BUILD SIMUL (2009) 2: 273 – 280 DOI 10.1007/s12273-009-9224-y

Numerical simulation of phase change heat transfer of a solar flat-plate collector with energy storage Research Article

Donghua Peng, Zhenqian Chen ( ) School of Energy and Environment, IIUSE, Southeast University, Nanjing 210096, China

Abstract

Keywords

The technical feasibility of an innovative solar collector is studied in this paper. A phase change material (paraffin) is used in the solar collector to store solar energy. This type of system combines both collection and storage of thermal energy into a single unit. The major advantages of the

solar energy,

phase change stores are their large heat storage capacity and isothermal behavior during the melting and solidifying processes. A negative aspect of paraffin is its low thermal conductivity

aluminum foams

which increases the melting and solidifying time for paraffin energy storage. In this paper, new aluminum foams infiltrated with paraffin are presented. It presents a two dimensional model describing the melting and solidifying processes of paraffin while accounting for both phase change heat transfer and natural convection. Apparent heat capacity method was used to simulate the melting and solidifying processes of paraffin. The simulation results show that the motion of the hot liquid paraffin plays an important role in increasing the heat transfer between

numerical simulation, paraffin,

Article History Received: 24 February 2009 Revised: 1 November 2009 Accepted: 2 November 2009 © Tsinghua University Press and Springer-Verlag 2009

paraffin and top surface of solar collector. The shape profile of the pure paraffin solid-liquid interface is determined by the synergistic relationship between its temperature and velocity field. Though aluminum foams impregnated with paraffin will limit motion of the hot liquid paraffin, the heat transfer ability is greatly improved. The distributions of the temperature in the paraffin with aluminum foams are more homogeneous compared with that of the paraffin without aluminum foams. Thus, use of aluminum foams infused with paraffin improves heat transfer and enhances paraffin’s melting and solidifying rates.

1

Introduction

E-mail: [email protected]

Building Systems and Components

The continuous increase in levels of greenhouse gas emissions and fuel prices are driving forces behind efforts to more effectively utilize renewable energy sources. In many parts of the world, direct solar radiation is considered to be one of the most promising alternative energy sources. Solar energy collectors are a special kind of heat exchangers that transform solar radiation energy to heat the medium, such as water or phase change materials. A major component of any solar system is the solar collector. This device absorbs the incoming solar radiation, converts it into heat, and then transfers this heat to a fluid (usually air, water, or oil) flowing through the collector (Kalogirou 2004). Flat-plate solar collectors are the most common solar water heating systems used in homes

and for solar space-heating (Sözen et al. 2008). Due to the discontinuity characteristics of solar energy and the development of building integration, a solar collector is needed to coordinate between architecture and environment. The integrated solar collector with energy storage is considered a promising technology for increasing the economic feasibility of low temperature solar systems that heat water for domestic, agricultural, and industrial applications. This type of system combines the collection and storage of thermal energy into a single unit. Compared with the conventional domestic water heating system, the proposed paraffinintegrated solar collector has several advantages: (a) anti-freeze protection is not required in cold areas; (b) the phase change stores have a large heat storage capacity and isothermal behavior during the melting and solidifying processes; and (c) it’s a simple system with no special requirements for maintenance and operation. However, a negative aspect of

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List of symbols C cp dp ep eg g hrp1 hcp1 hr12 hc12 hr2a

inertial coefficient (m–1) the specific heat of the paraffin (J/(kg·K)) the mean particle diameter (m) emittance of absorber plate emittance of glass gravitational acceleration (m/s2) the radiant heat transfer coefficient between the absorber plate and inner glass cover (W/(m2·K)) the convective heat transfer coefficient between the absorber plate and inner glass cover (W/(m2·K)) the radiant heat transfer coefficient between the two glass covers (W/(m2·K)) the convective heat transfer coefficient between the two glass covers (W/(m2·K)) the radiant heat transfer coefficient between the outer glass cover and the environment (W/(m2·K))

