Effect of gap thickness on a rectangular-cell compound-honeycomb solar collector

P e r g a m o n PII: S 0038 -092X ( 96 ) 00153-3

Solar Energy Vol. 60, No. 5, pp. 271-280, 1997 © 1997 Elsevier Science Ltd

All rights reserved. Printed in Great Britain 0038-092X/97 $17.00 + 0.00

E F F E C T O F G A P T H I C K N E S S O N A R E C T A N G U L A R - C E L L

C O M P O U N D - H O N E Y C O M B S O L A R C O L L E C T O R

H. Z. A B O U - Z I Y A N * and R. F. R I C H A R D S **.t • Department of Mechanical Power Engineering, Helwan University, Cairo 11718, Egypt and • * School of Mechanical and Materials Engineering, Washington State University, Pullman,

WA 99164-2920, U.S.A. ([email protected])

(Received 6 September 1995; revised version accepted 30 November 1996) (Communicated by BRIAN NORTON)

Abstract--Compound-honeycomb solar collectors employ a honeycomb to suppress natural convection and air gaps between the honeycomb and the absorber plate or the glazing to reduce conductive and radiative heat losses. Results of an experimental study on the effect of the thickness of these gaps on the total heat transfer across a compound honeycomb confined between two isothermal and low emissivity boundaries are presented. The honeycomb consists of rectangular cells with elevation aspect ratio 6.3 and plan aspect ratio 82 (15.8 mm thick, 206 mm wide and 2.5 mm deep), constructed from parallel glass strips. Plots of Nusselt number versus Rayleigh number are given for compound honeycombs with air gaps of thickness 1.6 mm, 3.3 nun, 6.4 mm and 9.6 mm above and below the honeycomb and for a compound-honeycomb layer with an air gap of thickness 6.4 mm below the honeycomb. Measurements are reported for tilt angles of 0 °, 30 ° and 60 ° where the long dimension of the rectangular cells in the honeycomb is horizontal. As the air gaps' thickness increase, coupled conductive-radiative heat transfer is reduced, while the critical Rayleigh number is also reduced and convective heat transfer increases. However, even for relatively thick air gaps, the decrease in critical Rayleigh number is moderate, and the rectangular-cell compound honeycomb is found to be an effective convection suppressor. A compound honeycomb with air gaps above and below the honeycomb is shown to be superior in suppressing convection to a compound honeycomb of equal total thickness with only one air gap below the honeycomb. © 1997 Elsevier Science Ltd.

1. INTRODUCTION

The use o f honeycombs to reduce hea t losses f rom f la t -plate solar col lec tors has been extens- ively studied. F r anc i a (1964) first p r o p o s e d the use o f very high aspect ra t io cyl indr ical honeycombs m a d e o f glass and ca rbon ized pape r to suppress rad ia t ive losses f rom a solar col lector . Ho l l ands (1965) in t roduced the idea o f selec- t ively t r ansmi t t ing honeycombs o f m o d e r a t e aspect ra t io to be used to suppress convect ive heat losses. As ear ly as 1971, Buchberg et al. (1971) had demons t r a t ed the super ior performance o f a solar col lec tor employ ing a selec- t ively reflecting rec tangular-cel l honeycomb.

The i m p o r t a n t design pa rame te r s for the par - t icular case o f rec tangular-cel l convec t ion suppressors have been exp lored in b o t h theore t ica l and exper imenta l studies. Edwards (1969) ana- lyzed the effect o f la tera l walls o f finite conduc- t ivi ty on convec t ion suppress ion. C a t t o n (1972) ex tended the analysis and showed the s t rong effect h o n e y c o m b wall conduc t iv i ty has on convect ion suppress ion. In par t icu la r , C a t t o n showed tha t as the h o n e y c o m b wall admi t t ance C = k f L / k t (where kf and k are the fluid and

tAuthor to whom all correspondence should be addressed.

h o n e y c o m b wall conduct iv i ty , respectively) increased, the cri t ical Rayle igh number for rec- t angu la r cells cou ld increase 20-fold. Edwards and Sun (1970) de mons t r a t e d tha t wall rad ia- t ion could act to increase the cri t ical Rayle igh number o f a rectangular-cel l honeycomb in the same way as wall conduct ion . They showed tha t the effect o f wall r ad i a t i on could be accounted for with an effective wall conduct iv i ty which was a funct ion o f wall emissivity, and which was greater than the ac tua l wall conduct iv i ty .

H o l l a n d s (1973) measu red the onset o f in- s tabi l i ty and convect ive hea t t ransfer across hor izonta l , air-fil led, square-cel l honeycombs fabr ica ted f rom polye thylene film, with aspect ra t ios in the range 0.8 < LID < 4.0. Hea t t ransfer measurements were made using a guard hea ted ca lor imeter , in an a p p a r a t u s in which the fluid Ray le igh n u m b e r could be con t ro l l ed by vary ing the a i r pressure. Cane et aL (1971) extended this w o r k by cons ider ing bo th square-cel l and hexagonal-ce l l hone yc ombs or iented at tilt angles f rom 0 ° (hea ted f rom below) to 90 ° (hea ted f rom the side).

A r n o l d et al. (1976) m a d e measurements o f hea t t ransfer across l iquid-fi l led rectangular-cel l honeycombs with e levat ion aspect ra t ios in the

271

272 H.Z. Abou-Ziyan and R. F. Richards

range O.08<L/D<I, at tilt angles from 0=0 (heated from below) to 0=180 (heated from above). Arnold et al. (1977) extended the previous work by considering the effect of the rectangular cells' plan aspect ratio, W/D. They found that heat transfer does not change for cells with W/D>4; that is, cells with W/D>4 can be considered essentially infinite. Smart et al. (1980) made heat transfer measurements across rectangular-cell honeycombs with elevation aspect ratios in the range 3<L/D<IO, at tilt angles from 0 = 0 (heated from below) to 0 = 90 (heated from the side).

