heat and fluid flow in rectangular solar air heater ducts having transverse rib roughness on...

Solar Energy Vol. 51, No. 1, pp. 31-37, 1993 DO38-O92X/93 $6.00 + .DO Prinled in the U.S.A. Copyright © 1993 Pergamon Press Ltd.

HEAT AND FLUID FLOW IN RECTANGULAR SOLAR AIR HEATER DUCTS HAVING TRANSVERSE RIB ROUGHNESS

ON ABSORBER PLATES

DHANANJAY GUPTA,* S. C. SOLANKI,** and J. S. SAINI** *Mechanical Engineering Department, Engineering College, Kota 324 009, India, **Department of

Mechanical and Industrial Engineering, University of Roorkee, Roorkee 247 667, India

Abstract--An experimental investigation has been carried out to determine the effect of transverse wire roughness on heat and fluid flow characteristics in transitionally rough flow region (5 < e ÷ < 70) for rectangular solar air heater ducts with an absorber plate having transverse wire roughness on its underside. The investigation covered a Reynolds number range of 3000-18000 for a duct aspect ratio of 6.8-11.5, relative roughness height of 0.018-0.052 at a relative roughness pitch of 10 encompassing a range of roughness Reynolds number between 5-70. Simple correlations for a Nusselt number and friction factor have been developed in terms of geometrical parameters of roughness, duct cross section, and the flow Reynolds number.

1. I N T R O D U C T I O N

The use of artificial roughness on heat transfer surfaces has been found to be an effective method of enhancement of a heat transfer coefficient, although it is ac- companied by a substantial increase in friction losses also. A number of investigators have studied the phe- nomenon of heat and fluid flow over rough surfaces. In one of the earliest systematic studies, Niku- radse[1]identified three flow regions depending on variation of friction factor with roughness Reynolds number and roughness height, namely: 1. Hydraulically smooth flow (0 < e ÷ < 5). In this

regime, the friction factor is a function of Reynolds number only as the roughness elements are com- pletely submerged in laminar sublayer and friction factor is not affected by roughness height.

2. Transitionally rough flow (5 < e + < 70). In this regime, the roughness elements extend slightly beyond the laminar sublayer resulting in additional resistance due to "form drag" and so the friction factor is a function of both relative roughness height and Reynolds number.

3. Fully rough flow (e + > 70). In this regime the roughness elements extend well beyond the laminar sublayer and friction factor depends only on relative roughness height and is independent of Reynolds number. Nikuradse [ 1 ] proposed a "law of wail," expressed

mathematically as:

u + = 2.5 ln(y/e) + R(e +) (1)

where R(e ÷) is the momentum transfer roughness function and it assumes a constant value in fully rough flow conditions for a given roughness geometry.

Dipprey and Sabersky[2]developed a heat momentum transfer analogy for flow in tubes having sand

31

grain roughness. The analogy has been used extensively for computation of heat transfer coefficient in flow through tubes, and is given as:

G ( e + , P r ) = [ ( f / 2 S t ) - l ] ( f /2 ) -°5 + R(e+). (2)

Webb et al.[ 3]extended the law of wall and the heat momentum transfer analogy to geometrically nonsimilar roughness and developed correlations valid for flow in circular tubes with transverse ribs and for fully rough flow (e ÷ > 35). These correlations have been used by Han[ 4 ] for computation of friction factor and heat transfer coefficient in square ducts with two opposite rib roughened surfaces.

Kader and Yaglom[5]developed a general relationship for coefficient of heat transfer for rough wall on the basis of general dimensional and similarity con- siderations.

Vilemas and Simonis[6], in an experimental investigation for flow of air in an annulus with inner tube having, on its outer surface, rectangular rib roughness, transverse to flow, have derived correlations for heat transfer coefficient and friction factor as: In fully rough region:

Nu = 0.029 Re°84pr°6~ n. (3)

In transitionally rough region:

Nu = (0.0053 - O.14e/d)Ret°95+7e/a)pr°6~b n (4)

where ~ is the ratio of absolute temperatures at wall and in flow. Friction factor in transitionally and fully rough regions is given by

f = [0.053 + 1.85(e/d)].Re -°°7. (5)

32 D. GUPTA, S. C. SOLANK|, and J. S. SAINI

It has been reported that in the course of transition from partial to fully rough region, a clear kinking in Nusselt number versus Reynolds number curves is observed, and the Reynolds number at which change in slope is observed, decreases with an increase in relative roughness height. The optimum operating parameters for the augmentation of heat transfer are the smaller possible height of roughness element, provided that the system operates in the region of the transition from partial to fully rough flow conditions.

