Development of a Numerical Simulation Methodology for PCM-Air Heat Exchangers Used in Decentralised Façade Ventilation Units

Abstract

This paper presents the development of a methodology for using simulation to test decentralised façade ventilation systems with PCM exchangers and its validation with experimental data. Two approaches were compared to simulate the operation of an exchanger filled with phase-change material. In Method A, the geometry consisted of an air domain and a phase-change material domain, located in the cylinders of the exchanger. In this method, the phase transition was not modelled, but the specific heat was made temperature-dependent, wherein within the limits of the melting point, the specific heat is increased to a level that mimics the amount of latent heat from melting and solidification of the phase-change material. In Method B, the geometry consisted only of the air domain, and the temperature was set on the cylinder wall surfaces at each time step using UDFs. When comparing the methods, the temperature difference at the individual measuring points was no greater than 1 K and the resulting exchanger efficiencies did not differ by more than 5%. It was noted that when the phase-change material was modelled in the software with Method A, the results provided better representation of the values obtained in the experiment. Validation of the models was carried out by comparing the experimental results from the real tests with the simulation results of methods A and B. It demonstrated that both models correctly reflected the operation of the exchanger, and that the efficiency results achieved did not differ by more than 6% compared to the experiment. A comparison of supply temperatures and exchanger efficiencies with numerical simulations using two methods is presented. Visual comparison of the temperature distribution in the flowing air and the temperature distribution on the cylinder walls is also presented. This article adds to existing scientific knowledge of computer simulation of exchangers used in façade ventilation units with phase-change material.

1. Introduction

The increase in energy consumption in recent years is a phenomenon caused by population growth, urbanisation, economic development and technological advances. Increased energy consumption leads to more extraction and burning of fossil fuels, subsequently having a negative impact on the environment. This situation is prompting researchers to seek innovative solutions to making more efficient use of available energy resources [1,2,3,4,5]. Examples of sustainable solutions for buildings were described by Krechowicz [6,7]. Increasing attention is being paid to the development and testing of heat exchangers in ventilation systems, enabling heat recovery and reducing energy consumption. By using heat exchangers in ventilation, there is a potential for up to 90% recovery, as written by A. Dodoo [8], resulting in a reduction in energy consumption of approximately 30%, as reported by L. Zhang et al. [9] and H. Manz et al. [10].

There is ongoing research into the use of phase-change materials in heat exchangers. These materials are distinguished by their great ability to store energy per unit volume over a narrow temperature range. Latent heat storage involves taking advantage of a material’s phase change to store thermal energy over a narrow temperature range. This approach provides a higher energy density than traditional heat storage, which stores energy in the same temperature difference [11].

Over the last year, there have been a number of research projects carried out to investigate different methods of applying PCMs (phase-change materials) in ventilation [12]. Most of the studies where PCMs were used involved centralised ventilation, and as E. Zender-Świercz points out [13], there are still not enough studies in decentralised ventilation. Heat recovery in decentralised façade ventilation is necessary to ensure thermal comfort [14]. Until now, the most common solution in decentralised ventilation units has been the use of ceramic exchangers [15,16]. No articles were found showing comparisons of how to simulate exchangers filled with phase-change material used for heat recovery in decentralised façade ventilation units.

This paper presents the development of a methodology for using simulation to test decentralised façade ventilation systems with PCM exchangers and its validation with experimental data. Two approaches were compared to simulate the operation of an exchanger filled with phase-change material. In Method A, the geometry consisted of an air domain and a phase-change material domain, located in the cylinders of the exchanger. In this method, the phase transition was not modelled, but the specific heat was made temperature-dependent, wherein within the limits of the melting point, the specific heat is increased to a level that mimics the amount of latent heat of melting and solidification of the phase-change material. In Method B, the geometry consisted of only the air domain, and the temperature was set on the cylinder wall surfaces at each time step using UDFs.

The aim of this study was to compare two approaches to numerical simulations of the decentralised façade ventilation unit’s analysed efficiency in Ansys Fluent software. This article adds to existing scientific knowledge of computer simulation of exchangers used in façade ventilation units with phase-change material.

2. Materials and Methods

The experimental research was carried out at the Microclimate Laboratory of the Kielce University of Technology. A decentralised façade ventilation unit was installed in the external partition. The unit consists of an air intake/extractor on the outdoor environment side with a reversible fan, a chamber for the heat exchanger and a supply/exhaust on the indoor environment side (Figure 1).

