Experimental investigation of solar air heater duct with discrete V-rib integrated with staggered elements

ABSTRACT

This paper presents an experimental investigation of heat transfer and friction factor in a rectangular duct with discrete V-rib integrated with staggered elements. The Reynolds number (Re) of 3000–12,000, ratio of staggered element size to rib height (r/e) of 2–5.5, relative roughness pitch (p/e) of 12, relative roughness height (e/Dh) of 0.045, flow angle of attack (α) of 60°, relative gap width (g/e) of 1, relative staggered element position (p’/p) of 0.65 and number of gaps (N_g) of 6. The maximum augmentation in Stanton number is 1.90 times over the smooth duct and maximum thermal efficiency is obtained 86% corresponding to ratio of staggered element size to rib height (r/e) of 3.5.

KEYWORDS:

• Solar air heater
• Stanton number
• friction factor
• thermal efficiency
• V-rib

1. Introduction

The economic growth of our country is powerfully affected by its energy utilisation. With the raise in population, energy need is enhancing day by day. Energy production by utilising fossil fuels is constantly damaging our environment. To build our environment clean utilisation of renewable energy resources is to be enhanced. The renewable resources are sufficient in nature and usable in broad range. Solar energy is greatest bountiful and assuring substitute. At the present time, there are so many ways to use solar energy and convert it into thermal energy. But the acknowledgement of solar energy technology depends on its efficiency and cost-effectiveness with some other factors (Sharma, Bharadwaj, and Varun 2017). Efficiency of solar air heater (SAH) duct is poor due to laminar sub-layer development. The main application of SAH is drying of crops and space heating, etc. The use of artificial roughness on absorber surface is useful and easy technique to augment convective heat transfer coefficient of air flowing inside the duct. It is due to turbulence created by artificial roughness element on the absorber surface of roughened duct breaks the laminar sub-layer. But artificial roughness also enhances the friction losses and leads to more power needed by blower for airflow. The important parameters that effect on performance of SAH duct are roughness pitch, height and flow angle of attack. Many experimental studies have been done on SAH duct with different forms of artificial roughness on absorber surface for the maximum enhancement in heat transfer and minimum frictional losses (Varun et al. 2009; Bharadwaj et al. 2017; Singh et al. 2015; Chaube, Sahoo, and Solanki 2006; Gupta and Kaushik 2009a; Kumar, Saini, and Saini 2012).

Literature survey indicates the first artificial roughness geometry reported in the form of transverse rib (Prasad and Mullick 1983; Prasad and Saini 1988; Gupta, Solanki, and Saini 1993; Verma and Prasad 2000). Transverse geometry was redesigned as discrete transverse later by Sahu and Bhagoria (2005). From further studies, it is examined that continuous inclined rib roughness gives better performance as compared to transverse continuous rib due to creation of two counters rotating secondary flow cell results enhance heat transfer (Gupta, Solanki, and Saini 1997). Continuous V-rib (Momin, Saini, and Solanki 2002; Karwa 2003), continuous arc-shaped (Saini and Saini 2008), W-shaped rib roughness (Lanjewar, Bhagoria, and Sarviya 2011), multi V-rib (Hans, Saini, and Saini 2010) and multi arc-shaped (Singh and Varun 2014) give better performance as compared to inclined rib due to creation of multiple counters rotating secondary flow cell. Gap provision in continuous shaped artificial roughness geometry such as inclined rib with gap (Aharwal, Gandhi, and Saini 2009), V-down with gap (Singh, Chander, and Saini 2011), arc-shaped with gap (Gill, Hans, and Singh 2017), V-ribs with symmetrical gaps (Maithani and Saini 2016, 2017a, 2017b), multi V-rib with gap (Kumar, Saini, and Saini 2013) and multi arc-shaped with gap (Pandey and Bajpai 2016) further augment the heat transfer because acceleration of flow through the gap and re-development of secondary flow. Provided staggered piece in front of the gap in broken V-rib (Patil, Saini, and Kumar 2012), broken arc-shaped rib (Gill et al. 2017) and multi-gap V-rib (Deo, Chander, and Saini 2016) further augment heat transfer because staggered element placed in the front of the gap divide flow on the top and on the two sides of it. It aggravates the turbulence mainly on the two sides of staggered element that agitate huge area as compared to roughness geometry with gap without staggered element.