All these studies used circular passages or square ducts with two opposite walls having rib roughness. However, an experimental investigation for rectangular ducts having rib roughness on one principal wall was reported by Sparrow and Tao[7]. They used the law of wall similarity for roughness functions:

R + = 0.685(e+) TM for e + < 120 (6)

R + = 1.18(e+) °'1°5 for e + > 120 (7)

G(e +) = 6.47(e+) °-297 (8)

where R + is the modified roughness function given by

R ÷ = [(e /D)/(P/e)]° '25R(e+). (9)

Prasad and Mullick[8]investigated the effect of transverse wire roughness on absorber plate and have suggested a simple linear relationship between the Nusselt number and Reynolds number from their experimental data.

Prasad and Saini[9], on the basis of law of wall similarity and heat momentum analogy, proposed re- lationships for friction factor and heat transfer coefficient in a solar air heater duct.

Dalle Donne and Meyer[10]proposed a transfor- mation method to obtain data applicable to reactor fuel elements from annulus experiments. The trans- formed friction and heat transfer data were correlated by single equations. Wilkie et al.[ll] proposed a procedure for the measurement of friction factor in rectangular channels which were not identically roughened, and they have shown that the absolute value of friction factor is up to 10% lower because of presence of smooth surface opposite to the rough surface. Wil- liams et al.[ 12 ] and White and White [ 13 ] have also investigated the effect of roughness on friction factor and heat transfer in annulus flow, and they have reported the effect of various roughness parameters on friction factor and heat transfer.

However, it is observed that most of the investigations relate to fully rough flow conditions and very little information is available for transitionally rough flow region, especially for a geometry under consid- eration in the present investigations. It has been, there- fore, considered necessary to develop general correlations to predict the friction factor and Nusselt number over a wider range of roughness heights and aspect ratios in a transitionally rough flow region, because the solar air heaters have been observed to be operating in transitionally rough region (e ÷ < 50) in most cases.

In the present work, experimental data have been col- lected for solar air heater ducts with absorber plates that have transverse wire roughness and operate in transitionally rough region. Details of experimental setup, data processing, and the development of correlations are being reported.

2. EXPERIMENTAL SETUP

The experimental solar air heater duct, as shown in Fig. la, consists of a wooden channel 2.64 m long and 0.2 m wide which includes three sections, namely, the entrance, test, and exit sections of 0.4, 1.64, and 0.6 m lengths, respectively. Three pairs of replaceable wooden strips, each 2.5 cm wide and 1.3, 1.85, and 2.2 cm high are used on the side of the channel for the fixing absorber plate to give a rectangular duct 15 cm wide and 1.3, 1.85, or 2.2 cm high. A piece of 6 mm thick plywood is used to cover the entrance and exit sections of the duct. The test section is covered with an absorber plate to form a rectangular test passage as shown in Fig. 1. A M.S. sheet of 22 SWG and 1.64 m X 0.20 m size was used as an absorber plate with the top surface painted with black board paint, and the lower surface having artificial roughness in the form of copper wires of 0.7, 0.8, 1.06, and 1.25 mm diameter, and oriented normal to axis of plate as shown in Fig. 2. The copper wires were attached to the absorber plate by means of sheet metal screws at both ends of the wire about 5 mm from the edge of the sheet. In order to ensure good contact with the plate, a very thin film of adhesive (araldite) was applied between the wire and the plate, and the wires were pressed tightly against the plate without any gap between the wire and the plate all along the length of the wire.

It has been proved conclusively, by many investigators[3,4,8]that the best performance is given for a relative roughness pitch of 10. Hence all the test surfaces have been prepared for a relative roughness pitch of 10. Four such surfaces were prepared and each one was tested for three different depths of duct. Each set consists of 7 or 8 runs for different flow rates (Reynolds numbers varying from 3000 to 18000). Tests have also been conducted on a conventional smooth absorber plate surface under similar geometrical and flow conditions to serve as the basis of comparison of results and to determine the enhancement of heat transfer coefficient and friction factor.