paraffin is its low thermal conductivity, which increases the melting and solidifying times. Many studies have examined how to enhance the thermal conductivity of phase change materials (PCMs). Experimental studies used melted PCMs mixtures to investigate the enhancement of the heat absorption of energy storage with multiple phase change materials (Wang et al. 2001). The results showed that use of multiple PCMs enhances the charging rate of the PCM energy storage. Velraj et al. (1999) performed a detailed investigation of different heat transfer enhancement methods used in latent heat thermal storage systems, such as the use of fins and lessing rings. They concluded that the application of these methods is highly suitable for solidification enhancement. Recent advances in the field of the cold storage were reviewed by Saito (2002). The PCM considered was the composite proposed and reported by Py et al. (2001), which has a high thermal conductivity and a stable thermal capacitance. Hawlader et al. (2003) investigated the performance of energy storage and release capacity of microencapsulated PCMs. The lumped capacitance and enthalpy methods were compared by Alva et al. (2006). A salt-hydrate phase-change material stored in the solar collector was presented by Rabin (1995). In this study, we use newly-developed high porosity aluminum foams infused with phase change material (paraffin) to store solar energy in order to enhance the effective thermal conductivity of the paraffin composite. Previous studies paid little attention to the natural convection of phase change material during the melting process. Thus we compared the melting and solidifying processes of paraffin with aluminum foams with that of pure paraffin. The heat transfer and natural convection processes are also analyzed. The numerical

hw hls K Lg T α

ε

λ

μ ρ σ

wind heat transfer coefficient (W/(m2·K)) the latent heat of paraffin (J/kg) permeability of the aluminum foams (m2) thickness of the glass cover (m) temperature (K) thermal expansion coefficient (K–1) porosity thermal conductivity (W/(m·K)) dynamic viscosity of liquid paraffin (kg/(m·s)) density (kg/m3) Stefan-Boltzmann constant (W/(m2·K4))

Subscripts l s

liquid paraffin solid paraffin

model is based on the volume averaging technique while the finite volume method has been used to discretize the heat diffusion equation. A line-by-line solver based on a tridiagonal matrix algorithm, TDMA, was used to iteratively solve the algebraic discretization equations. 2 2.1

Schematic and numerical solutions Physical model

The schematic of the proposed paraffin-solar collector is shown in Fig. 1. The model is a multilayer system consisting of the following elements: two transplant covers, two air layers, a selective absorber plate, and a 50 mm paraffin layer. The length of the collector is 500 mm. In order to efficiently calculate and build the mathematic model, it is simplified based on the following assumptions. (1) Paraffin is isotropic. (2) When paraffin is melted, the fluid is Newtonian. (3) The flow of liquid paraffin in aluminum foams abides by the Darcy-Brinkman-Forchheimer Law. (4) Phase transition occurs within a temperature range of 335 − 345 K. (5) In a single phase region, physical properties are temperature independent. Conversely, the physical properties in solid-liquid region are essentially linear with temperature. (6) The surface tension and curvature effects at the interface are assumed insignificant. (7) The influence of water flow through the serpentines pipe on the temperature field of the paraffin is ignored. (8) The ambient temperature is constant at 298 K.

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Mathematical model

Based on the above assumptions, the continuity, momentum, and energy equations can be written for the two-dimensional laminar flow of an incompressible Newtonian fluid in an unsteady-state regime. To determine the governing equations, we assumed that there is no viscous dissipation and that gravity acts in a vertical direction. The Boussinesq approximation is accepted in this article (Varol and Oztop 2008). The momentum equations for the melting paraffin in aluminum foams could be simplified as follows: Continuity equation ∂ρ ∂( ρu) ∂( ρv ) + + =0 ∂τ ∂x ∂y

(1)

Momentum equations ρl ∂u ρl ⎡ ∂(uu) ∂(uv ) ⎤ μ ∂ 2u ∂2u ∂p + 2⎢ + + ⎥ = − eff + ε ∂τ ε ⎢⎣ ∂x ε ∂x 2 ∂y 2 ∂y ⎥⎦ ∂x μ ρl C − + 1 u u + ρl gα(T − Tc )sin θ K K2

(

(

μ

(K +

)

ρl C K

1 2

) (3)

where, peff and Tc are the pressure (Pa) and the reference temperature (K) in the metal foams, respectively. Energy equation ∂( ρT ) ∂( ρuT ) ∂( ρvT ) ∂ λ ∂T ∂ λ ∂T + + = + ∂τ ∂x ∂y ∂x c p ∂x ∂y c p ∂ y

(

) (4)

where,

(6)

cs ⎧ ⎪ ⎪ ⎪ ⎪ h c + cl cp (T ) = ⎨⎪ ls + s ⎪ 2ΔT 2 ⎪ ⎪ cl ⎪ ⎪ ⎩

T < Tm − ΔT Tm − ΔT - T - Tm + ΔT

(7)

T > T m + ΔT

λs ⎧ ⎪ ⎪ ⎪ ⎪ λl − λs [T − (Tm − ΔT )] λ =⎪ ⎨ λs + ⎪ 2ΔT ⎪ ⎪ λ ⎪ ⎪ ⎩ l

T < Tm − ΔT Tm−ΔT - T - Tm + ΔT T > Tm + ΔT (8)

where, h ls is the latent heat of paraffin (J/kg); cp is the specific heat of the paraffin (J/(kg·K)); λ is the thermal conductivity of the paraffin (W/(m·K)); ΔT is the phase change transition temperature (K); Tm is the phase change temperature of the paraffin (K). Initial condition

