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Multi-layer PCM solidification in a finned triplex tube considering natural convection
Accepted Manuscript Multi-Layer PCM Solidification in a Finned Triplex Tube Considering Natural Convection Ali M. Sefidan, Atta Sojoudi, Suvash C. Saha, Michael Cholette PII: DOI: Reference:
S1359-4311(17)30729-9 http://dx.doi.org/10.1016/j.applthermaleng.2017.05.156 ATE 10471
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
3 February 2017 2 May 2017 27 May 2017
Please cite this article as: A.M. Sefidan, A. Sojoudi, S.C. Saha, M. Cholette, Multi-Layer PCM Solidification in a Finned Triplex Tube Considering Natural Convection, Applied Thermal Engineering (2017), doi: http://dx.doi.org/ 10.1016/j.applthermaleng.2017.05.156
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Multi-Layer PCM Solidification in a Finned Triplex Tube Considering Natural Convection Ali M. Sefidan1, Atta Sojoudi2, Suvash C. Saha3, Michael Cholette3 1
Young Researchers and Elite Club, Tabriz Branch, Islamic Azad University, Tabriz, Iran 2
Mechanical Engineering Department, University of Tehran, Tehran, Iran 3
School of Chemistry, Physics & Mechanical Engineering
Queensland University of Technology, 2 George St., GPO Box 2434, Brisbane QLD 4001, Australia
ABSTRACT Efficient latent heat storage systems represent an important opportunity to improve the thermal performance and operational capability of industrial systems (e.g. solar thermal). In this paper, numerical study is performed to evaluate the heat transfer and solidification features, phase change period and temperature distribution of double-layer Phase Changing Materials (PCM) in a finned triplex tube. A two-dimensional finite volume numerical technique is used to solve the governing equations considering conduction and convection heat transfer mechanisms at a fixed Rayleigh number of 106. After comparing the results for single and double layer configurations, possible arrangements of two different PCMs are discussed in terms of different thicknesses of each PCM, fin sizes and different heat transfer fluid temperatures. Results are illustrated as the form of temperature, liquid fraction, stream function and velocity magnitude contours and their changes over the freezing time. Variation of liquid fraction values, average and minimum temperatures of layers in a double-layer PCM are reported for better insight into the heat transfer features of the latent heat thermal energy storage system to enable uniform discharging designs and balance the phase changing rate within the whole annulus.
KEYWORDS: Numerical Simulation; Solidification; Multi-Layer PCM; Natural convection; Triplex tube; Fins.
1. INTRODUCTION Due to rising energy demands and limited resources, interest in designing energy storage systems for heating and cooling applications has rapidly increased in different many industries [1]. To this end, Latent Heat Storage (LHS) is one of the most promising techniques. In particular, the application of Phase Change Materials (PCMs) as LHS is well-established due to their large energy capacity, modest temperature fluctuation, chemical stabilities and small vapor pressure at their working temperature [2]. These specifications have made PCMs promising for many applications such as building structures [3], electronic cooling devices [4], recovering waste heat [5] and lots of other applications. Several recent studies regarding thermal energy storage systems (particularly their latent form) have optimized the amount of exchanged energy and improved their thermal conductivity. However, there are few studies, which include multi-layer arrangements of PCMs, which have significant potential to enhance the thermal performance of PCMs [6-12]. Farid and Kanzawa [6,7] evaluated the rate of heat transfer between PCMs which were filled in cylindrical containers and air flowed across them. They realized a significant enhancement in the performance of the system when they used various PCMs with different melting temperature in cylindrical containers. Two-layer PCM have been applied in buildings to provide a desirable indoor temperature for throughout the year [8]. However, utilizing one particular kind of PCM for the entire year is impossible because the PCM which is suitable for summer would remain in its solid state during the winter (and therefore store only sensible heat). Thus, designing multilayer PCMs including different PCMs which are suitable for both hot and cold seasons could lead to energy savings in buildings during the whole year. Another recent study regarding multilayer PCMs [9] has numerically evaluated the locations of two PCMs to maximize energy savings in air-conditioned area. Furthermore, the authors reported that combinations of two PCMs can reduce the energy consumption in the room regardless of annular weather changes. Brousseau et al. [10] investigated thermal behavior of various combinations of PCMs and subsequently used these properties to decrease the electricity consumption during peak times. Mosaffa et al. [11] numerically investigated the impacts of design factors on the energy storage performance of multiple-PCM within a rectangular channel. They used effective heat capacity approach in order to simulate pure conduction phase change process in PCMs and solve energy
equation considering convection terms in heat transfer fluid (HTF). Shadab S. and Khalid L. [12] used 2D numerical approach to study phase change process in different configurations of combined PCM slabs. Their main aim was to find any impact of using various arrangements of multiple PCM slabs with different melting temperatures and thermophysical properties on the total storage performance of system compared to using single kind of PCM. Their reports showed a dramatic increase in the amount of energy stored in using composite PCMs. There has been a great deal of research into designing storage units associated with cylinders and tubes to improve LHS efficiency. Researchers showed that thermo-physical properties of PCMs have significant effects on LHS performance [13-17]. In particular, the low thermal conductivity of PCMs has been widely discussed in literature [13-17]. Tao et al [13] have utilized an experimental approach to study effects of PCM thermo-physical properties on unit performance. They employed various PCMs with different properties to evaluate LHS performance and then reported the optimized performance. Similar numerical tests have also been conducted considering the impact of PCM physical properties and different geometries and materials of heat exchangers on the performance of LHS [14]. Improving heat transfer between the PCM and a particular boundary or fluid, researchers considered different ideas: extending surfaces using fins [15], employing excessive tubes [16] or utilizing micro-encapsulated PCMs [17]. Using fins is a common approach to elongate the interacting surface due to their simplicity and inexpensiveness. Several reports for various designs of fins in tubes containing inner and outer fins [18] and cylindrical or rectangular shaped fins are available. Wang et al. [19] numerically investigated the influences of fin geometry and conductivity of outer cylinder during the melting process of PCM. Mosaffa et al. [20] analytically studied the effects of radial fins on the solidification process of PCM in vertical shell and tube heat exchanger. They reported that freezing process took place more rapidly in cylindrical shell compared with a rectangular shell. Agyenim et al [21] carried out an experimental study within a horizontal concentric tube using Erythritol as a PCM to assess the effects of longitudinal and circular fins on heat transfer rate. Their results showed that longitudinal fins lead to a rise in thermal reaction during melting process. Rathod et al. [22] investigated the effects of longitudinal fins on freezing and melting cycles of paraffin as a PCM. Their experimental study was carried out in vertical shell and tube heat exchanger and showed a large decrease in the solidification and melting time of up to
43.6%, and 24.5% respectively by employing fins. One of the most recent fin design studies was done by Eslamnezhad et al. [23] for a triplex tube heat exchanger. In this study, the structure of fins was altered to increase the heat transfer rate and decrease melting time, while the surface area between the fins and PCM was kept constant. Sarviya et al [24] considered the effects of natural convection during numerical simulation of melting process within a solar storage system using longitudinal fins. Erek et al. [25,26] numerically studied the influences of radial fins in a horizontal latent heat storage system. They investigated the effects of fin radius and fin spacing on the heat transfer rate of the module. They reported that for a particular arrangement of fins, system performance will be increased considerably. Chiu and Martin [27] investigated the performance of shell-and-tube LHS unit considering the effects of various design parameters. They found that by reducing the fin spacing, heat transfer rate increases. Ismail et al. [28] performed an experimental and numerical simulation in order to evaluate the effects of fin design parameters of an annular container on the solidification rate and total energy stored by PCMs. Stritih [29] compared the melting and solidification rate of an LHS unit in two cases: with a finned surface and with plain surface. They found that solidification process is more dependent on presence of fins than melting process. Sciacovelli et al. [30] introduced innovative fins to improve the performance of shell-and-tube LHS unit. They performed a numerical method to optimize the geometry of Y-shaped fins with single and double bifurcations. Their results showed that system efficiency increases considerably by using optimized fins. They also designed optimal fins for different operating time of the unit. Taghilou and Talati [31,32] studied the melting and solidification of PCM within a rectangular finned container. They focused on the numerical approach based on the Lattice Boltzmann Method (LBM) to show how the fins accelerate the phase change process. They also discussed the effects of natural convection on the melting procedure of fixed and free solid phases defining the Rayleigh number. Employing a porous matrix saturated with PCM [33,34] and including nanoparticles [35-37] are other common methods which provide both higher energy storage capacity and higher diffusivity to compensate some deficiencies of PCMs. To the best of our knowledge based on literature, few experimental or numerical studies have been conducted about melting or solidification process incorporating multi-layer PCMs in the finned cylindrical geometry. Therefore, this paper presents a numerical study to investigate the
