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Article

Comparison of Triple-Tube Heat Exchanger and Spherical Ice Balls for Energy Storage Performance: A Numerical Study

by
Gülşah Karaca Dolgun
Department of Energy Systems Engineering, Technology Faculty, Muğla Sıtkı Koçman University, Kötekli, 48000 Menteşe, Türkiye
Energies 2025, 18(15), 4199; https://doi.org/10.3390/en18154199
Submission received: 6 July 2025 / Revised: 1 August 2025 / Accepted: 4 August 2025 / Published: 7 August 2025
(This article belongs to the Section J1: Heat and Mass Transfer)

Abstract

Ice energy storage systems have gained significant attention as sustainable solutions for energy management, particularly in applications with fluctuating energy demands. This study aims to compare two different designs, a triple-tube heat exchanger (TTHE) and spherical ice balls, the latter being the most widely used traditional design in the industry. The TTHE design was first analyzed theoretically, then optimized using Computational Fluid Dynamics (CFD) simulations, and validated by the literature. Finally, it was compared with spherical ice balls under identical conditions. The analyses were conducted for an ice storage volume of 1000 kg, with the complete solidification process designed to occur within 8 h. The results indicate that the TTHE reduced solidification time by 25% while simultaneously increasing energy storage by 8%. This study contributes to the advancement of sustainable energy technologies by providing a comparative analysis of spherical ice balls and triple-tube heat exchangers for optimizing ice storage systems. The implementation of a TTHE for thermal storage can lower energy costs, mitigate peak demand, and address the intermittency challenges associated with renewable energy sources.

