A Lozano
email: alozano@litec.csic.es

F Barreras

N Fueyo

S Santodomingo

THE FLOW IN AN OIL/WATER PLATE HEAT EXCHANGER FOR THE AUTOMOTIVE INDUSTRY

Keywords: plate heat exchangers, herringbone heat exchangers, flow visualization, flow numerical simulation

This paper presents an experimental and numerical work to analyze the flow in an oil/water plate heat exchanger for the automotive industry. The plate heat exchanger is designed as twenty-one equal plates assembled in a stack. Each plate has a series of grooves in the surface, and is mounted upside down with respect to the preceding one, so that channels are formed that should direct the fluid motion and increase the heat transfer area. The flow has been experimentally studied by means of planar laser-induced fluorescence (PLIF) to visualize its structure, and particle image velocimetry (PIV) with fluorescent particle tracers to measure its velocity. It has also been numerically simulated.

In both cases, it has been observed that, for the analyzed design and either for oil or water, the flow is not uniform, and preferentially moves along the lateral extremes of the plates that conform the heat exchanger.

INTRODUCTION

The increasingly restrictive laws regulating pollutant emissions from all kinds of automobiles, together with the continuous rising in the gasoline and diesel price justify the enormous research effort devoted to optimizing the efficiency of IC engines, and to reduce their maintenance costs. As an improving element, it has been suggested to include an oil/water heat exchanger to cool down the lubricating oil, preventing its degradation, extending its useful life, and enhancing the engine lubrication. As cooling fluid, the water from the car cooling circuit would be used. To be able to conveniently fit the exchanger near the car engine, it should be small and, preferably, light. Furthermore, to minimize costs, this unit should be simple and inexpensive. To fulfill all these requirements, serpentine, laminated, and parallel flow heat exchangers have been developed as an alternative to traditional fin-tube types.

An interesting possibility is to use a plate heat exchanger. This type of exchangers, introduced by Richard Seligman in 1923, consists of a series of thin corrugated metal plates that are piled up and clamped together, separated by sealing gaskets, so that the corrugations in adjacent plates form a series of channels, where the heat-exchanging fluids circulate [START_REF] Seligman | The plate heat exchanger in the food industries -Part I: Genesis of an idea[END_REF]. Although these devices where first devised for the dairy industry, they are becoming increasingly popular and now they are common in many chemical and process industries. Among other advantages, they are compact, easily manufactured, simple to maintain and clean, and have very high heat exchange coefficients, enhanced by the often turbulent flow [START_REF] Reppich | Use of high performance plate heat exchangers in chemical and process industries[END_REF]. They can have 50% less volume than a fined tube heat exchanger, and 60% less than a serpentine one for the same thermal performance. The plate corrugations contribute to increase the total interchange surface and the flow path, consequently increasing the fluid residence time. In this way, a heat transfer coefficient 3 to 4 times higher than that for smooth channels can be achieved [START_REF] Würfel | Experimental investigations of heat transfer and pressure drop during the condensation process within plate heat exchangers of the herringbone-type[END_REF]. The effect on the heat transfer coefficient is similar to that produced by helical micro fin tubes when compared to smooth ones [START_REF] Miyara | Condensation heat transfer of herringbone micro fin tubes[END_REF]. However, although several recent studies have discussed the thermal aspects of plate heat exchangers [START_REF] Ribeiro | An algorithm for steady-state simulation of plate heat exchangers[END_REF][START_REF] Gut | Modeling of plate heat exchangers with generalized configurations[END_REF], details of the internal flow distribution are, in most cases, still unknown.

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For this reason, this paper presents a study of the flow in a grooved plate heat exchanger with a herringbone configuration. The device here analyzed is a first prototype aimed for commercial purposes in the automotive industry, and the objective of the study is to evaluate its performance in order to improve it, and hence, the competitiveness of the system. Planar laser-induced fluorescence has been applied to visualize the streamlines, while particle image velocimetry has been employed to measure the velocity filed inside the plates. Simultaneously, the flow has also been numerically simulated using the CFD FLUENT code. An excellent agreement between experimental and numerical results have been obtained revealing interesting details of the flowfield.

DESCRIPTION OF THE EXPERIMENTS

The plate heat exchanger here studied is designed as a series of twenty-one equal plates that are stacked forming a pile, so that each plate is mounted upside down with respect to the preceding one (i.e. after an in-plane 180° rotation). The plates, made of aluminum, are small trays 6 cm x 9.5 cm with a depth of 0.5 cm. In its surface, there is a series of V-shaped grooves 0.9 mm deep, with a semi-circular cross-section, in a herringbone pattern (see, for example, [START_REF] Würfel | Experimental investigations of heat transfer and pressure drop during the condensation process within plate heat exchangers of the herringbone-type[END_REF][START_REF] Wang | Analysis of performance of steam condensation heat transfer and pressure drop in plate condensers[END_REF]). When assembled, the corrugations of both plates form a series of channels that are expected to force the fluid to flow in a zigzag trajectory in order to increase the heat transfer area. The fluids, oil or water, circulate in the gaps between two contiguous plates, in alternate layers. Each plate has four orifices, two at each end. When a pair of plates is stacked together, two orifices serve as flow inlet and outlet, while the other two form a passing cylinder, so that the fluid is conducted to the adjacent plates. Figure 1 a) shows one of the plates, while Fig. 1 b) is a sketch of the stacking arrangement.

The system is designed for water flow rates ranging from 13 to 20 l/min, and oil flow rates from 5 to 30 l/min. It might be relevant to indicate that although stainless steel is generally preferred in most exchangers designed for process industries, mainly due to corrosion, cleanliness or mechanical requirements, aluminum is the material of choice for most of the automotive ACCEPTED MANUSCRIPT heat exchangers. Almost 100% of the oil coolers such as the one presented in this study are made of aluminum because of its good thermal properties and low weight. For serial manufacturing, the aluminum plates are brazed together in a controlled atmosphere furnace to produce a completely sealed heat exchanger in one shot, which is very convenient for the mass volume productions of the automotive industry.

As representative of the whole heat exchanger, the flow between two plates has been analyzed, by planar laser-induced fluorescence visualization (PLIF) and particle image velocimetry (PIV). As both techniques require optical access, one of the plates has been an original unmodified one, supported by a 13,5 x 10,3 x 7,5 cm aluminum block. The other has been replaced by a transparent metacrylate piece, machined with the same embossed inner surface as the plates, but flat on the outer side, that was bolted to the aluminum block, sealing the joint with a rubber gasket. After machining, the piece had to be polished to achieve the transparency requirements needed to apply the experimental techniques. The assembly is shown in Fig. 2. The plate has been painted in black to minimize stray reflections. The setup is completed with a liquid tank, a 200 W pump capable of delivering a maximum flow rate of 100 l/h with a pressure head of 7 m, a regulation valve and a rotameter.

The working fluids have been water, and, replacing the motor oil, a mixture of 55% water and 45% glycerin adjusted to have the same kinematic viscosity of the oil, 6.5 cSt. This replacement, that obviously maintains dynamic similarity, poses several advantages.

The viscosity can be varied by modifiying the glycerin percentage, and the mixture is colorless, cleaner and is not naturally fluorescent as opposed to most oils, which becomes an inconvenience when a luminescent tracer is to be tracked. The resultant flow should be essentially identical as that for oil, because it is controlled by the Reynolds number that is the same for both fluids. Effects due to non-equal parameters such as surface tension have to be negligible, as they are not included in the governing equations.

