Numerical Study of a Cold Storage System for Air Cooling

Numerical Study of a Cold Storage System for Air Cooling

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ScienceDirect Availableonline Available Energy Procedia 00 (2017) 000–000

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Energy Procedia Procedia 00 139(2017) (2017)000–000 16–22 Energy

International Conference On Materials And Energy 2015, ICOME 15, 19-22 May 2015, Tetouan, Morocco, and the International Conference On Materials And Energy 2016, ICOME 16, 17-20 May 2016, La Rochelle, France The 15th International Symposium on District Heating and Cooling


Numerical Study of a Cold Storage System for Air Cooling Assessing the feasibility of using the heat demand-outdoor Laila Khatraa*, Hamid El Qarniaa, Mohammed El Ganaouib temperature function for a long-term district heat demand forecast

Cadi Ayyad University, Faculty of Sciences Semlalia, Department of Physics, P.O 2390, Fluid Mechanics and Energetic (affiliated to CNRST, P.O. 40000, Morocco a,b,c a URAC 27), Marrakesh, a b c c bLorraine University, Energetic Laboratory of Longwy, (FJV/LERMAB), Henri Poincaré Institute of Longwy, P.O. 54400, France

I. Andrić


*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre

IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France


Thanks to the advantages of storing the latent heat of melting, phase change materials (PCMs) are used in many applications including building air conditioning systems. This study examines the process of solidification of a PCM in an internally finned rectangular Abstract cold storage unit. The PCM, placed in the enclosure, is initially in heated liquid state having a temperature, Ti, higher than the melting point, Tm. Heat is transferred from the energy storage unit through the left vertical wall on which fins are attached. embedded in the PCM,addressed allow increasing heat transfer thanks to their exchange for surface. The left District These heatingfins, networks are commonly in the literature as one of the most additional effective solutions decreasing the wall is in contact with a vertical throughsector. which These heat transfer (air),high having an inlet which temperature, Ta,in, through lower than greenhouse gas emissions from duct the building systemsfluid require investments are returned the the heat melting point,toTm, in the downward direction. A parametric study policies, was conducted in orderintothehighlight the impact of sales. Due the flows changed climate conditions and building renovation heat demand future could decrease, operating parameters such as air inlet temperature and flow rate on the thermal behavior and thermal performance of the cold prolonging the investment return period. storage unit.scope of this paper is to assess the feasibility of using the heat demand – outdoor temperature function for heat demand The main

forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 ©buildings 2017 Thethat Authors. Published by Elsevierperiod Ltd. and typology. Three weather scenarios (low, medium, high) and three district vary in both construction Peer-review under responsibility of the scientific of ICOME 2015estimate and ICOME 2016.obtained heat demand values were renovation scenarios were developed (shallow,committee intermediate, deep). To the error,

compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). 1.The Introduction value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and Because scenarios of their large heat storage andfunction their isothermal phase change during per charging discharging renovation considered). On the capacity other hand, intercept increased for 7.8-12.7% decade and (depending on the processes, phase change materials (PCMs) have received great the attention many applications, especially, in latent coupled scenarios). The values suggested could be used to modify functionin parameters for the scenarios considered, and heat thermal energy storage systemsestimations. (LHTES) to store thermal energy. Among the main reports of a PCM described improve the accuracy of heat demand Keywords: Cold storage; PCM; fins; rectangular enclosure; parametric study

in the literature were applications for heating and cooling in buildings. When a temperature peak occurs, PCM © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Keywords: Heat demand; Forecast; Climate change E-mail address: [email protected] 1876-6102 © 2017 The Authors. Published by Elsevier Ltd.

Peer-review under responsibility of the scientific committee of ICOME 2015 and ICOME 2016. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.

1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of ICOME 2015 and ICOME 2016 10.1016/j.egypro.2017.11.166


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absorbs the excessive energy by a phase change (melting) and releases (solidification) the absorbed energy later when this peak has passed off. This technique is aims to store a large amount of heat or cold in storage volume in such a way that the temperature of the storage is kept under a specified temperature and at the same time the excess external energy is stored. Because of the low conductivity of PCMs, several heat-transfer enhancement techniques have been reported. Using fins has been proposed by various researchers [1, 2, 3, 4]. During solidification, the conduction is the main heat transfer in the solid PCM and the fins influence on the solidification is more than melting [5, 6]. That is why this paper is focused on cold storage, as an alternative method of cooling buildings, in finned rectangular enclosure. The basis of cooling by using PCMs is to absorb or release a high amount of coolness during a phase change at an extremely low temperature difference and relatively constant temperature. This case occurs during the solidification and melting processes. The PCM is solidified during the cold storage process and is melted during the cold release process. Here, the PCM is cooled and solidified using air, as the heat transfer fluid (HTF), flowing through a rectangular duct located on the left side of a PCM rectangular enclosure. The other sides are insulated. The main objective of this study is to investigate the effect of inlet HTF temperature and HTF flow rate on the thermal storage performance. Nomenclature fl q C, b X, Y


