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HEAT TRANSFER AND PRESSURE DROP IN AN ARTIFICIALLY ROUGHENED RECTANGULAR DUCT
Transport Phenomena in Heat and Mass Transfer J.A. Reizes (Editor) § 1992 Elsevier Science Publishers B. V. All rights reserved.
259
HEAT TRANSFER AND PRESSURE DROP IN AN ARTIFICIALLY ROUGHENED RECTANGULAR DUCT
L. Wu Ningxia Institute for the Application of New Technology, Yinchuan, Ningxia, P. R. China. P. Cooper Department of Mechanical Engineering University of Wollongong, Wollongong, NSW 2500, Australia.
ABSTRACT Experimental results for friction factor and heat transfer coefficient are presented for a rectangular air duct with one duct-wall heated and the others adiabatic. Two sets of results are presented where the heat transfer surface is: a) nominally smooth and b) artificially roughened with regularly spaced spherical segments. The latter models a particular type of solar air heater and the purpose of this study is to further the development of an optimal collector design where the roughness element size and pitch are important parameters in that application. The pressure drop and heat transfer results are compared with previous data for roughness elements with configurations similar to the present case. 1.
INTRODUCTION
Solar air collectors are characterised by relatively poor efficiencies when compared with collectors using water as the working fluid. The major cause of this is the poor heat transfer coefficient on the working fluid side, which leads to high absorber plate temperatures and, thus, high rates of heat loss to ambient air. Many methods have been suggested to enhance this heat transfer coefficient by increasing effective absorber area and increasing boundary layer disruption with artificial roughening elements. This paper describes work undertaken at the University of Wollongong to optimise the design of collectors utilising roughly hemispherical indentations on the working fluid side of the absorber plate. Such collectors are used in the People's Republic of China for air heating in hospitals (Qiying and Laner, 1987). This method of heat transfer enhancement has been chosen for its ease of practical implementation given the fabrication methods available locally. The solar collector absorber and duct are made from sheet steel and the indentations are formed by simply pressing a large ball-bearing on to the plate which is backed by a suitable die. Qiying and Laner (1987) reported improvements of 10-15% in collector efficiency over similar air collectors without such indentations. The present study sought to identify the most suitable size and pitch of such indentations with respect to pressure drop and heat transfer in the air collector duct. Previous literature on the topic indicated that a deal of work has been carried out for heat transfer from roughened surfaces in ducts but with no work immediately applicable to the geometry or working fluid in question. The first major theoretical contribution in the field of rough duct pressure drop was the Equivalent Sandgrain Roughness model proposed by Schlichting, 1936. This was based on experimental data by Nikuradse, 1933. Much work has been done by others since that time with Scaggs et al (1988) having recently presented detailed experimental and theoretical analyses of pressure drop in round ducts artificially roughened with elements including hemispheres and truncated cones with water as the working fluid.
260
Heater plate
Pressure tappings
Perspex insulation Surface temp, thermojunctions
FIGURE 2. Location of pressure tappings and heat transfer surface temperature measurement points Two sets of pressure drop experiments were conducted. One with nominally smooth duct walls and one with the upper surface artificially roughened with the heads of aluminium rivets as shown in Fig. 3. Initial tests were made to confirm that both pairs of pressure tappings gave identical results for both the smooth and rough duct cases. For the rough duct tests, static pressure drop along the duct was measured using the tappings in the upper face.
[^
24mm
f T 07.0 mm Air Flow
A"
12mm f ^ \ __!_
2mm
V 7ir FIGURE 3. Illustration of roughness element geometry (not to scale). Heat transfer tests were performed with the upper duct surfaces (smooth and rough) between the pressure tappings heated by means of a proprietary electrical heating mat. Power input to the latter was controlled by means of a variac transformer connected to a
261
Research on heat transfer in roughened ducts has been less extensive. Dipprey and Sabersky (1963) who investigated round ducts roughened with a granular surface, water being the heat transfer medium. Their work allowed a comparison to be made between the original pressure drop data of Nikuradse and heat transfer from surfaces of similar roughness characteristics. Webb et al (1971) conducted an investigation of regular rib-type roughnesses perpendicular to the direction of the flow of three different working fluids. A comprehensive correlation of heat transfer data for rib-type roughness was developed, based on the heat-momentum transfer analogy and law-of-the-wall similarity. The geometry of the air collector situation is one of a large-aspect ratio rectangular duct with uniform heat flux applied to one wall. Duffle and Beckman (1980) give a detailed review of past work in this field for smooth ducts. Prasad and Saini (1988) theoretically analysed air collectors with a roughened absorber surface and calculated pressure drop and heat transfer using a simple area-weighted method and the data of Webb et al (1971) to predict the characteristics of a collector with the absorber plate roughened. Their results showed reasonably good agreement with the experimental work of Prasad and Mullick (1983) on an air collector with the heat transfer surface enhanced by the addition of pin fins. The lack of heat transfer data directly related to the geometry of the solar collectors in used by Qiying and Laner (1987) led the present authors to conduct an experimental study of a scale model of the solar collectors in question with a view to using the theoretical work of others to predict the performance of surfaces using roughness elements of the same shape but of different pitch/dimensions. 2.
