Efficiency of Recycling Double-Pass V-Corrugated Solar Air Collectors

Abstract

The influence of recycling on double-pass solar air collectors with welding of the V-corrugated absorber has been studied experimentally and theoretically. Welding the V-corrugated absorber and the recycle-effect concept to the solar air collector was proposed to strengthen the convective heat-transfer coefficient due to turbulence promotion. Both the recycle effect and the V-corrugated absorber can effectively enhance the heat transfer efficiency compared to various designs such as single-pass, flat-plate double-pass, and double-pass wire mesh packed devices. Recycling operations and welding the V-corrugated absorber could enhance the collector efficiency by increasing the recycle ratio, incident solar radiations, and air mass flow rates. The most efficient and economical operating conditions were found at R ≈ 0.5, with relatively small hydraulic dissipated energy compensation. It was found that the turbulence intensity increase from welding the V-corrugated absorber into the solar air collector channel could compensate for the power consumption increase, when considering economic feasibility.

1. Introduction

New designs of solar air collectors with welding of the V-corrugated absorber into double-pass devices under recycling operations has been proposed and studied, as shown in Figure 1a,b. The experimental setup was fabricated with the V-shape corrugated absorber welded on the flat-plate solar air collector to validate the theoretical predictions calculated by mathematical modeling. A higher device performance was obtained with a recycling double-pass V-corrugated collector than with a flat-plate solar air collector of the same working dimensions. El-Sebaii and Shalaby [1] and Sevik [2] discussed the design and experimental investigation of solar dryers. Razika, et al. [3] and Al-Kayiem, Yassen [4] studied the inclination angel for the absorption–convection heat transfer behavior in a solar air collector. El-Sebaii and Al-Snani [5] investigated the effects of various selective coating materials on the collector’s performance. Improvement of solar collector efficiency in many devices has been investigated by introducing free convection [6] and force convection [7], extending heat transfer area [8], and increasing flow turbulence in a solar air heater channel with vortex generators [9,10] and welding V-ribs [11]. The application of the recycle effect concept to solar air heaters has been confirmed with technical feasibility in double-pass [12] and multi-pass [13] operations, and the recycling double-pass design with eddy promotion [14,15] results in enhancement of the convective heat-transfer coefficient. The new designs in the present study of solar air collectors were investigated, adopting the V-corrugated recycling double-pass device to increase the convective heat-transfer coefficients due to both the enhancement of flow turbulence and enlargement of the heat-transfer area, as shown in Figure 1a,b, respectively.

The purposes of the present study are: (a) to carry out theoretical predictions and experimental runs of operating the recycling double-pass V-corrugated solar air collector; (b) to investigate the influences of the recycle ratio and air mass flow rate on the heat-transfer efficiency enhancement and power consumption; (c) to investigate the economic feasibility of the new design of the recycling double-pass V-corrugated solar air collectors.

2. Theoretical Analysis

Consider the heat transfer in two subchannels with welding of the V-corrugated absorber plate to divide a parallel conduit of height $H_g$, length $L$ and width $W$, as shown in Figure 1a,b with the different air flow arrangements. Before entering the lower subchannel (flow pattern A), as shown in Figure 1a, the inlet air mass flow rate $\dot{m}$ and inlet temperature $T_{in}$ is premixed with the recycling air flow $R\dot{m}$ exiting from the upper subchannel with the outlet temperature $T_{a,L}$. The inlet air mass may flow through the upper channel firstly (flow pattern B), as shown in Figure 1b.

By following the same mathematical treatment and experimental methods performed in our previous work [16], except welding the V-corrugated absorber instead of packing wire mesh, the theoretical solutions of the temperature distributions of the flowing air in the lower and upper subchannels were obtained, making the energy balance on a finite system element, as shown in Figure 2. The various heat transfer coefficients at different components of the solar air heater were sketched in the thermal resistance network in Figure 3. The results are:

$$T_a(\xi )=C_1{e}^{Y_1\xi }+C_2{e}^{Y_2\xi }-\frac{B_3{B}_4-B_1{B}_6}{B_2{B}_4-B_1{B}_5}+T_s$$