U, V P l0 Dh A Af ef ef L Lf ec

S Lf Va(X)

liquid fraction Greek letters heat flux, W dimensionless time, (αm,l t)/ l02 τ constants (Eqs.5 and 6) θ dimensionless temperature, (T-Tm)/(Ti-Tm) dimensionless coordinates, x/l0, y/l0 λf fin spacing, m dimensionless height, H/l0 dimensionless fin spacing, λf/l0 λf dimensionless width, L/l0 δf fin- bottom enclosure wall distance, m dimensionless velocity, u/(αm,l/l0),v/(αm,l/l0) δ f dimensionless fin-bottom enclosure wall distance,δf/l0 dimensionless pressure, p/(αm,l/l0)2 ∆H latent heat of melting, (J/kg) reference length, m perpendicular ⊥ hydraulic diameter, m η peripheral distance aspect ratio of the enclosure (H/L) Subscripts aspect ratio of the fin (Lf/ef) m average, PCM or melting point fin thickness, m i initial dimensionless fin thickness, ef/l0 s solid width of the enclosure, m l liquid fin length, m in inlet dimensionless duct width, ec/l0 out outlet source term f fin dimensionless fin length, Lf/l0 a air 3l ν X dimensionless HTF velocity, y direction - 0 a Rey (1y−( )2 ) 2αm,l Dh


* Corresponding author. Tel.: (212) 613-018-993; Fax: (212)524-434-710 E-mail address: [email protected]

2. Description of problem The storage system studied in this work consists of an internally finned rectangular enclosure containing paraffin as PCM (fins made of Aluminum) (Fig. 1). The PCM, placed in the enclosure, is initially in heated liquid state having a temperature, Ti, higher than the melting point, Tm. Heat is extracted from the energy storage unit through the finned left vertical wall when cold air, as heat transfer fluid (HTF), having an inlet temperature, Ta,in, lower than the melting point, Tm, flows in the downward direction in a rectangular duct. The later has a width, ec, and is in

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contact with vertical left wall of PCM module as shown in Fig. 1. The thermophysical properties of PCM, fins and air are provided in Table 1. It should be noted that the amounts of the PCM and fins are kept constant in this study. They are proportional to the lengths l0 and l0f, respectively (l0 = (HL - 3 Lf ef)0.5, l0f2 = (Lf ef)0.5). l0 and l0f are maintained at the respective values of 0.06 m and 6.70 mm.

Fig. 1. Cold storage unit Table 1.Thermophysical properties of PCM, air and fins material. Propriety




Melting temperature, Tm (K)




Latent heat ∆H (KJ/kg)




Density ρ (kg/m )




Specific heat c (J/kg K)




Conductivity k (W/m K)




Dynamic viscosity µ (kg/ms)

3.375 x10-3


1.85 x10-5





Thermal dissipation β (K )



3. Analysis and modeling In this work, the conservation equations of mass, momentum and energy are developed to study the thermal and flow characteristics of the storage system. The energy equation for PCM is formulated using the enthalpy method developed by Voller [7]. 3.1. Simplifying assumptions The problem is two-dimensional and transient. The flow of HTF and liquid PCM are laminar. The HTF and liquid PCM are incompressible and Newtonian. The heat transfer fluid (air) flow is assumed hydrodynamically developed. The thermophysical properties of HTF and liquid and solid phases of PCM, which are provided in Table.1, are independent of temperature. For PCM, these properties are equal in both phases in temperature range [Ta,in , Ti] considered. The PCM is pure, homogeneous and isotropic. The contact between the PCM and solid areas is perfect and permanent. The solid PCM is immobilized, even if it is surrounded by liquid. The main modes of heat transfer in the PCM are conduction and natural convection. Viscous dissipation is neglected and the Boussinesq approximation is valid. 3.2. Conservation equations: Based on the above simplifying assumptions, the transient two dimensional Navier-Stokes and energy governing equations in non-dimensional forms are used in this study.