To illuminate the flow, a double cavity Quantel YG781C-10 pulsed Nd:YAG laser has been used, doubling the frequency of its emission to obtain 100 mJ pulses at 532 nm, with a pulse duration of 6 ns. In most PLIF and PIV experiments, the flow is sliced by a

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thin light sheet while the images are recorded at 90º to avoid geometric distortions. In this case it was not possible to illuminate the flow from the side. Hence, the laser beam has been expanded into a slightly divergent cylinder of light that impinged on the exchanger surface at a 60º angle, using a -25 mm f.l. spherical lens placed at 1 m of the heat exchanger assembly. The recording cameras have been located perpendicular to the flow. This arrangement (Fig. 3) does not introduce any perspective distortion in the images and eliminates any possible direct reflection of the laser light on the CCD arrays.

To visualize the flow pattern, Sulforhodamine B (Kiton Red) dissolved either in water or in the water/glycerin mixture has been selected as the luminescent tracer. The absorption spectrum of Sulforhodamine B has a maximum at 556 nm, hence excitation at 532 nm is very efficient [START_REF] Brackmann | Lambdachrome Laser Dyes[END_REF]. The fluorescence peak of this dye is located at 620 nm, which allows for an efficient discrimination between the emitted signal and the excitation laser light beam. To further decrease the background light, a Schott OG 550 filter has been placed in front of the camera lenses, blocking any residual 532 nm wavelength from the incident laser beam. The tracer has been injected in the heat exchanger plate inlet by means of a capillary tube with a diameter of 0.5 mm. To vary the injection point, the tube could be displaced across the inlet section.

To obtain the PIV image pairs, the flow has to be seeded with particles to scatter a fraction of the incoming light. Preliminary tests were performed with standard PVC particles, aluminum oxide platelets and glass spheres. However, as side illumination was not possible in this specific experimental set up, the contrast between the light scattered by the particles and reflections in the test rig was insufficient, even though the back plate was painted in flat black to improve it. To circumvent this inconvenient, fluorescent particles have been used. The particles were manufactured in the laboratory, by grinding a block of epoxy resin in which Sulforhodamine B had been dissolved before curing. To add the dye, Sulforhodamine solid powder was previously dissolved in ethanol. Although Sulforhodamine is soluble in water, adding water to the resin prevented it from solidifying appropriately. The powder obtained from the grinding process had to be sieved and classified afterwards into different groups depending of the particle sizes. It was

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experimentally verified that fluorescent particles with a diameter around 50 µm produced a satisfactory light emission, and also followed the small liquid flow structures. The flow conditions that have been tested are water flow rates of 1.3 l/min and 2.0 l/min and water/glycerin flow rates of 0.5, 1.0, 2.0 and 3.0 l/min. This flow rates are one tenth of the total flow rate that would circulate through the complete heat exchanger consisting of twenty-one plates.

DESCRIPTION OF THE NUMERICAL PROCEDURE

In addition to the experimental work detailed above, the device has been modeled with Computational Fluid Dynamics techniques using the CFD FLUENT code. As for the experimental work, the model comprises the channel between two neighboring exchanger plates. A mesh of tetrahedral cells has been used, totaling about 534,000 cells. Grid studies conducted with finer meshes (up to 740,000 cells) indicated that the results are gridindependent for this level of meshing. Figure 4 presents a detail of the computational domain, corresponding to the mesh on a fragment of the surface of one of the plates. The holes in the mesh correspond to contact points between the plate grooves, where soldering takes place during assembling.

Both water and oil flows have been analyzed, with water flow rates (per channel) ranging from 1.11 l/min to 2.08 l/min and oil ones from 0.45 l/min to 2.73 l/min. The corresponding Reynolds numbers, based on the average velocity in the cross-section and on the maximum channel width, vary from 2500 to 4700 for water and 100 to 600 for oil.

Accordingly, the water flow was simulated as turbulent, while the oil one was regarded as laminar. For the turbulent flow, two alternative turbulence models were used: the twoequation k-ε one [START_REF] Jones | The prediction of relaminarization with a twoequation model of turbulence[END_REF] and the one-equation Spalart-Allmaras one [START_REF] Spalart | A one-equation turbulence model for aerodynamic flows[END_REF], without any major difference on the results. The results presented here correspond to the k-ε model.

VISUALIZATION RESULTS

Water flow

When water is circulating, the flow pattern is similar for the two volumetric flow rates analyzed. When the dye is injected at the left side of the entrance orifice, it is observed that most of the liquid moves to the left, surrounding the blocked orifice, and travels downstream preferentially following the left channel, without moving along the corrugations. These streamlines extend until the lower part of the plate, where they bend again surrounding the blocked lower left orifice to end finally in the outlet orifice. 5 b) for a flow rate of 2.0 l/min. Here, the flow pattern is very similar to the preceding case, but the died water mixes more rapidly due to its higher speed, covering the whole plate area. Figure 6 shows a detail of an instantaneous image to stress the presence of eddies in the inlet region.

Water-glycerin mixture flow

For the water-glycerin mixture, the flow pattern is similar, but the more viscous fluid mixes worse because the flow is essentially laminar, and the streamlines are more clearly visible. Figures 7 a) to 7 d) are composite images displaying the 0.5, 1.0, 2.0 and 3.0 l/min flow rate cases. The dye injection points in each one are clearly identifiable. Again, the corrugations are not decisive in guiding the flow, and those fluid elements entering from the sides of the inlet orifice move preferentially to the sides of the plate. Occasionally, some died lines can be observed to follow the plate grooves, reflected in diagonal lines in the images. This behavior is more frequent for higher velocities. As could be expected, for increasing velocities and hence, increasing Reynolds numbers, the mixing improves and some small eddy structures can be observed especially at the exit. As opposed to the water case, vortices cannot be distinguished in the entrance orifice.

VELOCIMETRY RESULTS

Velocity measurements have been obtained for the central region of the plate. As previously stated, the image field of view has been 3.2 x 3.2 cm, so that two images have been required to cover the whole plate width, 6 cm, with a 0.2 cm overlap between them. Table 1 presents average velocity values for the right and the left images for all the flow conditions studied. It can be seen that the average longitudinal velocity is slightly higher on the right side of the plate, due to the non-symmetrical location of the plate inlet and outlet that are also displaced to the right. This difference is more noticeable for the more viscous fluid, for which the flow is less homogeneous. The horizontal velocity component is substantially lower than the vertical one. This result is in good agreement with the visualization images. The flow tends to move preferentially downwards, with relatively little influence of the diagonal grooves. Furthermore, in some cases, the streamlines present a zigzag shape, so it is logical that the average transverse velocity is close to zero.

Figure 8 shows some instantaneous velocity maps for a flow rate of 1.3 l/min of water, while Figure 9 depicts the corresponding ones to a water flow rate of 2.0 l/min. In all the processed images, bad vectors have been discarded, but neither smoothing nor interpolation has been applied. Some windows without any valid velocity vector correspond to the contact points between the upper and lower plates, as reflected in Fig. 4.

