Determination of the sensible heat effectiveness and pressure loss of a rotary regenerative heat exchanger using CFD

The paper presents a new method to determine the sensible effectiveness and pressure loss of rotary regenerative heat exchangers using computational fluid dynamics (CFD). It is based on CFD simulations of a single thermal wheel microchannel with a small cross-sectional area and thin walls, with cyclic inlet and outlet boundary conditions. Two unique measurement set-ups were designed and built for the experimental measurement of the heat exchanger characteristics. Five different types of thermal wheels were manufactured, measured, and simulated in ANSYS Fluent. All wheels achieve an effectiveness greater than 73% under certain (air flow) conditions, which is the minimum effectiveness required by Ecodesign (in the EU). For the examined exchangers, the effectiveness ranges from 66.5% to 83.3%, depending on the boundary conditions and geometric parameters of the rotors. The highest sensible effectiveness is achieved by heat exchangers with the largest heat exchange surface Ac; on the other hand, these wheels have the largest pressure loss. The paper discusses the use of a simplified ε-NTU correlation model for the HVAC systems (typically C* = 1). The correlation model and CFD results were compared and found to be different from each other. The results of the CFD simulation were compared with measurements to prove that the proposed simulation method can predict the behaviour of the real heat exchanger as a whole. It was demonstrated that the sensible effectiveness and pressure loss of the rotary heat exchanger predicted by the CFD simulations correspond well to the measured values within the measurement uncertainty ±1.3%. The proposed method can be used for the comparison of different rotary regenerative heat exchangers before their manufacturing and for verification that they meet the EU Ecodesign requirements set by the current legislation. It reduces the cost of the initial optimisation and testing of new designs.


Introduction
Heat exchangers are used in a wide range of applications, from refrigeration systems to heating, ventilation, and air conditioning (HVAC) (Zhang 2013). Their use in air conditioning is regulated by EU Commission Regulation No. 1253/2014 implementing the basic Directive 2009/125/EC of the European Parliament and of the Council with regard to Ecodesign requirements for ventilation units (EU 2014). According to this measure, all ventilation and air conditioning units introduced on the market from 2016 must have a high-efficiency heat recovery device. The energy consumption of HVAC systems represents a significant item in the total energy consumption of buildings, in which a heat recovery exchanger is a common part of these systems today. The arrangement of the air handling unit (AHU) also plays a role here (Liu et al. 2020).
The most suitable devices for heat recovery in central air conditioning systems are rotary regenerative heat exchangers (Mardiana-Idayu and Riffat 2012), which use a heat wheel composed of a large number of microchannels that rotate around its axis between two air streams. The transfer of heat between the streams is provided by the accumulation in the solid material of the heat wheel, that is, the walls of BUILD SIMUL (2023) 16: 869-887 https://doi.org/10.1007/s12273-022-0983-z Zmrhal et al. / Building Simulation / Vol. 16,No. 6 870 List of symbols Abbreviations AHU air handling unit CFD computational fluid dynamics HVAC heating, ventilation, and air conditioning the microchannels. The heat storage mass periodically passes through the hot air stream where the energy is stored and the cold air stream to which the heat is transferred and the storage mass is regenerated. In rotary regenerative heat exchangers, both sensible and latent heat can be transferred (Fu et al. 2019). The minimum sensible effectiveness of rotary heat exchangers has been prescribed by the EU Regulation no. 1253/2014 to 73%, effective from the year 2018. The effectiveness of heat transfer in a rotary heat exchanger depends on its design, the geometrical parameters of the heat wheel (Hajabdollahi and Shafiey Dehaj 2020;Güllüce and Özdemir 2020), the microchannels (Tran and Wang 2019), the rotation speed, and the airflow rate (Ruivo et al. 2015). The sensible effectiveness ranges from 50% to 85% (Alonso et al. 2015), commonly reaching around 80% (Farhat et al. 2022), while the heat wheel rotation speed is usually up to 20 RPM. Although the general target is to achieve the highest possible sensible effectiveness, the design of the rotary heat exchanger must take the simultaneous requirement for low pressure loss into account in order to maintain the low energy consumption of the fans (Hajabdollahi and Shafiey Dehaj 2020). For common rotary heat exchangers, the pressure loss is in the range of 50 to 200 Pa (Alonso et al. 2015).
Computational fluid dynamics (CFD) is a computer based simulation method that is often used to study fluid flow and heat transfer in various research applications. Simulations of the issues related to heat exchangers are frequently mentioned in the literature. Comprehensive review of CFD applications in the design and analysis of various types of heat exchangers was published in Bhutta et al. (2012). Regenerative heat exchangers were specifically targeted by studies of other authors, which were not mentioned in the review by Bhutta et al. (2012). For example, other authors investigated a mini-channel regenerative heat exchanger (Alfarawi et al. 2017). They modelled a set of adjacent tubular channels (a small section of a heat exchanger) with various diameters for each channel 0.5, 1.0 or 1.5 mm and found the simulation had good agreement with the measured data. The performance of a heat wheel for enthalpy recovery applications was studied by Çiftçi and Sözen (2017). A CFD analysis was used by Yamaguchi and Saito (2013) to predict the convective heat and mass transfer coefficients in the air channel and to develop a mathematical model for the analysis of the performance of rotary desiccant wheels. Rotary heat exchanger in a flue gas desulfurisation system was modelled by Özdemir and Serincan (2018) and another paper deals with developing a CFD-based virtual test rig for rotating heat exchangers (Corsini et al. 2015).