impacts of incorporating RT50 and RT35 as two different types of PCMs with various operating temperatures on the heat transfer features and the freezing performance in finned triplex-tube capsule. It is noteworthy to mention that RT series of PCMs are organic materials which are chemically inert and therefore have stable performance through the phase change cycles. Simulations are carried out considering natural convection effects on the flow structure and results are reported as average and minimum temperature variations of PCMs over freezing period, the whole solidification time, liquid fraction, stream function and velocity magnitude contours of each PCM. Effects of different arrangements and various thicknesses of PCMs with considering fins to have a better insight into the heat transfer phenomenon are discussed. 2. RESEARCH METHODOLOGY 2.1. Physical model and boundary conditions The physical model of the triplex tube capsule is displayed in Fig. 1. The inner cylinder radius is r0=10mm, the intermediate cylinder radius is r=30mm and the outer cylinder radius is R=60mm. The thickness of cylinders and employed fins are th=1mm and Aluminum pipes and fins are used for the triplex tube. Three different models are defined as in Fig. 2. Four fins are stretched from the inner cylinder to the outer one in model-1. In model-2 and model-3 the four radial fins are joined with a cylindrical fin and additional radial fins. To see the effects of employing double layer PCM, we separate model-3 into two sections, each with a different PCM. Further details of each of these models can be found in Table 1. The inner cylinder is used for heat transfer fluid (HTF) and two other annuluses (Sections A and B) are filled with two different PCMs (RT35 and RT50). Table 2 represents thermo-physical properties of two PCMs and solid Aluminum. A constant temperature boundary condition is applied for the inner wall of the smallest cylinder (Tinner is varied from 278K to 298K) while the outer wall of the largest cylinder is considered perfectly insulated. The initial temperature of the PCMs, containers and fins are Tini=323.1K at t=0sec which is higher than freezing point of both RT35 and RT50 and the PCMs are considered fully liquid. For t>0 the whole sections are subjected to constant temperature of the inner cylinder. Although the intermediate cylinder is attached to the inner cylinder and solidification process initiates from inside the inner cylinder boundary, heat is transferred through Aluminum fins, so it is possible for solidification to start in the outer cylinder prior to the completion of
solidification in the inner cylinder. In this study, all the cases are simulated until complete solidification of both of the PCMs. The Rayleigh number for each PCM is defined as in which ΔT is the difference between the solidification temperature of each PCM and the HTF temperature, β expresses thermal expansion coefficient, g is gravitational acceleration, D is the diameter of the section,
and α are kinematic viscosity and thermal
diffusivity of PCMs respectively. This number is fixed at 106 in all our simulations. 2.2. Governing equations During the solidification process, conduction heat transfer takes place through fins and solid state of PCMs while natural convection occurs in liquid phase of PCMs due to temperature gradients and leading density variation. Therefore, buoyancy driven flow should be considered for the liquid state of the PCM through sections A and B. Apart from temperature, density depends on the phase too, and it suddenly varies during melting or solidification process due to different thermophysical properties of solid and liquid phases. Therefore, two types of density changes should be taken into account during phase change processes. For example, most PCMs expand during melting process (
) and will have a volume shrinkage when they pass from solid to
liquid phase. This expanded volume affects the rate of phase change process and heat transfer features more considerable than a sudden density change [38]. So, if we consider a fixed volume for our computational domain, applying different density amounts for solid and liquid phases will not change our results significantly. Moreover, difference between solid and liquid densities of both RT35 and RT50 is less than 10% and setting negligible volume changes for PCMs seems acceptable. To develop a mathematical model, the liquid phase is considered for both PCMs while they are thermally coupled. Unsteady, laminar and incompressible flow is assumed for the liquid phase and attributed flow. As a whole, the following assumptions are made: 1) Constant thermo-physical properties for each phase; 2) Negligible volume changes of PCMs; 3) Boussinesq approximation for density variation of liquid phase; 4) Newtonian liquid phase; 5) Negligible viscous dissipation; 6) No slip boundary condition for cylinder walls and fins; 7) Negligible super cooling effect; 8) No heat transfer to the surroundings. The governing equations of the problem including continuity, momentum and thermal energy equations are defined as following:
Continuity equation: =0
(1)
Momentum equation: (2) Energy equation: (3) Where ρ is the density of the PCM, ui is the fluid velocity, μ is dynamic viscosity, p is pressure, g is the gravity acceleration, k is thermal conductivity, T is the fluid temperature, and h is sensible enthalpy of RT35 and RT50. This sensible enthalpy is defined as: (4)
The total enthalpy is:
(5) Where href is the reference enthalpy at the reference temperature Tref, cp is the specific heat, and ΔH attributes to the latent heat of PCM materials that leads a phase from liquid to solid state. The liquid fraction during the PCM solidification process, γ, is: (6)
(7)
Phase variation happens when the temperature is between solid and liquid phase temperature. The source term Si in momentum equation, Eq. (2), is:
(8)
Brent et al. [39] introduced porosity function, Eq. (8), which follows from the Carman Kozeny equations for the flow across porous media. Here, C determines the rate of velocity reduction to zero when the material changes from liquid to solid. The value is varied from 104 to 107 according to the PCM property. For current modeling, this value is taken to be 106 and ε is a very small value defined in Ref. [39]. Boussinesq approximation is as following [40]: (9)
in which ρl and β are the density of the PCM material at the freezing temperature and the thermal expansion coefficient, respectively. 2.3. Numerical model The unsteady pressure based method is utilized for the numerical modeling of the problem employing ANSYS FLUENT, V16. Modeling mushy zone, this Finite Volume Method (FVM) based code assumes ''pseudo'' porous medium for PCM sections with porosity equal to the liquid fraction. The porosity reduces from 1 (liquid) to 0 (solid) as the material solidifies and the velocities also fall to zero. Triangular shaped (unstructured) cells are selected for meshing the geometry which are finer close to the walls due to higher gradients of quantities. Second order accuracy is selected for discretization of momentum and energy equations. The PRESTO technique is employed for discretization pressure term. The value of convergence criterion for all equations is set to be 10-6 and a time step size of 0.2 sec is found to be small enough to ensure an independent and stable solution. The under-relaxation factors for the continuity, momentum and thermal energy are 0.5, 0.3 and 0.8 respectively. 2.4. Mesh independency and time-step independency Different number of cells were tested to evaluate dependency of the results on mesh number. Moreover, 3 different time step size were selected. Fig. 3 displays performed tests on mesh independency and time step size tests for liquid fraction values per time. It is seen that, results