1. Introduction

Ice thermal energy storage systems have garnered attention as sustainable and promising solutions for energy management, particularly in applications characterized by fluctuating energy demands. These systems can reduce both the grid’s energy load and energy costs by storing electricity during nighttime hours when electricity consumption is low. They also contribute to the reduction in fossil fuel consumption by integrating with renewable energy sources. The gradual depletion of economically viable fossil fuel reserves, combined with the growing global energy demand, has intensified the focus on sustainable alternative energy sources. However, improving the efficiency of existing energy-consuming systems or reducing process time is equally valuable as exploring alternative energy sources, particularly when factors such as cost-effectiveness, technological feasibility, and environmental impact are taken into account. The building sector comprises 40% of total energy consumption and 36% of the overall greenhouse gas emissions in the world [1,2]. Energy consumption in the industrial sector is considerable; however, electricity usage can be significantly reduced by using thermal energy storage (TES) to meet the heating and cooling demands. Emerging energy storage approaches hold promise for decarbonizing this sector. Ice storage systems, in particular, can be used to manage peak energy demand, thereby reducing both cooling loads and operating costs. An ice storage system supporting the air conditioning system of a hypermarket in Ankara, Türkiye, was studied both economically and thermodynamically. The hypermarket had a daily total cooling load of 8332 kWh, and 47% of this load—corresponding to the peak electricity tariff period—was covered by stored ice. Consequently, chillers could be turned off during peak tariff hours. The payback period of this system was calculated as three years, and the energy cost of air conditioning was reduced by 50% [3]. The optimization and multi-criteria evaluation of a 500 m3 ice energy storage system integrated into the cooling and heating supply networks of a campus building in Germany were performed by Griesbach et al. (2023). They developed a numerical model in Matlab Simulink and validated it with one year of real measured data. The system demonstrated a potential reduction in CO2 emissions of 37% under optimum operation compared to traditional heating and cooling methods [4]. In recent years, studies on TES have gained momentum in the electricity sector, aiming to reduce peak loads, decrease energy costs, and lower carbon emissions. Al-Ali and Modi (2022) investigated the economic viability of integrating ice thermal storage and batteries with utility-scale PV systems to decarbonize Qatar’s electrical industry, which is primarily dependent on gas generation. Their findings indicate that the deployment of ice storage and PV systems could reduce peak electricity demand and gas generation usage by 18% and 43%, respectively, while also lowering annual system costs by 20% at a gas price of QAR 3.3/MMBtu. However, due to extremely high seasonal cooling demands, ice thermal storage alone was not able to compete economically with the current gas-based generation systems [5]. Chen et al. (2019) analyzed the use of TES with PCM for cooling an office building via ventilation systems during summer in China. Nighttime ventilation enhanced the heat absorption capacity of the structural elements for the following day. When the set point temperature was increased from 24 °C to 28 °C, the seasonal electricity savings from the TES system improved from 9.2% to 33.6%, compared to a conventional nighttime ventilation system, and from 16.9% to 50.8% compared to a baseline scenario. Additionally, the TES unit was found to reduce the grid’s peak load in the morning by assisting the air conditioner [6]. Heine et al. (2021) investigated the cost and energy assessment of a packaged ice energy storage application in the U.S. and indicated that the average monthly demand decreased by between 25.9 kW and 49.1 kW. These values correspond to between 32.2% to 36.6% [7].
A spherical capsule can be readily fabricated and integrated into TES devices. ElGhnam et al. experimentally investigated the effects of the storage unit design parameters and operating conditions of the heat transfer fluid on the charging and discharging behavior of water within spherical cavities. The spherical containers were constructed from various materials (plastic, glass, brass, copper, and stainless steel) with different diameters. The experimental results demonstrated that the charging time decreased with the use of metallic and small-sized capsules, as well as lower temperatures and higher flow rates of the heat transfer fluid (HTF). It was also indicated that the thermal conductivity of the tank material had a relatively minor impact on the charging/discharging time [8]. Reddy et al. conducted an experimental study on the influence of capsule wall material on the solidification and melting processes of PCM within spherical capsules. The materials used for the capsules included aluminum, mild steel, and high-density polyethylene (HDPE). The system featured a flat plate solar collector, with water as the heat transfer fluid (HTF). The capsule material did not significantly improve the thermal performance of the TES unit. When comparing the thermal performance of capsule materials with high (aluminum: 240 W/m°C) and low (HDPE: 0.52 W/m°C) thermal conductivity, the reported difference was minimal (approximately 5%) [9]. Kousksou et al. modeled a two-dimensional cylindrical tank filled with ice capsules. The performance of the tank was analyzed in both vertical and horizontal orientations. They concluded that vertically positioned tanks operated more effectively. The tank was a metallic cylinder with a diameter of 0.95 m and a usable height of 1.42 m, yielding a total usable volume of 1 m3. A total of 2406 spherical ice capsules, each with an external diameter of 77 mm, were distributed randomly within the tank. Considering the thickness of the capsule shell, the ice occupied 50% of the tank’s volume [10].
Mouziraji et al. (2024) concluded that the staggered fin arrangement significantly improved the PCM discharge characteristics in a triplex-tube TES system. The optimized staggered arrangement increased the discharge rate by 30% and reduced the solidification time by 52% compared to the baseline scenario without fins. Additionally, the staggered fins increased the discharge rate by 16% and reduced the solidification time by 46% when compared to the inline fins [11]. Yan et al. (2022) investigated the use of Y-shaped fins in a triplex-tube LHTES system and found that the PCM system with the Y-shaped fins required only 34% of the time needed by the original system to achieve complete melting [12]. Similarly, the melting time of the PCM in the heat storage unit was reduced by 31.92% using the V-shaped fins with an optimal arrangement compared to the standard rectangular fins [13]. Utilizing a frustum-shaped tube with a 5 mm gap width, as opposed to a standard straight tube, enhanced the heat storage rate by 32.8% and reduced the melting time by 25.6% [14]. The solidification performance of the triplex-tube TES system improved by 50.19% through the addition of eight secondary inner tubes positioned between the two main tubes. Furthermore, it was concluded that the solidification performance of the T-shaped fins attached to both the inner and outer tubes was improved by 33% and 35%, respectively, compared to the initial configuration. The findings demonstrated that a multistage inner tube enhanced the solidification characteristics of PCM more effectively than fins alone [15]. Finally, the melting performance of the optimized T-LHTES model for the triplex tube was 23.87% better than the original model. The impact of fin length (30, 35, and 40 mm) on the melting performance was limited to less than 11.47%, and it remained inconclusive as to whether the thermal conductivity of the fins had a significant impact on the melting process [16]. Due to the dominance of PCM thermal conductivity over other parameters, the inclusion of metal foam in PCMs significantly reduced the melting time. The addition of porous material to single-layer PCM improved its melting performance by 92%. Similarly, for a three-layer PCM, the improvement was 88%. Furthermore, the efficiency of the three-layer PCM with metal foam was found to be 3% higher than that of the single-layer PCM with metal foam [17]. Beyne et al. (2023) developed and evaluated an analytical method for LTES heat exchangers. This method was applied to three basic geometries: pipe-in-pipe, spherical packed bed, and cylindrical modules. Among these, the pipe-in-pipe geometry demonstrated the highest performance, followed by the cylindrical and spherical modules [18].
There are numerous studies focused on ice storage in spherical balls—with and without fins—as well as on triple-tube heat exchangers (TTHEs), also with and without fins. However, to the best of the author’s knowledge, no comparative study has been conducted between these two systems. Given that spherical ice balls, a design with a long history, remain the most widely used method, it is crucial to assess the effectiveness of this traditional design under contemporary operating conditions. Therefore, this study presents a performance evaluation of the TTHE as an alternative to the widely adopted conventional design—spherical ice balls. The TTHE design is determined through theoretical analysis, optimized using Computational Fluid Dynamics (CFD), validated against data from the literature, and subsequently compared with the conventional ice ball design. The primary and most decisive criterion in the theoretical analyses is the ability to produce 1000 kg of ice (for ease of comparison) within 8 h. This duration is selected to help stabilize the daily energy consumption profile in Türkiye while also encouraging energy storage during periods of lower demand. To incentivize this, the Government of Türkiye has created three distinct tariff periods with different pricing: the daytime tariff (06:00–17:00), the peak tariff (17:00–22:00), and the nighttime tariff (22:00–06:00). Among these, the nighttime tariff, which has the lowest demand, is priced approximately 75% lower compared to the daytime tariff [3]. As described, energy consumption during these hours presents advantages in terms of overall energy management, and the prospect of utilizing the stored energy during daytime tariff periods is particularly appealing. Therefore, this study aims to introduce a system that is better aligned with the current conditions and expectations, offering reduced energy consumption and time savings, and to evaluate its advantages and disadvantages by comparing it with a conventional design.