As per literature provision of gap in inclined, arc-shaped and V-rib augment the heat transfer over continuous roughness geometry and also providing staggered element in front of gap further augment the heat transfer over a gap in arc-shaped and V-rib roughness geometry. In this present investigation is taken up to experimental study of SAH duct with discrete V-rib integrated with staggered elements having a different ratio of staggered element size to rib height (r/e). Objective for this experimental analysis are as follows;

1. Investigated the effect of ratio of staggered element size to rib height (r/e) friction factor (f), Stanton number (St) and Thermal efficiency (η_th).

2. Reported the best ratio of staggered element size to rib height (r/e) on the basis of maximum augmentation in heat transfer.

3. Empirical Correlation for Nusselt number (Nu) and friction factor (f) has been developed.

1.1. Roughness parameters

Figure 1 shows the sketch of discrete V-rib integrated with staggered elements. Figure 2 shows the pictorial view of roughness geometry on absorber surface. The roughness parameters are selected as per literature (Deo, Chander, and Saini 2016; Patel and Lanjewar 2018). Table 1 shows the operating and roughness parameters for the present investigation.

Figure 1. Schematic diagram of present roughness geometry

Figure 2. Pictorial view of roughness geometry

Table 1. Range of parameters of current investigation

S. No.	Roughness parameters	Range
1	W	200 mm
2.	H	25 mm
3.	p/e	12
4.	e/Dh	0.045
5.	α	60°
6.	g/e	1
7.	r/e	2, 3.5, 4.5 and 5.5
8.	p’/p	0.65
9.	Re	3000–12,000
10.	Ng	6

2. Experimental setup

2.1. Fabrication of experimental setup

The indoor test facility as per Duffie and Beckman (ASHRAE Standard 93 2003) as shown in Figure 3(a) is fabricated to examine the effect ratio of staggered element size to rib height (r/e) of discrete V-rib integrated with staggered elements on heat transfer and friction factor. A rectangular duct separated in three sections entrance, test and exit. The rectangular duct has a flow cross-section of 200 mm × 25 mm. An electric heater is used for supplying uniform heat flux of 1000 W/m² to the absorber plate having artificial roughness on its underside. Air extract over the duct by the blower and the flow rate of the air through the duct is controlled by a gate valve. The calibrated orifice plate is connected to U-tube manometer for measurement of flow rate of air. The orifice plate is calibrated with a Pitot tube. After achieving the steady state, the temperature measured at entrance, exit and top of the absorber plate by calibrated copper constantan thermocouples. Figure 3(b) indicates the position of 15 thermocouples fixed on the top of the absorber surface to measure its temperature. The thermocouple wire is fixed to the data logger, and data logger is connected to the computer to show the temperature readings. The pressure loss of the test section is measured with the help of digital micro-manometer (least count of 0.1 Pa).

Figure 3. (a) Sketch and actual photo of test setup (b) Position of thermocouples over absorber surface (c) Variation of absorber surface temperature

2.2. Data reduction

The similar procedure has been used by Ravi and Saini (2018), Kumar, Prajapati and Samir (2017) to calculate the following key parameters.

The average temperature of air T_f is determined by the average of air inlet and outlet temperature. The inlet temperature of air recorded one thermocouple and outlet temperature of air noted five thermocouples fixed in span wise.

(1) $T_o=\frac{T_{o1}+T_{o2}+T_{o3}+T_{o4}+T_{o5}}{5}$(1)

(2) $T_f=\frac{T_i+T_o}{2}$(2)

The absorber surface average temperature T_p is determined by the average of the temperature of 15 thermocouples at different locations on the top of absorber surface.

(3) $\begin{array}{rl}& T_P=\frac{1}{9}\left[T_1+T_2+\left(\frac{T_3+T_4+T_5)}{3}\right)+T_6+\left(\frac{T_7+T_8+T_9}{3}\right)\right.\\ & \left.+T_{10}+\left(\frac{T_{11}+T_{12}+T_{13}}{3}\right)+T_{14}+T_{15}\right]\end{array}$(3)

The pressure loss (∆P)_o across the orifice plate is used to determine the mass flow rate of air (m).