Objectives
The objective of this study was to analyse the pressure loss and the sensible effectiveness of rotary regenerative heat exchangers with different heat wheel geometries, as a function of the airflow rate and rotation speed, with the use CFD modelling and simulation.
Unlike the abovementioned studies, this paper targets the comprehensive CFD simulation study of the airflow in a single microchannel of the heat exchanger heat wheel during its rotation. The novelty of the paper is the development and presentation of the new method for the simulation of microchannels with a sinusoidal shape, a small cross-sectional area (<3 mm 2 ) and thin walls (0.5 to 0.7 μm). It is based on the analysis of one microchannel with cyclic inlet and outlet boundary conditions. The aim was to determine the microchannel sensible effectiveness and pressure loss for different geometries, to compare it with the values measured on real heat exchangers, and to prove that such a simplified model can realistically predict the performance of the whole heat exchanger. The proposed method can be used to compare design alternatives during the development of new types of rotary heat exchangers without the need for experimental measurements on the prototypes.
For the purpose of the current study, five different types of rotary regenerative heat exchangers were manufactured, measured, and simulated in ANSYS Fluent. They differed in their heat wheel geometric parameters, i.e., the geometry of the microchannels, the thickness of the heat storage material (walls of the microchannel) and the heat wheel depths. Two unique measurement set-ups were built for the experimental measurement of the sensible effectiveness and pressure loss of the heat exchangers. To the authors' best knowledge, there is very limited research reported on the use of CFD simulations in the transient testing of rotary heat exchangers with storage mass composed by thin-walled microchannels by such a combined CFD and experimental approach.

Traditional sizing and rating methods for rotary regenerative heat exchangers
The analytical methods to predict the operation characteristics of rotary heat exchangers were investigated at the beginning of the study. A thorough literature review was conducted to assess the alternatives to the experimental and numerical approaches in order to confirm whether they are necessary.
Non-dimensional parameters are commonly used for the design of heat exchangers and the prediction of their operating characteristics. In general, the sensible effectiveness of a rotary heat exchanger can be calculated with the use of the Number of Transfer Units (NTU) method and expressed by the following general correlation (Shah and Sekulić 2003): where C * and r C * are the heat capacity rate ratios.

Correlation ε-NTU
If the thermal resistance of the sheet metal layer is neglected, the thermal characteristic of the exchanger is NTU: For rotary heat exchangers used for heat recovery in HVAC, the dividing plane is usually in half of the wheel, half of the wheel is in the warm air stream (h), the other half is in the cold air stream (c). The total heat exchange surface of such an exchanger is c h The fluid-to-fluid heat capacity rate ratio is defined as and the wheel-to-fluid heat capacity rate ratio is The dimensionless characteristic ( ) hA * is then defined as For the interval of values 0.25  ( ) hA *  4, the influence of this parameter is negligible and for practical calculations in HVAC applications, ( ) hA * = 1 (Shah and Sekulić 2003). The relationship (2) can be simplified to Seo et al. (2018) Zmrhal et al. / Building Simulation / Vol. 16,No. 6 872 The basic thermal model ε-NTU for rotary regenerative heat exchangers was firstly presented by Coppage and London (1953) and later published in 1984 in the first edition of the manuscript of Kays and London (2018).
where ε 0 is the effectiveness of the counter-flow exchanger.
For C * = 1, ε 0 is defined as Equation (8) is often cited and serves as the basis for comparison of newly designed exchangers. Additional ε s -NTU correlations for the calculation of the sensible effectiveness are available in the literature. These correlations refine the basic model (8) or extend its validity to a lower rotation speed of the heat wheel.
The basic correlation (8) published in 1984 (Kays and London 2018) is only valid for a certain range of rotation speeds of the heat wheel and cannot be applied for lower speeds and the related lower heat capacity rate ratios of r C * < 0.32, as shown by Seo et al. (2018). The effect of the heat wheel rotation speed on the heat transfer efficiency was investigated later (Büyükalaca and Yılmaz 2002). The correlation that they presented has been verified experimentally, even for low speeds. It is possible to find a similar correlation (Worsøe-Schmidt 1991); however, it is not valid for low heat wheel rotation speeds (it is valid for 0.2 ≤ NTU ≤ 5; 0.5 ≤ C * ≤ 1 and r C * > 1). Shah (1975) developed a correlation for the results of Bahnke and Howard (1964), who were among the first to study the effect of longitudinal heat conductivity on the heat exchanger effectiveness. A modified form of the relationship has been published by Shah and Sekulić (2003). Fathieh et al. (2015) and Sanaye et al. (2008Sanaye et al. ( , 2009) used a correction factor for the exchanger cleanliness, however, without any further explanation. Cleanliness correction factor is used by Akbari et al. (2018). Fathieh et al. (2015) used a small test heat exchanger that was cyclically exposed to hot and cold air streams to investigate its properties. The issue of rotary heat exchanger evaluation by traditional semi-empirical methods was addressed also by De Antonellis et al. (2014a). They conducted an experiment to investigate two types of enthalpy heat exchanger (exchangers that transfer both heat and moisture). Both exchangers were made from aluminium sheet steel, one with a silica gel surface finishing and the other with calcium carbonate. Unfortunately, the given relationships for determining the sensible effectiveness were not universal, and they could be applied only for a specific range of the heat wheel rotation speed. Simonson and Besant (1999) presented correlations for the prediction of the sensible, latent, and total effectiveness of a rotary heat exchanger, which takes the change in the condition of the air into account, i.e., humidification, and an increase in temperature in the exchanger. Seo et al. (2018) developed a model of a rotary heat exchanger, which was used to derive a relationship to determine the thermal effectiveness applicable to all heat wheel speeds. They also derived the correction factor fc. A maximum error of 5% was found within the investigated ranges of NTU = 0.5 to 10. The results for higher speeds (6 to 16 RPM) show good agreement with the results presented by Kays and London (2018). However, for practical use in the field, they suggested to use more convenient simple empirical correlations that they also provided in their work.
Also, Abe et al. (2006) developed an analytical model of a rotary heat exchanger and presented the relationship for calculating the thermal effectiveness. Güllüce and Özdemir (2020) dealt with the optimisation of rotary regenerative heat exchangers in terms of the effectiveness and reduction in the total costs, including the investment costs. In their study, they used the relationship that accounts for the effect of longitudinal heat conduction taken from Shah and Sekulić (2003). The mathematical modelling of rotary heat exchangers was also dealt with by Nóbrega and Brum (2009).

