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Entrainment of refrigerated air curtains down a wall
Experimental Thermal and Fluid Science 30 (2006) 175–184 www.elsevier.com/locate/etfs
Entrainment of refrigerated air curtains down a wall Brandon S. Field, Eric Loth
*
Department of Aerospace Engineering, University of Illinois, Urbana-Champaign, 104 South Wright Street, Urbana, IL 61801, USA Received 3 January 2003; received in revised form 27 May 2003; accepted 22 January 2004
Abstract Refrigerated air curtains are used in open supermarket display cases as a barrier between the warm ambient air and the cold refrigerated air. Entrainment of ambient air into the curtain by shear layer mixing contributes to both the sensible and the latent heat load on the display case. To better understand the fluid dynamics which govern entrainment, velocity and temperature measurements of the curtains were made in a refrigerated display case, which was modified to allow a more fundamental flow. In particular, a vertical solid wall was installed to approximately represent a fully-stocked configuration. As such, negatively-buoyant wall jets (with high inflow turbulence) in the Reynolds number range of 4200–8000 and in the Richardson number range of 0.13–0.58 were examined. To define the air curtain vortex structures, flow visualization of the curtain interface was employed. The results of which showed that the entrainment of the ambient air was found to be governed by a variety of eddy engulfing structures. Particle Image Velocimetry was used to examine the velocity profiles of the air curtains in a non-intrusive manner, the measurements of which indicated negatively-buoyant acceleration following the jet exhaust, followed by a more linear curtain growth characteristic of isothermal wall jets. In addition, thermocouples were used to obtain the net increase in temperature of the curtain due to entrainment, where it was found that the dimensionless thermal energy loss decreased with decreasing Reynolds number. 2005 Elsevier Inc. All rights reserved. Keywords: Wall jets; Buoyancy; Turbulence; Air curtain; Refrigeration; Entrainment
1. Introduction Refrigerated air curtains are used on open supermarket display cases to keep ambient room air from entering the case while still allowing convenient physical access to products. There are many aspects to the thermal loading of a refrigerated display case, such as the radiant heat load from the ambient supermarket, the case lights that illuminate the product, the addition and removal of product by stockers and customers. However, the entrained ambient air into the air curtain is the largest energy loss [1]. According to some esti-
*
Corresponding author. Tel.: +1 217 244 5581; fax: +1 217 244 0720. E-mail address: [email protected] (E. Loth). 0894-1777/$ - see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2004.01.012
mates, 75% of the refrigeration load comes from the air curtain entrainment [1], and energy calculations preformed by the refrigeration industry have found the air curtain entrainment load can be as high as 90%. Since refrigeration accounts for roughly 50% of overall supermarket electricity consumption, air curtain entrainment plays a large role in supermarket energy usage. In addition, the high humidity levels of the entrained air accelerates the frosting of the evaporator coils (reducing their heat transfer and increasing the required frequency of defrost cycles). Therefore, minimizing the ambient air entrainment into the display case is critical to the overall system performance and efficiency. Most previous studies of refrigerated display cases have taken a ‘‘whole case’’ perspective (i.e. not focusing on the underlying fluid physics of the air curtain itself), and are thus empirical in nature. Specifically, most of the industrial research and design efforts have taken an
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energy-balance view of the air curtain entrainment, carefully controlling the temperature and humidity in the lab, measuring the electrical power drawn by the compressor and fans and the mass of condensate water from the evaporator coils over an extended time period to determine the energy loss from the case and curtain. Curtain velocity profiles have been empirically optimized with these methods, via testing different inlet flow deflectors to determine which produces the least entrainment. Exact velocity profiles are unknown because of the coarseness of the measuring devices used. In particular, most previous experiments have typically employed probe diagnostics, whereas it is desirable to use non-intrusive diagnostics (as used herein) to avoid potential flow disturbances. In order to understand the characteristics of refrigerated air curtains, a number of studies have been performed. Howell [2] quantified the detrimental effect of ambient relative humidity on the energy requirements of specific display cases. The humidity levels in the store were shown to contribute to the energy requirements of the case by means of latent heat infiltrating the case via entrainment. The experiments were specific to certain display cases since different case geometries affected the energy requirements. Other studies of air curtains include computational modeling of the air curtain assuming both turbulent and laminar conditions [3–5]. While including components such as fans and the evaporator coils, comparison to experimentally determined values show that all those predictions generally yielded qualitative comparison but poor quantitative representation of the curtain dynamics. Faramarzi [6] presents a simplified cooling load model for vertical display cases based on a breakdown of the cooling loads involved. Experimental and computational results of a display case were shown and used in the estimated breakdowns. However, the study concludes with the remark that the infiltration load is different for different cases (i.e. case specific) and that understanding of the thermo-fluid dynamics of the air curtain is required in order to provide a method to determine the entrainment rates. Cortella et al. [7] preformed a CFD simulation using an LES model for the air flow in a dual curtain display case. A comparison of experimental product temperature measurements and the air temperature (in the curtain and return ducts) to those determined numerically showed reasonable agreement. However, the overall heat load of the curtain on the refrigerator was not in complete agreement with the simulation results, probably because experimental velocity measurements inside the air curtain were not performed. This problem may also have been due to the complexity in the display case geometry, pointing to the need for a more fundamental investigation of the essential fluid dynamics.
