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Experimental study of air flow by natural convection in a closed cavity: Application in a domestic refrigerator
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Journal of Food Engineering 85 (2008) 547–560 www.elsevier.com/locate/jfoodeng
Experimental study of air flow by natural convection in a closed cavity: Application in a domestic refrigerator O. Laguerre a,*, S. Ben Amara a, M.-C. Charrier-Mojtabi b, B. Lartigue b, D. Flick c a
UMR Ge´nie Industriel Alimentaire, AgroParisTech-Cemagref-INRA, Cemagref, Parc de Tourvoie, BP 44, 92163 Antony Cedex, France b Universite´ Paul Sabatier – Laboratoire PHASE, E.A. 3208, 118 route de Narbonne, 31062 Toulouse Cedex 4, France c UMR Ge´nie Industriel Alimentaire, AgroParisTech-Cemagref-INRA, AgroParisTech, 16 rue Claude Bernard, 75231 Paris, France Received 23 February 2007; received in revised form 20 August 2007; accepted 20 August 2007 Available online 12 September 2007
Abstract An experiment was carried out using a refrigerator model in which heat is transferred by natural convection. This transfer takes place between a cold vertical wall and the other walls, which are exposed to heat losses. The air velocity measurements were undertaken using particle image velocimetry (PIV). Circular airflow was observed in the cavity: air flows downward along the cold wall and upward along the other walls. The maximum air velocity (0.2 m/s) was observed near the bottom of the cold wall. Non-stationary airflow with recirculation was observed along the horizontal bottom wall of the cavity. Airflow is very weak (<0.04 m/s) at the central zone and it is quasistagnant at the top. The velocity profile in the boundary layers of the empty refrigerator model was also investigated. The influence of temperature and surface area of the cold wall on air velocity were studied. It was found that the influence of the cold wall temperature on the air velocity is more significant than the surface area. In order to study the effect of obstacles on velocity profiles, the refrigerator model was filled with four blocks of hollow spheres. The air velocity in the case of filled refrigerator was compared with the results of the empty one. The air velocity is lower almost everywhere in the filled refrigerator model. The presence of the blocks seems to homogenise the air velocity. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Natural convection; Closed cavity; PIV; Air velocity profile; Domestic refrigerator
1. Introduction Domestic refrigerator is an appliance widely used in industrialized countries. There are approximately 1 billion domestic refrigerators worldwide (IIR, 2002). The demand in 2004 in the world was 71.44 million units (11.2 million in China, 10.7 million in USA, 4.43 in Japan, 3.36 in India, 3.14 in Brazil, . . ., JARN, 2005). In developing countries, the production is rising steadily: +30% of total production in 2000 (Billiard, 2005). In France, there are 1.7 refrigerators per household (AFF, 2001). Three types of domestic refrigerators are available in the market: static, brewed and no-frost. The static type (Fig. 1a) is widely used in *
Corresponding author. Fax: +33 1 40 96 60 75. E-mail address: [email protected] (O. Laguerre).
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Europe. In this case, heat is transferred principally by natural convection and airflow is due to variations in air density. These variations are essentially related to the temperature gradients: hot air is lighter than cold air. The cold air in contact with the evaporator (cold wall) flows downward. The air in contact with the other walls (warm walls) flows upward. Due to the principle of heat transfer, temperature heterogeneity is often observed in this type of refrigerator. The position of the evaporator (horizontal/vertical, top/bottom of the compartment) determines the location of cold and warm zones. The brewed type is a static refrigerator equipped with a fan (Fig. 1b). It promotes air circulation and the temperature decreases rapidly after door opening. Air temperature is more homogeneous in this case than in the static type but the energy consumption is higher due to the fan. In a
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Nomenclature g K H M Ra Rap Rac t Tamb Tc Tf DT u*
acceleration due to gravity (9.81 m/s2) permeability of the porous media (m2) height of cold wall or height of cavity (m) enlargement factor (ratio between real dimension and image) Rayleigh number Rayleigh number of porous media critical Rayleigh number time (s) external ambient temperature (°C or K) cold wall temperature (°C or K) internal air temperature (°C or K) temperature difference between the cold and warm walls (°C or K) dimensionless air velocity
Fig. 1. Three types of refrigerator: (a) static, (b) brewed and (c) no-frost (Roussille, 2002).
no-frost refrigerator (Fig. 1c), a fan (embedded in the back wall) pushes air to flow over the evaporator before entering into the refrigerating compartment. Air temperature is more homogeneous compared to the two other refrigerator types. Disadvantages of no-frost type are noise, energy consumption, drying on food surface and high price. Only the static refrigerator was studied in the present work in which a strong coupling between air velocity and temperature is observed. Temperature distribution in a refrigerator model was already presented (Laguerre, Ben Amara, & Flick, 2005). To complete this previous work, the air velocity field is now presented. Knowledge of air temperature and velocity profiles in a refrigerator is important for food quality control. Design of refrigerator can be modified or recommendations can be given to consumers, so that perishable food products are placed in low-temperature and well ventilated positions. Food products should also not disturb the boundary layer close to the evaporator wall. Indeed, obstacles in this location would reduce the heat transfer between cold wall and air and product could freeze. The objective of this work is to generate experimental data on air velocity distribution in a static domestic refrig-
uy uz u X
velocity in the height direction of the refrigerator model (m/s) velocity in the width direction of the refrigerator model (m/s) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi velocity magnitude (m/s) u ¼ u2y þ u2z distance of smoke particle displacement (m)
Greek symbols a thermal diffusivity of air (m2/s) ap thermal diffusivity of the porous media (m2/s) b thermal expansion coefficient (K1) m kinematic viscosity (m2/s) d thickness of boundary layer (m) dt time interval between a pair of images (s)
erator. This study allows gaining better insight into the mechanism of airflow by natural convection. Also, the data obtained can be used to compare with the modelling results. To achieve this objective, an experiment was carried out using a transparent refrigerator model, which makes it possible to visualize and measure the airflow by PIV (particle image velocimetry). This refrigerator model allows observing the same phenomena as those in a domestic refrigerator but with better-controlled boundary conditions and simpler geometry. The influence of the following operating conditions on the air velocity was studied: cold wall temperature (parameter related to thermostat setting), dimension of cold wall (parameter related to design of evaporator), product loading. Comparison of the results obtained for empty and loaded refrigerator makes it possible to determine the influence of obstacles on airflow in the refrigerator. 2. Literature review 2.1. Air flow in domestic refrigerators Several experimental studies were carried out on empty and loaded refrigerators (James & Evans, 1992; Masjuki et al., 2001). The objective was to analyze the effects of several parameters on the temperature in the refrigerating compartment (thermostat setting, frequency of door openings, filled volume, temperature and humidity of ambient air). However, few studies were carried out on airflow measurement due to the complexity of measurement techniques compared to the ones of temperature. Airflow measurement in a freezer compartment under real operating conditions was carried out by Lacerda, Melo, Barbosa, and
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Duarte (2005) using PIV. It was observed that the flow field was strongly influence by the temperature variations due to the ‘‘on” and ‘‘off” operation cycles of compressor. This behavior was attributed to natural convection and strong dependency of air viscosity. Another study on airflow in a ventilated domestic freezing compartment was carried out by Lee, Baek, Chung, and Rhee (1999). In this study a comparison of velocity field obtained by CFD simulation and by experiments (PIV measurements) was undertaken. These authors observed that the flow was very complex: jet-like flow around entrance ports, impinging and stagnation flow on the walls and a large recirculation flow in cavity. To our knowledge, no study was carried out on air velocity measurement in refrigerating compartment. Moreover, airflow being strongly influenced by the aspect ratio (height/width) of the cavity; the flow in freezer is therefore different from the one in refrigerating compartment. To obtain useful information on natural convection in a domestic refrigerator, airflow in some well known configurations will be presented: near a warm (or cold) vertical plate, empty cavity and cavity filled with product. The temperature of the cold wall is constant for these three configurations in spite that this temperature fluctuates due to the ‘‘on” and ‘‘off” compressor working cycles in a real refrigerator. 2.2. Airflow near a vertical plate For a first approach, literature on flow adjacent to a cold vertical plate placed in warm environment (without other limiting walls) can be applied for understanding airflow by natural convection near an evaporator of refrigerator. If a tracer (smoke for air, for example) is injected at one end of the plate to visualize the flow, laminar flow is firstly observed near the wall and then turbulence appears (Fig. 2). The air velocity (u) is zero at the plate surface, then, it increases rapidly when the distance from the plate increases to attain a maximum value (um). Air velocity then decreases and approaches zero, which is the velocity far from the plate. The zone of non-zero velocity (u > um/ 100) is called the hydrodynamic boundary layer and its thickness (d) increases in the flow direction (x). Heat transfer phenomena depend on the flow regimes (laminar or turbulent). Khalifa (2001a) presents a literature review of natural convection heat transfer correlation for vertical and horizontal plates; more than 40 articles are cited. 2.3. Airflow in empty closed cavity The most often studied case is a two-dimensional flow in an empty cavity with two opposite walls at different temperatures and two insulated walls. The position of the cold wall (bottom/top horizontal walls, vertical walls) in the empty cavity determines airflow. When the horizontal cold wall is located at the bottom of the cavity, stable temperature stratification is observed with the cold zone at the bot-
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y u um δ (x)
U∞ = 0 u um
x Fig. 2. Hydrodynamic boundary layer and velocity profile in natural convection flow.