Heat transfer calculation
The ε-NTU approach is a relatively fast and simple method to predict the sensible effectiveness of heat exchangers for different geometries. However, the NTU thermal characteristic depends on the heat transfer coefficient h that needs to be determined. As the flow of fluid in the microchannels of rotary heat exchangers is laminar (Re < 1000), the heat transfer coefficient h is calculated using the Nusselt number determined by the general correlation Nu = f(Geometry, Re, Pr), where the Geometry reflects the effect of the microchannel shape.
The solution for transferring heat from a fluid flowing in a microchannel (pipe) is defined either for developed flow (Graetz-Nussselt solution) or for undeveloped flow (Léveque solution). The validity of the solution for the undeveloped flow is limited to high values of the Graetz number: The flow of air in the microchannel of a heat exchanger develops quite quickly, and the solution for the undeveloped flow can be applied only in a limited region near the microchannel inlet. Consequently, in the fully developed laminar flow, the Nusselt number is constant and only depends on the geometry (shape of the microchannel) Nu = f(Geometry). The most commonly used relation (Shah and Bhatti 1987) applies to fully developed laminar flow in a sinusoidal wheel duct: where the geometric parameter α for the wave geometry channel according to Figure 3 is defined as

Methodology
The heat exchanger sensible effectiveness is defined as the ratio between the heat transfer rate and the ideal maximum possible heat transfer rate: where the heat capacity rates are If the heat capacity rates are identical ( c C  = h C  ), the sensible effectiveness of the heat exchanger according to Eq. (16) can be expressed as the ratio of the temperature difference on the given side of the heat exchanger (side of the heated or cooled air) to the maximum temperature difference in the heat exchanger (theoretically possible) The effectiveness defined in this way is used for the mutual comparison of exchangers, especially in the area of HVAC systems (with the exception of desiccation exchangers, which are not the subject of investigation in this contribution). For this reason, it is very important to maintain the condition c C  = h C  , or c M  = h M  (the differences in the air heat capacity c p,h and c p,c are negligible). Otherwise, the achieved effectiveness ε s cannot be compared.
The sensible effectiveness and pressure loss of a heat exchanger for HVAC applications is determined on the basis of the methodology described in EN 308. This methodology was used in the current study. In order to compare the characteristics of different heat exchangers, identical boundary conditions had to be maintained, see Table 1. The air temperatures were set to t c1 = 5 °C and t h1 = 25 °C for the cold side inlet and the hot side inlet, respectively, for the sensible effectiveness evaluation. The temperature of the air stream for the evaluation of the pressure loss t Δp was 20 °C. The study was carried out for three nominal airflow rates on the cold side of the heat exchanger c V  = 1400, 2800 and 4100 m 3 /h. The boundary conditions were chosen with regard to the practical (real) value of air velocity in front of the heat exchanger w = 1, 2 and 3 m/s. The mass flow rates of the cold and hot air for assessing the sensible effectiveness, as well as for the pressure loss evaluation, were equal c M  = h M  = Δp M  . The rotation speed of the heat wheel was in the range of 1 to 16 RPM for the experiments, and 2, 4, 8 and 12 RPM for the simulations. The pressure loss of each heat exchanger was evaluated when the heat wheel was not rotating.