Navaz et al. [8] recently performed an air curtain study comparing PIV results to a numerical simulation. The curtain parameters were varied to study their relative effects of inlet temperature and initial curtain velocity. Qualitative agreement between computational simulation and experiment were reported, where differences could be related to the substantial experimental uncertainty. As in other studies, the variation of inlet conditions was small (in this study, limited to a 0.8 C and 0.1 m/s variation) and the experiment and simulations were specific to the geometry of the display case studied. In addition, as in other studies there was no discussion of the air curtain vortex structures and dynamics. Since the air curtain flow is not well understood at typical conditions, it is instructive to consider its basic fluid dynamics components. Air curtain entrainment results from the shear layer mixing between the quiescent ambient room air and the refrigerated air curtain. Since the air curtain is cooler than the ambient room air and tends to ‘‘ride’’ along the front of the product, it produces a negatively-buoyant jet over an irregular wall. Based on the typical jet flow rates and Reynolds numbers, the air curtains reside in the transitional flow regime: not fully-turbulent, but not a laminar flow either. This complicating aspect has been cited as one of the reasons for poor predictions of the velocity field when fully-developed turbulence models are used [3]. In order to better understand the fundamental fluid dynamics of the air curtain, and avoid case-specific flow features, one may employ the geometric simplification of the display case whereby the products are replaced by a flat wall. This enables the air curtain to be modeled as a negatively-buoyant wall jet, a jet of high-density fluid moving downwards with the buoyancy force and the velocity of the jet in the same direction. For such a jet, there are three primary dimensionless parameters that can be used to characterize the flow: the Reynolds number (Re), the Richardson number (Ri) and the Grashof number (Gr). These parameters are defined here as Re ¼
V jet qjet H ; ljet
Gr ¼ Re2 Ri ¼
Ri ¼
ðqamb qjet ÞgH qamb V 2jet
qamb qjet gH 3 . 2 l qamb qjet jet
In the above, Vjet is the mean streamwise velocity at the start of the curtain, H is the width of the curtain at this point (the curtain inlet), g is the gravitational acceleration, q is density, and l is viscosity. The subscripts ‘‘jet’’ and ‘‘amb’’ refer to the curtain inlet and ambient room properties respectively. For refrigerated display cases in a conventional configuration and flow rate, the typical air curtain Richardson number value was
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found to be 0.3 and Reynolds numbers in the range of 5000–8000 [9]. There are several previous studies of conventional buoyant jets for a variety of Reynolds and Richardson numbers. At low speeds, a computational study of upwards laminar wall jets over a heated surface was carried out by Angirasa [10]. The corresponding Richardson numbers studied were in the range of 0.004–0.01. The jet was found to detach from the wall when Reynolds numbers were increased to the order of 100, leading to a decrease in heat transfer from the wall. For fully-turbulent flows (e.g. Re > 10,000), Ljuboja and Rodi [11] developed an extension of the k–e computational model for the behavior of a fully-turbulent buoyant wall jet that accounts for the buoyancy and wall effects and agrees well with experiments. Sangras et al. [12] observed turbulent wall plumes in the self-preserving region to measure mixture fractions, probability density functions and temporal power spectra. The turbulent mixing of the wall plumes were compared to that of free line plumes. The wall was observed to inhibit the large-scale turbulent motion and limit the mixing to one side of the flow, thus reducing the amount of mixing compared to a free line plume. However, no detailed investigations (with respect to flow visualization, velocity distributions, or thermal entrainment) have been conducted for the fluid physics of refrigerated flat-wall jets in the transitional flow Reynolds numbers (1000–10,000) or with substantial inflow turbulence levels. In the present study, this combination is investigated due to its strong relevance to refrigerated air curtains typical of display cases. In particular, the present study examines flow for a refrigerated display case which has been idealized into a wall jet with a uniform inlet velocity profile. This fundamental flow field was chosen as it retains the general properties of the curtain while eliminating case-specific issues particular to each manufacturer. The aspects of vortex dynamics, velocity profile evolution, and thermal entrainment are presented in this investigation for various Reynolds and Richardson numbers.
2. Methods 2.1. Flow facility The modifications to the display case (placing a wall on the face of the shelves and modifying of the deflector to produce a more uniform velocity profile) are discussed in Field and Loth [13] and pictured in Fig. 1. The height of the air curtain inlet, H, was 120 mm for the display case tested, and the x-axis was oriented downwards with the origin at the curtain inlet. The air curtain speed was varied by changing the blades of the two fans that provided the circulation of the air through
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Fig. 1. Idealizations made to the refrigerator case and thermocouple locations.
the case. Three different pairs of fan blades with the same diameter and different camber were used. The fan blades provided commercially with the case produced the highest air flow, and are called the ‘‘highspeed’’ fans. Two other sets of fan blades produced slower curtains, and are termed the ‘‘medium-speed’’ and ‘‘low-speed’’ fans (details are given in [9]). To estimate Vjet, the average streamwise velocity at the downstream location x = H was used. The temperature of the curtain, Tjet, was dependent on the speed of the curtain by means of the residence time in the evaporator coil, such that the Richardson numbers and Reynolds numbers of the air curtain were coupled. The resulting Reynolds numbers and Richardson numbers produced by the test conditions are given in Table 1. Note, that the conventional display case configuration (using the original fans and without the wall) produced an air curtain with a jet Reynolds number of 5300 and a jet Richardson number of 0.30, as well as a qualitatively similar velocity distribution to the wall jet case [9].
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Table 1 Test conditions Test condition
Reynolds number
Richardson number
Grashof number
Two low-speed fans One high-speed fan Two medium-speed fans Two high-speed fans
4200 4700 7500 8000
0.58 0.47 0.15 0.13
9.4 · 106 9.5 · 106 7.8 · 106 7.8 · 106
ness, d(x). The curtain thickness was defined for a given velocity profile as the distance from the wall (y) where the streamwise velocity reduces to 25% of the maximum streamwise velocity at a given streamwise location (x), i.e. d(x) y at Vx(y)/Vx,max = 0.25. The curtain thickness was determined for all cases at various x-locations and was then normalized by the curtain inlet height, H. 2.3. Temperature measurements
2.2. Velocimetry measurements and flow visualization For temperature measurements, three K-type thermocouples were installed in the display case in the locations shown in Fig. 1. The first thermocouple was located in the top duct just before the deflector and honeycomb to measure the initial temperature of the air curtain, Tjet. The second thermocouple was located outside the case and above the curtain inlet to measure the ambient room air, Tamb, that was entrained into the curtain. The third thermocouple was located in the capture region at the bottom of the case to measure the temperature of the captured air, Tcapture. The capture region was found generally to have a uneven temperature distribution so Tcapture was measured behind one of the fans to maximize the amount of mixing of the return air, so that the thermal measurements can represent the average entrainment for the entire curtain. An Omega HH611PLC data logger was used to record the three thermocouples simultaneously each minute. In order to assess (and avoid) the thermal transients due to start up, the temperature at various locations on the refrigerator cases were recorded during each experimental run. Fig. 2 is a plot of Tcapture, Tjet, and Tamb for the Ri = 0.13 curtain. An initial transient is seen when the case is turned on, and then the temperatures remain in a steady-state period for a few hours. If the case were allowed to run longer the frost growth at the evaporator would begin to affect the curtain temperature. Therefore, all the data were taken before the 25 20
T
capt
T
15
Periods of PIV data
jet
T
Temp (°C)
For velocity vector measurements over a given field of the wall jet modification of the display case, Particle Image Velocimetry (PIV) was used. PIV is a non-intrusive flow measuring technique that consists of a double-pulsed laser sheet that illuminates a cross-section of the seeded airflow. A cross-correlation digital camera captures two images of the illuminated seed particles in quick succession and correlates the differences in particle position to calculate a complete two-dimensional vector field. For PIV measurements the entire flow field was seeded uniformly in both the jet and ambient regions with tracer particles. The particles were thirty micron diameter glass particles, Microspheres by 3M, which had response times much less than the time scales of the flow. The jet exhaust at the top of the air curtain was seeded by injecting the particles upstream of the deflector to ensure uniform distribution near the measurement plane [9]. The ambient region of the flow was also seeded before each data collection period, by globally dispersing a large group of particles in front of the display case. However, for the qualitative visualization of the air curtain entrainment only the air curtain jet was seeded. This allowed a time-dependant animation of the interface between the jet flow and the ambient air along the full curtain length. In both cases, the images were captured using the laser and camera of the PIV system. Details of PIV and in particular the cross-correlation PIV technique are described by Keane and Adrian [14]. The PIV equipment used in these tests was provided by LaVision, Inc., and consisted of a pulsed Nd:Yag laser to provide illumination and a Kodak ES1.0 cross-correlation digital camera to capture the images. The crosscorrelation vector calculation routines employed here were those found in the DaVis software, version 5.5.4. Since the curtain length was larger than the field of view of the camera, the entire curtain was split into several fields of view to cover the entire curtain. For each field of view, 500 vector images were taken to produce the average velocities and statistical information for the curtain. For calculation of velocity statistics, local averaging of adjacent vectors was preformed to reduce statistical noise [9,13]. From the PIV-obtained velocity profiles, the momentum distribution was characterized by the curtain thick-
amb
10 5 0 -5 0
50
100
150
200
Elapsed time (min) Fig. 2. Transient temperature plots for Ri = 0.13 (Re = 8000).