tom and warm zone at the top. In this case, air is stagnant and heat transfer occurs principally by conduction. When the top horizontal wall is cold, unstable flow is observed (Ostrach, 1988) since heavier air is above lighter one. The state of unstable equilibrium occurs until a critical density gradient is exceeded. A spontaneous flow then results that eventually becomes steady and cellular-like. When a vertical wall is cold, circular flow is observed. This case is similar to the one of the majority of domestic refrigerator, since the evaporator is often inserted in the vertical back wall. Air flows downward along the cold wall and upward along the warm wall and air is almost stagnant in the centre of the cavity (Fig. 3). The flow regime is characterised by the Rayleigh number (Ra) defined as gbDTH 3 ð1Þ am For small Rayleigh number, Ra 6 103, the buoyancy-driven flow is weak and heat transfer is primarily by conduction. With increasing Rayleigh number, the cellular flow intensifies and becomes concentrated in thin boundary layers adjoining the sidewalls. The core becomes nearly stagnant, although additional cells can develop in the corners and the sidewall boundary layers eventually undergo transition to turbulence (Incropera & Dewitt, 1996). Thermal stratification is also observed with the warm zone at the top of the cavity and the cold zone at the bottom. Several experimental studies were carried out to measure air temperature and/or velocity in closed cavities (Ampofo & Karayiannis, 2003; Armaly, Li, & Nie, 2003; Betts & Bokhari, 2000; Mergui & Penot, 1996; Tian & Karayiannis, 2000). Ramesh and Venkateshan (2001) used a differential interferometer to visualize conditions in the boundary layer Ra ¼
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ever, the air velocity at the centre of the cavity is weakly influenced by Ra. Many correlations between airflow (Ra) and heat transfer (Nu) are proposed and a review on this subject was carried out by Bejan and Tien (1978). The literature on cavity filled with porous media can not be applied directly to the case of loaded domestic refrigerator principally due to the product dimension. For refrigerators, the ratio between the dimension of product and cavity is about 0.10 (5 cm product width and 50 cm cavity width) while this ratio is 60.02 for porous media. There is notably a great influence of product position in the stack on heat transfer compared to the case of porous media.
Fig. 3. Airflow in empty closed cavity (Tian & Karayiannis, 2000).
along the wall (105 < Ra < 106). They found that airflow is generally stable except in the corner. Mergui and Penot (1996) carried out a visualization of flow in an empty cavity using a laser tomography (Ra = 1.7 109); they observed the same phenomena as Ramesh and Venkateshan (2001). The Rayleigh number is a factor determining the heat transfer. Khalifa (2001b) and Incropera and Dewitt (1996) present correlations between Rayleigh and Nusselt numbers for two- and three-dimensional heat transfers in empty closed cavities. 2.4. Airflow in cavity filled by product The most classical configuration is the parallelepiped cavity filled with porous media. Many studies were carried out on two-dimensional heat transfer by natural convection with differentially heated vertical sidewalls and adiabatic horizontal walls. In the case of porous media, the Rayleigh number is defined as Rap ¼
gbDT H K ap m
ð2Þ
When Rap ? 0, the conduction heat transfer is dominant, airflow is very weak. The temperature distribution is onedimensional (dependent on width and independent on height of cavity) (Bories & Prat, 1995). When the Rayleigh number is higher than a critical value, transition regime characterizes by two-dimensional temperature distribution (dependent on width and height of cavity) is observed. When the Rayleigh increases and the value is higher than another critical value, airflow by natural convection occurs. This flow is quasi-1direction near walls and it is very weak at the centre of the cavity. Heat is transferred principally from the warm to the cold wall by the air circulation in the boundary layer. The thickness of the boundary layer (d) and the maximum velocity in this layer (um) are greatly influenced by Rayleigh number (d decreases, um increases when Ra increases). How-
Fig. 4. Refrigerator model: (a) global view and (b) side view.
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This was shown in our previous studies (Ben Amara, Laguerre, & Flick, 2004) which demonstrate the influence of theses parameters on the heat transfer at low air velocity (<0.2 m/s) in a stack of spheres. The motivation of this study is to enrich the knowledge on airflow in an empty and filled cavity with an application to domestic refrigerator. In this case, airflow is threedimensional and the warm walls are not maintained at fixed temperature (Dirichlet condition) but subjected to heat losses (Cauchy condition). 3. Materials and methods 3.1. Refrigerator model The internal dimensions of the refrigerator model are: 0.5 0.5 1 m (depth width height, precision ±0.001 m). It is composed of three vertical double glass
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walls (glass thickness of 6 mm and air thickness between glass walls of 10 mm) and one vertical aluminum wall (thickness of 2 cm, containing a coil) (Fig. 4). A low-temperature water–glycol mixture was prepared in a thermostatically controlled cooling bath to maintain a constant temperature in this aluminum wall. The top and bottom horizontal walls are made of PVC (thickness: 2 cm). All external walls are insulated using expanded polystyrene plates (thickness: 4 cm). These plates can be taken off to visualize airflow and allow air velocity measurement by PIV system through the double glass walls. The ambient external temperature was 20 °C and the global heat transfer coefficient of the composite glass walls (including polystyrene insulation) can be estimated from the thermal properties of the materials: 0.52 W/m2/K. The flow circuit of the water–glycol mixture is arranged in such a manner that either the entire surface of the aluminum plate or only the upper half is cooled.
Fig. 5. (a) PIV (particle image velocimetry) system for air velocity measurement and (b) time interval between a pair of images (3.5 ms) and between two couples (250 ms).
Table 1 Experimental conditions for measurement of air velocity by PIV system on the symmetry plane of the refrigerator model Condition in refrigerator model
Number of pairs of images per window
Dimension of each image (height width)
Dimension of interrogation area (height width)
Temperature of cold wall (°C)
Surface of cold wall
Empty
60
106 133 mm2
6.6 6.6 mm2
10 and 0
Filled with four blocks of hollow spheres
38
70 87 mm2
4.4 4.4 mm2
0
Entire and only top half Entire
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The refrigerator model is cooled for 24 h to assure the steady state heat transfer in the cavity, before the air velocity measurement. Oil smoke (particle diameter 1 lm data of manufacturer) is stored in a drawer located at the bottom of the refrigerator model. The trap is opened to introduce this smoke into the cavity, then, it is closed when enough smoke is present for measurement. When the smoke diffusion attains the equilibrium state (30 min), the air velocity is then measured by the PIV system. 3.2. PIV system The basic optical device for the PIV system is presented in Fig. 5. It is composed of a double pulse Nd-Yag Laser source (Quantel-Big Sky model CFR400-1000 Watts); which produces a light sheet for a short period by the aide of lens. A CCD video camera (1028 1024 pixels, Sensi-
Cam 12 BIT Cooled Imaging) placed perpendicular to the laser sheet allows images of smoke particle displacement. Several images were taken and they were used to calculate the air velocity. 3.3. PIV image treatment The laser light is formed into a sheet in the symmetry plane, and the resultant scattered light, which is at the same frequency as the incident laser, is recorded on the CCD camera. The time between two laser pulses was 3.5 ms and the time between the capture of two pairs of pictures was 250 ms. Several pairs of picture were recorded on each measurement window. Table 1 shows the number of pairs of pictures and the dimension of measurement window used in our experiment. The calculation of velocity vector was carried out on the measurement window by dividing
Fig. 6. (a) Empty refrigerator model, (a0 ) front view of the symmetry plane showing the position of windows for air velocity measurement in empty refrigerator model, (b) refrigerator model filled with four blocks of hollow spheres and (b0 ) front view of the symmetry plane showing the position of windows for air velocity measurement of the refrigerator model filled with hollow spheres.
