In view of the recent significant improvement in the standard of living, refrigerated display cases are extensively used in today’s supermarkets and grocery stores. To save precious floor-space and provide a large selling area, vertical display cabinets are the better choice than the horizontal ones [1]. Moreover, to attract consumers and hence increase sales, manufacturers developed open type display cases, as schematically shown in Fig. 1.1, with no obstacle between the products and customers [1-4]. In these display cases a cold air curtain is often used to produce an artificial barrier between the outside warm air in the ambient and inside cold air in the cabinets. The air curtain is essentially a two-dimensional cool air jet. Usually the air curtain is supplied from the top of a display case through a discharge honeycomb, flows over the open surface of the cabinet, and finally reaches a return air grille at the case bottom. In reality, an open display case is operated in a store environment and it exchanges heat and moisture with the surrounding air in the store. Besides, the outside warm and moist air can be entrained into the display case by the air curtain, which in turn can substantially lower the performance of the case. Note that the entrained warm and moist air into the cabinet becomes sensible and latent energy loads to the unit since it needs to be cooled and the moisture in it needs to be removed. Therefore a detailed understanding of the heat and mass transfer processes in open refrigerated display cases are needed to improve the performance of the systems. Especially, how the momentum, energy and moisture transports in the
cabinets are affected by the moist air entrained into the flow and buoyancy forces in the flow requires an in-depth investigation.
1.2 Literature Review
The literature relevant to the present study is reviewed in the following.
1.2.1 Cooling loads
The total cooling loads of a refrigerated display cabinet consists of sensible and latent components. The sensible portion includes heat conduction through physical envelopes of the cabinet, thermal radiation from the ambient to the cabinet, sensible infiltration, and heat gains from fan motors, anti-sweat heater and defrost. The latent portion comes from the entrainment of the moisture in the ambient into the cabinet through the air curtains. Ge and Tassou [5] used an implicit numerical method to simulate flow and heat transfer in a vertical display case and developed an correlation for the total heat transfer across an air curtain in terms of the ambient air enthalpy, initial dry-bulb temperature of air jet, temperature difference between the air inside the cabinet and injected air, and some air curtain properties such as the jet initial velocity, jet mass flow rate and jet length. Jet thickness is not directly included, but has some relationship with the jet velocity and mass flow rate. They also proposed a correlation for the return air temperature based on air temperature at the injection grille and ambient and on the air curtain length. The efficiency of the air curtain ε was defined by Cortella [1, 6] as heat flow rate from the load
total refrigerating capacity
ε= according
to the results from a numerical simulation by using a LES turbulence model. It was pointed out by Faramarzi [7, 8] that the infiltration of the moist air from the ambient into the cabinet was the largest constituent of the case cooling load. The infiltration load can be further divided into the sensible and latent parts. The sensible portion results from the temperature difference between the ambient and cabinet air. The
latent portion, however, results from the difference in the water vapor concentration between the air in the ambient and cabinet. Hence determining the infiltration load is considered as the most challenging aspect of the display case cooling load analysis.
1.2.2 Thermal entrainment factor
Entrainment of the ambient warm air into a display cabinet was found to increase the temperature of the products and the temperature near the return grille [8, 9]. Recently Chen & Yuan [4, 10] and Bhattacharjee & Loth [11] defined a thermal entrainment factor as r s
amb s
i i
i i
α= −
− = (enthalpy difference between the return and supply air) / (enthalpy difference between the ambient and supply air). If the air curtain does not cause any air entrainment, α will be equal to zero. On the contrary, the enthalpy of return air and α increase if the moist air entrainment increases. In practical situation α would be between zero and unity. Similarly, Navaz et al. [3]
introduced a parameter to characterize the portion of air mass spillage to the outside and infiltration into the case. Navaz et al. [3] and Bhattacharjee and Loth [11] also estimated the volumetric infiltration rate by integrating the negative horizontal velocity from the bottom edge of the opening at the air return grille to a location where U= 0. Chen & Yuan [4, 10] investigated how the thermal entrainment factor was affected by the Reynolds number (based on the jet length H) and Richardson number (based on the jet length H and temperature difference between the ambient and injection air, Rit = Grt / ReH2). They found that when the Richardson number decreased to 0.14, the infiltration rate arrived at a minimum. For a further reduction in Rit the infiltration rate would increase slightly due to the excessive mixing. They suggested that there existed a critical Richardson number to ensure the insulation of the air curtain at a given Grashof number. For increases in Re and Rit the thermal entrainment factor increases slightly, signifying that the momentum force would
promote the thermal entrainment but the buoyant force would suppress it.
1.2.3 Importance of ambient temperature and relative humidity In a numerical prediction Cortella [6] showed that the indoor environment in which display cases operated significantly affected the performance of air curtain.
Faramarzi and Kemp [12] experimentally tested several the refrigerated display cabinets subject to different relative humidities and noted that the higher indoor temperature and relative humidity yielded an increase in the case cooling loads for the display cases. In a combined CFD & experimental DPIV study, Navaz et al. [2]
found that the discharge average temperature exhibited a relatively slight effect on the flowfield structure in the cabinet. Combined experimental measurement and numerical prediction carried out by Howell et al. [13] showed that the sensible heat transfer was directly proportional to the temperature difference across the air curtain.