Recently, Hollands and Iynkaran (1985) pointed out a significant drawback to the use of honeycombs as convection suppressors in solar collectors. They showed that honeycomb devices may significantly increase coupled conductive-radiative heat losses from a collector, if the collector employs a selective surface absorber. The increased losses arise from heat conducted from the low emissivity absorber surface to the relatively higher emissivity honeycomb where it can be radiated to the collector glazing.

Hollands and Iynkaran suggested two solu- tions to this problem. First, radiative losses from a honeycomb can be minimized by either decreasing the honeycomb's emissivity to near zero, or increasing its emissivity to near unity. The selection of materials suitable to the harsh conditions inside a fiat-plate solar collector makes this option difficult. A second solution to the problem, put forth by Hollands and Iynkaran and by Linthorst (1985) simulta- neously, is to reduce the conduction coupling between the absorber and the honeycomb by leaving an air gap between the two. Hollands and Iynkaran dubbed the honeycomb with air gap a compound-honeycomb layer.

Hollands et al. (1992) subsequently presented heat transfer and solar transmittance measurements across a square-cell compound-honeycomb layer fabricated of FEP (fluorinated ethylene propylene) film, along with predictions of the performance of a solar collector employing the compound honeycomb.

An analytic model to predict coupled conductive-radiative heat transfer across a compound- honeycomb layer was developed by Hollands and Iynkaran (1993) building on earlier work of Hollands et al. (1984). The model showed a significant decrease in coupled heat transfer across the compound-honeycomb layer in comparison with a similar honeycomb. This

decrease in heat transfer was confirmed in a series of heat transfer measurements made on compound-honeycomb layers with aspect ratios in the range 2<L/D< 10.

However, while reducing coupled conductive-radiative heat losses, leaving an air gap between the honeycomb and the absorber runs the risk of reducing the honeycomb's ability to suppress convection. Hollands and Iynkaran (1985) considered this problem for a hexagonal honeycomb. Heat transfer measurements were made on a hexagonal plastic honeycomb with L/D=3.2 in an enclosure tilted at 0=45 ° from horizontal. The compound honeycomb had an air gap of thickness 6b=10mm introduced below a honeycomb of thickness L=33.7 mm (6b/L = 0.30). No significant increase in convective heat transfer was found over the case of the honeycomb with no air gap. In an earlier work, Edwards et al. (1976) studied the effect of the thickness of small air gaps on convective heat transfer in a rectangular-cell honeycomb. They introduced gaps both above (between honeycomb and cold plate) and below (between honeycomb and hot plate) rectangular-cell honeycombs, made from varnished paperboard, with aspect ratios L/D=4.05 and W/D=8.59. An air gap below the honeycomb of thickness 6b=l .5mm (6b/L=0.08) and air gaps above the honeycomb of thicknesses fit = 1.5, 2.3, 3.0, and 4.6 mm (6t/L=0.08, 0.12, 0.16, 0.24) were tested. Runs were made at tilt angles of 0 °, 15 °, and 30 °. The smallest gaps (6b/L=t~t/L=O.08) had little effect on convective heat transfer, in comparison with the honeycomb without gaps. For the cases with air gaps both above and below the honeycomb, the convective heat transfer either changed very little (t~b/L = 6t/L = 0.08) or was reduced (6b/L = 0.08 and 6t/L=O.12, 0.16, 0.24) when compared to compound honeycombs with no gaps.

The question naturally arises as to what the optimum thickness and placement of air gaps in a compound-honeycomb convection suppressor would be, to minimize total heat losses from a fiat-plate collector. Figure 1 shows the geometry of the compound-honeycomb solar collector under consideration. The bottom and top air gap thicknesses are denoted by 6b and 6, while L, IV, and D give the thickness, width and depth of the honeycomb's rectangular cells, and 0 is the collector's tilt angle from horizontal. Nondimensionalizing the gap thicknesses by the honeycomb thickness gives the bottom gap

Effect of gap thickness on a solar collector 273

Fig. 1. Geometry of a rectangular-cell, compound-honeycomb solar collector.

ratio, •b/L, the top gap ratio, 6t/L, and the total gap ratio, (rb + 6t)/L.

Previous works clearly indicate the value of air gaps to reduce heat losses in compound- honeycomb solar collectors, but do not give sufficient information for the designer to optimize the thickness or placement of the air gaps. The present work addresses this issue by investi- gating the effect on heat transfer, of gap thicknesses above and below a compound honeycomb. To this end, heat transfer measurements have been made across a rectangular-cell compound-honeycomb convection suppressor with a wide range of gap thicknesses above and below the honeycomb, and at various tilt angles.

2. EXPERIMENT

Heat transfer across each compound-honeycomb layer was measured using the apparatus described by Richards (1994). Shown in Fig. 2, the apparatus consists of an electrically heated aluminium hot plate and a water cooled brass cold plate, each 450 x 220 mm. A particular

Fig. 2. Cross-section of the experimental apparatus showing: (1) cooling water manifold, (2) brass cold plate, (3) cork sheet, (4) copper face sheet, (5) calorimeter, (6) aluminium hot plate, (7) support arms, (8) rectangular-cell honeycomb,

(9) air gaps and (10) phenolic spacers.

compound-honeycomb layer is inserted between the hot and cold plates, and heat transfer across the layer is determined from a calorimeter bolted into a pocket in the aluminium hot plate.

The calorimeter is constructed as a sandwich of a brass back plate, a cork inner layer, an inconel foil resistance heater and a copper face plate. An eight junction thermopile is strung across the cork inner layer between the copper face plate and the brass back plate. The electrical current to the foil resistance heater is controlled in such a way as to null the signal from the thermopile. When the thermocouple voltage is nulled, the copper face plate and brass back plate are at the same temperature, and all power dissipated as heat in the resistance heater is known to be transferred out the front of the copper face sheet. Measurement of the current and voltage drop across the resistance heater gives a direct measure of heat flux from the hot plate.