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it into small interrogation areas (size shown in Table 1). After cross-correlation of these pictures, a mean velocity field was calculated. The position of images taken by the camera was moved allowing the development of air velocity field all over the symmetry plane. It should be noticed that the time interval of 3.5 ms between two laser pulses was the optimum. If the time interval is too low, the distance of particle displacement is too short and consequently, the calculation of air velocity may conduct to error. If the time interval is too high, the particles appearing in the first image disappear in the second. The velocity calculation is thus impossible. For the filled refrigerator, one pixel corresponds to 70 lm and the interrogation is a square of 4.4 4.4 mm2 (for the empty refrigerator images are slightly larger: 6.4 6.4 mm2). The maximal velocity is about 0.25 m/s. Considering a case in which all the particle have a vertical velocity of 0.25 m/s, if 4/5 of the particles present in the interrogation area of the first image have to be still present in the second image, the time interval must be less than 3.5 ms. For this time interval the velocity measurement accuracy is about ±0.01 m/s (± half a pixel/time interval). The velocity of smoke displacement is assumed to represent the air velocity ð~ uÞ. Software (based on inter-correlation) is used to establish a velocity field from a pair of images by the following equation: 1 ~ u¼ M
~ X dt
! ð3Þ
3.4. Experimental conditions for airflow measurement The influence of the following operating conditions was studied: cold wall temperature, dimension of cold wall and presence of obstacle. – Cold wall temperature. In empty refrigerator model, two cold wall temperatures were studied: 10 °C (corresponding to the evaporator temperature at the end of the compressor work cycle) and 0 °C (corresponding to an average evaporator temperature during an ‘‘on” and ‘‘off” cycle). – Dimension of cold wall temperature. For domestic refrigerators, surface area of the cold wall can vary from the half to the entire back vertical wall. In our study, the aluminum wall of the empty refrigerator model was cooled either totally (100%), or only the top half (50%). – Presence of obstacle. Food products stored in a domestic refrigerator have different forms, dimensions (generally form 5–20 cm) and occupy volumes (from nearly empty to nearly full). As a first approach to understand the influence of obstacles, the refrigerator model was loaded by simple arranged objects. In our case, it consists in an aligned stack of hollow spheres considered as inert medium (without heat exchange with air), Fig. 6. The position of measured windows on the sym-
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Fig. 7. Experimental device for air temperature measurement.
metry plane was shown in this figure. Table 1 summarises the experimental conditions. 3.5. Experimental assembly for air temperature measurement To obtain complementary information, air temperature was measured in the refrigerator model. The objective of this measurement was to analyze the relation between air temperature and air velocity stability particularly in positions where high velocity fluctuations were observed. This measurement was carried out using tightened wires thermocouples (T-type, calibrated, 200 lm diameter, precision ±0.2 °C), Fig. 7. Due to the small wire diameter, airflow was very slightly disturbed by the presence of the thermocouples. Nine thermocouples were attached to a Plexiglas support on each side (5 ± 0.1 mm space between thermocouples). The height level of these thermocouples was adjusted in such a manner that the air temperature at the bottom and at the mid-height of the refrigerator model was measured. 4. Results and discussion 4.1. Velocity profile in empty refrigerator model The average air velocity (calculation from 60 pairs of images) on the symmetry plane of the refrigerator model is shown in Fig. 8, for cold wall maintained at 10 °C. For this experiment, the average temperature of the internal double glass walls was 5.1 °C (2.3 °C at 10 cm high, 4.2 °C at 50 cm and 8.7 °C at 90 cm). The experimental result agrees with the literature, circular airflow is observed in the cavity.
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Fig. 8. Air velocity field on the symmetry plane of empty refrigerator model measured by PIV: (a) velocity vector and (b) velocity magnitude. The entire cold wall was maintained at 10 °C.
Air flows downward along the cold wall with an increasing velocity. Air flows very slowly (u < 0.04 m/s) at the top of the cold wall and it attains the maximum value (0.24 m/s) at the bottom. Then, air flows upward along the double glass wall located oppositely with decreasing velocity until stagnation at the top of the wall. Also, air moves horizontally from the double glass wall to the cold wall (u < 0.04 m/s). Near the top wall, there is a zone of slightly higher velocity, with inclined velocity vectors. This is comparable to the cells observed in the corners in the two-dimensional case as mentioned in the literature review (Fig. 3). Laminar airflow (low velocity fluctuations compared to the average value calculated form 60 pairs of images) was globally observed in the cavity except at the bottom of the refrigerator model. At this position (height < 10 cm), unsteady air flow patterns were observed, Fig. 9. The instantaneous velocity field (obtained from one pair of images) near the bottom of the cavity at two successive instants is presented. A circular airflow pattern which moves in the same direction as the main flow from cold wall toward the opposite wall is shown.
The vertical velocity profiles in the hydrodynamic boundary layer near the cold wall and the double glass located oppositely are shown in Fig. 10a for three heights (10, 50 and 90 cm). Near the cold wall (Fig. 10b), the thickness of the boundary layer is small at the top (d ? 0) and it increases toward the bottom of the refrigerator model (d 3 cm). Vertical velocity is very slow outside boundary layer. Fig. 10c shows the air velocity profile near the double glass (warm wall) located in opposite to the cold wall. The velocity magnitude is much lower than near the cold wall: maximum velocity is about 0.05 m/s near the warm wall whereas it is about 0.25 m/s near the cold wall. This can be explained by the fact that there are three vertical warm walls where air flows upward whereas there is only one cold wall. Indeed, in steady state, the heat losses trough the glass walls (1.5 m2) has to be absorbed by the cold wall (0.5 m2). The temperature difference between the cold wall and air is therefore much higher than the temperature difference between glass wall and air. The ratio is typically between 3 and 5 (Laguerre et al., 2005). The recirculation at the bottom of the refrigerator model (height = 10 cm)
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may explain the large thickness of the boundary layer at this level (d 7 cm) compared to those at other levels (d 2 cm at 50 cm and 2.5 cm at 90 cm).
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To confirm the instability of airflow at the bottom of the cavity, Fig. 11 presents a plot of velocity versus time. It can be seen that airflow structures are sometimes quasi-periodic
Fig. 9. Displacement of air recirculation at the bottom of the symmetry plane of the empty refrigerator model (height: 0–10.6 cm and distance form the cold wall: 20–33.2 cm). Entire cold wall maintained at 10 °C.
Fig. 10. Vertical velocity profile (uy) at three height levels on the symmetry plane when the entire cold wall was maintained at 10 °C: (a) global view, (b) profile in boundary layer near the cold wall and (c) profile in boundary layer near the double glass wall.
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(period 2s). The air temperature fluctuations at the bottom of the cavity (measurement by thermocouples) confirm again the unsteadiness of the air flow, Fig. 12. This fluctuation is much more pronounced (Tmax Tmin = 0.9 °C) than that at the mid-height (Tmax Tmin = 0.1 °C).