EXPERIMENTAL APPARATUS AND PROCEDURE
A schematic diagram of the experimental system is shown in Fig. 1. The test duct was made to represent a scale model of the solar collectors described in (Qiying and Laner, 1987) and was installed in a commercially manufactured rig (a Plint™ air-flow and nozzle test rig). The latter comprised a calibrated inlet nozzle for determination of air flow rate, a straight section of smooth, 75mm internal diameter alloy tube, reducing sections either end of the test rectangular duct, and a fan unit. Air flow was controlled by means of variable fan speed and a slide valve on the outlet of the fan. The rectangular duct section was made from aluminium sheet and bar with internal dimensions of height 20mm, width 125mm and 1 metre in total length. Pressure tappings were located on both the upper and lower faces of the duct as shown in Fig. 2, a distance of 480mm apart. Pressure drops across the inlet nozzle and along the test section were measured by means of an inclined manometer with a resolution of 0.5mm of water.
Test duct
Round duct
Met
nozzle
FIGURE 1. Schematic of duct test rig (all measurements in mm).
262
230V alternating current supply. The heater was permanently affixed to an aluminium sheet and this was then clamped to the back of the upper duct surface. A heat sink compound was used to ensure good thermal contact between the two metal surfaces. The general arrangement of heating element, thermocouples, etc. is shown in Fig. 4. To minimize the axial conduction of heat from the heated part of the test duct, a strip of Perspex 5mm in length was inserted as indicated in Fig. 2. Air temperatures and heat transfer surface temperatures were measured by means of copper-constantan thermojunctions. These were referenced to a thermojunction in an icewater bath and the resulting differential e.m.f. was monitored by a digital multimeter of l|iV resolution (a "Fluke 45"). Each thermocouple was calibrated using an ice-water bath and steam test before installation in the apparatus. The surface temperature of the test duct was monitored at five locations along the centreline of the heated surface. Rectangular grooves were machined into the back face of the plate as conduits for the thermojunction wires. The entire test section was insulated from ambient air by rockwool 50mm thick which was covered in aluminium foil. Measurement of the air temperature rise through the 480mm test section was effected by a twelve-junction thermopile also monitored using the digital multimeter. The locations of the thermojunctions concerned are shown in Fig. 4. This arrangement conformed to the ASHRAE Standard for testing the performance of solar air collectors (ASHRAE, 1977). Each heat transfer data set was determined after changes in air and surface temperatures were deemed undetectable (this was after a period of 30 minutes to an hour).
Figure 4. Test duct cross-section (smooth heat transfer surface) showing location of thermopile elements Pressure drop data were reduced using the following definition of friction factor, f:
» -
*£$)
where Ap is the pressure drop along the test section, Dh is hydraulic diameter, L duct length, p is density and V mean duct air velocity. Heat transfer coefficients were calculated on the basis of the difference in arithmetic means of the heated surface and the inlet and outlet bulk air temperatures. The total rate of heat transfer was determined from the mean velocity, temperature rise and thermophysical properties of the air as determined from tables.
263
3.
RESULTS
Reduced pressure drop data for the smooth and rough ducts are presented in Fig. 5. The well known empirical correlation for smooth wall pipes (Drew et al, 1932) is also shown, i.e.:
t
4xf0.00140 +
0.125 Re<>..32 I
(2)
In the fully turbulent region, the experimental friction factors were low (by a factor of 0.89) in comparison to Equation (2), which has been reported by other workers using similar apparatus (Liu et al, 1984). The wide scatter of data at low Reynolds number are most likely due to transition region effects. The rough duct data show a less marked dependence on Reynolds number with an increase in magnitude of f over that for the smooth duct by a factor of between 1.8 and 2.0. However, the dependence of f on Reynolds number does indicate that the duct flow was far from "fully rough" at the Reynolds numbers considered.