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frost growth was significant. The periods of time in which PIV data were taken is shown on the plot to indicate that the temperatures remained reasonably constant within the data collection times. The thermal entrainment is characterized by the T T jet parameter: a ¼ Tcapture . In the limit of no thermal amb T jet entrainment across the curtain, Tcapture = Tjet and a has a value of zero. As the entrainment of ambient air
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into the curtain increases, a increases, reaching a maximum value of one only when all the air being drawn into the capture region is ambient air (Tcapture = Tamb). The net thermal energy loss due to entrainment can be determined per unit length of the display case by _ p DT , with the temperature difference being E ¼ mc measured from top to bottom of the curtain, DT = (Tcapture Tjet). This can be written in terms of the
Fig. 3. Sequential particle visualization of curtain, Re = 3700, Ri = 0.76. Time between frames is 0.133 s from x/H = 0.5 to x/H = 2.
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thermal entrainment parameter and Reynolds number as E = (Rel)cpa(Tamb Tjet). For a display case the parameters cp, l, and (Tamb Tjet) will be approximately constant, since they are specified by the design considerations. Non-dimensionalizing the energy loss by the product of these parameters, the energy loss due to thermal entrainment becomes E* = aRe. In this way, the product (aRe) can be used to represent the net thermal entrainment energy loss for a given display case, and was obtained for each of the refrigerated air curtain conditions.
3. Results 3.1. Flow visualization Fig. 3 shows sequential frames of the flow visualizations from the inlet of the curtain. Small and large-scale
vortices coexist at the interface of the flow and the growth and deformation of the vortices is evident. For example, the arrow in Fig. 3(c)–(f) follows the rapid growth of a single eddy over the distance of about 1.5H. Entrained ambient air is evident, especially when the eddy is seen in (f). This animation of the curtain development resembles the animations of the curtain temperature contours presented by Cortella et al. [7], but only the larger scale eddies are evident in the LES simulations, whereas the current visualization indicates a broad spectrum of eddy frequencies. In all the flow visualizations of the air curtains, the overall trend of the air curtain development is a continual growth of the eddies as they move from the inlet to the capture area at the bottom. The shear layer interface is dominated by eddies that can be seen as combinations of protrusions and indentations that form a wave pattern (similar to a Kelvin–Helmholtz instability) along the outer edge of the curtain. It is inside the indentations that
Fig. 4. Time-averaged streamline images of the curtain inlet for increasing Ri: (a) Ri = 0 (Re = 3800), (b) Ri = 0.13 (Re = 8000), (c) Ri = 0.15 (Re = 7500), (d) Ri = 0.47 (Re = 4700). The field of view in each image ranges approximately from x/H = 0.5 to x/H = 2.3.
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the ambient air primarily gets engulfed and entrained into the curtain. The complexity and volatility of the eddy interactions appear to be more exaggerated than those found in previous wall jet studies, indicating that the high levels of turbulence found in the air curtains (discussed below) produce increased mixing and entrainment. 3.2. Velocity measurements From the PIV measurements, the time-averaged streamlines can be obtained. For different Richardson numbers a marked difference is clearly seen at the top of the curtain, as shown in Fig. 4. As the Richardson number increases from 0 to 0.47, there is a greater tendency for the curtain width to get thinner immediately after the inlet. This inward deflection of the streamlines is a result of the negatively-buoyant acceleration of the refrigerated curtain. This buoyant effect is most pronounced at the curtain inlet; as the curtain continues downward it reaches a ‘‘neck’’ where its thickness reaches a minimum and then begins to grow in the same way as the isothermal curtain. This same effect has been seen in positively-buoyant plumes, for example Epstein and Burelbach [15] examined a circular jet of low-density fresh water oriented upwards into a tank of higher density salt-water brine and observed the same initial buoyant acceleration followed
Fig. 5. Streamwise velocity contours for refrigerated curtain, Ri = 0.47, Re = 4700, where highest velocities are red and lowest are in black.
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by a neck above which the jet spread. Similarly, Cetegen and Ahmed [16] examined buoyant circular jets for varying Reynolds numbers and noted overall initial jet shapes for varying Richardson numbers which were qualitatively similar to the initial shapes found here. Fig. 5 shows the false-color composite of the timeaveraged streamwise velocity contours for a refrigerated air curtain at Re = 4700 and Ri = 0.47. At the top of the curtain, the negatively-buoyant acceleration and jet width decrease can be qualitatively seen. However, below x/H = 4, the negative-buoyancy effects are no longer significantly accelerating the curtain, and the curtain growth proceeds in a qualitatively similar manner to an isothermal curtain [13]. This trend was representative of the curtains of other Richardson numbers. Fig. 6 shows the velocity profiles that were obtained from the time-averaged velocities of the refrigerated curtains of Ri = 0.13 (Re = 8000) and Ri = 0.47 (Re = 4700). As expected, the velocity profiles reveal that the interaction with the ambient air causes the curtain to spread immediately after injection. In contrast to the isothermal case which showed a consistent decrease in Vx,max [13], the refrigerated curtains exhibited buoyant
Fig. 6. Evolution of streamwise velocity profiles for refrigerated curtains, (a) Ri = 0.13, Re = 8000, (b) Ri = 0.47, Re = 4700.
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B.S. Field, E. Loth / Experimental Thermal and Fluid Science 30 (2006) 175–184 0
0 0.2
2
0.4 0.6
VRMS / Vjet Vx / Vjet
0.8
4
x/H
V / Vjet
Ri=0 (Re=3800-8500) Ri=0.13 (Re=8000) Ri=0.15 (Re=7500) Ri=0.47 (Re=4700)
1
6
1.2 0
0.2
0.4
0.6
0.8
1
1.2
y/H
a
8
0 10 0
0.2
V / Vjet
1
1.5
2
2.5
δ/H
0.4
VRMS / Vjet
Fig. 8. Curtain thickness development for refrigerated and isothermal curtains by Richardson number.