4.2. Influence of the cold wall temperature The measurement of air velocity field on the symmetry plane of the refrigerator model was carried out when the cold wall temperature was maintained at 10 °C and at 0 °C. The main difference between the results of these
Fig. 11. Air velocity variation at the bottom of the symmetry plane of the empty refrigerator model. Entire cold wall maintained at 10 °C.
Fig. 12. Air temperature variation at the bottom and at mid-height of refrigerator model.
Fig. 13. Influence of the cold wall temperature on the vertical velocity profile on the symmetry plane and at 50 cm height of empty refrigerator, entire cold wall maintained at 10 °C and 0 °C: (a) profile near the cold wall and (b) profile near the double glass wall.
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two experiments is the velocity profile in the boundary layer near to the cold wall. The lower cold wall temperature contributes to increasing the air velocity in the boundary layer along the y direction. For example, at 50 cm (Fig. 13), the maximum air velocity increases from
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0.19 m/s (cold wall at 0 °C) to 0.23 m/s (cold wall at 10 °C). The effect of the cold wall temperature on the air velocity is less significant near to the double glass wall located oppositely. This may be explained by the fact that the tem-
Fig. 14. Influence of the dimension of cold wall on the horizontal velocity profile on the symmetry plane and at 10 cm height of empty refrigerator, entire (100%) and only top half (50%) of the cold wall maintained at 10 °C: (a) profile near the cold wall and (b) profile near the double glass wall.
Fig. 15. Air velocity field on the symmetry plane of refrigerator model: (a) velocity vector of empty case, (a0 ) velocity magnitude of empty case, (b) velocity vector of filled cases and (b0 ) velocity magnitude of filled case. Entire cold wall maintained at 0 °C.
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Fig. 15 (continued)
perature difference between air and glass varies less than temperature difference between air and cold wall when cold wall temperature is modified. 4.3. Influence of the dimension of the cold surface The air velocity field was measured on the symmetry plane when the entire cold wall (100%) was maintained at 10 °C and when only the top half of the cold wall (50%) was maintained at 10 °C (Fig. 14). Considering the velocity profile near to the cold wall at 10 cm (Fig. 14-a), the maximum value of air velocity is higher in the case of 100% (0.24 m/s) than the one of 50% (0.20 m/s). The thickness of the boundary layer is relatively the same for both cases whereas the location of the maximum air velocity is different: 0.8 cm from the cold wall (100%) and 1.1 cm (50%). This can be explained as follows. In the case of 100%, the airflow near the cold wall is accelerated (by buoyancy forces) along the wall, therefore velocity increases. In the case of 50%, from mid-height to bottom, airflow near the wall is no more accelerated because its temperature is almost the same in the boundary
layer. On the contrary, the airflow decelerated due to wall friction and momentum diffusion occurs so that the boundary layer thickness increases. Near to the double glass wall (Fig. 14-b), the velocity profiles are slightly different. This is related to flow pattern differences (recirculation) in the bottom right corner. The velocity magnitude is lower near the double glass wall (maximum value 0.08 m/s) compared to the one near the cold wall (maximum value 0.23 m/s). The velocity profiles are not different at the top part of the refrigerator model (height P 50 cm) for both the experiment of entire cold wall and top half cold wall. 4.4. Influence of the obstacles The air velocity field on the symmetry plane was measured when the refrigerator model was filled with 4 blocks of hollow spheres (Fig. 15). The result was compared with the one of empty refrigerator model when the entire cold wall was maintained at 0 °C. Circular airflow was observed on the symmetry plane of refrigerator model filled with blocks as in the empty case: air flows downward near to the cold wall and upward near
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to the double glass wall located oppositely. The air velocity is more homogeneous with the presence of blocks. The maximum air velocity near the cold wall decreases from 0.20 m/s (empty refrigerator model) to 0.16 m/s (refrigerator model filled with blocks). The vertical air velocity profile at three height levels shown in Fig. 16 confirms the role of obstacles to decrease the maximum air velocity near the cold wall. This may be explained by the friction on the surface of spheres which decelerates the air velocity. The influence of obstacles on air velocity is less significant near the double glass wall except at the bottom level (10 cm high). At this position, the velocity profile is very different for the two cases (maximum air velocity of 0.07 m/s for empty
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case and 0.02 m/s for filled case). This may be due to the absence of recirculation in the filled refrigerator model. The flow reversal observed in Fig. 16c (for y = 90 cm) for the filled case may be explained by a small recirculation cell appearing in the corner (between the glass wall and the bloc of spheres). 5. Conclusions The measurement of air velocity in a refrigerator model was carried out using a PIV system. A circular airflow was observed in the cavity: air flows downward near the cold wall and air flows upward near the double glass wall situated oppositely. There is also weak horizontal airflow from the double glass to the cold wall. The maximum air velocity was observed near the bottom of the cold wall. Non-stationary flow with air recirculation was observed at the bottom of the refrigerator model. Air is stagnant at the top of the cavity. The data on air velocity field developed in this study give complementary information on air temperature field already presented in our previous study. This furthers the comprehension on the strong coupling between airflow and heat transfer by natural convection in closed cavity. At the top of the refrigerator model where air is stagnant, high temperature is observed. At the bottom, where nonstationary airflow is observed, the temperature is low and there are more fluctuations. The influence of three operating factors on the velocity profile at the symmetry plane was studied: cold wall temperature, cold wall dimension and obstacles. The cold wall temperature has more influence than the cold wall dimension. The influence on the air velocity is more significant near the cold wall than near the glass wall located oppositely. The lower the cold wall temperature, the higher the air velocity along this wall. The air velocity is more homogeneous when the refrigerator model is filled with obstacles (blocks of hollow spheres). The knowledge of the airflow and heat transfer in refrigerator may contribute to the design improvement of the appliances. Also, this knowledge can help the consumer to better use their refrigerator. Acknowledgements The authors would like to thank the French Ministry of Agriculture and the ‘‘Ile de France Regional Council” for their financial support. References
Fig. 16. Comparison of the vertical velocity profile on the symmetry plane of empty and filled refrigerator model. Entire cold wall maintained at 0 °C.
AFF, Association Francßaise du Froid (2001). Conseil National du Froid. Livre blanc sur les fluides frigorige`nes, Paris, 51p. Ampofo, F., & Karayiannis, T. G. (2003). Experimental benchmark data for turbulent natural convection in an air filled square cavity. International Journal of Heat and Mass Transfer, 46(19), 3551–3572. Armaly, B. F., Li, A., & Nie, J. H. (2003). Measurements in threedimensional laminar separated flow. International Journal of Heat and Mass Transfer, 46, 3573–3582.