0.1
-X.
*x
X) »>x>
:|Rbughduct
3x<*-
fcfc*x
>
1 I^Qnation 4
D
P
pj Smooth due
■a?D
QE
H^
T
^ 1 I P 1 nation 2
TI 0.01 1000
10000
Reynolds Number
FIGURE 5.
Plot of Friction Factor against Reynolds Number
100000
264
Heat transfer coefficients were calculated on the basis of the plane (i.e. undeveloped) heated surface areas for both rough and smooth ducts (0.0640m2) with the characteristic dimension for Re and Nu being the heat transfer hydraulic diameter (80mm). The reduced experimental results are shown in Fig. 6 together with the correlation given by Duffie and Beckman (1980) for the heat transfer coefficient between two semi-infinite flat plates, one of which is heated: Nu
=
0.0158 (Re)0-8
1VAAJ.U
-
(3)
^t
^be ^^:
*r*x
V
X*< N^n
innn -
cl X K O U i $hDu<^ ■ fc^i
3
B
Q
a
*Xi
□
N
1 QlSi noothduct
"^JEq.3 *^^
10.0 -
100000
10000 Reynolds Number, Re
FIGURE 6. Plot of Nusselt Number against Reynolds Number A plot of the pumping power factor F = (f/4).Re (as defined in Liu et al, 1984) is given in Fig. 7 for the smooth and rough duct data of the present work together with the correlation given by Liu et al (1984) for pin-fin enhancement of their heated solar collector duct surface.
265
^~ 1
1 1V 1
*
p
X
IN B -
x<<-
X 0
Rough duct lx; ILx X
x: 1 n
£ b) T
pin-fin data, Liu
Smooth duct
10000000000
1E+11
1E+12
1E+13
Pumping Power Factor, F.
FIGURE 7. Plot of Nusselt Number against Pumping Power Factor, F. 4.
DISCUSSION
Comparison of the rough duct pressure drop data with previous research by Scaggs et al (1988) was made using the "area weighted" approach of Prasad and Saini (1988) where the friction factor for the duct with only one rough surface is calculated from the area weighted average of the smooth and completely rough surface data. In the present case the following geometric parameters are of interest: L/do and e/Dn, where L, do and e are the roughness element pitch, diameter and height, respectively, and D n is the friction hydraulic diameter of the duct. Taking the roughness elements to be modelled as hemispheres of diameters that present the same cross-sectional area to the air flow as in the practical situation, then in the original solar collectors studied by Qiying and Laner (Qiying and Laner, 1987), L/do = 2.51 and e/Dn = 0.069. The magnitudes of these parameters have been duplicated in the present study (see Fig. 3). Using the area weighted average approach the rough duct experimental data of the present study were correlated using the friction factor for the duct with one rough surface, fmean> to be given by:
266
A r x fr fmean
+ A s x 0.89^0.00140 + ^ ^ j ) x 4
=
(A r + A s )
(4)
Ar and As are the areas of the rough and smooth surfaces of the duct, respectively; fr is the friction factor of the wholly rough duct surface which was approximated by fr = a.(Re)b, for which correlation of the experimental data yielded a = 0.0854 and b = -0.0325 (a plot of Equation (4) for these constants is given in Fig. 5). Scaggs et al (1988) investigated ducts roughened with hemispherical elements where L/do equalled 2, 4 and 8 and e/Dh equal to 0.0247 and 0.0123 (amongst other configurations). Friction factors were found to be determined primarily by L/c^; Reynolds number and e/Dh having a relatively minor influence by comparison. For the experimental conditions of Scaggs most closely related to the present study (i.e. data group A-l; L/do = 2 and e/Dh = 0.0247) fr was found to be approximated by 0.125(Re)"0048 for 104 < Re < 105. This is in qualitative agreement with the results of the present study. Heat transfer data in Fig. 6 show the smooth duct test results to be between 10 and 25% higher than predicted by Equation (3). This is most due to the fact that the present heated surface involved a developing thermal boundary layer in a duct of finite aspect ratio while Equation (3) is for fully developed flow. The degree of discrepancy is of the same order as reported for similar experiments elsewhere (Duffie and Beckman, 1980). The smooth duct Nusselt number data, Nus, were correlated by the relation Nus = 0.0312(Re)0-771. The degree of heat transfer enhancement afforded by the surface indentations at a given Reynolds number varied between a factor of 1.7 and 1.9 in the fully turbulent flow region. Rough surface heat transfer predicted by means of a heat/momentum transfer analogy of Equation 5 below, is also shown in Fig. 6:
m
N 0.5
Nur
=
Nusf^l
(5)
Here subscripts r and s refer to rough and smooth surfaces, respectively; fs is taken as Equation (3) multiplied by 0.89 to correlate the present smooth duct data; fr is taken to be equal to 0.0854(Re)~00325; and Nus represents the smooth duct data correlation of the present study. Equation (5) predicts the rough duct heat transfer rate within ±10%. The plot of Nusselt number against the pumping power factor F, Fig. 7, compares the method of enhancing heat transfer with surface indentations against that with pin fins placed between the heat transfer plate and the opposite adiabatic plate as reported in Liu et al (1984). The latter appears thermally more effective with the additional advantage that the pin fin geometry would be more difficult to fabricate and therefore less cost-effective in countries with limited manufacturing capability. Further work remains to be carried out on the apparatus with different sizes and surface densities of the hemispherical roughness elements. From experiments similar to those described above, the optimum roughness element arrangement for implementation in solar air heaters will then be determined.
267
5.
CONCLUSION
The present study has shown that for a large aspect ratio duct with one large wall (the heat transfer surface) artificially roughened with hemispherical roughness elements at air flow Reynolds numbers in the range 7000 to 5X104: a)
Pressure drop measurements have been correlated on an "area weighted" basis of the friction factors of wholly smooth and wholly rough ducts weighted appropriately.
b)
Heat transfer is enhanced by factors of between 1.7 and 1.9 over the smooth walled case. This degree of heat transfer enhancement is successfully predicted using the heat-momentum transfer analogy and experimental friction factor data.
c)
The hemispherical roughness element method of heat transfer enhancement compares favourably against pin-fin enhancement at the Reynolds numbers used in this study.
6.
REFERENCES
ASHRAE, 1977, Methods of Testing To Determine The Thermal Performance of Solar Collectors, The American Soc. of Heating, Refrigeration, and Air-Conditioning Engineers Standard 93-77, ANSI B198.1, pp. 12-13. Dipprey, D. F. and Sabersky, R. H., 1963, Heat and momentum transfer in smooth and rough tubes at various Prandtl numbers, Int. J. Heat Mass Transfer, vol. 6, pp. 329-353. Drew, T. B., Koo, E. C. and McAdams, W. H., 1932, The friction factor for clean round pipes, Trans. AIChE, vol. 28, pp. 56-72. Duffie, J. A. and Beckman, W. A., 1980, Solar Engineering of Thermal Processes, pp. 135-136, Wiley, New York. Liu, Y-H, Diaz, L. A. and Suryanarayana, N. V., 1984, Heat transfer enhancement in airheating flat-plate solar collectors, Trans. ASME, J. Solar Engineering, vol. 106, pp.358363. Nikuradse, J., 1933, Stromungsgesetze in Rauhen Rohren, VDI-Forchengsheft, vol. 361. Prasad, K. and Mullick, S. C, 1983, Heat transfer characteristics of a solar air heater used for drying purposes, Applied Energy, vol. 13, pp.83-89. Prasad B. N. and Saini, J. S., 1988, Effect of artificial roughness on heat transfer and friction factor in a solar air heater, Solar Energy, vol. 41, no. 6, pp. 555-560. Qiying, P. and Laner, W., 1987, A new type of solar air collector and its application in underground space air-conditioning, Proc. ASME-JSME-JSES Solar Energy Conf., Honolulu, pp. 634-637. Scaggs, W. F., Taylor, R. P. and Coleman, H. W., 1988, Measurement and Prediction of Rough Wall Effects on Friction Factor - Uniform Roughness Results, Trans. ASME, J. Fluids Eng., vol. 110, pp. 385-391. Schlichting, H., 1936, Experimentelle Intersuchungern Zum Rauhigkeits-Problem, Ingenieur-Archiv., vol. VII, no. 1, pp. 1-34. Webb, R. L., Eckert, E. R. G. and Goldstein, R. J., 1971, Heat transfer and friction in tubes with reneated-rih roughness Int J Hpnt Mnm Trrmifvr vr»1 1A nr* £fl1_A17
259
HEAT TRANSFER AND PRESSURE DROP IN AN ARTIFICIALLY ROUGHENED RECTANGULAR DUCT
L. Wu Ningxia Institute for the Application of New Technology, Yinchuan, Ningxia, P. R. China. P. Cooper Department of Mechanical Engineering University of Wollongong, Wollongong, NSW 2500, Australia.