2. Methodology

The methodology of this study is shown in Figure 1. In this study, the TTHE, which provides bi-directional heat transfer for the solidification of ice, is presented and compared with the industrial application. A detailed drawing of the TTHE and ice ball is given in Figure 2a,b. As can be seen, heat transfer occurs in two directions in the ice tube, while it is one-directional in the ice ball.
As a first step, the thermophysical properties of the HTF used to solidify the ice are determined during the design phase. These specifications are given in Table 1. The heat transfer fluid is chosen as water with 10% ethylene glycol added.
The second step involves selecting the diameters of the inner and outer tubes for the TTHE. The design of the TTHE incorporates two intertwined (concentric) pipes, with the volume between them serving as the region where ice forms. HTF flows through both the center and the outer surface of the TTHE, enabling ice to solidify via bi-directional heat transfer. As seen in Figure 2a, ice solidification begins simultaneously from both the inner surface of the outer pipe and the outer surface of the inner pipe and proceeds bi-directionally. In contrast, in a spherical ice ball, heat transfer occurs in only one direction (Figure 2b). Bi-directional heat transfer enhances the overall heat transfer rate compared to one-directional configurations.
Two main parameters are used as the basis for the theoretical analysis, and all analyzes are performed accordingly:
  • For ease of comparison, the formation of 1000 kg of ice is taken as a reference.
  • It is calculated that the ice formation is completed within an 8 h period—corresponding to the off-peak period (when the electricity price is low)—in order to minimize energy consumption and serve as a reference for future studies.
Assumptions and considerations:
  • Theoretical analyses are conducted using the film temperature. It is entirely expected to observe greater ice formation near the inlet due to relatively colder coolant and reduced ice formation toward the outlet. However, theoretical analyses based on the film temperature can be interpreted as representing an averaged effect, accounting for the thicker ice near the inlet and the thinner ice near the outlet.
  • Ice balls are assumed to have a perfect spherical geometry. From a mechanical strength perspective, such geometries are preferred due to the absence of sharp edges and a junction, and more importantly because they distribute pressure uniformly. A review of the relevant literature confirms that previous studies similarly adopt a perfect sphere assumption [19,20].
  • It is assumed that spherical ice balls occupy 50% of the total tank volume [10].
  • Both theoretical and CFD analyses neglect the heat losses through the tank’s walls.
In this study, the inner and outer pipe diameters, pipe length, and number of pipes of the TTHE; the diameter and number of spherical ice balls; and the corresponding tank volumes are calculated to store 1 ton of ice within 8 h. The methodology of this study is presented in Figure 1. The amount of ice formed and the corresponding stored energy are compared. The specification of the TTHE and ice ball systems and storage tank parameters are given in Table 2. High-density polyethylene (HDPE) with a 100 mm internal diameter and a 4 mm wall thickness is selected as an ice ball, based on industrial application. HDPE is commonly preferred in industrial applications due to its ease of manufacturing and its ability to accommodate a large number of balls within a single storage tank. This approach not only simplifies production but also minimizes excessive weight. Additionally, it facilitates the straightforward replacement of an individual ice ball in the event of maintenance.
The selection of the inner and outer pipes for the TTHE requires multiple iterative calculations. This is because the ice thickness—and therefore the ice volume formed on the surfaces after 8 h—may either fall below or exceed the physical ice-holding capacity of the tubes. If the volume is too low, complete ice formation along the tube length will not be achieved. If it exceeds the maximum, the analysis becomes invalid. Figure 1 illustrates this condition with a representative example.
In addition, the effect of using different materials for the TTHE and ice balls on heat transfer was investigated during the preliminary study phases, taking into account the differences in their thermal conductivity coefficients. The results revealed that although stainless steel exhibits relatively high thermal conductivity, the most influential parameter affecting overall thermal resistance during time-dependent ice formation is the thickness and thermal conductivity of the ice itself. These findings are consistent with those reported in the literature [8,9]. In another study, Xu et al. (2023) experimentally and numerically investigated the material properties of coils in ice storage performance. Ice storage time with steel pipe is reduced by 40.9% and 9.30% compared to HDPE and reinforced-HDPE, respectively. Although the difference in thermal conductivity between steel pipe (40.0 W/(m·K)) and reinforced-HDPE (2.8 W/(m·K)) was large, no significant differences were observed between ice storage times [21]. The time-dependent thermal resistance caused by ice formation is presented in Figure 3. At t = 0, no ice has yet formed, and the initial heat transfer rate is calculated as 175 kW. As ice forms over time, this heat transfer rate gradually decreases. This reduction is attributed to the low thermal conductivity of ice and its increasing thickness, which causes it to act as an insulating layer. Consequently, the total heat transfer rate declines over time. This phenomenon has been accounted for in all theoretical calculations and CFD analyses conducted in this study.
It is indicated that the thermal conductivity of the capsule materials has minimal impact on the charging and discharging times of the TES unit [8], as well as on its overall thermal performance [9]. Therefore, as previously noted, plastic-based materials are selected for the ice balls.
To produce a total of 1000 kg of ice, 37 TTHE units and 2100 ice balls are required, based on the specifications given in Table 2. For both geometries, identical storage tank volumes are calculated to achieve the same ice storage capacity. However, while only 37 intertwined steel tubes are required for the TTHE system, 2100 spherical balls are required for the ice ball system. Table 3 presents the thermophysical properties of ice and water at 0 °C.

