equations as suggested by Kumar and Saini [32]. Whenever convergence problems are noticed, the solution is started using the first order upwind discretization scheme and continued with the second order upwind scheme. The governing equations for mass and momentum conservation are solved with a segregated approach in steady state, where equations are sequentially solved with implicit linearization. In the present simulation, the convergence criteria between two consecutive iterations is set to be relative deviation less than 106 for energy equation and less than 103 for solution in velocity and continuity equation. The above discussed numerical method and procedure for different rib shapes have been validated in the authors’ previous works [34–39] by comparing the numerical and experimental data of turbulent flows through the artificially roughened solar air heater.

3. Results and discussion The numerical analysis has been performed for artificially roughened solar air heater with equilateral triangular sectioned rib roughness on the absorber plate and the results are presented in this section. The average heat transfer/flow friction characteristics of the artificially roughened solar air heater are explored first, and then the effects of flow/roughness parameters are discussed. The results have been compared with those obtained in case of smooth ducts operating under similar operating conditions to dis-

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Fig. 15. The contour plot of pressure for Re = 5000 and e/D = 0.03 at a relative roughness pitch of (a) P/e = 10, (b) P/e = 15, (c) P/e = 20 and (d) P/e = 25.

cuss the enhancement in heat transfer and friction factor on account of artificial roughness. 3.1. Heat transfer The present numerical results on average heat transfer characteristics in an artificially roughened solar air heater with equilateral triangular sectioned rib roughness on the absorber plate are presented in the form of average Nusselt number. In this study the Nusselt number has been computed numerically using the 2dimensionally developed CFD model. Fig. 5(a–c) shows the effect of Reynolds number on average Nusselt number for different values of relative roughness pitch and relative roughness height. In all cases, the presence of equilateral triangular sectioned rib produces higher averaged Nusselt number than that of smooth solar air heater, as expected. The equilateral triangular sectioned ribs can lead to superior heat transfer performance because of the secondary flow induced by the rib top. This secondary flow has the form of two counterrotating vortices, which carry cold fluid from the central core region toward the ribbed walls. These cells, interacting with the main flow, affect the flow reattachment and recirculation between ribs and interrupt boundary layer growth downstream of the reattachment regions. From this figure, it is observed that the average Nusselt number of the roughened duct with respect to the smooth duct, increase with increasing values of Reynolds number in all cases as expected. The velocity increases with increasing value of Reynolds number, which results in enhanced

heat transfer rate. As the Reynolds number increases the roughness elements begin to project beyond the laminar sub-layer. Laminar Sub-layer thickness decreases with an increase in the Reynolds number. In addition to this there is local contribution to the heat removal by the vortices originating from the roughness elements. This increases the heat transfer rate as compared to the smooth surface. This is also because the equilateral triangular sectioned ribs disturb the development of the boundary layer of the fluid flow and increase the turbulent intensity caused by increase in turbulent dissipation rate and turbulent kinetic energy. Fig. 6(a–c) shows the same data as in Fig. 5(a–c), but now plotted average Nusselt number against relative roughness pitch (P/e) at specific values of Reynolds number. Fig. 6 shows the effect of relative roughness pitch on the average Nusselt number for different values of Reynolds number and for fixed value of relative roughness height. It is observed that the average Nusselt number tends to increase as the relative roughness pitch decreases for a fixed value of relative roughness height. This is due to the increase in the number of reattachment points over the absorber plate. Number of reattachment points over the absorber plate increases with the decrease in relative roughness pitch. As the relative roughness pitch reduces, both the average turbulent intensity and the flow acceleration increases with the decrease of relative roughness pitch, which causes an increase of the average Nusselt number. With the increased value of relative roughness pitch, there is less number of occurrences of boundary layer separation and reattachment on the absorber plate. Also, for high value of relative

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Fig. 16. The contour plot of pressure for Re = 5000 and P/e = 14.29 at a relative roughness height of (a) e/D = 0.021, (b) e/D = 0.03 and (c) e/D = 0.042.