Description of the investigated heat exchangers
The investigated rotary regenerative heat exchangers consisted of a heat wheel that was housed in a sheet steel casing with structural frame and thermal insulation, see Figure 1. Such heat exchanger module was divided by a horizontal middle bar. The top half of the heat wheel was placed in the stream of cold air and the bottom half in the stream of hot air; the streams were counterflow. The whole heat exchanger module could be slid into the measurement set-up. A wide variety of materials are used in manufacturing of heat exchanger heat wheels (Borodulin and Nizovtsev 2018): aluminium alloys, various types of plastics (Smith and Svendsen 2015;Chung et al. 2016), special materials based on cellulose, etc. The most common material is an aluminium sheet or aluminium foil with a thickness in the range of 0.04 to 0.1 mm. For this study, an aluminium sheet was chosen for the manufacturing of the investigated heat wheels. The aluminium alloy AW-8011A/H18 was used, with a specific heat capacity c r = 920 J/(kg·K), density ρ r = 2710 kg/m 3 , and thermal conductivity λ r = 215 W/(m·K) (Matmatch 2022).
The heat wheels of the regenerative heat exchangers were manufactured by winding alternating corrugated and flat aluminium sheets in roder to form microchannels in the shape of waves. This way, a porous heat storage mass was created, see Figure 2. The diameters of the heat wheel D can be produced in a wide range from 200 to 6000 mm. Heat wheels with a diameter of 1010 mm were manufactured for the study. The diameter of the inlet opening of the heat exchanger was 1000 mm. The heat wheels were powered by a stepper motor with belt transmission. The heat wheels analysed in this study differed in the shape of the microchannels, thickness of the heat storage material (walls of the microchannels) and their depths. Five different geometries were designed, manufactured, and simulated. Figure 3 shows a schematic diagram of the geometry with an indication of the main geometric parameters that are listed in Table 2.
The HX1 heat wheel was manufactured from an aluminium sheet with the thickness of 0.07 mm, all other heat wheels (HX2 to HX5) were manufactured from an aluminium sheet with the thickness of 0.05 mm. The height of the microchannels was 1.6 mm in all cases (common microchannel height is in the range of 1.4 to 2.3 mm). The heat wheel depth l is usually in the range of 100 to 200 mm, while 200 mm is the standard depth. The maximum depth of the heat wheel is limited by the pressure loss Δp of the heat exchanger and the related energy consumption of the fans. The standard depth of 200 mm was tested in the cases of HX1 and HX2 heat exchangers. However, heat wheels of different depths (170, 140 and 110 mm) were also investigated, and the influence of the depth on the heat exchanger effectiveness and pressure loss was assessed.
The hydraulic diameter of the heat wheel microchannel d hy , the heat transfer surface A c , and the weight of the heat wheel storage mass m r are listed in

CFD Simulation
A numerical study of the airflow in a single microchannel of the rotary regenerative heat exchanger was carried out with the use of CFD. Numerical 3D models were created in Ansys DesignModeller on the basis of technical drawings of the microchannels. Each model was divided into two regions, the fluid region and the solid region (microchannel wall). The following adjustments were made to the geometry arising from the methodology used and the nature of the CFD simulations:  Filling of the sharp corners at the base of the microchannels, for easier creation of the numerical mesh;  Only half of the thickness of the solid walls of the microchannels was modelled; the remaining part of the walls were approximated in the computational model by a symmetrical boundary condition for heat transfer. As the differences from the original geometry were very small, negligible effects on the simulated flow, pressure drop, heat transfer, and energy storage in the walls were expected.
Each numerical model was imported into the ANSYS Meshing software and meshed with a surface mesh on the inlet and outlet sides of the microchannel, see Figure 4. The longest edge size of the surface mesh cells was limited to 0.13 mm. This default cell size was manually adjusted in various locations to provide a finer mesh for the numerical simulation. The thin solid (aluminium) walls of the channels were meshed with three layers of cells, see the detail in Figure 4. A prismatic cell mesh was created in the near wall fluid region for the accurate calculation of the temperature and velocity profiles and heat transfer between the air and the solid material. The height of the first prismatic cell (adjacent to the wall) was 5×10 −3 mm, the growth factor was 1.2, and 16 layers of cells were formed, see the detail in Figure 4.
The surface mesh of the inlet and outlet sides was used as the base for the volumetric mesh and the discretisation of the entire spatial model. A structured hexahedral mesh with constant cell size in the direction of the airflow was used in the model; i.e., the sweep method was used along the length of the microchannel, see Figure 5. The dimension of the cells in this direction was 0.3 mm. A conformal mesh was used at the interface of the solid and fluid regions of the model. The volumetric mesh quality evaluation in all the created models was based on the commonly used indicators. In all cases, the recommendations for the skewness and orthogonal quality of the cells were met. The maximum value of the skewness was 0.55, the minimum value of the orthogonal quality was 0.65. The numbers of the computational cells for the microchannels of different types are listed in Table 3.