2.1. Theoretical Analysis

According to the Fourier heat conduction law, the heat conduction is calculated by Equation (1) [22]:
Q ˙ = k A d T d x
where k is the thermal conductivity, which depends on the material type and temperature, A is the surface cross-sectional area of the cylinder, dx is the thickness of the heat transfer region, and dT is the temperature difference across that region.
The thermal resistance in the cylinder is calculated by Equation (2) [22]:
R = l n r 2 / r 1 2 π k p i p e L
where k is the thermal conductivity, L is the length of the cylinder, r2 is the outer radius, and r1 is the inner radius. The heat transfer in the cylinder is calculated by Equation (3) [22]:
Q = k p i p e T 2 T 1 l n r 2 / r 1 2 π L
where T1 is the temperature at radius r1 and T2 is the temperature at radius r2. The thermal resistance in the sphere is calculated by Equation (4) [22]:
R = r 2 r 1 4 π k s p h e r e r 1 r 2
where k is the thermal conductivity, r2 is the outer radius, and r1 is the inner radius. The heat transfer in the cylinder is calculated by Equation (5) [22]:
Q = k s p h e r e T 2 T 1 r 2 r 1 4 π L r 1 r 2
The flow in the pipe can be laminar or turbulent. The Reynolds number determines this. The Reynolds number in the flow in the pipe is found by Equation (6) [22].
R e D =   u a v e D v = 4 m ˙ μ D π
where uave is the average flow rate in the pipe (m/s), D is the pipe inner diameter (m), and v is the kinematic viscosity (m2/s). If the Reynolds number is lower than 2300, the flow inside the pipe is laminar. Dittus and Boelter give Equation (7) [22] for fully developed turbulent flow in the pipe in the situations of R e D 10000 , 0.6 P r 160 , and L / D 10 .
N u D = 0.023 R e D 0.8   P r n
Here, if the fluid in the pipe heats up, n is 0.4, and if it cools down, n is 0.3. The Reynolds number in the flow outside the pipe is as follows [22]:
R e D = u D v = ρ u D μ
where u is the velocity of the fluid flowing perpendicular to the pipe and D is the outer diameter of the pipe. For the external flow in the pipe, if Recritical > 2 × 105, turbulent flow exists there. For the external flow in the pipe, the Nusselt number is calculated by Equation (9) [22]. The average Nusselt number is calculated by Equation (9) for the conditions of RePr > 0.2 and perpendicular flow to the pipe. Values at film temperatures are used.
N u D = 0.3 + 0.62 R e 1 / 2 P r 1 / 3 1 + 0.4 P r 2 / 3   0.25 1 + R e 282000 5 / 8 4 / 5
The Reynolds number in staggered arrangement (for ice balls) is calculated by Equation (10) [22].
R e D = u m a x D v = ρ u m a x D μ
where u m a x is the maximum velocity through ice balls and calculated by Equation (11) [22].
u m a x = S t 2 ( S D D ) u
where S t is the transverse pitch between tube centers and S D is the diagonal pitch between tube centers. The Nusselt number in staggered arrangement (for ice balls) is calculated by Equation (12) [22].
N u D = 0.35 ( S t S L ) 0.2 ( R e D ) 0.6 P r 0.36 ( P r P r s ) 0.25
where S L is the longitudinal pitch between tube centers and P r s is the Prandtl number on the surface.
The heat transfer coefficient is calculated by Equation (13) [22].
h = N u D k D
The logarithmic mean temperature difference for internal flow is obtained using Equation (14) [22], where ΔT1 is the temperature difference at point 0 of the heat exchanger and ΔT2 is the temperature difference at point L of the heat exchanger.
T l o g = T 2 T 1 l n T 2 T 1 = T 1 T 2 l n T 1 T 2

2.2. Numerical Analysis

The geometry was created with SolidWorks 2023 and was meshed in ANSYS 2019 R1. During the meshing process, the solid and ice volumes were divided toward the pipe walls and meshed separately as an external model to clearly observe the effects near the wall (Figure 4).
All solid and PCM volumes were named volumetrically, and the inner and outer pipe walls—where boundary conditions are applied—and the fluid inlet and outlet regions were appropriately defined.
In Fluent software, an “unsteady” (time-dependent) analysis is performed, and gravity is also included in the solution. The “Melting & Solidification” model is employed as the primary solution model, and the “Energy Equation” is included in the governing equations. The phase change analysis is based on the enthalpy–porosity method, which eliminated the need for continuously tracking the solid–liquid interface. Since the governing equations resemble single-phase equations, they can be easily applied to multidimensional problems. For turbulent flow, k-e and k-omega models are used as viscous models.
During the material definition phase, the thermophysical properties for the relevant solid elements and ice are defined, taking into account the separation of the liquid phase/solid phase, independently of temperature. A coupled algorithm is used as a solution. The final design is presented by comparing the numerical and theoretical results.
  • Volume fraction equation
The continuity equations of the two phases for a phase change material where the primary phase is liquid and the secondary phase is solid can be expressed as follows [23]:
1 ρ l t α l ρ l + α l ρ l v l = 0
1 ρ s t α s ρ s + α s ρ s v s = 0
  • The momentum equation
The velocity field is produced by solving a single-momentum equation for the entire domain and sharing it with the following phases [23]:
t ρ v + ρ v v = p + μ v + v T + F
The momentum equation is connected on the two phases’ volume fractions through their properties, ρ and μ.
The energy equation for a volume of fluid model (VOF) for two phases is shared below [23]:
t ρ E + v ρ E + ρ = k e f f T
where keff is the effective thermal conductivity. Energy (E) is handled as mass-averaged variables in the VOF model [23]:
E = α l ρ l E l + α s ρ s E s α l ρ l + α s ρ s
The energy equation is expressed as follows when the phase changing of the material is taken into account, as in this study [23]:
t ρ E s + ρ v E s = k e f f T