λ

)

)

1.75(1 − ε) dp ε 3

(2)

v v + ρl gα(T − Tc )cos θ

(

C=

Boundary conditions

∂p ρl ∂v ρl ⎡ ∂(vv ) ∂(uv ) ⎤ μ ∂2v ∂2v + 2⎢ + + ⎥ = − eff + ε ∂τ ε ⎣⎢ ∂y ε ∂x 2 ∂y 2 ∂x ⎦⎥ ∂y −

(5)

T (x , y ,0) = Tinit

)

(

dp2 ε 3 150(1 − ε)2

dp is the mean particle diameter (m); ε is the porosity of the aluminum foams; K is the permeability of the aluminum foams (m2); μ is dynamic viscosity of the liquid paraffin (kg/(m·s)); θ is the tilt angle of the collector. The apparent heat capacity and effective thermal conductivity of the paraffin in different phase zones are introduced as

Fig. 1 Schematic of the solar collector with energy storage

2.2

K=

∂T = q − U t (T − Tf ) τ > 0; y = L ∂y

(9)

∂T =0 ∂x

τ > 0; y = 0

(10)

∂T =0 ∂x

τ > 0; x = 0, x = L

(11)

where, q is the solar irradiance (W/m2); Ut is the heat loss coefficient on the top surface of solar collector (W/(m2·K)); Tf is the atmosphere temperature (K); L is the solar collector thickness (m) . The effective thermal conductivity of porous media can be calculated as follows (Chen and Wei 2007): λe =

λ1λ2 (1 − ω) λ1 + ωλ2

(12)

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where, λ1 = (1 − ε) λg + ελf λ2 =

(13)

λg λf (1 − ε) λf + λg ε

(14)

λg is the thermal conductivity of the aluminum frame and λf is the thermal conductivity of paraffin inside the aluminum foams (W/(m·K)), ω is ratio of vertical to total channels. In this paper, the vertical channels process a large proportion of conductivity compared with horizontal channels, so ε is 0.9, ω is 0.98. For annual use, a solar collector is installed , such that the title angle is on buildings at south latitude 32° . Heat flux is shown in Fig. 2 (Zhang 2007) and the 32° thermophysical properties of paraffin and aluminum are presented in Table 1.

an upward direction. The approximate method has found acceptance among researchers (El-Sebaii 1997; Chaudhuri 1998) in the area of solar thermal applications. Others (Agarwal and Larson 1981; Duffie and Beckman 1991) presented their own empirical formulae, but they were not as accurate in correlating with variables in other ranges. Samdarshi and Mullick (1991) proposed an analytical expression for the calculation of Ut in double glazed, flat-plate collectors as follows: U t−1 = (hrp1 + hcp1 )−1 + (hr12 + hc12 )−1

hrp1 =

+ (hr2a + hw )−1 + 2Lg / λg

(15)

σ (Tp2 + T12 )(Tp + T1 ) 1/ ep + 1/ eg − 1

(16)

hr2a = σeg (T22 + Ta2 )(T2 + Ta )

2.3

Proposed method for predication of the heat loss coefficient

The top heat loss coefficient (Ut) is evaluated by considering convection and radiation losses from the absorber plate in

hr12 =

σ (T22 + T12 )(T2 + T1 ) 2/ eg − 1

(17)

(18)

The radiant heat-transfer coefficient and the convective heat-transfer coefficient between the absorber plate and the inner glass cover are hrp1 and hcp1, respectively. The radiant heat-transfer coefficient hr12 and convective heat-transfer coefficient hc12 between the two glass covers can be obtained like hrp1, hcp1. The radiant heat-transfer coefficient between the outer glass cover and ambient temperature is expressed as hr2a. To estimate the temperature of the outer glass cover, T2, we used the following empirical relations (Samdarshi and Mullick 1991). The sky temperature is assumed equal to ambient temperature. An approximate value of the outer glass cover temperature, T2, can be obtained by considering the following relationship: T2 − Ta R2a = = Φout Tp − Ta Rp1 + R12 + R2a Fig. 2 Hourly variations of total solar irradiance Table 1 Material properties of the materials used for heat transfer Materials

Paraffin

Aluminum

Melting point (℃)

62 − 72

—

Latent heat (kJ/kg)

224

—

Density (kg/m3) Specific heat (kJ/(kg·K)) Thermal conductivity (W/(m·K))