roughness pitch, a thicker boundary layer is developed after flow reattachment between the ribs. However, for high value of relative roughness pitch, there will be poorer enhancement in heat transfer also due to the smaller contribution of the rib-top Nusselt number. For too small rib pitch-to-height ratios the flow that separates after each rib does not reattach in the inter-rib region where a weak recirculating flow, resulting in low heat transfer conditions occurs. For too large rib spacing the reattachment point at the wall is reached and a boundary layer begins to grow before the succeeding rib is encountered, reducing the heat transfer. Hence, there is an

optimum value of relative roughness pitch which gives the maximum average heat transfer (i.e., Nusselt number). At the optimum value of relative roughness pitch (P/e) the flow does reattach close to the next rib. Equilateral triangular sectioned rib with relative roughness pitch of 7.14 provides the maximum value of average Nusselt number for the range of parameters investigated. The maximum enhancement in the Nusselt number over the smooth duct is found to be 207.3% within the range of parameters investigated. Fig. 7 shows the effect of relative roughness height on the average Nusselt number for different values of Reynolds number and for fixed value of relative roughness pitch. It is observed that the average Nusselt number tends to increase as the relative roughness height increases for a given value of relative roughness pitch. As the relative rib height increases, the asymmetric velocity profiles in the fluid mix locally more vigorously due to the stronger secondary flow and more recirculation. Higher relative roughness height (e/D) might produce more reattachment of free shear layer which generates a strong secondary flow hence there is an optimum value of relative roughness height which gives the maximum average heat transfer (i.e., Nusselt number). Equilateral triangular sectioned rib with relative roughness height of 0.042 provides the maximum value of average Nusselt number for the range of parameters investigated. Fig. 8 shows the same data as in Fig. 7, but now plotted average Nusselt number against relative roughness height at specific values of Reynolds number. It shows the effect of Reynolds number on the average Nusselt number for different values of relative roughness height and for fixed value of relative roughness pitch. It is observed that the value of average Nusselt number increases with increasing values of roughness height attributed to more number of interruptions in the flow path. Then the effective cross-sectional area of the duct is reduced and this causes the increase of the strength of secondary flow motion with increasing local Reynolds number i.e., flows velocity. It is also observed that the average Nusselt number tends to increase as the Reynolds number increases in all cases as expected. As discussed above, the average Nusselt number is significantly enhanced by the presence of equilateral triangular sectioned rib roughness compared to a smooth duct of a solar air heater. This is because the equilateral triangular sectioned ribs disturb the development of the boundary layer of the fluid flow and increase the turbulent intensity caused by increase in turbulent dissipation rate and turbulent kinetic energy. The thermal phenomena of the artificially roughened solar air heater having equilateral triangular sectioned rib can be easily understood by examining the contour map of turbulent kinetic energy and turbulent intensity. Fig. 9 presents the contour map of turbulent kinetic energy for different Reynolds number at fixed P/e = 7.14 and e/D = 0.042. The peak values of turbulent kinetic energy are observed close to the top heated absorber plate and between the first and second rib. This is due to acceleration and strong shear between the ribs. A substantial decrease in the turbulent kinetic energy is observed for the successive inter-rib regions. Fig. 10 presents the contour map of turbulent intensity for different Reynolds number at fixed P/ e = 7.14 and e/D = 0.042. The peak values of turbulent intensity are predicted near the absorber plate and between the region of first and second rib, and then it decreases with increase in distance from the absorber plate. High level of turbulent intensity leads to a high level of heat transfer. The intensity of shear layer is greater in the vicinity of the ribs as compared to that in the smooth solar air heater as the flow tries to retain in flow direction and hence higher turbulent intensity is seen there. Finally it can be concluded that the heat transfer (i.e., Nusselt number) is strongly dependent on the relative roughness height (e/D) and relative roughness pitch (P/e) of equilateral triangular sectioned rib together with the flow Reynolds number (Re). It is ob-