(1)

$$T_b(\xi )=\frac{Y_1-B_5}{B_4}{C}_1{e}^{Y_1\xi }+\frac{Y_2-B_5}{B_4}{C}_2{e}^{Y_2\xi }+\frac{B_3{B}_5-B_2{B}_6}{B_2{B}_4-B_1{B}_5}+T_s$$

(2)

The definitions of $B_i$, $G_i$, $M_i$, $Y_i$, $C_i$, $F_i$, and $I_i$ are referred to in the Appendix A. In obtaining the above results for the steady-state one-dimensional mathematical formulation, the boundary conditions are:

$$z=0,T_a\left(0\right)=T_{a,0}=\frac{T_{in}+R{T}_b(0)}{1+R}$$

(3)

$$z=L,T_a\left(1\right)=T_{a,L},T_b\left(1\right)=T_{b,L}$$

(4)

The outlet temperature of $T_{a,L}$ can be calculated from Equation (1).

$$T_a(1)=C_1{e}^{Y_1}+C_2{e}^{Y_2}-\frac{B_3{B}_4-B_1{B}_6}{B_2{B}_4-B_1{B}_5}+T_s$$

(5)

The useful energy gained by the flowing air was estimated from the energy balance on the lower subchannel, upper subchannel, and whole solar air collector with the known inlet and outlet temperatures, respectively.

$$Q_u=\dot{m}(1+R)C_p(T_{a,L}-T_{a,0})+\dot{m}{C}_p(T_{b,0}-T_{b,L})=\dot{m}{C}_p(T_{a,L}-T_{a,i})$$

(6)

The collector efficiency ${\eta }_V$ of the recycling double-pass V-corrugated solar air collector was obtained from the actual useful energy gained by the airflow and the incident solar radiation as:

$$\begin{array}{cc}\hfill {\eta }_V& =\frac{Q_u\left(\mathrm{Useful}\mathrm{gain}\mathrm{of}\mathrm{energy}\mathrm{carried}\mathrm{away}\mathrm{by}\mathrm{air}\right)}{I_0{A}_c\left(\mathrm{Total}\mathrm{solar}\mathrm{radiation}\mathrm{incident}\right)}\hfill \\ & =\frac{\dot{m}{C}_p(T_{a,L}-T_{a,i})}{I_0{A}_c}=\frac{I_0{\tau }_g^2{\alpha }_p-U_L(T_{p,m}-T_s)}{I_0}\hfill \end{array}$$

(7)

The average absorber temperature was readily obtained, equating the terms of Equation (7) as:

$$T_{p,m}=T_s+(I_0{\tau }_g^2{\alpha }_p/U_L)-\frac{\dot{m}{C}_p(T_{a,L}-T_{a,i})}{A_c{U}_L}$$

(8a)

$$=T_s+(I_0/U_L)({\tau }_g^2{\alpha }_p-{\eta }_V)$$

(8b)

3. Experimental Setup

The recycling double-pass solar air collectors are welded to four units of V-shape stainless steel absorbing plate of 7 × 10⁻⁵ m thickness on the bottom plate to divide the air flow conduit of width W, length L, and height H_g into two subchannels, as shown in Figure 4 (flow pattern A). A photo of the experimental device was taken and shown in Figure 5. Three configurations of solar air collectors, such as the downward single-pass device, recycling double-pass wire mesh, and recycling double-pass V-corrugated absorber were investigated theoretically and experimentally. The experimental runs were conducted using a blower (Teco 3 Phase Induction Motor, Model BL model 552, Redmond Co, Owosso, MI, USA) to supply the ambient air, and the air mass flow rate was measured using an anemometer (Kanmax Japan Inc., Osaka, Japan). The device parameters [17] and operating conditions are as follows: L = W = 0.3 m; H_g = 0.062 m; k_s = 46.64 W/m·K; ${\tau }_g$ = 0.875; ${\alpha }_p$ = 0.95; ${\epsilon }_g$ = 0.94; ${\epsilon }_p$ = 0.8; ${\epsilon }_R$ = 0.94; $I_0$ = 830 and 1100 W/m²; $T_{in}$ = 293,303 and 313 K; $V$ = 1.0 m/s; $\dot{m}$ = 0.0107, 0.0161 and 0.0214 kg/s; $T_s$ = 293 K, σ = 5.68 × 10⁻⁸ W/m²·K⁴. The calculation methods for flow pattern B are similar to those in the previous section of flow pattern A. A comparison of both flow patterns in Figure 6 indicates a greater collector performance improvement in operating flow pattern A is higher than that in the flow pattern B. Therefore, all the theoretical predictions and experimental works were carried out using flow pattern A as an illustration in the present study. The evaluation procedure for collector efficiency is now described. With known device geometries (W, L, H_g), physical properties (k_s, ${\tau }_g$, ${\alpha }_p$, ${\epsilon }_g$, ${\epsilon }_p$, ${\epsilon }_R$, $C_p$, $\mu$, $\rho$) and the given operating conditions ($I_0$, $T_{in}$, $V$, $\dot{m}$, $T_s$), a temporary ${\eta }_V$ is first estimated from Equation (7) using Equation (8a) for calculating $T_{a,L}$ once $T_{p,m}$ is assumed. The $T_{p,m}$ value is thus re-checked using Equation (8b) by continued iterations, and the final value ${\eta }_V$ was obtained until the last value meets the required convergence. The theoretical predictions were obtained by substituting the specified values of physical properties and operation conditions into the appropriate equations, and the results are represented in Figure 7 and Figure 8 for comparison. The influence of the recycle ratio on collector efficiencies of theoretical predictions and experimental results for various incident solar radiations, recycle ratios, and air mass flow rates are presented in Figure 7 and Figure 8, respectively.