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The continuity (Eq.1), momentum (Eqs. (2 and 3)) and energy equations (Eqs.4 (PCM and fins) and 5 (Air)) are as follows: ∂ (U ∂X

• The continuity equation: • The momentum equations:


∂ (V ∂Y



= 0

  ∂ 2U ∂ (U ) ∂ (UU ) ∂ (VU ) ∂P + + =+ Pr   2 ∂τ ∂X ∂Y ∂X   ∂X

  ∂ 2U   + SU + 2    ∂Y  


  ∂ 2V   ∂ 2V   ∂ (V ) ∂ (UV ) ∂ (VV ) ∂P + + =+ Pr   + +SV 2  2  ∂τ ∂X ∂Y ∂Y   ∂ X   ∂Y  


 ∂ θ   ∂ θ   ∂ (θ ) ∂ (U θ ) ∂ (V θ ) + + = α  + + Sθ 2  2  ∂τ ∂X ∂Y  ∂X   ∂Y  


• The PCM-fin energy equation:



 ∂ 2θa   ∂ 2θ a   ∂ ( θ a ) ∂ (V a ( X ) θ a ) + = α a  + + S θa 2  2  ∂τ ∂Y   ∂X   ∂ Y  

• The air energy equation:


The expressions of the source terms, SU, SV, Sθ, Sθa, and the dimensionless HTF velocity Va(X) appearing in the equations (2), (3) and (4) are given as follows: 2 (1 - f l ) l o2 SU = - C

SV = - C





+ b)

U (C = C

2 (1 - f l )




+ b


k m ,l / c



V + Ra Pr θ


1 ∂ fl = ; Sθ = 0 f S te ∂ τ


Sθ = 0 a

3 l0 ν a X 2 ) ) ; (C te = V a ( X ) = - C t e R e y (1 − ( 2 α m ,l D ec


(9) (10)


The Rayleigh, Stefan, Prandtl, and Reynolds numbers are respectively: Ra =

ν c ∆T gβl03 ∆T ρ v Dh , Ste = m,l , Pr = m,l , Re y = a a α m,l νm,l αm,l ∆H f µa


SU and SV (eqs.6 and 7) are functions of Darcy porosity used to reduce gradually the velocity of a finite value in the liquid phase to zero in the solid regions (solid PCM, wall, fins). The constant 'C' reflects the morphology of the solidification front, whose value is set, in this study, to 109 kg.m-3.s-1 and 'b' is a small constant introduced to avoid division by zero in the case of a zero liquid fraction, i.e, 0.005. Sθm (eq.8) introduces the effect of the latent heat of phase change, ∆H, into the energy equation. This effect is accounted for by considering the variation in time of the liquid fraction, fl. 3.3. Initial and boundary conditions The initial and boundary conditions for the conservation equations are as follows: • At τ = 0: θ m = θ a = θ i = 1; U = V = 0 ; f l = 1 • Left wall of duct:

∂θa ∂X

= 0

∂θ f ∂θa = k f ;U = V = 0 ∂X ∂X ∂θ ∂θ • HTF-PCM interface: k a a = k m m ; U = V = 0 ∂X ∂X

• HTF-Fin interface:

• Inlet of duct: θ a = θ in



(12) (13) (14) (15) (16)

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• Exit of duct: ∂ θ a = 0 ∂Y • Fin-PCM interface: θ = θ , k f m


(17) f

∂θ ∂Y


= km

∂θ ∂Y

(18) m

• Adiabatic wall: ∂ θ m = 0 ; U = V = 0 Where η (X or Y) ⊥ to the wall


The PCM, fin and air dimensionless thermal diffusivity and conductivity are respectivily: α m = f l + (1- f l ) (α m,s /αm,l ); k m = f l + (1- f l ) ( k m,s /km,l )


α f = α f / α m ,l ; k f = k f /k m ,l


α a = α a /α m ,l ; k a = k a /k m,l



4. Numerical method and validation The conservative equations were discretized using the finite volume method and the power law [8]. The SIMPLE (Semi Implicit Method for Pressure Linked Equation) algorithm, developed by Patankar [8], is used to treat the coupling pressure/velocity. The resulting algebraic equations are solved using the Tri-Diagonal Matrix Algorithm (TDMA). In order to validate the reliability of the foregoing mathematical model, a comparison between the numerical results of the present study and those obtained by other researchers [9] has been made. These authors studied the solidification of superheated PCM (Table 1) in a rectangular finned enclosure with constant temperature left wall. The left vertical wall is maintained at a temperature of 287.16 K. The other walls are adiabatic. The PCM is initially at a temperature of 303.16 K higher than the melting point (301.16 K). When air circulates in the rectangular duct (Fig. 1), with a high flow rate (high velocity), the temperature of the left wall of the PCM enclosure becomes equal to that of the inlet air (287.16 K).