Boundary conditions and numerical solution
The target of the CFD simulations was to analyse the airflow and heat transfer in the microchannels, including the energy accumulation in the walls during the periodic alternation of the airflow direction and inlet air temperature caused by the rotation of the heat wheel across hot and cold streams.
The CFD simulations were solved using the ANSYS Fluent 2020 R2 software. The numerical solution of the governing equations was based on the finite volume method (Patankar 1980). All the simulations were solved as non-isothermal laminar flow of air that was considered as an incompressible ideal gas and its properties (density, heat capacity, and thermal conductivity) were calculated as a function of temperature. The Second Order scheme was chosen for the discretisation of the pressure equation as it is recommended for laminar flow in a duct (ANSYS 2018). The convective terms in the transport equations were solved using the second order upwind discretisation scheme. A segregated solver was used to solve the governing equations, and the PISO algorithm was applied to couple the pressure and velocity fields. The flow was considered to be unsteady. All the calculations were performed in double precision, as it has previously been found that airflow simulations converge better in the double precision mode.
Boundary conditions of constant velocity and temperature were prescribed at the inlet of the microchannels. Table 4 summarises the values for the calculation of sensible effectiveness (both the hot and cold air streams) and for the calculation of the microchannel pressure drop. The velocities were calculated based on the air density corresponding to the required inlet temperature, required mass flow rate of the air, the heat wheel cross-section area and the porosity of the heat storage mass (89.7% for the HX1 heat exchanger and 92.4% for the HX2 to HX5 heat exchangers). The boundary condition at the microchannel outlet was a pressure outlet type with prescribed static pressure difference of 0 Pa. The no-slip boundary condition was set for the inner surface of the channel (interface of the solid and fluid regions). The symmetry boundary condition was defined on the external surface of the aluminium wall.
During the heat exchanger rotation, each microchannel periodically crosses the region of the hot airflow and the region of cold air counterflow. This was approximated in the simulation by periodic changes in the airflow direction and temperature during the calculation. A Fluent journal file was created to control the interchanging of the inlet and outlet boundary conditions on opposite sides of the microchannel in specified time intervals. Figure 6 shows the time course of the area-averaged temperature at both sides of the HX1 microchannel during the calculation for different rotation speeds. It is possible to see that each periodic cycle of calculation consisted of a hot phase (i.e., the hot air inlet on the hot side of the heat exchanger) and a cold phase (i.e., the cold air inlet on the cold side). The temperature and airflow direction did not change for the calculation of the pressure loss of the microchannel (there was no alternation of the hot and cold airflow, as the heat wheel was not rotating).
The rotation of the microchannel around the heat wheel axis was approximated in the simulation using the Sliding Mesh method, as it is advised for unsteady calculations (ANSYS 2018). The position of the model in the coordinate system was changing during the calculation. A microchannel at a distance of 0.25 m from the rotation axis of the heat wheel was simulated. The simulation time step was set to 0.01 s. Eight iterations were computed during each time step, which was sufficient for good convergence of the simulations. The duration of the hot and cold phases of the cycle for the simulated rotation speeds and the related number of iterations are summarised in Table 5.

Grid independence study
A grid independence study was performed to verify that the results of the CFD simulations were independent to the resolution of the numerical mesh. Four models of the HX5 microchannel were created, with various mesh resolutions -one was discretised by the default mesh, as described above, one by a fine mesh and two by coarse meshes. Table 6 lists the main mesh parameters, namely: the maximum size of the surface cell on the inlet and outlet of the microchannel (max. cell size); the number of layers and the height of the first prismatic cell near the wall (1 st cell size, no. of layers); the number of cells dividing the thin solid material of the microchannel wall (solid wall div.); the dimension of the cells along the length of the microchannel (sweep dim.); and the number of cells of the computational mesh (no. of cells). Figure 7 shows the comparison of the inlet surface mesh for the four compared cases.
The four CFD models with different mesh resolutions were used in simulations with the heat wheel rotation speed of 12 RPM and the nominal airflow rate 4100 m 3 /h. The sensible effectiveness and pressure loss of the microchannel were evaluated, as these were the main outcomes of the numerical study described in this paper. The results are summarised in Table 7.
Two models with coarse mesh (Coarse 1 and Coarse 2) predicted lower pressure loss and lower sensible effectiveness    than the model with default mesh (Default). The difference in the pressure loss and effectiveness was 1 Pa and 0.8%, respectively for the coarsest mesh case (Coarse 1). On the other hand, the model with the fine mesh (Fine) produced the pressure loss higher by 0.1 Pa and the effectiveness higher by 0.1% than the default mesh model. The default mesh was used in the current study, in order to achieve good consistency of the results, but still keeping a reasonable computational time of the simulations, because many variants were calculated and compared during the numerical study.

Measurement of the sensible effectiveness
An extensive experimental study was performed to compare and validate the results obtained from the CFD simulations. The measurement set-up is presented in Figure 8. Figure 9 shows the assembled system for the experimental measurement of the sensible effectiveness of rotary heat exchangers. It consists of two air ducts (top and bottom) connected to the top and bottom chambers of the heat exchanger. The top air duct is used to transport the cold air (top-c), the bottom air duct is used to transport the hot air (bottom-h). All the ducts were covered with 30 mm thick thermal insulation to prevent heat losses. There were two fans in each duct branch (top: fan-c1 and fan-c2; bottom: fan-h1 and fan-h2), placed on both sides of the heat exchanger (HX). This enabled one to adjust the pressure conditions on the heat exchanger. The measurements were carried out with an overpressure in the HX top chamber, while the pressure difference between the top and bottom chambers Δp t-b was 1 to 10 Pa. The thermally insulated casing of the heat exchanger was equipped with sampling points to measure the static pressures before and after the heat wheel. The static pressure sampling was carried out multiple times, always at four points in both the top and bottom chambers of the heat exchanger. The exchanger was powered by the stepper motor (M) with a frequency converter for the rotation speed control. Electric heaters installed in both duct branches (EH-c1 and EH-h1) were used to heat the air; a cooler (CC-c1) was installed in the top branch to cool the cold air stream. Orifices were used to measure airflow rate (Orifice-h and Orifice-c). The principle of the airflow rate measurement using an orifice track is described, for example, in Zmrhal and Boháč (2021). A Pt100 wire was used to measure the air temperature at the inlets and outlets of the heat exchanger. It was strung across the cross-section of each heat exchanger chamber. The heat exchanger was properly sealed in the measuring chamber to reduce leaks and heat losses so that the measurement results could be compared with the CFD simulation.
The following data were recorded to assess the sensible effectiveness of the investigated heat exchangers: the air temperatures at the inlets (t c1 and t h1 ) and the outlets (t c2 and t h2 ) of the heat exchanger; the mass flow rates c M  and h M  that were evaluated on the basis of the pressure differences caused by the fluid flow through the orifices Δp c and Δp h . The measurements were carried out for each tested condition  for the duration of 1 hour. The results were evaluated for the last 30 minutes, after the cyclic steady state was reached.