Moffat [18] determined the experimental uncertainty of each individual measurement directly from the experimental run as follows:

$$S_{{\eta }_{exp}}={\left\{{\displaystyle \sum _{i=1}^{N_{exp}}\frac{{\left({\eta }_{exp,i}-{\overline{\eta }}_{exp,i}\right)}^2}{N-1}}\right\}}^{1/2}$$

(9)

and the mean value of the resulting experimental uncertainty was defined by:

$$S_{{\overline{\eta }}_{\exp }}=\frac{S_{{\eta }_{\exp }}}{\sqrt{N_{\exp }}}$$

(10)

Estimations of the experimental uncertainty for $I_0$ = 830 and $I_0$ = 1100 W/m² with three air mass flow rates were calculated. The mean experimental uncertainty of the measurements in Figure 7 and Figure 8 ranged between 2.60 × 10⁻³ ≤ $S_{{\overline{\eta }}_{\exp }}$ ≤ 7.46 × 10⁻³. Meanwhile, the difference of the experimental results from the theoretical predictions may be defined as:

$$E=\frac{1}{N_{\exp }}{\displaystyle \sum _{i=1}^{N_{\exp }}\frac{\left|{\eta }_{theo,i}-{\eta }_{\exp ,i}\right|}{{\eta }_{theo,i}}}\times 100\%$$

(11)

Difference deviations between the theoretical and experimental values were quantified and calculated using Equation (11) within 0.13 ≤ $E$ ≤ 2.85 under two solar radiation incidents for two configurations without (flat-plate type) and with attaching wire mesh. A fairly good agreement between theoretical predictions and experimental runs was achieved.

4. Collector Efficiency Improvement

By following the same mathematical treatment and experimental methods performed in our previous work [16], except welding the V-corrugated absorber instead of packing with wire mesh, the device performance improvements of the three types of recycling double-pass devices, namely flat-plate, wire mesh, and V-corrugated devices, were defined as the improvement of each collector’s efficiency, $I_D$, $I_W$ and $I_V$ , as defined by Equations (12)–(14), respectively, relative to that of the downward-type single-pass device of the same working dimensions, as follows:

$$I_D=\frac{\mathrm{collector}\mathrm{efficiency}\mathrm{of}\mathrm{flat}-\mathrm{plate}\mathrm{double}-\mathrm{pass}\mathrm{device},{\eta }_D}{\mathrm{collector}\mathrm{efficiency}\mathrm{of}\mathrm{downward}\sin \mathrm{gle}-\mathrm{pass}\mathrm{device},{\eta }_S}-1$$

(12)

$$I_W=\frac{\mathrm{collector}\mathrm{efficiency}\mathrm{of}\mathrm{wire}\mathrm{mesh}\mathrm{double}-\mathrm{pass}\mathrm{device},{\eta }_W}{\mathrm{collector}\mathrm{efficiency}\mathrm{of}\mathrm{downward}\sin \mathrm{gle}-\mathrm{pass}\mathrm{device},{\eta }_S}-1$$