Five 28 gauge copper constantan thermocouples are mounted along the axial center line of the ribbed wall at an equal interval of 0.4 m each and five thermocouples inserted inside the duct and located midway and 0.4 m apart in air along the center line of the duct. This procedure is in line with the measurements as reported in[3,8,13,14]where a similar number of thermocouples have been used for measurement of an average plate temperature. Han et aL [ 15 ] have shown that the wall temperature paralleled the bulk mean air temperature at a distance of 3 to 5 diameters down stream from the start of heating, and the difference of average plate and air temperatures can be used for cal-

Heat and fluid flow in rectangular heater ducts

23~V

OUT~P~UT INPUT

®

®

®

1. AIR INLET

2. ENTRANCE SECTION

3- TEST SECTION

4. EXIT SECTION

5. ORIFICE METER

6. MANOMETER

7. BLOWER

8. AIR OUTLET

9. MOTOR

10. VARIAC

Fig. l (a). Schematic diagram of experimental setup.

33

®

/~Ov SUPPLY

culation of the Nusselt number. One thermocouple and one mercury thermometer having a least count of 0. I °C each, have been used at inlet and outlet of the test section to measure the bulk air temperatures. A digital microvoltmeter is used for the measurement of

thermocouple output. The thermocouples have been calibrated using a standard thermometer.

Two pressure tappings were installed along the bot- tom wall at the center line 1.6 m apart. A microma- nometer having a least count of 0.01 mm was employed

0 I~'~ - . ~ ;.~__..~______________O 2 - . . . . - . . - - . . . . T, .., ,. __.~-----~:=~--To blower

ls4o fi

F 22 t

blower

@ @ @ @

Enterance section 400x150 @

Test section 1640x150 @

Exit section 600x150 @

T h e r m o c o u p t e s • @ Fig. 1 (b). Details of duct.

GLass wool insulation

Heater plate

Roughened absorber plate

Pressure tappings

34 D. GUPTA, S. C. SOLANKI, and J. S. SAINI

_ W i r e s

i "t ~ •

Absorber ptote

Average values of air density p, specific heat Cp, and kinematic viscosity ~ at a pressure of 742 mm of mercury and temperature of 35°C[16]were used for computations. The maximum uncertainties in measurement of various parameters were calculated as:

t Fig. 2. Roughened absorber plate.

Friction factor = ___ 0.0412

Stanton number = _+ 0.0438

Nusselt number = + 0.0487

Reynolds number = _+ 0.0212.

to measure the pressure drop across the test section. Flow through the duct was measured by means of a calibrated orifice meter connected to an inclined U tube manometer having an angle of inclination of 10.5 o to the horizontal plane.

An electric heater of identical dimensions as those of absorber plate, consisting of nine flat strip heaters mounted on a thick metal plate, was used to provide uniform heat flux to the absorber plate. The heater assembly was covered with layers of 2.0 cm thick as- bestos rope insulation and 4.0 cm thick glass wool insulation. The heater was kept 2.5 cm above the absorber plate with the help of porcelain spacers. The power supply to the heater plate assembly was conducted through a 230 V A.C. single phase variac to provide a heat flux of about 800 W / m 2, to match with the order of mean intensity of solar radiations available.

3. DATA REDUCTION

Steady state values of the plate and air temperature at various locations were measured for a given heat flux and mass flow rate of air. Mean plate and air temperatures were computed for a test section using the local values. Heat supplied to the air, heat transfer coefficient, and, subsequently, the Stanton number were computed on the basis of bulk air temperature rise as follows:

q = mCp(to - ti) (10)

h = q /Ap( tp - ta) ( l l )

St = h / o V C p . (12)

Average friction factor was computed using the pressure drop by means of the following expression:

f = ( Ap. D / 2 V z. L ' O ) (13)

Roughness Reynolds number e + and Roughness functions R (e +) were then computed using the following expressions:

e+ = ( e / D ) R e ( f ] 2 ) °5 (14)

R ( e +) = ( 2 / f ) °5 + 2.5 l n (2e /D)

+ 2.5 l n ( 2 W / ( W + H)) + 2.5. (15)

The range of parameters covered in this investigation is given below.