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Bejan, A., & Tien, C. L. (1978). Natural convection in a horizontal porous medium subjected to an end-to-end temperature difference. ASME Journal of Heat Transfer, 100, 191–198. Ben Amara, S., Laguerre, O., & Flick, D. (2004). Experimental study of convective heat transfer during cooling with low air velocity in a stack of objects. International Journal of Thermal Sciences, 43, 1212–1221. Betts, P. L., & Bokhari, I. H. (2000). Experiments on turbulent natural convection in a closed tall cavity. International Journal of Heat and Mass Transfer, 21, 675–683. Billiard, F. (2005). Refrigerating equipment, energy efficiency and refrigerants. Bulletin of the International Institute of Refrigeration, 85(1), 12–25. Bories, S., & Prat, M. (1995). Transferts de chaleur dans les milieux poreux. Techniques de l’Inge´nieur, traite´ ge´nie e´nerge´tique. IIR, International Institute of Refrigeration (2002). Report on refrigeration sector achievements and challenges (77p). Incropera, F. P., & Dewitt, D. P. (1996). Fundamentals of heat and mass transfer (4th ed.). John Wiley & Sons. James, S. J., & Evans, J. (1992). The temperature performance of domestic refrigerators. International Journal of Refrigeration, 15(5), 313–319. JARN, Japan Air Conditioning, Heating & Refrigeration (2005). 157, 41. Khalifa, A. J. N. (2001a). Natural convective heat transfer coefficient – A review I. Isolated vertical and horizontal surfaces. Energy Conversion and Management, 42, 491–504. Khalifa, A. J. N. (2001b). Natural convective heat transfer coefficient – A review II. Surfaces in two and three dimensional enclosures. Energy Conversion and Management, 42, 505–517. Lacerda, V. T., Melo, C., Barbosa, J. R., & Duarte, P. O. O. (2005). Measurements of the air flow field in the freezer compartment of a top-
mount no-frost refrigerator: The effect of temperature. International Journal of Refrigeration, 28, 774–783. Laguerre, O., Ben Amara, S., & Flick, D. (2005). Experimental study of heat transfer by natural convection in a closed cavity: Application in a domestic refrigerator. Journal of Food Engineering, 70, 523–537. Lee, I. S., Baek, S. J., Chung, M. K., & Rhee, D. (1999). A study of air flow characteristics in the refrigerator using PIV and computational simulation. Journal of Flow Visualisation and Image Processing, 6, 333–342. Masjuki, H. H., Saidur, R., Choudhury, I. A., Mahlia, T. M. I., Ghani, A. K., & Maleque, M. A. (2001). The applicability of ISO household refrigerator-freezer energy test specifications in Malaysia. Energy, 26(7), 723–737. Mergui, S., & Penot, F. (1996). Convection naturelle en cavite´ carre´e diffe´rentiellement chauffe´e: investigation expe´rimentale a` Ra = 1.69 109. International Journal of Heat and Mass Transfer, 39(3), 563–574. Ostrach, S. (1988). Natural convection in enclosures. Journal of Heat Transfer, 110, 1175–1190. Ramesh, N., & Venkateshan, S. P. (2001). Experimental study of natural convection in a square enclosure using differential interferometer. International Journal of Heat and Mass Transfer, 44, 1107–1117. Roussille, K. (2002). Froid: Mode d’emploi. Le Particulier Pratique, n° 272 (pp. 24–33). Tian, Y. S., & Karayiannis, T. G. (2000). Low turbulence natural convection in an air filled square cavity. Part I: The thermal and fluid flow fields. International Journal of Heat and Mass Transfer, 43, 849–866.
Journal of Food Engineering 85 (2008) 547–560 www.elsevier.com/locate/jfoodeng
Experimental study of air flow by natural convection in a closed cavity: Application in a domestic refrigerator O. Laguerre a,*, S. Ben Amara a, M.-C. Charrier-Mojtabi b, B. Lartigue b, D. Flick c a
UMR Ge´nie Industriel Alimentaire, AgroParisTech-Cemagref-INRA, Cemagref, Parc de Tourvoie, BP 44, 92163 Antony Cedex, France b Universite´ Paul Sabatier – Laboratoire PHASE, E.A. 3208, 118 route de Narbonne, 31062 Toulouse Cedex 4, France c UMR Ge´nie Industriel Alimentaire, AgroParisTech-Cemagref-INRA, AgroParisTech, 16 rue Claude Bernard, 75231 Paris, France Received 23 February 2007; received in revised form 20 August 2007; accepted 20 August 2007 Available online 12 September 2007
Abstract An experiment was carried out using a refrigerator model in which heat is transferred by natural convection. This transfer takes place between a cold vertical wall and the other walls, which are exposed to heat losses. The air velocity measurements were undertaken using particle image velocimetry (PIV). Circular airflow was observed in the cavity: air flows downward along the cold wall and upward along the other walls. The maximum air velocity (0.2 m/s) was observed near the bottom of the cold wall. Non-stationary airflow with recirculation was observed along the horizontal bottom wall of the cavity. Airflow is very weak (<0.04 m/s) at the central zone and it is quasistagnant at the top. The velocity profile in the boundary layers of the empty refrigerator model was also investigated. The influence of temperature and surface area of the cold wall on air velocity were studied. It was found that the influence of the cold wall temperature on the air velocity is more significant than the surface area. In order to study the effect of obstacles on velocity profiles, the refrigerator model was filled with four blocks of hollow spheres. The air velocity in the case of filled refrigerator was compared with the results of the empty one. The air velocity is lower almost everywhere in the filled refrigerator model. The presence of the blocks seems to homogenise the air velocity. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Natural convection; Closed cavity; PIV; Air velocity profile; Domestic refrigerator
1. Introduction Domestic refrigerator is an appliance widely used in industrialized countries. There are approximately 1 billion domestic refrigerators worldwide (IIR, 2002). The demand in 2004 in the world was 71.44 million units (11.2 million in China, 10.7 million in USA, 4.43 in Japan, 3.36 in India, 3.14 in Brazil, . . ., JARN, 2005). In developing countries, the production is rising steadily: +30% of total production in 2000 (Billiard, 2005). In France, there are 1.7 refrigerators per household (AFF, 2001). Three types of domestic refrigerators are available in the market: static, brewed and no-frost. The static type (Fig. 1a) is widely used in *
Corresponding author. Fax: +33 1 40 96 60 75. E-mail address: [email protected] (O. Laguerre).
0260-8774/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2007.08.023
Europe. In this case, heat is transferred principally by natural convection and airflow is due to variations in air density. These variations are essentially related to the temperature gradients: hot air is lighter than cold air. The cold air in contact with the evaporator (cold wall) flows downward. The air in contact with the other walls (warm walls) flows upward. Due to the principle of heat transfer, temperature heterogeneity is often observed in this type of refrigerator. The position of the evaporator (horizontal/vertical, top/bottom of the compartment) determines the location of cold and warm zones. The brewed type is a static refrigerator equipped with a fan (Fig. 1b). It promotes air circulation and the temperature decreases rapidly after door opening. Air temperature is more homogeneous in this case than in the static type but the energy consumption is higher due to the fan. In a
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Nomenclature g K H M Ra Rap Rac t Tamb Tc Tf DT u*
acceleration due to gravity (9.81 m/s2) permeability of the porous media (m2) height of cold wall or height of cavity (m) enlargement factor (ratio between real dimension and image) Rayleigh number Rayleigh number of porous media critical Rayleigh number time (s) external ambient temperature (°C or K) cold wall temperature (°C or K) internal air temperature (°C or K) temperature difference between the cold and warm walls (°C or K) dimensionless air velocity
Fig. 1. Three types of refrigerator: (a) static, (b) brewed and (c) no-frost (Roussille, 2002).