Solid

837.7

Liquid

772.2

Solid

3.2

Liquid

2.8

Solid

0.35

Liquid

0.15

2719 0.871

(19)

The factor Фout is a function of the individual heat-transfer coefficients. An empirical relation for the factor Фout is obtained as a function of the variables Tp, εp and hw: Φout = (0.0021Tp + 0.57ep − 0.146)h−w0.4

(20)

From Eq. (19): T2 = Ta + Φout (Tp − Ta )

202.4

That is

(21)

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T2 = Ta + h−w0.4 (0.0012Tp + 0.37ep − 0.146 )(Tp − Ta )

(22)

The value of the inner glass temperature, T1, can be obtained by considering the relationship Tp − T1 Rp1 = = Φin Tp − T2 Rp1 + R12

(23)

The resistance to the heat transfer from the plate to the glass is not a function of the wind heat-transfer coefficient. An empirical relation for Фin is obtained as a function of ep only, Φin = 0.7 − 0.34ep

(24)

From Eq. (23): T1 = Tp − Φin (Tp − T2 )

(25)

That is T1 = Tp − (0.7 − 0.34ep )(Tp − T2 )

(26)

are investigated. The simulated results are presented in Figs. 3 − 10. Figure 3 shows the temperature distributions of paraffin after 3 hours of solar radiation. Heat is mainly transferred by conduction from the hot absorber surface to the inner paraffin at the beginning of the melting process. The distributions of temperature in the pure paraffin are nonuniform. The temperature at the upside of the collector is much higher than at the backside. A sharp decrease in the temperature gradient can be seen in the solar collector with pure paraffin. In Fig. 3(b), the temperature distribution in the paraffin with aluminum foams is uniform. This is because the effective thermal conductivity of the composite is much higher than that of pure paraffin. After formation of a liquid layer around the absorber plate, the liquid phase moves inward due to the buoyancy force. Because of the high viscous effect at the beginning, the paraffin is in a mush region and the natural convection is ignored, but is still considered when the paraffin is melted. The temperature distributions of pure paraffin and composite at 16:00 are shown in Fig. 4(a) and (b), respectively. At this time, the paraffin has melted. Due to natural convection, the liquid phase starts to move inward, and due

where, Tp is the temperature of absorber plate (K); Ta is the ambient temperature (K); ep and eg are the emittance from the absorber plate and the glass, respectively; R is the heat transfer resistance (K/W). The subscripts a, p, 1 and 2 denote atmosphere, absorber plate, inner glass cover, and outer glass cover, respectively. 2.4

Numerical solution

The governing equations are discretized using a finite volume approach. The standard Semi-implicit Method for Pressure Linked Equations Consistent (SIMPLEC) algorithm is used to solve the coupled continuity and momentum equations. A fully implicit formulation is used for the time-dependent terms. A line by line solver based on a tri-diagonal matrix algorithm is used to iteratively solve the algebraic discretized equations. A calculation program is used to simulate the paraffin melting and solidifying processes. In this simulation, the ambient temperature is 298 K during the day and night. The initial temperature of paraffin is 298 K at 6:00. The solar irradiance from 18:00 to 6:00 on the second day is zero. 3

Results and discussion

The temperature distribution of pure paraffin as an energy storage medium and the high porosity aluminum foams saturated with paraffin as a composite energy storage material

Fig. 3 (a) The temperature (K) distributions of paraffin without aluminum foams with solar radiation at 9:00, (b) the temperature distributions of paraffin with aluminum foams with solar radiation at 9:00

278

to the buoyancy force, the isothermal is different from that shown in Fig. 3. The temperature of pure paraffin at the top of collector is about 31℃ higher than that at the bottom of collector because of the low thermal conductivity of paraffin wax. While in Fig. 4(b), the temperature at the top of collector is less than 1℃ higher than that at the bottom of collector because of the high thermal conductivity of paraffin with aluminum foams. The temperature distributions of paraffin with solar radiation at 6:00 on the second day are showed in Fig. 5. From 18:00 to 6:00 on the second day, the solar radiation is zero. The process of the solar collector is solidifying. As shown in Fig. 5(a), the paraffin temperature at the top of collector is about 20℃ higher than that at the bottom of collector. The paraffin at top of the collector is not complete in the solid or mush region and some of them is also in liquid region. While in Fig. 5(b), all of the paraffin is in the solid region, and the temperature is 345 K. Figure 6 shows the flow field of the pure paraffin with solar radiation at 6:00 on the second morning. Because the top temperature exceeded 345 K, the liquid motion is