for different number of cells and time step size are very close to each other, so, in order to reduce computational cost and also having enough accuracy, number of 22558 cells with 0.2sec time step size were selected. 2.5. Validation To validate our employed numerical model, some cases from Ref. [18] have been regenerated in order to compare with our results. These comparisons are displayed in Fig. 4. As it is seen, our numerical solution agrees suitably with both numerical and experimental results of mentioned reference. 3. RESULTS AND DISCUSSIONS 3.1. Effects of employing double-layer PCM and fins At first, before expressing the effects of employing double-layer PCM, model-1 and model-2 are simulated to analyze the effects of using fins and more compartments (model-2 in Fig. 2) on solidification process. The results of model-1 in which the whole annulus was filled with a single PCM (first RT35, then RT50) are shown in Fig. 5. This figure displays liquid fraction, minimum and average temperature of two mentioned cases during solidification process. It is seen that RT35 solidified after almost 7300sec while RT50 needed approximately 6000sec. This is attributed to the fact that, difference between heat transfer fluid temperature (288K) and solidification temperature of RT50 (323K) is higher than that of RT35 (308K) which lead to higher rate of heat transfer in the first case. The minimum temperature of two PCMs dropped quickly to 288K and then stayed at this level for the rest of the solidification process and no significant difference was seen between two cases over the time. Due to contact between the inner cylinder and PCM in section A, this pattern is repeated for other simulations again. The average temperature of RT35 was lower than RT50 at the end of the process since the freezing time for RT35 was longer than RT50. The simulation results using model-2 are displayed in Fig. 6. As it is seen, by employing fins of model-2 which have been shown in Fig. 2, there are a considerable decrease in freezing time. The whole solidification process dipped by almost 25% using RT35 but the figure for RT50
decreased by about 48%. The minimum and average temperature for two sections are displayed separately in Fig. 6, and the lowest average and minimum temperature did not differ significantly in comparison with model-1. According to these initial results, which was strongly related to the thermo-physical properties of materials, two other numerical tests were performed (model-3) to ensure the applicability and efficiency of multi-layer PCM capsule. The two different arrangements of model-3 were simulated. A comparison of these arrangements with H=R-r and r/r0=3 are shown in Figs. 7. Fig. 7-a displays liquid fraction of two arrangements for different sections during the solidification process. It can be seen that when RT35 was placed in section A (arrangement type-1) it solidified later than when RT50 was placed in the same section (arrangement type-2). This was due to the previously mentioned fact that RT50 had a higher temperature difference with HTF and solidified sooner than RT35. For section B, again RT50 (arrangement type-1) solidified sooner than RT35, because in spite of the fact that section B was far from heat transfer source, RT50 repeatedly had benefitted from its high temperature difference between HTF rather than RT35. According to the results, the whole freezing period in arrangement type-2 took more time in comparison with arrangement type-1. The whole period for arrangement type-1 was 3125sec while the number for arrangement type-2 was 5421sec. The minimum temperature for the both arrangements were same for section A because of straight touch with inner wall. But for section B, minimum temperature for two arrangements was a little different, this refers to the solidification temperature of the PCMs. Although in terms of average temperature, RT35 was lower in both sections (both arrangements) than RT50, because both of PCMs were solidifying and since their operating temperatures were different, in each arrangement, the average temperature of RT50 was major than that of RT35. According to our results which were discussed before, arrangement type-1 (RT35 in section A and RT50 in section B) was used for the rest of simulations due to lower overall solidification time. The freezing time for arrangement type-1 (model 3) is close to that of model-2 when RT50 was used. When using two different PCMs, the PCM in section A solidified sooner in model-2 than for model-3. Solidification time for different models are reported in table 3. As it is seen, the solidification rate in arrangement type-1 is rather equal for both sections in comparison with model-2.
3.2. Effects of thicknesses of each PCM in the double-layer PCM By keeping R and r0 fixed, effects of thickness of each PCM (r/r0 ratio) in the double-layer PCM was investigated. The influence of varying r/r0 are displayed in Fig. 8. Fig. 8-a illustrates liquid fraction of two sections during solidification process for various thicknesses of PCMs. It is known that large area leads to higher Rayleigh number, therefore increasing the r/r0 ratio and thus natural convection effects became stronger in section A. In spite of this fact, as the r/r0 ratio increased RT35 took longer to solidify. Besides, the size of section A and consequently the embedded material size (RT35) became larger in this case. Again, in section B, by decreasing the amount of material which was filled in, the freezing time went down. For r/r0=5 in particular, the amount of material was too small the heat transfer area was relatively high. Therefore, the solidification process took less time in comparison with other r/r0 ratios. From Fig. 8-b, the minimum temperature in section A was the same for different thicknesses at all times. However, in section B the minimum temperature of various cases reached to almost a same amount of almost 290K at the end of the period in different times. Fig. 8-c shows that the average temperature of RT35 in section A for different thicknesses remained close to 294K at the end of the period but in different times. The figure for r/r0=2 was a bit different. However, the RT50 in section B experienced lower temperatures for higher r/r0. 3.3. Effects of fin size (H) in section B The influence of H on liquid fractions of two sections are shown in Fig. 9-a. It is seen that for larger H, the time needed for solidification of section B was shorter. Larger H enhanced the effect of fin on heat removal from section B. Consequently, higher H fins affected negatively on section A and thus section B solidified faster for larger H. In Fig. 9-b, the minimum temperature of section A did not differ for all sizes of H and passing time, but for section B, there was a bit difference between various cases in time. The average temperature of section A (Fig. 9-c) was reduced gently for lower H, while higher H leaded to decrease in the average temperature in section B. Fig. 10-a to Fig. 10-e display the liquid fraction, temperature, stream function and velocity magnitude contours for various H size during t=100sec to t=3000sec. Rotating cells (due to natural convection) can be seen for section A at early, but as the area of A was solidified the size
of cells was reduced and natural convection effects diminished. Rotating cells activated in section B at the later stages of the simulation. As the size of H was increased number of cells increased. The velocity magnitude was higher for larger H at later times and this fact improved the efficiency of solidification process for section B. 3.4. Effects of HTF temperature Fig. 11-a shows heat transfer fluid temperature effect on liquid fractions of the both sections. It can be seen that the lower the temperature of heat transfer fluid, the sooner the both section turn into solid state. This effect is related to the higher rate of heat transfer for lower HTF temperatures. From Fig. 11-b it is seen that minimum temperature was lower for small HTF temperature at both sections. Average temperature of the both sections had the same status as minimum temperature as it is shown in Fig. 11-c. 4. CONCLUSIONS Numerical experiments have been performed to study solidification process of multi-layer PCM within a fined triplex capsule. RT35 and RT50 were used for two sections of the annulus regions. A two-dimensional Finite Volume numerical technique was used to solve the governing equations considering conduction and convection heat transfer mechanisms. Different arrangements of layers, fin sizes, intermediate cylinder sizes and heat transfer fluid temperature were tested and following outcomes are stated:
Employing fins of model-2 (Fig. 2), has decreased the whole freezing period considerably.
By using two different PCMs (multi-layer PCM), the solidification rate in two sections takes place more simultaneously in comparison with using one kind of PCM in both sections in the same container and fins.
Employment of RT35 for section A and RT50 for section B led to faster solidification process as opposed to RT50 in section A and RT35 in section B.
With the increase of r/r0 ratio, section A became larger and the embedded material took much longer to solidify, but it decreased the solidification time in section B.
Larger H enhanced the effect of fin on heat removal from section B and consequently, higher H fins affected negatively on section A.
Average temperature of section A was reduced gently for lower H, while higher H leaded to decrease in the average temperature in section B.
Lower heat transfer fluid (HTF) temperatures lead to quick solidification rate in both sections.
Average and minimum temperature of both sections reached the lower amounts when the HTF temperature was small.
