Thermohydraulic Characteristics of Mixed Convection in Rectangular and Square Plain Ducts and Ducts with
Twisted-Tape Inserts
S. K. SAHA
Mechanical Engineering Department
BengalEngineeringCollege(A Deemed University)
Howrah 711 103, West Bengal
INDIA
Abstract: -The present paper reports the results of an experimental investigation of the UWHF heat transfer andisothermal pressure drop characteristics of combined free andforced convection laminar flow of servotherm mediumoil through horizontal rectangular and square plainducts and ducts inserted with full-length twisted tapes, short-length twisted tapes and regularly spaced twisted-tape elements. Bothfriction factor and Nusselt number increase withdecreasing y and AR for AR ≤ 1 and increasing Re, Swand Pr. As the tape-length decreases, both friction factor and Nusselt number decrease. Friction factor increases as s decreases and Nusselt number increases as s increases. The flow is divided into free convection, combined free and forced convection and forced convection zones.Isothermalfriction factor correlation and comprehensive Nusseltnumber correlation have been developed to predict datareasonably well in the entire range of parameters. Performance evaluation showed that short-length twisted tapes are worse and regularly spaced twisted-tape elements are better than the full-length twisted tapes.
Key-Words : - Mixed Convection, Laminar Flow, Twisted-Tape,Heat Transfer Augmentation, Swirl Flow, UniformWall Heat Flux.
1Introduction
Various types of twisted tapes are used for laminar flow heat transfer augmentation [1-10]. Patil [11] studied the friction and the heat transfer characteristics of laminar swirl flow of pseudoplastic type power-law fluid in a circular tube using varying width full-length twisted tapes under a uniform wall temperature condition. Saha et al. [12] have experimentally studied the friction and heat transfer characteristics of laminar swirl flow through a circular tube fitted with regularly spaced twisted-tape elements.Saha and Dutta [13] have made an experimental thermohydraulic study of laminar swirl flow through a circular tube fitted with twisted tapes.Manglik et al. [14] have worked in the scaling and correlation of low Reynolds number swirl flows and friction factors in circular tubes with twisted-tape inserts. In this paper experimental results of pressure drop and heat transfer measurements of mixed convection in rectangular and square plain ducts and ducts with twisted tapes, along with the correlations for friction factor and Nusselt number, are reported.
2Experimental Setupand Operating Procedure
A schematic diagram of the experimental set up is shown in
Fig. 1. The set-up consists of (i) a storage tank in which the working fluid is stored, (ii) a working fluid circulating loop, (iii) the test section, (iv) the calming section (v) an accumulator and (vi) a cooling water supply system. The working fluid, Servotherm Medium Oil, was circulated through the loop by a gear pump driven by a 2 kW electric motor. An accumulator in the circulating loop limited fluctuation of the pressure. A pressure gauge indicated the delivery pressure of the pump. Isothermal pressure drop measurements were taken in Perspex ducts. The heat transfer test section was smooth 18/8 (18% chromium, 8% nickel) stainless steel duct. The test section was 2m long. Test section was heated electrically by wrapping uniformly two nichrome heater wires. The heater wires were connected through autotransformers. All the ducts had width of 13 mm. The square duct had a depth of 13 mm and two rectangular ducts had depths of 26 mm and 39 mm giving aspect ratios, AR of 1, 0.5 and 0.333. The twist ratios of the twisted tapes were y = 2.692, y = 5.385, y = 2.597, y = 5.193, y = 2.308 and y = 4.615. The space ratios were s=2.692, s=5.385, s=2.597, s=5.193, s=2.308, s=4.615. The power supplied to the test section was measured by calibrated Wattmeters. The inlet and outlet bulk fluid temperatures to the test section were measured by thermocouples. The mixing chamber at the exit of the test section was meant for thorough mixing of the circulating fluid. A three junction thermopile was used to record the temperature rise of the working fluid in the test section accurately. Teflon spacer discs reduced axial conduction of heat at the ends of the test section. Test section had 28 thermocouples brazed at seven axial positions ( each axial position had four thermocouples; one each at the middle of four edges of the cross-section) on the outer surface of the duct wall to measure its temperature. The test section duct was thermally well insulated. There were ten pressure taps made of small pieces of Perspex tubes. The circulating fluid was cooled by water in a coil-in-shell heat exchanger. The actual flow rate was measured by collecting the working fluid in a container. The time of collection was recorded by a stop watch. The thermocouples were connected to a 36 point selector switch box, which in turn was connected to Hewlett-Packard digital multimeter and a single cold junction at 00C.The twisted tapes were made in the laboratory from a 0.5 mm thick stainless steel strip. Tape-fin effect was eliminated by covering the twisted tapes with insulating tapes before these were inserted into the test section.