For both water flow rates, the lateral channels at the plate edges are clearly visible. In the

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upper right corner of the left area maps, the velocity vectors tend to deviate towards the left, due to the expansion after the entrance through the inlet orifice that would be located

NUMERICAL RESULTS

The simulation results are largely in line with the experimental findings. Figure 12 a) presents the water flow pattern as indicated by the streamlines arising from the inlet orifice, for the case with a flow rate of 1.67 l/min. This can be compared with the corresponding visualization images for a similar flow in Fig. 5. Once a provision is made for the effect of diffusion of the dye in the experimental setup for this turbulent flow, several common features that can be seen in the flow structure as revealed by the experimental approach are also present in the computational one. Thus, the flow can be seen as being preferentially longitudinal, and only occasionally following the direction of the grooves. One of these occasions is the expansion of the inlet flow to fill the central region of the plate (marked A in Fig. 13), where the flow moves along the grooves; Fig. Figure 13 shows the mass flow rate per unit area on the central cross-section of the exchanger for the water and for oil. The calculations indicate that the flow distribution for oil is more uniform than it is for water, for which the peripheral streams turn out to have a higher velocity. However, the mass flow rate distribution when water is circulating is more symmetrical with respect to the plate longitudinal axis, while for oil it is visibly displaced to the side where the inlet and outlet orifices are located. This fact is in good agreement with the measurements presented in Table 1, where a higher left-right asymmetry is evidenced for the water/glycerin mixture, which increases as the flow rate rises.

CONCLUSIONS

An experimental study has been performed to analyze the flow between two plates of an oil/water heat exchanger designed for the automotive industry. In the experiments, the oil has been replaced by a water/glycerin mixture with the same kinematic viscosity. The flow structure has been studied using PLIF visualization and PIV velocity measurements with fluorescent particle tracers, and has been simulated with a CFD code. With both fluids, water and water/glycerin, and for all the flow rates tested, the streamlines follow similar patterns. The flow moves preferentially and with higher velocities along the lateral channels, at the sides of the plate. The plate has V-shaped grooves in a herringbone configuration that should force the fluid in a zigzag path. However, this purpose is only partially fulfilled. For water, the mixing is higher and fluid elements entering from any point of the inlet can circulate along the grooves, although again, those streamlines starting from the inlet edges tend to occupy the lateral channels. In the case of the water/glycerin mixture, this behavior is more pronounced. Only the fluid elements entering from the central part of the inlet move through the central part of the plate, poorly following the corrugations. In this sense, it can be concluded that the objective of maximizing the residence time and the heat exchange surface has not been successfully achieved, and the plate design can be optimized. A first modification that should improve the flow would be to extend the corrugations a bit more into the lateral channels, thus reducing their width.

It has also been demonstrated that the numerical simulations reflect with high accuracy all the flow features observed experimentally. Hence, CFD can be used as a powerful predictive tool to improve the plate design.

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Fluid

  Two CCD cameras have been used as imaging devices. In the visualization experiments, a 6 x 8 cm field of view has been registered with a Princeton Instruments slow scan camera, with a 50 mm f#1.2 Nikon lens with an approximate resolution of 200 µm/pixel. For the PIV measurements, a PivCam 10-30 camera with an interlined 9 µm 1024 x 1024 Kodak CCD has been employed with a f#2.8, 60 mm macro Nikon lens, covering a 3.2 x 3.2 cm field of view with a resolution of 30 µm/pixel. The time interval between paired images has varied between 150 µs and 1 ms.

  In a similar way, for injection points on the right side of the entrance, the streamlines connect with the exit flowing in parallel to the right edge of the plate, without penetrating the central region. Only when the dye is injected from the central vertical diameter of the inlet, the fluid is observed to sometimes move along the grooves. From these injection points the streamlines open in an eye shape, covering most of the central part of the plate. Figure 5 a) shows the superposition of three images with left, center and right dye injection points for a water flow rate of 1.3 l/min. The eddies clearly visible in both the inlet and outlet orifices are indicative of the turbulent nature of the flow. A similar superposition of three images is depicted in Fig.

  above the area covered by the right side images. Similarly, in the lower part of the left area images, the velocity vectors are displaced towards the right, as they direct to the outlet orifice. For the same reason, vectors in the lower right part of Figs. 8 and 9 are slightly oriented towards the left. In the central region, velocity values are lower, with the streamlines following a certain zigzag patterns. Two velocity maps for the water/glycerin mixture are shown in Figures 10 and 11 for 0.5 l/min flow rate, and 3 l/min condition, respectively. Again, the flow structure is analogous to that obtained for the water cases. The preferential displacement along the side channels is apparent, with some sinuous movement in the central part. Again, streamlines are curved to the left in the upper right corner, and to the right in the lower part, approaching the outlet.

5

 5

  a) corroborates experimentally the existence of such a pattern for the water flow. Another clear similarity is the existence of a stream, marked B in figure 12, which arises at the back of the inlet orifice and moves around the blocked orifice along the periphery of the device. At the exit orifice, C, a large-scale eddy is induced by the curved boundary of the plate. Typical calculated results for oil are shown in Fig. 12 b), for a flow rate of 0.91 l/min. These can be compared with the visualization results of figure 7 b), for a flow rate of 1 l/min. As for the experimental work, the calculated average flow patterns from oil and water do not differ significantly, the main qualitative difference being the absence of the exit eddy.

Fig. 1 :

 1 Fig. 1: Heat exchanger studied: a) one of the aluminum plates that forms the stack in the final assembly, b) sketch of the stacking procedure.

Fig. 2 :

 2 Fig. 2: Experimental assembly using a black-painted original plate and a mechanized and polished metacrylate cover piece.

Fig. 3 :

 3 Fig. 3: Optical arrangement used for both visualization and PIV experiments.

Fig. 4 :

 4 Fig. 4: Detail of the computational mesh.

Fig. 5 :

 5 Fig. 5: Experimental flow visualization showing the superposition of three images with left, center and right dye injection points for two constant water flows: a) 1.3 l/min., b) 2 l/min.

Fig. 6 :

 6 Fig. 6: Close-up of the inlet region showing the presence of small eddies. Flow conditions correspond to a water flow rate of 2.0 l/min.

Fig. 7 :

 7 Fig. 7: Set of images for the water/glycerin mixture corresponding to flow rates of a) 0.5 l/min, b) 1.0 l/min, c) 2.0 l/min d) 3.0 l/min. Injection points are clearly discernible.

Fig. 8 :

 8 Fig. 8: Velocity map for water flowing at 1.3 l/min.

Fig. 9 :

 9 Fig. 9: Velocity map for water flowing at 2.0 l/min.

Fig. 10 :

 10 Fig. 10: Velocity map for water/glycerin mixture at a flow rate of 0.5 l/min.

Fig. 11 :

 11 Fig. 11: Velocity map for water/glycerin mixture corresponding to a flow rate of 3.0 l/min.

Fig. 12 :

 12 Fig. 12: Streamlines for a) water (flow rate: 1.67 l/min) and b) oil (flow rate; 0.91 l/min).

Fig. 13 :

 13 Fig. 13: Computed mass flow rate per unit area on the exchanger cross-section for water (top, flow rate: 1.67 l/min) and for oil (bottom, flow rate; 0.91 l/min).

Table 1 :

 1 Average velocity values for the right and left images for the different experimental conditions studied.

		Flow rate	Left area	Right area
		(l/min)
			U horiz (m/s)	V vert (m/s)	U horiz (m/s)	V vert (m/s)
		1.3	0.004	0.21	0.03	0.30
	Water	2.0	-0.007	0.39	-0.003	0.61
		0.5	-0.002	0.095	0.017	0.10
	Water +	1.0	-0.004	0.16	0.027	0.42
	glycerin	2.0	-0.009	0.28	0.083	0.69
		3.0	-0.018	0.48	0.15	1.12

ACKNOWLEDGEMENTS

This work has been supported by Valeo Engine Cooling.