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Chiu, J. N., & Martin, V. (2012). Submerged finned heat exchanger latent heat storage design and its experimental verification. Applied Energy, 93, 507-516. Ismail, K. A. R., Alves, C. L. F., & Modesto, M. S. (2001). Numerical and experimental study on the solidification of PCM around a vertical axially finned isothermal cylinder. Applied Thermal Engineering, 21(1), 53-77. Stritih, U. (2004). An experimental study of enhanced heat transfer in rectangular PCM thermal storage. International Journal of Heat and Mass Transfer, 47(12), 2841-2847. Sciacovelli, A., Gagliardi, F., & Verda, V. (2015). Maximization of performance of a PCM latent heat storage system with innovative fins. Applied Energy, 137, 707-715. Taghilou, M., & Talati, F. (2016). Numerical investigation on the natural convection effects in the melting process of PCM in a finned container using lattice Boltzmann method. International Journal of Refrigeration, 70, 157-170. Talati, F., & Taghilou, M. (2015). Lattice Boltzmann application on the PCM solidification within a rectangular finned container. Applied Thermal Engineering, 83, 108-120. Lafdi, K., Mesalhy, O., & Shaikh, S. (2007). Experimental study on the influence of foam porosity and pore size on the melting of phase change materials. Journal of Applied Physics, 102(8), 083549. Mesalhy, O., Lafdi, K., Elgafy, A., & Bowman, K. (2005). Numerical study for enhancing the thermal conductivity of phase change material (PCM) storage using high thermal conductivity porous matrix. Energy Conversion and Management, 46(6), 847867. Bechiri, M., & Mansouri, K. (2016). Analytical study of heat generation effects on melting and solidification of nano-enhanced PCM inside a horizontal cylindrical enclosure. Applied Thermal Engineering, 104, 779-790. Liu, M. J., Zhu, Z. Q., Fan, L. W., & Yu, Z. T. (2016, July). An Experimental Study of Inward Solidification of Nano-Enhanced Phase Change Materials (NePCM) Inside a Spherical Capsule. In ASME 2016 Heat Transfer Summer Conference collocated with the ASME 2016 Fluids Engineering Division Summer Meeting and the ASME 2016 14th International Conference on Nanochannels, Microchannels, and Minichannels (pp. V002T08A016-V002T08A016). American Society of Mechanical Engineers. Dhaidan, N. S., Khodadadi, J. M., Al-Hattab, T. A., & Al-Mashat, S. M. (2013). Experimental and numerical investigation of melting of NePCM inside an annular container under a constant heat flux including the effect of eccentricity. International Journal of Heat and Mass Transfer, 67, 455-468. Alexiades, V. (1992). Mathematical modeling of melting and freezing processes. CRC Press. Brent, A. D., Voller, V. R., & Reid, K. T. J. (1988). Enthalpy-porosity technique for modeling convection-diffusion phase change: application to the melting of a pure metal. Numerical Heat Transfer, Part A Applications, 13(3), 297-318. Ye, W. B., Zhu, D. S., & Wang, N. (2011). Numerical simulation on phase-change thermal storage/release in a plate-fin unit. Applied Thermal Engineering, 31(17), 38713884.
Figures:
Fig. 1: Physical model of the capsule.
Model-1: all the 4 fins and both cylinders are Aluminum, containing one kind of PCM
Model-2: all the fins (in Blue) and both cylinders are Aluminum, containing one kind of PCM
Model-3: the same as model-2, but it is separated into 2 sections and two kinds of PCMs are placed in each section
Fig. 2: Geometry and definition of our simulated models
Fig. 3-a: Liquid fraction of RT50 per time in arrangement type-1 (RT35 placed in Section-A and RT50 placed in Section-B), with 3 different number of cells and fixed time step size of 0.2 sec
Fig. 3-b: Liquid fraction of RT35 per time in arrangement type-1 (RT35 placed in Section-A and RT50 placed in Section-B), with different time step sizes and fixed 22558 number of cells
Case A - Ref [18] Case B - Ref [18] Case A - Present Study Case B - Present Study
Liquid Fraction
0.8
0.6
0.4
0.2
0
50
100
150
200
250
Time (minutes)
Fig. 4: Comparison of results of our simulation in terms of average temperature and liquid fraction with the results of Ref. [18]
Fig. 5: Liquid fraction, minimum and average temperature using Model-1, THTF=288K
Section A
Section B
Fig. 6-a: Liquid fraction of each PCM using Model-2, THTF=288K, r/r0=3 and H is R-r.
Section A
Section B
Fig. 6-b: Minimum temperature of each PCM using Model-2, THTF=288K, r/r0=3 and H is R-r.
Section A
Section B
Fig. 6-c: Average temperature of each PCM using Model-2, THTF=288K, r/r0=3 and H is R-r.
Section A
Section B
Fig. 7-a: Liquid fraction of each PCM in each section during the solidification process for arrangement type-1 (RT35 in Section-A and RT50 in Section-B) and arrangement type-2 (RT50 in Section-A and RT35 in Section-B) when THTF=288K, r/r0=3 and H is R-r.
Section A
Section B
Fig. 7-b: Minimum temperature of each PCM in each section during the solidification process for arrangement type-1 and type-2 when THTF=288K, r/r0=3 and H is R-r.
Section A
Section B
Fig. 7-c: Average temperature of each PCM in each section during the solidification process for arrangement type-1 and type-2 when THTF=288K, r/r0=3 and H is R-r.
Section A (RT35)
Section B (RT50)
Fig. 8-a: Effect of r/r0 on liquid fraction of each PCM in each section during the solidification process for arrangement type-1 for THTF=288K and H is R-r.
Section A (RT35)
Section B (RT50)
Fig. 8-b: Effect of r/r0 on minimum temperature of each PCM in each section during the solidification process for arrangement type-1 when THTF=288K and H = R-r.
Section A (RT35)
Section B (RT50)
Fig. 8-c: Effect of r/r0 on average temperature of each PCM in each section during the solidification process for arrangement type-1 when THTF=288K and H is R-r.
Section A (RT35)
Section B (RT50)
Fig. 9-a: Effect of H on liquid fraction of each PCM in each section during the solidification process for arrangement type-1 when THTF=288K and r/r0=3.
Section A (RT35)
Section B (RT50)
Fig. 9-b: Effect of H on minimum temperature of each PCM in each section during the solidification process for arrangement type-1 when THTF=288K and r/r0=3.
Section A (RT35)
Section B (RT50)
Fig. 9-c: Effect of H on average temperature of each PCM in each section during the solidification process for arrangement type-1 when THTF=288K and r/r0=3.
H=0
H=0.5
H= Fig. 10-a: Stream function and velocity magnitude (Left), temperature and liquid fraction (Right) contours for arrangement type-1 and different H when THTF=288K, t=100 sec and r/r0=3.
H=0
H=0.5
H= Fig. 10-b: Stream function and velocity magnitude (Left), temperature and liquid fraction (Right) contours for arrangement type-1 and different H when THTF=288K, t=1000 sec and r/r0=3.
H=0
H=0.5
H= Fig. 10-c: Stream function and velocity magnitude (Left), temperature and liquid fraction (Right) contours for arrangement type-1 and different H when THTF=288K, t=3000 sec and r/r0=3.
Section A (RT35)
Section B (RT50)
Fig. 11-a: Effect of heat transfer fluid temperature on liquid fraction of each PCM in each section during the solidification process for arrangement type-1 (RT35 in Section-A and RT50 in Section-B) when THTF=288K, r/r0=3 and H is R-r.
Section A (RT35)
Section B (RT50)
Fig. 11-b: Effect of heat transfer fluid temperature on minimum temperature of each PCM in each section during the solidification process for arrangement type-1 (RT35 in Section-A and RT50 in Section-B) when THTF=288K, r/r0=3 and H is R-r.
Section A (RT35)
Section B (RT50)
Fig. 11-c: Effect of heat transfer fluid temperature on average temperature of each PCM in each section during the solidification process for arrangement type-1 (RT35 in Section-A and RT50 in Section-B) when THTF=288K, r/r0=3 and H is R-r.