A 250 mm diameter ventilation duct, located 1 m above the floor, feeds/removes air through the ventilation grille. The bench does not represent an actual ventilation installation; it only allows heat recovery efficiency evaluation. This is an innovative solution, and the heat exchanger itself has been granted utility model protection under number Ru.072910 [17]. The chamber for the exchanger is 255 mm long, 260 mm wide and 300 mm high.

The façade ventilation unit, thanks to the integrated Ventur ARC4-250C-012T reversible fan from Venture Industries (Kiełpin, Poland), operates in alternating cycles of supply and exhaust. An automated control system was used to manage the timed cycles, which allowed specific times to be set for the supply and exhaust cycles and regulated the fan frequency (Figure 1). The analysis focused on device operation in one-minute cycles. The mean flow velocity during the supply cycle was 1.8 m/s and 2.0 m/s during the exhaust cycle. The ventilation air volumes were 318 m³/h and 353 m³/h, respectively.

The tests were conducted for an internal temperature of 20 °C in accordance with EN 16798-1:2019-06 [18], and with an outdoor temperature that oscillated between −5 °C and 13 °C. Measurements were carried out under actual conditions in February–March 2023. The chamber contained a heat exchanger constructed from aluminium cylinders with a wall thickness of 1 mm (

Table 1. Heat exchanger parameters.

10 × 1 mm Heat Exchanger
External tube diameter—do (mm)	10
Internal tube diameter—di (mm)	8
Transverse tube pitch—St (mm)	20
Row pitch—Sl (mm)	10
Staggered tube	layout
Number of rows—N	25
Number of tubes—n	313
Tube height—H (mm)	300
Surface area of a heat exchanger—A (m2)	2.95
PCM volume—V (dm3)	4.72

), filled with a phase-change material formed from jojoba oil. A phase-change material is intended to provide heat recovery by collecting energy from the exhaust air and returning that energy during supply. The exact arrangement of cylinders in the exchanger is shown in Figure 2 and Figure 3.

During the exhaust cycle, the exhaust air has a temperature of approximately 20 °C and flows around aluminium cylinders filled with phase-change material, giving off thermal energy. Once the direction of the fan is changed, the supply cycle begins, during which the cold outside air flowing through the unit removes the thermal energy that was accumulated during the exhaust from the cylinders filled with phase-change material.

Ten stabilised cycles were selected from all measurements, representing similar conditions. Based on these, the temperature efficiency was determined according to Equation (1) in order to validate the simulation models analysed.

$${\eta }_t=\frac{t_2-t_1}{t_3-t_1}·100\left[\%\right]$$

(1)

where

• $t_1$—mean outdoor temperature for the cycle (mean of two thermocouples M2, M3);
• $t_2$—mean supply temperature for the cycle (mean of three thermocouples M4, M5, M6);
• $t_3$—mean internal temperature for the cycle (thermocouple M1).

Thermocouples M2, M3, M4, M5 and M6 were placed in the façade ventilation device (Figure 4). Thermocouple M1 monitored the temperature inside the room. Registration took place with a time step of 5 s. The tests performed were used to prepare

Table 2. Heat recovery exchanger efficiency.

	t1 [K]	t2 [K]	t3 [K]	ηt
1	280.03	286.35	293.03	48.63%
2	280.00	286.33	293.02	48.61%
3	280.05	286.34	293.00	48.56%
4	280.04	286.32	293.01	48.39%
5	279.95	286.29	293.02	48.55%
6	280.06	286.31	293.07	48.04%
7	279.98	286.32	293.02	48.57%
8	280.03	286.31	293.00	48.40%
9	280.05	286.34	293.01	48.52%
10	280.13	286.36	293.03	48.23%
Mean	280.03	286.33	293.02	48.45%
SD	0.049	0.021	0.020	0.002

, in which the mean temperature efficiency of heat recovery was calculated for the case described above.

Based on the foregoing experiment, two 3D transient-state simulation models were compared using Ansys Fluent v. 22 software designed for simulation utilising the computational fluid dynamics (CFD) numerical fluid dynamics technique. The airflow was analysed with heat transfer taken into account. The laws of mass, momentum and energy conservation were used as the basis for the numerical simulation performed.

The k-omega SST (shear–stress transport) turbulence model was used for the simulations to account for the effects of turbulence on airflow. This model is one of the most widely used turbulence models in Ansys Fluent, due to its effectiveness in modelling both the boundary layer and the interaction zone between the boundary layer and the free stream. The k-omega SST model is a hybrid that combines the advantages of the k-epsilon model and the k-omega model, as well as providing seamless transitions between them. It includes a modified definition of turbulent viscosity that incorporates the limitation of shear stress values where an undesirable pressure change has occurred. With this model, it is possible to more accurately model airflow in equipment such as heat exchangers [19,20].