The cold plate is also constructed as a sandwich of a brass back plate, a cork inner layer, and a copper face plate, with a four junction thermopile strung between the brass back plate and the copper face plate. The cold plate is able to function as a back-up heat flux meter, though during the present work it was not used in any of the heat transfer measurements. To maintain known radiative boundary conditions, the copper face plates for both the calorimeter and the cold plate are kept highly polished, and have emissivities of 6 t = C b =0.04.

The entire apparatus can be inserted into a cylindrical pressure vessel, with the long dimension of the hot and cold plates aligned with the axis of the cylindrical vessel. The pressure vessel can be evacuated down to 1 Torr or pressurized up to 3000 Torr absolute. The pressure vessel is supported on four wheels, allowing it to be rotated about its axis so that the apparatus inside can be oriented at any tilt angle about the long axis of the hot and cold plates. In the present work when the hot plate is situated below the cold plate, lying in a plane perpendic- ular to the gravity vector (horizontal), the tilt angle is taken to be 0 °.

A particular compound-honeycomb layer configuration is assembled by stacking up from the aluminium hot plate: first, phenolic spacers for the hot side (bottom) air gap; second, the rectangular-cell honeycomb, made up of an array of glass slats held in a phenolic frame; and third, phenolic spacers for the cold side (top) air gap. The brass cold plate completes


the stack. The entire apparatus, including the compound-honeycomb layer, is then fastened tightly together by four bolts which pass through holes in the ends of the hot and cold plates, and the spacers and slat frame. Aluminized Mylar taped around the edges of the apparatus completely encloses the compound-honeycomb layer.

The rectangular-cell honeycomb consists of an array of soda-lime glass slats, each 215 mm in length, 15.8 mm wide and 0.53 mm thick, held in place by a phenolic frame. The frame is made of four 16.3 x 9.4 mm rectangular cross- section phenolic bars glued together to form a 440 x 220 mm rectangle. A fifth bar spans the frame between the two long sides of the rectangle to divide it into two 220 mm squares. Slots cut in the short (220 mm) sides and the cross bar of the phenolic frame, spaced 3.04 mm apart, hold the glass slats. With a glass slat in each slot of the frame, rectangular cells with an elevation aspect ratio of L / D = 6 . 3 , and a plan aspect ratio of W / D = 82, are created, with the long dimension of the rectangular cells, W, parallel to the long dimension of the phenolic frame.

The thicknesses of the air gaps on either side of the rectangular-cell honeycomb, in the compound-honeycomb layer, were determined by sets of phenolic spacers milled to nominal thicknesses of 1.6, 3.2, 6.4 and 9.5 mm. To verify the air gap thicknesses created by these spacers, the total thickness of each compound-honeycomb layer was measured using a micrometer depth gauge inserted through holes in the hot plate. Subtracting the known thickness of the honeycomb (the glass slat width or 15.8 mm) from the measured total thicknesses of each compound-honeycomb layer gave the air-gap thicknesses. For the compound-honeycomb layers with equal air gaps above and below the honeycomb the air gaps were measured to be 6b = 6t = 1.6, 3.3, 6.4, and 9.5 ram, giving air gap ratios of 6b/L = 6 t /L = 0.10, 0.21, 0.40, and 0.60. For the compound honeycomb with an air gap below the honeycomb, but no air gap above the honeycomb, the air gap was measured to be 6b=6.5mm, giving an air gap ratio of fib/L=0.41. For the case in which no phenolic spacers were used, the small difference between the glass slat width (15.8 mm) and the phenolic frame thickness (16.3mm) meant that very small air gaps of thickness c~b=c~t=0.013 mm resulted, giving air gap ratios of6b/L= 6t /L = 0.01.

For each given compound-honeycomb layer, heat transfer measurements were made under steady state conditions, over a range of Rayleigh numbers. Here Rayleigh number is defined as:

g ArL R a = - - (1)

where g is gravitational acceleration, /~ is the volume coefficient of expansion for air, AT is the temperature difference between the hot and cold plates and v and e are the kinematic viscosity and thermal diffusivity of air, each evaluated at the average of the hot and cold plate temperatures. The length scale, Lt, is the total thickness of the compound-honeycomb layer, which is equal to the sum of the honeycomb thickness and the bottom and top air gap thicknesses:

Lt =L+6b +6t. (2)

Rayleigh number for the compound-honeycomb layer was controlled by varying air pressure in the pressure vessel, while the hot and cold plate temperatures were held constant.

Below a critical Rayleigh number the air in the compound-honeycomb layer is quiescent and heat transfer across the layer is by radiation and conduction only. Above the critical Rayleigh number cellular convection is present. To differentiate between heat transfer caused by cellular convection and heat transfer resulting from coupled conduction-radiation, both a subcritical Nusselt number and a supercritical Nusselt number are defined.

First, to quantify conduction and radiation across the compound slat layer, heat transfer measurements made at Rayleigh numbers below the critical Rayleigh number are also presented in terms of a subcritical Nusselt number:

qoLt Nuo - (3)

k f A T

where qo is the measured heat flux across a quiescent compound-honeycomb layer, kf is the conductivity of air, evaluated at the mean temperature in the compound-honeycomb layer, and AT is the temperature difference between the hot and cold plates. The subcritical Nusselt number gives the ratio of heat transfer across a quiescent compound-honeycomb layer to the heat transfer across an equivalent quiescent plane air layer. As a result, the subcritical Nusselt number represents the augmentation of conduction and radiation heat transfer due to


the presence of the compound-honeycomb layer.