Tables:
Table 1 Description of Models and Arrangements Descriptions Section-A Model-1 Model-2 RT35 or RT50 Model-3 RT35 or RT50 Arrangement type-1 RT35 Arrangement type-2 RT50
Table 2 Thermo-physical properties of PCMs and Aluminum Thermo-physical Properties Density ( ) ( ) Thermal Conductivity ( ) Dynamic Viscosity ( ) Melting Heat ( ) Solidification Temperature ( )
Section-B The same PCM as section-A The opposite PCM of section-A RT50 RT35
RT 35 820 2100 0.2 0.0027 157000 308
Table 3 Solidification time for different models Model
Description
PCM
Section
Solidification time
Model 1
Plane fines
RT 35 RT 50
With more compartments and fines
RT 35
Model 2
The same as model 2, but with two kinds of PCMs
Arrangement type 1
A B A B A B A B
7295 sec 5921 sec 2483 sec 5457 sec 1383 sec 3162 sec 2785 sec 3125 sec 1245 sec 5421 sec
Model 3
RT 50
Arrangement type 2
RT 50 780 2000 0.2 0.006 168000 323
Aluminum 2719 871 202.4 -
Nomenclature C
Porous section constant ( Specific Heat (
)
)
Greek Symbols α
thermal diffusivity (
)
dt
Time step size (sec)
thermal expansion coefficient (
g
Gravity (
kinematic viscosity (
h
Sensible enthalpy (
H
Enthalpy (
H
Fins height
K
Conductivity (
L
Latent heat (
p r0 r R Ra S t T th u
Pressure (Pa) Inner cylinder radius (mm) Intermediate cylinder radius (mm) Outer cylinder radius (mm) Rayleigh Number Source term added to the momentum Time (sec) Temperature (K) Thickness of cylinders and fins (mm) Velocity ( )
) )
)
Liquid Fraction (-)
)
Constant amount (-) Dynamic Viscosity ( Density (
)
)
) Subscriptions i,j ini inner HTF l s outer PCM
directions initial Inner cylinder Heat Transfer Fluid liquid solid Outer cylinder Phase Change Material
)
Highlights
Solidification of multilayer PCM within a fined triplex capsule is modelled. A two-dimensional finite volume numerical technique is used for simulations. Variation of liquid fraction values and PCM layers temperatures are reported.
S1359-4311(17)30729-9 http://dx.doi.org/10.1016/j.applthermaleng.2017.05.156 ATE 10471
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
3 February 2017 2 May 2017 27 May 2017
Please cite this article as: A.M. Sefidan, A. Sojoudi, S.C. Saha, M. Cholette, Multi-Layer PCM Solidification in a Finned Triplex Tube Considering Natural Convection, Applied Thermal Engineering (2017), doi: http://dx.doi.org/ 10.1016/j.applthermaleng.2017.05.156
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Multi-Layer PCM Solidification in a Finned Triplex Tube Considering Natural Convection Ali M. Sefidan1, Atta Sojoudi2, Suvash C. Saha3, Michael Cholette3 1
Young Researchers and Elite Club, Tabriz Branch, Islamic Azad University, Tabriz, Iran 2
Mechanical Engineering Department, University of Tehran, Tehran, Iran 3
School of Chemistry, Physics & Mechanical Engineering
Queensland University of Technology, 2 George St., GPO Box 2434, Brisbane QLD 4001, Australia
ABSTRACT Efficient latent heat storage systems represent an important opportunity to improve the thermal performance and operational capability of industrial systems (e.g. solar thermal). In this paper, numerical study is performed to evaluate the heat transfer and solidification features, phase change period and temperature distribution of double-layer Phase Changing Materials (PCM) in a finned triplex tube. A two-dimensional finite volume numerical technique is used to solve the governing equations considering conduction and convection heat transfer mechanisms at a fixed Rayleigh number of 106. After comparing the results for single and double layer configurations, possible arrangements of two different PCMs are discussed in terms of different thicknesses of each PCM, fin sizes and different heat transfer fluid temperatures. Results are illustrated as the form of temperature, liquid fraction, stream function and velocity magnitude contours and their changes over the freezing time. Variation of liquid fraction values, average and minimum temperatures of layers in a double-layer PCM are reported for better insight into the heat transfer features of the latent heat thermal energy storage system to enable uniform discharging designs and balance the phase changing rate within the whole annulus.
KEYWORDS: Numerical Simulation; Solidification; Multi-Layer PCM; Natural convection; Triplex tube; Fins.
1. INTRODUCTION Due to rising energy demands and limited resources, interest in designing energy storage systems for heating and cooling applications has rapidly increased in different many industries [1]. To this end, Latent Heat Storage (LHS) is one of the most promising techniques. In particular, the application of Phase Change Materials (PCMs) as LHS is well-established due to their large energy capacity, modest temperature fluctuation, chemical stabilities and small vapor pressure at their working temperature [2]. These specifications have made PCMs promising for many applications such as building structures [3], electronic cooling devices [4], recovering waste heat [5] and lots of other applications. Several recent studies regarding thermal energy storage systems (particularly their latent form) have optimized the amount of exchanged energy and improved their thermal conductivity. However, there are few studies, which include multi-layer arrangements of PCMs, which have significant potential to enhance the thermal performance of PCMs [6-12]. Farid and Kanzawa [6,7] evaluated the rate of heat transfer between PCMs which were filled in cylindrical containers and air flowed across them. They realized a significant enhancement in the performance of the system when they used various PCMs with different melting temperature in cylindrical containers. Two-layer PCM have been applied in buildings to provide a desirable indoor temperature for throughout the year [8]. However, utilizing one particular kind of PCM for the entire year is impossible because the PCM which is suitable for summer would remain in its solid state during the winter (and therefore store only sensible heat). Thus, designing multilayer PCMs including different PCMs which are suitable for both hot and cold seasons could lead to energy savings in buildings during the whole year. Another recent study regarding multilayer PCMs [9] has numerically evaluated the locations of two PCMs to maximize energy savings in air-conditioned area. Furthermore, the authors reported that combinations of two PCMs can reduce the energy consumption in the room regardless of annular weather changes. Brousseau et al. [10] investigated thermal behavior of various combinations of PCMs and subsequently used these properties to decrease the electricity consumption during peak times. Mosaffa et al. [11] numerically investigated the impacts of design factors on the energy storage performance of multiple-PCM within a rectangular channel. They used effective heat capacity approach in order to simulate pure conduction phase change process in PCMs and solve energy
equation considering convection terms in heat transfer fluid (HTF). Shadab S. and Khalid L. [12] used 2D numerical approach to study phase change process in different configurations of combined PCM slabs. Their main aim was to find any impact of using various arrangements of multiple PCM slabs with different melting temperatures and thermophysical properties on the total storage performance of system compared to using single kind of PCM. Their reports showed a dramatic increase in the amount of energy stored in using composite PCMs. There has been a great deal of research into designing storage units associated with cylinders and tubes to improve LHS efficiency. Researchers showed that thermo-physical properties of PCMs have significant effects on LHS performance [13-17]. In particular, the low thermal conductivity of PCMs has been widely discussed in literature [13-17]. Tao et al [13] have utilized an experimental approach to study effects of PCM thermo-physical properties on unit performance. They employed various PCMs with different properties to evaluate LHS performance and then reported the optimized performance. Similar numerical tests have also been conducted considering the impact of PCM physical properties and different geometries and materials of heat exchangers on the performance of LHS [14]. Improving heat transfer between the PCM and a particular boundary or fluid, researchers considered different ideas: extending surfaces using fins [15], employing excessive tubes [16] or utilizing micro-encapsulated PCMs [17]. Using fins is a common approach to elongate the interacting surface due to their simplicity and inexpensiveness. Several reports for various designs of fins in tubes containing inner and outer fins [18] and cylindrical or rectangular shaped fins are available. Wang et al. [19] numerically investigated the influences of fin geometry and conductivity of outer cylinder during the melting process of PCM. Mosaffa et al. [20] analytically studied the effects of radial fins on the solidification process of PCM in vertical shell and tube heat exchanger. They reported that freezing process took place more rapidly in cylindrical shell compared with a rectangular shell. Agyenim et al [21] carried out an experimental study within a horizontal concentric tube using Erythritol as a PCM to assess the effects of longitudinal and circular fins on heat transfer rate. Their results showed that longitudinal fins lead to a rise in thermal reaction during melting process. Rathod et al. [22] investigated the effects of longitudinal fins on freezing and melting cycles of paraffin as a PCM. Their experimental study was carried out in vertical shell and tube heat exchanger and showed a large decrease in the solidification and melting time of up to