2.3. Mesh Independence Study

The CFD analyses were repeated using three different mesh structures: low, acceptable, and high density and quality. Numerous theoretical analyses and CFD simulations were conducted to achieve the reference conditions of producing 1000 kg of ice within 8 h. CFD analyses were initially performed using the theoretically optimized TTHE tube diameters and temperature of the HTF. Following model validation, the same analyses were repeated using three different mesh densities and qualities. The initial analysis was conducted on a mesh consisting of 56,500 nodes and 55,000 elements, with a minimum orthogonality quality of 0.9965, and skewness values ranging from a minimum of 0.003 to a maximum of 0.47. Subsequently, analyses were performed with a mesh comprising 16,350 nodes and 15,900 elements, achieving a minimum orthogonality quality of 0.999, and skewness values ranging from a minimum of 0.0017 to a maximum of 0.0277. Very similar results were obtained in both analyses.
Finally, a low-density mesh consisting of 1600 nodes and 1450 elements was used. The results obtained with the acceptable and high-density mesh structures showed a difference of only 0.6%, whereas comparisons between the low and acceptable density meshes revealed discrepancies of up to 11% in some cases. Consequently, the mesh structure with acceptable density and quality was selected, and all subsequent analyses were conducted using this configuration. The mesh structure for the ice tube is provided in Figure 4.

2.4. Model Validation

In this study, the inner and outer pipe diameters, pipe length and number of pipes of the TTHE, diameter of the spherical ball, number of spherical balls, and tank volumes are calculated iteratively to store 1000 kg of ice within 8 h, as can be seen in Figure 1. Similarly, the temperature of the HTF is also determined through iterative calculations. To validate this study, all input data from the most closely related work in the literature, which openly and fully shares its input data, were applied. Input data such as the thermophysical properties of the heat transfer fluid and the geometric dimensions of the TTHE were used in the proposed calculation method and model. The results obtained from this study show strong agreement with those reported by Kundu et al. [24]. The validation figure for the referenced study is presented below (Figure 5).