ABSTRACT Experimental results for friction factor and heat transfer coefficient are presented for a rectangular air duct with one duct-wall heated and the others adiabatic. Two sets of results are presented where the heat transfer surface is: a) nominally smooth and b) artificially roughened with regularly spaced spherical segments. The latter models a particular type of solar air heater and the purpose of this study is to further the development of an optimal collector design where the roughness element size and pitch are important parameters in that application. The pressure drop and heat transfer results are compared with previous data for roughness elements with configurations similar to the present case. 1.
INTRODUCTION
Solar air collectors are characterised by relatively poor efficiencies when compared with collectors using water as the working fluid. The major cause of this is the poor heat transfer coefficient on the working fluid side, which leads to high absorber plate temperatures and, thus, high rates of heat loss to ambient air. Many methods have been suggested to enhance this heat transfer coefficient by increasing effective absorber area and increasing boundary layer disruption with artificial roughening elements. This paper describes work undertaken at the University of Wollongong to optimise the design of collectors utilising roughly hemispherical indentations on the working fluid side of the absorber plate. Such collectors are used in the People's Republic of China for air heating in hospitals (Qiying and Laner, 1987). This method of heat transfer enhancement has been chosen for its ease of practical implementation given the fabrication methods available locally. The solar collector absorber and duct are made from sheet steel and the indentations are formed by simply pressing a large ball-bearing on to the plate which is backed by a suitable die. Qiying and Laner (1987) reported improvements of 10-15% in collector efficiency over similar air collectors without such indentations. The present study sought to identify the most suitable size and pitch of such indentations with respect to pressure drop and heat transfer in the air collector duct. Previous literature on the topic indicated that a deal of work has been carried out for heat transfer from roughened surfaces in ducts but with no work immediately applicable to the geometry or working fluid in question. The first major theoretical contribution in the field of rough duct pressure drop was the Equivalent Sandgrain Roughness model proposed by Schlichting, 1936. This was based on experimental data by Nikuradse, 1933. Much work has been done by others since that time with Scaggs et al (1988) having recently presented detailed experimental and theoretical analyses of pressure drop in round ducts artificially roughened with elements including hemispheres and truncated cones with water as the working fluid.
260
Heater plate
Pressure tappings
Perspex insulation Surface temp, thermojunctions
FIGURE 2. Location of pressure tappings and heat transfer surface temperature measurement points Two sets of pressure drop experiments were conducted. One with nominally smooth duct walls and one with the upper surface artificially roughened with the heads of aluminium rivets as shown in Fig. 3. Initial tests were made to confirm that both pairs of pressure tappings gave identical results for both the smooth and rough duct cases. For the rough duct tests, static pressure drop along the duct was measured using the tappings in the upper face.
[^
24mm
f T 07.0 mm Air Flow
A"
12mm f ^ \ __!_
2mm
V 7ir FIGURE 3. Illustration of roughness element geometry (not to scale). Heat transfer tests were performed with the upper duct surfaces (smooth and rough) between the pressure tappings heated by means of a proprietary electrical heating mat. Power input to the latter was controlled by means of a variac transformer connected to a
261
Research on heat transfer in roughened ducts has been less extensive. Dipprey and Sabersky (1963) who investigated round ducts roughened with a granular surface, water being the heat transfer medium. Their work allowed a comparison to be made between the original pressure drop data of Nikuradse and heat transfer from surfaces of similar roughness characteristics. Webb et al (1971) conducted an investigation of regular rib-type roughnesses perpendicular to the direction of the flow of three different working fluids. A comprehensive correlation of heat transfer data for rib-type roughness was developed, based on the heat-momentum transfer analogy and law-of-the-wall similarity. The geometry of the air collector situation is one of a large-aspect ratio rectangular duct with uniform heat flux applied to one wall. Duffle and Beckman (1980) give a detailed review of past work in this field for smooth ducts. Prasad and Saini (1988) theoretically analysed air collectors with a roughened absorber surface and calculated pressure drop and heat transfer using a simple area-weighted method and the data of Webb et al (1971) to predict the characteristics of a collector with the absorber plate roughened. Their results showed reasonably good agreement with the experimental work of Prasad and Mullick (1983) on an air collector with the heat transfer surface enhanced by the addition of pin fins. The lack of heat transfer data directly related to the geometry of the solar collectors in used by Qiying and Laner (1987) led the present authors to conduct an experimental study of a scale model of the solar collectors in question with a view to using the theoretical work of others to predict the performance of surfaces using roughness elements of the same shape but of different pitch/dimensions. 2.