Performance of the thermocouples was checked. The oil flow rate was controlled to the desired value by adjusting the valves. Heat flux was controlled by autotransformers. A steady state was obtained after 3 to 4 hours. All thermocouple readings were noted. The mass flow rate of oil was measured. The power input to the test section was measured.The friction factors were calculated from the pressure drop measured by manometer. The local Nusselt numbers were axially averaged by Simpson’s rule of numerical integration.
Uncertainty analysis was carried out as suggested by Kline and McClintock [15] and the uncertainty involved in the estimation of friction factor and Nusselt number were within + 5% and + 8%, respectively.
3Results and Discussion
Various parameters are presented before the results are presented and discussed.
Dh = (4 A' )/ P ; A' = w. d ;
w = width of the duct cross-section ;
d = depth of the duct cross-section ;
P = perimeter = 2 ( w+ d ) ;
δ = 0.0005 m ; y = H/Dh
Sw = Resw / (√ y ) = ( Re/√ y ) ( π / (π – 4 δ / Dh )) ( 1 + (π / 2y )2 )0.5
Resw = ( ρVsDh)/µ
Re = (ρV0 Dh)/µ
Vs = Va [(1+(π/2y)2]0.5
V0 = ; Va =
A0 =π(Dh)2/4 ;
Ac =[π(Dh)2/4]-δDh
(fRe )sw, y = ∞ = 17.355 ( ( π + 2 – 2 δ / Dh ) / ( π – 4 δ / Dh))2
[determined currently by
experiments for rectangular and square ducts. ]
( fRe)sw = ( fRe) (( π – 4 δ / Dh ) / π ) ( 1 + (π / 2y )2)-1
(fRe) is based on the envelope or
plain duct dimensions.
f = ( 1 / 2 ) [ ( ∆ Pz ) / ( ρ (V0 )2) ]
( Dh / z );
z = Length of pressure drop
measurement, m
Reax = ( ρ Va Dh ) / µ ;
Ra = Rayleigh no. = Gr. Pr;
Ls = L ( 1+(π/2y)2 )1/2
fsw = ∆ P Dh / ( 2 ρLs )
= f ( L / Ls ) ( Vo / Vs )2
Data have been generated for:
Hydraulic diameter, Dh = 13 mm,
17.33 mm, 19.50 mm
Aspect ratio, AR = 1, 0.5, 0.333
Twist ratio, y 2.5, 5.0
Space ratio, s 2.5, 5.0
Twisted-Tape length, l = 1, 0.9, 0.7, 0.5
Mass flow rate, -- 1.185 – 42.050
kg / min
Reynolds number, Re --- 30 < Re
< 1100
Prandtl number, Pr --- 80 < Pr < 500
Heat flux, q" – 1105 – 29461 W / m2
∆ Tb = Tbo – Tbi --- 2 – 20oC
∆ T = Twi – Tb --- 1.5 – 25oC
3.1Short-Length Twisted-Tape
Friction Factor Results
Effect of Twist Ratio
Figures 2-3show the effects of twist ratio ( y ) on friction factor. Friction factor increases as the twist ratio decreases, i.e. the tape-twist increases for a given twisted-tape length and the aspect ratio since the swirl intensity increases and the friction surface area increases. However, the increase in friction factor is not very large since y=5.0 does not make very large difference in swirl intensity from that in case with y = 2.5 and the velocity profile does not get much flatter in case of y = 5.0 than that in case of y = 2.5.