To quantify the effect of cellular convection, a supercritical Nusselt number is defined to be:

( q - qo)Lt Nu~ = l + (4)

k fAT

where q is the measured heat flux across the compound-honeycomb layer, and q0, kf, and AT are the same as in the definition of Nuo. The supercritical Nusselt is unity below the critical Rayleigh number. Above the critical Rayleigh number, the supercritical Nusselt is proportional to the augmentation of heat transfer across the compound-honeycomb layer caused by natural convection.

Uncertainty in measured Nusselt numbers, which was a function of the uncertainty in the measurement of electrical power to the calorimeter, the uncertainty in the thermal conductivity of air, the uncertainty in the total gap thickness, and back losses from the calorimeter, was estimated to be __+ 3%. The uncertainty in Rayleigh number, resulting from the uncertainty in total gap thickness, mean gap temperature, gap temperature difference, air pressure, and uncertainty in the kinematic viscosity and thermal diffusivity of air, was estimated to be __+ 3%.

3. RESULTS AND DISCUSSION

Subcritical Nusselt numbers measured for the compound-honeycomb layers are shown plotted in Fig. 3 versus the total air gap thickness ratio, (6b+6t)/L. The relatively high conductivity (k=0.8 W m -1 K - l ) , high emissivity ( e~ 1.0) glass slats significantly increase heat transfer across the compound-honeycomb layer over what would be expected for an air layer. However, as expected, increasing the thickness of the air gaps in the compound-honeycomb layer greatly reduces the heat transfer, although the returns diminish as the sum of the gap thicknesses approaches the honeycomb thickness, o r ( t ~ b J r ~t)/L approaches unity.

The ability of a compound-honeycomb layer to suppress convection in a horizontal ( 0=0 °) configuration can be judged by reference to Fig. 4. In the figure supercritical Nusselt number is plotted versus Rayleigh number. Open symbols represent experimental measurements, and lines represent predictions for limiting cases. Consider first the two limiting cases given in the figure: an air layer, and a rectangular-cell honeycomb. These two limiting cases give upper

o £ t - (1) e~

E

Z

09 09

z

. i - , . D t . . t o

09

5

4

3 o

O 2 o

1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0 i i i i i

0 . 0 0 2 0 . 4 0 6 0 .8 1 .0

T o t a l G a p - T h i c k n e s s Ra t i o , (8 b + ~t)/L

.2

Fig. 3. Measured subcritical Nusselt number versus total gap-thickness ratio, (rb + 6t)/L, for compound honeycombs with gap-thickness ratios 6b/L = 6t/L = 0.01, 0.10, 0.21, 0.40,

0.60, and 6b/L=0.40 , 6t/L=0.01.

4.5

Z 4 .0

(1)

.o 3 .5 E ..,1

Z = 3 .0

= 2.5 Z

o = 2 .0 , m 1_

Ol

1.0

o ~o/L = 8t/L = 0.60

[] &o/L = ~ /L = 0.40

zx 15b/L = cSt/L = 0.21

v adL = ~ /L = 0.10

O (Sb/L = (St/I. = 0.01

. . . . Honeycomb

~ -- Air Layer o

[ ]

B zx

~7 r7 o

A

A ~7

©

A

&[]

0.0 0 .5 1.0 1.5 2 .0 2 .5 3 .0

R a x 10 "s

Fig. 4. Measured supercritical Nusselt number versus Rayleigh number for horizontal compound honeycombs (tilt angle 0=0 °) w i th gap-thickness ratios

6b/L=6t/L=O.O1, 0.10, 0.21, 0.40 and 0.60.

and lower bounds on convective heat transfer in the compound honeycomb studied here. In the air layer, indicated with a solid line, natural convection starts at the well known critical Rayleigh number of Ra = 1.7 x 103. The Nusselt number subsequently rises rapidly. The second limiting case, a simple rectangular-cell, glass- walled honeycomb with elevation aspect ratio 6.4 and plan aspect ratio 82, is indicated with a dashed line. The critical Rayleigh number, Racr= 1.9 x l0 s, has been predicted following Catton (1972), and the increase in heat transfer


caused by convection predicted by the empirical correlation given by Smart et al. (1980).

Heat transfer measurements made with the rectangular-cell honeycomb in place and no spacers (fb/L = f t /Z = 0 . 0 1 ) are shown with open diamonds in Fig. 4. The data are seen to be in close agreement with the predicted heat transfer for the simple honeycomb. The onset of convection is delayed until Racr= 1.9 x 105, as predicted by Catton, and the slope of the data matches the correlation of Smart et al.

It is useful to point out here that the high critical Rayleigh number predicted and measured for the simple honeycomb constructed of glass slats is a consequence of the relatively high conductivity of the soda-lime glass. In comparison, Edwards and Sun report a measurement of critical Rayleigh number for a rectangular-cell honeycomb of dimensions L = 19 mm, D =4.69 mm, and W=40.3 mm (elevation aspect ratio L/D = 4.1 ) constructed of low conductivity varnished paperboard walls as R a c r = l . 7 x 103, while Smart, Hollands and Raithby give Racr = 6.52 x 1 0 4 for a rectangular- cell honeycomb of elevation aspect ratio L/D = 5, made of the intermediate conductivity poly- ethylene film.

Data for a honeycomb with air gaps above and below of widths fib = fit = 1.6 mm (fb/L = 6t/L = 0.10) are shown with downward- pointing triangles in Fig. 4. Introducing the air gaps is seen to have no effect on critical Rayleigh number (Ra¢r = 1.9 x 105). However, convective heat transfer appears to rise somewhat faster for the compound honeycomb with 1.6 mm air gaps than for the simple honeycomb without air gaps. These results are in partial agreement with the findings of Edwards et al., who found no difference in heat transfer between rectangular-cell honeycombs with air gaps of 1.5 mm (6b/L=ft /L=O.08) above and below, and simple honeycombs with no air gaps.