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A.S. Yadav, J.L. Bhagoria / International Journal of Heat and Mass Transfer 70 (2014) 1016–1039 Table 7 Friction factor enhancement ratio predicted by CFD analysis for different values of P/e and e/D. D = 33.33 mm

Friction factor enhancement ratio

e (mm)

e/D

P (mm)

P/e

Re = 3800

Re = 5000

Re = 8000

Re = 12,000

Re = 15,000

Re = 18,000

0.7

0.021

10 15 20 25

14.29 21.43 28.57 35.71

2.320 2.152 2.011 1.918

2.304 2.136 2.005 1.905

2.269 2.083 1.959 1.872

2.256 2.067 1.932 1.853

2.237 2.031 1.914 1.846

2.210 2.021 1.904 1.827

1

0.03

10 15 20 25

10 15 20 25

2.722 2.505 2.361 2.258

2.703 2.493 2.349 2.238

2.653 2.442 2.306 2.194

2.617 2.412 2.275 2.165

2.594 2.395 2.261 2.136

2.574 2.381 2.254 2.129

1.4

0.042

10 15 20 25

7.14 10.71 14.29 17.86

3.356 3.000 2.835 2.701

3.246 2.991 2.814 2.659

3.186 2.938 2.765 2.641

3.138 2.879 2.727 2.625

3.130 2.853 2.724 2.610

3.176 2.833 2.726 2.603

Bold characters indicate maximum values.

2.2

e/D=0.021, P/e=14.29 e/D=0.021, P/e=21.43

2.0

THPP=(Nu r/Nu s )/(f r/f s )

1/3

e/D=0.021, P/e=28.57 e/D=0.021, P/e=35.71

1.8

e/D=0.03, P/e=10 e/D=0.03, P/e=15 e/D=0.03, P/e=20

1.6

e/D=0.03, P/e=25 e/D=0.042 P/e=7.14 e/D=0.042 P/e=10.71

1.4 e/D=0.042 P/e=14.29 e/D=0.042 P/e=17.86

1.2 2000

4000

6000

8000

10000 12000 14000 16000 18000 20000

Re Fig. 17. Variation of thermo-hydraulic performance parameter with Reynolds number for different values of relative roughness height e/D and relative roughness pitch P/e.

Table 8 Computational grid densities and corresponding wall y+. S. No. Mesh Mesh Mesh Mesh Mesh

1 2 3 4 5

3.2. Flow friction

Number of cells

First y+

204,321 287,467 364,817 432,187 518,732

28.321 18.231 6.523 1.962 1.102

served that the average Nusselt number tends to increase as the relative roughness pitch decreases for a fixed value of relative roughness height and it tends to increase as the relative roughness height increases for a fixed value of relative roughness pitch. The maximum enhancement in the Nusselt number is 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 and it occurs at a Reynolds number of 15,000 (Fig. 5(c)). The enhancement in average Nusselt number over the smooth duct for different value of relative roughness pitch and relative roughness height are presented in Table 6.

The present numerical results on average flow friction characteristics in artificially roughened solar air heater with equilateral triangular sectioned rib roughness on the absorber plate are presented in the form of average friction factor. In this study the average friction factor has been computed numerically using the 2dimensionally developed CFD model. Fig. 11(a–c) shows the effect of Reynolds number on average friction factor for different values of relative roughness pitch and relative roughness height. In all cases, the presence of equilateral triangular sectioned rib produces higher averaged friction factor than that of smooth solar air heater, as expected. Presence of equilateral triangular sectioned rib, which is inserted into a duct of a solar air heater, results in an obstruction of the flow. The flow blockage due to the presence of the equilateral triangular sectioned rib is a vital factor to cause a high pressure drop. In this case all configurations of investigated ribs cause a regular boundary layer separation and re-attachment. This is reflected