Fig. 2.Solid fraction time variation

Fig. 2 shows the solid fraction variation with time for the case with constant left vertical wall temperature and that for which air flows in the rectangular duct with high Reynolds number. This figure reveals that there is an acceptable agreement between the two numerical results. 5. Results and discussion The cold storage unit dimensions considered in this study, A, Af, λ f ,, δ f and ec ,, are maintained at the respective values; 4, 5, 0.33, 0.67 and 0.083. The values of Rayleigh, Ra, Stefan, Ste, and Prandlt, Pr, numbers are, respectively, 6.357x106, 0.02 and 30.375. Models of the storage are run with different inlet air temperatures, Ta,in and different air velocities, va, in the ranges [0°C (θa,in = -14) ; 4°C (θa,in = -12); 10°C (θa,in = -9); -14°C (θa,in = -7)] and [0.5 m/s (Re = 318.11); 1.0 m/s (Re = 636.22); 1.5 m/s (Re = 954.32)], respectively. Fig .3 illustrates the effects of inlet air temperature, Ta,in, and inlet air velocity on the time variation of the PCM


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solid fraction, fs, removed heat flux from PCM, q, (Figs. 3a and b) and outlet air temperature, Ta,out, (Fig. 3c) respectively. From Figures, it is clear that the decrease in the inlet air temperature, Ta,in, leads to an enhancement in the heat transfer, and as a result the PCM solidification rate increases, and the outlet air temperature drops faster. These results can be justified by the fact that as Ta,in, decreases, the effective temperature difference (Tm - Ta,in) increases as the driven potential for the diffusion and solidification process. Then, the lower the inlet air temperature, the higher is the heat flux extracted from PCM and faster is the solidification process and automatically the shorter is the total solidification time. These figures also reveal that the increase in the inlet air velocity improves the returned heat flux and leads to a rapid solidification and reduction in the outlet air temperature. This is evident, since increasing flow rate results in a higher Reynolds number and an increase in heat transfer from the PCM to air. Consequently, the higher air velocity corresponds to a rapid solidification, higher extracted heat flux and a rapid decrease in outlet air temperature.

Fig. 3. Time wise variation of solid fraction and removed heat flux ((a) and (b)) and outlet air temperature (c).

The decrease of heat flux and outlet air temperature as time passes can be explained by the increase of PCM solid thickness and, then, of the conductive thermal resistance with time. When the solidification touches its end, extracted heat flux associated to smaller inlet air temperature or higher air velocity drops quickly. This is due to the rapid growing of the solid PCM layer and consequently to the associated higher conductive thermal resistance. 6. Conclusion A numerical investigation is presented for the solidification process in an internally finned rectangular thermal energy storage unit using air as heat transfer fluid. In this study, we focus on cold storage problem. The effects of operating parameters as air velocity and inlet air temperature on the performance of the cold storage unit are analyzed. It is found that an increase of air velocity or a decrease of inlet air temperature leads to a decrease in solidification time, an increase of extracted heat flux from PCM and a rapid drop of outlet air temperature. The presented numerical model provides a good prediction of the performance of thermal storage systems in building applications during cold storage process. But, it is useful to investigate cyclic process (solidification-melting) designs for air conditioning systems for various climatic conditions. References [1] Mosaffa AH, Talati F, Basirat Tabrizi H, Rosen MA. Analytical modeling of PCM solidification in a shell and tube finned thermal storage for air conditioning systems. Energy and Buildings 2012;49:356–361. [2] Al-Abidi AA, Mat S, Sopian K, Sulaiman MY, Mohammada ThA. Numerical study of PCM solidification in a triplex tube heat exchanger with internal and external fins. International Journal of Heat and Mass Transfer 2013;61:684–695. [3] Gharebaghi M, Sezai I. Enhancement of heat transfer in latent heat storage modules with internal fins. Numerical Heat Transfer Part A 2008;53:749–765. [4] Butala V, Stritih U. Experimental investigation of PCM cold storage. Energy and Buildings 2009;41:354–359. [5] Lamberg P, Lehtiniemi R, Henell AM. Numerical and experimental investigation of melting and freezing processes in phase change material storage. International Journal of Thermal Science 2004;43:277–287.


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[6] Stritih U. An experimental study of enhanced heat transfer in rectangular PCM storage. Int J Heat Mass Transf 2004;47:2841–2847. [7] Voller VR, Cross M, Markatos NC. An enthalpy method for convection/diffusion phase change. Int. J. for Num. Meth. Engng 1987;24:271284. [8] Patankar SV. Numerical Heat Transfer and Fluid Flow. Washington: Hemisphere; 1980. [9] Khatra L, El Qarnia H, El Ganaoui M, Lakhal EK. Numerical investigation of heat transfer solidification in a rectangular enclosure with internally horizontal partial fins. Computational Thermal Sciences 2015;7,293-312.