EXPERIMENTAL APPARATUS AND PROCEDURE
A schematic diagram of the experimental system is shown in Fig. 1. The test duct was made to represent a scale model of the solar collectors described in (Qiying and Laner, 1987) and was installed in a commercially manufactured rig (a Plint™ air-flow and nozzle test rig). The latter comprised a calibrated inlet nozzle for determination of air flow rate, a straight section of smooth, 75mm internal diameter alloy tube, reducing sections either end of the test rectangular duct, and a fan unit. Air flow was controlled by means of variable fan speed and a slide valve on the outlet of the fan. The rectangular duct section was made from aluminium sheet and bar with internal dimensions of height 20mm, width 125mm and 1 metre in total length. Pressure tappings were located on both the upper and lower faces of the duct as shown in Fig. 2, a distance of 480mm apart. Pressure drops across the inlet nozzle and along the test section were measured by means of an inclined manometer with a resolution of 0.5mm of water.
Test duct
Round duct
Met
nozzle
FIGURE 1. Schematic of duct test rig (all measurements in mm).
262
230V alternating current supply. The heater was permanently affixed to an aluminium sheet and this was then clamped to the back of the upper duct surface. A heat sink compound was used to ensure good thermal contact between the two metal surfaces. The general arrangement of heating element, thermocouples, etc. is shown in Fig. 4. To minimize the axial conduction of heat from the heated part of the test duct, a strip of Perspex 5mm in length was inserted as indicated in Fig. 2. Air temperatures and heat transfer surface temperatures were measured by means of copper-constantan thermojunctions. These were referenced to a thermojunction in an icewater bath and the resulting differential e.m.f. was monitored by a digital multimeter of l|iV resolution (a "Fluke 45"). Each thermocouple was calibrated using an ice-water bath and steam test before installation in the apparatus. The surface temperature of the test duct was monitored at five locations along the centreline of the heated surface. Rectangular grooves were machined into the back face of the plate as conduits for the thermojunction wires. The entire test section was insulated from ambient air by rockwool 50mm thick which was covered in aluminium foil. Measurement of the air temperature rise through the 480mm test section was effected by a twelve-junction thermopile also monitored using the digital multimeter. The locations of the thermojunctions concerned are shown in Fig. 4. This arrangement conformed to the ASHRAE Standard for testing the performance of solar air collectors (ASHRAE, 1977). Each heat transfer data set was determined after changes in air and surface temperatures were deemed undetectable (this was after a period of 30 minutes to an hour).
Figure 4. Test duct cross-section (smooth heat transfer surface) showing location of thermopile elements Pressure drop data were reduced using the following definition of friction factor, f:
» -
*£$)
where Ap is the pressure drop along the test section, Dh is hydraulic diameter, L duct length, p is density and V mean duct air velocity. Heat transfer coefficients were calculated on the basis of the difference in arithmetic means of the heated surface and the inlet and outlet bulk air temperatures. The total rate of heat transfer was determined from the mean velocity, temperature rise and thermophysical properties of the air as determined from tables.
263
3.
RESULTS
Reduced pressure drop data for the smooth and rough ducts are presented in Fig. 5. The well known empirical correlation for smooth wall pipes (Drew et al, 1932) is also shown, i.e.:
t
4xf0.00140 +
0.125 Re<>..32 I
(2)
In the fully turbulent region, the experimental friction factors were low (by a factor of 0.89) in comparison to Equation (2), which has been reported by other workers using similar apparatus (Liu et al, 1984). The wide scatter of data at low Reynolds number are most likely due to transition region effects. The rough duct data show a less marked dependence on Reynolds number with an increase in magnitude of f over that for the smooth duct by a factor of between 1.8 and 2.0. However, the dependence of f on Reynolds number does indicate that the duct flow was far from "fully rough" at the Reynolds numbers considered.