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250 A

No. of cells= 518732 No. of cells= 432187 No. of cells= 364817 No. of cells= 287467 No. of cells= 204321

D

B

200

Local Nusselt number

C

150

100

50

0 40

42

44

46

48

50

Position, mm Fig. 18. Effect of different grid densities on local Nusselt number prediction at Re = 15,000 and P/e = 7.14 along the heated surface of the fifth rib.

in an increased pressure drop and therefore an increased friction factor in the roughened duct compared to a smooth duct. With higher blockage of the duct of a solar air heater, pressure drop increases with no significant increase in heat transfer. From this figure, it is seen that the average friction factor of the roughened duct with respect to the smooth duct, tends to decrease as the Reynolds number increases in all cases as expected because of the suppression of laminar sub-layer. Fig. 12(a–c) shows the same data as in Fig. 11(a–c), but now plotted average friction factor against relative roughness pitch (P/ e) at specific values of Reynolds number. Fig. 12 shows the effect of relative roughness pitch on the average friction factor for different values of Reynolds number and for fixed value of relative roughness height. It is observed that the average friction factor tends to decrease as the relative roughness pitch increases for a given value of relative roughness height. This is due to the decrease in number of interruptions in the flow path over the absorber plate, which decreases with the increase in relative roughness pitch for a given value of relative roughness height. It also happens because duct of solar air heater contains less equilateral triangular sectioned rib at higher pitch which results in low flow friction in

the duct. On the other hand, with more ribs per unit surface area, there will be very high pressure drop due to the additional momentum loss. Hence, for low value of relative roughness pitch, there will be higher enhancement in friction factor. Equilateral triangular sectioned rib with relative roughness pitch of 7.14 provides the maximum value of average friction factor for the range of parameters investigated. The maximum enhancement in the friction factor over the smooth duct is found to be 235.6% within the range of parameters (Fig. 12(c)). Fig. 13 shows the effect of relative roughness height on the average friction factor for different values of Reynolds number and for fixed value of relative roughness pitch. It is observed that the average friction factor tends to decrease as the relative roughness height increases for a given value of relative roughness pitch. This is due to the suppression of viscous sub-layer for fully developed turbulent flow in the roughened duct. Equilateral triangular sectioned rib with relative roughness height of 0.042 provides the maximum value of average friction factor for the range of parameters investigated. Fig. 14 shows the same data as in Fig. 13, but now plotted average friction factor against relative roughness height at specific values of Reynolds number. It shows the effect of Reynolds number on the average friction factor for different values of relative roughness height and for fixed value of relative roughness pitch. It is observed that the average friction factor tends to increase as the relative roughness height increases for a given value of relative roughness pitch. This is due to the fact that increasing values of relative roughness height attributes to more interruptions in the flow path through the duct of an artificially roughened solar air heater. This can also be attributed to the dissipation of dynamic pressure of the fluid due to flow blockage and higher surface area. It is also observed that the average friction factor tends to decrease as the Reynolds number increases in all cases as expected. As discussed above, the average friction factor is significantly enhanced by the presence of equilateral triangular sectioned rib roughness compared to a smooth duct of a solar air heater. The flow blockage due to the presence of the equilateral triangular sectioned rib is a dynamic factor to cause a high pressure drop. The hydraulic phenomena of the artificially roughened solar air heater having equilateral triangular sectioned rib can be easily understood by examining the contour map of pressure. Fig. 15 presents the contour map of pressure for different value of relative rough-

Table 9 The comparisons of optimum value of relative roughness pitch (P/e) between present numerical and previous experimental results. S. No.