Vx / Vjet
0.6 0.8 1 1.2 0
b
0.5
0.2
0.4
0.6
0.8
1
1.2
y/H
Fig. 7. Initial streamwise velocity and RMS velocity profiles for (a) Ri = 0.47, Re = 4700 and (b) Ri = 0, Re = 4600 curtains.
acceleration until roughly x/H of 4. As the Richardson number of the curtains increases, the flow acceleration is more pronounced. These two effects will be seen to counter each other in terms of growth of curtain thickness, since d is defined based on the local peak velocity at a given x/H. After the accelerating regime, the spreading of the curtain is much more apparent. However, it is interesting that in the range of x/H studied here, the peak velocity is not seen to decrease significantly. Fig. 7(a) shows the streamwise velocity profile and turbulence intensity profile at this downstream location for the Ri = 0.47 curtain (Re = 4700) and Fig. 7(b) shows the same profiles for the Re = 4600 isothermal curtain (Ri = 0). The initial curtain turbulence calculated from the velocity profiles showed that all the air curtains had substantial initial turbulence, with VRMS/Vjet inside the curtain of about 5% at the downstream location of x/H = 1. The locations of the peak turbulence levels coincide with the locations of the largest gradients in the velocity profiles, as is typical for shear flows. Fig. 8 shows the curtain thickness for various Richardson numbers. The curtain thickness for isothermal (Ri = 0) curtains at various speeds (Re = 3800, 4600,
7600, and 8500) are shown with the same symbol, since the results were roughly independent of Reynolds number, whereas the refrigerated curtains of Ri = 0.13, 0.15, and 0.47 are shown individually. The thinning of the curtain due to negatively-buoyant acceleration is again seen to dominate the initial region of the curtain development. The higher Richardson number curtain is the most affected by the buoyant acceleration, and the two curtains of similar Richardson number (0.13 and 0.15) are similarly affected up to x/H of about 5. After that, a significant difference developed between these two curtains, with the Ri = 0.13 curtain spreading at a faster rate than the Ri = 0.15 curtain. This was unexpected but may be attributed to the difference in initial turbulence levels found in the curtains, with the Ri = 0.13 curtain having a significantly higher initial turbulence level than the other two curtains (as much as 10%). In general, decreasing the refrigerated curtain velocity from Re = 8000 to Re = 4700 led to a reduced curtain thickness due to the negatively-buoyant acceleration effect, and further Re reductions associated with Ri increases may lead to increased wall jet stability due to increased buoyancy forces. Universal to all the curtains, however is that after the region of buoyant acceleration at the curtain inlet, all of the curtains grow nearly linearly with x/H. 3.3. Thermal measurements The average thermal entrainment, a, was calculated for the three refrigerated curtains and is listed in Table 2. The thermal entrainment is seen to decrease slightly with decreasing Richardson number, which corresponds
B.S. Field, E. Loth / Experimental Thermal and Fluid Science 30 (2006) 175–184 Table 2 Thermal entrainment of curtains Richardson number
Reynolds number
Thermal entrainment
0.47 0.15 0.13
4700 7500 8000
0.43 0.39 0.37
4000 3500 3000
α Re
2500 2000 1500 1000 500 0 4000
5000
6000
7000
8000
9000
Re Fig. 9. Relative thermal entrainment, aRe vs. Re for refrigerated curtains.
to increasing Reynolds number. While one might expect the negative-buoyancy to help stabilize the curtain and thus reduce the overall thermal entrainment ratio, the opposite trend is observed. Most probably, the necking of the air curtain after the inlet increases the edge instabilities which increase the mixing and entrainment into the air curtain. The energy loss due to thermal entrainment, (aRe), is plotted with varying Re in Fig. 9. The relative thermal entrainment is seen to decrease somewhat with decreasing Reynolds number, implying that the net amount of latent heat and humidity that gets entrained will decrease as the Reynolds number decreases. Since the Reynolds number of the refrigerated air curtain was not tested below Re = 4700, it is difficult to say whether this trend continues for lower Reynolds numbers. However, there may exists a Reynolds number beyond which a further decrease in the air curtain velocity would yield a loss in the curtain integrity, such as the curtain detachment from the wall that was observed for isothermal curtains in [13]. In addition, a minimum convection speed is often necessary in refrigerated display cases to accommodate transient loading and radiative loading requirements. However, aside from these two aspects, reducing air curtain velocity tends to reduce the dimensional thermal energy entrainment. 4. Conclusions As is the case for isothermal air curtains, the entrainment of ambient air was primarily due to eddy engulf-
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ment which arises from shear layer interactions and is enhanced by high initial turbulence levels in the curtains. The addition of the buoyant acceleration of the refrigerated air curtain caused the curtain velocity streamlines to initially neck inwards. This effect was increasingly pronounced at increasing Richardson numbers and resulted in a sharp decrease in curtain thickness near the curtain inlet and a general decrease in overall curtain thickness. Further downstream, the curtain thickness growth was similar to that seen in isothermal (Ri = 0) curtains. For isothermal curtains with similar Reynolds numbers, the velocity field development has been seen to be roughly independent of curtain Reynolds number, indicating that the differences in curtain thickness are primarily attributed to negatively-buoyant effects. The thermal entrainment ratio, a, was seen to increase slightly with increasing Richardson number, indicating that the buoyant acceleration encourages the edge instabilities which lead to entrainment. However, the energy loss due to thermal entrainment, aRe, was seen to reduce with increasing Richardson number (decreasing Reynolds number). This implies that overall energy loss from the air curtain could be reduced by reducing the Reynolds number of the curtain for a given temperature difference. However in refrigerated display cases, a minimum convection speed is necessary to accommodate transient loading and radiative loading requirements.
Acknowledgments This study was funded by the Air Conditioning and Refrigeration Center at the University of Illinois at Urbana-Champaign (UIUC). The refrigerated display case used in the study was provided by Hussmann Co. in Bridgeton, MO. In addition, Pega Hrnjak of UIUC provided valuable assistance with the configuration of the refrigeration case and interpretation of the results.
References [1] P. Adams, The intereffect of supermarket refrigeration and air conditioning, ASHRAE CH-85-09 No. 1, 1985, pp. 423–433. [2] R. Howell, Effects of store relative humidity on refrigerated display case performance, ASHRAE Transactions 99 (1993) 667–678. [3] B. George, D. Buttsworth, Investigation of an open refrigeration cabinet using computational simulations with supporting experiments, in: Proceedings of the ASME International Mechanical Engineering Congress and Exposition, November 2000. [4] J. Baleo, L. Guyonnaud, C. Solliec, Numerical simulation of air flow distribution in a refrigerated display case air curtain, in: Proceedings of International Congress of Refrigeration 1995, vol. II. [5] D. Stribling, S. Tassou, D. Marriott, A two-dimensional CFD model of a refrigerated display case, ASHRAE Transactions 103 (1997) 88–94.
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[6] R. Faramarzi, Efficient display case refrigeration, ASHRAE Journal 41 (11) (1999) 46–54. [7] G. Cortella, M. Manzan, G. Comini, CFD simulation of refrigerated display cabinets, International Journal of Refrigeration 24 (2001) 250–260. [8] H.K. Navaz, R. Faramarzi, M. Gharib, D. Dabiri, D. Modarress, The application of advanced methods in analyzing the performance of the air curtain in a refrigerated display case, ASME Journal of Fluids Engineering 124 (2002) 756– 764. [9] B. Field, E. Loth, An air curtain along a wall with high inlet turbulence, ASME Journal of Fluids Engineering 126 (3) (2004) 391–398. [10] D. Angirasa, Interaction of low-velocity plane jets with buoyant convection adjacent to heated vertical surfaces, Numerical Heat Transfer, Part A 35 (1999) 67–84.