As the thickness of the air gaps above and below the rectangular-cell honeycomb is further increased, the critical Rayleigh numbers for the compound-honeycomb layers are seen to decrease, although the decrease in critical Rayleigh number is slower for larger air gap widths. For example, the compound honeycomb with 3.2 mm air gaps (6u/L = 6t/L = 0.21), indicated with upward-pointing triangles, has a critical Rayleigh number o fRa~ = 1.0 x 105. The compound honeycomb with larger air gaps with ~b = I~t = 6.4 mm (6b/L = 6t/L = 0.40), indicated with squares, has a smaller critical Rayleigh

number of Rac,= 8.0 x 104. The compound honeycomb with the largest air gaps with 6b = 6t = 9.6 mm (fb/L = 6t/L = 0.60), indicated with circles, also has a critical Rayleigh number of Rac,= 8.0 x 104. As gap thickness increases, and critical Rayleigh number decreases, convective heat transfer across the compound-honeycomb layers is augmented. The augmentation of convective heat transfer, like the reduction in critical Rayleigh number, is seen to change more slowly for larger gap thickness.

Increasing the thickness of air gaps in a compound-honeycomb layer reduces the ability of the compound-honeycomb layer to suppress convection. However, even if the compound honeycomb is less effective than the simple honeycomb in suppressing convection, the compound honeycomb is still much more effective in delaying the onset of convection than an air layer. The critical Rayleigh numbers measured for the rectangular-cell compound-honeycomb layers with air gap ratios of 6b/L=f t /L=0.21-0 .60 are 45 to 50 times greater than that for an air layer.

Figures 5 and 6 show measurements for compound-honeycomb layers inclined at tilt angles of 0 = 30 ° and 60 °, respectively. Data are given for compound-honeycomb layers with air gap thicknesses of ~b=f t=3 .2 , 6.4, and 9 .6mm (6b/L=ft /L=0.21, 0.40, and 0.60). In Fig. 5, where data is shown for tilt angle 0=30 °, a dashed line is used to indicate the maximum Nusselt number envelope for measurements

£ Z

0 ..Q E '-I

Z

=3 Z

0 . t -

O9

3.0

2.5

2.0

1.5

o 6b/L = 6t/L = 0.60

(Sb/L = 6 t /L = 0.40 /-

. . . . 6b/L = ~t/L = 0.21 o 0 / / /

/ / /

0 / 0 / / []

0 // 0 t /

/ /

0 / [ 3 / I

0 [] I / 1.0 - ~ .......... a . . . ~ . . . . . . . . . . . . . . . . . . ~ ............

. . . . i . . . . i . . . . j . . . . i . . . . J . . . .

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Ra x 10 .5

Fig. 5. Measured supercritical Nusselt number versus Rayleigh number for compound honeycombs, at tilt angle 0 = 30 °, with gap-thickness ratios 6b/L = 6t/L = 0.40 and 0.60 and the maximum Nusselt number envelope for

¢~b/L = 6t/L = 0.21.


3 .0

Z L. .

0~ 2.5 . , O

E Z

2.0 O 3

Z

O

:---- 1.5 i - .o (1,)

,,.,,

¢j')

o a d L = 6t /L = 0 . 6 0 o

[] 6b/L = 6 i lL = 0 . 4 0 o o O

6b/k = ,5t/L = 0.21oO []

o

[]

[]

0 [ ]

E3

1.o ,<, ,.?;:,: :..:..

0 . 0 0 .5 1 .0 1 .5 2 .0 2 . 5 3 .0

Ra x 10 "5

Fig. 6. Measured supercritical Nusselt number versus Rayleigh number for compound honeycombs, at tilt angle 0=60 °, with gap-thickness ratios 6b/L=ft/L=0.21, 0.40

and 0.60.

taken in the compound-honeycomb layer with gap thickness 6b = f t = 3.2 m m (fb/L = f t /

L=0.21) . The reason for the use of the maximum Nusselt number envelope instead of the actual data can be seen in Fig. 7.

In Fig. 7, the actual measurements for that case are indicated with triangles, along with a dashed line similar to that in Fig. 5, showing the maximum Nusselt number envelope. The data are similar to data for other cases, below a Rayleigh number of about R a = 2 . 2 x 105. In this range, the measured Nusselt numbers are

3.0

=~ ~, (Sb/L = ,St/L = 0.21 Z A ~" 2.5 ............. NUma x enve lope .,~JE-

- i A / _z _, 2 . 0

Z

• = 1 .5 .'-' /

Q,.

1 . 0 ............ A......,~ ............ z~ ' ~ b ~ ..................................... . . . . i . . . . i . . . . i . . . . i . . . . i . . . .

0.0 0.5 1.0 1.5 2.0 2.5 3.0

R a x 1 0 -5

Fig. 7. Measured supercritical Nusselt number versus Rayleigh number for a compound honeycomb, at tilt angle 0 = 30 °, with gap-thickness ratios 6b/L = 6t/L = 0.21, with the

maximum Nusselt number envelope indicated.

unity below the critical Rayleigh number of Racr= l .7 × 105, and then rise sharply. Aside from the expected uncertainty, the data lie in a narrow band. In contrast, above a Rayleigh number of Ra =2.2 x 105, the data no longer lie in a narrow band, but spread out in a cloud. For example, at a Rayleigh number of Ra = 2.5 × 105, Nusselt numbers were measured ranging from Nu= 1.85 to Numa x =2.50. To sim- plify Fig. 5, the envelope of maximum measured Nusselt numbers was chosen to represent the 6 b = f t = 3 . 2 mm ( fb /L=f t /L=0.21) case in the plot, rather than the data seen in Fig. 7.

The trends seen in horizontal compound- honeycomb layers are also seen in tilted compound-honeycomb layers. At each of the given tilt angles, the critical Rayleigh number of the compound-honeycomb layer decreases and the convective heat transfer increases, as the air gap thickness increases.