Frédéric Kuznik
email: frederic.kuznik@insa-lyon.fr

Joseph Virgone

Jean Noel

Optimization of a Phase Change Material Wallboard for Building Use

Keywords: optimization, phase change material, wallboard, energy storage, thermal flow

In construction, the use of Phase Change Materials (PCM) allows the storage/release of energy from the solar radiation and/or internal loads. The application of such materials for lightweight construction (e.g., a wood house) makes it possible to improve thermal comfort and reduce energy consumption. A wallboard composed of a new PCM material is investigated in this paper to enhance the thermal behavior of a lightweight internal partition wall. The paper focuses on the optimization of phase change material thickness. The in-house software CODYMUR is used to optimize the PCM wallboard by the means of numerical simulations. The results

show that an optimal PCM thickness exists. The optimal PCM thickness value is then calculated for use in construction.

Introduction

Because we spend most of our time in enclosed spaces, technology to improve the thermal comfort of buildings has steadily increased, causing a corresponding increase in energy consumption. As aIn consequence, this has increased the release of polluting agents into the natural environment. Integrating phase change materials (PCM) into building walls is a potential method for reducing energy consumption in passively designed buildings. This tendency is confirmed by numerous papers. For a review, see in [START_REF] Tyagi | PCM Thermal Storage in Buildings: A State of Art[END_REF].

The use of PCM materials for construction has been a subject of considerable interest in the last decade. An interesting feature is that they can store latent heat energy, as well as sensible energy. As the temperature increases, the material changes phase from a solid to a liquid. As this physical reaction is endothermic, the PCM absorbs heat. Similarly, when the temperature decreases, the material changes phase from a liquid to a solid. As this reaction is exothermic, the PCM releases heat.

The main disadvantage of light weight buildings is their low thermal inertia.

Obviously, they tend to undergo large temperature fluctuations due to external cooling or heating loads. Using PCM materials in such buildings allows the reduction of temperature fluctuations. This have been proven in several numerical studies [START_REF] Heim | Numerical modeling and thermal simulation of phase change material with ESP-R[END_REF], [START_REF] Helmut | Thermal performance of phase change wallboard for residential cooling application[END_REF], [START_REF] Manz | Simulation of adiation induced melting and solidification in the bulk of a translucent building façade[END_REF], [START_REF] Ibanez | An approach to the simulation of PCMs in building applications using TRNSYS[END_REF]. The main problem lies in how to include PCM in building walls.

A new product, developed by the Dupont de Nemours company is composed of 60% of phase change material included in a polymeric structure. The final product looks like a relatively flexible panel. The innovation, in this case, consists in the encapsulation of a significant quantity of active PCM in a thermoplastic polymer which, after transformation into a relatively thin panel, allows for easy installation in any type of building envelope.

In this paper, the optimal value of the PCM wallboard thickness is investigated. First of all, the optimization assumptions are developed concerning optimal wallboard thickness. In order to calculate the optimal value, the inhouse numerical code CODYMUR is used and the results show that an optimal value exists, according to daily external and internal temperature fluctuations.

Optimization assumptions

This section is devoted to a summary of the assumptions used in this paper during the optimization process. First of all, the physical characteristics of the PCM are developed. The second part deals with the configuration retained for the optimization calculation. The last part presents some heuristic arguments of the optimal research.

Phase change material tested

The new product tested was created by the Dupont de Nemours Society.

It is composed of 60% of micro-encapsulated paraffin, which has a melting temperature of about 22 • C. The final form of the PCM material (figure 1) is a flexible sheet with a density of ρ P CM = 1019kg/m 3 .

The PCM material heat capacity was measured using a differential scanning calorimeter. The thermal analysis was performed in a range of 0 • C -34 • C with heating rates of 2 • C/min. The figure 2 shows the measured values of PCM specific heat c. This nearly Gaussian distribution corresponds to a narrow phase change [START_REF] Darkwa | Simulation of phase change drywalls in a passive solar building[END_REF].

The thermal conductivity of the PCM material was measured using a guarded hot-plate apparatus. The figure 2 shows that under the melting temperature, the thermal conductivity is about 0.22W/mK and decreases, over the melting temperature to about 0.18W/mK.

Studied configuration 2.2.1 General assumptions

One important hypothesis used during the optimization implementation is that heat transfer is unidirectional in building walls. This assumption is widely used for the thermal simulations of buildings.

The PCM wallboard is used in lightweight buildings (or caravans) to reduce room air temperature fluctuations, in particular when overheating occurs [START_REF] Kuznik | Energetic Efficiency of Room Wall Containing PCM Wallboard: A Full-Scale Experimental Investigation[END_REF].

Then, the wall tested is composed, from the outside, of 2cm of wood, a variable insulating material (like glass wool) with a thickness e ins (for the basic configuration e ins = 10cm ), a variable PCM thickness e P CM and 1cm of plaster. A complete description of this test wall is shown in figure 3, and the thermophysical properties of the materials are given in table 1. The exterior and interior heat transfer coefficients are respectively h e = 25W/m 2 K and h i = 7W/m 2 K.

The insulation thickness e ins can vary, but a minimum value is necessary to ensure a correct wall global insulation. In our optimization process, the minimum value of the thickness must fulfill the requirement of the French thermal rules [START_REF] Rt | Arrêté d'application du 24 mai 2006[END_REF] given by the U-value of the wall, U < 0.47W/m 2 K. The U-value is calculated via:

1 U = 1 h e + e wp λ wp + e ins λ ins + e p λ p + 1 h i (1)
Using the given thermophysical properties of table 1, the minimum thickness of insulation is 8cm with the wall considered.

External conditions

For the building configuration, outdoor boundary conditions and indoor thermal loads are specified while indoor air temperatures may change in time.

The main outdoor conditions are external air temperature and solar radiation.

These conditions are taken into account using the equivalent temperature T eq calculated using:

T eq = T e + αS h e (2)
with T e the exterior air temperature, S the total solar radiations, α the solar absorption coefficient of the surface and h e the exterior convective heat transfer.

Figure 4 shows the equivalent temperature calculated for a south vertical wall in Paris in July. From this figure, the assumption of a sinusoidal evolution for exterior equivalent air temperature can be used. Then the optimization process is held using a sinusoidal evolution of the exterior temperature between 15 • C and 35 • C and within a period of 24h. The impact of external conditions is also studied using a sinusoidal evolution of the exterior temperature between 10 • C and 40 • C.

Internal conditions

The interior air temperature is influenced by outdoor conditions, internal loads and , of course, the building composition. Similarly to the assumption used for exterior temperature, a sinusoidal evolution for the interior air temperature is used. For the interior temperature, the selected sinusoidal evolution is taken between T i,max and T i,min , with a phase difference of τ with exterior air temperature. As the PCM melting temperature is around 22 • C, only cases with T i,min < 22 • C < T i,max are considered. The boundary conditions are summarized in figure 5.

Heuristic arguments

The objective of the optimization process is to increase the storage capacity using as little PCM as possible. Two competing trends exist concerning the use of phase change material wallboards in buildings.

When the thickness becomes sufficiently small, the PCM is nearly isothermal.

The storage energy process is then only due to temperature changes. In this case, the larger the wallboard, the more important the storage capacity. The storage capacity is then proportional to PCM volume. As the heat transfer is unidirectional, the energy stored by the PCM is proportional to wallboard thickness e P CM . In conclusion, in the e P CM → 0 limit, the total energy stocked varies in ∼ e 1 P CM . This trend is indicated by the small-e P CM asymptote plotted in figure 6.