[11] M. Ljuboja, W. Rodi, Prediction of horizontal and vertical turbulent buoyant wall jets, ASME Journal of Heat Transfer 103 (1981) 343–349. [12] R. Sangras, Z. Dai, G. Faeth, Mixture fraction statistics of plane self-preserving buoyant turbulent adiabatic wall plumes, ASME Journal of Heat Transfer 121 (1999) 837–843. [13] B. Field, E. Loth, Measurements of air curtain entrainment, in: Proceedings of ASME FEDSM 2001, May 2001. [14] R. Keane, R. Adrian, Theory of cross-correlation analysis of PIV images, Applied Science Research 49 (1992) 191–215. [15] M. Epstein, J. Burelbach, Vertical mixing above a steady circular source of buoyancy, International Journal of Heat and Mass Transfer 44 (2001) 525–536. [16] B. Cetegen, T. Ahmed, Experiments on the periodic instability of buoyant plumes and pool fires, Combustion and Flame 93 (1993) 157–184.
Entrainment of refrigerated air curtains down a wall Brandon S. Field, Eric Loth
*
Department of Aerospace Engineering, University of Illinois, Urbana-Champaign, 104 South Wright Street, Urbana, IL 61801, USA Received 3 January 2003; received in revised form 27 May 2003; accepted 22 January 2004
Abstract Refrigerated air curtains are used in open supermarket display cases as a barrier between the warm ambient air and the cold refrigerated air. Entrainment of ambient air into the curtain by shear layer mixing contributes to both the sensible and the latent heat load on the display case. To better understand the fluid dynamics which govern entrainment, velocity and temperature measurements of the curtains were made in a refrigerated display case, which was modified to allow a more fundamental flow. In particular, a vertical solid wall was installed to approximately represent a fully-stocked configuration. As such, negatively-buoyant wall jets (with high inflow turbulence) in the Reynolds number range of 4200–8000 and in the Richardson number range of 0.13–0.58 were examined. To define the air curtain vortex structures, flow visualization of the curtain interface was employed. The results of which showed that the entrainment of the ambient air was found to be governed by a variety of eddy engulfing structures. Particle Image Velocimetry was used to examine the velocity profiles of the air curtains in a non-intrusive manner, the measurements of which indicated negatively-buoyant acceleration following the jet exhaust, followed by a more linear curtain growth characteristic of isothermal wall jets. In addition, thermocouples were used to obtain the net increase in temperature of the curtain due to entrainment, where it was found that the dimensionless thermal energy loss decreased with decreasing Reynolds number. 2005 Elsevier Inc. All rights reserved. Keywords: Wall jets; Buoyancy; Turbulence; Air curtain; Refrigeration; Entrainment
1. Introduction Refrigerated air curtains are used on open supermarket display cases to keep ambient room air from entering the case while still allowing convenient physical access to products. There are many aspects to the thermal loading of a refrigerated display case, such as the radiant heat load from the ambient supermarket, the case lights that illuminate the product, the addition and removal of product by stockers and customers. However, the entrained ambient air into the air curtain is the largest energy loss [1]. According to some esti-
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Corresponding author. Tel.: +1 217 244 5581; fax: +1 217 244 0720. E-mail address: [email protected] (E. Loth). 0894-1777/$ - see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2004.01.012
mates, 75% of the refrigeration load comes from the air curtain entrainment [1], and energy calculations preformed by the refrigeration industry have found the air curtain entrainment load can be as high as 90%. Since refrigeration accounts for roughly 50% of overall supermarket electricity consumption, air curtain entrainment plays a large role in supermarket energy usage. In addition, the high humidity levels of the entrained air accelerates the frosting of the evaporator coils (reducing their heat transfer and increasing the required frequency of defrost cycles). Therefore, minimizing the ambient air entrainment into the display case is critical to the overall system performance and efficiency. Most previous studies of refrigerated display cases have taken a ‘‘whole case’’ perspective (i.e. not focusing on the underlying fluid physics of the air curtain itself), and are thus empirical in nature. Specifically, most of the industrial research and design efforts have taken an
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energy-balance view of the air curtain entrainment, carefully controlling the temperature and humidity in the lab, measuring the electrical power drawn by the compressor and fans and the mass of condensate water from the evaporator coils over an extended time period to determine the energy loss from the case and curtain. Curtain velocity profiles have been empirically optimized with these methods, via testing different inlet flow deflectors to determine which produces the least entrainment. Exact velocity profiles are unknown because of the coarseness of the measuring devices used. In particular, most previous experiments have typically employed probe diagnostics, whereas it is desirable to use non-intrusive diagnostics (as used herein) to avoid potential flow disturbances. In order to understand the characteristics of refrigerated air curtains, a number of studies have been performed. Howell [2] quantified the detrimental effect of ambient relative humidity on the energy requirements of specific display cases. The humidity levels in the store were shown to contribute to the energy requirements of the case by means of latent heat infiltrating the case via entrainment. The experiments were specific to certain display cases since different case geometries affected the energy requirements. Other studies of air curtains include computational modeling of the air curtain assuming both turbulent and laminar conditions [3–5]. While including components such as fans and the evaporator coils, comparison to experimentally determined values show that all those predictions generally yielded qualitative comparison but poor quantitative representation of the curtain dynamics. Faramarzi [6] presents a simplified cooling load model for vertical display cases based on a breakdown of the cooling loads involved. Experimental and computational results of a display case were shown and used in the estimated breakdowns. However, the study concludes with the remark that the infiltration load is different for different cases (i.e. case specific) and that understanding of the thermo-fluid dynamics of the air curtain is required in order to provide a method to determine the entrainment rates. Cortella et al. [7] preformed a CFD simulation using an LES model for the air flow in a dual curtain display case. A comparison of experimental product temperature measurements and the air temperature (in the curtain and return ducts) to those determined numerically showed reasonable agreement. However, the overall heat load of the curtain on the refrigerator was not in complete agreement with the simulation results, probably because experimental velocity measurements inside the air curtain were not performed. This problem may also have been due to the complexity in the display case geometry, pointing to the need for a more fundamental investigation of the essential fluid dynamics.