43.6%, and 24.5% respectively by employing fins. One of the most recent fin design studies was done by Eslamnezhad et al. [23] for a triplex tube heat exchanger. In this study, the structure of fins was altered to increase the heat transfer rate and decrease melting time, while the surface area between the fins and PCM was kept constant. Sarviya et al [24] considered the effects of natural convection during numerical simulation of melting process within a solar storage system using longitudinal fins. Erek et al. [25,26] numerically studied the influences of radial fins in a horizontal latent heat storage system. They investigated the effects of fin radius and fin spacing on the heat transfer rate of the module. They reported that for a particular arrangement of fins, system performance will be increased considerably. Chiu and Martin [27] investigated the performance of shell-and-tube LHS unit considering the effects of various design parameters. They found that by reducing the fin spacing, heat transfer rate increases. Ismail et al. [28] performed an experimental and numerical simulation in order to evaluate the effects of fin design parameters of an annular container on the solidification rate and total energy stored by PCMs. Stritih [29] compared the melting and solidification rate of an LHS unit in two cases: with a finned surface and with plain surface. They found that solidification process is more dependent on presence of fins than melting process. Sciacovelli et al. [30] introduced innovative fins to improve the performance of shell-and-tube LHS unit. They performed a numerical method to optimize the geometry of Y-shaped fins with single and double bifurcations. Their results showed that system efficiency increases considerably by using optimized fins. They also designed optimal fins for different operating time of the unit. Taghilou and Talati [31,32] studied the melting and solidification of PCM within a rectangular finned container. They focused on the numerical approach based on the Lattice Boltzmann Method (LBM) to show how the fins accelerate the phase change process. They also discussed the effects of natural convection on the melting procedure of fixed and free solid phases defining the Rayleigh number. Employing a porous matrix saturated with PCM [33,34] and including nanoparticles [35-37] are other common methods which provide both higher energy storage capacity and higher diffusivity to compensate some deficiencies of PCMs. To the best of our knowledge based on literature, few experimental or numerical studies have been conducted about melting or solidification process incorporating multi-layer PCMs in the finned cylindrical geometry. Therefore, this paper presents a numerical study to investigate the
impacts of incorporating RT50 and RT35 as two different types of PCMs with various operating temperatures on the heat transfer features and the freezing performance in finned triplex-tube capsule. It is noteworthy to mention that RT series of PCMs are organic materials which are chemically inert and therefore have stable performance through the phase change cycles. Simulations are carried out considering natural convection effects on the flow structure and results are reported as average and minimum temperature variations of PCMs over freezing period, the whole solidification time, liquid fraction, stream function and velocity magnitude contours of each PCM. Effects of different arrangements and various thicknesses of PCMs with considering fins to have a better insight into the heat transfer phenomenon are discussed. 2. RESEARCH METHODOLOGY 2.1. Physical model and boundary conditions The physical model of the triplex tube capsule is displayed in Fig. 1. The inner cylinder radius is r0=10mm, the intermediate cylinder radius is r=30mm and the outer cylinder radius is R=60mm. The thickness of cylinders and employed fins are th=1mm and Aluminum pipes and fins are used for the triplex tube. Three different models are defined as in Fig. 2. Four fins are stretched from the inner cylinder to the outer one in model-1. In model-2 and model-3 the four radial fins are joined with a cylindrical fin and additional radial fins. To see the effects of employing double layer PCM, we separate model-3 into two sections, each with a different PCM. Further details of each of these models can be found in Table 1. The inner cylinder is used for heat transfer fluid (HTF) and two other annuluses (Sections A and B) are filled with two different PCMs (RT35 and RT50). Table 2 represents thermo-physical properties of two PCMs and solid Aluminum. A constant temperature boundary condition is applied for the inner wall of the smallest cylinder (Tinner is varied from 278K to 298K) while the outer wall of the largest cylinder is considered perfectly insulated. The initial temperature of the PCMs, containers and fins are Tini=323.1K at t=0sec which is higher than freezing point of both RT35 and RT50 and the PCMs are considered fully liquid. For t>0 the whole sections are subjected to constant temperature of the inner cylinder. Although the intermediate cylinder is attached to the inner cylinder and solidification process initiates from inside the inner cylinder boundary, heat is transferred through Aluminum fins, so it is possible for solidification to start in the outer cylinder prior to the completion of
solidification in the inner cylinder. In this study, all the cases are simulated until complete solidification of both of the PCMs. The Rayleigh number for each PCM is defined as in which ΔT is the difference between the solidification temperature of each PCM and the HTF temperature, β expresses thermal expansion coefficient, g is gravitational acceleration, D is the diameter of the section,
and α are kinematic viscosity and thermal
diffusivity of PCMs respectively. This number is fixed at 106 in all our simulations. 2.2. Governing equations During the solidification process, conduction heat transfer takes place through fins and solid state of PCMs while natural convection occurs in liquid phase of PCMs due to temperature gradients and leading density variation. Therefore, buoyancy driven flow should be considered for the liquid state of the PCM through sections A and B. Apart from temperature, density depends on the phase too, and it suddenly varies during melting or solidification process due to different thermophysical properties of solid and liquid phases. Therefore, two types of density changes should be taken into account during phase change processes. For example, most PCMs expand during melting process (
) and will have a volume shrinkage when they pass from solid to
liquid phase. This expanded volume affects the rate of phase change process and heat transfer features more considerable than a sudden density change [38]. So, if we consider a fixed volume for our computational domain, applying different density amounts for solid and liquid phases will not change our results significantly. Moreover, difference between solid and liquid densities of both RT35 and RT50 is less than 10% and setting negligible volume changes for PCMs seems acceptable. To develop a mathematical model, the liquid phase is considered for both PCMs while they are thermally coupled. Unsteady, laminar and incompressible flow is assumed for the liquid phase and attributed flow. As a whole, the following assumptions are made: 1) Constant thermo-physical properties for each phase; 2) Negligible volume changes of PCMs; 3) Boussinesq approximation for density variation of liquid phase; 4) Newtonian liquid phase; 5) Negligible viscous dissipation; 6) No slip boundary condition for cylinder walls and fins; 7) Negligible super cooling effect; 8) No heat transfer to the surroundings. The governing equations of the problem including continuity, momentum and thermal energy equations are defined as following:
Continuity equation: =0
(1)
Momentum equation: (2) Energy equation: (3) Where ρ is the density of the PCM, ui is the fluid velocity, μ is dynamic viscosity, p is pressure, g is the gravity acceleration, k is thermal conductivity, T is the fluid temperature, and h is sensible enthalpy of RT35 and RT50. This sensible enthalpy is defined as: (4)
The total enthalpy is:
(5) Where href is the reference enthalpy at the reference temperature Tref, cp is the specific heat, and ΔH attributes to the latent heat of PCM materials that leads a phase from liquid to solid state. The liquid fraction during the PCM solidification process, γ, is: (6)
(7)
Phase variation happens when the temperature is between solid and liquid phase temperature. The source term Si in momentum equation, Eq. (2), is:
(8)
Brent et al. [39] introduced porosity function, Eq. (8), which follows from the Carman Kozeny equations for the flow across porous media. Here, C determines the rate of velocity reduction to zero when the material changes from liquid to solid. The value is varied from 104 to 107 according to the PCM property. For current modeling, this value is taken to be 106 and ε is a very small value defined in Ref. [39]. Boussinesq approximation is as following [40]: (9)