(4) $m=C_d{A}_o{\left[\frac{2\rho {(\mathrm{\Delta }P)}_o}{1-{\beta }^4}\right]}^{0.5}$(4)

The velocity of air is determined from Equation (5)(5) $V=\frac{m}{\rho WH}$(5) :

(5) $V=\frac{m}{\rho WH}$(5)

The Re for flow of air in the duct is determined from Equation (6)(6) $Re=\frac{V{D}_h}{\upsilon }$(6) :

(6) $Re=\frac{V{D}_h}{\upsilon }$(6)

The pressure loss in test section (∆P)_d is used to determine the friction factor (f):

(7) $f=\frac{D_h\times \mathrm{\Delta }p}{\left(2\times L\times V^2\times \rho \right)}$(7)

D_h is defined as:

$D_h=\frac{4WH}{2\left(W+H\right)}$

Useful heat gain is the heat transfer to the air from the heated absorber surface and is obtained from the known values of air inlet and outlet temperatures T_i and T_o, respectively.

(8) $Q_u=m\times C_P\times \left(T_O-T_i\right)$(8)

Heat loss is determined as Gupta and Kaushik (2009b).

(9) $Q_L=I{A}_p-Q_u$(9)

The average heat transfer coefficient is determined from Equation (10)(10) $h=\frac{Q_u}{A_p\left(T_P-T_f\right)}$(10) :

(10) $h=\frac{Q_u}{A_p\left(T_P-T_f\right)}$(10)

where A_p is the area of the absorber plate (A_p = Width of the roughened plate × Length of the roughened plate)

The heat transfer coefficient is used to calculate the Nu:

(11) $Nu=\frac{\left(h\times D_{{ }_h}\right)}{k}$(11)

Stanton number (St) is defined as:

(12) $St=\frac{Nu}{RePr}$(12)

η_th is defined as:

(13) ${\eta }_{th}=\frac{Q_u}{I{A}_p}$(13)

Uncertainty analysis has been done as per method of Kline and McClintock (Kline and McClintock 1953) and uncertainty range in Re, Nu and f is 1.79–4.38%, 3.29–4.60% and 3.63–9.59%, respectively.

3. Results and discussions

3.1. Set-up validation

The experimental values of Nu and f for smooth surface are compared with the values of Nu and f are obtained from the correlations of Modified Dittus-Boelter (Sadik, Shah, and Aung 1987) and Modified Blasius (Bhatti and Shah, 1987) as indicates in Figure 4 and 5.

(14) $f_s=0.085\times {\left(Re\right)}^{-0.25}$(14)

Figure 4. Variation of experimental and theoretical value of Nu

Figure 5. Variation of experimental and theoretical value of f

For rectangular duct, 2R_av/D_e = (1.156 +H/W – 1)/(H/W)

(15) $f_s=0.085\times {\left(Re\right)}^{-0.25}$(15)

Maximum deviation of experimental and theoretical value of Nu and f is obtained 7.13% and 5.11%, respectively.

3.2. Flow field near the rib roughness wall

It is considered that augmentation in Nu and f in the rib roughened duct are because changes in the flow field near the rib roughened wall. Many investigators in the earlier (Momin, Saini, and Solanki 2002; Karwa 2003; Singh, Chander, and Saini 2011; Patil, Saini, and Kumar 2012; Gill et al. 2017) have reported the effect of V-rib on Nu augmentation because the travel of divided secondary flow along the two elements of V-rib. The provision of a gap in an element of V-rib passes the secondary flow by that enhances the velocity of flow down-stream of the gap. The higher velocity jets passed through the gaps boost turbulence between the successive ribs. This helps to enhance the local heat transfer coefficient in relatively low heat transfer region. The staggered element in front of gap divides the flow in top and two sides of it. V-rib with gap and staggered element generate more turbulence as compared to V-rib with gap because scattering of the main flow from the staggered element. As the staggered element placed in the path of secondary flow jets passed from the gaps, the staggered element may be preferably placed in the region where it divides the flow passed through the gaps after extracting a maximal amount of heat and permitting the reattachment of flow near the next gap. Figure 6 shows the flow pattern of the fluid over the roughened surface.