Trends in the measurements for compound- honeycomb layers with a given air gap thickness at different tilt angles can be seen by comparing Figs 4-6. For the compound-honeycomb layer with the smallest air gaps, f b = f t = 3 . 2 m m (fb/L = f t /L = 0.21), critical Rayleigh number increases and convective heat transfer decreases monotonically as tilt angle increases from 0 ° to 30 ° to 60 ° . This result is in qualitative agreement with Edwards et al. (1976), who found that the convective heat transfer from a rectangular-cell compound honeycomb with 3.0 mm air gaps above and below consistently decreased as tilt angle increased from 0 ° to 15 ° to 30 °. In contrast, for the compound honeycomb with the larger air gaps of f ib=f t=6 .4 mm (fb/L = f t /Z = 0.40) and fb = f t = 9.6 m m ( fb /L=f t /L=0.60) , convective heat transfer first decreases as tilt angle goes from 0 ° to 30 °, and then increases at tilt angle goes from 30 ° to 60 ° . Likewise, for the compound honeycomb with air gaps of thickness 6 b = f t = 6 . 4 m m (6b/L=ft/L=0.40), critical Rayleigh number first increases as tilt angle goes from 0 ° to 30 °, and then decreases as tilt angle goes from 30 ° to 60 ° . For the case with f b = f t = 9 . 6 m m (t~b/L =bt/L = 0 . 6 0 ) , critical Rayleigh number decreases monotonically as tilt angle increases.

The effect of the position of the air gaps is illustrated in Fig. 8. In the figure, Nusselt number measurements are given for two compound-honeycomb layers with air gaps in different arrangements, made at tilt angles of 0 °, 30 ° and 60 °. The open symbols indicate measurements made on a compound-honey-


4 . 5

z 4.0 L .

0 )

-~ 3.5 "1

z ~ 3.0 (11 CO

~ 2.5

= 2.0

a. 1.5

1.0

• 8 = 0 °, 8b/L= 0.41,St/L = 0.01

• O = 30 °, 8b/L = 0.41, ~St/L = 0.01

• e = 60 °, 8b/L = 0.41, 5t/L = 0.01 O

o e = 0 °, 8b/L = 8t/L = 0.21

. . . . 0 = 30 °, 5b/L = 8t/L = 0.21 •

z~ 0 = 60 °, 5b/L = 8t/L = 0.21 o l

0 i i I I • • /I

I/ ~0 0 • ii

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Ra x 10 -5

Fig. 8. Measured supercritical Nusselt number versus Rayleigh number for a compound honeycomb with gap- thickness ratios 6b/L = fit/L = 0.21, and a compound honeycomb with gap-thickness ratios 6b/L=0.41, fit/L=0.01, at

tilt angles 0 = 0 °, 30 ° and 60 °.

comb layer with air gaps o f equal thickness above and below the honeycomb: ~b=CSt=3.2 m m ( f b / L = 6 t / L = 0 . 2 1 ) . The solid symbols indicate measurements made on a compound -honeycomb layer with an air gap below the honeycomb but no air gap above the honeycomb: 6 b = 6 . 4 m m and 6t=0.01 m m (6b/L =0.41 and 6t /L=O.O1) . The total air gap thickness is equivalent in bo th cases: 6b + 6t = 6.4 m m [(5b + 6t) /L = 0.41]. In addition, the coupled conduct ive-radia t ive heat transfer, as indicated by the measured values o f subcritical Nusselt number shown in Fig. 3, are also equal in bo th cases.

Figure 8 shows that the c o m p o u n d honeycomb with air gaps above and below the honeycomb is superior to the c o m p o u n d honeycomb with only one air gap below the honeycomb in suppressing the onset o f cellular convection, at all tilt angles. However, once the instability has set in, the rise in Nusselt number appears to be more rapid for the c o m p o u n d honeycomb with gaps above and below the honeycomb, than for the c o m p o u n d honeycomb with only one gap below the honeycomb. The result is that total heat transfer is less for the c o m p o u n d honeycomb with air gaps above and below than for the c o m p o u n d honeycomb with a single air gap below until relatively high Rayleigh numbers a round R a = 2 . 0 x l0 s.

The heat transfer measurements given in Figs 4 -8 can be used to optimize the design for a rectangular-cell c o m p o u n d - h o n e y c o m b solar

collector. Figures 9 and 10 illustrate how the opt imizat ion could be accomplished. The two figures show design curves for a solar collector with c o m p o u n d - h o n e y c o m b convect ion suppressors o f various air gap thickness ratios, when the collector is operated with an absorber

4.0 " 7 3(

~, 3.5 E ~ . 3.0

e -

"E 2.5 ._m O

:= 2.0

8 ~ 1.5

1.o

• .r 0 .5 O

0.0

"~i \ ' , ........ \ - - - _ . . . . 1 \ ' X ....... \

\ ~ . ...... \ ~ .... / \ /

. . . . A i r Layer "~'--. . . " - . z ~ ~ - /

. . . . . . H o n e y c o m b " ~ - , / /

8b/L = Bt/L = 0.60 ~ /

. . . . . 5b/L = 5t/L = 0 .40

..... 5b/L = 5t/L = 0.21

- - - - - 5b/L = 8t/L = 0.10 . . . . i . . . . i . . . . i . . . . i . . . .

0 10 20 3O 40 50

Tota l G a p Th ickness , L t (mm)

Fig. 9. Top heat loss coefficients for horizontal solar collectors (tilt angle 0=0 °) employing compound honeycombs with gap-thickness ratios 6b/L = filL = 0.10, 0.21, 0.40, 0.60, operating with absorber plate temperature Tp=50°C, at ambient temperature Ta=25°C and total gap temperature difference AT=25°C, plotted against total gap thickness, L t. Also shown are top heat loss coefficients for a solar collector without a convection suppressor and for a solar

collector with a honeycomb convection suppressor.