0.1
-X.
*x
X) »>x>
:|Rbughduct
3x<*-
fcfc*x
>
1 I^Qnation 4
D
P
pj Smooth due
■a?D
QE
H^
T
^ 1 I P 1 nation 2
TI 0.01 1000
10000
Reynolds Number
FIGURE 5.
Plot of Friction Factor against Reynolds Number
100000
264
Heat transfer coefficients were calculated on the basis of the plane (i.e. undeveloped) heated surface areas for both rough and smooth ducts (0.0640m2) with the characteristic dimension for Re and Nu being the heat transfer hydraulic diameter (80mm). The reduced experimental results are shown in Fig. 6 together with the correlation given by Duffie and Beckman (1980) for the heat transfer coefficient between two semi-infinite flat plates, one of which is heated: Nu
=
0.0158 (Re)0-8
1VAAJ.U
-
(3)
^t
^be ^^:
*r*x
V
X*< N^n
innn -
cl X K O U i $hDu<^ ■ fc^i
3
B
Q
a
*Xi
□
N
1 QlSi noothduct
"^JEq.3 *^^
10.0 -
100000
10000 Reynolds Number, Re
FIGURE 6. Plot of Nusselt Number against Reynolds Number A plot of the pumping power factor F = (f/4).Re (as defined in Liu et al, 1984) is given in Fig. 7 for the smooth and rough duct data of the present work together with the correlation given by Liu et al (1984) for pin-fin enhancement of their heated solar collector duct surface.
265
^~ 1
1 1V 1
*
p
X
IN B -
x<<-
X 0
Rough duct lx; ILx X
x: 1 n
£ b) T
pin-fin data, Liu
Smooth duct
10000000000
1E+11
1E+12
1E+13
Pumping Power Factor, F.
FIGURE 7. Plot of Nusselt Number against Pumping Power Factor, F. 4.
DISCUSSION
Comparison of the rough duct pressure drop data with previous research by Scaggs et al (1988) was made using the "area weighted" approach of Prasad and Saini (1988) where the friction factor for the duct with only one rough surface is calculated from the area weighted average of the smooth and completely rough surface data. In the present case the following geometric parameters are of interest: L/do and e/Dn, where L, do and e are the roughness element pitch, diameter and height, respectively, and D n is the friction hydraulic diameter of the duct. Taking the roughness elements to be modelled as hemispheres of diameters that present the same cross-sectional area to the air flow as in the practical situation, then in the original solar collectors studied by Qiying and Laner (Qiying and Laner, 1987), L/do = 2.51 and e/Dn = 0.069. The magnitudes of these parameters have been duplicated in the present study (see Fig. 3). Using the area weighted average approach the rough duct experimental data of the present study were correlated using the friction factor for the duct with one rough surface, fmean> to be given by:
266
A r x fr fmean
+ A s x 0.89^0.00140 + ^ ^ j ) x 4
=
(A r + A s )
(4)
Ar and As are the areas of the rough and smooth surfaces of the duct, respectively; fr is the friction factor of the wholly rough duct surface which was approximated by fr = a.(Re)b, for which correlation of the experimental data yielded a = 0.0854 and b = -0.0325 (a plot of Equation (4) for these constants is given in Fig. 5). Scaggs et al (1988) investigated ducts roughened with hemispherical elements where L/do equalled 2, 4 and 8 and e/Dh equal to 0.0247 and 0.0123 (amongst other configurations). Friction factors were found to be determined primarily by L/c^; Reynolds number and e/Dh having a relatively minor influence by comparison. For the experimental conditions of Scaggs most closely related to the present study (i.e. data group A-l; L/do = 2 and e/Dh = 0.0247) fr was found to be approximated by 0.125(Re)"0048 for 104 < Re < 105. This is in qualitative agreement with the results of the present study. Heat transfer data in Fig. 6 show the smooth duct test results to be between 10 and 25% higher than predicted by Equation (3). This is most due to the fact that the present heated surface involved a developing thermal boundary layer in a duct of finite aspect ratio while Equation (3) is for fully developed flow. The degree of discrepancy is of the same order as reported for similar experiments elsewhere (Duffie and Beckman, 1980). The smooth duct Nusselt number data, Nus, were correlated by the relation Nus = 0.0312(Re)0-771. The degree of heat transfer enhancement afforded by the surface indentations at a given Reynolds number varied between a factor of 1.7 and 1.9 in the fully turbulent flow region. Rough surface heat transfer predicted by means of a heat/momentum transfer analogy of Equation 5 below, is also shown in Fig. 6:
m
N 0.5
Nur
=
Nusf^l
(5)
Here subscripts r and s refer to rough and smooth surfaces, respectively; fs is taken as Equation (3) multiplied by 0.89 to correlate the present smooth duct data; fr is taken to be equal to 0.0854(Re)~00325; and Nus represents the smooth duct data correlation of the present study. Equation (5) predicts the rough duct heat transfer rate within ±10%. The plot of Nusselt number against the pumping power factor F, Fig. 7, compares the method of enhancing heat transfer with surface indentations against that with pin fins placed between the heat transfer plate and the opposite adiabatic plate as reported in Liu et al (1984). The latter appears thermally more effective with the additional advantage that the pin fin geometry would be more difficult to fabricate and therefore less cost-effective in countries with limited manufacturing capability. Further work remains to be carried out on the apparatus with different sizes and surface densities of the hemispherical roughness elements. From experiments similar to those described above, the optimum roughness element arrangement for implementation in solar air heaters will then be determined.