Navaz et al. [8] recently performed an air curtain study comparing PIV results to a numerical simulation. The curtain parameters were varied to study their relative effects of inlet temperature and initial curtain velocity. Qualitative agreement between computational simulation and experiment were reported, where differences could be related to the substantial experimental uncertainty. As in other studies, the variation of inlet conditions was small (in this study, limited to a 0.8 C and 0.1 m/s variation) and the experiment and simulations were specific to the geometry of the display case studied. In addition, as in other studies there was no discussion of the air curtain vortex structures and dynamics. Since the air curtain flow is not well understood at typical conditions, it is instructive to consider its basic fluid dynamics components. Air curtain entrainment results from the shear layer mixing between the quiescent ambient room air and the refrigerated air curtain. Since the air curtain is cooler than the ambient room air and tends to ‘‘ride’’ along the front of the product, it produces a negatively-buoyant jet over an irregular wall. Based on the typical jet flow rates and Reynolds numbers, the air curtains reside in the transitional flow regime: not fully-turbulent, but not a laminar flow either. This complicating aspect has been cited as one of the reasons for poor predictions of the velocity field when fully-developed turbulence models are used [3]. In order to better understand the fundamental fluid dynamics of the air curtain, and avoid case-specific flow features, one may employ the geometric simplification of the display case whereby the products are replaced by a flat wall. This enables the air curtain to be modeled as a negatively-buoyant wall jet, a jet of high-density fluid moving downwards with the buoyancy force and the velocity of the jet in the same direction. For such a jet, there are three primary dimensionless parameters that can be used to characterize the flow: the Reynolds number (Re), the Richardson number (Ri) and the Grashof number (Gr). These parameters are defined here as Re ¼
V jet qjet H ; ljet
Gr ¼ Re2 Ri ¼
Ri ¼
ðqamb qjet ÞgH qamb V 2jet
qamb qjet gH 3 . 2 l qamb qjet jet
In the above, Vjet is the mean streamwise velocity at the start of the curtain, H is the width of the curtain at this point (the curtain inlet), g is the gravitational acceleration, q is density, and l is viscosity. The subscripts ‘‘jet’’ and ‘‘amb’’ refer to the curtain inlet and ambient room properties respectively. For refrigerated display cases in a conventional configuration and flow rate, the typical air curtain Richardson number value was
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found to be 0.3 and Reynolds numbers in the range of 5000–8000 [9]. There are several previous studies of conventional buoyant jets for a variety of Reynolds and Richardson numbers. At low speeds, a computational study of upwards laminar wall jets over a heated surface was carried out by Angirasa [10]. The corresponding Richardson numbers studied were in the range of 0.004–0.01. The jet was found to detach from the wall when Reynolds numbers were increased to the order of 100, leading to a decrease in heat transfer from the wall. For fully-turbulent flows (e.g. Re > 10,000), Ljuboja and Rodi [11] developed an extension of the k–e computational model for the behavior of a fully-turbulent buoyant wall jet that accounts for the buoyancy and wall effects and agrees well with experiments. Sangras et al. [12] observed turbulent wall plumes in the self-preserving region to measure mixture fractions, probability density functions and temporal power spectra. The turbulent mixing of the wall plumes were compared to that of free line plumes. The wall was observed to inhibit the large-scale turbulent motion and limit the mixing to one side of the flow, thus reducing the amount of mixing compared to a free line plume. However, no detailed investigations (with respect to flow visualization, velocity distributions, or thermal entrainment) have been conducted for the fluid physics of refrigerated flat-wall jets in the transitional flow Reynolds numbers (1000–10,000) or with substantial inflow turbulence levels. In the present study, this combination is investigated due to its strong relevance to refrigerated air curtains typical of display cases. In particular, the present study examines flow for a refrigerated display case which has been idealized into a wall jet with a uniform inlet velocity profile. This fundamental flow field was chosen as it retains the general properties of the curtain while eliminating case-specific issues particular to each manufacturer. The aspects of vortex dynamics, velocity profile evolution, and thermal entrainment are presented in this investigation for various Reynolds and Richardson numbers.
2. Methods 2.1. Flow facility The modifications to the display case (placing a wall on the face of the shelves and modifying of the deflector to produce a more uniform velocity profile) are discussed in Field and Loth [13] and pictured in Fig. 1. The height of the air curtain inlet, H, was 120 mm for the display case tested, and the x-axis was oriented downwards with the origin at the curtain inlet. The air curtain speed was varied by changing the blades of the two fans that provided the circulation of the air through
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Fig. 1. Idealizations made to the refrigerator case and thermocouple locations.
the case. Three different pairs of fan blades with the same diameter and different camber were used. The fan blades provided commercially with the case produced the highest air flow, and are called the ‘‘highspeed’’ fans. Two other sets of fan blades produced slower curtains, and are termed the ‘‘medium-speed’’ and ‘‘low-speed’’ fans (details are given in [9]). To estimate Vjet, the average streamwise velocity at the downstream location x = H was used. The temperature of the curtain, Tjet, was dependent on the speed of the curtain by means of the residence time in the evaporator coil, such that the Richardson numbers and Reynolds numbers of the air curtain were coupled. The resulting Reynolds numbers and Richardson numbers produced by the test conditions are given in Table 1. Note, that the conventional display case configuration (using the original fans and without the wall) produced an air curtain with a jet Reynolds number of 5300 and a jet Richardson number of 0.30, as well as a qualitatively similar velocity distribution to the wall jet case [9].
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Table 1 Test conditions Test condition
Reynolds number
Richardson number
Grashof number
Two low-speed fans One high-speed fan Two medium-speed fans Two high-speed fans
4200 4700 7500 8000
0.58 0.47 0.15 0.13
9.4 · 106 9.5 · 106 7.8 · 106 7.8 · 106
ness, d(x). The curtain thickness was defined for a given velocity profile as the distance from the wall (y) where the streamwise velocity reduces to 25% of the maximum streamwise velocity at a given streamwise location (x), i.e. d(x) y at Vx(y)/Vx,max = 0.25. The curtain thickness was determined for all cases at various x-locations and was then normalized by the curtain inlet height, H. 2.3. Temperature measurements
2.2. Velocimetry measurements and flow visualization For temperature measurements, three K-type thermocouples were installed in the display case in the locations shown in Fig. 1. The first thermocouple was located in the top duct just before the deflector and honeycomb to measure the initial temperature of the air curtain, Tjet. The second thermocouple was located outside the case and above the curtain inlet to measure the ambient room air, Tamb, that was entrained into the curtain. The third thermocouple was located in the capture region at the bottom of the case to measure the temperature of the captured air, Tcapture. The capture region was found generally to have a uneven temperature distribution so Tcapture was measured behind one of the fans to maximize the amount of mixing of the return air, so that the thermal measurements can represent the average entrainment for the entire curtain. An Omega HH611PLC data logger was used to record the three thermocouples simultaneously each minute. In order to assess (and avoid) the thermal transients due to start up, the temperature at various locations on the refrigerator cases were recorded during each experimental run. Fig. 2 is a plot of Tcapture, Tjet, and Tamb for the Ri = 0.13 curtain. An initial transient is seen when the case is turned on, and then the temperatures remain in a steady-state period for a few hours. If the case were allowed to run longer the frost growth at the evaporator would begin to affect the curtain temperature. Therefore, all the data were taken before the 25 20
T
capt
T
15
Periods of PIV data
jet
T
Temp (°C)
For velocity vector measurements over a given field of the wall jet modification of the display case, Particle Image Velocimetry (PIV) was used. PIV is a non-intrusive flow measuring technique that consists of a double-pulsed laser sheet that illuminates a cross-section of the seeded airflow. A cross-correlation digital camera captures two images of the illuminated seed particles in quick succession and correlates the differences in particle position to calculate a complete two-dimensional vector field. For PIV measurements the entire flow field was seeded uniformly in both the jet and ambient regions with tracer particles. The particles were thirty micron diameter glass particles, Microspheres by 3M, which had response times much less than the time scales of the flow. The jet exhaust at the top of the air curtain was seeded by injecting the particles upstream of the deflector to ensure uniform distribution near the measurement plane [9]. The ambient region of the flow was also seeded before each data collection period, by globally dispersing a large group of particles in front of the display case. However, for the qualitative visualization of the air curtain entrainment only the air curtain jet was seeded. This allowed a time-dependant animation of the interface between the jet flow and the ambient air along the full curtain length. In both cases, the images were captured using the laser and camera of the PIV system. Details of PIV and in particular the cross-correlation PIV technique are described by Keane and Adrian [14]. The PIV equipment used in these tests was provided by LaVision, Inc., and consisted of a pulsed Nd:Yag laser to provide illumination and a Kodak ES1.0 cross-correlation digital camera to capture the images. The crosscorrelation vector calculation routines employed here were those found in the DaVis software, version 5.5.4. Since the curtain length was larger than the field of view of the camera, the entire curtain was split into several fields of view to cover the entire curtain. For each field of view, 500 vector images were taken to produce the average velocities and statistical information for the curtain. For calculation of velocity statistics, local averaging of adjacent vectors was preformed to reduce statistical noise [9,13]. From the PIV-obtained velocity profiles, the momentum distribution was characterized by the curtain thick-
amb
10 5 0 -5 0
50
100
150
200
Elapsed time (min) Fig. 2. Transient temperature plots for Ri = 0.13 (Re = 8000).