no-frost refrigerator (Fig. 1c), a fan (embedded in the back wall) pushes air to flow over the evaporator before entering into the refrigerating compartment. Air temperature is more homogeneous compared to the two other refrigerator types. Disadvantages of no-frost type are noise, energy consumption, drying on food surface and high price. Only the static refrigerator was studied in the present work in which a strong coupling between air velocity and temperature is observed. Temperature distribution in a refrigerator model was already presented (Laguerre, Ben Amara, & Flick, 2005). To complete this previous work, the air velocity field is now presented. Knowledge of air temperature and velocity profiles in a refrigerator is important for food quality control. Design of refrigerator can be modified or recommendations can be given to consumers, so that perishable food products are placed in low-temperature and well ventilated positions. Food products should also not disturb the boundary layer close to the evaporator wall. Indeed, obstacles in this location would reduce the heat transfer between cold wall and air and product could freeze. The objective of this work is to generate experimental data on air velocity distribution in a static domestic refrig-
uy uz u X
velocity in the height direction of the refrigerator model (m/s) velocity in the width direction of the refrigerator model (m/s) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi velocity magnitude (m/s) u ¼ u2y þ u2z distance of smoke particle displacement (m)
Greek symbols a thermal diffusivity of air (m2/s) ap thermal diffusivity of the porous media (m2/s) b thermal expansion coefficient (K1) m kinematic viscosity (m2/s) d thickness of boundary layer (m) dt time interval between a pair of images (s)
erator. This study allows gaining better insight into the mechanism of airflow by natural convection. Also, the data obtained can be used to compare with the modelling results. To achieve this objective, an experiment was carried out using a transparent refrigerator model, which makes it possible to visualize and measure the airflow by PIV (particle image velocimetry). This refrigerator model allows observing the same phenomena as those in a domestic refrigerator but with better-controlled boundary conditions and simpler geometry. The influence of the following operating conditions on the air velocity was studied: cold wall temperature (parameter related to thermostat setting), dimension of cold wall (parameter related to design of evaporator), product loading. Comparison of the results obtained for empty and loaded refrigerator makes it possible to determine the influence of obstacles on airflow in the refrigerator. 2. Literature review 2.1. Air flow in domestic refrigerators Several experimental studies were carried out on empty and loaded refrigerators (James & Evans, 1992; Masjuki et al., 2001). The objective was to analyze the effects of several parameters on the temperature in the refrigerating compartment (thermostat setting, frequency of door openings, filled volume, temperature and humidity of ambient air). However, few studies were carried out on airflow measurement due to the complexity of measurement techniques compared to the ones of temperature. Airflow measurement in a freezer compartment under real operating conditions was carried out by Lacerda, Melo, Barbosa, and
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Duarte (2005) using PIV. It was observed that the flow field was strongly influence by the temperature variations due to the ‘‘on” and ‘‘off” operation cycles of compressor. This behavior was attributed to natural convection and strong dependency of air viscosity. Another study on airflow in a ventilated domestic freezing compartment was carried out by Lee, Baek, Chung, and Rhee (1999). In this study a comparison of velocity field obtained by CFD simulation and by experiments (PIV measurements) was undertaken. These authors observed that the flow was very complex: jet-like flow around entrance ports, impinging and stagnation flow on the walls and a large recirculation flow in cavity. To our knowledge, no study was carried out on air velocity measurement in refrigerating compartment. Moreover, airflow being strongly influenced by the aspect ratio (height/width) of the cavity; the flow in freezer is therefore different from the one in refrigerating compartment. To obtain useful information on natural convection in a domestic refrigerator, airflow in some well known configurations will be presented: near a warm (or cold) vertical plate, empty cavity and cavity filled with product. The temperature of the cold wall is constant for these three configurations in spite that this temperature fluctuates due to the ‘‘on” and ‘‘off” compressor working cycles in a real refrigerator. 2.2. Airflow near a vertical plate For a first approach, literature on flow adjacent to a cold vertical plate placed in warm environment (without other limiting walls) can be applied for understanding airflow by natural convection near an evaporator of refrigerator. If a tracer (smoke for air, for example) is injected at one end of the plate to visualize the flow, laminar flow is firstly observed near the wall and then turbulence appears (Fig. 2). The air velocity (u) is zero at the plate surface, then, it increases rapidly when the distance from the plate increases to attain a maximum value (um). Air velocity then decreases and approaches zero, which is the velocity far from the plate. The zone of non-zero velocity (u > um/ 100) is called the hydrodynamic boundary layer and its thickness (d) increases in the flow direction (x). Heat transfer phenomena depend on the flow regimes (laminar or turbulent). Khalifa (2001a) presents a literature review of natural convection heat transfer correlation for vertical and horizontal plates; more than 40 articles are cited. 2.3. Airflow in empty closed cavity The most often studied case is a two-dimensional flow in an empty cavity with two opposite walls at different temperatures and two insulated walls. The position of the cold wall (bottom/top horizontal walls, vertical walls) in the empty cavity determines airflow. When the horizontal cold wall is located at the bottom of the cavity, stable temperature stratification is observed with the cold zone at the bot-
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y u um δ (x)
U∞ = 0 u um
x Fig. 2. Hydrodynamic boundary layer and velocity profile in natural convection flow.
tom and warm zone at the top. In this case, air is stagnant and heat transfer occurs principally by conduction. When the top horizontal wall is cold, unstable flow is observed (Ostrach, 1988) since heavier air is above lighter one. The state of unstable equilibrium occurs until a critical density gradient is exceeded. A spontaneous flow then results that eventually becomes steady and cellular-like. When a vertical wall is cold, circular flow is observed. This case is similar to the one of the majority of domestic refrigerator, since the evaporator is often inserted in the vertical back wall. Air flows downward along the cold wall and upward along the warm wall and air is almost stagnant in the centre of the cavity (Fig. 3). The flow regime is characterised by the Rayleigh number (Ra) defined as gbDTH 3 ð1Þ am For small Rayleigh number, Ra 6 103, the buoyancy-driven flow is weak and heat transfer is primarily by conduction. With increasing Rayleigh number, the cellular flow intensifies and becomes concentrated in thin boundary layers adjoining the sidewalls. The core becomes nearly stagnant, although additional cells can develop in the corners and the sidewall boundary layers eventually undergo transition to turbulence (Incropera & Dewitt, 1996). Thermal stratification is also observed with the warm zone at the top of the cavity and the cold zone at the bottom. Several experimental studies were carried out to measure air temperature and/or velocity in closed cavities (Ampofo & Karayiannis, 2003; Armaly, Li, & Nie, 2003; Betts & Bokhari, 2000; Mergui & Penot, 1996; Tian & Karayiannis, 2000). Ramesh and Venkateshan (2001) used a differential interferometer to visualize conditions in the boundary layer Ra ¼
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ever, the air velocity at the centre of the cavity is weakly influenced by Ra. Many correlations between airflow (Ra) and heat transfer (Nu) are proposed and a review on this subject was carried out by Bejan and Tien (1978). The literature on cavity filled with porous media can not be applied directly to the case of loaded domestic refrigerator principally due to the product dimension. For refrigerators, the ratio between the dimension of product and cavity is about 0.10 (5 cm product width and 50 cm cavity width) while this ratio is 60.02 for porous media. There is notably a great influence of product position in the stack on heat transfer compared to the case of porous media.
Fig. 3. Airflow in empty closed cavity (Tian & Karayiannis, 2000).
along the wall (105 < Ra < 106). They found that airflow is generally stable except in the corner. Mergui and Penot (1996) carried out a visualization of flow in an empty cavity using a laser tomography (Ra = 1.7 109); they observed the same phenomena as Ramesh and Venkateshan (2001). The Rayleigh number is a factor determining the heat transfer. Khalifa (2001b) and Incropera and Dewitt (1996) present correlations between Rayleigh and Nusselt numbers for two- and three-dimensional heat transfers in empty closed cavities. 2.4. Airflow in cavity filled by product The most classical configuration is the parallelepiped cavity filled with porous media. Many studies were carried out on two-dimensional heat transfer by natural convection with differentially heated vertical sidewalls and adiabatic horizontal walls. In the case of porous media, the Rayleigh number is defined as Rap ¼
gbDT H K ap m
ð2Þ
When Rap ? 0, the conduction heat transfer is dominant, airflow is very weak. The temperature distribution is onedimensional (dependent on width and independent on height of cavity) (Bories & Prat, 1995). When the Rayleigh number is higher than a critical value, transition regime characterizes by two-dimensional temperature distribution (dependent on width and height of cavity) is observed. When the Rayleigh increases and the value is higher than another critical value, airflow by natural convection occurs. This flow is quasi-1direction near walls and it is very weak at the centre of the cavity. Heat is transferred principally from the warm to the cold wall by the air circulation in the boundary layer. The thickness of the boundary layer (d) and the maximum velocity in this layer (um) are greatly influenced by Rayleigh number (d decreases, um increases when Ra increases). How-
Fig. 4. Refrigerator model: (a) global view and (b) side view.
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This was shown in our previous studies (Ben Amara, Laguerre, & Flick, 2004) which demonstrate the influence of theses parameters on the heat transfer at low air velocity (<0.2 m/s) in a stack of spheres. The motivation of this study is to enrich the knowledge on airflow in an empty and filled cavity with an application to domestic refrigerator. In this case, airflow is threedimensional and the warm walls are not maintained at fixed temperature (Dirichlet condition) but subjected to heat losses (Cauchy condition). 3. Materials and methods 3.1. Refrigerator model The internal dimensions of the refrigerator model are: 0.5 0.5 1 m (depth width height, precision ±0.001 m). It is composed of three vertical double glass
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walls (glass thickness of 6 mm and air thickness between glass walls of 10 mm) and one vertical aluminum wall (thickness of 2 cm, containing a coil) (Fig. 4). A low-temperature water–glycol mixture was prepared in a thermostatically controlled cooling bath to maintain a constant temperature in this aluminum wall. The top and bottom horizontal walls are made of PVC (thickness: 2 cm). All external walls are insulated using expanded polystyrene plates (thickness: 4 cm). These plates can be taken off to visualize airflow and allow air velocity measurement by PIV system through the double glass walls. The ambient external temperature was 20 °C and the global heat transfer coefficient of the composite glass walls (including polystyrene insulation) can be estimated from the thermal properties of the materials: 0.52 W/m2/K. The flow circuit of the water–glycol mixture is arranged in such a manner that either the entire surface of the aluminum plate or only the upper half is cooled.