The penetration time for transient heat conduction t p can be evaluated by [START_REF] Bejan | Convection Heat Transfer[END_REF]:

t p ∼ (e/2) 2 α ( 3
)
where α is the thermal diffusivity of the medium. When e is large, the time needed for the heat to penetrate the PCM becomes larger than 12h: and the storage process cannot be complete during a day. Consider next the limit in which e P CM is large enough to consider a semi-infinite material. Increasing e P CM has no effect on the quantity of stocked energy: in the large-e P CM limit, the total energy stocked varies as ∼ e 0 P CM (constant value). This second asymptote has been added to figure 6.

The arguments presented below suggest the existence of an optimal thickness, but analytically determining this value is a laborious task. For this reason, numerical simulations are necessary to find the most appropriate value of e P CM .

Numerical modeling of Phase Change Materials

The optimization process of the PCM wallboard is performed with the help of numerical simulations. For that purpose, a home made code called CODYMUR is used. This code, developed for thermal simulations of building walls, has been adapted to take into account PCM. The first part of the section is a general presentation of the code, while the second part deals with the needed

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3.2 Modifications of CODYMUR

General concepts

The preceding version of CODYMUR [START_REF] Virgone | logiciels de simulation des ponts thermiques et du comportement thermique d'une paroi en régime variable[END_REF], [START_REF] Virgone | Développement d'outils d'études dynamiques en thermique du bâtiment[END_REF] supposed that all thermophysical properties of the materials were constant. That made it possible to carry out integration in time by an implicit method. In our case, the density remains constant (equal to 1019kg/m 3 ). On the other hand, conductivity and specific heat are variable with the temperature of PCM. Also, it was necessary to carry out the following modifications:

• enter conductivity and specific heat varying with temperature,

• modify the integration in time method: use of an explicit method with automatic time step modification.

Formulation of the thermal problem

The unidirectional heat transfer problem is given by:

• heat conduction equation ρ dH dt = div (-q) with q = -∇T (4)

• initial conditions

T (x, t = 0) = T 0 (x) ( 5 )
• boundary conditions

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩
q. n| e = -h e (T (x = 0, t) -T e (t))

q. n| i = -h i (T (x = e, t) -T i (t)) ( 6)

dH dt = dH dT . dT dt ( 7
)
and

C(T ) = dH dT (8)
Then, equation 4 becomes [START_REF] Feustel | Thermal performance of phase change wallboard for residential cooling application[END_REF], [START_REF] Manz | Simulation of adiation induced melting and solidification in the bulk of a translucent building façade[END_REF]:

ρC (T ) dT dt = div (-q) ( 9 )
A weak formulation of the problem in the calculation domain Ω which boundary is Γ gives:

Ω ρC (T ) φ i dT dt = Ω φ i div (-q)dΩ ∀ φ i continuous in Ω = Ω div (-φ i q) -λ (T ) ∇φ i ∇T dΩ = -Γ φ i q n| Γ dΓ - Ω λ (T ) ∇φ i ∇T dΩ ( 10
)
With T (x, t) = T j (t)φ j (x), equation 10 is:

j dT j dt . Ω ρC (T ) φ i φ j dΩ = - Γ φ i q n| Γ dΓ - j T j ⎡ ⎣ Ω λ (T ) ∇φ i ∇φ j dΩ ⎤ ⎦ (11)
If the functions are linear on the interval [x i , x i+1 ], the quantity ∇φ i ∇φ j is constant and the gradient is also constant. In this interval, Ω λ (T ) dΩ is:

Ω λ (T ) dΩ = x i+1 x i λ (T ) dx = dx dt T (x i+1 ) T (x i ) λ (T ) dT ( 12
)
Integration over time in this system is carried out by an explicit Euler scheme, with an automatic time step calculation: indeed, the characteristic time of this system can become very small and it is necessary to adapt the time step according to the stiffness of the system ( [START_REF] Kuznik | Energetic Efficiency of Room Wall Containing PCM Wallboard: A Full-Scale Experimental Investigation[END_REF]). The mass matrix, via the heatstorage capacity, is a function of time: it is thus recomputed at each time step.

Determination of the PCM optimal thickness

This section is devoted to the determination of optimal PCM thickness. The first part shows the existence of the optimum and its calculation for a specific case. The following parts are concerned with the estimation of the impact of some parameters: insulation thickness, outdoor condition, phase difference and indoor condition. Finally, the optimal value is commented. In order to find the optimal thickness, a set of numerical experiments is held using the modified version of CODYMUR presented in section 3 and for the test case described in section 2. For each thickness e P CM , the heat density

ACCEPTED MANUSCRIPT

fluxes at the interior and exterior surfaces are computed. Then the stored energy E s per square meter of wall is calculated for a complete day. Obviously, the released energy is equal to the stored one for a repetitive day.

Figure 6 shows that the stored energy is optimal for a PCM thickness of around 1cm. Layers in which the thickness is higher than this value are less interesting concerning energy storage: for a temperature swing with a period less than 24h, only a maximum of 1cm of PCM is really affected by heat loads.

The value of e P CM = 0mm corresponds to the storage capacity of the wall without PCM. The inertia of the light weight wall is double with 1cm of phase change material wallboard whereas the total wall thickness and weight only increase respectively by 4% and 20%.

An interesting phenomenon concerns the presence of a peak figure 6. When e P CM > e P CM,opt , not all the PCM wallboard is affected by the thermal flow.

Nevertheless, the global resistance of the wall increases because of the insulating effect of PCM. Then the thermal flow which passes through the wall decreases, and decreases the storable energy capacity. When e P CM is large enough, the thermal flow cannot pass through the wallboard and then the PCM acts like semi-infinite material: it is a horizontal asymptote.

Impact of the insulation thickness

Impact of outdoor air swing

The impact of the outdoor air condition is evaluated using two different swings:

a

Impact of phase difference

The figure 7-(c) shows the curves obtained for four phase differences τ : τ = -4h, τ = -2h, τ = 0h , τ = +2h and τ = +4h, the other parameters corresponding to the reference case of part 4.1. The optimal value varies between 9mm and 11.5mm.

Impact of indoor air swing

The indoor air temperature swing is a very important parameter of the problem. To evaluate its impact, three cases are tested: the reference case, a few fluctuations case with T i,min = 20

ACCEPTED MANUSCRIPT

to the reference case.

Figure 7-(d) shows the impact of indoor air swings. The optimum value varies between 9mm and 15mm. However, the higher value correspond to a nonrealistic case because the purpose of the PCM is to reduce significantly the indoor air temperature swing.

Conclusions concerning the optimum

The reference test case shows an optimum of about 10mm. Even if the optimal thickness value of PCM depends mainly on the indoor air swing, the value of 10mm corresponds to a good compromise considering the realty of the swings considered.

In order to illustrate the effect of 10mm of PCM compared to other materials, figure 8 summarizes the maximum stockable energy between 18 • C and 26 • C for 10mm of material and for 24h.

Conclusions

The use of phase change material wallboards allows the enhancement of the thermal inertia of buildings. In order for its use with an optimal storage effect during a complete day, the PCM thickness must be optimized. An optimization process was performed using a test case of a lightweight wall and interior/exterior temperature evolutions within a period of 24h.