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frost growth was significant. The periods of time in which PIV data were taken is shown on the plot to indicate that the temperatures remained reasonably constant within the data collection times. The thermal entrainment is characterized by the T T jet parameter: a ¼ Tcapture . In the limit of no thermal amb T jet entrainment across the curtain, Tcapture = Tjet and a has a value of zero. As the entrainment of ambient air
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into the curtain increases, a increases, reaching a maximum value of one only when all the air being drawn into the capture region is ambient air (Tcapture = Tamb). The net thermal energy loss due to entrainment can be determined per unit length of the display case by _ p DT , with the temperature difference being E ¼ mc measured from top to bottom of the curtain, DT = (Tcapture Tjet). This can be written in terms of the
Fig. 3. Sequential particle visualization of curtain, Re = 3700, Ri = 0.76. Time between frames is 0.133 s from x/H = 0.5 to x/H = 2.
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thermal entrainment parameter and Reynolds number as E = (Rel)cpa(Tamb Tjet). For a display case the parameters cp, l, and (Tamb Tjet) will be approximately constant, since they are specified by the design considerations. Non-dimensionalizing the energy loss by the product of these parameters, the energy loss due to thermal entrainment becomes E* = aRe. In this way, the product (aRe) can be used to represent the net thermal entrainment energy loss for a given display case, and was obtained for each of the refrigerated air curtain conditions.
3. Results 3.1. Flow visualization Fig. 3 shows sequential frames of the flow visualizations from the inlet of the curtain. Small and large-scale
vortices coexist at the interface of the flow and the growth and deformation of the vortices is evident. For example, the arrow in Fig. 3(c)–(f) follows the rapid growth of a single eddy over the distance of about 1.5H. Entrained ambient air is evident, especially when the eddy is seen in (f). This animation of the curtain development resembles the animations of the curtain temperature contours presented by Cortella et al. [7], but only the larger scale eddies are evident in the LES simulations, whereas the current visualization indicates a broad spectrum of eddy frequencies. In all the flow visualizations of the air curtains, the overall trend of the air curtain development is a continual growth of the eddies as they move from the inlet to the capture area at the bottom. The shear layer interface is dominated by eddies that can be seen as combinations of protrusions and indentations that form a wave pattern (similar to a Kelvin–Helmholtz instability) along the outer edge of the curtain. It is inside the indentations that
Fig. 4. Time-averaged streamline images of the curtain inlet for increasing Ri: (a) Ri = 0 (Re = 3800), (b) Ri = 0.13 (Re = 8000), (c) Ri = 0.15 (Re = 7500), (d) Ri = 0.47 (Re = 4700). The field of view in each image ranges approximately from x/H = 0.5 to x/H = 2.3.
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the ambient air primarily gets engulfed and entrained into the curtain. The complexity and volatility of the eddy interactions appear to be more exaggerated than those found in previous wall jet studies, indicating that the high levels of turbulence found in the air curtains (discussed below) produce increased mixing and entrainment. 3.2. Velocity measurements From the PIV measurements, the time-averaged streamlines can be obtained. For different Richardson numbers a marked difference is clearly seen at the top of the curtain, as shown in Fig. 4. As the Richardson number increases from 0 to 0.47, there is a greater tendency for the curtain width to get thinner immediately after the inlet. This inward deflection of the streamlines is a result of the negatively-buoyant acceleration of the refrigerated curtain. This buoyant effect is most pronounced at the curtain inlet; as the curtain continues downward it reaches a ‘‘neck’’ where its thickness reaches a minimum and then begins to grow in the same way as the isothermal curtain. This same effect has been seen in positively-buoyant plumes, for example Epstein and Burelbach [15] examined a circular jet of low-density fresh water oriented upwards into a tank of higher density salt-water brine and observed the same initial buoyant acceleration followed
Fig. 5. Streamwise velocity contours for refrigerated curtain, Ri = 0.47, Re = 4700, where highest velocities are red and lowest are in black.
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by a neck above which the jet spread. Similarly, Cetegen and Ahmed [16] examined buoyant circular jets for varying Reynolds numbers and noted overall initial jet shapes for varying Richardson numbers which were qualitatively similar to the initial shapes found here. Fig. 5 shows the false-color composite of the timeaveraged streamwise velocity contours for a refrigerated air curtain at Re = 4700 and Ri = 0.47. At the top of the curtain, the negatively-buoyant acceleration and jet width decrease can be qualitatively seen. However, below x/H = 4, the negative-buoyancy effects are no longer significantly accelerating the curtain, and the curtain growth proceeds in a qualitatively similar manner to an isothermal curtain [13]. This trend was representative of the curtains of other Richardson numbers. Fig. 6 shows the velocity profiles that were obtained from the time-averaged velocities of the refrigerated curtains of Ri = 0.13 (Re = 8000) and Ri = 0.47 (Re = 4700). As expected, the velocity profiles reveal that the interaction with the ambient air causes the curtain to spread immediately after injection. In contrast to the isothermal case which showed a consistent decrease in Vx,max [13], the refrigerated curtains exhibited buoyant
Fig. 6. Evolution of streamwise velocity profiles for refrigerated curtains, (a) Ri = 0.13, Re = 8000, (b) Ri = 0.47, Re = 4700.
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B.S. Field, E. Loth / Experimental Thermal and Fluid Science 30 (2006) 175–184 0
0 0.2
2
0.4 0.6
VRMS / Vjet Vx / Vjet
0.8
4
x/H
V / Vjet
Ri=0 (Re=3800-8500) Ri=0.13 (Re=8000) Ri=0.15 (Re=7500) Ri=0.47 (Re=4700)
1
6
1.2 0
0.2
0.4
0.6
0.8
1
1.2
y/H
a
8
0 10 0
0.2
V / Vjet
1
1.5
2
2.5
δ/H
0.4
VRMS / Vjet
Fig. 8. Curtain thickness development for refrigerated and isothermal curtains by Richardson number.