Relative roughness pitch, P/e = 10

Relative roughness height, e / D = 0.018 to 0.052

Aspect ratio of duct, W / H = 6.8 to 11.5

Reynolds number, Re = 3000 to 18000.

4. RESULTS AND DISCUSSION

As pointed out earlier, the present investigation in- corporated the range of roughness geometries and flow parameters resulting in roughness Reynolds numbers lying between 5-70 and hence related to transitionally rough flow region only. Important results of this investigation are discussed below.

4.1 Stanton number variation A typical plot of Stanton number against Reynolds

number is shown in Fig. 3. The Stanton number increases initially with increasing Reynolds number up to approximately 12000 where it attains a maximum value and registers a slight fall thereafter. This trend of variation in Stanton number is in agreement with the observations of Dipprey and Sabersky[2]. The point of maxima, however, depends on relative roughness height and shifts to lower values of Reynolds numbers for larger relative roughness heights. However, many investigators [ 3,4 ] have reported that the Stanton number decreases monotonously with increase in Reynolds numbers for a given roughness configuration.

10.0

r ¢1 o

x

O3

1.0

t I I

H = 1 . 8 5 c m • =0 .8 mm

• St

Fig. 3. Stanton number vs. Reynolds number.

I I i I t t ,

2 20

Re x 10-3

Heat and fluid flow in rectangular heater ducts

This is basically because the range of their study fell in a fully rough region.

4.2 Momentum transfer roughness function R ( e + ) Figure 4 shows the variation of momentum transfer

roughness function R(e +) with roughness Reynolds number e + . It is observed that the roughness function increases, though slightly, as the roughness Reynolds number increases, and hence it is a function of both the relative roughness height and Reynolds number. It is in agreement with the observations reported by Nikuradse [ 1 ].

As discussed earlier, the roughness function be- comes independent of flow parameters (Reynolds number and roughness Reynolds number) in fully rough region and depends only on the geometrical parameters. This value can be used for determination of friction factor irrespective of Reynolds number or roughness Reynolds number provided the flow is in fully rough region. However, in transitionally rough flow region, the roughness function is dependent on roughness Reynolds number also in addition to geometrical parameters. Sheriff and Gumley [ 14 ] have also made a similar observation. They have evaluated the roughness function as 4.65 for transverse ribs (P/e = 10) in fully rough region (e + > 70). However, in transitionally rough region, the value of the roughness function has been found to vary with Reynolds number. Sparrow and Tao [ 7 ], in their investigation in the roughness Reynolds number range of 50 to 600 in rectangular ducts with one principal wall having transverse rib roughness, have defined a modified roughness function showing that the roughness function does not assume a constant value for a given roughness, and varies with Reynolds numbers for such geometries even at high roughness Reynolds numbers.

20

+ GI

r r

H = 2 . 2 c m e e = 1 . 2 5 m m + e = l . 0 6 m m

e = 0 . 8 m m o e = O . ? m m

2 I i i i i i ,

s 10 e4-

Fig. 4. Momentum transfer roughness function vs. roughness Reynolds number.

10.0

c )

X

1.0 2

* H = 2 . 2 c m .I- H = 1 .85cm . H = 1 . 3 e m

e = 1.25 rnm

4- +

÷* ,+

Re x 10 -3 Fig. 5. Friction factor vs. Reynolds number.

35

4-

i I

20

The standard error for this correlation was computed as 10.9% and regression coefficient as 0.711. Fig- ure 6 shows a plot of ratio of experimental value of friction factor to that predicted by eqn (16) against Reynolds number. It shows that out of 81 data points, 74 points (91.4%) lie within +15% of the predicted value. Hence the correlation represented by eqn (16) can be used for satisfactory prediction of friction factor for solar air heater ducts having transverse rib roughness.