Because of the transient analysis being used, the PISO (pressure implicit with splitting of operators) calculation scheme was utilised, constituting a pressure–velocity combination scheme belonging to the SIMPLE algorithm family. A time step of 1 s was set, and the maximum number of iterations was set to a time step of 30. The iterative convergence of the solution was assessed by observing the residues of the solved equations and the temperature values at the points corresponding to the thermocouple locations. A sum of absolute normalised residuals for all cells in the considered domain less than 10⁻⁷ for energy and 10⁻⁴ for other variables meant that the solution had achieved convergence.

A convection boundary condition was established on the exchanger housing walls, taking the heat transfer coefficient (68 W/m²K) into account. A boundary condition was established on the surfaces between the domains of air and phase-change material, taking the thickness of the cylinder representing a 1 mm aluminium layer into account. Due to the simulation of the exchanger half in the cross-sectional plane, a symmetry boundary condition was applied. According to the operation of the façade ventilation unit outlined in the section above, the inlet and outlet conditions were determined according to the supply or exhaust cycle. The control used execute commands to vary the inlet and outlet plane according to the cycle and to change the supply and exhaust boundary conditions. During the supply cycle, the inlet was the plane on the outside, while the outlet was the plane on the inside (Figure 5). During the exhaust cycle, the planes were swapped, i.e., the plane on the outer side became the outlet and the plane on the inner side became the inlet (Figure 6). A velocity-inlet/pressure-outlet boundary condition type was used. Temperatures and flow velocities at the boundaries were extracted from the measured data presented above. Air velocities were modelled as cycle-time averages of 1.8 m/s during supply and 2.0 m/s during exhaust. According to the measured data, the supply and exhaust temperatures were determined on planes in the immediate vicinity of the exchanger and were 280.05 K for the supply cycle and 291.35 K for the exhaust cycle. A turbulence intensity of 5% and a turbulence length scale of 0.25 m were used.

The tests carried out were modelled numerically through two methods to simulate heat accumulation by the phase-change material used in the exchanger. Method A involved modelling the material filling the exchanger by appropriately modelling its physical parameters, taking into account the heat of phase transition directly in Ansys Fluent. Method B consisted of creating an external user-defined function (UDF) script to define the changing temperature on the cylinder walls in the exchanger, taking the heat accumulation by the phase-change material into account.

2.1. Method A

The geometry of the analysed model reflects the heat recovery exchanger described above, which is part of the façade ventilation unit. Half of the exchanger was modelled in order to reduce the size of the model (Figure 7) The geometry consists of an air domain and a phase-change material domain located in the cylinders of the exchanger. The cylinder and housing walls were modelled as virtual walls with an assigned thickness of 0.001 m and thermal parameters of aluminium.

The geometry of the heat exchanger was meshed in Fluent Meshing using the polyhexcore method, which generates a hexahedral mesh inside the model and a polyhedral mesh with a boundary layer at the walls. Grid convergence was carried out by comparing three grids (

Table 3. Grid data used to establish convergence—Method A.

	Cells [-]	Minimum Size [mm]	Maximum Size [mm]	Offset Method Type	Number of Layers [-]	First Height [mm]
Mesh 1	6,080,135	2	15	last ratio	4	0.03
Mesh 2	7,401,137	1.5	15
Mesh 3	8,842,337	1	10

) of different densities. The mesh achieving convergence was selected, and the number of elements in the mesh was 8,842,337 (Figure 8). The size of the elements in the mesh varies according to the local geometry, with the smallest elements being 1 mm and the largest 15 mm. In areas where a detailed representation of the geometric structure is required, the element size is smaller, and the element size is larger in areas where the geometry is more regular. Mesh compaction was applied at the surfaces between which heat transfer takes place in the form of a wall layer using the last ratio method, where the number of layers was 4 and the transmission ratio was 0.3 (Figure 9). The height of the first near-wall layer was 0.03 mm, and this was determined using a method of successive approximations to obtain a y+ parameter of approximately 1–2.