Effect of Twisted-Tape Length
Figures 4-5 show the effects of twisted-tape length ( l ) on friction factor. Friction factor decreases as the twisted-tape length decreases for a given twist ratio and the aspect ratio since the friction surface area decreases and the swirl decays early and perhaps straight flow sets in. It is also observed that the larger the tape-length the more prominent the effect of tape-length and as the twisted-tape becomes shorter beyond a certain point, the effect of tape-length is not very palpable since the effect of swirl developed to its full intensity is more important than the frictional surface area. The Figs. also show that the tighter the tape-twist the more prominent the effect of twisted-tape length since the swirl persists further downstream of the twisted-tape and the setting-in of straight flow is delayed.
Effect of Duct Aspect Ratio
Figures 6-7 show the effects of aspect ratio of the duct on friction factor. It is observed that the effect of aspect ratio is by far the most prominent and it is extremely palpable. As the aspect ratio (1) decreases, the friction factor increases for a given twist ratio and twisted-tape length; and this effect is evenly palpable irrespective of the values of twist ratio and tape-length. This can be appreciated since the lower the aspect ratio the more the mixing of the more-asymmetric velocity profiles and the secondary motion and associated momentum loss.
Nusselt Number Results
The heat transfer experiments were conducted for all the cases as it was done for pressure drop measurements. Figures 8-13 show the effects of twist ratio, twisted-tape length and duct aspect ratio on Nusselt number. All observations for heat transfer measurements are generally true in the similar way as those were for pressure drop measurements. However, it is observed that the effect of duct aspect ratio is not as conspicuous as it was in case of pressure drop measurements. This can be explained from the fact that, for the moderate Prandtl number range as in the present investigation, the thermal boundary layer is very thin and the duct aspect ratio does not have significant effect on thermal boundary layer thickness and the consequent convective thermal resistance.
3.2Regularly Spaced Twisted-Tape Elements
Friction Factor Results
Effect of Duct Aspect Ratio
Figure 14 shows the effect of duct aspect ratio on friction factor and it is observed that, for a given y and s, the friction factor increases with the decrease of duct aspect ratio ( < 1 ). Friction factor sharply increases when aspect ratio decreases from unity to 0.5. However, friction factor does not increase as much when aspect ratio decreases from 0.5 to 0.333. This observation is true for all y and s. This is explained from the fact that as the aspect ratio decreases from unity up to a certain value, the secondary flow causes vigorous mixing and consequent increase in pressure drop; this effect is not very conspicuous when the duct aspect ratio continues to decrease beyond that.
Effect of Twist Ratio
Figure 15 shows the effect of twist ratio on friction factor. For a given aspect ratio and space ratio, the friction factor increases with decrease in twist ratio; although the increase is not very sharp. This is quite palpable and precludes any further explanation.
Effect of Space Ratio
Figure 16 shows the effect of space ratio on friction factor. For a given twist ratio and aspect ratio, friction factor increases as s decreases because of more frequent mixing and associated momentum loss. Also small s means more number of twisted tape elements and more friction surface and more pressure loss.
Nusselt Number Results
Figures 17-19 show the effects of duct aspect ratio, twist ratio and space ratio on Nusselt number. All observations for heat transfer measurements are generally true in the similar way as those were for pressure drop measurements. However, it is observed that the effect of space ratio is reverse and more prominent than that was in case of pressure drop measurements. Here, the Nusselt number increases with increase in s for a given aspect ratio and twist ratio. This is due to the fact that, for viscous flow as in the present case, the buoyancy force in annular space region becomes more important than the decaying swirl flow.
4Correlations
For square duct as well as rectangular ducts of aspect ratio, AR,having full-length twisted-tape inserts the correlation has been found to be
× R-1.46 ---- (1)
where R =AR, for AR 1 and R= for AR > 1.