Numerical simulations were held using a homemade software modified to take into account phase change materials. The results concerning stored energy in a complete day function of PCM thickness showed that the optimal thickness is 1cm. This 1cm wallboard allows a doubling of the thermal inertia of the building. This stored energy prevents building rooms from overheating during hot days, and during the night, the released energy increases the minimum air temperature. On the whole, PCM allows a decrease in temperature fluctuations inside rooms.

Given that the software analyzes only the behavior of a single wall, it is not possible to have a direct coupling between this wall and the temperature of the room: it would therefore be necessary to treat the entire room, to take into account solar radiation and air treatment systems. However, the analysis of flows exchanged with a room's interior side of a wall enabled us to quantify the energy stored and released by the wall with a probable assumption of interior temperature changes. This allowed us to calculate the optimal thickness of PCM to be included in room walls.

3. 1

 1 Presentation of numerical code CODYMUR CODYMUR allows for the study of the thermal behavior of a wall, supposing unidirectional heat transfer, under dynamic conditions. It was developed at the Thermal Sciences Center of Lyon in 2002. Considering a wall, external conditions available are climatic data (for various French sites), temperatures, solar radiations,... CODYMUR carries out calculations for temperatures within a wall as well as thermal flows at the surfaces, as a function of time. The results make it possible to analyze the influence of parameters like the constitution of the wall (thicknesses, materials used for the layers, respective positions of the layers...). The studied wall is made of multiple layers associated with a parameter list characterizing heat exchange (absorption of short wavelength radiation and total surface thermal resistances). The initial conditions are either a temperature solution of the stationary problem at the initial moment, or the temperature of the preceding calculation. The boundary conditions are defined by interior and exterior conditions (which correspond obviously to climatic conditions). An environment has two variables: the air temperature and the solar radiative fluxes. A demonstration version of CODYMUR (without the PCM) is freely available [13].

4. 1

 1 Existence of the optimum: case of τ = 0h, T i, min = 18 • C, T i, max = 25 • C and e ins = 10cm

Figure 7 -

 7 Figure 7-(a) shows the curves obtained for four insulating material thicknesses: e ins = 8cm, e ins = 10cm,e ins = 15cm and e ins = 20cm, and other parameters corresponding to the reference case of part 4.1. From this figure, the insulation thickness doesn't affect the optimum PCM thickness value. This is due to the

  sinusoidal evolution of the exterior temperature between 15 • C and 35 • C and the same evolution excepting the minimal and maximal temperatures which are respectively 10 • C and 40 • C. The other parameters are those of the reference case of part 4.1. The figure 7-(b) shows the results obtained for the optimum value. The external condition doesn't much affect the optimal PCM thickness value. Once again, this is due to the insulating material.

Fig. 1 .Fig. 2 .

 12 Fig. 1. DuPont de Nemours material.

Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .

 3456 Fig. 3. Test wall composition.

Fig. 7 .

 7 Fig. 7. Impact of various parameters on optimal PCM thickness.


R Cabello
email: cabello@emc.uji.es

D Sánchez

R Llopis

E Torrella

Keywords: carbon dioxide, CO 2, refrigerating plant, optimum pressure, gas-cooler, transcritical cycle

This work presents the experimental evaluation of the energy efficiency and optimal gas-cooler pressures of a single-stage refrigerating plant working with carbon dioxide as refrigerant in transcritical conditions. The performance of the plant was tested at three different evaporating temperatures (-0.9, -10.1 and -18.1 ºC), for three gas-cooler refrigerant outlet temperatures (31.2, 33.6 and 40.0 ºC.) at each evaporating temperature and in a wide range of gas-cooler pressures (74.4 to 104.7 bar).

The experimental tests enabled us to calculate accurately the optimal gas-cooler pressures and compare them with the most commonly used relations to define this value in single-stage refrigerating cycles operating with carbon dioxide in transcritical conditions. Furthermore, an analysis of the reduction in energy efficiency produced in the plant if the optimum pressure is not well defined is also presented.

Introduction

The greenhouse effect associated to artificial refrigerants [START_REF]The Montreal Protocol on Substances That Deplete the Ozone Layer[END_REF][START_REF]The Kyoto Protocol to the United Nations Framework Convention on Climate Change[END_REF] is forcing the scientific community to devise and develop solutions related to the air-conditioning and refrigeration fields in order to avoid this problem. Many efforts are focused on using natural refrigerants, such as hydrocarbons (butane, propane and isobutane) [START_REF] Wongwises | Experimental investigation of hydrocarbon mixtures to replace HFC-134a in an automotive air conditioning system[END_REF] and carbon dioxide [START_REF] Lorentzen | Revival of carbon dioxide as a refrigerant[END_REF][START_REF] Pearson | Carbon Dioxide -new uses for an old refrigerant[END_REF], because of their low or minimal contribution to direct greenhouse effect [START_REF] Wang | Perspectives for natural working fluids in China[END_REF][START_REF] Sand | Energy and Global Warming Impacts of HFC Refrigerants and Emerging Technologies[END_REF].

Among these groups of natural refrigerants, with a minimal impact on the environment, carbon dioxide seems to be the trend for the future owing to its safety characteristics, but a lot of effort needs to be made in order to overcome the technical problems and in order to achieve a level of energy efficiency comparable with that achieved using HFCs.

Within carbon dioxide technical advantages, it could be highlighted its high heat transfer coefficients in the supercritical region [START_REF] Kima | Fundamental process and system design issues in CO 2 vapor compression systems[END_REF] and its high pressure levels combined with low specific volumes, which allow the size of the components to be reduced. On the side of disadvantages, carbon dioxide needs special equipment due to the high working pressures, and a special regulation it is required because temperature and pressure are decoupled in the supercritical working region and a maximum efficiency is presented [START_REF] Kima | Fundamental process and system design issues in CO 2 vapor compression systems[END_REF][START_REF] Sarkar | Optimization of a Transcritical CO 2 heat pump cycle for simultaneous cooling and heating applications[END_REF].

Experimental results from prototypes in the automobile industry [START_REF] Brown | Comparative analysis of an automotive air conditioning systems operating with CO 2 and R134a[END_REF][START_REF] Liu | Experimental investigation of a CO 2 automotive air conditioner[END_REF] have shown that it is possible to obtain a similar level of energy efficiency with respect to R134a, but for the time being, this comparison could not be extended to other applications.

Some other researchers are experimenting in other sectors, examples being Girotto et al. [START_REF] Girotto | Commercial refrigeration system using CO 2 as the refrigerant[END_REF] in commercial refrigeration with two-stage compression systems, Cavallini et al.

[13] and others [START_REF] Rozhentsev | Some design features of a CO 2 air conditioner[END_REF] in air conditioning, Nekså [START_REF] Nekså | CO 2 heat pump systems[END_REF][START_REF] Neksa | CO 2 -heat pump water heater: characteristics, system design and experimental results[END_REF] in heat pumps where the results are quite good, and some others that are developing new cycle configurations [START_REF] Robinson | Efficiencies of transcritical CO 2 cycles with and without an expansion turbine[END_REF][START_REF] Boewe | Contribution of an internal heat exchanger to transcritical R744 cycle performance[END_REF] and new elements [START_REF] Cavallini | Properties of CO 2 as a refrigerant[END_REF][START_REF] Casson | Optimisation of the throttling system in a CO 2 refrigerating machine[END_REF]. But what is common to all transcritical carbon dioxide applications is the existence of an optimal pressure in the gas-cooler at which the maximum efficiency of the refrigerating cycle is achieved. Liao et al. [START_REF] Liao | A correlation of optimal heat rejection pressures in transcritical carbon dioxide cycles[END_REF], Sarkar et al.