3. Results and Discussion

In this study, two different systems—the TTHE and the spherical ice ball, which is the most widely used conventional design in the industry—are compared, and an ice storage system that reduces both operation time and energy consumption is proposed. All analyses are conducted based on an 8 h period, referred to as the off-peak tariff, during which electricity prices are lower. A storage capacity of 1000 kg of ice is used as a reference point to facilitate easier comparison. The TTHE design is optimized using CFD analysis, validated with data from the literature, and then compared with the conventional industrial application (ice balls).
Initially, the TTHE design was developed using an HTF temperature of −2 °C and 8 h operation period as a reference, and CFD analyses were performed and compared with those for ice balls. However, the results revealed that under these conditions, complete ice solidification within the ice balls occurred in 10.7 h, not 8 h. Based on these initial findings, the results were interpreted, and in order to enable a more accurate comparison, the theoretical analyses were repeated under modified conditions that allowed for full solidification of the ice balls within 8 h, specifically at a cooling water temperature of −2.7 °C. Both systems were then compared under these two distinct operating conditions. The ice formation process for the TTHE at −2 °C cooling water temperature is presented in Figure 6, while the ice formation for the ice balls under both −2 °C and −2.7 °C conditions is presented in Figure 7. The film temperature (defined as the average of the inlet and outlet temperatures) was used as the input for all analyses. As expected, greater ice formation was observed near the inlet due to relatively colder HTF, with a corresponding decrease toward the outlet. Nonetheless, theoretical analyses that utilize the film temperature can be interpreted as representing an averaged effect, accounting for the thicker ice layer near the inlet and thinner near layer the outlet.
The theoretical analysis for the TTHE was optimized through CFD analysis. At an HTF temperature of −2 °C, the results show that although the maximum possible ice thickness in the ice balls is 50 mm, only 30 mm of ice forms after 8 h. The time required for complete solidification of the remaining 20 mm is calculated to be approximately 2.7 h. In other words, the same ice mass that can be achieved with TTHE in 8 h required 10.7 h with spherical ice balls, indicating a time saving of up to 25%. Furthermore, in the analyses conducted to ensure complete solidification of the ice balls within 8 h, it was determined that the cooling fluid supply temperature must be reduced to −2.7 °C. Under these adjusted conditions, the total time required for ice formation in TTHEs is found to be only 6 h.
The velocity of the HTF for both systems is set to 1.5 m/s to ensure fully developed turbulent flow conditions. Several theoretical analyses were conducted by varying the flow velocity. As expected, the heat transfer coefficient increased with higher flow velocities. However, as ice formation progresses, the impact of increased velocity becomes negligible due to the dominant influence of the thermal conductivity and thickness of the ice layer (Figure 8). Over time, this effect completely diminishes. Similarly, with respect to material selection, the results indicate that the ice thickness and its thermal conductivity have a more significant effect on the transfer performance than the flow velocity. These findings are consistent with the literature [24]. Kundu et al. (2024) [24] reported that inlet temperature significantly affects uniform melting and reduces melting time, whereas inlet velocity has a minimal effect due to the dominant influence of natural convection. Therefore, unnecessarily increasing the flow velocity will not enhance heat transfer. In practical applications, it would only cause excessive pressure losses and necessitate the use of a more powerful pump or motor, leading to an increase in energy consumption.
In the TTHE, solidification occurs on both the inner and outer surfaces of the tubes. Ice formation due to cooling from the center of the tube is referred to as ‘inner’, while that due to cooling from the outer surface is referred to as ‘outer’. It is observed that ice thickness increases rapidly during the initial hours but slows down after a certain point. This is because the formed ice layer acts as thermal insulation, creating resistance to heat transfer. Consequently, heat transfer decreases over time, leading to a reduction in the rate of ice formation. This insulating resistance caused by ice is taken into account in the calculations. When comparing ice thicknesses on the inner and outer surfaces, a greater accumulation is observed on the outer surface, attributed to its larger heat transfer area. As seen in the figure corresponding to the 28,880th second, some water remains unfrozen. The total ice thickness is 52 mm; however, a 1 mm inner radius of the tube is intentionally left unfrozen to ensure the safety of the heat exchanger, considering the volumetric expansion of water upon freezing.
The time-dependent formation of ice on the inner and outer surfaces of the TTHE and on ice balls at −2 °C and −2.7 °C is given in Figure 9. As expected, the rate of ice solidification decreases over time due to the insulation effect of the ice layer, which reduces heat transfer. Complete ice solidification in the TTHE (21 mm on the inner surface; 31 mm on the outer surface; 52 mm ice in total) is achieved in 8 h at −2 °C and in 6 h at −2.7 °C. For the ice ball (50 mm total thickness), complete ice solidification takes 10.7 h at −2 °C and 8 h at and −2.7 °C.
The variation in the total ice weight and total energy stored with respect to time are given in Figure 10 and Figure 11, respectively. The outer tube of TTHEs stores 761.4 kg of ice, the inner tube of TTHEs stores 252.4 kg of ice, and the ice balls store 1003.5 kg of ice. As expected, changing the HTF temperature does not affect the total stored energy but only alters the solidification time. At an HTF temperature of −2 °C, a total of 1000 kg of ice is stored within 8 h using TTHEs and within 10.7 h using ice balls. When the HTF temperature is reduced to −2.7 °C, the same amount of ice is stored within 6 h using TTHEs and within 8 h using ice balls. This demonstrates a time saving of up to 25% when using TTHEs. For the TTHE, the distribution of stored energy is found to be 75% on the outer surface and 25% on the inner surface, respectively. This confirms that energy storage on the inner pipe surface is also quite effective. After 8 h, the amount of energy stored in TTHEs is 8% higher than that in the spherical ice balls. This demonstrates the advantage of TTHEs, primarily due to the bi-directional solidification. Although the energy required to produce the same amount of ice is identical, the actual energy transferred is reduced in ice balls due to the higher thermal resistance of the thicker ice layer forming along a single radial direction, as explained in the Methodology and illustrated in Figure 3. In contrast, in TTHEs, bi-directional ice formation results in thinner ice layers on both the inner and outer surfaces, leading to lower overall thermal resistance. This has a direct impact on the heat transfer rate (Figure 3), ice formation time, and the total energy consumed.
The variation in the heat transfer rate (for 1000 kg of ice) with respect to time is given in Figure 12. To better illustrate the trend, the figure is divided into two parts: the first hour of solidification is given on the left, and the rest of the operation is given on the right. During the first hour of solidification, the heat transfer rate is relatively high due to the absence of an ice layer, and it was calculated as 175 kW for the TTHE. As ice begins to form, it acts as thermal insulation, introducing resistance to the heat transfer. This increasing thermal resistance, caused by the low thermal conductivity of ice, results in a decrease in the heat transfer rate and a slower rate of ice formation. This behavior was taken into account in all analyses and is consistent with the findings in the literature. The solidification rate decreases over time due to the growing thermal resistance at the sphere’s wall surface [25]. Kumar et al. (2001) also reported that the transformation of water into ice increases thermal resistance in ice bank systems [26].
As can be seen in Figure 12, during the first hour, the TTHE demonstrates a significantly higher heat transfer rate than the ice balls. At the end of the first hour, approximately 70 kg of ice had formed on the outer surface of the inner tube and approximately 300 kg on the inner surface of the outer tube in the TTHE, while the ice balls produced around 260 kg of ice. This reflects a 42% increase in ice formation compared to the ice balls. The primary reason for this outcome is the thermal resistance caused by the thickness of the formed ice layers and the significantly larger heat transfer surface area of the TTHE than the ice balls. Although from the end of the 1st hour to the beginning of the 5th hour the total heat transfer rate becomes slightly higher in the ice ball system, the total ice produced during this 5 h period is 820 kg for the TTHE and 770 kg for the ice balls. In summary, between the 1st and 5th hours, both the TTHE and spherical ice balls exhibited similar trends in terms of ice thickness development (Figure 9). However, in terms of total ice mass, the TTHE achieved a higher amount of ice formation. During this period, the TTHE experienced greater ice accumulation, which led to higher thermal resistance compared to the ice balls, thereby resulting in a lower heat transfer rate. Nevertheless, this does not imply that less ice was formed; on the contrary, due to its bi-directional ice solidification capability, the TTHE proved to be more advantageous. The change observed in the heat transfer rate at the end of the 5th hour can be explained as follows: for the ice balls, 20 mm thick ice had formed (out of a possible 30 mm), while the TTHE system had formed 42 mm of ice (18 mm on the outer surface of the inner tube and 24 mm on the inner surface of the outer tube), out of a possible 52 mm. This suggests that ice ball formation was only halfway completed, while the TTHE was nearing the end of the process.
Considering the total potential ice thickness for both designs, it is evident that the TTHE system approaches completion by the 5th hour, whereas nearly half of the PCM in the ice ball system is still in the liquid phase.