in which ρl and β are the density of the PCM material at the freezing temperature and the thermal expansion coefficient, respectively. 2.3. Numerical model The unsteady pressure based method is utilized for the numerical modeling of the problem employing ANSYS FLUENT, V16. Modeling mushy zone, this Finite Volume Method (FVM) based code assumes ''pseudo'' porous medium for PCM sections with porosity equal to the liquid fraction. The porosity reduces from 1 (liquid) to 0 (solid) as the material solidifies and the velocities also fall to zero. Triangular shaped (unstructured) cells are selected for meshing the geometry which are finer close to the walls due to higher gradients of quantities. Second order accuracy is selected for discretization of momentum and energy equations. The PRESTO technique is employed for discretization pressure term. The value of convergence criterion for all equations is set to be 10-6 and a time step size of 0.2 sec is found to be small enough to ensure an independent and stable solution. The under-relaxation factors for the continuity, momentum and thermal energy are 0.5, 0.3 and 0.8 respectively. 2.4. Mesh independency and time-step independency Different number of cells were tested to evaluate dependency of the results on mesh number. Moreover, 3 different time step size were selected. Fig. 3 displays performed tests on mesh independency and time step size tests for liquid fraction values per time. It is seen that, results
for different number of cells and time step size are very close to each other, so, in order to reduce computational cost and also having enough accuracy, number of 22558 cells with 0.2sec time step size were selected. 2.5. Validation To validate our employed numerical model, some cases from Ref. [18] have been regenerated in order to compare with our results. These comparisons are displayed in Fig. 4. As it is seen, our numerical solution agrees suitably with both numerical and experimental results of mentioned reference. 3. RESULTS AND DISCUSSIONS 3.1. Effects of employing double-layer PCM and fins At first, before expressing the effects of employing double-layer PCM, model-1 and model-2 are simulated to analyze the effects of using fins and more compartments (model-2 in Fig. 2) on solidification process. The results of model-1 in which the whole annulus was filled with a single PCM (first RT35, then RT50) are shown in Fig. 5. This figure displays liquid fraction, minimum and average temperature of two mentioned cases during solidification process. It is seen that RT35 solidified after almost 7300sec while RT50 needed approximately 6000sec. This is attributed to the fact that, difference between heat transfer fluid temperature (288K) and solidification temperature of RT50 (323K) is higher than that of RT35 (308K) which lead to higher rate of heat transfer in the first case. The minimum temperature of two PCMs dropped quickly to 288K and then stayed at this level for the rest of the solidification process and no significant difference was seen between two cases over the time. Due to contact between the inner cylinder and PCM in section A, this pattern is repeated for other simulations again. The average temperature of RT35 was lower than RT50 at the end of the process since the freezing time for RT35 was longer than RT50. The simulation results using model-2 are displayed in Fig. 6. As it is seen, by employing fins of model-2 which have been shown in Fig. 2, there are a considerable decrease in freezing time. The whole solidification process dipped by almost 25% using RT35 but the figure for RT50
decreased by about 48%. The minimum and average temperature for two sections are displayed separately in Fig. 6, and the lowest average and minimum temperature did not differ significantly in comparison with model-1. According to these initial results, which was strongly related to the thermo-physical properties of materials, two other numerical tests were performed (model-3) to ensure the applicability and efficiency of multi-layer PCM capsule. The two different arrangements of model-3 were simulated. A comparison of these arrangements with H=R-r and r/r0=3 are shown in Figs. 7. Fig. 7-a displays liquid fraction of two arrangements for different sections during the solidification process. It can be seen that when RT35 was placed in section A (arrangement type-1) it solidified later than when RT50 was placed in the same section (arrangement type-2). This was due to the previously mentioned fact that RT50 had a higher temperature difference with HTF and solidified sooner than RT35. For section B, again RT50 (arrangement type-1) solidified sooner than RT35, because in spite of the fact that section B was far from heat transfer source, RT50 repeatedly had benefitted from its high temperature difference between HTF rather than RT35. According to the results, the whole freezing period in arrangement type-2 took more time in comparison with arrangement type-1. The whole period for arrangement type-1 was 3125sec while the number for arrangement type-2 was 5421sec. The minimum temperature for the both arrangements were same for section A because of straight touch with inner wall. But for section B, minimum temperature for two arrangements was a little different, this refers to the solidification temperature of the PCMs. Although in terms of average temperature, RT35 was lower in both sections (both arrangements) than RT50, because both of PCMs were solidifying and since their operating temperatures were different, in each arrangement, the average temperature of RT50 was major than that of RT35. According to our results which were discussed before, arrangement type-1 (RT35 in section A and RT50 in section B) was used for the rest of simulations due to lower overall solidification time. The freezing time for arrangement type-1 (model 3) is close to that of model-2 when RT50 was used. When using two different PCMs, the PCM in section A solidified sooner in model-2 than for model-3. Solidification time for different models are reported in table 3. As it is seen, the solidification rate in arrangement type-1 is rather equal for both sections in comparison with model-2.
3.2. Effects of thicknesses of each PCM in the double-layer PCM By keeping R and r0 fixed, effects of thickness of each PCM (r/r0 ratio) in the double-layer PCM was investigated. The influence of varying r/r0 are displayed in Fig. 8. Fig. 8-a illustrates liquid fraction of two sections during solidification process for various thicknesses of PCMs. It is known that large area leads to higher Rayleigh number, therefore increasing the r/r0 ratio and thus natural convection effects became stronger in section A. In spite of this fact, as the r/r0 ratio increased RT35 took longer to solidify. Besides, the size of section A and consequently the embedded material size (RT35) became larger in this case. Again, in section B, by decreasing the amount of material which was filled in, the freezing time went down. For r/r0=5 in particular, the amount of material was too small the heat transfer area was relatively high. Therefore, the solidification process took less time in comparison with other r/r0 ratios. From Fig. 8-b, the minimum temperature in section A was the same for different thicknesses at all times. However, in section B the minimum temperature of various cases reached to almost a same amount of almost 290K at the end of the period in different times. Fig. 8-c shows that the average temperature of RT35 in section A for different thicknesses remained close to 294K at the end of the period but in different times. The figure for r/r0=2 was a bit different. However, the RT50 in section B experienced lower temperatures for higher r/r0. 3.3. Effects of fin size (H) in section B The influence of H on liquid fractions of two sections are shown in Fig. 9-a. It is seen that for larger H, the time needed for solidification of section B was shorter. Larger H enhanced the effect of fin on heat removal from section B. Consequently, higher H fins affected negatively on section A and thus section B solidified faster for larger H. In Fig. 9-b, the minimum temperature of section A did not differ for all sizes of H and passing time, but for section B, there was a bit difference between various cases in time. The average temperature of section A (Fig. 9-c) was reduced gently for lower H, while higher H leaded to decrease in the average temperature in section B. Fig. 10-a to Fig. 10-e display the liquid fraction, temperature, stream function and velocity magnitude contours for various H size during t=100sec to t=3000sec. Rotating cells (due to natural convection) can be seen for section A at early, but as the area of A was solidified the size
of cells was reduced and natural convection effects diminished. Rotating cells activated in section B at the later stages of the simulation. As the size of H was increased number of cells increased. The velocity magnitude was higher for larger H at later times and this fact improved the efficiency of solidification process for section B. 3.4. Effects of HTF temperature Fig. 11-a shows heat transfer fluid temperature effect on liquid fractions of the both sections. It can be seen that the lower the temperature of heat transfer fluid, the sooner the both section turn into solid state. This effect is related to the higher rate of heat transfer for lower HTF temperatures. From Fig. 11-b it is seen that minimum temperature was lower for small HTF temperature at both sections. Average temperature of the both sections had the same status as minimum temperature as it is shown in Fig. 11-c. 4. CONCLUSIONS Numerical experiments have been performed to study solidification process of multi-layer PCM within a fined triplex capsule. RT35 and RT50 were used for two sections of the annulus regions. A two-dimensional Finite Volume numerical technique was used to solve the governing equations considering conduction and convection heat transfer mechanisms. Different arrangements of layers, fin sizes, intermediate cylinder sizes and heat transfer fluid temperature were tested and following outcomes are stated:
Employing fins of model-2 (Fig. 2), has decreased the whole freezing period considerably.
By using two different PCMs (multi-layer PCM), the solidification rate in two sections takes place more simultaneously in comparison with using one kind of PCM in both sections in the same container and fins.