Fig. 5. (a) PIV (particle image velocimetry) system for air velocity measurement and (b) time interval between a pair of images (3.5 ms) and between two couples (250 ms).
Table 1 Experimental conditions for measurement of air velocity by PIV system on the symmetry plane of the refrigerator model Condition in refrigerator model
Number of pairs of images per window
Dimension of each image (height width)
Dimension of interrogation area (height width)
Temperature of cold wall (°C)
Surface of cold wall
Empty
60
106 133 mm2
6.6 6.6 mm2
10 and 0
Filled with four blocks of hollow spheres
38
70 87 mm2
4.4 4.4 mm2
0
Entire and only top half Entire
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The refrigerator model is cooled for 24 h to assure the steady state heat transfer in the cavity, before the air velocity measurement. Oil smoke (particle diameter 1 lm data of manufacturer) is stored in a drawer located at the bottom of the refrigerator model. The trap is opened to introduce this smoke into the cavity, then, it is closed when enough smoke is present for measurement. When the smoke diffusion attains the equilibrium state (30 min), the air velocity is then measured by the PIV system. 3.2. PIV system The basic optical device for the PIV system is presented in Fig. 5. It is composed of a double pulse Nd-Yag Laser source (Quantel-Big Sky model CFR400-1000 Watts); which produces a light sheet for a short period by the aide of lens. A CCD video camera (1028 1024 pixels, Sensi-
Cam 12 BIT Cooled Imaging) placed perpendicular to the laser sheet allows images of smoke particle displacement. Several images were taken and they were used to calculate the air velocity. 3.3. PIV image treatment The laser light is formed into a sheet in the symmetry plane, and the resultant scattered light, which is at the same frequency as the incident laser, is recorded on the CCD camera. The time between two laser pulses was 3.5 ms and the time between the capture of two pairs of pictures was 250 ms. Several pairs of picture were recorded on each measurement window. Table 1 shows the number of pairs of pictures and the dimension of measurement window used in our experiment. The calculation of velocity vector was carried out on the measurement window by dividing
Fig. 6. (a) Empty refrigerator model, (a0 ) front view of the symmetry plane showing the position of windows for air velocity measurement in empty refrigerator model, (b) refrigerator model filled with four blocks of hollow spheres and (b0 ) front view of the symmetry plane showing the position of windows for air velocity measurement of the refrigerator model filled with hollow spheres.
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it into small interrogation areas (size shown in Table 1). After cross-correlation of these pictures, a mean velocity field was calculated. The position of images taken by the camera was moved allowing the development of air velocity field all over the symmetry plane. It should be noticed that the time interval of 3.5 ms between two laser pulses was the optimum. If the time interval is too low, the distance of particle displacement is too short and consequently, the calculation of air velocity may conduct to error. If the time interval is too high, the particles appearing in the first image disappear in the second. The velocity calculation is thus impossible. For the filled refrigerator, one pixel corresponds to 70 lm and the interrogation is a square of 4.4 4.4 mm2 (for the empty refrigerator images are slightly larger: 6.4 6.4 mm2). The maximal velocity is about 0.25 m/s. Considering a case in which all the particle have a vertical velocity of 0.25 m/s, if 4/5 of the particles present in the interrogation area of the first image have to be still present in the second image, the time interval must be less than 3.5 ms. For this time interval the velocity measurement accuracy is about ±0.01 m/s (± half a pixel/time interval). The velocity of smoke displacement is assumed to represent the air velocity ð~ uÞ. Software (based on inter-correlation) is used to establish a velocity field from a pair of images by the following equation: 1 ~ u¼ M
~ X dt
! ð3Þ
3.4. Experimental conditions for airflow measurement The influence of the following operating conditions was studied: cold wall temperature, dimension of cold wall and presence of obstacle. – Cold wall temperature. In empty refrigerator model, two cold wall temperatures were studied: 10 °C (corresponding to the evaporator temperature at the end of the compressor work cycle) and 0 °C (corresponding to an average evaporator temperature during an ‘‘on” and ‘‘off” cycle). – Dimension of cold wall temperature. For domestic refrigerators, surface area of the cold wall can vary from the half to the entire back vertical wall. In our study, the aluminum wall of the empty refrigerator model was cooled either totally (100%), or only the top half (50%). – Presence of obstacle. Food products stored in a domestic refrigerator have different forms, dimensions (generally form 5–20 cm) and occupy volumes (from nearly empty to nearly full). As a first approach to understand the influence of obstacles, the refrigerator model was loaded by simple arranged objects. In our case, it consists in an aligned stack of hollow spheres considered as inert medium (without heat exchange with air), Fig. 6. The position of measured windows on the sym-
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Fig. 7. Experimental device for air temperature measurement.
metry plane was shown in this figure. Table 1 summarises the experimental conditions. 3.5. Experimental assembly for air temperature measurement To obtain complementary information, air temperature was measured in the refrigerator model. The objective of this measurement was to analyze the relation between air temperature and air velocity stability particularly in positions where high velocity fluctuations were observed. This measurement was carried out using tightened wires thermocouples (T-type, calibrated, 200 lm diameter, precision ±0.2 °C), Fig. 7. Due to the small wire diameter, airflow was very slightly disturbed by the presence of the thermocouples. Nine thermocouples were attached to a Plexiglas support on each side (5 ± 0.1 mm space between thermocouples). The height level of these thermocouples was adjusted in such a manner that the air temperature at the bottom and at the mid-height of the refrigerator model was measured. 4. Results and discussion 4.1. Velocity profile in empty refrigerator model The average air velocity (calculation from 60 pairs of images) on the symmetry plane of the refrigerator model is shown in Fig. 8, for cold wall maintained at 10 °C. For this experiment, the average temperature of the internal double glass walls was 5.1 °C (2.3 °C at 10 cm high, 4.2 °C at 50 cm and 8.7 °C at 90 cm). The experimental result agrees with the literature, circular airflow is observed in the cavity.
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Fig. 8. Air velocity field on the symmetry plane of empty refrigerator model measured by PIV: (a) velocity vector and (b) velocity magnitude. The entire cold wall was maintained at 10 °C.
Air flows downward along the cold wall with an increasing velocity. Air flows very slowly (u < 0.04 m/s) at the top of the cold wall and it attains the maximum value (0.24 m/s) at the bottom. Then, air flows upward along the double glass wall located oppositely with decreasing velocity until stagnation at the top of the wall. Also, air moves horizontally from the double glass wall to the cold wall (u < 0.04 m/s). Near the top wall, there is a zone of slightly higher velocity, with inclined velocity vectors. This is comparable to the cells observed in the corners in the two-dimensional case as mentioned in the literature review (Fig. 3). Laminar airflow (low velocity fluctuations compared to the average value calculated form 60 pairs of images) was globally observed in the cavity except at the bottom of the refrigerator model. At this position (height < 10 cm), unsteady air flow patterns were observed, Fig. 9. The instantaneous velocity field (obtained from one pair of images) near the bottom of the cavity at two successive instants is presented. A circular airflow pattern which moves in the same direction as the main flow from cold wall toward the opposite wall is shown.