Investigator/s

Roughness geometry

Optimum value of relative roughness pitch (P/e)

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

Prasad and Mullick [3] Prasad and Saini [4] Gupta et al. [5] Momin et al. [10] Bhagoria et al. [11] Jaurker et al. [13] Layek et al. [14] Saini and Saini [16] Aharwal et al. [17] Saini and Verma [18] Varun et al. [19] Bopche and Tandale [20] Kumar et al. [21] Hans et al. [22] Lanjewar et al. [23] Singh et al. [24] Sethi et al. [26] Kumar et al. [27] Karwa and Chitoshiya [28] Kumar et al. [29] Prasad [30] Present numerical study

Transverse wire rib roughness Transverse wire rib roughness Inclined wire rib (non- transverse rib) roughness V-shaped rib roughness Transverse wedge shaped rib roughness Rib-grooved roughness Chamfered rib-grooved roughness Arc shaped rib roughness Inclined continuous rib roughness with gap Dimple-shaped rib roughness Combination of transverse and inclined rib roughness Inverted U-shaped turbulators Discrete W-shaped rib roughness Multi V-shaped rib roughness 60° W-shaped rib roughness Discrete V-down rib roughness Dimple shaped elements arranged in angular fashion (arc) Multi V-shaped rib roughness with gap V-down discrete rib roughness Multi V-shaped ribs roughness with gap Transverse wire rib roughness Equilateral triangular sectioned rib roughness

P/e = 12.7 P/e = 10 P/e = 10 P/e = 10 P/e = 7.57 P/e = 6 P/e = 6 P/e = 10 P/e = 10 P/e = 10 P/e = 8 P/e = 6.67 P/e = 10 P/e = 8 P/e = 10 P/e = 8 P/e = 10 P/e = 10 P/e = 10.63 P/e = 8 P/e = 10 P/e = 7.14

A.S. Yadav, J.L. Bhagoria / International Journal of Heat and Mass Transfer 70 (2014) 1016–1039

ness pitch (P/e) at fixed value of Reynolds number, Re = 5000 and relative roughness height, e/D = 0.03. As the air enters the roughened region of duct of an artificially roughened solar air heater, the air starts to accelerate, result in increase of pressure drop. The pressure drop is more profound for the higher value of Reynolds number flow. In general, the resulting friction is much higher in a roughened rectangular duct than smooth duct of a solar air heater and it must be considered as a key factor in any practical design. The contour plot of pressure for different increasing values of relative roughness height at a fixed value of Reynolds number, Re = 5000 and relative roughness pitch, P/e = 14.29 have been demonstrated in Fig. 16. Consequently, it can be concluded that the average friction factor is strongly dependent on the relative roughness pitch (P/e) and relative roughness height (e/D) of equilateral triangular sectioned rib together with the flow Reynolds number (Re). It is observed that 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. The maximum enhancement in the friction factor is 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 and it occurs at a Reynolds number of 3800. The enhancement in average friction factor over the smooth duct for different value of relative roughness pitch and relative roughness height are presented in Table 7. 3.3. Performance evaluation Use of artificial roughness on the absorber plate in the form of equilateral triangular sectioned rib generates local wall turbulence or interrupts the laminar sub-layer due to flow separation and reattachment between the consecutive equilateral triangular sectioned ribs, which reduces thermal resistance and significantly boost the rate of heat transfer. However, the use of artificial roughness on the heat transfer surface in the form of equilateral triangular sectioned rib results in higher pressure drop and hence greater pumping power requirements. So, it is necessary that turbulence must be generated only in the region very close to the absorber plate, i.e. in the laminar sub-layer only. Hence, in order to make the use of artificial roughness more effective, the height of equilateral triangular sectioned rib should be kept small, primarily in the laminar sub-layer region, so that the increases in the friction will not be disproportionate to the increase in heat transfer. It has been observed that the rate of increment of average heat transfer is