4.4 Heat transfer correlation In most of the previous investigations [ 2-4,8,17,18 ],

in which laws of similarity have been used for computation of heat transfer, the Stanton number is in- variably used in preference to the Nusselt number, probably because the expressions for the Stanton number turn out to be similar in form to those for friction factor, and the two parameters are related through the Reynolds analogy and Dipprey and Sa- bersky's analogy. However, other investigators [ 5,6,8 ],

f = O.06412(e/D)°°=9(W/H)°237(Re)-°Jss. (16)

4.3 Friction factor correlation In view of the above discussion a simple correlation

was developed to predict the friction factor for wider range of roughness and passage geometries. The experimental data of this present investigation was used to plot friction factor versus Reynolds number in Fig. 5, which reveals that the use of power law is possible in predicting the values of friction factor.

The experimental data were used to correlate the friction factor with roughness parameter (e/D), duct geometry (W~ H), and flow parameter (Re). The correlation obtained is given below:

36 D. GUPTA, S. C. SOLANKI, and J. S. SAIN|

1.5

-I

1./,

1.3

1.2

1.1

1.0

0.9

O . e

0-7

0.6

0 .5 2

" . • " . • " - . • , o •

• o • •• . . •

• • . . . - t

• . • •

I I I | I I I I

/* 6 a lo lz ~ is la zo

Re x 10 - 3

Fig. 6. Ratio of friction factor (experimental) and friction factor (predicted) vs. Reynolds number.

1.4

Z

1.2

1.1

1C

0S

0 8

0-7

0-6 2

e + less t h o n 35

# # % • • %°

• ,=': : • • . • ;

I I I I I I I 1

4 6 8 10 12 14 16 18 20

Re x 10 -3

Fig. 8. Ratio of Nusselt number (experimental) to Nusselt number (predicted) vs. Reynolds number.

who did not use the roughness functions for analysis of their results, used a more conventional parameter, a Nusselt number, to develop heat transfer correlations. A similar correlation was developed for the present case also.

Variation of the Nusselt number with the Reynolds number is shown in Fig. 7. Using the experimental data, the following correlations have been obtained for the Nusselt number: for e ÷ < 35

Z

100

10

• H= 2 2 c m

+ H = 1 8 c m • .+

• H = 1 3 c m ~ ~.

e = 1.25turn ~-

+

te-

1 i i i i i i i

2 2O

Re x 1 0 - 3

Fig. 7. Nusselt number vs. Reynolds number.

Nu = 0.000824 (e/D) -o.178 ( W / H ) 0.2ss (Re) 1.062 ( 17 )

and for e ÷ > 35

Nu = O.O0307(e/D)-°a69(W/H)°245(Re) °'st2. (18)

The standard error for these correlations was computed as 6.2% and 6.8%, respectively, and regression coefficients as 0.991 and 0•973, respectively. Figure 8 gives a plot of ratio of experimental values of the Nus- selt number to those predicted by eqns ( 17 ) and (18) against Reynolds numbers. It can be seen that out of 87 data points, 73 data points (83.9%) lie within _+10%. Hence the correlations, eqns (17) and (18), can be used satisfactorily for the prediction of the Nusselt number in solar air heater ducts in the range of parameters investigated.

5. CONCLUSIONS

From this experimental study in transitionally rough flow region in solar air heater ducts, with absorber plates having transverse wire roughness, the following conclusions can be drawn. 1. The behavior of the Stanton number in a transi-

tionally rough flow region is different from its behavior in a fully rough flow region, and hence the correlations for roughness functions R(e +) and G(e+), available in a fully rough flow region, cannot be used for solar air heater ducts•

2. Correlations (eqns [ 16-18 ]) for transitionally rough flow regions have been developed for the range of investigation. The correlations show good agreement between the predicted and experimental values of the heat transfer coefficient and friction factor.

Heat and fluid flow in rectangular heater ducts 37

NOMENCLATURE

Ap area of absorber plate, m 2 Cp specific heat of air, J /kg K D equivalent diameter of duct (4 x Area of cross section/

perimeter), m e height of roughness, roughness wire diameter, m

f average friction factor [ eqn ( 13 )] H depth of the duct, m h convective heat transfer coefficient, W/ m 2 K L distance between two pressure tappings in test section,

m k thermal conductivity of air, W/ m K

m mass flow rate of air, kg/s Ap pressure drop across test section, Pa

q rate of heat transfer to air, W ta average air temperature in test section, °C ti temperature of air at inlet to test section, °C to temperature of air at outlet to test section, °C tp average plate temperature, °C

u* shear velocity (rw/Ü) °5, m/s V velocity of air in test section, m/s

W width of duct, m y distance from wall, m o air density, kg/m s , air kinematic viscosity, m2/s