4. Conclusions

This study aims to present the TTHE system, which is more suitable for current conditions and expectations, offering greater energy storage capacity and time savings. It also seeks to evaluate the advantages and disadvantages of this design by comparing it with the traditionally popular spherical ice ball design, which has a long-established history. In this context, the TTHE design is determined through theoretical analysis, optimized using CFD, validated by data from the literature, and finally compared with the conventional ice ball design. The entire energy storage process is designed to produce 1000 kg of ice within 8 h, in alignment with Türkiye’s electricity tariff system, where the nighttime electricity rates are approximately 75% lower than the daytime rates, thereby incentivizing energy storage during periods of low demand. The key findings of this study are as follows:
  • The TTHE can store up to 8% more energy compared to ice balls under the same conditions (time, temperatures, etc.).
  • The TTHE can achieve the formation of the same amount of ice in 25% less time compared to ice balls under the same conditions.
  • Considering the benefits in terms of production and operational efficiency, high-density polyethylene (HDPE) was selected as the material for the ice balls. However, it has been observed that the primary determining factor is not the selected material (whether stainless steel or plastic) but rather the thickness of the ice layer.
  • Achieving fully developed turbulent flow is sufficient to ensure optimal conditions. Increasing the flow velocity does not provide a significant improvement in terms of heat transfer; instead, it leads to excessive pressure losses, necessitating a more powerful motor with higher energy consumption.
  • Accordingly, producing 1 ton of ice requires approximately 2100 ice balls, and manufacturing them from stainless steel is not economically feasible. Factors such as ease of production, ease of operation and maintenance, flexibility, and risk of leakage should be considered during the decision-making process.
  • In the TTHE system (based on the pipe diameters selected in this study), ice formation is observed to be 25% on the inner pipe surface and 75% on the outer pipe surface. Despite accounting for 75% of the total ice formation, the outer pipe surface yielded a thinner ice layer due to its larger diameter compared to the ice balls. A similar observation applies to the inner pipe as well. As previously noted, a thinner ice layer, which constitutes the primary limiting factor for heat transfer, has a significantly positive impact on overall system performance.
  • For TTHEs, the ratio of ice volume to the total volume of the thermal storage tank is calculated as 52.6%, which is slightly higher than that of the ice-ball-based thermal storage tank.
  • In total, 37 TTHEs (to produce 1 ton of ice) can be installed and dismantled vertically on the tank, allowing for the optional use of different phase change materials inside.
In conclusion, the TTHE system demonstrates greater suitability in terms of energy efficiency, required operation time, ease of production, operation and maintenance, design flexibility, and reduced risk of leakage. In particular, the intermittency challenges of renewable energy sources can be mitigated through the use of thermal energy storage systems. While storing electricity in batteries remains a costly option, thermal storage tanks offer a more economical alternative. Energy consumption related to ventilation, air conditioning, and heating/cooling demands can be reduced by advancing storage technologies. Thermal storage systems also enable peak shaving and cost reduction by shifting energy usage to off-peak periods. For future studies or industrial applications, higher storage volumes may be explored by varying pipe diameters and HTF temperatures. It is thought that this study will provide valuable insights for future studies and practical implementations.

Funding

This research received no external funding.

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.

Conflicts of Interest

The author declares no conflict of interest.

Nomenclature

Asurface cross-sectional area of cylinderm2
dxthickness of the heat transfer zone of the materialm
dTtemperature difference°C
kthermal conductivityW m−1 K−1
keffeffective thermal conductivityW m−1 K−1
kpipethermal conductivity of the pipeW m−1 K−1
hheat transfer coefficientW m−2 K−1
Llength of the cylinderm
r2outer radiusm
r1inner radiusm
Rthermal resistance in the cylinder°C/W
T1the temperature at radius r1°C
T2the temperature at radius r2°C
Wcompelectricity consumption of the compressorW
Q ˙ heat conduction in cylindrical tanksW
Qheat transfer in the cylinderW
QHgenerated heat in the condenser W
QCheat removed from the cold reservoir W
Ddiameter of the pipem
m mass flow ratekg/s
v the kinematic viscosity of the fluidm2 s−1
R e D Reynolds number-
PrPrandtl number-
P r S Prandtl number on surface-
N u D Nusselt number-
S t the transverse pitch between tube centersm
S D the diagonal pitch between tube centersm
S L the longitudinal pitch between tube centersm
α volume fraction-
ρ densitykg m−3
Etotal energy per unit massm2 s−2
Abbreviations
COPCoefficient of performance
CFDComputational Fluid Dynamics
HTFHeat transfer fluid
HDPEHigh density polyethylene
PCMPhase change material
TESThermal energy storage
TTHETriple-tube heat exchanger
Subscripts
lliquid phase
ssolid phase
aveaverage