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comparatively less than the rate of increment of average friction factor for increasing rib height. The present CFD investigation shows that the artificially roughened solar air heater with relative roughness pitch of 7.14, and relative roughness height of 0.042 provide maximum value of average Nusselt number at a higher value of Reynolds number, Re = 15,000. Same artificially roughened solar air heater with similar relative roughness pitch and relative roughness height result in the maximum value of average friction factor at a lower value Reynolds number Re = 3800. It is, therefore, necessary to determine the optimal rib dimension and arrangement such that the heat transfer coefficient is maximized while keeping the friction losses at the minimum possible value. A parameter that facilitates simultaneous consideration of thermal and hydraulic performance as defined by Webb and Eckert [44] is given by Eq. (8). The result of this parameter higher than one declares the usefulness of applying an enhancement scheme and used to compare the performance of number of arrangements to decide the best among these. Fig. 17 exhibits the effect of Reynolds number (Re) on the thermo-hydraulic performance parameter for different values of relative roughness height and relative roughness pitch. It has been found that the value of thermo-hydraulic performance parameter varies between 1.36 and 2.11 within the range of the parameters investigated. The thermo-hydraulic performance parameter initially tends to increase with the rise of Reynolds number and then decreases with the further rise of Reynolds number. This appears due to the fact that at relatively higher values of relative roughness height, the reattachment of free shear layer might not occur and the rate of heat transfer enhancement will not be proportional to that of friction factor as stated by Prasad and Saini [4]. Hence there is an optimum value of relative roughness height, relative roughness pitch and Reynolds number which give the maximum thermo-hydraulic performance parameter. It is observed that solar air heater roughened with equilateral triangular sectioned rib with P/e = 7.14, e/D = 0.042 at a Reynolds number Re = 15,000 provide better thermo-hydraulic performance parameter for the investigated range of parameters. 3.4. Validation of CFD model For the validation of the present numerical model, the outcomes are verified in a number of ways to confirm the validity of the present CFD analysis. Tests for the confirmation of grid independence of the proposed model is first carried out by increasing the grid density until further enhancement shows a difference of less than

Table 10 The comparisons of optimum value of roughness height (e/D) between present numerical and previous experimental results. S. No.

Investigators

Roughness geometry

Optimum value of relative roughness height (e/D)

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

Prasad and Saini [4] Momin et al. [10] Bhagoria et al. [11] Jaurker et al. [13] Layek et al. [14] Saini and Saini [16] Aharwal et al. [17] Saini and Verma [18] Varun et al. [19] Bopche and Tandale [20] Kumar et al. [21] Hans et al. [22] Lanjewar et al. [23] Singh et al. [24] Sethi et al. [26] Kumar et al. [27] Karwa and Chitoshiya [28] Kumar et al. [29] Present numerical study

Transverse wire rib roughness V-shaped rib roughness Transverse wedge shaped rib roughness Rib-grooved roughness Chamfered rib-grooved roughness Arc shaped rib roughness Inclined continuous rib roughness with gap Dimple-shaped rib roughness Combination of transverse and inclined rib roughness Inverted U-shaped turbulators Discrete W-shaped rib roughness Multi V-shaped rib roughness 60° W-shaped rib roughness Discrete V-down rib roughness Dimple shaped elements arranged in angular fashion (arc) Multi V-shaped rib roughness with gap V-down discrete rib roughness Multi V-shaped ribs roughness with gap Equilateral triangular sectioned rib roughness

e/D = 0.033 e/D = 0.032 e/D = 0.033 e/D = 0.0363 e/D = 0.04 e/D = 0.0422 e/D = 0.037 e/D = 0.0379 e/D = 0.030 e/D = 0.0398 e/D = 0.0388 e/D = 0.043 e/D = 0.03375 e/D = 0.043 e/D = 0.036 e/D = 0.043 e/D = 0.047 e/D = 0.043 e/D = 0.042