4.0 "7 v ~, 3 .5

E

~ . . 3 . 0 ..¢

• " 2 .5 C 0 )

2.0 0

o 1.5 ¢ 0 o f )

o, 1.0

-I- 0.5 C t .

19- 0.0

ii \\~ 0 = 300

/! ~\\ \ / \ ~ / - ~ t _ \

. . . . A i r Laye r . . . . . - - -~:

6

. . . . . 5b/L = ~ / L = 0.40 O = 60 °

............... 5b/L = 5t/L = 0.21

. . . . i . . . . i . . . . i . . . . i . . . .

0 10 20 30 40 50

Tota l G a p Th ickness , L t (mm)

Fig. 10. Top heat loss coefficients for solar collectors at tilt angles 0= 30 ° and 60 °', employing compound honeycombs with gap-thickness ratios 6JL = 6t/L = 0.21, 0.40, 0.60, operating with absorber plate temperature Tp = 50°C, at ambient temperature T= = 25°C and total gap temperature difference AT=25°C, plotted against total gap thickness, Lt. Also shown are top heat loss coefficients for a solar collector

without a convection suppressor.


plate temperature of Tp=50°C. The ambient temperature is Ta = 25°C, and the gap temperature difference is AT= 25°C. The figures were produced by first fitting polynomial expressions to the supercritical Nusselt number versus Rayleigh number data given in Figs 4-6. The resultant expressions, along with the subcritical Nusselt number measurements given in Fig. 3, were then used to find the total heat transfer across a given compound-honeycomb layer as a function of the layer's total thickness.

In Figs 9 and 10, the top heat loss coefficient for the solar collector, h, is plotted against the collector's total gap thickness, L t. Figure 9 gives the top heat loss coefficient for horizontal solar collectors ( 0 = 0 °) with bottom and top air gaps of equal thickness, 6b/L = 6t/L = 0.10, 0.21, 0.40, 0.60. Also given for comparison in Fig. 9 are the heat loss coefficients for a solar collector with no convection suppressor, and for a collector with a honeycomb convection suppressor. Figure 10 gives the top heat loss coefficient for solar collectors inclined at tilt angles 0= 30 ° and 60 ° , with bottom and top air gaps of equal thickness 6b/L=6t/L=0.21, 0.40, 0.60. Also given in Fig. 10 are the heat loss coefficients for a solar collector with no convection suppression.

Figure 9 shows that the top heat loss coefficient for a horizontal solar collector ( 0=0 °) could be minimized for the given operating conditions by employing a compound honeycomb with 6b/L=6t/L=0.60 and L t=35 mm. However, Fig. 10 shows that if the collector were intended to be operated under the same conditions, but at a tilt angle of 0 = 30 ° or 60 °, the top heat loss coefficient would be minimized with the smaller air gap ratios of 6b/L = ~t/Z = 0.40. In both cases, the reduction in top heat losses over a solar collector with no convection suppression is significant.

Several qualifications must be placed on these results. First and foremost, the experimental measurements on which Figs 9 and 10 are based were made on compound-honeycomb layers confined between two low emissivity plates. This set of radiative boundary conditions would be unusual for a flat-plate solar collector. More usual would be either two high emissivity boundaries (flat black absorber plate and glass cover) or a low emissivity hot boundary and a high emissivity cold boundary (selective surface absorber plate and glass cover). Second, the present study did not include measurements in

compound honeycombs with air gap ratios greater than ¢$b/L = 6t/L = 0.60. Consequently, it is an open question whether larger air gaps would have resulted in even lower top heat loss coefficients for the case of the horizontal collector (0 = 0 °) under these conditions. Finally, the absorber plate and ambient temperatures, Tp and Ta, normally vary during the operation of a solar collector. A true optimization of a compound-honeycomb collector would require minimizing the top heat loss coefficient not just at one set of temperatures, but over the entire range of expected operating temperatures. For some operating temperatures, total gap thicknesses of greater than 50 mm might be called for, which would necessitate extending Figs 9 and 10 to larger values of L t.

4. CONCLUSIONS

The effects of air gap thickness on a rectangular-cell compound-honeycomb layer are two- fold. First, air gaps act to break the conductive path from the absorber plate to the honeycomb and from the honeycomb to the collector glazing, and so reduce the coupled conductive-radiative heat losses. As a consequence, increasing the air gap thickness causes the conductive-radiative transfer to decrease, although with diminishing returns as the sum of the gap thicknesses approaches the honeycomb thickness. Second, air gaps also reduce the ability of the compound honeycomb to suppress convection. For the smallest gap ratio tested, 6b/L=~t/L=O.lO, the increase in convective heat transfer is minimal. As gap thickness grows, the increase in convection in the compound honeycomb grows. However, the relative decrease in critical Rayleigh number and increase in convective heat transfer diminishes for the larger gap thicknesses. For a horizontal compound-honeycomb layer with air gap ratios of ~b/L=6I/L=0.21-0.60 the critical Rayleigh number is reduced between a factor of 2 to 3, from the case of a simple honeycomb with no air gaps. However, even with this reduction the compound-honeycomb layer remains an effective convection suppressor. Critical Rayleigh numbers for these rectangular-cell compound honeycombs are still 45 to 50 times greater than the critical Rayleigh number for a horizontal air layer. Reductions in the critical Rayleigh numbers for compound-honeycomb layers at tilt angles of 30 ° and 60 ° are somewhat greater.


The dis t r ibut ion of air gaps in a compound- honeycomb layer affects its ability to reduce heat losses. A c o m p o u n d honeycomb with air gaps above and below the honeycomb has been shown to be more effective at suppressing convection than a c o m p o u n d honeycomb with only a single air gap below the honeycomb.