Measurement of the pressure loss
The measurement set-up shown in Figure 8 allows for the measurement of the pressure loss of the entire heat exchanger module, as manufactured for an installation to a HVAC system. However, during the experiments it was found that the pressure loss of the inserted heat exchanger module depends on factors related to the measurement set-up and boundary conditions (pressure ratios in the heat exchanger chambers, leakages, etc.). Therefore, a dedicated measurement set-up was assembled for the more precise measurement of the pressure loss due to the airflow through the heat wheel itself (pressure loss of the microchannels), see Figure 10 and Figure 11.  The principle of the pressure loss measurement is described, for example, in the paper by Zmrhal and Boháč (2021). The measurement set-up was equipped with a fan with rotation control, an orifice for airflow rate measurement, and a short circular duct with a length of 160 mm, equipped with sampling points to measure the pressure. A circular duct was pressed onto the front of the heat wheel; the interface between the heat wheel surface and the duct was sealed to prevent unwanted air intake. The pressure differences on the orifice and on the heat wheel were measured with the use of micromanometers (M1 and M2). The pressure loss between sampling points 1 and E was determined from the difference in the fluid level Δh M1 of micromanometer M1: where α M1 is the angle of inclination of the micromanometer and ρ s is the density of the used fluid (ethanol The type A standard uncertainty was calculated as The type B standard uncertainty was calculated as The combined standard uncertainty was calculated as The expanded uncertainty was calculated as The coverage factor k is usually in the range of 2 to 3. The current study used k = 2.78. Similarly, the uncertainty of the heat wheel pressure loss was determined (Zmrhal and Boháč 2021). The pressure loss was measured indirectly by the measurement of the height of ethanol column Δh and determining its density ρ s from the measured temperature t s .
The uncertainties of both sensible effectiveness and pressure loss measurements are summarized in Table 8.

Results of the CFD simulations
The sensible effectiveness and pressure loss of the heat wheel microchannels with the different geometries at the selected airflow rates were determined by numerical analysis. The CFD simulation also provided detailed information about the velocity and temperature fields in the microchannels and about the development of the velocity and temperature profiles along the distance from the microchannel inlet. Figure 12 shows the velocity isosurfaces in cross-sections of the HX1 microchannel at 1 mm and 2.5 mm from the inlet, for different rotation speeds (similar velocity fields were observed for all five simulated microchannels). It is evident that the rotation around the heat wheel axis should be considered in the CFD analysis in order to correctly simulate the development of the velocity profile of the airflow in the inlet region. In this region, the rotation has a significant effect on the velocity profile which reaches higher values in one of the sharp corners of the microchannel (see Figure 12). It can be seen that, at higher exchanger rotation speeds, the deformation of the airflow velocity profile at the inlet region of the microchannel is bigger.
As the laminar flow develops along the length of the microchannel, the effect of the rotation decreases, see Figure 13. It was found that approx. 10 mm from the inlet of the microchannel, the effect of the rotation on the velocity profile is already small. The effect of the rotation on the temperature profile is less prominent and extends to approx. 5 mm from the inlet. From the temperature isosurfaces in Figure 13, it is clear that the temperature of the microchannel wall is homogeneous; this is caused by the high thermal conductivity of aluminium. A distinct temperature profile with a "core" in the centre of the microchannel is formed in the air stream. A stagnation field with a temperature close to the temperature of the aluminium walls can be observed in the sharp corners at the base of the microchannel. This reduces the sensible effectiveness as the corners are not efficiently used for forced convection and provides scope to optimise the microchannel geometry, considering the technological limitations of the manufacturing process.
The main target of the CFD simulations was to determine the sensible effectiveness of the investigated microchannels. The effectiveness was calculated using Eq. (18) as the ratio of the temperature difference on the cold side of the heat exchanger to the maximum temperature difference. Area-weighted temperatures at the inlet and outlet of the microchannel were used. The temperatures were time-averaged over the period of the cold phase of the cycle. The results were evaluated only after the cyclic steady state was reached, i.e., after reaching constant time averaged temperatures at the inlet and outlet of the microchannel during the hot (t h1 ) and cold (t c1 ) phase of the periodic cycle, during the unsteady simulation. Figure 14 shows the sensible effectiveness ε s of the investigated microchannels as obtained by the CFD analysis for all the simulated rotation speeds and airflow rates. It is evident that the higher the rotation speed of the heat wheel is and / or the lower the airflow rate is, the higher the heat exchanger effectiveness. The maximum values of effectiveness are summarised in Table 9, which were reached for a rotation speed 12 RPM.   From the comparison of the results for the microchannels HX2 to HX5 (same cross-section geometry, different length), it is evident that the longer the microchannel, the higher the effectiveness. This is related to the increase in the heat transfer surface. The highest effectiveness ε s was achieved by the HX2 type microchannel, which is the longest microchannel with the largest circumference of the crosssection profile, i.e. the larges heat transfer surface.
Using CFD simulations, it was found that the microchannels HX1 to HX3 achieve the sensible effectiveness of ε s > 73% for all the flow rates tested, meeting the requirements of the Ecodesign directive on ventilation units (EU regulation no. 1253(EU regulation no. /2014. The HX4 and HX5 microchannels meet the Ecodesign requirements only for some (lower) airflow rates.
The pressure loss of the simulated microchannels was evaluated after equalising the temperatures at the inlet and outlet t h1 = t c1 = 20 °C. The results are summarised in the Table 10. It is evident that the different microchannel geometry leads to different pressure losses Δp, which affects the energy consumption of the fans. As expected, the longer the microchannel or the higher the airflow rate through the heat exchanger, the higher the pressure loss, which results in a higher energy consumption. The influence of the microchannel profile can be seen from the comparison of the HX1 and HX2 microchannels which have the same length (200 mm). The pressure loss of the HX1 microchannel is higher as there is a higher velocity due to the lower porosity of the heat storage mass, and it also has a smaller hydraulic diameter.