[9], Kauf [START_REF] Kauf | Determination of the optimum high pressure for transcritical CO 2 refrigeration cycles[END_REF] and Chen et al. [START_REF] Chen | The optimum high pressure for CO 2 transcritical refrigeration systems with internal heat exchangers[END_REF] have worked, from a theoretical point of view, on the definition of this optimal pressure and its dependence on the refrigerating cycle variables, which are mainly the refrigerant outlet temperature in the gas-cooler (related to environment temperature in the case of Chen and Kauf) and the evaporating temperature.

In this work, we present the experimental evaluation of the energy efficiency of a carbon dioxide refrigerating facility working in transcritical conditions for several evaporating pressures at various refrigerant outlet temperatures in the gas-cooler, where the cycle efficiency was evaluated for a wide range of gas-cooler pressures. The experimental results were used to compare the optimal pressure allocation with the expressions proposed by the authors [START_REF] Sarkar | Optimization of a Transcritical CO 2 heat pump cycle for simultaneous cooling and heating applications[END_REF][START_REF] Liao | A correlation of optimal heat rejection pressures in transcritical carbon dioxide cycles[END_REF][START_REF] Kauf | Determination of the optimum high pressure for transcritical CO 2 refrigeration cycles[END_REF][START_REF] Chen | The optimum high pressure for CO 2 transcritical refrigeration systems with internal heat exchangers[END_REF]; the deviations of these expressions from the experimental values and their implications in the COP of the plant are also discussed in this work.

Experimental plant description

The main equipment that makes up the experimental plant developed to carry out the evaluation of carbon dioxide as refrigerant working in a transcritical cycle (Figure 1) is: a 4kW semi-hermetic single-stage vapour compressor, a double stage expansion system with an liquid receiver between stages, concentric counter current gas-cooler and evaporator and internal heat exchanger, as shown in Figure 2, although in this paper only the results obtained while operating without the internal heat exchanger are presented. The double stage expansion system consists of a pressostatic expansion valve (back-pressure) that is employed for the first expansion and an electronic expansion valve for the second. The first expansion stage, performed by the pressostatic expansion valve, allows the gas-cooler outlet pressure to be controlled, and the second enables us to control the evaporating process by means of the electronic expansion valve whose sensors are placed at the inlet and outlet of the evaporator. The liquid receiver is placed after the first expansion stage in order to regulate the mass of refrigerant in the plant. with an analogical signal obtained from the inverter drive of the compressor, which was calibrated by means of a frequency analyser system with an accelerometer placed on the compressor head. All the sensors were calibrated, and the calibration range and accuracies are those shown in Table 1. All the signals were collected by a data acquisition system and processed on-line using a LABVIEW-based application developed by the authors [START_REF] Llopis | Monitorización en tiempo real del comportamiento energético de máquinas de producción de frío usando técnicas avanzadas de adquisición de señales[END_REF] that uses the REFPROP dynamic routines [START_REF] Lemmon | Refprop v. 7.0[END_REF] to obtain the thermodynamic properties of carbon dioxide and water, and interpolated polynomials from the ASHRAE Handbook [START_REF]Handbook Fundamentals[END_REF] for the properties of the ethylene-glycol mixture.

Table 1. Accuracies of the measurement devices

Test procedure and data validation

Operation and efficiency of transcritical carbon dioxide refrigerating systems are highly influenced by pressure and refrigerant temperature at the gas-cooler outlet [START_REF] Kima | Fundamental process and system design issues in CO 2 vapor compression systems[END_REF][START_REF] Cavallini | Properties of CO 2 as a refrigerant[END_REF], these variables being independent in the supercritical region and, therefore, the test campaign was designed in accordance with the independence of these variables. The experimental tests were performed for fixed gas-cooler refrigerant outlet temperatures operating at fixed evaporating temperatures while varying the gas-cooler pressure. The campaign consisted of 92 steady-state tests, each lasting 20 minutes, which are grouped into 9 sets depending on the gas-cooler outlet temperature and evaporating temperature, as shown in Table 2. The tests were performed at two compressor speeds (1450 and 1120 rpm).

Table 2. Experimental data test range Thermodynamic properties of the refrigerant in the plant were evaluated using temperature and pressure measurements except for the point corresponding to the refrigerant outlet of the gas-cooler, whose enthalpy was estimated using a steady-state energy balance with the secondary fluid in the gas-cooler, as well as the gas-cooler outlet temperature used to perform the tests (presented in Table 2). This methodology was applied because in the critical point region a small error in the measurement of the temperature or pressure implies a large error in the enthalpy calculation. The evaporator inlet enthalpy of the refrigerant was evaluated considering the two expansion processes isenthalpic, and data validation was performed by comparing the secondary fluid heat transfer in the evaporator to the heat transfer in the refrigerant using the above mentioned enthalpy. The results of the validation for all the tests are presented in Figure 3, showing an agreement within ± 5%.

Experimental data analysis and discussion

In this section, the experimental results concerning energetic efficiency and optimal pressure of the carbon dioxide refrigerating plant working in a single-stage configuration are presented and analysed. 2). maximum efficiency is given for a certain gas-cooler pressure, as presented by several authors [START_REF] Kima | Fundamental process and system design issues in CO 2 vapor compression systems[END_REF][START_REF] Liao | A correlation of optimal heat rejection pressures in transcritical carbon dioxide cycles[END_REF]. This optimal gas-cooler pressure strongly depends on the refrigerant outlet temperature, the optimal pressure value being higher when the refrigerant outlet temperature is also higher. In addition, this optimum pressure value depends on the evaporating temperature, since the lower evaporating temperature is the higher the optimal gas-cooler pressure will be. Furthermore, a high COP decrease was measured when the gas-cooler pressure was below the optimal value -a decrease that gets higher as the gas-cooler refrigerant outlet temperature approaches the critical temperature of carbon dioxide (30.978ºC), as shown in Figure 8, and when the evaporating temperature is higher. Kauf [START_REF] Kauf | Determination of the optimum high pressure for transcritical CO 2 refrigeration cycles[END_REF] reported a small variation in the allocation of the optimal pressure while varying the compressor speed, but in this case this possible variation was neglected because the variation in the compressor speed between tests ( 330 rpm) was lower than that considered by Kauf ( 1000 rpm).

Several authors [START_REF] Sarkar | Optimization of a Transcritical CO 2 heat pump cycle for simultaneous cooling and heating applications[END_REF][START_REF] Liao | A correlation of optimal heat rejection pressures in transcritical carbon dioxide cycles[END_REF][START_REF] Kauf | Determination of the optimum high pressure for transcritical CO 2 refrigeration cycles[END_REF][START_REF] Chen | The optimum high pressure for CO 2 transcritical refrigeration systems with internal heat exchangers[END_REF] have obtained theoretical expressions to define the optimal gas-cooler pressure in a refrigerating cycle similar to the one analysed in this paper. All of them, except Kauf [START_REF] Kauf | Determination of the optimum high pressure for transcritical CO 2 refrigeration cycles[END_REF], consider a single-stage refrigerating cycle working with an internal heat exchanger in their mathematical reasoning, but the final expressions presented are simplified by considering null efficiency in this heat exchanger, so all the expressions can be compared to the values obtained experimentally.

All the above expressions are based on several assumptions that differ from one another and also vary with the experimental behaviour of the facility. Thus, Liao and Sarkar considered an ideal compression process and neglected the influence of superheating at compressor suction in the optimal pressure; however, a real compression process based on experimental data on real compressors was considered in the expressions of Chen and Kauf, who also neglected the degree of superheating at compressor suction.