Employment of RT35 for section A and RT50 for section B led to faster solidification process as opposed to RT50 in section A and RT35 in section B.
With the increase of r/r0 ratio, section A became larger and the embedded material took much longer to solidify, but it decreased the solidification time in section B.
Larger H enhanced the effect of fin on heat removal from section B and consequently, higher H fins affected negatively on section A.
Average temperature of section A was reduced gently for lower H, while higher H leaded to decrease in the average temperature in section B.
Lower heat transfer fluid (HTF) temperatures lead to quick solidification rate in both sections.
Average and minimum temperature of both sections reached the lower amounts when the HTF temperature was small.
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Figures:
Fig. 1: Physical model of the capsule.
Model-1: all the 4 fins and both cylinders are Aluminum, containing one kind of PCM
Model-2: all the fins (in Blue) and both cylinders are Aluminum, containing one kind of PCM
Model-3: the same as model-2, but it is separated into 2 sections and two kinds of PCMs are placed in each section
Fig. 2: Geometry and definition of our simulated models
Fig. 3-a: Liquid fraction of RT50 per time in arrangement type-1 (RT35 placed in Section-A and RT50 placed in Section-B), with 3 different number of cells and fixed time step size of 0.2 sec
Fig. 3-b: Liquid fraction of RT35 per time in arrangement type-1 (RT35 placed in Section-A and RT50 placed in Section-B), with different time step sizes and fixed 22558 number of cells
Case A - Ref [18] Case B - Ref [18] Case A - Present Study Case B - Present Study
Liquid Fraction
0.8
0.6
0.4
0.2
0
50
100
150
200
250
Time (minutes)
Fig. 4: Comparison of results of our simulation in terms of average temperature and liquid fraction with the results of Ref. [18]
Fig. 5: Liquid fraction, minimum and average temperature using Model-1, THTF=288K
Section A
Section B
Fig. 6-a: Liquid fraction of each PCM using Model-2, THTF=288K, r/r0=3 and H is R-r.
Section A
Section B
Fig. 6-b: Minimum temperature of each PCM using Model-2, THTF=288K, r/r0=3 and H is R-r.
Section A
Section B
Fig. 6-c: Average temperature of each PCM using Model-2, THTF=288K, r/r0=3 and H is R-r.
Section A
Section B
Fig. 7-a: Liquid fraction of each PCM in each section during the solidification process for arrangement type-1 (RT35 in Section-A and RT50 in Section-B) and arrangement type-2 (RT50 in Section-A and RT35 in Section-B) when THTF=288K, r/r0=3 and H is R-r.
Section A
Section B
Fig. 7-b: Minimum temperature of each PCM in each section during the solidification process for arrangement type-1 and type-2 when THTF=288K, r/r0=3 and H is R-r.
Section A
Section B
Fig. 7-c: Average temperature of each PCM in each section during the solidification process for arrangement type-1 and type-2 when THTF=288K, r/r0=3 and H is R-r.
Section A (RT35)
Section B (RT50)
Fig. 8-a: Effect of r/r0 on liquid fraction of each PCM in each section during the solidification process for arrangement type-1 for THTF=288K and H is R-r.
Section A (RT35)
Section B (RT50)
Fig. 8-b: Effect of r/r0 on minimum temperature of each PCM in each section during the solidification process for arrangement type-1 when THTF=288K and H = R-r.
Section A (RT35)
Section B (RT50)
Fig. 8-c: Effect of r/r0 on average temperature of each PCM in each section during the solidification process for arrangement type-1 when THTF=288K and H is R-r.
Section A (RT35)
Section B (RT50)
Fig. 9-a: Effect of H on liquid fraction of each PCM in each section during the solidification process for arrangement type-1 when THTF=288K and r/r0=3.
Section A (RT35)
Section B (RT50)
Fig. 9-b: Effect of H on minimum temperature of each PCM in each section during the solidification process for arrangement type-1 when THTF=288K and r/r0=3.
Section A (RT35)
Section B (RT50)
Fig. 9-c: Effect of H on average temperature of each PCM in each section during the solidification process for arrangement type-1 when THTF=288K and r/r0=3.
H=0
H=0.5
H= Fig. 10-a: Stream function and velocity magnitude (Left), temperature and liquid fraction (Right) contours for arrangement type-1 and different H when THTF=288K, t=100 sec and r/r0=3.
H=0
H=0.5
H= Fig. 10-b: Stream function and velocity magnitude (Left), temperature and liquid fraction (Right) contours for arrangement type-1 and different H when THTF=288K, t=1000 sec and r/r0=3.
H=0
H=0.5
H= Fig. 10-c: Stream function and velocity magnitude (Left), temperature and liquid fraction (Right) contours for arrangement type-1 and different H when THTF=288K, t=3000 sec and r/r0=3.
Section A (RT35)
Section B (RT50)
Fig. 11-a: Effect of heat transfer fluid temperature on liquid fraction of each PCM in each section during the solidification process for arrangement type-1 (RT35 in Section-A and RT50 in Section-B) when THTF=288K, r/r0=3 and H is R-r.
Section A (RT35)
Section B (RT50)
Fig. 11-b: Effect of heat transfer fluid temperature on minimum temperature of each PCM in each section during the solidification process for arrangement type-1 (RT35 in Section-A and RT50 in Section-B) when THTF=288K, r/r0=3 and H is R-r.
Section A (RT35)
Section B (RT50)
Fig. 11-c: Effect of heat transfer fluid temperature on average temperature of each PCM in each section during the solidification process for arrangement type-1 (RT35 in Section-A and RT50 in Section-B) when THTF=288K, r/r0=3 and H is R-r.
Tables:
Table 1 Description of Models and Arrangements Descriptions Section-A Model-1 Model-2 RT35 or RT50 Model-3 RT35 or RT50 Arrangement type-1 RT35 Arrangement type-2 RT50
Table 2 Thermo-physical properties of PCMs and Aluminum Thermo-physical Properties Density ( ) ( ) Thermal Conductivity ( ) Dynamic Viscosity ( ) Melting Heat ( ) Solidification Temperature ( )
Section-B The same PCM as section-A The opposite PCM of section-A RT50 RT35
RT 35 820 2100 0.2 0.0027 157000 308
Table 3 Solidification time for different models Model
Description
PCM
Section
Solidification time
Model 1
Plane fines
RT 35 RT 50
With more compartments and fines
RT 35
Model 2
The same as model 2, but with two kinds of PCMs
Arrangement type 1
A B A B A B A B
7295 sec 5921 sec 2483 sec 5457 sec 1383 sec 3162 sec 2785 sec 3125 sec 1245 sec 5421 sec
Model 3
RT 50
Arrangement type 2
RT 50 780 2000 0.2 0.006 168000 323
Aluminum 2719 871 202.4 -
Nomenclature C
Porous section constant ( Specific Heat (
)
)
Greek Symbols α
thermal diffusivity (
)
dt
Time step size (sec)
thermal expansion coefficient (
g
Gravity (
kinematic viscosity (
h
Sensible enthalpy (
H
Enthalpy (
H
Fins height
K
Conductivity (
L
Latent heat (
p r0 r R Ra S t T th u
Pressure (Pa) Inner cylinder radius (mm) Intermediate cylinder radius (mm) Outer cylinder radius (mm) Rayleigh Number Source term added to the momentum Time (sec) Temperature (K) Thickness of cylinders and fins (mm) Velocity ( )
) )
)
Liquid Fraction (-)
)
Constant amount (-) Dynamic Viscosity ( Density (
)
)
) Subscriptions i,j ini inner HTF l s outer PCM
directions initial Inner cylinder Heat Transfer Fluid liquid solid Outer cylinder Phase Change Material
)
Highlights
Solidification of multilayer PCM within a fined triplex capsule is modelled. A two-dimensional finite volume numerical technique is used for simulations. Variation of liquid fraction values and PCM layers temperatures are reported.