267
5.
CONCLUSION
The present study has shown that for a large aspect ratio duct with one large wall (the heat transfer surface) artificially roughened with hemispherical roughness elements at air flow Reynolds numbers in the range 7000 to 5X104: a)
Pressure drop measurements have been correlated on an "area weighted" basis of the friction factors of wholly smooth and wholly rough ducts weighted appropriately.
b)
Heat transfer is enhanced by factors of between 1.7 and 1.9 over the smooth walled case. This degree of heat transfer enhancement is successfully predicted using the heat-momentum transfer analogy and experimental friction factor data.
c)
The hemispherical roughness element method of heat transfer enhancement compares favourably against pin-fin enhancement at the Reynolds numbers used in this study.
6.
REFERENCES
ASHRAE, 1977, Methods of Testing To Determine The Thermal Performance of Solar Collectors, The American Soc. of Heating, Refrigeration, and Air-Conditioning Engineers Standard 93-77, ANSI B198.1, pp. 12-13. Dipprey, D. F. and Sabersky, R. H., 1963, Heat and momentum transfer in smooth and rough tubes at various Prandtl numbers, Int. J. Heat Mass Transfer, vol. 6, pp. 329-353. Drew, T. B., Koo, E. C. and McAdams, W. H., 1932, The friction factor for clean round pipes, Trans. AIChE, vol. 28, pp. 56-72. Duffie, J. A. and Beckman, W. A., 1980, Solar Engineering of Thermal Processes, pp. 135-136, Wiley, New York. Liu, Y-H, Diaz, L. A. and Suryanarayana, N. V., 1984, Heat transfer enhancement in airheating flat-plate solar collectors, Trans. ASME, J. Solar Engineering, vol. 106, pp.358363. Nikuradse, J., 1933, Stromungsgesetze in Rauhen Rohren, VDI-Forchengsheft, vol. 361. Prasad, K. and Mullick, S. C, 1983, Heat transfer characteristics of a solar air heater used for drying purposes, Applied Energy, vol. 13, pp.83-89. Prasad B. N. and Saini, J. S., 1988, Effect of artificial roughness on heat transfer and friction factor in a solar air heater, Solar Energy, vol. 41, no. 6, pp. 555-560. Qiying, P. and Laner, W., 1987, A new type of solar air collector and its application in underground space air-conditioning, Proc. ASME-JSME-JSES Solar Energy Conf., Honolulu, pp. 634-637. Scaggs, W. F., Taylor, R. P. and Coleman, H. W., 1988, Measurement and Prediction of Rough Wall Effects on Friction Factor - Uniform Roughness Results, Trans. ASME, J. Fluids Eng., vol. 110, pp. 385-391. Schlichting, H., 1936, Experimentelle Intersuchungern Zum Rauhigkeits-Problem, Ingenieur-Archiv., vol. VII, no. 1, pp. 1-34. Webb, R. L., Eckert, E. R. G. and Goldstein, R. J., 1971, Heat transfer and friction in tubes with reneated-rih roughness Int J Hpnt Mnm Trrmifvr vr»1 1A nr* £fl1_A17