Comparison of the CFD simulation results with measured values
The aim of the study was to verify whether the proposed simulation method, based on an analysis of one microchannel with cyclic inlet and outlet boundary conditions, can predict the behaviour of the real heat exchanger as a whole. The main concern was the relatively small dimensions of the microchannel and, in this regard, the main unknown was the thermal behaviour of the thin-walled heat storage material (0.05 and 0.07 mm) during the calculation.

Sensible effectiveness
The comparison of the simulated sensible effectiveness with the results of the measurement is shown in Figure 15. The comparison indicates a good agreement of the measured and simulated values with respect to the uncertainty of the measurement of ±1.3%. It can be concluded that the simulation of a single heat wheel microchannel can be used to predict the effectiveness of the whole heat exchanger, regardless of the other factors affecting the measurement (e.g., heat exchanger leakages). The largest differences in the results can be observed for the HX5 microchannel in the region of the low sensible effectiveness values that are obtained for low rotation speed (2 RPM). This region is characterised by a fast increase in the heat exchanger sensible effectiveness (Büyükalaca and Yılmaz 2002) , which could have caused the deviation between the measured and simulated values.

Pressure loss
In order to verify the microchannel pressure loss determined from the CFD simulations, measurements were carried out according to the methodology described in Section 2.3.2. The results of the measurements are displayed in Figure 16, including the uncertainty U Δp . The measured values are fitted with regression lines and related to the volume airflow rate through a single microchannel of the heat exchanger. It is clear from the measurements that the microchannel with the smallest hydraulic diameter d hy and the biggest length, i.e., microchannel HX1, has the highest pressure loss, as expected and predicted by CFD simulations. Figure 17 shows the comparison of the measured pressure loss with the values obtained from the CFD simulations. It can be seen that the simulation results match the measured values with a deviation less than 5%, while the uncertainty of the measurement is U Δp = ±3.3 Pa. It has been demonstrated