Recently, Chen & Yuan [4] experimentally demonstrated that the air temperature rise between the discharge and return grilles was slightly affected by the change in the relative humidity of the ambient air. As the ambient temperature increases at a constant relative humidity, the air humidity ratio also increases and hence the latent heat transfer across the air curtain increases with infiltration. Howell [14] developed a numerical procedure to evaluate the effects of relative humidity on the energy performance of refrigerated display cabinets and showed that a decrease in the store relative humidity from 55% to 35% would reduce the open display case energy consumption by 29%.
1.2.4 Effects of discharge air velocity
The total heat transfer through an air curtain was found to be directly proportional to the initial jet velocity [11, 15]. By comparing the CFD and experimental results, Navaz et al. [2] noted that a small air discharge velocity still could entrain the ambient air and a less stable air curtain would break up before
reaching the bottom section of the cabinet. Cortella et al. [1] used a Large Eddy Simulation (LES) turbulence model to predict a two-curtain display case. They found that the most stable flow configuration in the cabinet was obtained when the inner air curtain had a lower velocity. Besides, in combined CFD prediction and experimental measurment Navaz et al. [3] noted that the entrained air flow rate was a function of the turbulence intensity and Reynolds number of the air flow at the discharge grille (based on the discharge grille width). For a high Re at DAG (discharge air grille) the air entrainment rate increased with the turbulence intensity at the DAG. When Re is between 3,200 and 3,400 a minimum entrainment rate is obtained, and at this Re range the air curtain momentum stays nearly intact. Cui &
Wang [16] used a commercial software FLUENT to predict the transport processes in a cabinet and introduced a parameter, UI, to describe the uniformity of the air velocity distribution at the discharge grille. A low inlet UI value is preferred in air energy-efficient design for a display case. Chen & Yuan [4] found that when Re was raised from 4100 to 4500 experimentally, the temperature inside the cabinet decreased roughly 1-1.5 ℃, and the cabinet temperature was more uniform. Besides, the temperature difference between the discharge and return air is smaller.
Axell and Fahlen [17] carried out experimental measurement and numerical simulation and argued that a relatively small discharge velocity should be recommended in designing the air curtain of a display case. However, a small discharge velocity would possess insufficient initial momentum to prevent the invading of the warm moist air from the outside.
1.2.5 Effects of air flow from the perforated back panels
It was suggested by Navaz et al. [3] and Chen and Yuan [4] that the air flow from the perforated back panels not only provided air curtain stability by reducing the entrained warm ambient air, but also helped the air temperature in the case to
immediately stabilize after any intrusion. Navaz et al. [3] indicated that any intrusion could cause the warm air to penetrate into the lower shelves and became stagnant there. In an experimental investigation Chen & Yuan [4] tested different perforation densities and found that the heat load dropped slightly for an increase in the perforation density.
1.2.6 Effects of discharge width and length of air curtain and jet turbulence intensity
The ratio of the opening height H of a cabinet to the width bj of the discharge jet was also noted to be an important factor in influencing the performance of air curtains [10, 18, 19]. Chen & Yuan [4] and Besbes et al. [19] showed that as the H / bj ratio was decreased, the higher energy efficiency was obtained and the critical Richardson number was higher. The flow pattern and heat transfer characteristics of the air curtain could be affected significantly by the value of the H / bj ratio [4, 10, 21, 22]. Axell & Fahlen [17] manifested that the air flow in the air curtain could be divided into a transition, a fully developed and a recovery regions. Besides, the flow rate was constant in the transition region. In the fully developed region, the air flow slows down. While in the recovery region, the air velocity profile and flow rate depend on the design of the return grille. Loerke and Nagib [20] used a honeycomb to reduce the turbulence intensity. A largely unidirectional flow at the discharge was obtained by using a honeycomb to reduce the transverse fluctuating velocity. Howell et al. [13] noted that the initial turbulence intensity ranging from 0% to 7% exhibited strongest effects on the heat transfer. However, for the turbulence intensity exceeding 8 to 10%, the initial turbulence shows little influence on the total heat transfer through the air curtain. Navaz et al. [3] indicated that the turbulence intensity at the air discharge, measured by DPIV and laser Doppler velocimetry (LDV), reached a maximum at the boundary between the static ambient air and air
curtain and the interfaces between the inner curtain and outer curtain. Besides, the increasing turbulence kinetic energy could subsequently increase the turbulence intensity and entrainment rate. Van and Howell [18] also showed that the air curtain length yl was dependent on the initial turbulent intensity Ti. They proposed a relation
l i j
y = (5.39 - 0.266T )b . Moreover, the length of the initial region of the air curtain decreases with an increase in the turbulence intensity due to the increasing mixing.
1.3 Objective of Present Study
The above literature review clearly indicates that a better design of refrigerated display cabinets is still an important goal to the refrigeration industry. Minimizing the infiltration of the warm and humid outside air into the cabinets through improving the performance of air curtains is therefore essential in this design. In the present study a two-dimensional numerical simulation will be conducted to explore the detailed momentum, heat and mass transfer processes in an open vertical refrigerated display case. Attention will be focused on how the parameters associated the air curtain affect the transport processes in the display case and hence the performance of the cabinet.
Fluorescent Light
Fig. 1.1 Schematic diagram of a multi-deck open refrigerated display case
CHAPTER 2
MATHMATICAL FORMULATION
The physical model adopted here and the governing equations used to numerically predict the transport processes in a vertical refrigerated display case are described in this chapter.