Experimental analysis of fluid flow and heat transfer in a finned tube thermosyphon system.

Rao, M. Basaveswara ; Sharma, K.V. ; Rajasekhar, Y. 等

Introduction

Flat plate collectors (FPC) are sophisticated greenhouses that trap the incident solar energy to heat water. The FPC's are used to obtain hot water for applications in the temperature range up to 600C. The most important feature of the thermosyphon type solar flat plate collector is its operation without the use of an electrical pump. This makes the system work with negligible operating and maintenance cost and hence widely used for domestic hot water requirements. The heat transfer takes place to fluid medium by circulation in a closed loop under natural convection. It requires that a storage tank be located at a higher elevation to maintain proper head for flow of water by gravity. The design of such systems requires information on the rate of heat transfer and resulting flow and their interactions with various parameters governing the process. This has drawn the attention of the many researchers in the area of solar energy to conduct both theoretical and experimental studies to determine the heat transfer rate and to estimate the losses prevailing in the FPC. The energy absorbed by the flowing fluid can be determined if the mass flow rate of the fluid under specified conditions is known there by the efficiency and the losses from the collector can be calculated.

Experimental Setup

Test Setup

To investigate the flow characteristics of a closed loop thermosyphon system, indoor tests are performed with fin tube assembly set at an angle of 20[degrees] inclination (latitude of Hyderabad) with the horizontal. The fin tube assembly consisting of a copper tube (12mm dia, 18 SWG thick) with two fins (11.5 cm wide, 24 SWG thick) attached 180[degrees] apart with selective coating is used along the 1.97 m length in the experimental setup. This forms part of a conventional solar flat plate collector, rather than the usual nine-fin tube array. The glass wool insulation at the bottom of the conventional FPC is replaced with Aerocon insulating panel measuring 2.0 x 0.3 m on which the single fin tube assembly is fixed. The effective area of the fin-tube assembly measures approximately 0.24 [m.sup.2].

Apparatus

To sense the temperature changes of water inside the tube at different values of applied heat flux, an array of six thermocouples is inserted three inside and three outside the tube along the liquid flow line. The junctions of Iron-Constantan thermocouples are fixed inside a small diameter copper tube. 'Araldite' epoxy material is used to prevent corrosion due to contact of water with thermocouple during working conditions. A hole is drilled to this copper tube for the iron-constantan thermocouple end to be in contact with the flowing fluid, located at the center of the tube and fixed inside with the adhesive epoxy material. All the thermocouples used in the present setup are so chosen that they can measure up to 120[degrees]C. A flat strip heater of 500W capacity is provided to supply heat uniformly along the fin tube assembly which is curved one. To have proper contact between the tube and the heater for transfer of heat uniformly all along the fin, the gap between the two is filled with 14micron thin aluminum foil so that the heat transfer from heater to fin takes place effectively. The convection heat loss to environment from the heater is arrested by rock wool insulation, which is stuffed on top of the heater strip and covered with aluminum sheet and fixed to Aerocon panel with bolts. Provision is made to control the flux through a voltage regulator provided in the control panel. The whole assembly of Aerocon panel along with single finned tube is placed over an adjustable iron stand of 1.2 m x 0.5 m x 1.5 m such that the inclination of the assembly can be varied. A cylindrical water tank of 25 cm dia and 1 m length of 50 liter capacity made of mild steel (18 SWG thick) is provided on a stand. The tank has provision for cold water inlet from the water mains and a closed loop with the test apparatus with PVC hosepipe connected to inlet and outlet headers. The water tank is insulated with a 2-inch thick rock wool insulation material. To study the effect of heat flux on the mass flow rate and heat transfer coefficient to fluid, the heat flux is changed from 100W/[m.sup.2] to 1000W/[m.sup.2] by adjusting the input current through the control panel. The control panel consists of a Voltmeter, Ammeter, Digital temperature indicator, power on/off switch, a 12 channel female pin to connect the thermocouples and an autotransformer.

Readings of the Experiment are taken at ambient temperature with distilled water. The temperatures from various thermocouples are noted at regular time intervals. As the mass flow rate of water is very low the flow rate, the flow is measured manually, by collecting a standard volume of hot water leaving the FPC, through a tap connected to the tank. The time taken for collection of known volume of hot water is noted and from which the mass flow rate of water through the experimental setup simulating FPC is estimated.