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Figure 1. The methodology of the study.
Figure 1. The methodology of the study.
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Figure 2. (a) Schematic representation of the THE. (b) Schematic representation of the ice balls.
Figure 2. (a) Schematic representation of the THE. (b) Schematic representation of the ice balls.
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Figure 3. The time-dependent thermal resistance caused by ice formation for the TTHE and spherical ice ball.
Figure 3. The time-dependent thermal resistance caused by ice formation for the TTHE and spherical ice ball.
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Figure 4. Mesh details for the TTHE.
Figure 4. Mesh details for the TTHE.
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Figure 5. The variation in the liquid fraction over time.
Figure 5. The variation in the liquid fraction over time.
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Figure 6. The time-dependent formation of ice in the TTHE at −2 °C HTF temperature.
Figure 6. The time-dependent formation of ice in the TTHE at −2 °C HTF temperature.
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Figure 7. The time-dependent formation of ice in ice ball at −2 °C and −2.7 °C HTF temperatures.
Figure 7. The time-dependent formation of ice in ice ball at −2 °C and −2.7 °C HTF temperatures.
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Figure 8. The time-dependent heat transfer rate for the TTHE according to HTF velocity.
Figure 8. The time-dependent heat transfer rate for the TTHE according to HTF velocity.
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Figure 9. The variation in ice thickness over time of the TTHE and ice ball at −2 °C and −2.7 °C HTF temperatures.
Figure 9. The variation in ice thickness over time of the TTHE and ice ball at −2 °C and −2.7 °C HTF temperatures.
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Figure 10. The variation in total ice weight over time of the TTHE and ice ball at −2 °C and −2.7 °C HTF temperatures.
Figure 10. The variation in total ice weight over time of the TTHE and ice ball at −2 °C and −2.7 °C HTF temperatures.
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Figure 11. The variation in total storage energy over time of the TTHE and ice ball at −2 °C and −2.7 °C HTF temperatures.
Figure 11. The variation in total storage energy over time of the TTHE and ice ball at −2 °C and −2.7 °C HTF temperatures.
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Figure 12. The variation in heat transfer over time of the TTHE (outer tube, inner tube, and total ice tube) and ice ball at −2 °C HTF temperature.
Figure 12. The variation in heat transfer over time of the TTHE (outer tube, inner tube, and total ice tube) and ice ball at −2 °C HTF temperature.
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Table 1. Thermophysical properties of HTF.
Table 1. Thermophysical properties of HTF.
HTF
Inner tube velocity(m/s)1.50
Outer velocity *(m/s)1.50
Inlet temperature(°C)−2.00
Density(kg/m3)1073
Kinematic viscosity(m2/s)1.55 × 10−6
Specific heat capacity(J/kg°C)3515
Thermal conductivity(W/m°C)0.56
* according to preliminary studies.
Table 2. Specification of the TTHE, ice ball, and storage tanks.
Table 2. Specification of the TTHE, ice ball, and storage tanks.
Ice Ball Specifications
Internal diameter(mm)100
Thickness(mm)4.0
Thermal conductivity(W/m°C)0.45
Storage tank diameter(mm)1100
Assumed ice/total volume *(%)50
Usable height(mm)2000
* according to Kousksou et al. [10].
TTHE specifications
Outer tube diameter(mm)139.7
Thickness(mm)2.0
Inner tube diameter(mm)26.9
Thickness(mm)2.0
Length of tube(mm)2000
Thermal conductivity(W/m°C)16.40
Storage tank diameter(mm)1100
Usable height *(mm)2000
* according to staggered arrangement with 60°
Table 3. Properties of ice and water at 0 °C.
Table 3. Properties of ice and water at 0 °C.
Ice (0 °C)Water (0 °C)
Density(kg/m3)9171000
Latent heat of melting(kJ/kg)333.6-
Thermal conductivity coefficient(W/m°C)2.250.561
Kinematic viscosity(m2/s)-1.77 × 10−6
Thermal diffusion coefficient(m2/s)1.17 × 10−61.30 × 10−7
Specific heat(kJ/kg°C)20674210
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Karaca Dolgun, G. Comparison of Triple-Tube Heat Exchanger and Spherical Ice Balls for Energy Storage Performance: A Numerical Study. Energies 2025, 18, 4199. https://doi.org/10.3390/en18154199

AMA Style

Karaca Dolgun G. Comparison of Triple-Tube Heat Exchanger and Spherical Ice Balls for Energy Storage Performance: A Numerical Study. Energies. 2025; 18(15):4199. https://doi.org/10.3390/en18154199

Chicago/Turabian Style

Karaca Dolgun, Gülşah. 2025. "Comparison of Triple-Tube Heat Exchanger and Spherical Ice Balls for Energy Storage Performance: A Numerical Study" Energies 18, no. 15: 4199. https://doi.org/10.3390/en18154199

APA Style

Karaca Dolgun, G. (2025). Comparison of Triple-Tube Heat Exchanger and Spherical Ice Balls for Energy Storage Performance: A Numerical Study. Energies, 18(15), 4199. https://doi.org/10.3390/en18154199

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