Dimensionless parameters

e /D P/e

e + G(e +)

R + R(e ÷)

bl + Nu Pr

Re St

relative roughness height relative roughness pitch roughness Reynolds number [eqn (14)] heat transfer roughness function [ eqn (2) ] modified roughness function [eqn (9)] momentum transfer roughness function [eqn ( 15 )] dimensionless velocity, V~ u*, Nusselt number, h D / k Prandtl number, p • v. Cp/k Reynolds number, V . D/u Stanton number, h / o V C p or Nu. Re. Pr

REFERENCES

1. J. Nikuradse, Laws of flow in rough pipes, NACA TM 1292 (1950).

2. D. F. Dipprey and R. H. Sabersky, Heat and momentum transfer in smooth and rough tubes at various Prandtl numbers, Int. J. Heat Mass Trans. 6, 329-353 (1963).

3. R. L. Webb, E. R. G. Eckert, and R. J. Goldstein, Heat transfer and friction in tubes with repeated rib roughness, Int. J. Heat Mass Trans. 14, 601-617 ( 1971 ).

4. J. C. Han, Heat transfer and friction in channels with two opposite rib roughened walls, Trans. ASME, J. Heat Trans. 106, 774-781 (1984).

5. B.A. Kader and A. M. Yaglom, Turbulent heat and mass transfer from a wall with parallel roughness ridges, Int. J. Heat Mass Trans. 20, 345-357 (1977).

6. J. V. Vilemas and V. M. Simonis, Heat transfer and friction of rough ducts carrying gas flow with variable physical properties, Int. Z Heat Mass Trans. 28( I ), 59-68 (1985).

7. E. M. Sparrow and W. Q. Tao, Enhanced heat transfer in a flat rectangular duct with streamwise periodic dis- turbances at one principal wall, Trans. ASME. Z Heat Trans. 105, 851-861 (1983).

8. K. Prasad and S. C. Mullick, Heat transfer characteristics of a solar air heater used for drying purposes, Appl. Energy 13, 83-93 (1983).

9. B. N. Prasad and J. S. Saini, Effect of artificial roughness on heat transfer and friction factor in a solar air heater, Solar Energy 41,555-560 (1988).

10. M. Dalle Donne and L. Meyer, Turbulent convection heat transfer from rough surfaces with two-dimensional ribs, Int. ,L Heat Mass Trans. 22, 583-620 (1979).

11. D. Wilkie, M. Cowan, P. Burnett, and T. Burgoyone, Friction factor measurements in a rectangular channel with walls of identical and non-identical roughness, Int. J. Heat Trans. 10, 611-621 (1967).

12. F. Williams, M. A. M. Pirie, and C. Warburton, Heat transfer from surfaces roughed by ribs, In: Augmentation of convective heat and mass transfer, ASME, New York, pp. 35-43 (1970).

13. W. J. White and L. White, The effect of rib profile on heat transfer and pressure loss properties of transversely fibbed roughened surfaces, In: Augmentation of convective heat and mass transfer, ASME, New York, p. 4454 (1970).

14. N. Sheriff and P. Gumley, Heat transfer and friction properties of surfaces with discrete roughnesses, Int. J. Heat Mass Trans. 9, 1297-1329 (1966).

15. J. C. Han and J. S. Park, Developing heat transfer in rectangular channels with rib turbulators, Int. ,L Heat Mass Trans. 31, 183-195 (1988).

16. James R. Weity, Fundamentals o f momentum, heat and mass tran~fer, 3rd. ed., John Wiley & Sons, New York (1984).

17. E. A. Cortes and R. Piacentini, Improvement of the efficiency of the efficiency of a bare solar collector by means of turbulence promoters, Appl. Energy 36, 253-261 (1990).

18. S. C. Lau, R. T. Kukreja, and R. D. McMillin, Effect of V-shaped ribs arrays on turbulent heat transfer and friction of fully developed flow in a square channel, Int. Z Heat Mass Trans. 34, 1605-1616 ( 1991 ).

heat and fluid flow in rectangular solar air heater ducts having transverse rib roughness on...

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