[FIGURE 1 OMITTED]

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Formulation of The Problem

The values of Reynolds number calculated are less than 2300, obtained for different input values of heat flux in the range of 100-1000 W/[m.sup.2], the flow is in the developing region. The data from the experiments are compared with theory and the relevant expressions are presented in the Appendix. Considering flow through a small diameter pipe (length-to-diameter ratio is low) the v-momentum equation and the second derivatives in u-velocity and temperature appearing in the momentum and energy balance equations are neglected.

Results and Discussion

From theoretical analysis of hydrodynamically and thermally developing flow inside tube geometry, the variation of heat transfer coefficients is shown in Fig. 3 for Re = 900 and 1800, Pr = 3 and 5. The increase in Re is to extract more thermal energy from the wall and hence higher values of Nusselt number can be observed. This data is obtained from the experimental thermosyphon system, inclined at an angle of 20[degrees] with the horizontal. The range of Grashof Number (Gr) calculated for the given inclination angle is from 2.5 x [10.sup.4] to 1 x [10.sup.9]. To determine the effect of Gr on local Nusselt, theoretical results are shown plotted in Fig.4. The effect of increase of Gr is to enhance buoyancy force and hence higher heat transfer rates can be expected. Fig. 5 is shown plotted for the average values of heat transfer coefficients varying with Reynolds number for different values of Pr. The data obtained from experiments is shown together with the theoretical results which are in close agreement indicating the validity of the theoretical model proposed. To further validate the experimental data, the regression equation of Siddiqui [1997] for estimation of (Nu Gr/Pr) with Reynolds number is shown for the present data in Fig. 6. The equation of Sarma et al [2003] for estimation of friction factor in the developing flow with flow Reynolds number is plotted in Fig. 7. Evidently, the friction factor decreases with increasing value of Re. Morrison [1972, a] has evaluated the mass flow rate of water in an experimental thermosyphon system. He found that the flow rates lie between 0.02 ml/s to 10 ml/s approximately for low to high fluxes absorbed by the system. However, no equation was proposed to relate the flow rate with heat flux. The mass flow rates from different sources are shown plotted in Fig. 8 for different values of heat absorbed. The present experimental data obtained from a conventional FPC available in the Centre for Energy Studies, is plotted in Fig. 8 against the data obtained by Morrison [1972, b] to test the validity. All the data points are in close agreement as evident from Fig. 8. The deviation of the values obtained under steady state and that of the transient is [+ or -] 20%. These data points are set to regression analysis to help in determining the mass flow through a thermosyphon system for a given quantity of absorbed flux. The variation of Inlet, Outlet temperature of water for different ambient conditions and increasing heat flux is shown in Fig.9. It is observed that the Inlet and outlet temperature of water increases exponentially with increasing heat flux.

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Conclusions

Theoretical and experimental studies have been conducted on the single finned tube thermosyphon system. The conclusions are summarized as follows:

(1) The local heat transfer coefficient decrease from high values at the entrance region representing the developing boundary layer near the entry and gradual decrease in the remaining length representing the developing flow.

(2) The average heat transfer coefficient increase with increase in heat flux and is in close agreement with the values obtained under actual operating conditions.

(3) The mass flow rates increases with increase in heat flux. The increase of mass flow rate is in satisfactory agreement with the values obtained by Morrison [1].

(4) The Reynolds number of flow increases with increase in heat flux and the flow gradually turns to forced laminar from mixed laminar regime.

Nomenclature

Nu          Nusselt number (hd/k)

Ra          Rayleigh number, Gr.Pr

Re          Reynolds Number

d           diameter of the tube, m

g           Acceleration due to gravity, m/[s.sup.2]

Gr          Grashof number, g[beta]'[d.sup.3] ([DELTA]T)/
            [[upsilon].sup.2]

Pr          Prandtl number

h           convective heat transfer coefficient, [Wm.sup.-2] [K.sup.-1]

L           spacing between the absorber plate and glass cover

[DELTA]T    Temperature difference, [degrees]C

[T.sub.pm]  Absorber Plate mean Temperature, [degrees]C

Z           Non Dimensional Distance Greek symbols

[sigma]     Stefan-Boltzman constant, [Wm.sup.-2] [K.sup.-4]

[beta]'     Film Temperature, [K.sup.-1]