Vx / Vjet
0.6 0.8 1 1.2 0
b
0.5
0.2
0.4
0.6
0.8
1
1.2
y/H
Fig. 7. Initial streamwise velocity and RMS velocity profiles for (a) Ri = 0.47, Re = 4700 and (b) Ri = 0, Re = 4600 curtains.
acceleration until roughly x/H of 4. As the Richardson number of the curtains increases, the flow acceleration is more pronounced. These two effects will be seen to counter each other in terms of growth of curtain thickness, since d is defined based on the local peak velocity at a given x/H. After the accelerating regime, the spreading of the curtain is much more apparent. However, it is interesting that in the range of x/H studied here, the peak velocity is not seen to decrease significantly. Fig. 7(a) shows the streamwise velocity profile and turbulence intensity profile at this downstream location for the Ri = 0.47 curtain (Re = 4700) and Fig. 7(b) shows the same profiles for the Re = 4600 isothermal curtain (Ri = 0). The initial curtain turbulence calculated from the velocity profiles showed that all the air curtains had substantial initial turbulence, with VRMS/Vjet inside the curtain of about 5% at the downstream location of x/H = 1. The locations of the peak turbulence levels coincide with the locations of the largest gradients in the velocity profiles, as is typical for shear flows. Fig. 8 shows the curtain thickness for various Richardson numbers. The curtain thickness for isothermal (Ri = 0) curtains at various speeds (Re = 3800, 4600,
7600, and 8500) are shown with the same symbol, since the results were roughly independent of Reynolds number, whereas the refrigerated curtains of Ri = 0.13, 0.15, and 0.47 are shown individually. The thinning of the curtain due to negatively-buoyant acceleration is again seen to dominate the initial region of the curtain development. The higher Richardson number curtain is the most affected by the buoyant acceleration, and the two curtains of similar Richardson number (0.13 and 0.15) are similarly affected up to x/H of about 5. After that, a significant difference developed between these two curtains, with the Ri = 0.13 curtain spreading at a faster rate than the Ri = 0.15 curtain. This was unexpected but may be attributed to the difference in initial turbulence levels found in the curtains, with the Ri = 0.13 curtain having a significantly higher initial turbulence level than the other two curtains (as much as 10%). In general, decreasing the refrigerated curtain velocity from Re = 8000 to Re = 4700 led to a reduced curtain thickness due to the negatively-buoyant acceleration effect, and further Re reductions associated with Ri increases may lead to increased wall jet stability due to increased buoyancy forces. Universal to all the curtains, however is that after the region of buoyant acceleration at the curtain inlet, all of the curtains grow nearly linearly with x/H. 3.3. Thermal measurements The average thermal entrainment, a, was calculated for the three refrigerated curtains and is listed in Table 2. The thermal entrainment is seen to decrease slightly with decreasing Richardson number, which corresponds
B.S. Field, E. Loth / Experimental Thermal and Fluid Science 30 (2006) 175–184 Table 2 Thermal entrainment of curtains Richardson number
Reynolds number
Thermal entrainment
0.47 0.15 0.13
4700 7500 8000
0.43 0.39 0.37
4000 3500 3000
α Re
2500 2000 1500 1000 500 0 4000
5000
6000
7000
8000
9000
Re Fig. 9. Relative thermal entrainment, aRe vs. Re for refrigerated curtains.
to increasing Reynolds number. While one might expect the negative-buoyancy to help stabilize the curtain and thus reduce the overall thermal entrainment ratio, the opposite trend is observed. Most probably, the necking of the air curtain after the inlet increases the edge instabilities which increase the mixing and entrainment into the air curtain. The energy loss due to thermal entrainment, (aRe), is plotted with varying Re in Fig. 9. The relative thermal entrainment is seen to decrease somewhat with decreasing Reynolds number, implying that the net amount of latent heat and humidity that gets entrained will decrease as the Reynolds number decreases. Since the Reynolds number of the refrigerated air curtain was not tested below Re = 4700, it is difficult to say whether this trend continues for lower Reynolds numbers. However, there may exists a Reynolds number beyond which a further decrease in the air curtain velocity would yield a loss in the curtain integrity, such as the curtain detachment from the wall that was observed for isothermal curtains in [13]. In addition, a minimum convection speed is often necessary in refrigerated display cases to accommodate transient loading and radiative loading requirements. However, aside from these two aspects, reducing air curtain velocity tends to reduce the dimensional thermal energy entrainment. 4. Conclusions As is the case for isothermal air curtains, the entrainment of ambient air was primarily due to eddy engulf-
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ment which arises from shear layer interactions and is enhanced by high initial turbulence levels in the curtains. The addition of the buoyant acceleration of the refrigerated air curtain caused the curtain velocity streamlines to initially neck inwards. This effect was increasingly pronounced at increasing Richardson numbers and resulted in a sharp decrease in curtain thickness near the curtain inlet and a general decrease in overall curtain thickness. Further downstream, the curtain thickness growth was similar to that seen in isothermal (Ri = 0) curtains. For isothermal curtains with similar Reynolds numbers, the velocity field development has been seen to be roughly independent of curtain Reynolds number, indicating that the differences in curtain thickness are primarily attributed to negatively-buoyant effects. The thermal entrainment ratio, a, was seen to increase slightly with increasing Richardson number, indicating that the buoyant acceleration encourages the edge instabilities which lead to entrainment. However, the energy loss due to thermal entrainment, aRe, was seen to reduce with increasing Richardson number (decreasing Reynolds number). This implies that overall energy loss from the air curtain could be reduced by reducing the Reynolds number of the curtain for a given temperature difference. However in refrigerated display cases, a minimum convection speed is necessary to accommodate transient loading and radiative loading requirements.
Acknowledgments This study was funded by the Air Conditioning and Refrigeration Center at the University of Illinois at Urbana-Champaign (UIUC). The refrigerated display case used in the study was provided by Hussmann Co. in Bridgeton, MO. In addition, Pega Hrnjak of UIUC provided valuable assistance with the configuration of the refrigeration case and interpretation of the results.
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[11] M. Ljuboja, W. Rodi, Prediction of horizontal and vertical turbulent buoyant wall jets, ASME Journal of Heat Transfer 103 (1981) 343–349. [12] R. Sangras, Z. Dai, G. Faeth, Mixture fraction statistics of plane self-preserving buoyant turbulent adiabatic wall plumes, ASME Journal of Heat Transfer 121 (1999) 837–843. [13] B. Field, E. Loth, Measurements of air curtain entrainment, in: Proceedings of ASME FEDSM 2001, May 2001. [14] R. Keane, R. Adrian, Theory of cross-correlation analysis of PIV images, Applied Science Research 49 (1992) 191–215. [15] M. Epstein, J. Burelbach, Vertical mixing above a steady circular source of buoyancy, International Journal of Heat and Mass Transfer 44 (2001) 525–536. [16] B. Cetegen, T. Ahmed, Experiments on the periodic instability of buoyant plumes and pool fires, Combustion and Flame 93 (1993) 157–184.