The parameters of the phase-change material, jojoba oil in the analysed case, were modelled. Based on the literature [21,22,23,24] density of 867 kg/m³, thermal conductivity 0.15 W/m·K and linear viscosity for temperature 263.15 K–0.0418 kg/m·s and for temperature 363.15 K–0.008 kg/m·s, were assumed. For simplification and to focus on the main goal, which is the modelling of latent heat accumulation, it was decided to model jojoba oil as a fluid, for which a linear course of viscosity was assumed, reflecting the approximate physical properties of jojoba oil.

The simulations of latent heat accumulation were modelled in the software as an increase in the specific heat parameter within the melting point by the magnitude of the heat of phase transition using the results of DSC tests [23]. This method does not model the phase transition, but makes the specific heat dependent on temperature instead. The specific heat value within the melting point, which is 287.85 K, is increased from 10,810 J/kgK to 131,650 J/kgK. The increased specific heat maintained during a 1 K temperature change allows the model to represent the accumulation of 131,650 J/kg of latent heat from melting and solidification (Figure 10). This solution made it unnecessary to use the phase transformation methods built into Fluent while still allowing the Fluent solver to be used to calculate the temperature distribution.

2.2. Method B

Method B relies on the use of UDFs to simulate heat accumulation from the phase-change material filling the exchanger in order to establish the temperature on the exchanger cylinder walls during the heat exchange processes.

The geometry used in model B differs from that used in model A by omitting the phase-change material domain. In this case, only the air domain is simulated, where the key areas are those on which the cylinder wall temperature is simulated at a given point in the supply/exhaust cycle using UDFs. As in Method A, the cylinder and housing walls were not modelled in the geometry, but their parameters were included as boundary conditions (Figure 11).

The meshing of the geometry was performed in Fluent Meshing using the polyhexcore method. Grid convergence was carried out by comparing three grids (

Table 4. Grid data used to establish convergence—Method B.

	Cells [-]	Minimum Size [mm]	Maximum Size [mm]	Offset Method Type	Number of Layers [-]	First Height [mm]
Mesh 1	3,515,461	1	15	last ratio	6	0.03
Mesh 2	3,860,896	0.6	12
Mesh 3	4,907,155	0.3	10

) of different densities. A mesh was selected that achieved convergence, where the smallest elements were 0.3 mm in size and the largest were 10 mm in size. The number of elements in the mesh was 4,907,155 (Figure 10). At the surfaces between which heat transfer takes place, mesh compaction was applied in the form of a wall layer using the last-ratio method, where the number of layers was 6 and the transmission ratio was 0.3 (Figure 12 and Figure 13). The height of the first adjacent layer was 0.03 mm, and this was determined experimentally to give a y+ parameter of approximately 1.

The temperature on the cylinder wall surfaces was set using UDFs at each time step, taking a virtual cylinder wall with a 1 mm thick aluminium layer into account. An individual UDF was assigned to each of the 163 modelled cylinder walls to determine the wall surface temperature at each time step. This solution resulted in an even temperature distribution on the cylinder walls. The UDFs work on the basis of defined constants and data loaded from Ansys Fluent software. In the UDFs, constants such as the material’s melting and solidification temperature (287.85 K), latent heat of melting and solidification (131,650 J/kg), material mass of a single cylinder (0.303 kg), specific heat (10,810 J/kgK), initial material temperature, initial material phase (solid or liquid) and cylinder identifier have been defined. First, the initial temperature profiles on the cylinder walls are defined, followed by a data exchange between Ansys Fluent and the UDFs. The next step uses the collected data as the initial conditions in the next time step, where the phase of the material is checked and a new temperature is calculated. If the temperature of the material is below the melting point, no phase transformation takes place and a new temperature is calculated according to the principles of heat flow. If the temperature of the material exceeds the melting point, a phase transformation occurs and the amount of heat required for a complete phase change is calculated. Further heat flow calculations are then performed until a new equilibrium state is reached. The calculation of the new temperature of an element is based on a heat balance equation that includes mass, specific heat and heat supplied to/from the system in a time step and the temperature difference between the time steps. The calculations described above are based on the following formulae:

• Heating/cooling of material

$$\mathrm{Q}·∆\mathrm{t}=\mathrm{m}·\mathrm{c}·∆\mathrm{T}$$

(2)

where

• $\mathrm{Q}$—heat delivered to/by the system per time step [W];
• $∆\mathrm{t}$—time step [s];
• $\mathrm{m}$—weight of tube insert [kg];
• $\mathrm{c}$—specific heat of insert [J/(kgK)];
• $∆\mathrm{T}$—temperature difference between time steps [K]:

$$∆\mathrm{T}={\mathrm{T}}_{\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{p}}-{\mathrm{T}}_{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{v}\mathrm{i}\mathrm{o}\mathrm{u}\mathrm{s}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{p}}$$