[upsilon]   kinematic viscosity

[delta]     Inclination angle of the pipe

[alpha]     Tilt angle of the collector tube with the horizontal

[theta]     Temperature Ratio

Appendix

Considering flow through a small diameter pipe (diameter-to-length ratio is low) the v-momentum equation, the second derivatives in u-velocity and temperature appearing in the momentum and energy balance equations are neglected. Thus the governing equations in radial coordinates can be written as

1/r [partial derivative]/[partial derivative]r (v r) + [partial derivative]u/[partial derivative]z = 0 (1)

u [partial derivative]u/[partial derivative]z + v [partial derivative]u/[partial derivative]r = -1/[rho] [partial derivative]p/[partial derivative]z + v ([[partial derivative].sup.2]u/[partial derivative][r.sup.2] + 1 [partial derivative]u/r [partial derivative]r) + g (2)

u [partial derivative]T/[partial derivative]z + v [partial derivative]T/[partial derivative]r = v/Pr ([[partial derivative].sup.2]T/[partial derivative][r.sup.2] + 1 [partial derivative]T/r[partial derivative]r]) (3)

Let [[rho].sub.0] be the atmospheric pressure. Consider the pressure and gravity terms on RHS from the momentum, balance equation.

- [partial derivative]p/[partial derivative]z + [rho] g = [partial derivative] (p - [p.sub.0)/[partial derivative]z [[rho].sub.0] g + [rho] g cos[delta] (4)

- [partial derivative]p/[partial derivative]z + [rho] g = -[partial derivative] (p - [p.sub.0)/[partial derivative]z + [rho] g [beta] [T - [T.sub.0) cos[delta] (5)

[partial derivative]u/[partial derivative]z + v [partial derivative]u/[partial derivative]r = -1/[rho] [partial derivative] (p - [p.sub.0)/[partial derivative]z + v ([[partial derivative].sup.2]u/[partial derivative][r.sup.2] + 1/r [partial derivative]u/[partial derivative]r + [rho] g [beta] (T - [T.sub.0]) cos[delta] (6)

where,

T = Inlet temperature of the fluid.

T0 = outlet temperature of the fluid.

The numerical solution to these equations for the case where both the velocity and temperature profiles are developing is determined. The velocity and temperature profiles are considered to be symmetrical about the center line of the pipe and the radial velocity component,?, is therefore zero at the center line.

The following are the boundary conditions valid in this case

At r = 0; [partial derivative]u/[partial derivative]r = 0, v = 0, [partial derivative]T/[partial derivative]r = 0

At the wall, the velocity component is zero and the temperature constant and specified, i.e., the boundary conditions at the wall are:

At r = [r.sub.0] : U = 0,v = 0, T = [T.sub.w]

[r.sub.0], being the radius of the pip, i.e., [r.sub.0] = </DO>2 where D is the diameter of the pipe. The governing equations are written in terms of the following dimensionless variables:

U = u/[u.sub.m], V = vRePr/[u.sub.m], P = (p - [p.sub.0)/[rho][u.sup.2.sub.m]

Z = z/Re Pr D, R = r/D, [theta] = (T - [T.sub.0])/([T.sub.W] - [T.sub.0])

References

[1] G.L. Morrison (1972, a), "Thermosyphon Circulation in Solar Collectors", Solar Energy Vol.24, pp 191-198

[2] G.L. Morrison (1972, b), "Transient response of Thermosyphon Solar Collectors", Solar Energy, Vol.24, pp. 41-55.

[3] M. Altamush Siddiqui (May 1997), "Heat transfer and fluid flow studies in the collector tubes of a closed-loop natural circulation solar water heater", Energy Conversion and Management, Volume 38, Issue 8, Pages 799-812.

[4] P.K. Sarma, T.Subramanyam, P.S.Kishore, V.Dharma Rao, (2003), "A Novel method to determine the convective heat transfer in the Entry region of a tube".

M. Basaveswara Rao * (1), K.V. Sharma (#) and Y. Rajasekhar (#)

* Swami Vivekananda Institute of Technology (SVIT), Secunderabad, A.P, India - 500 003.

(#) Centre for Energy Studies, JNTUH College of Engineering, Kukatpally, Hyderabad, A.P, India - 500 085. E-mail: cesjntu@yahoo.com

(1) Corresponding author: E-mail: blmalladi@gmail.com