The opt imizat ion of a rectangular-cell , com- p o u n d - h o n e y c o m b solar collector with air gaps of equal thickness above and below has been demonst ra ted for a single set of operat ing temperatures. In the case of a hor izontal solar collector ( 0 = 0 °) the greatest reduct ion in top heat loss coefficient was found for a c o m p o u n d honeycomb with 6b/L = tSt/L = 0.60. For a solar collector tilted from the horizontal (0 = 30 ° and 60 ° ) the greatest reduct ion in top heat loss coefficient was found with t S b / L = 6 t / L = 0 . 4 0 .

Since the heat losses f rom a horizontal collector were minimized for a c o m p o u n d honeycomb with the largest air gap thickness ratio considered, it is an open quest ion whether increasing the air gap thickness ratio to a value greater than 6 b / L = 6 t / L = 0 . 6 0 would reduce the heat loss coefficient even more.

Final ly, it is impor tan t to note that the use of c o m p o u n d honeycombs as convect ion suppressors in solar collectors enables the consider- a t ion of a wider variety of materials for honeycomb construct ion. By breaking the conduct ion path to the honeycomb, the designer need no longer be limited to the use of low conduct ivi ty and low emissivity honeycomb materials. This new freedom is especially impor- tant, since honeycombs made of higher conductivity and higher emissivity materials can be significantly more effective in suppressing convection than those made of low conduct ivi ty and low emissivity materials.

5. NOMENCLATURE

D h

k kr L Lt

Nuo NuB

q

qo

Ra t

Th, To IV

depth of honeycomb cell (north-south), m top heat loss coefficient for compound-honeycomb solar collector, W m -2 K -1 conductivity of honeycomb wall, W m - t K- t conductivity of air, W m- 1 K- t thickness of honeycomb, m total thickness of compound-honeycomb layer, m subcritical Nusselt number, defined in eqn (3) supercritical Nusselt number, defined in eqn (4) measured heat flux across compound-honeycomb layer, W m -2 measured heat flux across quiescent compound- honeycomb layer, W m -2 Rayleigh number, defined in eqn ( 1 ) thickness of honeycomb cell wall, m temperature of hot and cold plates, respectively, K width of honeycomb cell (east-west), m

Greek symbols

~t thermal diffusivity of air, m 2 s- 1 fl volume coefficient of expansion or air, K-

fit thickness of air gap above honeycomb, m 6b thickness of air gap below honeycomb, m e emissivity of honeycomb wall v kinematic viscosity of air, m 2 s-1

AT Th-Tc, K

R E F E R E N C E S

Arnold J. N., Catton I. and Edwards D. K. (1976) Experi- mental investigation of natural convection in inclined rectangular regions of differing aspect ratio. J. Heat Transfer 98, 67-71.

Arnold J. N., Edwards D. K. and Catton I. (1977) Effect of tilt and horizontal aspect ratio on natural convection in rectangular honeycombs, J. Heat Transfer 99, 120-122.

Buchberg H., Lalude O. A. and Edwards D. K. (1971) Performance characteristics of rectangular honeycomb solar-thermal converters. Solar Energy 13, 193-221.

Cane R. L. D., HoUands K. G. T., Raithby G. D. and Unny T. E. (1971) Free convection heat transfer across inclined honeycomb panels. Z Heat Transfer 99, 86-91.

Catton I. (1972) Effect of wall conduction on the stability of a fluid in a rectangular region heated from below. J. Heat Transfer 94, 446-452.

Edwards D. K. (1969) Suppression of cellular convection by lateral walls. J. Heat Transfer 91, 145-150.

Edwards D. K. and Sun W. M. (1970) Prediction of the onset of natural convection in rectangular honeycomb structures. Int. Solar Energy Soc. Conf., Melbourne, Paper No. 7/62.

Edwards D. K., Arnold J. N. and Catton I. (1976) End- clearance effects on rectangular-honeycomb solar collectors. Solar Energy 18, 253-257.

Francia G. (1964) Un nouveau collecteur de l'energie rayon- nant solaire--theorie et verification experimentales. Proc. United Nations Conf. New Sources of Energy, Rome, 21-23 August 1961, 35/S/71, United Nations, New York.

Hollands K. G. T. (1965) Honeycomb devices in fiat plate solar collectors. Solar Energy 9, 159-164.

Hollands K. G. T. (1973) Natural convection in horizontal thin-walled honeycomb panels. J. Heat Transfer 95, 439-444.

Hollands K. G. T. and Iynkaran K. (1985) Proposal for a compound-honeycomb collector. Solar Energy 34, 309-316.

Hollands K. G. T. and Iynkaran K. (1993) Analytic model for the thermal conductance of compound honeycomb transparent insulation with experimental validation. Solar Energy 51, 223-227.

Hollands K. G. T., Iynkaran K,, Ford C. and Platzer W. J. (1992) Manufacture, solar transmission, and heat transfer characteristic of large-celled honeycomb transparent insulation. Solar Energy 49, 381-385.

Hollands K. G. T., Raithby G. D., Russell F. B. and Wilkin- son R. G. (1984) Coupled radiative and conductive heat transfer across honeycomb panels and through single cells. Int. J. Heat Mass Transfer 27, 2119-2131.

Linthorst S. J. M. (1985) Natural convection suppression in solar collectors, Ph.D. Thesis, Delft Technical Univer- sity, Dutch Efficiency Bureau, Pijnacker, The Nether- lands, ISBN 90 6231 138 5/CIP.

Richards R. F. (1994) Thermal stability of a diathermanous fluid in a multi-layer system with partially transparent radiating boundaries. Int. J. Heat Mass Transfer 37, 2101-2111.

Smart D. R., HoUands K. G. T. and Raithby G. D. (1980) Free convection heat transfer across rectangular-celled diathermanous honeycombs. J. Heat Transfer 102, 75-80.

Documents

Effect of gap thickness on a rectangular-cell compound-honeycomb solar collector