(3)

• Phase transformation

$${\mathrm{Q}}_{\mathrm{p}\mathrm{h}\mathrm{a}\mathrm{s}\mathrm{e}}=\mathrm{m}·{\mathrm{c}}_{\mathrm{u}\mathrm{t}}$$

(4)

where

• ${\mathrm{Q}}_{\mathrm{p}\mathrm{h}\mathrm{a}\mathrm{s}\mathrm{e}}$—heat required for complete transformation [J];
• $\mathrm{m}$—weight of tube insert [kg];
• ${\mathrm{c}}_{\mathrm{u}\mathrm{t}}$—phase transition energy [J/(kg)].

The values of Q and Δt are retrieved in real time from the program. The heat value substituted into the equation is the value from the current time step, which corresponds to the completion of calculations for the current time step. The time step in the equation is the same as the one defined in Fluent.

3. Results and Discussion

Conducting simulations using two methods during one-minute supply and exhaust cycles using a 10 mm diameter cylinder exchanger filled with jojoba oil allowed comparison of their fit with the actual experiment. Figure 14 shows the mean temperature course at points M4, M5 and M6 during two stabilised supply-and-exhaust cycles.

According to the phases of the cycle, the temperature was maintained during the exhaust at a pre-set mean exhaust air temperature determined by the experiment. During the supply air phase, Method A achieved temperatures between 286.3 and 287 K, while with Method B temperatures oscillated between 286.9 and 287.5 K. The mean temperature difference between the two methods was 0.6 K. Both methods had similar temperature variations during the supply/exhaust cycle. When comparing the average values obtained with the temperature calculated on the basis of the experiment of 286.33 K, the differences were 0.28 K for Method A and 0.86 K for Method B.

Such temperature values translate into the efficiency level of the unit, which is shown in Figure 15. The efficiency for Method A oscillated between 47.5 and 52.5% and between 52.5 and 57% for Method B. The results of the two cases differed by a mean of 4.5%.

Nevertheless, attention should be paid to the disturbances that occurred after a change in airflow direction, caused by a temporary lack of convergence of results in the first seconds.

The averaged temperature efficiency of heat recovery with Method A was 49.73% and with Method B it was 54.22%. Comparing these values to the efficiency of 48.45% calculated from the experimental data, the differences were 1.28% for Method A and 5.77% for Method B. Both methods A and B represent the operation of the exchanger. Method A was more accurate in reproducing experimental results.

Table 5. Visualisation of the air temperature during the supply/exhaust cycle for methods A and B.

	Method A	Method B
Exhaust cycle
Supply cycle

shows a comparison of methods A and B by visualising the temperature of the air washing over the exchanger cylinders during the supply/exhaust cycle. The view shows a cross-section through the centre of symmetry of the exchanger. The right arm faces the internal environment and the left arm faces the external environment. The visualisation shows the change in air temperature as it flows through the exchanger.

Figure 16 shows a comparison of methods A and B by visualising the temperature on the exchanger cylinder walls during the supply cycle. The right side faces the internal environment and the left side faces the external environment. The visualisation shows the temperature distribution on the cylinder walls during exchanger operation. The difference in temperature distributions on the individual cylinders is visible. Method A shows unevenness in the temperature distribution on individual cylinders, while method B shows uniform temperatures on individual cylinders due to the modelling method.

The analysis carried out represents an innovative study of heat recovery exchangers in ventilation units for alternating supply and exhaust air. There are no studies in the literature on jojoba oil use for heat accumulation from exhaust air, and this paper fills the research gap in this area.

4. Conclusions

The following key conclusions can be drawn from the results obtained:

-

When comparing the methods, the temperature difference at the individual measuring points was no greater than 1 K and the resulting exchanger efficiencies did not differ by more than 5%;

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Validation has shown that both models correctly reflect the operation of the exchanger and that the efficiency results achieved do not differ by more than 6%;

-

The differences between the results may be due to the fact that Method A used the Fluent solver to model the temperature distribution on the cylinders, while Method B used the UDFs to set a uniform temperature across the cylinders;

-

It was noted that in Method A, where the phase-change material was modelled in the software, the results provided better representation of the values obtained in the experiment;

-

Method B has the advantage of shorter calculation time and lower computing power requirements;

-

Depending on individual needs, the user can choose the optimal method, taking higher accuracy or shorter calculation times into account.