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1% in two consecutive sets of results and then numerical results are validated by comparing with available analytical solutions or widely accepted numerical results. To captures boundary layer properly, the mesh should be correctly generated. For turbulent flows, calculation of the y+ value of the first node point helps in doing that. This dimensionless distance is defined as: y+ = yus/t, where us is the friction velocity. For that and because the wall distance y+ is involved in the selection of the appropriate near-wall treatment, we do a grid test for increasing the grid density until further enhancement shows a difference of less than 1% in two consecutive sets of results. Five different grid densities (204,321 cells, 287,467 cells, 364,817 cells, 432,187 cells and 518,732 cells) are applied to select the appropriate mesh size that adapt with near-wall treatment (wall functions or near-wall modeling). This is achieved by refining the mesh, with particular attention to the first grid point off the wall. Table 8 shows selected computational mesh and the corresponding wall y+ values. Fig. 18 shows the results of local Nusselt numbers along the heated surface of the fifth rib with the RNG k–e turbulence model for five different grid densities of 204,321 cells, 287,467 cells, 364,817 cells, 432,187 cells and 518,732 cells. It is found that the relative deviation of the local Nusselt numbers between solutions of 518,732 cells and 432,187 cells is less than 1% at Re = 15,000. Hence, the mesh with 432,187 cells with a near wall elements spacing of y+  2 has been selected for all cases considered herein. The CFD technique has been used as it is powerful tool for dealing with the wide range of parameters and complicated analysis which cannot be done through experimental investigations. The particular disadvantage of CFD technique is their limited range of validation. Before furnishing the result obtained from the present CFD analysis, it is required to validate with the existing experimental data. The literature survey also revealed that most of the results of the analysis using the chosen parameters in the present study had not been studied before. Therefore, it is truly difficult for validation of the results obtained from the present analysis for artificially roughened solar air heater having equilateral triangular sectioned rib roughness on the absorber plate. However, in order to verify the CFD results, trends of outcomes from the present CFD investigation have been compared with available experimental results with different roughness geometries. Similar trends for heat transfer and fluid friction were observed by Prasad and Saini [4], Gupta [5], Saini and Saini [6], Momin et al. [10] Bhagoria et al. [11], Jaurker et al. [13], Layek et al. [14], Karmare and Tikekar [15], Saini and Saini [16], Aharwal et al. [17], Saini and Verma [18], Bopche and tandale [20], Kumar et al. [21], Hans et al. [22], Lanjewar et al. [23], Singh et al. [24], Sethi et al. [26], Kumar et al. [27], Kumar et al. [29], Prasad [30] and Verma and Prasad [41], even though the roughness geometries studied in their experiments were different from the present investigation. A literature search in this field revealed that within a certain limiting values of relative roughness pitch, artificially roughened solar air heater performs thermo-hydraulically better than that of a smooth solar heater. This limiting value of relative roughness pitch has been found to lies in the range of 6–10. The comparison of optimum value of relative roughness pitch with other geometries available in the literature is presented in Table 9. On comparison, it has been observed that the value of relative roughness pitch for present numerical model is found to be 7.14 and it is found to fall in-between the accepted range i.e., 6 and 12. Further, literature search in this area also revealed that the optimum value of relative roughness height generally lies between 0.03–0.047. Table 10 shows the comparison of optimum value of relative roughness height between present CFD simulation and available experimental results. On comparison, it has

been observed that the value of relative roughness height for present numerical model is found to be 0.042 and it is found to fall in-between the accepted range i.e., 0.03 and 0.047. Finally it has been observed that proposed model of artificially roughened solar air heater predicts the experimental data quite accurately. The objective of this work was to propose a CFD model for predicting the heat transfer and flow friction phenomenon in an artificially roughened solar air heater having equilateral triangular sectioned rib roughness. This CFD study result in significant savings in computation power and time and makes parametric studies feasible. Ultimately, this CFD model has the advantages of reduced cost, time and ability to optimize design significantly without much investment in the real experiment. Present CFD model of solar air heater is used to improve the convective heat transfer coefficient in many practical applications i.e., space heating, crop drying, industrial activities (drying/heating) such as chemical, pharmaceutical, limited areas of textiles and hosieries, tannery, edible oil, etc. 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. 4. Conclusions 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

A.S. Yadav, J.L. Bhagoria / International Journal of Heat and Mass Transfer 70 (2014) 1016–1039

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.

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