Peng and Chen / Building Simulation / Vol. 2, No. 4

considered. Figure 5(a) shows that the top of the pure paraffin is liquid and that the temperature of lower portion of the collector is higher than that of upside collector. The velocity direction is therefore different from that of 10 hours

Fig. 5 (a) The temperature distributions of paraffin without aluminum foams with solar radiation at 6:00 on the second day, (b) the temperature distributions of paraffin with aluminum foams with solar radiation at 6:00 on the second day

Fig. 4 (a) The temperature distributions of paraffin without aluminum foams with solar radiation at 16:00, (b) the temperature distributions of paraffin with aluminum foams with solar radiation at 16:00

Fig. 6 The flow field of paraffin without aluminum foams with solar radiation at 6:00 on the second day

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after solar radiation. The temperature difference is small near the solid region, so the velocity gradient relatively smooth. In the top domain, the velocity gradient drops sharply. In this paper, the temperature and velocity field are synergistic. The solid-liquid interface for the pure paraffin at different times during the melting /solidifying cycles is displayed in Fig. 7. At the beginning of the melting period, 9 h, a considerable thickness of paraffin has melted. The melted region at the top became thicker due to the motion of hot liquid natural convection. Thus, after 10 h of solar radiation, the curve became increasingly sharp. At 6:00 on the next morning, the tendency of the solid-liquid interface is different from that of other times. The liquid region is offside. As shown in Figs. 5(a) and 6, there is some paraffin wax that did not solidify by 6:00 on the next morning. The shape profile of the solid-liquid interface is determined by both the temperature and velocity field. As shown in Fig. 4(a), the temperature gradient of the liquid pure paraffin is similar to the solid-liquid interface, which suggests that the direction of the heat flux points to the melting interface. Because of the existence of the solid-liquid interface, the temperature gradient of the solid pure paraffin is minor. Figure 8 shows the variation in the liquid fraction at different time. From the curves, pure paraffin in the solar collector is not completely melting and about 20% of paraffin wax is in a solid state. However, the paraffin with aluminum foams matrix in the solar collector is rapidly melting and it melts completely in approximately 370 seconds. Due to the low thermal conductivity of the pure paraffin, the solidifying time of pure paraffin in the solar collector is also longer than that of paraffin with aluminum foams in the solar collector. The response time or the time for melting and solidifying is a key factor in designing any energy storage system, especially applications that are restricted to a limited time for energy absorption. The melting and solidifying time of the energy storage depends mainly on

the thermal properties of the energy storage material. The higher the thermal conductivity, the better response this energy storage can achieve. Thus, the composite paraffin solar collector is more effective than a pure paraffin wax solar collector in energy storage. Figure 9 shows temperature distributions in x direction at the bottom of solar collector. At 9:00, the paraffin has not melted. The temperature does not change with the horizontal coordinates. The temperature in the composite paraffin is about 13℃ higher than that of pure paraffin wax. When the pure paraffin starts to melt, the isothermal is not straight due to the natural convection of the hot liquid

Fig. 7 The solid-liquid interface for pure paraffin at different solar radiation time

Fig. 9 The temperature distributions in x direction at the bottom of solar collector

Fig. 8 Variation in the liquid fraction over time

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paraffin. The temperature gradually increases at the top of the pure paraffin collector. We observed that the convection heat transfer in the liquid phase plays an important role in the melting process, and that the melting and solidification times can be changed by placing the paraffin storage in different positions. At 16:00, the bottom temperature of pure paraffin changes quickly. The temperature of composite is approximately 32℃ higher than that of pure paraffin beside x = 0 mm position. Because of the liquid paraffin convection, the pure paraffin temperature at x = 500 mm is nearly equal to the composite temperature. The temperature in the pure paraffin is inhomogeneous, and the natural convection of liquid phase plays an important role in enhancing temperature. 4

Conclusions

This study numerically examines phase change heat transfer of paraffin with aluminum foams in the PCM-integrated solar collector. The results show that the use of aluminum foams in the paraffin has considerable impact on both the heat transfer enhancement and melting / solidifying rate of paraffin. The effective thermal conductivity of paraffin is greatly increased with the use of aluminum foams. The temperature distributions of paraffin with aluminum foams are more uniform than that of paraffin without the aluminum foams. And the time of melting and solidifying of paraffin with the aluminum foams is greatly decreased compared with that of pure paraffin. With the solar radiation, the pure paraffin in the solar collector can not completely melt and some remains in the solid phase, while the paraffin with aluminum foams in the solar collector can completely melt in short time. The results also show that the motion of the hot liquid paraffin plays an important role in increasing the temperature of the top layer of paraffin. Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 50776015) and the National Key Technologies R&D Program of China (Grant No. 2007BA000875-04).

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