Comparison of the CFD simulation results with the ε-NTU correlation
A comparison of the CFD simulation results with the correlating ε-NTU model (Kays and London 2018) is shown in Figure 18. The results are displayed for all the investigated exchangers HX1 to HX5 and are colour-grouped according to the measurement boundary conditions (see Table 1).  Boundary conditions 1 correspond to the blue points, 2 -red points, 3 -yellow points. It is clear from the results that the CFD calculations performed for a nominal airflow of 2800 m 3 /h (red points, NTU = 3 to 4.5), correspond well to the simplified ε-NTU model. Conversely, for lower airflows (1400 m 3 /h -blue points, NTU = 5 to 8.5) the correlation calculation indicates higher values (by 6% to 8%), and for higher airflows (4200 m 3 /h -yellow points, NTU = 1.8 to 3) slightly lower values (by 1% to 5%).
As described above, the NTU calculation depends substantially on the heat transfer coefficient in the rotor channel h or on a suitable choice of the correlation Nu fd = f (α) or Nu x = f(Gz). Thus, the choice of the correlation significantly affects the result of the calculation, where the current literature does not establish a uniform and universal procedure for this.
A number of dimensionless correlations to express Nu for laminar flow of fluid through a channel with a small cross-sectional area can be found in the literature. When dealing with the modelling of rotary regenerative heat exchangers, several authors have inconsistently approached the choice of the correlation. Moreover, there are two types of boundary conditions applicable to the walls of the heat exchanger microchannel for the heat transfer calculations. The condition T defines a constant wall temperature t w on the whole heat transfer surface (the wall temperature does not change along the length of the microchannel). Condition H refers to a constant heat flux density from the wall surface and the resulting constant wall temperature on the perimeter of the channel in any selected cross-section perpendicular to the channel axis (the temperature changes along the length of the microchannel). It is of question which of the two types to use and when.
According to Shah and Sekulić (2003), the boundary condition H must be applied in counter-flow heat exchangers with C *  1. De Antonellis et al. (2014b) used the correlation for the fully developed flow and the T type boundary condition in his model. Wu et al. (2006) used a relation for a circular channel shape and the T type boundary condition, similar to Büyükalaca and Yılmaz (2002), Fathieh et al. (2015), Alhusseny and Turan (2016), Yadav and Yadav (2014) or Ruan et al. (2012). Stiesch et al. (1995) used the H type boundary condition, stating that the boundary condition on the walls of the rotary heat exchanger channel is closer to type H than to type T. Melian et al. (2021) modified the relationship for circular pipes according to Gnielinski (2010) and used the type H boundary condition. Ruan et al. (2012) and Kanaś et al. (2019) used the type H boundary condition. Niu and Zhang (2002) stated that the boundary condition on the walls of the rotary heat exchanger channels is neither type T nor type H, but due to the low temperature difference in the channel, the T condition can be used. They also stated that it is possible to use the H type boundary condition, but it is difficult to achieve these conditions for non-circular channels. Sanaye et al. (2008) incorrectly used the relationship according to Mikheev in their model (Bergman et al. 2011) which is only valid for Re > 10 4 , i.e., for turbulent flow (there is laminar flow in the channels of heat exchangers).
It is evident that the choice of the correct correlation Nu = f(Geometry, Re, Pr) is a very complex issue, has a major influence on the obtained results, and there is no universal or generally accepted correlation available. Moreover, the geometry of the heat exchanger microchannels and the selection of boundary conditions also play a significant role. Thus, the results of the analytical calculations can be misleading and they are suitable mainly for the rough estimation of heat exchanger characteristics. Measurements or CFD simulations are an alternative that can lead to more precise determination of the heat exchanger characteristics.
For an accurate prediction of the thermal behaviour of the exchanger, it is more appropriate to use CFD simulations according to the presented procedure, than the semi-empirical correlation models. CFD yields results with good agreement with the measured values (as demonstrated in Figure 15), while the correlation models show high variance in the results depending on the basic assumptions for the calculation (see Figure 18). On the other hand, the simulation calculation is time-consuming both for the model preparation and calculation time.

Conclusions
The paper presents a new method to determine the sensible effectiveness and pressure loss of rotary regenerative heat exchangers using CFD simulations. The target was to create a numerical model of a single microchannel with a small cross-section area and thin walls and verify that the model can predict the sensible effectiveness and pressure loss of the heat exchanger as a whole. This was undertaken by comparing the simulation results with measurements performed on two unique measurement set-ups assembled for the current study. Five cases with different geometries of heat exchangers (respectively, microchannels) were investigated.
The paper presents the following findings:  A new CFD simulation method to determine the effectiveness and pressure loss of a single microchannel of a heat exchanger heat wheel was proposed; it is intended for simulations of microchannels with a small cross-sectional area and thin walls.  Two unique measurement set-ups were designed and assembled to determine the sensible effectiveness and pressure loss of rotary regenerative heat exchangers.
 The method to evaluate the uncertainty of the measurements of the sensible effectiveness and pressure loss was described.  Five different heat exchanger heat wheels were manufactured and the results of an extensive experimental study were compared with the results of the CFD simulations; the uncertainty of the sensible effectiveness measurement was U ε = ±1.3%, the uncertainty of the pressure loss measurement was U Δp = ±3.3 Pa.  It was demonstrated that the CFD simulation of a single microchannel using the proposed method can predict the sensible effectiveness and pressure loss of the rotary heat exchanger as a whole; the results of the CFD simulation correspond well to the measured values within the uncertainty of the measurement, except for the measurements of the pressure loss at a very low rotation speed (in this study n = 2 RPM) of the HX5 heat exchanger.  The effect of heat exchanger heat wheel depth (i.e., microchannel length) and the airflow rate on the sensible effectiveness was investigated; it was found that all the tested heat exchangers meet the minimum sensible effectiveness of 73% required by the EU Ecodesign directive at a certain flow rate, while three of the designs meet the minimum effectiveness for all the tested flow rates.  The effect of the heat exchanger heat wheel microchannel geometry on the pressure loss was investigated as an important factor in the energy consumption for the air transport (energy consumption of the fans). The presented approach can be used to compare different rotary regenerative heat exchangers before they are manufactured, which reduces the cost of the initial optimisation and testing of new design options. The disadvantage of the CFD approach can be the time required to prepare the model and the calculation time related to the available computational power. However, it has been shown that the analytical or semi-empirical approach can be misleading and the measurements are expensive, as they must be performed by an accredited testing laboratory or a complex experimental track including energy management and a control and monitoring systems are required. Moreover, in the case of measurements, only a limited number of heat wheel samples can be manufactured and tested.

Future work
The proposed calculation method in CFD will be used in the future for the development of a new geometry of the rotor wheel of rotary regenerative exchangers with the aim of achieving high heat recovery effectiveness and, at the same time, low pressure losses to reduce the energy consumption of the fans. Although the CFD method is relatively computationally time-consuming, it can be advantageously used to optimise the design of a new rotor geometry.