(13)

$$I_V=\frac{\mathrm{collector}\mathrm{efficiency}\mathrm{of}\mathrm{double}-\mathrm{pass}\mathrm{V}-\mathrm{corrugated},{\eta }_V}{\mathrm{collector}\mathrm{efficiency}\mathrm{of}\mathrm{downward}\sin \mathrm{gle}-\mathrm{pass}\mathrm{device},{\eta }_S}-1$$

(14)

in which ${\eta }_D$, ${\eta }_W$, ${\eta }_S$ and ${\eta }_V$ denote collector efficiencies of the double-pass flat-plate device, multi-pass flat-plate device, the baffled device with fins attached, the downward-type single-pass device, and the V-corrugated device, respectively. The present work is actually the extension of previous work [16], except with welding of the V-corrugated absorber. The collector efficiencies of ${\eta }_D$, ${\eta }_W$ and ${\eta }_S$ were investigated in our previous work [16] and the collector efficiency improvements of $I_D$, $I_W$ and $I_V$ for the devices of the flat-plate, wire mesh, and V-corrugated absorbers were calculated in Equations (12)–(14), respectively, for comparison.

5. Results and Discussion

The calculation methods and procedures were performed exactly the same as those of our previous work [16], and thus, the results will be discussed. All the theoretical predictions and experimental results of ${\eta }_D$, ${\eta }_W$ and ${\eta }_V$ increase with the recycle ratio and incident solar radiations, as seen from Figure 7 and Figure 8.

It is indicated from Figure 7 and Figure 8 that the collector efficiency of the V-corrugated solar air collector is higher than those of the flat-plate and wire mesh devices. The collector efficiency increase with recycle ratio and air mass flow rate, especially for the V-corrugated device when operating at the higher recycle ratio, as confirmed by

Table 1. Theoretical predictions of heat-transfer efficiency improvements in a V-corrugated device of ${\eta }_V$ and $I_V$ for $I_0$ = 830 W/m² and $I_0$ = 1100 W/m².

Mass Flow Rate	Recycle Ratio	I0 = 830 (W/m2)		I0 = 1100 (W/m2)
m (kg/h)	R	${\mathit{\eta }}_{\mathit{V}}$	${\mathit{I}}_{\mathit{V}}(\%)$	${\mathit{\eta }}_{\mathit{V}}$	${\mathit{I}}_{\mathit{V}}(\%)$
38.52	0.25	0.487	57.60	0.510	69.51
	0.5	0.511	65.52	0.535	77.85
	0.75	0.538	73.99	0.563	86.88
	1	0.565	82.89	0.592	96.58
	1.25	0.593	91.86	0.623	106.87
	1.5	0.608	96.79	0.655	117.45
	1.75	0.618	99.97	0.685	127.48
	2	0.632	104.58	0.704	134.01
57.96	0.25	0.503	35.98	0.530	45.62
	0.5	0.526	42.07	0.553	52.01
	0.75	0.565	52.76	0.578	58.86
	1	0.597	61.34	0.622	70.99
	1.25	0.630	70.32	0.658	80.84
	1.5	0.663	79.15	0.697	91.55
	1.75	0.676	82.65	0.744	104.32
	2	0.688	85.97	0.766	110.40
77.04	0.25	0.508	21.94	0.508	29.34
	0.5	0.536	28.46	0.536	36.06
	0.75	0.580	39.11	0.580	43.41
	1	0.614	47.29	0.614	55.44
	1.25	0.651	56.04	0.651	64.83
	1.5	0.688	65.03	0.688	75.58
	1.75	0.703	68.68	0.703	85.69
	2	0.715	71.41	0.715	92.99