For short-length twisted-tape inserts inside square and rectangular ducts, the fully developed isothermal friction factor is correlated by log-linear regression fit as
× R-1.46 (1+ aX + bX2 + cX3 ) –(2)
where R =AR, for AR 1 and R= for AR > 1 and
a = -8.51E-2b=7.16E-3
c=-2.81E-4 and X=(1-l)0.2Sw0.425
For regularly spaced twisted-tape elements inserts inside square and rectangular ducts, the fully developed isothermal friction factor is correlated by log-linear regression fit as
× R-1.46 (1+ aX + bX2 + cX3 ) –(3)
where R =AR, for AR 1 and R= for AR > 1 and
a = 2.86E-3b=-1.23E-5c=1.45E-8 and X=Sw0.425 s exp(ds)
For constant wall heat flux applied to square and rectangular ducts fitted with full-length twisted tapes, the length-averaged Nusselt number correlation has been found by log-linear regression fit
× ( R + 0.1 )0.15 ---(4)
where R =AR for AR 1 and R=for AR < 1.
For short-length twisted-tape insert in square and rectangular ducts under constant wall heat flux, the length-averaged Nusselt number is correlated as
× ( R + 0.1 )0.15 ×
( 1 + aX + bX2 + cX3 ) ------(5)
where R =AR for AR 1 and R=for AR < 1 and
a=-6.18E-3b=4.15E-5
c=-5.96E-8X=(1-l)0.2Sw0.531Pr0.3
For regularly spaced twisted-tape elements insert in square and rectangular ducts under constant wall heat flux, the length-averaged Nusselt number is correlated as
× ( R + 0.1 )0.15 ×
( 1 + aX + bX2 + cX3 ) ------(6)
where R =AR for AR 1 and R=for AR < 1 and
a=1.48E-3b=-8.16E-7
c=1.32E-10X=Sw0.531Pr0.3 s exp(ds).
All correlations have been found to predict the experimental data within + 20 % .
5Conclusions
The flow is divided into three zones : forced convection, combined free and forced convection and free convection causing secondary flow induced by buoyancy effect due to fluid density gradient.
The present experimental data and the performance evaluation show that the short-length twisted-tape in square and rectangular ducts, through which laminar flow occurs under constant wall heat flux boundary condition, performs worse than the full-length twisted-tape. However, regularly spaced twisted-tape elements perform significantly better than the full-length twisted tapes.
Nomenclature
A: heat transfer area, m2
Ac : flow cross-sectional area, m2
Ao: plain duct flow cross-sectional
area, m2
AR : L/H, aspect ratio, dimensionless.
Cp : constant pressure specific heat,
J/kgK
D : internal diameter (hydraulic
diameter) of the duct, m
Dh : hydraulic diameter of the test
duct [=(4Ac/P)], m
d : diameter of the rod, m
f : fully developed friction factor,
dimensionless
fsw : swirl flow friction factor,
dimensionless
g : gravitational acceleration, m/s2
Gr: Grashof number
[gβρ2 (Dh)3∆Tw/µ],
dimensionless
Gz : Graetz number [Cp/kL],
dimensionless
H : pitch for 1800 rotation of twisted-
tape, m
h : heat transfer coefficient,
W/(m2K).
k : fluid thermal conductivity,
W/(mK).
L : axial length, m
: mass flow rate, kg/min
Nu : axially averaged Nusselt number
[(hDh)/k], dimensionless
∆P : pressure drop, N/m2
P : wetted perimeter in the particular
cross-section of the duct, m
Pr : fluid Prandtl number [(µCp)/k],
dimensionless
Ra : Rayleigh number = Gr Pr
Reax : Reynolds number based on axial
velocity, dimensionless
Resw : Reynolds number based on swirl
velocity, dimensionless
Re : Reynolds number based on plain
duct diameter [ρVaDh)/µ],
dimensionless
Sw : dimensionless swirl parameter
∆T : wall to fluid bulk temperature
difference, K
Va : mean axial velocity, m/s
Vo : mean velocity based on plain duct
diameter, m/s
Vs : axial swirl velocity at duct
wall, m/s
y : twist ratio = (H/Dh), strip ratio,
dimensionless.
Greek Symbols :
β : coefficient of isobaric thermal
expansion, K-1
δ : tape thickness, m
µ : fluid dynamic viscosity
kg/ms.
ρ : density of the fluid,
kg/m3.
Subscripts :
ax : at axial flow condition
b : at bulk fluid temperature
h : hydraulic diameter
sw : at swirl flow condition
w : at duct wall temperature
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