Moreover, the range of validity of the expressions is different. Liao developed his expression for an evaporating temperature range from -10 to 20ºC and gas-cooler refrigerant outlet temperature from 30 to 60ºC; Sarkar considered an evaporating temperature from -10 to 10ºC and 30 to 50ºC for the gas-cooler refrigerant outlet temperature (this expression was obtained for a heat pump/refrigerating cycle combination but it is also considered), and both Chen and Kauf developed their expressions for a constant evaporating temperature of 5.3ºC and for an environment temperature from 35 to 50ºC. Nevertheless, only Kauf expressed the mathematical relation using the gas-cooler refrigerant outlet temperature as a variable by considering a gas-cooler approach temperature of 2.9ºC, while Chen expressed his relation by using an experimental fitted curve (5) obtained from experimental data [START_REF] Brown | Comparative analysis of an automotive air conditioning systems operating with CO 2 and R134a[END_REF]. The relation [START_REF] Pearson | Carbon Dioxide -new uses for an old refrigerant[END_REF] that represents the approach between the gas-cooler refrigerant outlet temperature and the air temperature was obtained from a gas-cooler cooled with air, but it is also considered in this work.

+ ⋅ - ⋅ - = - env env env o GC T T T T (5)
Given that the assumptions taken in order to develop the mathematical expressions to define the optimal gas-cooler pressure differ from the experimental behaviour of the real refrigerating cycle, a comparison between the optimal gas-cooler pressures obtained with expressions (1) to ( 4) and the optimal gas-cooler pressures from the experimental tests is presented. In order to compare the optimal values a simplified model was adjusted from experimental data to model the compressor power consumption and cooling capacity, and with this model the optimal values in the experimental tests were obtained.

Table 3 presents the experimental optimal gas-cooler pressures and their deviations with respect to the optimal pressures obtained using the authors' expressions inside their validity range, except for Chen's and Kauf's, which are not within the validity range but are also considered in order to analyse the influence of the evaporating pressure on the optimum pressure of the gas-cooler. The comparison shows that the best expression that matches the experimental results is the Sarkar's, which has a maximum deviation below 1.5%. Liao's expression presents a deviation smaller than 5% but the one presented by Kauf does not represent the experimental behaviour of the facility, mainly because this expression neglects the influence of the evaporating pressure in the optimal pressure allocation and this variable exerts an important influence on the gas-cooler optimal pressure, as seen in Figures 5 to 7. But on the other hand, the expression developed by Chen represents the experimental behaviour of the facility accurately, although it does not consider the influence of the evaporating pressure. However, it does consider an isentropic efficiency obtained from experimental data [START_REF] Brown | Comparative analysis of an automotive air conditioning systems operating with CO 2 and R134a[END_REF] and a correlation for the gascooler approach.

From the comparison presented in Table 3, it can be concluded that the expressions that best fit the experimental behaviour of the plant are the ones that consider an ideal compression process (Liao and Sarkar), an assumption that it is not real but works well according to the results.

Table 3. Experimental gas-cooler optimal pressures and deviations from authors' expressions

The importance of the definition of the optimal gas-cooler pressure lies in the reduction in energy efficiency that occurs if this value is not well defined. This reduction in efficiency, according to the experimental plant, is represented in Figure 8 for operation at an evaporating temperature of -1ºC and with several gas-cooler refrigerant outlet temperatures. The lines in Figure 8, which show the reduction in COP when the gascooler pressure is not optimum also represent the optimal values obtained with the expressions presented above. Figure 8 shows that the reduction in COP due to a deviation with respect to the optimum pressure is higher when the gas-cooler refrigerant outlet temperature is close to the critical temperature, and this reduction is larger if the pressure is under the optimal value, as seen in Figures 5 to 7. Furthermore, if the authors' expressions are used to obtain the optimum pressure the reductions in COP in the real plant reach a maximum of 1.25% in the case of Liao's expression, 0.2% in the case of Sarkar's, 0.6% in the case of Chen's and 12% in the case of Kauf's .

Figure 8. Reduction in COP for optimal pressure deviation in % at an evaporating temperature of -1ºC for several gas-cooler outlet temperatures

As can be seen in Figure 8, it is obvious that refrigerating plants that use carbon dioxide as refrigerant need a precise system to control their operation in optimal conditions since a small error in precision in the gas-cooler pressure causes a high reduction in the efficiency of the plant. If the precision error could not be avoided it should overestimate the optimal pressure, since the reduction in COP is then smaller than if the optimal pressure is underestimated.

Conclusions

In this work the energy efficiency and the optimal gas-cooler pressures of an experimental single-stage refrigerating plant operating with carbon dioxide as refrigerant in a transcritical cycle have been presented. The results show that the optimal gas-cooler pressures depend on the gas-cooler refrigerant outlet temperature as well as on the evaporating temperature.

The experimental optimal gas-cooler pressures were contrasted with the most commonly used relations to define this value, which are Liao's, Kauf's, Chen's and Sarkar's expressions. Results show that the one that best represents the experimental performance of the plant is Sarkar's, although this expression was developed considering an ideal compression process and a simultaneous heat pump/refrigerating cycle combination.

Furthermore, it can be concluded that a precise system to control the gas-cooler pressure is needed in this type of refrigerating plants, since a small error in pressure causes a strong reduction in efficiency, and if the precision error could not be avoided it should overestimate the optimal pressure since the reduction in COP is then smaller than if the optimal pressure is underestimated.

Figure 1 .Figure 2 .

 12 Figure 1. Experimental carbon dioxide refrigerating plant

Figure 3 .

 3 Figure 3. Energy balance validation at the evaporator

Figure 4

 4 Figure 4 presents the experimental measurements of cooling capacity, compressor

Figure 4 .

 4 Figure 4. Compressor power consumption, refrigerant mass flow rate and cooling

Figure 5 .Figure 6 .Figure 7 .

 567 Figure 5. COP at an evaporating temperature of -18.1ºC for different gas-cooler outlet

Figure 1 .Figure 2 .Figure 3 .Figure 4 .Figure 5 .Figure 6 .Figure 7 .Figure 8 .Figure 1 ACCEPTED MANUSCRIPT 25 Figure 2 Figure 8

 1234567812528 Figure 1. Experimental carbon dioxide refrigerating plant

  3

  •h -1 )

	Subscripts
	BP	pressostatic expansion valve
	dis	compressor discharge
	env	environment
	g	water / ethylene-glycol mixture
	GC	gas-cooler
	hp	high pressure
	i	element inlet
	IHX	internal heat exchanger
	inMot	inlet port to compressor
	lp	low pressure
	LR	liquid receiver
	O	evaporator
	o	element outlet
	opt	optimum
	ref	refrigerant
	suc	compressor suction
	w	water

Table 1 .

 1 Accuracies of the measurement devices

	TABLES
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	" # $ % ' (	# &		$ $	# &	)!	* # +$ %
	, %+	) (	# $ + -	. % $ # &	* # +$ %
	&	%	$ % '/	0$ $ &		* # +$ %
			+	1%	$ $ % # $ %-+ $ -	)* # +$ %

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Acknowledgments

The authors are indebted to Frost-Trol S.A. (www.frost-trol.com) and the Spanish Ministry of Education and Science (ENE2006-09972/CON) for the economical support given to the present work and for the grant BES-2007-16820 linked to the Ministry project.