. Restated, the collector efficiency ${\eta }_V$ increases with increasing recycle ratios and air mass flow rates due to a higher convective heat-transfer coefficient being achieved. Furthermore, Figure 9 gives a graphical representation of the collector performance improvements of $I_D$, $I_W$, and $I_V$ for the flat-plate, wire mesh packed, and V-corrugated double-pass devices under the same operating conditions, respectively. The collector performance improvement decreases with the air mass flow rate to a more remarkable extent, while the improvement increases with the recycle ratio, as shown in Figure 9 and Table 1 as well. However, the collector efficiency improvement of the V-corrugated solar air collector is better than other recycling configurations such as flat-plate and wire mesh packed solar air collectors for all mass flow rates and recycle ratios. Moreover, the hydraulic dissipated energy and power consumption increases owing to recycling double-pass operation with the V-corrugated absorber are defined as:

$$P_V=\dot{m}(1+R)\ell w_{f,a}+\dot{m}\ell w_{f,b}=\dot{m}(1+R)\frac{2f_{F,a}{\overline{v}}^{2}L}{D_{e,a}}+\dot{m}\frac{2f_{F,b}{\overline{v}}^{2}L}{D_{e,b}},$$

(15)

double-pass V-corrugated device.

$$f_{F,i}=f+y\frac{W}{L},$$

(16)

for V-corrugated device [19], i = a, b.

$$f=\frac{24}{Re},y=0.9,\mathrm{for}Re<2550$$

(17)

$$f=0.0094,y=2.92{Re}^{-0.15},\mathrm{for}2550<Re<{10}^4$$

(18)

$$f=0.059{Re}^{-0.2},y=0.73,\mathrm{for}{10}^4<Re<{10}^5$$

(19)

The power consumption increase for the double-pass V-corrugated devices $I_{P,V}$ is defined relative to that in the downward single-pass operation $P_S=\dot{m}\ell w_{f,s}=\frac{2f_{F,S}{\overline{v}}^{2}L}{D_{e,S}}$ as:

$$I_{P,V}=\frac{P_V-P_S}{P_S},$$

(20)

the V-corrugated device.

Similarly, for the flat-plate device and wire mesh packed device:

$$I_{P,D}=\frac{P_D-P_S}{P_S},$$

(21)

the flat-plate device.

$$I_{P,W}=\frac{P_W-P_S}{P_S},$$

(22)

the wire mesh packed device.

The effects of various recycle ratios and air mass flow rates on the ratio of both the efficiency improvement and the power consumption, $I_D/I_{P,D}$, $I_W/I_{P,W}$ and $I_V/I_{P,V}$ for various configurations were calculated and presented for comparison and for making an economic judgement to demonstrate feasible operating conditions. The higher value of $I_V/I_{P,V}$ is obtained in operating recycling double-pass V-corrugated solar air collectors, as demonstrated in Figure 10. The extent of collector efficiency improvement is more notable with recycle ratio for the recycling double-pass V-corrugated solar air collectors than for the flat-plate and wire mesh packed devices. With this comparison, the advantage of the present design is evident.

6. Conclusions

The strategies for improving the performance of recycling double-pass V-corrugated solar air collectors are either the preheating effect or enhancing the convective heat-transfer coefficient. The improvement of collector efficiency in such devices with welding of the V-corrugated absorber has been investigated analytically and experimentally. The introduction of external recycling creates a positive effect on the heat transfer, which provides better collector efficiency due to the enhanced convective heat-transfer coefficient. This is caused by an increase in the turbulence of air flowing above and under the V-corrugated absorber. The improvement in device performance is obtainable by using a recycling double-pass V-corrugated device rather than without recycling or by using flat-plate devices, as indicated in Figure 7 and Figure 8. Moreover, the ratio of $I_V/I_P$ , alongside recycle ratio and air mass flow rate, were represented in Figure 10 to investigate the optimal operation conditions for considering the economic feasibility of various double-pass configurations. The present findings can be summarized as follows: (1) Application of the recycling double-pass V-corrugated solar air collector is technically and economically feasible as compared to both of the flat-plate and wire mesh packed solar air collectors; (2) Collector performance increases with increasing the recycle ratio but with decreasing the air mass flow rate, and with the inlet air flowing through the lower channel first (flow pattern A), device performance is higher than that in the device with the inlet air flowing through the upper channel first (flow pattern B); (3) The optimal recycle ratio for both economic and technical operation, with relatively small compensation for increased hydraulic dissipated energy, was found to be R ≈ 0.5; (4) The advantage of the present device is evident, and the present study provides an important contribution to solar air collectors by coupling external recycling and different geometric designs of absorbing plates.