Figure 6. Flow pattern for discrete V-rib integrated with staggered elements

3.3. Variation of Stanton number ratio (St_r/St_s) and friction factor ratio (f_r/f_s) with Reynolds number (Re)

Figure 7 and 8 indicate Stanton number ratio (St_r/St_s) and friction factor ratio (f_r/f_s) for different ratios of staggered element size to rib height (r/e) against Re. For the ratio of staggered element size to rib height (r/e) of 3.5, Stanton number ratio (St_r/St_s) is 1.58–1.90 over the range of Re investigated. Similarly, for the ratio of staggered element size to rib height (r/e) of 2, 4.5 and 5.5, Stanton number ratio (St_r/St_s) is 1.34–1.67, 1.50–1.80 and 1.42–1.69, respectively, over the range of Re investigated. The maximum augmentation of Stanton number is found to be 1.90 times that of the smooth surface for the ratio of staggered element size to rib height (r/e) of 3.5 at Re of 7803. For the ratio of staggered element size to rib height (r/e) of 3.5, friction factor ratio (f_r/f_s) is 2.11–3.07 over the range of Re investigated. Similarly, for the ratio of staggered element size to rib height (r/e) of 2, 4.5 and 5.5, friction factor ratio (f_r/f_s) is 2.5–3.24, 2.22–3.01 and 2.33–3.08, respectively, the range of Re investigated. Maximum value of friction factor is obtained 3.24 times that of the smooth surface for the ratio of staggered element size to rib height (r/e) of 2 at Re of 11,916.

Figure 7. Stanton number ratio vs Re

Figure 8. Friction factor ratio vs Re

3.4. Variation of thermal efficiency (η_th) against Reynolds number (Re)

Figure 9 indicates the variation of thermal efficiency (η_th) for different ratio of staggered element size to rib height (r/e) against Reynolds number (Re) and temperature rise parameters (∆T/I). From the figures, it indicate the η_th of SAH duct with roughened and smooth surface increases with increasing Re. It is due to the η_th is a function of useful heat gain (Q_u) and as the Re increases the rate of heat transfer increases, therefore the η_th increasing. The result indicates that the SAH duct with roughened surface having ratio of staggered element size to rib height (r/e) of 3.5 gives maximum η_th as compared to roughened surface having r/e of 2, 4.5 and 5.5, and also smooth surface entire range of Re.

Figure 9. Thermal efficiency (η_th) vs Re

4. Correlation for Nusselt number (Nu) and friction factor (f)

Data obtained from the experiment are used to development of statistical correlation on the basis of regression analysis. Figure 10 plotted Nu against Re for all data are obtained from the experiment. The power-law equation between Nu and Re is given below

(16) $Nu=A_o(Re{)}^{0.9248}$(16)

Figure 10. Plot of Nu vs Re

where constant A_o is a function r/e. The value of (Nu/Re^0.9248 = A_o) is plotted in Figure 11 as a function of r/e. Finally empirical correlation for Nu:

(17) $Nu=0.0084{\left(Re\right)}^{0.9248}{\left(\frac{r}{e}\right)}^{0.0748}$(17)

Figure 11. Plot of Nu/Re^0.9248 vs r/e

An identical method has been adopted for correlation development of friction factor (f).

Figure 12 plotted f against Re for all data are obtained from the experiment. The power-law equation between f and Re is given below:

(18) $f=B_o(Re{)}^{-0.2355}$(18)

Figure 12. Plot of f vs Re

where constant B_o is a function r/e. The value of (f/Re^−0.2355 = B_o) is plotted in Figure 13 as a function of r/e. Finally, empirical correlation for f:

(19) $f=0.2151{\left(Re\right)}^{-0.2355}{\left(\frac{r}{e}\right)}^{-0.0644}$(19)

Figure 13. Plot of f/Re^−0.2355 vs r/e

Comparison of experimental and predicted values of Nu and f plotted in Figure 14 and 15. From the figures, it is observed that the deviations are ±14% and ±11% for Nu and f, respectively.

Figure 14. Plot of Nu_predicted vs Nu_{experimental.}

Figure 15. Plot of f_predicted vs f_{experimental.}

5. Conclusion

The current experimental analysis has been done to augmentation the thermal performance of SAH duct with roughened surface. The following conclusions are based on above results:

1. Discrete V-rib integrated with staggered elements considerably augments the heat transfer over the smooth surface. The augmentation in Stanton number lies in the range of 1.34–1.90 for a range of Re investigated.

2. The maximum augmentation in Stanton number is obtained corresponding to the ratio of staggered element size to rib height (r/e) of 3.5.

3. The maximum increase in friction factor lies in the range of 2.11–3.24 for a rage of Re studied. In addition, ratio of staggered element size to rib height (r/e) of 2 gives maximum friction loss as compared to r/e of 3.5, 4.5 and 5.5.

4. Empirical correlation for Nu and f has been developed.

Disclosure Statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Sumer Singh Patel

Sumer Singh Patel is a Ph.D. research scholar in the Department of Mechanical Engineering of Maulana Azad National Institute of Technology Bhopal.

Atul Lanjewar

Dr. Atul Lanjewar working as Associate Professor in the Department of Mechanical Engineering of Maulana Azad National Institute of Technology Bhopal.