The vertical velocity profiles in the hydrodynamic boundary layer near the cold wall and the double glass located oppositely are shown in Fig. 10a for three heights (10, 50 and 90 cm). Near the cold wall (Fig. 10b), the thickness of the boundary layer is small at the top (d ? 0) and it increases toward the bottom of the refrigerator model (d 3 cm). Vertical velocity is very slow outside boundary layer. Fig. 10c shows the air velocity profile near the double glass (warm wall) located in opposite to the cold wall. The velocity magnitude is much lower than near the cold wall: maximum velocity is about 0.05 m/s near the warm wall whereas it is about 0.25 m/s near the cold wall. This can be explained by the fact that there are three vertical warm walls where air flows upward whereas there is only one cold wall. Indeed, in steady state, the heat losses trough the glass walls (1.5 m2) has to be absorbed by the cold wall (0.5 m2). The temperature difference between the cold wall and air is therefore much higher than the temperature difference between glass wall and air. The ratio is typically between 3 and 5 (Laguerre et al., 2005). The recirculation at the bottom of the refrigerator model (height = 10 cm)
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may explain the large thickness of the boundary layer at this level (d 7 cm) compared to those at other levels (d 2 cm at 50 cm and 2.5 cm at 90 cm).
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To confirm the instability of airflow at the bottom of the cavity, Fig. 11 presents a plot of velocity versus time. It can be seen that airflow structures are sometimes quasi-periodic
Fig. 9. Displacement of air recirculation at the bottom of the symmetry plane of the empty refrigerator model (height: 0–10.6 cm and distance form the cold wall: 20–33.2 cm). Entire cold wall maintained at 10 °C.
Fig. 10. Vertical velocity profile (uy) at three height levels on the symmetry plane when the entire cold wall was maintained at 10 °C: (a) global view, (b) profile in boundary layer near the cold wall and (c) profile in boundary layer near the double glass wall.
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(period 2s). The air temperature fluctuations at the bottom of the cavity (measurement by thermocouples) confirm again the unsteadiness of the air flow, Fig. 12. This fluctuation is much more pronounced (Tmax Tmin = 0.9 °C) than that at the mid-height (Tmax Tmin = 0.1 °C).
4.2. Influence of the cold wall temperature The measurement of air velocity field on the symmetry plane of the refrigerator model was carried out when the cold wall temperature was maintained at 10 °C and at 0 °C. The main difference between the results of these
Fig. 11. Air velocity variation at the bottom of the symmetry plane of the empty refrigerator model. Entire cold wall maintained at 10 °C.
Fig. 12. Air temperature variation at the bottom and at mid-height of refrigerator model.
Fig. 13. Influence of the cold wall temperature on the vertical velocity profile on the symmetry plane and at 50 cm height of empty refrigerator, entire cold wall maintained at 10 °C and 0 °C: (a) profile near the cold wall and (b) profile near the double glass wall.
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two experiments is the velocity profile in the boundary layer near to the cold wall. The lower cold wall temperature contributes to increasing the air velocity in the boundary layer along the y direction. For example, at 50 cm (Fig. 13), the maximum air velocity increases from
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0.19 m/s (cold wall at 0 °C) to 0.23 m/s (cold wall at 10 °C). The effect of the cold wall temperature on the air velocity is less significant near to the double glass wall located oppositely. This may be explained by the fact that the tem-
Fig. 14. Influence of the dimension of cold wall on the horizontal velocity profile on the symmetry plane and at 10 cm height of empty refrigerator, entire (100%) and only top half (50%) of the cold wall maintained at 10 °C: (a) profile near the cold wall and (b) profile near the double glass wall.
Fig. 15. Air velocity field on the symmetry plane of refrigerator model: (a) velocity vector of empty case, (a0 ) velocity magnitude of empty case, (b) velocity vector of filled cases and (b0 ) velocity magnitude of filled case. Entire cold wall maintained at 0 °C.
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Fig. 15 (continued)
perature difference between air and glass varies less than temperature difference between air and cold wall when cold wall temperature is modified. 4.3. Influence of the dimension of the cold surface The air velocity field was measured on the symmetry plane when the entire cold wall (100%) was maintained at 10 °C and when only the top half of the cold wall (50%) was maintained at 10 °C (Fig. 14). Considering the velocity profile near to the cold wall at 10 cm (Fig. 14-a), the maximum value of air velocity is higher in the case of 100% (0.24 m/s) than the one of 50% (0.20 m/s). The thickness of the boundary layer is relatively the same for both cases whereas the location of the maximum air velocity is different: 0.8 cm from the cold wall (100%) and 1.1 cm (50%). This can be explained as follows. In the case of 100%, the airflow near the cold wall is accelerated (by buoyancy forces) along the wall, therefore velocity increases. In the case of 50%, from mid-height to bottom, airflow near the wall is no more accelerated because its temperature is almost the same in the boundary
layer. On the contrary, the airflow decelerated due to wall friction and momentum diffusion occurs so that the boundary layer thickness increases. Near to the double glass wall (Fig. 14-b), the velocity profiles are slightly different. This is related to flow pattern differences (recirculation) in the bottom right corner. The velocity magnitude is lower near the double glass wall (maximum value 0.08 m/s) compared to the one near the cold wall (maximum value 0.23 m/s). The velocity profiles are not different at the top part of the refrigerator model (height P 50 cm) for both the experiment of entire cold wall and top half cold wall. 4.4. Influence of the obstacles The air velocity field on the symmetry plane was measured when the refrigerator model was filled with 4 blocks of hollow spheres (Fig. 15). The result was compared with the one of empty refrigerator model when the entire cold wall was maintained at 0 °C. Circular airflow was observed on the symmetry plane of refrigerator model filled with blocks as in the empty case: air flows downward near to the cold wall and upward near
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to the double glass wall located oppositely. The air velocity is more homogeneous with the presence of blocks. The maximum air velocity near the cold wall decreases from 0.20 m/s (empty refrigerator model) to 0.16 m/s (refrigerator model filled with blocks). The vertical air velocity profile at three height levels shown in Fig. 16 confirms the role of obstacles to decrease the maximum air velocity near the cold wall. This may be explained by the friction on the surface of spheres which decelerates the air velocity. The influence of obstacles on air velocity is less significant near the double glass wall except at the bottom level (10 cm high). At this position, the velocity profile is very different for the two cases (maximum air velocity of 0.07 m/s for empty
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case and 0.02 m/s for filled case). This may be due to the absence of recirculation in the filled refrigerator model. The flow reversal observed in Fig. 16c (for y = 90 cm) for the filled case may be explained by a small recirculation cell appearing in the corner (between the glass wall and the bloc of spheres). 5. Conclusions The measurement of air velocity in a refrigerator model was carried out using a PIV system. A circular airflow was observed in the cavity: air flows downward near the cold wall and air flows upward near the double glass wall situated oppositely. There is also weak horizontal airflow from the double glass to the cold wall. The maximum air velocity was observed near the bottom of the cold wall. Non-stationary flow with air recirculation was observed at the bottom of the refrigerator model. Air is stagnant at the top of the cavity. The data on air velocity field developed in this study give complementary information on air temperature field already presented in our previous study. This furthers the comprehension on the strong coupling between airflow and heat transfer by natural convection in closed cavity. At the top of the refrigerator model where air is stagnant, high temperature is observed. At the bottom, where nonstationary airflow is observed, the temperature is low and there are more fluctuations. The influence of three operating factors on the velocity profile at the symmetry plane was studied: cold wall temperature, cold wall dimension and obstacles. The cold wall temperature has more influence than the cold wall dimension. The influence on the air velocity is more significant near the cold wall than near the glass wall located oppositely. The lower the cold wall temperature, the higher the air velocity along this wall. The air velocity is more homogeneous when the refrigerator model is filled with obstacles (blocks of hollow spheres). The knowledge of the airflow and heat transfer in refrigerator may contribute to the design improvement of the appliances. Also, this knowledge can help the consumer to better use their refrigerator. Acknowledgements The authors would like to thank the French Ministry of Agriculture and the ‘‘Ile de France Regional Council” for their financial support. References
Fig. 16. Comparison of the vertical velocity profile on the symmetry plane of empty and filled refrigerator model. Entire cold wall maintained at 0 °C.
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